Answer:
Find an integer k for which the roots of the equation will be rational and unequal. To find a value of k that makes the roots rational and unequal the discriminant must be greater than 0 and a perfect square.
Step-by-step explanation:
So if k=0 or k=5 the roots will be rational and unequal. hope this helps you :)
Each child in a certain class is required to have school supplies of 1 notebook and 2 pencils. One notebook costs $1.09 and one pencil costs $0.59. With $15, what is the maximum number of children that can be provided with the required supplies? (Assume no tax.) Will mark Brainlist
Answer:
6 children
Step-by-step explanation:
Given
[tex]1\ Pencil = \$0.59[/tex]
[tex]1\ Notebook = \$1.09[/tex]
Required
Determine the number of students that can get pencils and notes worth $15
First, we need to calculate the amount that can be allotted to a child
[tex]1\ child= 1\ Notebook + 2\ Pencils[/tex]
[tex]1\ child= 1 * \$1.09 + 2 * \$0.59[/tex]
[tex]1\ child= \$1.09 + \$1.18[/tex]
[tex]1\ child= \$2.27[/tex]
From the given parameters, we have that
[tex]n\ children= \$15[/tex]
Where n is the number of child
Represent both as ratios;
[tex]1 : 2.27 = n : 15[/tex]
Convert to division
[tex]\frac{1}{2.27} = \frac{n}{15}[/tex]
Multiply both sides by 15
[tex]15 * \frac{1}{2.27} = \frac{n}{15} * 15[/tex]
[tex]\frac{15}{2.27} = n[/tex]
[tex]6.608 = n[/tex]
[tex]n = 6.608[/tex]
Because "a child" is discrete, we have to round down the above figure to
[tex]n = 6[/tex]
Hence, the maximum number of children that can be provided with supplies worth $15 is 6
What is the solution to the system of linear equations? Write you answer as a coordinate. 2x − y = 4 5x + 2y = 10 Show All Work !!
Answer:
(2, 0)
Step-by-step explanation:
2x - y = 4
5x + 2y = 10
Solve by elimination by multiplying the top equation by 2, so the y values will cancel out (-2y + 2y = 0)
4x - 2y = 8
5x + 2y = 10
Add them together and solve for x:
9x = 18
x = 2
Plug in 2 as x in one of the equations to find y:
2x - y = 4
2(2) - y = 4
4 - y = 4
-y = 0
y = 0
The solution is (2, 0)
If F(x) = x - 7 and G(x) = x3, what is G(F(x))
[tex]g(f(x))=(x-7)^3=x^3 - 21 x^2 + 147 x - 343[/tex]
Machine A and Machine B are each used to make 660 widgets. It takes Machine A x hours longer to produce 660 widgets than Machine B. Machine B produces y % more widgets per hour than Machine A. How long does it take Machine A to make 660 widgets?
Answer:
A. x + 100x/y
Step-by-step explanation:
Machine A= x hours longer to produce 660 widget than machine B
Machine B produces y% more widget per hour than machine A
let
b = Number of hours it takes Machine B to make 660 widgets.
Time taken for Machine A to make the 660 widgets = x + b.
Rate of Machine B = 660/b
Rate of Machine A = 660 / (x + b).
Machine B produces y% more widgets per hour than Machine A:
660 / (x + b)(1 + y/100) = 660/b
1 / (x + b)(1 + y/100) = 1 / b
Multiply both sides by (x+b)
1 + y/100 = (x + b)/b
1 + y/100 = x/b + 1
Subtract 1 from both sides
y/100 = x/b
Take the inverse of both sides
100/y = b/x
Make b the subject
100x/y = b
b=100x/y
The time taken for Machine A to make the 660 widgets is x + b = x + 100x/y.
Answer is A. x + 100x/y
The following equation is often referred to as Euler's Formula; e^pii+1=0 Use what you know about complex numbers to show that this equation is true. In other words, show that e^pii+1=0 __ If someone could please help me understand the proof and the answer to this ill give you brainliest!! thank you
Answer:
[tex]\large \boxed{e^{i\pi}+1=0}[/tex]
Step-by-step explanation:
Hello, please consider the following.
For any x real number,
[tex]e^{ix}=cos(x)+i\cdot sin(x)\text{, right? So}\\\\e^{i\pi}=cos(\pi)+i\cdot sin(\pi)\\\\e^{i\pi}=-1+i\cdot 0=-1\\\\\text{ We add 1 to both sides of the equation.}\\\\\large \boxed{e^{i\pi}+1=0}\\[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
factorize 12p2q -9q2
Answer:
[tex] \boxed{3q(4 {p}^{2} - 3q)}[/tex]Step-by-step explanation:
[tex] \mathsf{ 12 {p}^{2} q - 9 {q}^{2} }[/tex]
In such an expression, the factor which is present in all terms of the expression is taken out as common and each term of the expression should be divided by the common factor to get another factor.
Factor out 3q from the expression
[tex] \mathsf{ = 3q(4 {p}^{2} - 3q)}[/tex]
Hope I helped!
Best regards!
Factorization of 12p²q-9q² is 3q(4p²-3q).
What is Factorization?Factorization is defined as breaking an entity into a product of another entity, or factors, which when multiplied together give the original number.
Here, given expression is, 12p²q-9q²
Now, by factorizing this we get,
3q(4p²-3q)
Hence, required factorization is 3q(4p²-3q)
To learn more on factorization click:
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For the given graph, a. describe the end behavior,
b. determine whether it represents an odd-degree or even-degree polynomial function, and
c. state the number of real zeros.
Answer:
See below.
Step-by-step explanation:
A)
The end behavior is basically how the function behaves as it approaches negative or positive infinity.
As the function approaches negative infinity, we can see that the graph is going up. In other words:
[tex]f(x)\rightarrow\infty\text{ as }x\rightarrow-\infty[/tex]
As the function approaches positive infinity, we can see that the graph is going down. In other words:
[tex]f(x)\rightarrow-\infty\text{ as }x\rightarrow\infty[/tex]
B)
In even-degree polynomials, both ends of the graph will be going the same way. In this graph, the two ends are going opposite ways so this is an odd-degree function.
C)
The number of real zeros is simply the amount of times the graph crosses the x-axis. In the graph, the function does this three times. Thus, the number of real zeros is 3.
describe the type of correlation between two variables on a graph
Answer:
We often see patterns or relationships in scatterplots. When the y variable tends to increase as the x variable increases, we say there is a positive correlation between the variables. When the y variable tends to decrease as the x variable increases, we say there is a negative correlation between the variables.
Step-by-step explanation:
plz mark as brainlist
The correlation between two variables on a graph gives the relationship between those variables. Depending on the nature of these variables plotted on the graphs, the correlation is named.
What is meant by correlation?In a scatterplot, the data points of an individual with two distinct variables are related. This relationship is called 'correlation'. The relationship between any two variables plotted on any graph is named to be a correlation.Depending on the type of relation between the variables, the correlation is categorized into three major types. They are
i) Positively correlation
ii) Negative correlation
iii) No correlation
What is meant by positively correlated?The variables plotted on a graph are said to be positively correlated, if both the variables increase with respect to each other.E.g.: In a graph, if the values of y increase as the value of x increases, then they are said to be positively correlated.What is meant by negatively correlated?The variables plotted on a graph are said to be negatively correlated, if one of the variables increases, the other variable get decreases.E.g.: In a graph if the values of y decrease as the value of x increases, then they are said to be negatively correlated.What is meant by no correlation?The data points for the two variables are plotted randomly on the graph. If there is no relation between any two points of those two variables, then such a relation is said to be 'no correlation'.E.g.: In a graph, if the values of x and y are randomly located, then there is no correlation between them.Learn more about correlation on a graph here:
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If 48% of the students in a certain college are female and there are 1440 female students, what is the total number of students in the college?
Answer:
3000 students
Step-by-step explanation:
If 48% of the students are female, and there are 1440 female students, we can set up a percentage proportion, assuming x is the total amount of students.
[tex]\frac{1440}{x} = \frac{48}{100}[/tex]
We can use the cross products property to find the value of x.
[tex]1440\cdot100=144000\\\\144000\div48=3000[/tex]
Hope this helped!
HEEEEEEELLLLLLLPPPPPP!!!! Given the following perfect square trinomial, find the missing term: x2 − 16x + ___ 8 16 32 64
Answer:
64
Step-by-step explanation:
(x-8)^2
derived from the middle term divided by 2
Answer:
64
Step-by-step explanation:
x^2 − 16x + ___
Complete the square
Take the coefficient of the x term
-16
Divide by 2
-16/2 = -8
Then square it
(-8)^2 = 64
What are the irrational numbers between minus 12 and plus 49
Answer:
First, an irrational number is a number that has infinite digits after the decimal point, in such way that those digits do not form any pattern.
The irrational set is called a dense set, wich means that in between two elements of the set, we can find infinite other elements of the set.
For example, between 1 and 2, we have
1.12312412513513532....
1.123224124312432432....
and between those two numbers, we can find infinite irrational numbers, and so on.
Then between -12 and +49, we have infinite irrational numbers.
order of operation
3⋅6−2+2
Answer:
18
Step-by-step explanation:
3⋅6−2+2
Use PEMDAS = Parentheses, Exponent, Multiplication, Division, Addition, Subtraction
First we multiply, then add or subtract so,
18 - 2 + 2
Now we subtract,
16 + 2
Now we add,
18
Find the distance between the two points (8, 3), (0, -3)
Answer:
The answer is 10 unitsStep-by-step explanation:
The distance between two points can be found by
[tex] \sqrt{ ({x _{1} - x_{2} })^{2} + ({y_{1} } - y_{2} )^{2} } [/tex]
where
(x1 , y1) and (x2 , y2) are the points
The distance between (8, 3), (0, -3) is
[tex] \sqrt{ ({8 - 0})^{2} + ({3 + 3})^{2} } [/tex]
[tex] = \sqrt{ {8}^{2} + {6}^{2} } [/tex]
[tex] = \sqrt{64 + 36} [/tex]
[tex] = \sqrt{100} [/tex]
We have the final answer as
10 unitsHope this helps you
Which of the following is NOT a principle of making inferences from dependent samples? Choose the correct answer below. A. The hypothesis test and confidence interval are equivalent in the sense that they result in the same conclusion. B. The t-distribution serves as a reasonably good approximation for inferences from dependent samples. C. There is some relationship whereby each value in one sample is paired with a corresponding value in the other sample. D. Testing the null hypothesis that the mean difference equals 0 is not equivalent to determining whether the confidence interval includes 0.
Answer:
D. Testing the null hypothesis that the mean difference equals 0 is not equivalent to determining whether the confidence interval includes 0
Step-by-step explanation:
Dependent samples are samples that are related to one another.
In a hypothesis test, the hypothesis test and the confidence interval are equivalent in the sense that they result in the same conclusion.
However, in an hypothesis test , we fail to reject the null hypothesis if the rejection region is greater than the t-test statistics. It is therefore crucial to understand that if the true mean is zero. the confidence interval level for the mean of differences within the lower limit and the upper limits must contain zero , which implies the mean difference and the confidence interval are equivalent.
Can someone pls help and explain it
Answer:
(7,-4) ; 12
Step-by-step explanation:
Basically, three corners of a rectangle are already on the graph. If you put a dot at (7,-4), that is the last corner(vertex) that finishes the rectangle
Then to find base of the rectangle, you find the length of the longer side, (the distance between the x coordinates). So you would subtract -5 from 7 and get 12, and 12 is the length of your base.
6a+2b-6c+4 if a=5,b=3,and c=-1
Answer:
46
Step-by-step explanation:
First, start off by substituting the values of a, b, and c, into the equation.
We know a = 5, b = 3, and c = -1, so now substitute.
6a + 2b - 6c + 4
6(5) + 2(3) - 6(-1) + 4
Now that we've substituted the values, we can solve the equation.
6(5) + 2(3) - 6(-1) + 4
30 + 6 + 6 + 4
= 46
So, the answer is 46.
I hope this helps! ôヮô
Answer:
46
Step-by-step explanation:
All you need to do is subsitute the variable with what it says the number is.
Let's first start out with 6a from the equation. We know that a= 5, so that means it wants you to multiply 6 by 5, which is 30.
Now let's do 2b. It says b= 3, so do 2 times 3. It equals 6.
So far we have 30+6-6c+4
Let's do -6c. We know that c= -1, so let's multiply -1 and -6. Negative and negative equals positive. And 6 times 1 is 6. So the outcome is positive 6.
We got 30+6+6+4
Solve.
30+6= 36
36+6= 42
And 42+4= 46. :)
. (08.01 MC) 1. Find the volume of a cylinder with a diameter of 8 inches and a height that is three times the radius. Use 3.14 for pi and round your answer to the nearest hundredth. (Hint: You may only enter numerals, decimal points, and negative signs in the answer blank) (4 points) 2.(08.01 MC) Given a soda can with a volume of 36 and a diameter of 4, what is the volume of a cone that fits perfectly inside the soda can? (Hint: only enter numerals in the answer blank). (4 points)
Answer:
602.88 in³
12
Step-by-step explanation:
Formula for volume of a cylinder = πr² · h
radius (r) = 1/2(diameter)
1. Set up the equation
radius = 4
(3.14)(4²)(3·4)
2. Solve
3.14(16)(12) = 602.88 in³
Formula for volume of a cone = 1/3πr² · h
The formula of a cone is 1/3 the volume of a cylinder. Therefore, a cone that fits perfectly within the dimensions of a cylinder would have a volume equal to 1/3 of the volume of the cylinder.
1. Set up the equation and solve
36 ÷ 3 = 12
Gene is playing a game with a bag of marbles. 3 of the marbles are blue, 4 are green, and 7 are yellow. See below for awarded prizes. $2 green $0.5 yellow $4 blue What is the expected cost (or payout for Gene's game?
Answer:
$23.5Step-by-step explanation:
Gene is playing a game with a bag of marbles. If 3 of the marbles are blue, 4 are green, and 7 are yellow and awarded prices for the marbles are $2 green $0.5 yellow $4 blue, the expected payout for Gens game is expressed as shown;
If a blue marble costs $4, 3 blue marbles will cost 3*$4 = $12
If a green marble costs $2, 4 green marbles will cost 4*$2 = $8.0
If a yellow marble costs $0.5, 7 yellow marbles will cost 7*$0.5 = $3.5
Total payout for Gene's game will be the equivalent to $12+ $8 + $3.5 = $23.5.
Hence Gene expected cost will be $21.5
What are the vertical and horizontal asymptotes for the function f(x)=
3x2/x2-4
Answer: f(x) will have vertical asymptotes at x=-2 and x=2 and horizontal asymptote at y=3.
Step-by-step explanation:
Given function: [tex]f(x)=\dfrac{3x^2}{x^2-4}[/tex]
The vertical asymptote occurs for those values of x which make function indeterminate or denominator 0.
i.e. [tex]x^2-4=0\Rightarrow\ x^2=4\Rightarrow\ x=\pm2[/tex]
Hence, f(x) will have vertical asymptotes at x=-2 and x=2.
To find the horizontal asymptote , we can see that the degree of numerator and denominator is same i.e. 2.
So, the graph will horizontal asymptote at [tex]y=\dfrac{\text{Coefficient of }x^2\text{ in numerator}}{\text{Coefficient of }x^2\text{ in denominator}}[/tex]
i.e. [tex]y=\dfrac{3}{1}=3[/tex]
Hence, f(x) will have horizontal asymptote at y=3.
PLS HELP ME I WILL GUVE YOU BRAINLIST AND A THANK YOU!!!!!
Answer: 35
Step-by-step explanation:
If you take the three angles shown, it's total is 180
So take the two angles you know, and subtract them from 180
Now we have 100 left, and we can subtract 30 to be left with 2x.
Now divide what is left by two, which is 70
70/2=35
Answer:
x = 35
Step-by-step explanation:
So we know that a straight line is equal to 180 degrees. So from there we can add the two 40 degrees to get 80 degrees. Now we can solve for x. So 180 - 80 = 100
2x + 30 = 100
Subtract 30 from both sides
2x = 70
Divide both sides by 2
x = 35
I need help please will give you 5 stars and good rating
Answer:
Step-by-step explanation:
Answer:
x=12
Step-by-step explanation:
To solve for the variable, we must isolate the variable, which is x.
[tex]\sqrt{x+4} -3=1[/tex]
3 is being subtracted from the square root of x+4. The inverse of subtraction is addition. Add 3 to both sides of the equation.
[tex]\sqrt{x+4} -3+3=1+3[/tex]
[tex]\sqrt{x+4} =1+3[/tex]
[tex]\sqrt{x+4} =4[/tex]
The square root of x+4 is being taken. The inverse of a square root is a square. Square both sides of the equation.
[tex](\sqrt{x+4})^2 =4^2[/tex]
[tex]x+4=4^2[/tex]
Evaluate the exponent.
4^2= 4*4=16
[tex]x+4=16[/tex]
4 is being added to x. The inverse of addition is subtraction. Subtract 4 from both sides of the equation.
[tex]x+4-4=16-4[/tex]
[tex]x=16-4[/tex]
[tex]x=12[/tex]
The solution to this equation is x=12.
A box contains 20 equal-sized balls, numbered 1 to 20. Two balls are drawn at random simultaneously. What is the probability that the numbers on the two balls will differ by more than 2
Answer:
P = 0,7947 or 79,47%
Step-by-step explanation:
We have 20 balls, the total possible outcomes drawn two balls simultaneously is:
C = m! /n! *( m - n )!
C = 20!/2! *( 20 - 2)!
C= 20*19*18!/ 2* 18!
C = 20*19/2
C = 190
Now the number of successful outcomes x ( those where balls differ by more than 2 is)
x = total numbers of outcomes - 20 ( outcomes differing in 1 ) - 19 (outcomes differing in 2 )
x = 190 - 39
x = 151
Then the probability of drawing tw balls with numbers differing n mr than two is
P = successful outcomes / total outcomes
P = 151/190
P = 0,7947 or 79,47%
The graph shows the distance in miles of a runner over x hours. What is the average rate of speed over the interval [9, 11]? There are four points connected by a curve on the graphs. The points are (0, 0), (5, 1), (9, 6), (11, 11). Two-fifths 1 2 Five-halves
Answer:
Below
Step-by-step explanation:
Let f be our function:
● f(9) = 6
● f(11) = 11
Let m be the average speed over the interval [9,11]
● m = [f(11)-f(9)] / 11-9
● m = 11-6 / 2
● m = 5 / 2
● m = 2.5
So the answer is five halves.
Answer:
5/2
Step-by-step explanation:
D on edge
Write an expression for the shaded area
Answer:
4x(x+2) - x(3x+5)
Step-by-step explanation:
the area of the whole box is 4x(x+2)
to find the area of the shaded portion you have to subtract the area of the tiny box from the big box
the area of the tiny box is x(3x+5)
so, 4x(x+2) - x(3x+5) is the expression you can use to find the area of the shaded portion
Please answer this question now
Answer:
Surface Area = 85.75 ft²
Step-by-step explanation:
Surface area of pyramid = ½(Perimeter of triangular base * slant height of pyramid) + Area of triangular base
Perimeter of triangular base = sum of all sides of the triangular base = 5+5+5 = 15 ft
Slant height of pyramid = 10 ft
Area of triangular base = ½*base of triangle*height of triangle = ½*5*4.3 = 10.75 ft²
Plug in the above values:
Surface Area = ½(15*10) + 10.75
= (15*5) + 10.75
= 75 + 10.75
Surface Area = 85.75 ft²
Mr Hamar had rupees 4,400 hie purchase 6 kg of rice at Rupess 75 for KG ,2 packets of oil at rupees 125 per packet and he gave rupees 3,300 to his wife if he divided the remaining Sum between his son and daughter equally find the share of each of them
Step-by-step explanation:
Total rupees= 4400
Price of 6kg rice = 75 x 6 = 450
Price of 2 packets oil = 125 x 2 = 250
Amount given to wife = 3300
Total = 450 + 250 + 3300 = 4000
Remaining amount = 4400 - 4000 = 400
Share of son and daughter = 400 ÷ 2 = 200
So his son and daughter both get 200
Please answer now question
Answer:
v=168
Step-by-step explanation:
help asap will give 10 points
Answer:
False
Step-by-step explanation:
[tex]( {9}^{9} ) \times ( {9}^{ - 20} ) \\ = {9}^{9 + ( - 20)} \\ = {9}^{ - 11} [/tex]
Answer:
I'm pretty sure its false
can u help me. if answer is correct, i will give u brainliest
Answer:
135 units²
Step-by-step explanation:
The area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
To calculate h use Pythagoras' identity on the right triangle on the left
h² + 8² = 17²
h² + 64 = 289 ( subtract 64 from both sides )
h² = 225 ( take the square root of both sides )
h = [tex]\sqrt{225}[/tex] = 15 , thus
A = 9 × 15 = 135 units²
Nazia has two quarts of a 30% acid solution and four pints of a 20% acid solution. If she mixes them, what will be the concentration of the resulting solution? [1 quart = 2 pints]
Answer: Acid concentration will be 25%.
Step-by-step explanation:
Solution 1: 2 quarts(=4 pints) of a 30% acid
concentration = 0.3*4 = 1.2
Solution 2: 4 pint of a 20% acid
concentration = 4*0.2 = 0.8
Final solution: total volume = 4 pints + 4 pints = 8 pints
Final Concentration:
[tex]\frac{1.2+0.8}{8}[/tex] = 0.25
In the resulting mixture, the concentration is 25% of acid solution.
