Answer:
[tex]x ^{m - 3} \div x^{m - 4} \\ \frac{ {x}^{m - 3} }{ {x}^{m - 4} } \\ \frac{ {x}^{m - 3 - m + 4} }{x} \\ \frac{ {x}^{1} }{x} \\ x \: and \: x \: will \: cancel \: each \: other \: hence \: answer \: will \: be \: 1[/tex]
Triangle A”B”C is formed using the translation (x+1,y+1) and the dilation by a scale factor of 3 from the origin. Which equation explains the relationship of BC and B”C? PLEASE HELP
9514 1404 393
Answer:
(b) BC = B"C"/3
Step-by-step explanation:
Choices A, C, D are all different ways of expressing the same relationship, and they are all incorrect.
B"C" is segment BC after dilation by a factor of 3, so it is 3 times as long as BC. That is, BC is 1/3 the length of B"C", choice B.
We are given both the slope and y-intercept so writing the equation in slope-intercept form is a breeze! Label both the slope and y-intercept and them substitute them into the general form of slope-intercept form. So, y=4x−3.
Answer:
below
Step-by-step explanation:
hope it is well understood?
The slope is 4 and y- intercept is 13
What is slope?A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.
A slope exists Numerical calculation of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment stands as the proportion of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).
Given
Slope
y = 4x-3
dy/dx = 4
slope = 4
intercepts y = 4(4) 3
y = 16-3
y = 13
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The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 6 cm/s. When the length is 12 cm and the width is 8 cm, how fast is the area of the rectangle increasing
Answer:
Step-by-step explanation:
This is a super simple problem. I'm going to walk through it as I do when I teach this to my students for the first time.
We are given a rectangle. We are told to find how fast the area is changing under certain conditions. That tells us that the main equation for this problem is the area formula for a rectangle which is
[tex]A=lw[/tex]. If we are looking for the rate at which the rectangle's area is changing, that means that we need to find the derivative of the area implicitly. This derivative is found using the product rule because the length is being multiplied by the width:
[tex]\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}[/tex] . If our unknown is the rate at which the area is changing, [tex]\frac{dA}{dt}[/tex], that means that everything else has to have a value (because you can only have one unknown in an equation). Here's what we're told:
The length of the rectangle is increasing at a rate of 7 cm/s, so that satisfies our [tex]\frac{dl}{dt}[/tex];
the width is increasing at a rate of 6 cm/s, so that satisfies our [tex]\frac{dw}{dt}[/tex];
and all of this is going on when the length = 12 and the width = 8. It looks like everything will have a value except for our unknown. Filling in:
[tex]\frac{dA}{dt}=12(6)+8(7)[/tex] and
[tex]\frac{dA}{dt}=72+56[/tex] so
[tex]\frac{dA}{dt}=128\frac{cm^2}{s}[/tex]
The soil samples for the next field indicate that fertilizer coverage needs to be
greater. To achieve this, you need to increase flow rate. How would you achieve
this?
A. Increase speed to approximately 7.1 mph so that you cover the field more
quickly
B. Increase the engine speed to approximately 2,000 rpm
C. Decrease speed to approximately 6.0 mph so that you cover the field more
slowly
D. Shift to second gear so that the engine speed slows
Answer:
A. Increase speed to approximately 7.1 mph so that you cover the field more.
Step-by-step explanation:
The soil samples for the next field require more fertilizer coverage therefore there is need for more field coverage by the equipment. The speed of the tractor will be increase to 7.1 mph so that greater area can be covered in lesser time.
Complete the square to solve the equation below.
Check all that apply.
x^2-10x-4=10
1. Move terms to the left side
2.Subtract the numbers
3.Use the quadratic formula
4.Simplify
5.Separate the equations
6.Solve
Rearrange and isolate the variable to find each solution.
Solution,
Solution
x=5±√39
What is the answer to this question in the picture
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Answer:
[tex]\displaystyle\sqrt{x+7}-\log{(x+2)}[/tex]
Step-by-step explanation:
It's pretty straightforward. You want ...
f(x) - g(x)
Substituting the given function definitions gives ...
[tex]\displaystyle\boxed{\sqrt{x+7}-\log{(x+2)}}[/tex]
I need help with this
Answer:
Statement A is correct
Step-by-step explanation:
Statement A is correct: Model A1 (0.25) is more prefered than Model C3 (0.15)
A tent maker wishes to support a 8-ft tent wall by attaching cable to the top of it, and then
anchoring the cable 7 feet from the base of the tent.
How long of a cable is needed?
Round your answer to the nearest tenth of a foot.
Answer with a numeric value only. That is, do not include "ft" or "feet" with your response.
Cable
Ground
Answer:
10.6
Step-by-step explanation:
A simple sketch of the question would give a right angled triangle. So that we can easily apply the Pythagoras theorem to determine the length of the cable required.
Let the length of the cable required be represented by x.
[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]7^{2}[/tex]
= 64 + 49
[tex]x^{2}[/tex] = 113
x = [tex]\sqrt{113}[/tex]
= 10.63
x = 10.6
The length of the cable required is 10.6 in feet.
The length of the cable needed to support the tenth wall is approximately 10.6 ft.
The situation forms a right angle triangle.
Right angle triangle:Right angle triangle has one of it side as 90 degrees.
Therefore,
The tent wall is the opposite side of the triangle.
The table feet from the base of the tent is the adjacent side of the triangle.
Using Pythagoras's theorem the cable needed can be found.
Therefore,
c² = 8² + 7²c² = 64 + 49
c = √113
c = 10.6301458127
length of the cable ≈ 10.6 feet
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Tony calculates that 3 cubic metres of concrete is enough for the path.
He decides to use a concrete mix which has:
• cement = 1 part
• sand = 2 parts
gravel = 3 parts
How many cubic metres of gravel does Tony need?
0.5
Answer:
1.5 cubic metres
Step-by-step explanation:
Given that in a concrete mix, cement makes up 1 part, sand makes up 2 parts and gravel makes up 3 parts.
The total number of parts = 1 + 2 + 3 = 6 parts.
The amount of marvel present the concrete mix = amount of marvel / total mix
= 3 parts / 6 parts = 1/2
Since 3 cubic metres of concrete is enough for the path, hence the amount of gravel needed is:
Amount of gravel = 1/2 * 3 cubic metres of concrete = 1.5 cubic metres
. if f(x+3)=x+6 find inverse of function f(x)
Answer:
g(x)=x-3
Problem:
If f(x+3)=x+6 find inverse of function f(x).
Step-by-step explanation:
Let u=x+3, then x=u-3.
Make this substitution into our given:
f(u)=(u-3)+6
Simplify:
f(u)=u+(-3+6)
f(u)=u+3
Now let's find the inverse of f(u)...
Or if you prefer rename the variable...
f(x)=x+3
Now, we are going to solve y=x+3 for x.
Subtracting 3 on both sides gives: y-3=x.
Interchange x and y: x-3=y.
So the inverse of f(x)=x+3 is g(x)=x-3.
Answer:
The answer is g(x)=x-3
Step-by-step explanation:
If f(x+3)=x+6 find inverse of function f(x).
Let u=x+3, then x=u-3.
Make this substitution into our given:
f(u)=(u-3)+6
Simplify:
f(u)=u+(-3+6)
f(u)=u+3
Now let's find the inverse of f(u)...
Or if you prefer rename the variable...
f(x)=x+3
Now, we are going to solve y=x+3 for x.
Subtracting 3 on both sides gives: y-3=x.
Interchange x and y: x-3=y.
So the inverse of f(x)=x+3 is g(x)=x-3.
A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.7 hours.
Group of answer choices
A. 0.1946
B. 0.1285
C. 0.1469
D. 0.1346
Answer:
b. 01285 esa es, espero este buena y que te ayude
Let W be the solution set to the homogeneous system x + 2y + 3z = 0 2x + 4y + 6z = 0 Then W is a subspace of R3. Compute The Distance Between Y =[1 1 1] And W.
Answer:
Step-by-step explanation:
From the given information:
We can see that:
[tex]x + 2y + 3z = 0 --- (1) \\ \\ 2x + 4y + 6z = 0 --- (2)[/tex]
From equation (1), if we multiply it by 2, we will get what we have in equation (2).
It implies that,
x + 2y + 3z = 0 ⇔ 2x + 4y + 6z = 0
And, W satisfies the equation x + 2y + 3z = 0
i.e.
W = {(x,y,z) ∈ R³║x+2y+3z = 0}
Now, to determine the distance through the plane W and point is;
[tex]y = [1 \ 1 \ 1]^T[/tex]
Here, the normal vector [tex]n = [1\ 2\ 3]^T[/tex] is related to the plane x + 2y + 3z = 0
Suppose θ is the angle between the plane W and the point [tex]y = [1 \ 1 \ 1]^T[/tex], then the distance is can be expressed as:
[tex]||y|cos \theta| = \dfrac{n*y}{|n|}[/tex]
[tex]||y|cos \theta| = \dfrac{[1 \ 2\ 3 ]^T [1 \ 1 \ 1] ^T}{\sqrt{1^2+2^2+3^2}}[/tex]
[tex]||y|cos \theta| = \dfrac{[1+ 2+ 3 ]}{\sqrt{1+4+9}}[/tex]
[tex]||y|cos \theta| = \dfrac{6}{\sqrt{14}}[/tex]
[tex]||y|cos \theta| = 3\sqrt{\dfrac{2}{7}}[/tex]
H(0)=_______________
Answer:
5
Step-by-step explanation:
the only point in the chart, which has x=0 as coordinate, is the point up there at y=5.
and that is automatically the result. there is not anything else to it.
Use the t-distribution to find a confidence interval for a mean mu given the relevant sample results. Give the best point estimate for mu, the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed. A 95% confidence interval for mu using the sample results x-bar equals 76.4, s = 8.6, and n = 42.
Point estimate = ?
Margin of error = ?
Answer:
Point estimate = 76.4
Margin of Error = 2.680
Step-by-step explanation:
Given that distribution is approximately normal;
The point estimate = sample mean, xbar = 76.4
The margin of error = Zcritical * s/√n
Tcritical at 95%, df = 42 - 1 = 41
Tcritical(0.05, 41) = 2.0195
Margin of Error = 2.0195 * (8.6/√42)
Margin of Error = 2.0195 * 1.327
Margin of Error = 2.67989
Margin of Error = 2.680
Y=2.5x+5.8
When x=0.6
Answer:
7.3
Step-by-step explanation:
y=2.5x+5.8
=2.5×0.6+5.8
= 1.5+.8
=7.3
Write out the sample space for the given experiment. Use the following letters to indicate each choice: O for olives, M for mushrooms, S for shrimp, T for turkey, I for Italian, and F for French. When deciding what you want to put into a salad for dinner at a restaurant, you will choose one of the following extra toppings: olives, mushrooms. Also, you will add one of following meats: shrimp, turkey. Lastly, you will decide on one of the following dressings: Italian, French
Answer: He can make 36 different salds
Step-by-step explanation:
Find the slope of the line which passes through the points A (-4, 2) and B (1,5).
Answer:
3/5 so A.
Step-by-step explanation:
Answer:
slope = [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (1, 5)
m = [tex]\frac{5-2}{1-(-4)}[/tex] = [tex]\frac{3}{1+4}[/tex] = [tex]\frac{3}{5}[/tex]
The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 7 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken.
(a) Show the sampling distribution of the sample mean annual rainfall for California.
(b) Show the sampling distribution of the sample mean annual rainfall for New York.
(c) In which of the preceding two cases, part (a) or part (b), is the standard error of x smaller? Why?
The standard error is [larger, smaller] for New York because the sample size is [larger, smaller] than for California.
Answer:
a) [tex]E(\bar x) = \mu_{1} = 22[/tex] inches
The sampling distribution of the sample means annual rainfall for California is 1.278.
b)
[tex]E(\bar x) = \mu_{2} = 42[/tex] inches
The sampling distribution of the sample means annual rainfall for New York is 1.0435.
c)
Here, The standard error of New York is smaller because the sample size is larger than for California.
Step-by-step explanation:
California:
[tex]\mu_{1} = 22[/tex] inches.
[tex]\sigma_{1}[/tex] = 7 inches.
[tex]n_{1}[/tex] = 30 years.
New York:
[tex]\mu_{2} = 42[/tex] inches.
[tex]\sigma_{2}[/tex] = 7 inches.
[tex]n_{2}[/tex] = 45 years.
a)
[tex]E(\bar x) = \mu_{1} = 22[/tex] inches
[tex]\sigma^{p} _{\bar x} = \frac{\sigma_{1} }{\sqrt n_{1} } \\\\\\\sigma^{p} _{\bar x} = \frac{7}{\sqrt 30} \\\\\sigma^{p} _{\bar x} = 1.278[/tex]
b)
[tex]E(\bar x) = \mu_{2} = 42[/tex] inches
[tex]\sigma _{\bar x} = \frac{\sigma_{2} }{\sqrt n_{2} } \\\\\\\sigma_{\bar x} = \frac{7}{\sqrt45} \\\\\sigma _{\bar x} = 1.0435[/tex]
c)
Here, The standard error of New York is smaller because the sample size is larger than for California.
Simplify.
Multiply and remove all perfect squares from inside the square roots. Assume z is positive.
√z ∗ √30z^2 ∗ √35z^3
Answer:
Step-by-step explanation:
You need to put parentheses around the radicands.
√z · √(30z²) · √(35z³) = √(z·30z²·35z³)
= √(1050z⁶)
= √(5²·42z⁶)
= √5²√z⁶√42
= 25z³√42
The obtained expression would be 25z³√42 which is determined by the multiplication of the terms of expression.
What is Perfect Square?A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operations is called the arithmetic operator.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
We have been the expression as:
⇒ √z · √(30z²) · √(35z³)
Multiply and remove all perfect squares from inside the square roots
⇒ √(z·30z²·35z³)
⇒ √(1050z⁶)
⇒ √(5²·42z⁶)
Assume z is positive.
⇒ √5²√z⁶√42
⇒ 25z³√42
Therefore, the obtained expression would be 25z³√42.
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PLEASE HELPPPP
The cost function in a computer manufacturing plant is C(x) = 0.28x^2-0.7x+1, where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands. Determine the minimum production cost.
Given:
The cost function is:
[tex]C(x)=0.28x^2-0.7x+1[/tex]
where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands.
To find:
The minimum production cost.
Solution:
We have,
[tex]C(x)=0.28x^2-0.7x+1[/tex]
It is a quadratic function with positive leading efficient. It means it is an upward parabola and its vertex is the point of minima.
If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then the vertex of the parabola is:
[tex]\text{Vertex}=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]
In the given function, [tex]a=0.28, b=-0.7, c=1[/tex]. So,
[tex]-\dfrac{b}{2a}=-\dfrac{-0.7}{2(0.28)}[/tex]
[tex]-\dfrac{b}{2a}=1.25[/tex]
Putting [tex]x=1.25[/tex] in the given function to find the minimum production cost.
[tex]C(x)=0.28(1.25)^2-0.7(1.25)+1[/tex]
[tex]C(x)=0.28(1.5625)-0.875+1[/tex]
[tex]C(x)=0.4375+0.125[/tex]
[tex]C(x)=0.5625[/tex]
Therefore, the minimum production cost is 0.5625 million dollars.
Answer:
The minimum cost is 0.5625.
Step-by-step explanation:
The cost function is
C(x) = 0.28x^2 - 0.7 x + 1
Differentiate with respect to x.
[tex]C = 0.28x^2 - 0.7 x + 1\\\\\frac{dC}{dt} = 0.56 x - 0.7\\\\\frac{dC}{dt} = 0\\\\0.56 x - 0.7 = 0\\\\x = 1.25[/tex]
The minimum value is
c = 0.28 x 1.25 x 1.25 - 0.7 x 1.25 + 1
C = 0.4375 - 0.875 + 1
C = 0.5625
What is the range of the function f(x) = 3x2 + 6x – 8?
O {yly > -1}
O {yly < -1}
O {yly > -11}
O {yly < -11}
Answer:
Range → {y| y ≥ -11}
Step-by-step explanation:
Range of a function is the set of of y-values.
Given function is,
f(x) = 2x² + 6x - 8
By converting this equation into vertex form,
f(x) = [tex]3(x^2+2x-\frac{8}{3})[/tex]
= [tex]3(x^2+2x+1-1-\frac{8}{3})[/tex]
= [tex]3[(x+1)^2-\frac{11}{3}][/tex]
= [tex]3(x+1)^2-11[/tex]
Vertex of the parabola → (-1, -11)
Therefore, range of the function will be → y ≥ -11
The range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}
What is the range of a function?The range of a function is the set of output values of the function
Since f(x) = 3x² + 6x - 8, we differentiate f(x) = y with respect to x to find the value of x that makes y minimum.
So, df(x)/dx = d(3x² + 6x - 8)/dx
= d(3x²)/dx + d6x/dx - d8/dx
= 6x + 6 + 0
= 6x + 6
Equating the experssion to zero, we have
df(x)/dx = 0
6x + 6 = 0
6x = -6
x = -6/6
x = -1
From the graph, we see that this is a minimum point.
So, the value of y = f(x) at the minimum point is that is a t x = - 1 is
y = f(x) = 3x² + 6x - 8
y = f(-1) = 3(-1)² + 6(-1) - 8
y = 3 - 6 - 8
y = -3 - 8
y = -11
Since this is a minimum point for the graph, we have that y ≥ -11.
So, the range of the function is {y|y ≥ -11}
So, the range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}
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The length of a rectangle is 4 in longer than its width.
If the perimeter of the rectangle is 32 in, find its area.
Answer:
60 sq in
Step-by-step explanation:
Perimeter = 2l + 2w
If l = w+4
Perimeter = 2(w+4) + 2w
Perimeter = 4w+8
32 = 4w + 8
24 = 4w
6 = w
If w = 6, l = 6+4 = 10
Area = l * w
Area = 10 * 6
Area = 60
establish this identity
Answer:
see explanation
Step-by-step explanation:
Using the identities
tan x = [tex]\frac{sinx}{cosx}[/tex] , sin²x = 1 - cos²x
sin2x = 2sinxcosx
Consider left side
cosθ × sin2θ
= [tex]\frac{sin0}{cos0}[/tex] × 2sinθcosθ ( cancel cosθ )
= 2sin²θ
= 2(1 - cos²θ)
= 2 - 2cos²θ
= right side , then established
Evaluating functions (pic attached)
f(x) = 2x³ - 3x² + 7
f(-1) = 2(-1)³ - 3(-1)² + 7
=> f(-1) = 2(-1) - 3(1) + 7
=> f(-1) = -2 -3 + 7
=> f(-1) = 2
f(1) = 2(1)³ - 3(1)² + 7
=> f(1) = 2(1) - 3(1) + 7
=> f(1) = 2 -3 + 7
=> f(1) = 6
f(2) = 2(2)³ - 3(2)² + 7
=> f(2) = 2(8) - 3(4) + 7
=> f(2) = 16 - 12 + 7
=> f(2) = 11
Two containers designed to hold water are side by side, both in the shape of a
cylinder. Container A has a diameter of 10 feet and a height of 8 feet. Container B has
a diameter of 12 feet and a height of 6 feet. Container A is full of water and the water
is pumped into Container B until Container A is empty.
To the nearest tenth, what is the percent of Container B that is empty after the
pumping is complete?
Container A
play
Container B
10
d12
8
h6
O
Answer: Volume of Cylinder A is pi times the area of the base times the height
π r2 h = (3.1416)(4)(4)(15) = 753.98 ft3
Volume of Cylinder B is likewise pi times the area of the base times the height
π r2 h = (3.1416)(6)(6)(7) = 791.68 ft3
After pumping all of Cyl A into Cyl B
there will remain empty space in B 791.68 – 753.98 = 37.7 ft3
The percentage this empty space is
of the entire volume is 37.7 / 791.68 = 0.0476 which is 4.8% when rounded to the nearest tenth
.
Step-by-step explanation: I hope that help you.
Note: you may not need to type in the percent sign.
===========================================================
Explanation:
Let's find the volume of water in container A.
Use the cylinder volume formula to get
V = pi*r^2*h
V = pi*5^2*8
V = 200pi
The full capacity of tank A is 200pi cubic feet, and this is the amount of water in the tank since it's completely full.
We have 200pi cubic feet of water transfer to tank B. We'll keep this value in mind for later.
-----------------------
Now find the volume of cylinder B
V = pi*r^2*h
V = pi*6^2*6
V = 216pi
Despite being shorter, tank B can hold more water (since it's more wider).
-----------------------
Now divide the results of each section
(200pi)/(216pi) = 200/216 = 25/27 = 0.9259 = 92.59%
This shows us that 92.59% of tank B is 200pi cubic feet of water.
In other words, when all of tank A goes into tank B, we'll have tank B roughly 92.59% full.
This means the percentage of empty space (aka air) in tank B at this point is approximately 100% - 92.59% = 7.41%
Then finally, this value rounds to 7.4% when rounding to the nearest tenth of a percent.
if √3CosA = sin A , find the acute angle A
Answer:
Here is your answer.....
Hope it helps you....
If in 1 month you can make 6 carpets, how many days will it take for making 10 carpets?
Si en 1 mes puedes hacer 6 alfombras, ¿cuántos días se necesitarán para hacer 10 alfombras?
Step-by-step explanation:
6 carpets=1month
10 carpets=?
1month=31 days
10 /6*31
51
Step-by-step explanatio
Solve the equation 10 + y√ = 14
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Answer:
y = 16
Step-by-step explanation:
Perhaps you want to solve ...
10 +√y = 14
√y = 4 . . . . . . subtract 10
y = 4² = 16 . . . square both sides
What is the equation of the line that passes through the point (-4, 2) and has a
slope of -2?
Step-by-step explanation:
use the equation of the straight line
y-y1=m (x-x1)
y-2=-2(x+4)
y-2= -2x-8
y= -2x-8+2
y= -2x-6
I hope this helps
How long will it take for a home improvement loan for 22,800to earn interest of 608.00at 8 %ordinary interest
9514 1404 393
Answer:
120 days
Step-by-step explanation:
Using the formula for simple interest, we can solve for t:
I = Prt
t = I/(Pr) = 608/(22800×.08) = 608/1824 = 1/3 . . . . year
For "ordinary interest", a year is considered to be 360 days, so 1/3 year is ...
(1/3)(360 days) = 120 days
It will take 120 days for the loan to earn 608 in interest.
