Since, area of square patch of fabric = 2.25 square inches
Area of square of side 's' = [tex]s^2[/tex]
Since, area of square patch of fabric = 2.25 square inches
[tex]2.25 = s^2[/tex]
[tex]s = \sqrt{2.25}[/tex]
s = 1.5 inches
Therefore, the side length of the patch is 1.5 inches.
Final answer:
To determine the side length of a square with an area of 2.25 square inches, take the square root of the area, which is 1.5 inches.
Explanation:
To find the side length of a square patch of fabric that is 2.25 square inches, we need to understand that the area of a square is given by the formula Area = side × side (or side2). Given that the area is 2.25 square inches, we set up the equation side2 = 2.25.
Now, to find the side, we take the square root of both sides of the equation:
√(side2) = √2.25side = 1.5Therefore, the side length of the square patch is 1.5 inches.
Use the diagram below to answer questions 4-5.
what is the value of x?
309×29 solve it by using regrouping and partial products
4500 people ride the city bus every day on average about how many people ride the bus each hour
In one study, it was found that the correlation coefficient between two variables is -0.93.
Which statement is true?
A. There is a weak positive association between the variables.
B. There is a weak negative association between the variables.
C. There is a strong positive association between the variables.
D. There is a strong negative association between the variables.
The correlation coefficient of -0.93 suggests a strong negative association between the two variables. Thus, option D is the correct answer.
Explanation:In the study, it was found that the correlation coefficient between two variables is -0.93, implying a strong relationship between the two variables. But because the coefficient value is negative, it means that there's a strong negative association between the variables. In other words, as one variable increases, the other decreases, and vice versa.
A correlation coefficient ranges from -1 to 1. The strength of the correlation is determined by the absolute value of the coefficient - the closer to 1 (or -1), the stronger the correlation. Positive values indicate a direct relationship, where both variables move in the same direction, while negative values indicate an inverse relationship, where the variables move in opposite directions.
Therefore, in your given options, the right choice is D. There is a strong negative association between the variables.
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Is the inequality always, sometimes, or never true? 3x -4<3(x-2)
Which system of linear inequalities is graphed? {y>2x+1x+y<−2 {y<2x+1x+y>−2 {y≤2x+1x+y≥−2 {y≥2x+1x+y≤−2 The image is a system of linear inequalities graphed on a coordinate plane with increments of 1 and x and y axis ranging from negative 5 to 5. A dashed line passes through the points begin ordered pair 0 comma 1 end ordered pair and begin ordered pair 1 comma three end ordered pair. The shading is above the line. The other line passes through begin ordered pair 0 comma negative 2 end ordered pair and begin ordered pair negative 2 comma zero end ordered pair. The shading is below this line.
Let us check the slope of y-intercepts of the given lines in the graph first.
The y-intercept of above line is 1 and slope of
Rise/run = 2/1 (Moving 2 units up and 1 unit right).
So, the equation should be
y=2x+1
Y-intercept of second line is -2 and slope is
Rise/run = -1/1 (Moving 1 unit down and 1 unit right).
So, the equation should be
y=-x-2.
Now, we need to check the shaded portion for inequality signs.
We have both lines dotted.
So, the inequality signs would be just < or >.
For y=2x+1 line : Shading is on the left side.
On the left side of the line y=2x+1, the y-values are greater than on right side.
Therefore, we got first inequality y>2x+1
For y=-x-2 line : Shading is on the down of the line.
On the down of the line y=-x-2, the y-values are less than up side of the line.
Therefore, second inequality would be
y<-x-2 or y+x<-2
Therfore, correct option is first option y>2x+1 and y+x<-2.
Answer:
A was the answer.
Step-by-step explanation:
i took the test.
On Monday, you realize that a significant theft occurred between 6PM Friday and 8AM Monday. You have good video tape of the time period. How many minutes of tape are there to review?
For this one, find out how many hour have passed per day with 6 pm Friday being where you start.
6 pm Friday- 6 pm Saturday =24
6 pm Saturday - 6 pm Sunday= 24
6 pm Sunday - 6 am Monday = 12 hours
6 am Monday until 8 am Monday= 2 hours
Now just add the amount of hours together
24+24+12+2= 62 hours
Now convert that to minutes.
There are 60 minutes in 1 hour. You multiply the amount of hours by 60 to get the minutes.
62 hours times 60 minutes in 1 hour
62*60= 3720.
So you will have a total of 3,720 minutes of tape to review.
Answer: 3,720
Step-by-step explanation:
If 2 lemons cost 15cent how many can be bought for 60cent
You could buy 8 lemons for 60 cents.
If f(x) varies directly with x2 and f(x)=10 what is the value of f(x) when x=3
If f(x) varies directly with [tex]x^2[/tex]
If f(x) varies directly with x then we use equation f(x) = kx
where k is the constant of proportionality
So equation becomes [tex]f(x) = kx^2[/tex]
We use the information and find out k
f(x)= 10
[tex]f(x) = kx^2[/tex]
[tex]10= kx^2[/tex]
[tex]k = \frac{10}{x^2}[/tex]
now we use the value of k and find the value of f(x) when x=3
[tex]f(x) = \frac{10}{x^2}*x^2[/tex]
f(x) = 10
The value of f(x) = 10 when x= 3
The value of f(x) when x=3 is 90.
If f(x) varies directly with x2 and is given that f(x)=10 when x=1 (since 1 squared is 1), we can express the direct variation as f(x) = k × x2, where k is the constant of variation. To find the value of k, we use the information that f(1)=10. Thus, 10 = k × 12, which means k=10.
Now that we know k=10, we can find f(x) when x=3. We substitute x with 3 in the equation f(x) = 10 × x2, yielding f(3) = 10 × 32 = 10 × 9 = 90. Therefore, the value of f(x) when x=3 is 90.
I'd really appreciate it if anyone could help! :) I'll give Brainliest!
The graph of a function is shown below these choices.
Select all the statements that correctly describe this function.
The equation that represents this function is f(x)=−7x+1.
The equation that represents this function is f(x)=x−7.
The range of this function is increasing as the domain increases.
The range of this function is decreasing as the domain increases.
Answer:
The equation that represents this function is f(x)=x−7.The range of this function is increasing as the domain increases.Step-by-step explanation:
The line in the graph has a rise of 1 for each run of 1, so its slope is 1/1 = 1. The slope (x-coefficient) of the function f(x) = -7x+1 is -7, so that is not the function shown in the graph.
The wording "the range ... is increasing as the domain increases" is a bit unusual. Usually "domain" and "range" refer to intervals or sets of values over which the function is defined. While it is true that extending the interval of definition (domain) of the function will extend the range of values it produces, we suspect this is supposed to suggest that the slope of the line is positive. (As you pick increasing elements from the domain, the function will map those values to increasing elements of the range.)
What is the midpoint of the line segment with endpoints (-1,7) and (3,-3)
A(2,2)
B(1,2)
C(2,4)
D(1,4)
Hey there!!
Co-ordinates for midpoint when two endpoints are given :
... [tex]\frac{x2+x1}{2} , \frac{y2+y1}{2}[/tex]
Given endpoints :-
... ( -1, 7 ) ( 3, -3 )
... [tex]\frac{3-1}{2},\frac{-3+7}{2}[/tex]
... [tex]\frac{2}{2},\frac{4}{2}[/tex]
... [tex]1,2[/tex]
Hence, the midpoint is ( 1,2 )
Hope my answer helps!
The midpoint of the line segment with endpoints (-1,7) and (3,-3) would be (1, 2).
What are the coordinates of the midpoint of the line segment AB?Suppose we've two endpoints of a line segment:
A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
[tex]x = \dfrac{p+m}{2}\\and \\y = \dfrac{q+n}{2}[/tex]
Given endpoints ; ( -1, 7 ) ( 3, -3 )
[tex]x = \dfrac{-1+3}{2}\\\\\\x = 1\\y = \dfrac{7-3}{2}\\\\ y = 2[/tex]
Hence, the midpoint is ( 1,2 ).
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Help with algebra please
The range = [0 , ∞)
We read from the y axis. The graph exists from y = 0 to infinity.
Select the correct answer. If `f(x) = 2x^2 - 4x - 3` and `g(x) = (x - 4)(x + 4)`, find `f(x) - g(x).` a. `4x + 13` b. `x^2 - 4x + 13` c. `3x^2 - 4x + 13` d. `-4x^2 - 4x + 13`
f(x) = 2x² - 4x - 3
g(x) = (x - 4)(x + 4) = x² - 16
f(x) - g(x) = 2x² - 4x - 3 - (x² - 16)
= 2x² - 4x - 3 - x² + 16
= x² - 4x + 13
Answer: B
Amy invested $223 in the bank and a year later has $280.98. By what percent has the amount changed?
Answer:
26% increase
Step-by-step explanation:
Answer:
26% increase
Step-by-step explanation:
[ Please help ] The equation of a line is shown below.
y = -1/3x - 24
What is the equation of a line which is perpendicular to this line and passes through (1, 27) (1 point)
y = 3x - 24
y = 7x - 24
y = 7x + 24
y = 3x + 24
ANSWER
The correct answer is D
EXPLANATION
The slope of the given line
[tex] =-\frac{1}{3}[/tex]
The line perpendicular to it has slope
[tex]=\frac{-1}{\frac{-1}{3}} =3[/tex]
If the line passes through
[tex](1,27)[/tex]
Then the equation is given by
[tex]y-y_1=m(x-x_1)[/tex]
[tex]\Rightarrow y-27=3(x-1)[/tex]
[tex]\Rightarrow y=3x-3+27[/tex]
[tex]\Rightarrow y=3x+24[/tex]
Equation of the required line which is perpendicular to this line and passes through (1, 27) is y= 3x+24
The equation of the given line is y = -1/3x - 24
Comparing it with the standard form i.e y=mx+c
where 'm' is the slope of the line
and 'c' is the y-intercept of the line
we get 'm=-1/3' and 'c=-24'
Now if two lines are perpendicular the relation between their slopes 'm1' and 'm2' is given as
m1*m2=-1
Thus here m1=-1/3;
(-1/3)*m2=-1
m2=3
Therefore slope of any line perpendicular to y = -1/3x - 24 would be m2=3
Also given that the line passes through the point (1, 27)
Thus if a line having slope as 'm' and passing through the point (x1,y1) its equation is given as:
[tex]y-y_{1}=m(x-x_{1})[/tex]
here [tex](x1,y1)=(1,27)[/tex]
and [tex]m=3[/tex]
Thus required equation would be:
y-27 = 3*(x-1)
y-27 = 3x-3
y = 3x-3+27
y= 3x+24
The cashier has been directed to sell bread for half off its regular price of $1.98. What is the sale price?
A video game randomly chooses your car color and type. The probability of getting a red car is 0.20, and the probability of getting a convertible is 0.40.
Event A = You get a red car.
Event B = You get a convertible.
A and B are independent events if _____.
A.The probability of getting a red car or a convertible is 0.60.
B.The probability of getting a red car or a convertible is 0.08.
C.The probability of getting a red convertible is 0
D.The probability of getting a red convertible is 0.08
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
Event A: You get a red car
and
[tex]P(A)=0.20[/tex]
Similarly,
Event B: You get a convertible
and
[tex]P(B)=0.40[/tex]
So, if A and B are independent , then they must satisfy,
[tex]P(A).P(B)=P(A\cap B)[/tex]
So,
[tex]P(A\cap B)=0.4\times 0.2=0.08[/tex]
Hence, Option 'D' is correct, which states that the probability of getting a red convertible is 0.08.
Answer:
D.The probability of getting a red convertible is 0.08
Step-by-step explanation:
ap3x
what is the finance charge on $13,300 financed at 7.9 percent for 4 years if the monthly payment per $100 is $2.44?
A.) $13,300
B.) $2,276.96
C.) 1,457.68
D.) $15,576.96
SOMEONE HELP ME PLZ!!!
If you borrowed $100, then your monthly payment is $2.44
If you borrowed $200, then your monthly payment is 2*2.44 = 4.88
etc etc
We can set up a proportion
2.44/100 = x/13300
to figure out the monthly payment x. Cross multiply and solve for x
2.44*13300 = 100*x
100x = 2.44*13300
100x = 32452
x = 32452/100
x = 324.52
So the monthly payment is $324.52
An alternative way to get this monthly payment is to apply 2.44% to 13300, which is another way to view the phrase "monthly payment per $100 is 2.44"
------------------
There are 48 months in 4 years (start with 12 mon = 1 yr, then multiply both sides by 4) so we multiply 48 by the monthly payment to get the result 48*324.52 = 15,576.96. This is the total amount you have to pay back which is the principal plus interest.
Subtract off the principal (amount borrowed) to find the interest or finance charge: 15,576.96 - 13,300 = 2,276.96
Answer: Choice B
The finance charge on $13,300 financed at 7.9 percent for 4 years is $12,975.48.
Explanation:To calculate the finance charge, we need to first find the total amount financed. We can do this by multiplying $13,300 by the monthly payment per $100, which is $2.44. $13,300 divided by 100 is 133, so we multiply 133 by 2.44 to get $324.52. Now, we can calculate the finance charge by subtracting the total amount financed from the original loan amount. $13,300 minus $324.52 is $12,975.48. Therefore, the finance charge is $12,975.48.
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What is the point of completing a value assessment while searching for a career?
a) to use the resources of a qualified career counselor
b) to understand what kind of values are of interest to employers
c) to reveal how your own values may match certain career choices
d) to determine how many personal and work values you have
Answer:
c) to reveal how your own values may match certain career choices
Step-by-step explanation:
1. Is the following system consistent or inconsistent?
8x + y + 4 = 0
y = -8x - 4
2. Is the following system consistent or inconsistent?
7x + 6 = -2y
-14x -4y + 2 = 0
3. Is the following system consistent or inconsistent?
-2x - 2y = 6
10x + 10y = -30
4. Is the following system consistent or inconsistent?
2y = x - 7
-2x - 6y = -14
5. Is the following system consistent or inconsistent?
y = 2x + 5
-2x + y = -2
Answer with Explanation:
If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.
If a system has no solution, it is said to be inconsistent . Represent parallel lines.
1) 8x + y + 4 = 0
y = -8x - 4
If we solve equation 8x + y + 4 = 0 for y, we get
y = -8x -4
So, both equations are same. That means both lines are same. So infinite many solutions.
System is consistent
2) Both line slope are same and parallel to each other.
So, no solution
System is inconsistent.
3) Both equation represent the same line. So, infinite many solution.
System is consistent.
4) Both lines are intersect at a point.
Intersection point is (7,0).
5) Both lines are parallel. So, no solution.
System is inconsistent.
Jane, Andre, and Maria pick apples. Andre picks 3 times as many pounds as Maria. Jane picks 2 times as many pounds as Andre. The total weight of the apples is 840 pounds. How many pounds of apples does Andre pick?
A) 84 pounds
B) 252 pounds
C) 504 pounds
D) 840 pounds
Let Maria = X
Andre = 3x ( 3 times as many as Maria)
Jane = 2(3x) = 6x ( 2 times as many as Andre)
All 3 need to equal 840 pounds:
X + 3x + 6X = 840
Combine like terms:
10X = 840
Divide both sides by 10:
X = 840 / 10
X = 84
Maria = X = 84 pounds
Andre = 3x = 3(84) = 252 pounds
Jane = 6x = 6(84) = 504 pounds
504 + 252 + 84 = 840 pounds.
Andre picked 252 pounds.
The answer is B.
Hi,
Jane, Andre, and Maria pick apples. Andre picks 3 times as many pounds as Maria. Jane picks 2 times as many pounds as Andre. The total weight of the apples is 840 pounds. How many pounds of apples does Andre.
Lets say andre picked 252!
Andre - 252
Maria - 252 / 3 = 84
Jane - 252 x 2 = 504
504 + 252 + 84 = 840
Answer:
B) 252 pounds
The graph is a transformation of which of the following functions?
i think its the second option but im not sure.
Consider the parrent function [tex]y=\sqrt{x}.[/tex] The graph of this function you can see in the attached diagram (red line).
1. Reflect this graph about the x-axis, then the function becomes [tex]y=-\sqrt{x}[/tex] (blue line).
2. Translate the reflected graph 2 units up, then the function becomes [tex]y=-\sqrt{x} +2[/tex] (green line).
Answer: correct choice is B.
Witch number is a factor of 18 but not a mutiple of 3?
can someone help me, please
Solve for w by simplifying both sides of the equation, then isolating the variable.
The answer is A.
I do not know how to do this need help
Remark
First of all you have to declare the meaning of g(f(x)) After you have done that, you have to make the correct substitution.
Givens
f(x) = 4x^2 + x + 1
g(x) = x^2 - 2
Discussion
What the given condition g(f(x)) means is that you begin with g(x). Write down g(x) = x^2 - 2
Wherever you see an x on either the left or right side of the equation, you put fix)
Then wherever you see f(x) on the right you put in what f(x) is equal to.
Solution
g(x) = x^2 - 2
g(f(x)) = (f(x))^2 - 2
g(f(x)) = [4x^2 + x + 1]^2 - 2
f(x)^2 =
4x^2 + x + 1
4x^2 + x + 1
16x^4 + 4x^3 + 4x^2
4x^3 + x^2 + x
4x^2 + x + 1
16x^4 + 8x^3 + 9x^2 + 2x + 1
Answer
g(f(x)) = 16x^4 + 8x^3 + 9x^2 + 2x + 1 - 2
g(f(x)) = 16x^4 + 8x^3 + 9x^2 + 2x - 1
Why the expressionY+y+y and3y are equivalent
Answer:
Because if you add the amount of Ys together it equals 3y
Step-by-step explanation:
What interger describes withdrawing $100 from your bank account?
The required integer is -100$.
It is required to find the integer.
What is integer?An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Zero is not a fraction or decimal of any number. It is neither positive nor negative.
Given:
The given integer describes withdrawing $100 from your bank account.
According to given question we have,
-100$
negative one hundred
or
minus one hundred
Therefore, the required integer is -100$.
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Cara is grocery shopping and needs chicken and steak for the barbeque she is having on Saturday. Chicken is $2.99 per pound and steak is $5.79 per pound. She knows she wants to spend exactly $50 on meat. If c represents pounds of chicken and s represents pounds of steak, which equation represents this situation?
2.99s + 5.79c = 50
8.78m = 50
c + s = 50
2.99c + 5.79s = 50
chicken: ($2.99) c
steak: ($5.79) s
chicken + steak = total
2.99c + 5.79s = 50
Answer: D
Fia's goal was to raise $5,000 to help protect the manatees. She raised $3,500. What percent of her goal did she achieve
In order to turn a ratio into a percentage, you have to turn the given fraction into an equivalent fraction with denominator 100. So, you have
[tex] \dfrac{3500}{5000}=\dfrac{x}{100} [/tex]
Solving for x, you get
[tex] x=\dfrac{3500\cdot 100}{5000} = \dfrac{3500}{50} = \dfrac{350}{5} = 70 [/tex]
So, they achieved the 70% of their goal.
PLEASEE HELP!! <3 100 POINTSS
Which table of ordered pairs represents a proportional relationship?
To tell isf a table is proportional, divide y by x,
if all sets are the same it is proportional.
First table:
3 / -3 = -1
2 / -4 = -2
-1 and -2 are not the same
Table 2:
1/-1 = -1
3/-3 = -1
5/-5 = -1
These are all the same.
Table 2 is correct.
To find porportionality, you must note that: the x and y must have the same value throughout the table when multiplied.
For example:
x | y
------------
1 | 2
2 | 4
etc.
In this case, it is multiplied by 2. Now let us look at the problem
---------------------------------------------------------------------------------------------------------------------------
Table 2 is your answer because, you are multiplying -1 each time
x(-1) = y is your equation
To check, plug in the x, and see if the y is the same value
(-1)(-1) = 1 (True)
(-3)(-1) = 3 (True)
(-5)(-1) = 5 (True)
---------------------------------------------------------------------------------------------------------------------------
hope this helps