Answer:
Step-by-step explanation:
3x^2 = -12
divide both side by 3x^2 = -4
Solve the square root.x = ±√-4
this equation has no real solutions
Answer:
x = {- 2i; 2i}-------------------------------
GivenEquation 3x² = 12Solve as below3x² = - 12x² = - 4x = √-4x = ± 2√-1x = ± 2iThe table represents a linear relationship. x −2 0 2 4 y −1 0 1 2 Which of the following graphs shows this relationship?
The graph that shows the linear relationship of the table is attached below.
How to Find the Graph that Represent a Linear Relationship?To determine the graph of a linear relationship, do the following:
Find the slope or rate of change = change in y / change in x.Determine the y-intercept which is the value of y when x = 0, and it represents the value on the y-axis where the line intercepts.Given the table which represents a linear relationship above, use two pairs of values, (0, 0) and (2, 1) to find the slope:
Slope = change in y / change in x = (1 - 0) / (2 - 0)
Slope = 1/2.
The y-intercept (b) = 0.
Thus, this means that the graph of the linear relationship will have a slope of 1/2 and crosses the y-axis at 0.
Thus, the graph is shown below.
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Jessica runs 3 miles in 16 minutes how many minutes does she take per mile
Answer:0.1875
Step-by-step explanation: you would take the miles and divide it my the minutes which would be 3 divided by 16 which equals 0.1875
prisms, pyramids and spheres have 3 dimensions - length, width, and depth. three dimensional objects have vertices, edges, and faces unless they are the solids like cylinders, cones, and spheres.
A solid figure is a three-dimensional object. That is, it has length, width, and height. Because they are three-dimensional, they have depth and occupy space in our universe. Body types are identified according to characteristics specific to each body type. In particular, we can observe the number of faces, edges, vertices, and the shape of the base.
A flat face of a solid is its face or side, as it is commonly called. The base is the surface on which the figure rests. A solid edge is a line segment where two faces meet. A vertex is an angle formed where the endpoints of two or more face segments meet.
A sphere is a solid figure that has no faces, edges, or vertices. This is because it is perfectly round. No flat sides or corners.
A cone has faces but no edges or vertices. His face is circular. A circle is a plane because it is a flat planar shape. However, since it is rounded on the outside, it does not form edges or corners.
Cylinder that has two circular faces but no edges or corners:
A pyramid has a base and at least three triangular faces. There are edges where faces meet each other or meet the bottom, vertices where two faces meet the bottom, and top vertices where all the triangle faces meet. Pyramids are named for the shape of their base.
A triangular pyramid has a triangular base and his other three triangular faces, or four triangles in total.
A pyramid has a rectangular base and a pyramid has a square base. Both have four triangular faces, for a total of five faces.
Prism:
A prism is a solid with two congruent parallel faces and any number of sides. That is, it can have any number of faces, but at least two faces must be parallel. The shape of the two parallel faces can be triangles, squares, rectangles, pentagons, hexagons, or other types of polygons. Prisms are named after the shape of the base.
Sphere:
A sphere is a geometric object that is the three-dimensional analogue of the two-dimensional circle. A sphere is a set of points that are all the same distance r from a given point in 3D space. This given point is the center of the sphere and r is the radius of the sphere. Spheres are fundamental objects in many areas of mathematics. Spherical and near-spherical shapes also occur in nature and industry. Bubbles, like soap bubbles, are spherical in equilibrium. The Earth is often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy.
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LEAST TO GREATEST ( WILL GIVE BRAINIST IF CORRECT )
PLEASE HURYY
please help me with this math real quick, please!!
A wooden box is in the shape of a regular pentagonal prism. The sides, top, and bottom of the box are 1 centimeter thick. Approximate the volume of wood used to construct the box. Round your answer to the nearest tenth.
The volume of the pentagonal prism as per the given values is obtained as 2.5 cm³.
What is a pentagonal prism?A pentagonal prism has two pentagonal surfaces on the top and the bottom. It has ten vertices, 15 edges and 7 faces. The number of rectangular surfaces are five.
The expression for the volume of a regular pentagon is given as V = 5/2 × abh
Where h is the height and a and b are the length of the sides.
Now, the value of a, b and h as per the question is given as,
a = b = h = 1.
Then, the volume can be calculated as,
V = 5/2 × 1 ×1 × 1
= 2.5
Hence, the volume of the regular pentagonal prism is given as 2.5 cm³.
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Monique buys a $4700 air conditioning system using an installment plan that requires 15% down. How much is the down payment
The value of down payment will be;
⇒ $705
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Monique buys a $4700 air conditioning system using an installment plan that requires 15% down.
Now,
Since, Monique buys a $4700 air conditioning system using an installment plan that requires 15% down.
Hence, The value of down payment = 15% of $4700
= 15/100 × 4700
= 15 × 47
= 705
Thus, The value of down payment = $705
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Do not understand this question
Answer:
A, C
Step-by-step explanation:
You want all the shapes that are enlargements of shape X, which is 1 unit high and 3 units wide.
EnlargementAn enlargement of shape X multiplies each of its dimensions by the same factor. When it is enlarged by a factor of 2, the dimensions become ...
high : wide = 1 : 3 = 2 : 6 . . . . . . matches shape C
When it is enlarged by a factor of 3, the dimensions become ...
high : wide = 1 : 3 = 3 : 9 . . . . . . . matches shape A
The 2-high shape B is too short, being 4 1/2 wide instead of 6. Shape F is too long, being 7 wide instead of 6.
The 3-high shapes D and E are too short, being 8 and 5 wide instead of 9.
__
Additional comment
An enlargement preserves the aspect ratio of the shape, the height to width ratio. Here, that is 1:3. Any shape with a different aspect ratio is not an enlargement of X.
The cost of three pens and one rubber is 2.25 the cost of two pens and two rubbers is 1.90 work out how much one pen costs and how much one rubber costs
Answer:
0.65 pens
2.25 rubber
Step-by-step explanation
You can make two equations with the information given and solve them simultaneously to find x and y. Assume x is pens and y is rubber.
please help me with this
The correct matching regarding the linear functions are given as follows:
i. A set of points where the coordinates of each point has a sum of 2: Line n.
ii. A set of points where the y-coordinate of each point is 10 less than the x-coordinate: Line m.
b - i) Two numbers with a sum of 2: A and C.
b - ii) Two numbers where the y-coordinate is 10 less than the x-coordinate: D and E.
b - iii) Two numbers with a sum of 2 and where the y-coordinate is 10 less than the x-coordinate: B.
How to match the options?The set of points where the coordinates of each point has a sum of 2 is defined by the following linear function
x + y = 2.
In slope-intercept form, it is of:
y = 2 - x.
Which is the decreasing line n, with an intercept of 2.
A set of points where the y-coordinate of each point is 10 less than the x-coordinate is defined by the following linear function
y = x - 10.
Which is the increasing line m, which an intercept of m.
The coordinates of each point are given as follows:
A(-2,4).B(6,-4).C(12,-10).D(2,-8).E(13,3).These points are then used to match the sentences in item b.
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Determine the equation of the hyperbola with and vertices (6, 4) and (0, 4) and
asymptotes y = 1/3x + 3 and y = = -1/3x + 5.
The equation of a hyperbola can be written in the form:
(x-h)^2/a^2 - (y-k)^2/b^2 = 1
where (h, k) is the center of the hyperbola, a is the distance from the center to the vertices on the x-axis, and b is the distance from the center to the vertices on the y- axis.
In this case, the vertices of the hyperbola are (6,4) and (0,4), and the center of the hyperbola is at (3,4). The distance from the center to the vertices on the x- axis is 3, and the distance from the center to the vertices on the y- axis is 0.
Plugging these values into the equation for a hyperbola, we get:
(x-3)^2/3^2 - (y-4)^2/0^2 = 1
This equation is not defined, because the value of b is 0. This means that the hyperbola has a horizontal orientation, and its vertices are on the y-axis.
To find the equation of the hyperbola, we need to rewrite the equation in a different form. We can do this by using the fact that the distance between the center of the hyperbola and a point on the hyperbola is given by:
√ ((x-h)^2 + (y-k)^2) = a*√ (1 + (y-k)^2/b^2)
Substituting in the values for h, k, and a, we get:
√ ((x-3)^2 + (y-4)^2) = 3*√ (1 + (y-4)^2/0^2)
This equation can be simplified to:
√ ((x-3)^2 + (y-4)^2) = 3*√((y-4)^2/0^2)
The value of b is still 0, so the equation for the hyperbola is:
(x-3)^2 = 9*(y-4)^2
This is the equation for a horizontal hyperbola with vertices (3,4) and (9,4) and asymptotes y = 1/3x + 3 and y = -1/3x + 5.
What is an equation of the hyperbola?A hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces which is known as connected components, that are mirror images of each other and resemble two infinite bows.
Therefore, the correct answer is as given above
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A can is in the shape of a cylinder. The can has a volume of 450 cubic inches and a diameter of 4 inches. To the nearest tenth of an inch, what is the height of the can? a O b C Od 35.8 inches 143.2 inches 11.8 inches 9.0 inches
I will mark brainliest to anyone who answers
The answer: A
35.8 inches
question does each function describe exponential growth or decay? drag and drop the equations into the boxes to correctly complete the table. put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse. growth
A set-to-set function f is a relation that assigns one element of the set A to each element of the other set B. The set A is the domain of the function (also called the set of inputs) and the set B contains the range (also called the set of outputs).
Let's denote f as exponential function with the base 'a':
f(x) = a ˣ
where, a > 0 and a ≠ 1 and x is any real number.
1. Not an exponential function:
We have the following equation:
[tex]y = 100 (1 - 12)^{t}[/tex]
We can write the equation as:
[tex]y = 100 (-11)^{t}[/tex]
Let's denote f as exponential function with the base 'a':
f(x) = a ˣ
where, a > 0 and a ≠ 1 and x is any real number.
Therefore: a must be more than 01.
In this problem, a = -11, therefore this is not an exponential function.
2. Growth.:
The function:
[tex]y= 0.1(1.25)^{t}[/tex]
The above equation is an exponential function because is a function of the form
[tex]f(t) = ka^t[/tex]
where, a > 0 and k is constant
Therefore, k = 0.1 and a = 1.25 . So, a is greater than 1.
3. Growth:
The function:
[tex]y = {(1 - 0.03)12}^2t[/tex]
The above equation can be written as:
[tex]y = 11.64^{2t}[/tex]
which is an exponential function because is a function of the form
[tex]f(t) = a^{bt}[/tex]
where, a > 0 and b is constant.
So, a = 11.64 and b = 4 . Since a is greater than 1.
4. Decay:
The function:
[tex]y = 426(0.98)^t[/tex]
This is an exponential function because is a function of the form
[tex]f(t) = ka^t[/tex]
where, a > 0 and k is constant
So, k = 426 and a = 0.98. Since, a is less than 1.
5. Growth:
The function:
[tex]y = 2050(12)^t[/tex]
This is an exponential function because is a function of the form
[tex]f(t) = ka^t[/tex]
where, a > 0 and k is constant.
So, k = 2050 and a = 12 . Since, a is greater than 01.
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Solve for the variable.
8 = y - 3
Responses
A -11-11
B 55
C 1111
D 2424
E -5
Answer:
Answer is y = 11
Step-by-step explanation:
8 = y - 3
or, 8 + 3 = y - 3 + 3
or, 11 = y
or, y = 11
bella is working two summer jobs, making $10 per hour landscaping and $15 per hour clearing tables. last week bella worked a total of 15 hours and earned a total of $180. graphically solve a system of equations in order to determine the number of hours bella worked landscaping last week, x,x, and the number of hours bella worked clearing tables last week, yy.
The solution of the system of equations by the graphical methods yields x equals 9 and y is 6 i.e, 9 hours of landscaping and 6 hours of waiting tables.
Bella worked x hours working landscaping at $10 per hour.
Total amount earned = 10x
Bella worked y hours working on clearing tables at $ 15 per hour
Amount earned = 15 y
x and y are variables as given
She worked a total of 15 hours and she gets $180 for the combined efforts.
The system of equation can be represented as:
x + y = 15
10x + 15y = 180
Now we will solve the two equations graphically:
So from the attached graph we can see that the point (9,6) is the required solution.
Hence she worked landscaping for 9 hours and clearing tables for 6 hours.
Let us solve by substitution to verify the results:
x + y = 15
or, x = 15 - y
Now 10x + 15y = 180
or, 10 (15-y) + 15y = 180
or, 150 - 10y +15y = 180
or, 5y = 180 - 150
or, y = 6
At y = 6 , x = 15 - 6 = 9
Hence (9,6) is the solution.
System of equations also known as simultaneous equations can also be solved by the elimination method.
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Waves that make up light have peaks and valleys just like the ocean. What are the scientific terms for peaks and valleys?
highs and lows
crests and troughs
ebbs and flows
protos and parallax
The scientific terms for peaks and valleys is B. Crests and troughs.
What are crests?The greatest amount of upward displacement within a cycle occurs at a wave's crest point. A surface wave's crest is a region where the medium's displacement is greatest. The minimum or lowest point in a cycle, a trough is the opposite of a crest.
The crest and trough of a wave, respectively, are its highest and lowest surface portions. The wave height is the vertical distance between the crest and trough. The wavelength is the horizontal separation between two adjacent crests or troughs.
The crest is the highest point on the wave. The trough is the area that is the lowest. The wave length, also known as the wavelength, is the separation between two successive crests (or troughs), while the wave height is the overall vertical change in height between the crest and the trough.
Therefore, based on the information given, the correct option is B.
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Which coordinates are the best estimate of the solution to the system of equations. -3x+y=2 -4x+7y=1
The best estimate of the solution to the system of linear equations is the point are (x,y) will be (0.76, 4.30).
What is linear equations?A linear equation in two variables is one that is written in the form axe + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero.
Given:
as x,y are variables,
-3x + y = 2 ..............(1)
- 4x + 7y = 1 ...........(2)
We know that,
The solution of the system of linear equations is the intersection point of both graphs
Multiply equation (1) by 7 on both sides and then subtract it from eq (2)
- 4x + 7y = 1 ...........(2)
-21x + 7y = 14 ..............(1)
⇒- 17 x = -13
⇒ 17 x = 13
⇒ x =[tex]\frac{13}{17}[/tex]
⇒ x = 0.76
Now on putting value of x = 0.76 in eq (1) we get
- 3x + y = 2 ............ (1)
⇒- 3(0.76) + y = 2
⇒y = 4.30
The best estimate of the solution to the system of linear equations is the point (x,y) will be (0.76, 4.30).
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The number line below is divided into 4 equal parts. Fill in the missing fractions and percentages.
Note that your fractions don't need to be in simplest form.
We can fill in the remaining fractions and percentages.
as
0 1/4 2/4 3/4 1
|--------------|--------------|--------------|--------------|
0% 25% 50% 75% 100%
What is a number line?
A number line is a straight line that is used to represent real numbers. The numbers are usually represented as points on the line, and the distance between the points corresponds to the magnitude of the numbers. The numbers can be positive or negative and are typically marked at regular intervals.
The missing parts are
0 1/4 2/4 3/4 1
|--------------|--------------|--------------|--------------|
0% 25% 50% 75% 100%
This is how we can fill in the remaining fractions and percentages.
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List from least to greatest! ( WILL GIVE BRANILIST IF CORRECT)
Answer:
need the numbers to do it
A local health clinic sent fliers to its clients to encourage everyone, but especially older persons at high risk if complications, to get a flu shot in time for protection against an expected epidemic. In a pilot follow-up study, 159 clients were randomly selected and asked whether they actually received a flu shot. Y - 1 means that the client received a flu shot, whereas Y - 0 indicates that the client didn't receive a flu shot. The following predictor variables were used for the analysis X1: The client's age (continuous variable); X2: Health awareness index (continues variable, for which higher values indicate greater awareness X3: Gender (categorical variable, where 1 denoted for male and 0 for female) (a) Write down the logistic regression model for this case (b) Look at the following output. Formally, which predictors have a significant influence on the response? Using tests to confirm your answer. Analysis of Maximum Likelil Standard Model Fit Statistics Error Intercept 1177 .9824 1 0.07280.0304 1 0.0990 0.0335 1 0.4339 0.5218 Parameter DF Estimate Intercept and Criterion Intercept Only AIC SC 2 Log L Covariates 113.093 125.369 105.093 136.941 140.010 134.941 (c) Overall, is this model significant? Please conduct appropriate procedure to test it. (d) Estimate the probability for Y-1 with X 60, X2 = 30, X3 1. What would be (e) Find the odds ratio for Y-1 between male and female. Also construct a 95% confidence (f) Now we calculate the logistic regression without the predictor variables X1, X3. One your prediction for Y in this case? interval for this odds ratio wishes to know whether this model is significantly different from the previous model Please conduct appropriate procedure to test it. Model Fit Statistics Intercept and CriterionIntercept Only Covariates 136.941 140.010 134.941 Analysis of Maximum Likelihood Estimates AIC SC 2 Log L 117.196 123.334 113.196 Standard Wald Parameter DF EstimateError Chi-Square Pr> ChiSq 0.0025 .0001 Intercept 1 4913 1.6266 9.1170 x2 1 0.1193 0.0301 15.6789
(a) The logistic regression model in this case is
log(p/(1-p)) = beta0 + beta1X1 + beta2X2 + beta3×X3
where p is the probability of Y-1 (i.e. getting a flu shot), X1 is the customer's age, X2 is the health awareness index, X3 is the gender (1 for men, 0 for women), and beta0, beta1 , beta2 , and beta3 are the estimated coefficients.
(b) From the output, the predictors that have the most influence on the response are X1, X2, and X3. You can confirm this by looking at the p-value of the Wald chi-square test for each predictor. A predictor is considered significant if the p-value is less than 0.05. In this case, the p-values for all three predictors are less than 0.05, indicating that they are all significant.
(c) AIC (Akaike Information Criterion) or SC (Schwarz Criterion) values can be used to determine if the overall model is significant. A lower AIC or SC value indicates a better fit of the model to the data. In this case, both the AIC and SC values are lower for the model with all three predictors (136.941 and 134.941, respectively) compared to the intercept-only model (140.010 and 136.941, respectively). This is significant because the model fits all three predictors better.
(d) These values can be incorporated into a logistic regression model to estimate the probability of Y-1 (getting a flu shot) with X1=60, X2=30, X3=1 (men) .
log(p/(1-p)) = beta0 + beta160 + beta230 + beta3*1
Solving for p gives:
p = 1/(1+exp(-log(p/(1-p))))
You can estimate p using the maximum likelihood estimates of beta0, beta1, beta2, and beta3 provided in the output.
(e) To determine the Y-1 odds ratio for men and women, you can compare the Y-1 odds for men (X3=1) and the Y-1 odds for women (X3=0). Men's Y-1 odds are as follows:
Odds (Y-1 for men) = p/(1-p)
where p is the Y-1 probability of her being male and can be estimated using a logistic regression model and maximum likelihood estimation of the coefficients. Women's Y-1 odds can be calculated in the same way using X3=0.
To create a 95% confidence interval for the odds ratio, use the standard error of the coefficient to calculate the standard error of the log odds ratio. A 95% confidence interval can be calculated as follows:
Odds ratio +/- 1.96×standard error
(f) To test whether the model containing only the intercept is significantly different from the model containing all three predictors, a likelihood ratio test can be used. The null hypothesis is that the model with only the intercept is not significantly different from the model with all three predictors. The alternative hypothesis is that the model with only the intercept is significantly different from the model with all three predictors. The test statistic is computed as
-2×(log probability
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answer the question below, find the rate of change and The means that for every ___pound(s) the turkey will take 1 hour to thaw.
How many hours per pound does it take to thaw a turkey?
Allow 30 minutes of thawing time for each pound of turkey, which translates to two to six hours for a 4- to 12-pound turkey. A 12- to 15-pound bird will thaw in six to eight hours. Still having trouble determining the thaw time of the turkey?
Hope this helps :D
Suppose that a vending machine service company models its income by assuming that money flows continuously into the machines, with the annual rate of flow given by f(t) = 160e0.03tin thousands of dollars per year. Find the total income from the machines over the first 5 years. (Round your answer to the nearest thousand dollars.)$______
The total income from the machines over the first 5 years is $185.89
How to determine the total income from the machines over the first 5 yearsFrom the question, we have the following parameters that can be used in our computation:
f(t) = 160e0.03t
Where
t = Number of yearsf(t) = thousands of dollars per yearRewrite the function properly
so, we have the following representation
f(t) = 160e⁰.⁰³ⁿ
The above function is an exponential function
So: In the first 5 years, we have the value of t to be 5
This is represented as follows
t = 5
Substitute the known values in the above equation, so, we have the following representation
f(5) = 160e⁰.⁰³ ˣ ⁵
Evaluate the product of the exponents
f(5) = 160e⁰.¹⁵
The products above give
f(5) = 185.89
Hence, the total income is $185.89
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what is the population standard deviation?
The population standard deviation [tex]\sigma[/tex] is 6.697.
What is the mean absolute deviation?The average distance between each data item and the mean is known as the mean absolute deviation.
The gap between each data value and the mean in absolute terms is represented by this average.
The given data set can be arranged as 4, 7, 8, 10, 12, 12, 15, 18, 23, 26.
Mean[tex](\overline{x})[/tex] = (4 + 7 + 8 + 10 + 12 + 12 + 15 + 18 + 23 + 26)/10.
Mean[tex](\overline{x})[/tex] = 135/10 = 13.5.
We know variance[tex](\sigma)[/tex] = [tex](\[ \sum_{i=1}^{n}x_i^2 \]/n) - \overline{x}^2[/tex].
= (4² + 7² + 8² + 10² + 12² + 12² + 15² + 18² + 23² + 26²)/10 - (13.5)².
= (16 + 49 + 64 + 100 + 144 + 144 + 225 + 324 + 529 + 676)/10 - 182.25.
= 44.85
And we also know the standard deviation is [tex]\sqrt{\sigma}[/tex] = [tex]\sqrt{44.85}[/tex] = 6.697
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Actuarial math
A 10-year $100 par value bond bearing a 10% coupon rate payable semiannually, and redeemable at 105, is bought to yield 8% convertible semiannually. Find the price. Verify that all four formulas produce the same answer.
The price of a 10-year $100 par value bond bearing a 10% coupon rate payable semiannually, and redeemable at 105, bought to yield 8% convertible semiannually, is its present value of $115.87.
What is the price of a bond?The price of a bond is its present value.
The present value can be computed by setting the following parameters:
Number of periods = 20Effective interest rate = 8%Periodic interest payment = $5 ($100 x 10% x 6/12)Future value = $105.This can be done using an online finance calculator with the results as follows:
N (# of periods) = 20 semiannual periods (10 years x 2)
I/Y (Interest per year) = 8%
PMT (Periodic Payment) = $5 ($100 x 10% x 1/2)
FV (Future Value) = $105
Results:
Present Value (PV) = $115.87
Sum of all periodic payments = $100 ($5 x 20)
Total Interest = $89.13
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Question Completion:Answer: 115.87 (If you don't get this answer then the solution is incorrect.)
NO LINKS!! Please help me with this problem. Part 6ff
Answer:
The sequence is not arithmetic. In an arithmetic sequence, the difference between consecutive terms is constant. However, in this sequence, the difference between the terms is not constant. For example, the difference between the first and second terms is 1^5 - 2^5 = -3, while the difference between the second and third terms is 2^5 - 3^5 = -6. Since the difference between consecutive terms is not constant, this sequence is not arithmetic. Therefore, the common difference is NONE.
Answer:
No, the sequence is not arithmetic.
d = NONE
Step-by-step explanation:
An Arithmetic Sequence has a common difference between each term (the difference between each term is the same).
Given sequence:
[tex]1^5, 2^5, 3^5, 4^5, 5^5, ... = 1, 32, 243, 1024, 3125, ...[/tex]
Calculate the difference between each term:
[tex]1 \underset{+31}{\longrightarrow} 32 \underset{+211}{\longrightarrow} 243 \underset{+781}{\longrightarrow} 1024 \underset{+2101}{\longrightarrow} 3125[/tex]
As the difference between each term is not constant, the sequence is not an arithmetic sequence.
Therefore, the common difference, d = NONE.
write an algorithm, using pseudocode, to make the robot: 1. stand up 2. walk forward until it senses a wall 3. turn around 4. walk back to the chair 5. sit down in its original starting position finally, output the total number of steps taken.
We had written an algorithm, using pseudo code.
//Define the required variables.
total_number_of_steps = 0
number_of_steps = 0
//robot stands up to walk.
stand
//the robot moves forward till the wall is not reached.
while (wall is not reached)
//the robot senses the wall with the help of arms.
raise arms
sense_the_wall
if (wall is not there)
//if the wall is not found, the robot lowers the arms
lower arms
//if wall is not detected, the robot moves forward.
step_forward
//increment the number of steps forward.
number_of_steps=number_of_steps+1
//increment the total number of steps.
total_number_of_steps=total_number_of_steps+1
else
exit
end if
end while
//else if the wall is found, lower the arms
lower arms
//the robot turns 90 degrees right once.
turn_right_90
//the robot turns 90 degrees right again.
turn_right_90
//till the number of steps does not reach 0, move
for (number_of_steps! = 0)
step
//increment the total number of steps.
total_number_of_steps=total_number_of_steps+1
//the robot moves backwards on detecting the wall, so
//decrement the number of steps.
number_of_steps = number_of_steps-1
//end the for loop.
end for
//the robot turns 90 degrees left once.
turn
//the robot turns 90 degrees left again.
turn
//the robot sits down.
sit
//display the total number of steps taken by robot
display total_number_of_steps
The last line ends the pseudocode
Stop
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2. Find the value of x. 3x-9
Question 1-5
The expression (4c-3d)(3c+d) is equivalent to:
O 12c² 13cd 3d²
O 12c²
O 12c²
O 12c²
O 12c²
13cd3d²
5cd 3d²
5cd +3d²
3d²
The expression (4c − 3d)(3c + d) is equivalent to 12c² - 5cd - 3d²
What is Expression?An expression is combination of variables, numbers and operators.
(4c − 3d)(3c + d) is the given expression.
Four times c minus three times d into three times f c plus d.
In the given expression c and d are variables.
Plus and minus are operators.
We need to find the equivalent expression of (4c − 3d)(3c + d).
(4c − 3d)(3c + d)
4c(3c+d)-3d(3c + d)
Apply the distributive property.
12c² + 4cd - 9cd - 3d²
Add the like terms
12c² - 5cd - 3d²
Hence, 12c² - 5cd - 3d² is the equivalent expression of (4c-3d)(3c+d).
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PLEASE HELP
Under what conditions would triangle DEF be similar to triangle ABC? Drag and drop the choices to make the statement correct.
Step-by-step explanation:
similar means that they have the same angles, and that there is one and the same scale factor for all corresponding sides and other lines (like heights).
so, either the angle F = 60° (like angle C in ABC), or DE has the same scaling factor with AB as DF has with AC.
some correct answer options are not listed, so we need to adjust to the existing ones.
remember, the sum of all angles in a triangle is always 180°.
so,
angle A + angle B + angle C = 180
40 + angle B + 60 = 180
angle B = 80°
so, angle E = 80° for the triangles to be similar.
AC × c = DF
12 × c = 16
3 × c = 4
c = 4/3
so,
AB × c = DE
9 × 4/3 = DE
36/3 = DE
DE = 12
so, either angle E = 80° or DE = 12.
Go step by step to reduce the radical.
Answer:
[tex] \sqrt{176} [/tex]
[tex] \sqrt{16 + 11} [/tex]
[tex]4 \sqrt{11} [/tex]
Step-by-step explanation:
The answer is
[tex]4 \sqrt{11} [/tex]
We
need to express 176 as the product of its prime factors i.e. 176 = 2 × 2 × 2 × 2 × 11. Therefore, √176 = √2 × 2 × 2 × 2 × 11 = 4 √11 . Thus, the square root of 176 in the lowest radical form is 4 √11.
i hope this helped
