Answers
Question 5:
Step 1
From the figure, we can say that vertically opposite angles are equal.
Step 2:
From the diagram,
Related Questions
Determine whether the function is linear. If it is, State the rate of change.Question 8
Answers
Question 8.
Given the table:
x -7 -5 -3 -1 0
y 11 14 17 20 23
To determine if the function is linear, let's calculate to see if the rate of change is constant.
The x-values need to have a constant rate of change and the y-values need to have a constant rate of change.
If the function has a constant rate of change, then the functioncan be said to be linear.
To calculate the rate of change, we have:
[tex]\begin{gathered} x2-x1=-5\text{ - (-7) = -5 + 7 = 2} \\ \\ x3-x2=-3-(-5)=-3+5=2 \\ \\ x4-x3=-1-(-3)=-1+3=2 \\ \\ x5-x4=0-(-1)=0+1=1 \\ \\ We\text{ can se}e\text{ the x-values do not have a constant rate of change} \end{gathered}[/tex][tex]\begin{gathered} y2-y1=14-11=3 \\ \\ y3-y2=17-14=3 \\ \\ y4-y3=20-17=3 \\ \\ y5-y4=23-20=3 \\ \\ \text{The y-values have a constant rate of change} \end{gathered}[/tex]Since the x-values do not have a constant rate of change that means the function is not linear.
ANSWER:
The table does not represent a linear function
Determine the equation of the straight line that passes through the point (-2, -4)and is perpendicular to the line y +2x=1
Answers
If the line is perpendicular to:
[tex]y=-2x+1[/tex]the we know that the slope will be the negative reciproc of the slope so the new slope is:
[tex]m=\frac{1}{2}[/tex]So the equation is:
[tex]y=\frac{1}{2}x+b[/tex]So we can replace the coordinate (-2,-4) and solve for b so:
[tex]\begin{gathered} -4=\frac{1}{2}(-2)+b \\ -4+1=b \\ -3=b \end{gathered}[/tex]So the final equation is:
[tex]y=\frac{1}{2}x-3[/tex]How many ways can we award a 1st, 2nd, and 3rd place prize among eight contestants?
Answers
We have:
- There are 8 choices for awarding first prize.
- Then there are 7 choices for awarding second prize.
- And there are 6 choices for awarding third prize.
Therefore, there are:
[tex]8\cdot7\cdot6=336\text{ ways}[/tex]Answer: 336 ways
Alex’s paycheck was for $624.65. If Alex worked 32.5 hours, what is his rate of pay?
Answers
In order to know the rate of pay, we need to divide the value of the paycheck ($624.65) by the total hours Alex worked (32.5 hours):
$624.65/(32.5 hours) = $624.65/(32.50 hours) = $62465/(3250 hours)
Now, to solve this division, we can do as follows:
Therefore, the rate of pay is
$19.22/hour
Find the area of 11.4 and 7.4
Answers
let,
lenght (l)=11.4 , and width (b)=7.4
so,
[tex]\begin{gathered} \text{area}=l\times b \\ =11.4\times7.4 \\ =84.36 \end{gathered}[/tex]area=84.36
Name the quadrant in which each of the point lies. (-2,5)
Answers
The quadrants have the following division.
Since the points (-2, 5) is located on the negative side of the x-axis, and in the positive side of the y axis, it belongs to the second quadrant.
The answer is quadrant II
I need help with this math question I already solved the first question but I don't understand the second.
Answers
We can solve this question using cross multiplication,
If the number of students who sleep 6 hours a day increases by, this means we'll have a total of 6 students who sleep 6 hours a day.
We want the ratio to be same: 15%
Then we can write:
[tex]\frac{6}{N}=\frac{15\%}{100\%}[/tex]6 students are the 15%, then N students are the 100%
Now solve for N:
[tex]\begin{gathered} 6·100=15·N \\ \end{gathered}[/tex][tex]N=\frac{600}{15}[/tex][tex]N=40[/tex]The answer is 40 students are expected.
This is a reasonable answer, given that if the number of students who sleep 6 hours doubles, for the rate to remain the same, the total of students must double.
12 Stefanie is painting her bedroom. She can paint 12 1/3 square feet in 1/5 of an hour. How many square feet can she paint in one hour?
Answers
stephanie can paint 12 1/3 square feet in 1/5 of an hour. So,
[tex]undefined[/tex]Filling in Table (decreasing)Dependent QuantityA Helicopter flying at 3509 feet begins its descent. Itdescends at a rate of 41 feet per minuteIndependent Quantity0Complete the missing part of the tables, and make afunction that describes the Helicopter's decent133222Your answer: Not there yet, keep working3140Share with Class
Answers
(0,3509)
(1,3468)
(3,3386)
(7,3222)
(9,3140)
h=3509-41x
Explanation
Step 1
as we can see, the independent quantity is the time , and the dependent quantity is the heigth because it depends on the time.
then when time = o, t=o
[tex]0\Rightarrow3509\text{ ft}[/tex]after 1 minute the helicopter has descended 41 ft, then
when time = 1, t=1
[tex]\begin{gathered} heigth_1=3509-(1\cdot41) \\ heigth_1=3509-41 \\ heigth_1=3468 \\ (1,3468) \end{gathered}[/tex]when t=3
[tex]\begin{gathered} heigth_3=3509-(3\cdot41) \\ heigth_3=3509-123 \\ heigth_3=3386 \end{gathered}[/tex]when heigth=3222
[tex]\begin{gathered} \text{heigth}_x=3509-(x\cdot41) \\ 3222=3509-41x \\ \text{subtract 3509 in both sides} \\ 3222-3509=3509-41x-3509 \\ -287=-41x \\ \text{divide both sides by -41} \\ \frac{-287}{-41}=\frac{-41x}{-41} \\ 7=x \\ \text{hence}(7,3222) \end{gathered}[/tex]when heigth=3140
[tex]\begin{gathered} \text{heigth}_x=3509-(x\cdot41) \\ \text{3140}=3509-41x \\ subtract\text{ 3509 in both sides} \\ \text{3140-3509}=3509-41x-3509 \\ -369=-41x \\ \text{divide both sides by -41} \\ \frac{-369}{-41}=\frac{-41x}{-41} \\ 9=x \\ x=9,\text{then} \\ (9,3140) \end{gathered}[/tex]Step 2
now, the equation is
[tex]\begin{gathered} \text{Heigth}=3509-41x \\ h=3509-41x \\ \text{where} \\ h\text{ is the heigth in ft and t is the time in minutes} \end{gathered}[/tex]I hope this helps you
hello I'm having some difficulty on this question thank you for viewing it and helping me
Answers
The simple interest charged by the lender on Alonzo is $ 126 and the amount paid after 6 years is $ 826.
Principal amount of loan = $ 700
Time period = 6 years
Interest rate = 3 %
The simple interest is charged by the lender:
The interest will be:
SI = p × r × t / 100
Substitute the values, we get that:
SI = 700 × 3 × 6 / 100
SI = 7 × 3 × 6
SI = $ 126
The amount paid by Alonzo after 6 years will be:
Amount = $ 700 + $ 126
A = $ 826
Therefore, the simple interest charged by the lender on Alonzo is $ 126 and the amount paid after 6 years is $ 826.
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Solve fort.-t = 9(t – 10)t=Stuck? Watch a video or us
Answers
We are to solve for t in the equation given
To do this, we have to expand the bracket
Expanding, we have
-t = 9(t-10)
-t = 9t - 90
Collecting the like terms, we have
90 = 9t + t
90 = 10t
Dividing both sides by 10 to get t, we have
[tex]\begin{gathered} t=\frac{90}{10} \\ t=9 \end{gathered}[/tex]Therefore the value of t is 9.
using the graph below wich graphs shows the mapping of ABCD to A'B'C'D for a dilation with center (0,0) and a scale factor of 3
Answers
The rule for a dilation with center at (0,0) and scale factor k is:
[tex](x,y)\rightarrow(kx,ky)[/tex]Find the transformed vertices A'. B', C' and D' using this rule:
[tex]A(-2,3)\rightarrow A^{\prime}(3\times-2,3\times3)=A^{\prime}(-6,9)[/tex]Similarly, the coordinates of B', C' and D' wil be:
[tex]\begin{gathered} B^{\prime}(6,12) \\ C^{\prime}(6,-3) \\ D^{\prime}(-9,3) \end{gathered}[/tex]Plot A', B', C' and D' along with A, B, C and D:
A clothing store is donating socks to various charities. The store gave 6 regular packs and 5 value packs to a homeless shelter, which contained a total of 163 pairs of socks. For foster children, the store donated 6 regular packs and 4 value packs, which equaled 146 pairs. How many pairs of socks are in each pack?
Answers
Let r and v be the number of socks ina regular pack and value pack, respectively. Since the store gave 6 regular packs and 5 value packs which contained 163 pair of socks, we can write
[tex]6r+5v=163[/tex]Similarly, since the store donated 6 regular packs and 4 value pack which add 146 pair of socks, we can write
[tex]6r+4v=146[/tex]Then, we have the following system of equations:
[tex]\begin{gathered} 6r+5v=163\ldots(a) \\ 6r+4v=146\ldots(b) \end{gathered}[/tex]Solving by elimilation method.
By multiplying equation (b) by -1, we have an equivalent system of equations:
[tex]\begin{gathered} 6r+5v=163 \\ -6r-4v=-146 \end{gathered}[/tex]Then, by adding both equations, we have
[tex]v=17[/tex]Now, in order to obtain the number of socks in a regular pack, we must substitute the last result into equation (a). It yields,
[tex]6r+5(17)=163[/tex]which gives
[tex]6r+85=163[/tex]By subtracting 85 to both sides, we have
[tex]6r=78[/tex]Then, r is given by
[tex]\begin{gathered} r=\frac{78}{6} \\ r=13 \end{gathered}[/tex]Therefore, the answer is: There are 13 pairs of socks in each regular pack and 17 pairs in each value pack.
What is the distance between the points (-9, 4) and (3,-12)? A 12 units B. 16 units c. 20 units D. 28 units
Answers
Answer:
C
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 9, 4 ) and (x₂, y₂ ) = (3, - 12 )
d = [tex]\sqrt{(3-(-9))^2+(-12-4)^2}[/tex]
= [tex]\sqrt{(3+9)^2+(-16)^2}[/tex]
= [tex]\sqrt{12^2+256}[/tex]
= [tex]\sqrt{144+256}[/tex]
= [tex]\sqrt{400}[/tex]
= 20 units
can u help solve problem
Answers
To multiply the matixes, we'll look at their elements
[tex]A=\begin{bmatrix}{A_1} & {A_2} & {A_3} \\ {} & {} & {} \\ {} & {} & \end{bmatrix},\text{ B=}\begin{bmatrix}{B_1} & {} & {} \\ {B_2} & {} & \\ {B_3} & {} & {}\end{bmatrix}[/tex]In order to get AB, we simply use the following formula
[tex]AB=A_1\cdot B_1+A_2\cdot B_2+A_3\cdot B_3[/tex]In this case
[tex]AB=3\cdot1+4\cdot2+5\cdot3+6\cdot4=3+8+15+24=50[/tex]Since both matrixes have 4 elements. Thus
[tex]AB=50[/tex]how to answer this system of equations using cramer's rule
Answers
Given:
Given the system of equations:
[tex]\begin{gathered} c+w+p=456 \\ c-p=80 \\ p=2w-2 \end{gathered}[/tex]Required: Solution of the system using Cramer's rule
Explanation:
The system of equations can be rewritten as
[tex]\begin{gathered} c+p+w=456 \\ c-p+0w=80 \\ 0c+p-2w=-2 \end{gathered}[/tex]Write down the augmented matrix.
[tex]\begin{bmatrix}{1} & {1} & {1} & {456} \\ {1} & {-1} & {0} & {80} \\ {0} & {1} & {-2} & {-2} \\ {} & {} & {} & {}\end{bmatrix}[/tex]Calculate the main determinant.
[tex]\begin{gathered} D=\det\begin{bmatrix}{1} & {1} & {1} \\ {1} & {-1} & {0} \\ {0} & {1} & {-2}\end{bmatrix} \\ =1\left(2-0\right)-1\left(-2-1\right) \\ =2+3 \\ =5 \end{gathered}[/tex]Substitute the c-column with RHS and find the determinant.
[tex]\begin{gathered} D_c=\det\begin{bmatrix}{456} & {1} & {1} \\ {80} & {-1} & {0} \\ {-2} & {1} & {-2}\end{bmatrix} \\ =456\left(2-0\right)-80\left(-2-1\right)-2\left(0+1\right) \\ =912+240-2=1150 \end{gathered}[/tex]Substitute the p-column with RHS and find the determinant.
[tex]\begin{gathered} D_p=\det\begin{bmatrix}{1} & {456} & {1} \\ {1} & {80} & {0} \\ {0} & {-2} & {-2}\end{bmatrix} \\ =1(-160-0)-1(-912+2) \\ =-160+910 \\ =750 \end{gathered}[/tex]Substitute the w-column with RHS and find the determinant.
[tex]undefined[/tex]The ratio of the amount of money Rachel saved to the amount of money Timothy saved was12 : 13. After Timothy spent $27, Rachel had 3 times as much as Timothy,A. How much did Rachel save?b How much did they save altogether at first?
Answers
For a)
Before
Rachel : Timothy
12 : 13
After
Rachel : Timothy
3 : 1
In order to have the same amount for Rachel
12: 4
Timothy
13units -4 units =9 units
9units=$27
1 unit=27/9
1unit = $3
For Rachel
Rachel saved $36
b)
Total units at first =12+13=25
If 1units is $3
25 units is 3x25
25 units is $75
They saved together 75
ANSWER
Rachel saved $36
They saved together 75
Which tree is growing faster?Tree 2Tree 1 is growing 2 week 2 4 6 8 10inches every week. inches5 10 15 20 25tallHint: First calculate the unit rate for Tree 2.Enter the number that belongs in the numerator.Unit Rate[?]=inches/week
Answers
Calculating the unit rate for Tree 2 we have the following
[tex]\text{Unit Rate }=\frac{5\text{ inches}}{2\text{ week}}\text{ }=\frac{10\text{ inches}}{4\text{ week}}\text{ }=\frac{15\text{ inches}}{6\text{ week}}[/tex]When simplified the unit rate is
[tex]\frac{5}{2}\text{ inches/week}[/tex]This is 2.5 inches per week. Compared to Tree 1,
The temperature of a solution in a science experiment is -6.2°C. Jesse wants to raise the temperature so that it is positive. (a) Give an example of a number of degrees Celsius by which Jesse could raise the temperature. (b) Write a equation to represent the solution.
Answers
Hello!
First, the temperature is -6.2ºC, and Jesse wants to raise it until be positive.
(a) Give an example of a number of degrees Celsius by which Jesse could raise the temperature.If we add 6.2ºC, we will obtain a temperature equal to 0ºC, right? So, to the temperature be positive you can choose any temperature greater than 6.2º.
For example, I'll choose 15ºC.
(b) Write an equation to represent the solution. We will write the current temperature plus the temperature that we will add, then we obtain the new temperature, look:
-6.2ºC + 15ºC = 8.8ºC
ESFind the distance d(P. P2) between the points P, and P2-omennsP. = (-4.3)P2 = (3.2)ERE!(P, P2) =O(Simplify your answer. Type an exact answer using radicals as needed.)1 Guit2 Gunents
Answers
We have two points and we need to calculate the distance between them.
The points are P1(-4,3) and P2(3,2).
We can apply the following formula for the distance between points:
[tex]D=\sqrt{(x_2-x_1)^2}+(y_2-y_1)^2[/tex][tex]\begin{gathered} D=\sqrt{(3-(-4))^2}+(3-2)^2 \\ D=\sqrt{7^2+1^2}=\sqrt{49+1}=\sqrt{50}=\sqrt{(25\cdot2})=5\sqrt{2} \end{gathered}[/tex]The answe is 5 times the square root of 2:
[tex]D=5\sqrt{2}[/tex]Determine the equation of the line that goes through the point (4, 4) with -1/4 slope. Enter your answer in slope-intercept form.Enter EquationPls see picture
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
From the information given,
m = - 1/4
the line passes through the point (4, 4). This means that
x = 4, y = 4
We would find c by substituting m = - 1/4, x = 4 and y = 4 into the slope intercept equation. We have
4 = - 1/4 * 4 + c
4 = - 1 + c
Adding 1 to both sides of the equation,
4 + 1 = - 1 + 1 + c
c = 5
By substituting m = - 1/4 and c = 5 into the slope intercept equation, the equation of the line is
y = - x/4 + 5
use the point slope formula in the given points to choose the correct linear equation in slope intercept formfor ( 4,-3) and (-2,5)
Answers
The point-slope formula is
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope of a line passing through the point (x₁, y₁).
Also, the slope m of a line passing through points (x₁, y₁) and (x₂, y₂) is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this problem, the line passes through points (4, -3) and (-2, 5). Thus, we have:
x₁ = 4
y₁ = -3
x₂ = -2
y₂ = 5
Then, the slope is
[tex]m=\frac{5-(-3)}{-2-4}=\frac{5+3}{-6}=\frac{8}{-6}=-\frac{4}{3}[/tex]And the equation in point-slope form is
[tex]y-(-3)=-\frac{4}{3}(x-4)[/tex]Now, we need to rewrite this equation in slope-intercept form. The slope-intercept equation of a line with slope m and y-intercept b is
[tex]y=mx+b[/tex]Thus, we need to isolate y on the left side of the equation to obtain the slope-intercept form, as follows:
[tex]\begin{gathered} y+3=-\frac{4}{3}x-\frac{4}{3}(-4)\text{ using the distributive property of multiplication over addition} \\ \\ y+3=-\frac{4}{3}x+\frac{16}{3} \\ \\ y+3-3=-\frac{4}{3}x+\frac{16}{3}-3 \\ \\ y=-\frac{4}{3}x+\frac{16}{3}-\frac{9}{3} \\ \\ y=-\frac{4}{3}x+\frac{7}{3} \end{gathered}[/tex]Therefore, the slope-intercept form of that linear equation is
[tex]y=-\frac{4}{3}x+\frac{7}{3}[/tex]Complete the following equation. Your answers will be algebraic expressions. (a+bi)^2= _____ + 2abiHint: think of i as an ordinary variable and then replace i^2 with -1.
Answers
The given expression is:
[tex](a+ib)^2[/tex]Expand to get:
[tex]\begin{gathered} (a+ib)^2=a^2+i^2b^2+2abi \\ =a^2-b^2+2abi \end{gathered}[/tex]The value is as above since it is given that i^2=-1.
So the expansion is:
[tex](a+ib)^2=a^2-b^2+2abi[/tex]The blank should be:
[tex]a^2-b^2[/tex]which expression can be used to find the length of the side of the triangle represented by the vertices (5,5) and (7,-3) on the graph?
Answers
In order to determine the correct expression for the length of the side, consider that the distance in between two points (x1,y1) and (x2,y2) is given by the following formula:
d = √((x2 - x1)² + (y2 - y1)²)
if (x1,y1) = (5,5) and (x2,y2) = (7,-3) you have for d:
d = √((7 - 5)²+(5 - (-3))²)
There are 130 people at a meeting. Theyeach give a Valentine's Day card toeveryone else. How many cards weregiven?
Answers
Permutations
Suppose there are only two people in the meeting. Person A gives a card to person B and vice-versa. Two cards were given.
Now we have 3 people. Person A gives two cards. Person B gives two cards. Person C gives two cards. Total = 6 cards given.
Each people gives a card to everyone else (except themselves, of course) and it's done by everyone in the meeting, thus for 130 people:
130 x 129 = 16,770 cards were given
Solve the system of equations:3x+y=6 2x+3y=11
Answers
Answer:
(1,3)
Explanation:
Given the system of equations:
[tex]f(x)=\begin{cases}3x+y=6 \\ 2x+3y=11\end{cases}[/tex]To solve the system using the elimination method, multiply the first equation by 3.
[tex]\begin{gathered} f(x)=\begin{cases}9x+3y=18 \\ 2x+3y=11\end{cases} \\ \text{Subtract} \\ 7x=7 \\ \text{Divide both sides by 7} \\ \frac{7x}{7}=\frac{7}{7} \\ x=1 \end{gathered}[/tex]Next, substitute x=1 into any of the equations to solve for y.
[tex]\begin{gathered} 3x+y=6 \\ 3(1)+y=6 \\ y=6-3 \\ y=3 \end{gathered}[/tex]The solution to the system of equations is (x,y)=(1, 3).
1) 42,58, 67,55, 40, 69, 66, 51, 46, 48, 68 Minimum : Q: Q2: Q, Maximum :
Answers
EXPLANATION
Minimum
The first Quartile is the value separating the lower quarter and higher three - quarters of the data set.
The first quartile is computed by taking the median of the lower half of a sorted set.
Arranging terms in ascending order
40, 42 , 46, 48, 51, 55, 58, 66, 67, 68, 69
Here, we can see that:
Minimum = 40
Maximum = 69
Q2=55 (median)
Taking the lower half of the ascending set:
Counting the number of terms in the data set:
{40, 42 , 46, 48, 51, 55, 58, 66, 67, 68, 69}
{1, 2 , 3, 4, 5, 6, 7, 8, 9, 10, 11}
The number of terms in the data set is:
11
Since the number of terms is odd, take the elements below the middle one, that is, the lower 5 elements.
40, 42 , 46, 48, 51
Median of 40, 42 , 46, 48, 51:
The number of terms in the data set is 5.
Since the number of terms is odd, the median is the middle element of the sorted set.
Q1: 46
------------------------------------
Q3:
Since the number of terms is odd, take the elements above the middle one, that is, the upper 5 elements.
58, 66, 67, 68, 69
The number of terms in the data set is
5
Since the number of terms is odd, the median is the middle element of the sorted set.
Q3=67
------------------------------------------------------------------------------------
Interquartile Range:
The interquartile range is the difference of the first and third quartiles
We have that:
Q1=46
Q3=67
Computing the difference between 67 and 46:
67-46= 21
Interquartile Range=21
-------------------------------
Answers:
Minimum = 40
Q1=46
Q2=55 (median)
Q3=67
Maximum = 69
Interquartile Range=21
Simplify.
Radical sign 45x
9
Answers
Answer:
20.12461179
Step-by-step explanation
InequalitiesEvaluate. Show your work or explain how you arrived at your answer.-|-34|
Answers
The value of -|-34| is -34
-|-34|
Apply absolute rule: |-a|=a, a>0 =-34
The absolute value (or modulus)| x | of a real number x is its non-negative value regardless of its sign. For example, 5 has an absolute value of 5, and 5 has an absolute value of 5. A number's absolute value can be conceived of as its distance from zero along the real number line.
Absolute values for real numbers occur in a wide range of mathematical contexts. Absolute values, for example, are defined for complex numbers, quaternions, ordered rings, fields, and vector spaces. In numerous mathematical and physical contexts, the absolute value is intimately related to the concepts of magnitude, distance, and norm.
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Write the equation of the line in standard form that passes through point P(-5,7) andPerpendicular to the equation of the line y=-x+2.
Answers
The given equation is
[tex]y=-x+2[/tex]We have to find a new line perpendicular to the given line and must pass through P(-5,7).
First, we use the definition of perpendicularity for two lines.
[tex]m_1\cdot m_2=-1[/tex]Where one of the slopes is equal to -1 because the coefficient of x in the given equation is -1. Let's find the other slope.
[tex]\begin{gathered} m\cdot(-1)=-1 \\ m=1 \end{gathered}[/tex]This means the new perpendicular line has a slope of 1.
Now, we use the slope we found, the point P, and the point-slope formula, to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-7=1(x-(-5)) \\ y-7=x+5 \\ y=x+5+7 \\ y=x+12 \end{gathered}[/tex]Therefore, the equation of the new perpendicular line is y = x + 12.