Using the image below. Write the equation of the line fully simplified slope-intercept form. NO SPACES BETWEEN TERMS * just letting you know the answer is not y=-5x+2 or y=6x+2
Answers
The slope-intercept form is
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept
The rule of the slope of a line that passes through points (x1, y1) and (x2, y2) is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]From the given graph, the line passes through points (1, -4) and (0, 2)
Let (x1, y1) = (1, -4) and (x2, y2) = (0, 2)
[tex]\begin{gathered} m=\frac{2-(-4)}{0-1} \\ m=\frac{2+4}{-1} \\ m=\frac{6}{-1} \\ m=-6 \end{gathered}[/tex]Substitute the value of m in the form of the equation
[tex]y=-6x+b[/tex]Since the line intersects the y-axis at point (0, 2)
Then the y-intercept is 2
Then b = 2
The equation of the line is
[tex]y=-6x+2[/tex]Related Questions
12) Determine if the number is rational (R) or irrational (I)
Answers
Given
[tex]number=\sqrt{17}[/tex]Find
Determine if the number is rational or irrational.
Explanation
It cannot be expressed in the form of p/q , where q is not equal to 0.
so , it is irrational number.
Final Answer
Therefore , the number is irrational.
Can I please just get the answer I’m trying to get this class done before the 10th……
Answers
Given:
The batting averages are given in stemplot way.
The objective is to determine what batting average does 0.35│6 denotes.
Explanation:
In stemplot method, the stem represents all common digits other than one place value in the given set of data. The leaf represents the variation of once place for the respective stem data.
Then the given expression 0.35│6 represents the stem value as 0.35 and 6 as the leaf value.
Thus. one occurence of batting average is 0.356.
Hence, option (B) is the correct answer.
Question 25 of 27Which of the following is an example of independent events?OA. Rolling a 6 on a number cube and spinning a 7 on a spinnerB. Drawing a jack from a standard deck of cards and then drawing a2 without replacing the jackC. Selecting a green marble from a bag of 10 different coloredmarbles and then selecting a second green marble without puttingthe first backOD. Owning cows and living on a dairy farm
Answers
Independent events are events where one event occurring or not does not affect whether the other one happens.
Pulling two cards out of a deck of cards, when you don't replace the first card, or pulling two marbles from a bag, where you don't replace the first marble, are not independent. By removing the first card/marble, you've change the situation for the second draw.
Using a spinner and rolling a die are totally independent, since they are different objects and what happens on one does not impact what will happen on the other.
And if you live on a dairy farm, that creates a better chance of being involved with dairy production and cows, so those are not independent.
Option A has two independent events.
Which value of x makes the equation 4x+9=x+6 true?
Answers
Answer:
x=-1
Explanation:
Given the equation:
[tex]4x+9=x+6[/tex]First, we subtract 9 from both sides.
[tex]\begin{gathered} 4x+9-9=x+6-9 \\ 4x=x-3 \end{gathered}[/tex]Next, we subtract x from both sides.
[tex]\begin{gathered} 4x-x=x-x-3 \\ 3x=-3 \end{gathered}[/tex]Finally, we divide both sides by the number beside x which is 3.
[tex]\begin{gathered} \frac{3x}{3}=\frac{-3}{3} \\ x=-1 \end{gathered}[/tex]The value of x that makes the equation true is -1.
Large balloons are sold in packages of 12. Select the expressions that can represent the total number of balloons in p packages of largeballoonsA 12-PB. 12*pC. P+12D. P-12E 12p
Answers
Since each package has 12 balloons if we buy p packages the total number of ballons will be given by tha multiplication of 12 by p, that is:
[tex]12p[/tex]Therefore the answer is B and E.
Graph each inequality.Do I have to make the equation say y<??
Answers
x + y =< 2
y =< 2 - x Yes, in the inequality y must be alone
4.-
Yes, you must look at the point of the sign if the y is to the left of the sign (<) you must shade the area below the line. if the y is to the right of the sign(<), you must shade the area abocve the line.
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Find the constant of proportionality when x = 2 and y = 1.5.Record your answer and fill in the bubbles on your answer document. Be sure to usethe correct place value.
Answers
If y is proportional to x, we have this equation:
[tex]y=kx[/tex]If x = 2 and y = 1.5, then the constant is:
[tex]k=\frac{y}{x}=\frac{1.5}{2}=0.75[/tex]The constant of proportionality is k = 0.75
I am trying to place the second point at 12.5. My graph only extend to -10.
Answers
We have to graph the line y = -2/5*x-5.
To do that, we need two points that belong to the line.
We can give two arbitrary values to x and calculate y using the equation of the line.
For example, for x=0, we get:
[tex]x=0\Rightarrow y(0)=-\frac{2}{5}\cdot0-5=-5[/tex]Then, the point is (0,-5).
Now, if we make x = 5, we can calculate y as:
[tex]x=5\Rightarrow y(5)=-\frac{2}{5}\cdot5-5=-2-5=-7[/tex]Then, we get the point (5, -7).
Using this two points we can graph the line as:
NOTE: In the case that the graph is limited to certain intervals in x or y, we have to try with different values of x until we find two points within the range shown by the graph.
In this case, (0,-5) and (5,-7) will be located within the range shown.
Question 9 of 10If bis an explanatory variable and cis the corresponding response variable,which of these would be represented by the vertical axis on a scatterplot?O A. b БB. Neither b nor cOC. Both band cD. CSUBMIT
Answers
The response variable is dependent variable , and depends on the explanatory variable. The explanatory variable is independant variable and always represented on the horizontal axis.
The dependent variable (or response varaible) is represented on the vertical axis. So C is represented on the vertical axis of scatter plot.
Need help with number 2 not sure how to solve it all
Answers
B(x) will be given by:
[tex]B(x)=100x-5[/tex]Part 1:
x = 9
[tex]B(9)=100(9)-5=900-5=895[/tex]Part 2:
x = 10.34
[tex]B(10.34)=100(10.34)-5=1034-5=1029[/tex]Part 3:
[tex]B(9)+B(10.34)=895+1029=1924[/tex]Place the numbers in order fromgreatest to least27, 62%, -0.062,65,0.
Answers
Answer
Explanation
To arrange this numbers in the required order, we need to simplify each of them and then compare them.
√3 = 1.732
172% = (172/100) = 1.72
-1.7 = -1.7
1 7/10 = 1 + 0.7 = 1.7
-0.7 = -0.7simplify each of them and then compare them.
Solve the system of equations using elimination.8x - 5y = 13-16x - 10y = -6Show your work here:Solution:
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Solve the system of equations using elimination.
[tex]\begin{gathered} \text{8 x - 5y = 13 -- equation 1} \\ -16\text{ x - 10y = - 6 -- equation 2} \end{gathered}[/tex]Step 2:
Given,
[tex]\begin{gathered} 8x\text{ - 5y = 13 -- equation 1} \\ \text{equation 1 multiplied by 2, we have that:} \\ 16\text{ x - 10y = 26 -- equation 3} \\ -16\text{ x -10 y = - 6 -- equation 2} \end{gathered}[/tex][tex]\begin{gathered} equation\text{ 3 + equation 2, we have that:} \\ -10y\text{ + -10 y = 26 + (-6)} \\ -20y\text{ = 20} \\ \text{Divide both sides by -20, we have that:} \\ y\text{ = }\frac{20}{-20} \\ y\text{ = -1} \end{gathered}[/tex]Now, since y = -1 , we put the value of y = -1 in equation 1,
[tex]\begin{gathered} 8\text{ x- 5y = 13 --equation 1} \\ 8x\text{ - 5 ( -1 ) = 13} \\ 8x\text{ + 5 = 13} \\ 8x\text{ = 13 - 5} \\ 8\text{ x= 8} \\ \text{Divide both sides by 8 , we have that:} \\ x\text{ = }\frac{8}{8} \\ x\text{ = 1} \end{gathered}[/tex]CONCLUSION:
The final answer =
[tex]\text{ x= 1 , }y\text{ = - 1}[/tex]'
Is this relation a function?
{(1, 3), (2, 3), (3, 4), (4, 5)}
No, because at least one output maps to more than one input.
No, because at least one output maps to more than one input.
Yes, because every input has exactly one output.
Yes, because every input has exactly one output.
No, because at least one input maps to more than one output.
No, because at least one input maps to more than one output.
Answers
The given relation {(1, 3), (2, 3), (3, 4), (4, 5)} is a function. Therefore, the correct statement is "Yes, because every input has exactly one output."
Relation:
A relation is a relationship between the x and y-coordinates. It must maps inputs to outputs.
Given,
Here we have the relation
{(1, 3), (2, 3), (3, 4), (4, 5)}
Now, we have to find whether this relation is a function or not.
We know that, a relation is said to be a relation is a function if the x values map to only one y - value. Simply said that if a relation is one-to-one or many-to-one it is a function.
Based on this rule, here each input has exactly one output. therefore, the given relation is said to be a function.
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One of the two persons P or Q is to solve a technical problem with chances ½ and ¼, respectively. Find the probability that the technical problem is solved.A.1/8B.3/8C.5/8D.7/8
Answers
The probability that the technical problem is solved can be defined as follows:
The probability that P solves the problem or probability that Q solves the problem or probability that both (P and Q) solve the problem
The probability that P solves the problem = 1/2
The probability that Q solves the problem= 1/4
The probability that both solve the problem = (1/2) x (1/4) = 1/8
The probability that the technical problem is solved =
[tex]\begin{gathered} \frac{1}{2}\text{ + }\frac{1}{4}\text{ -}\frac{1}{8} \\ =\frac{4+2-1}{8} \\ \frac{5}{8} \end{gathered}[/tex]The correct option is C
A survey claims that the percent of a city's residents that favor building a new football stadium is likely between 52.3% and 61.7%. What was the sample proportion (what percent of the people in the sample survey said that they wanted to build a new stadium )?
Answers
The confidence interval for the sample proportion is calculated using the following formula:
[tex]\lbrack p\lbrack\text{hat\rbrack}\pm Z_{1-\frac{\alpha}{2}}\cdot\sqrt[]{\frac{p\lbrack hat\rbrack(1-p\lbrack hat\rbrack)}{n}}\rbrack[/tex]Where p[hat] represents the sample proportion. As you see you add/subtract the margin of error to the sample proportion to determine both bonds of the interval, which means that the sample proportion is in the middle of the interval.
The percent of residents in favor of building a new football stadium is between 52.3% and 61.7% → the sample proportion used to determine this interval is in the middle of both bonds. To calculate the said value you have to find the average of both values:
[tex]52.3\%The sample proportion used to estimate the interval was p[hat]=0.57
A chemist wishes to mix a solution that is 6% acid. She has on hand 14 liters of a 4% acid solution and wishes to add some 10% acid solution to obtain the desired 6% acid solution. How much 10% acid solution should she add?
Answers
she should add 7 liters of 10% acid solution
Explanation
Step 1
set the equation:
a) let X represents the amount os solution that is 4% acid
let Y represents the amount os solution that is 10% acid
so
I)
[tex]\begin{gathered} \frac{4}{100}X+\frac{10}{100}Y=\frac{6}{100}(x+y) \\ \end{gathered}[/tex]if he has 14 liters of 4% acid solution
[tex]x=14[/tex][tex]\begin{gathered} \frac{4}{100}X+\frac{10}{100}Y=\frac{6}{100}(X+Y) \\ \frac{4}{100}*14+\frac{10}{100}Y=\frac{6}{100}(X+Y) \\ 0.56+0.1Y=0.06(14+Y) \\ 0.56+0.1Y=0.84+0.06Y \\ \end{gathered}[/tex]Step 2
solve the equation :
[tex]\begin{gathered} 0.56+0.1Y=0.84+0.06Y \\ subtract\text{ 0.06Y in both sides} \\ 0.56+0.1Y-0.06Y=0.84+0.06Y-0.06Y \\ 0.56+0.04Y=0.84 \\ subtract\text{ 0.56 in both sides} \\ 0.56+0.04Y-0.56=0.84-0.56 \\ 0.04Y=0.28 \\ divide\text{ both sides by 0.04} \\ \frac{0.04Y}{0.04}=\frac{0.28}{0.04} \\ Y=7 \end{gathered}[/tex]therefore,
she should add 7 liters of 10% acid solution
I hope this helps you
#3 What does the slope tell you about the rate of change in elavation during Ryan’s uphill climb? What was the total elevation change?
Answers
Solution
Step 1:
Let find the slope
[tex]\begin{gathered} Slope\text{ = }\frac{Change\text{ in elevation}}{Change\text{ in time}} \\ S\text{lope = }\frac{1500\text{ - 300}}{120\text{ - 0}} \\ Slope\text{ = }\frac{1200}{120} \\ Slope\text{ = 10} \end{gathered}[/tex]His answer and these calculations are correct because he followed all the steps correctly to findtwo points' slope.
Step 2; First we need to determine how many different slopes there are on the given graph. Assume time is represented in minutes and distance is represented in meters. There are three in this graph, one goes from 0 minutes to 120 minutes and the second one is from 120 minutes to 150 minutes. The final one goes from 150 to 180 minutes. To calculate the speed of traveling we convert the distance traveled into a constant period of time i.e. an hour.
Question1
What does the slope tell you about the rate of change in elavation during Ryan’s uphill climb?
The first slope(line) tell us that Ryan travels from 300 meters to 1,500 meters from 0 minutes to 120 minutes.
meaning he traveled 1200 meters in 120 minutes which is equal to 600meters per hour or 0.6km/h.
In the second line, Ryan's travels no distance from 120 minutes to 150 minutes. So he was at rest and did not travel in this period of time.
In the third line (slope) , Ryan travels from 1,500 meters to 300 meters from 150 minutes to 180 minutes. So he traveled 1,200 meters in 30 minutes. This equals 2,400 meters per hour, which is 2.4 kilometers per hour.
Final answer
The slope tell you about the rate of change in the elevation during Ryan's uphill climb that:
Ryan ascends at a speed of 0.6 kilometers per hour for the two hours, takes rest for half an hour and then descends at 2.4 kilometers per hour for the half-hour.
Question 2
What is the total elevation change?
Elevation gain is the total amount you will climb in a day, and elevation loss is the total amount you will descend in a day. For example, if you climb 1000 feet, descend 500 feet, and then climb an additional 300 feet, the elevation gain would be 1300 feet and the elevation loss would be 500 feet.
From the graph?
Elevation gain = 1200 feet
Elevation loss = 1200 feet
4.) Miles has saved about $41. He wants to buy an iPod for $129 in 4 months. How much moneydoes he need to save each month to buy the iPod?
Answers
Miles has saved about $41. He wants to buy an iPod for $129 in 4 months.
So first, we need to subtract the amount that he has already saved.
[tex]\$129-\$41=\$88[/tex]Now we need to divide this amount by 4 months.
[tex]\frac{\$88}{4}=\$22[/tex]Therefore, Miles needs to save $22 each month to buy the iPod.
Complete the explanation of how you know whether the triangles are similar. If possible, find the Indicated length. A Р 2.0 1.7 во 1.2 C R. Because two pairs of angles are congruent, the triangles are similar by the select) QR =
Answers
When two triangles have two pairs of angles congruent, it means that the third pair of angles also is congruent.
Then, the trianglers are similar by AA (Angle, angle) similar triangle theorem.When two triangles are similar the ratio between corresponding sides is the same.
Corresponding sides in the given triangles:
CB and QR
AC and PR
AB and PQ
[tex]\frac{QR}{CB}=\frac{PR}{AC}=\frac{PQ}{AB}[/tex]Then, as you know the measure of AC and corresponding side CB you use the next to find the measure of side QR:
[tex]\frac{QR}{CB}=\frac{PR}{AC}[/tex]Use the given measures and find QR:
[tex]\begin{gathered} \frac{QR}{1.2}=\frac{1.7}{2.0} \\ \\ QR=\frac{1.7}{2.0}(1.2) \\ \\ QR=\frac{2.04}{2.0} \\ \\ QR=1.02 \end{gathered}[/tex]QR=1.02Warren flipped a coin and rolled a 20-sided number cube. What is the probability that his coin landed on tails and his number cube rolled a factor of 20? answer as a simplified fraction.
Answers
Warren flipped a coin and rolled a 20-sided number cube. What is the probability that his coin landed on tails and his number cube rolled a factor of 20? answer as a simplified fraction.
we have that
the probability that his coin landed on tails is
P=1/2
and
Factors of 20 are ----> 1,2,4,5,10,20
so
The probability that his number cube rolled a factor of 20 is
P=6/20=3/10
therefore
the probability that his coin landed on tails and his number cube rolled a factor of 20 is equal to
P=(1/2)*(3/10)
P=3/20Question 6 of 13Use a calculator to find the correlation coefficient of the data set.X13LO5y2014106916 4
Answers
Given
The data,
[tex][/tex]3.Find the values of x and y. Leave your answers in simplest radical form.6022yxX =y =Page
Answers
To calculate the values of x and y we need to apply the trigonometric relations to the right triangle. For this we will use the sine and cosine, their expressions are shown below:
[tex]\begin{gathered} \sin (\alpha)=\frac{\text{ opposite cathetus}}{\text{ hypothenuse}} \\ \cos (\alpha)=\frac{\text{ adjacent cathetus}}{\text{ hypothenuse}} \end{gathered}[/tex]Where alpha is the angle we know, the opposite cathetus is the cathetus that is farther from the angle and the adjacent cathetus is the cathetus that is closer to the angle. With this in mind we can use the data from the problem to calculate x and y.
[tex]\begin{gathered} \sin (60)=\frac{x}{22} \\ 0.866=\frac{x}{22} \\ x=22\cdot0.866=19.052 \end{gathered}[/tex][tex]\begin{gathered} \cos (60)=\frac{y}{22} \\ 0.5=\frac{y}{22} \\ y=0.5\cdot22=11 \end{gathered}[/tex]The value of x is equal to 19.052 and y is equal to 11.
If v, = (2,4) and v2 = (-1,5), then w,-V is equal to which of the following?O 18O (-2. 20)O 22O (8.-5)
Answers
We are given the following matrix:
[tex]A=\begin{bmatrix}{4} & {-7} & {} \\ {-2} & {1} & {} \\ {} & {} & {}\end{bmatrix}[/tex]We are asked to determine the coefficients of:
[tex]A^{-1}[/tex]Which is the inverse matrix. To do that let's remember that the inverse of a 2 by 2 matrix of the form:
[tex]A=\begin{bmatrix}{a_1} & {a_2} & {} \\ {a_3} & {a_4} & {} \\ {} & {} & {}\end{bmatrix}[/tex]is:
[tex]A^{-1}=\frac{1}{\det A}\begin{bmatrix}{a_4} & {-a_2} & {} \\ {-a_3} & {a_1} & {} \\ {} & {} & {}\end{bmatrix}[/tex]The value of the determinant of A (det A) is given by:
[tex]\det A=a_1a_4-a_2a_3[/tex]Replacing we get:
[tex]A^{-1}=\frac{1}{a_1a_4-a_2a_3}\begin{bmatrix}{a_4} & {-a_2} & {} \\ {-a_3} & {a_1} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Replacing the values:
[tex]A^{-1}=\frac{1}{(4)(1)-(-7)(-2)}\begin{bmatrix}{1_{}} & {7_{}} & {} \\ {2_{}} & {4_{}} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Solving the operations:
[tex]A^{-1}=-\frac{1}{10}\begin{bmatrix}{1_{}} & {7_{}} & {} \\ {2_{}} & {4_{}} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Or:
[tex]A^{-1}=\begin{bmatrix}{-\frac{1}{10}_{}} & {-\frac{7}{10}_{}} & {} \\ -{\frac{1}{5}_{}} & {-\frac{2}{5}_{}} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Therefore, we have:
[tex]\begin{gathered} a=-\frac{1}{10} \\ b=-\frac{7}{10} \\ c=-\frac{1}{5} \\ d=-\frac{2}{5} \end{gathered}[/tex]the u.s senate has 100 members. after a certain election, there were 6 more democrats than republicans, with no other parties represented. how many memebrs of each party were there in the senate?
Answers
As per the unitary method, the number of democrats are 53 and the number of republicans are 47.
Unitary method:
Unitary method is the process of finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given,
The U.S senate has 100 members. after a certain election, there were 6 more democrats than republicans, with no other parties represented.
Here we need to find the number of democrats and the number of republicans.
Let us consider the number of Republican's be "x"
And then the number of Democrats is "x+6".
We know that the total number of members in the senate is 100.
So, it can be written as
x + (x + 6) = 100
2x + 6 = 100
2x = 100 - 6
2x = 94
x = 94/2
Then the value of x is,
x = 47
Therefore, there are 47 republicans in the senate then the number of democrats is
x + 6 => 47 + 6 => 53
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a midwestern music competition awarded 40 ribbons. the number of blue ribbons awarded was 2 less than the number of white ribbons. the number of red ribbons was 3 more than the number of white ribbons. how many of each kind of ribbon was awarded
Answers
By the concept of basic equation there are 13 white ribbons, 11 blue ribbons and 16 red ribbons.
What are basic equation?When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. An equation is an algebraic statement that demonstrates two mathematical expressions are equivalent in algebra, and this is how it is most usually used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." When two expressions are joined by an equal sign, a mathematical statement is called an equation. An equation is something like 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable.
r + w + b = 40
b = w - 2
r = w + 3
now we sub
(w + 3) + w + (w - 2) = 40
3w + 1 = 40
3w = 40 - 1
3w = 39
w = 39/3
w = 13
<=== 13 white ribbons
b = w - 2
13 - 2 = 11
<=== 11 blue ribbons
r = w + 3.
13 + 3 = 16
<=== 16 red ribbons
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Mr mustard bought a bag of citrus tree fertilizer. He used 1/5 of the bag for his orange tree and 2/3 of the bag for his lemon tree. About how much of the fertilizer does he have left?A. 0.5 B. 0.8 C. 0 D. 0.1
Answers
Problem
Mr mustard bought a bag of citrus tree fertilizer. He used 1/5 of the bag for his orange tree and 2/3 of the bag for his lemon tree. About how much of the fertilizer does he have left?
Solution
For this problem we know that the total bag represent 1 and since he used 1/5 for the orange tree and 2/3 for the lemon tree we can do the following operation to find the remaining space:
[tex]1-\frac{1}{5}-\frac{2}{3}[/tex]And after solve the operation we got:
[tex]\frac{4}{5}-\frac{2}{3}=\frac{2}{15}[/tex]And if we convert to decimals we got 2/15= 0.133
Then the best approximation for this case would be:
D. 0.1
Which is the image of vertex T after the hexagon is rotated 180 degreesabout the origin?
Answers
Answer:
Image of vertex T: (5,2)
Step-by-step explanation:
It will be rotated 180 degrees about the origin. This means that the x-value of T will stay the same, while the y-value will be the same distance as now, just in a different direction.
Current position: -2
Distance from the origin: |-2 + 0| = 2
New coordenate: 0 + 2 = 2
Current value of x: 5
Image of vertex T: (5,2)
List the coordinates coordinates of vertices of trapezoid ABCD after it has been rotated 90 Counterclockwise bout the origin and then reflected over the x-axis. A(-5,-3) B(-4,0),c(-2,0),D(O,-3)
Answers
Answer:
The coordinates of the final image is;
[tex]A^{\prime\prime}(3,5),B^{\prime\prime}(0,4),C^{\prime}^{\prime}(0,2),D^{\prime}^{\prime}(3,0)[/tex]Explanation:
From the question, the pre-image was been rotated 90 Counterclockwise bout the origin.
Which has a rule;
[tex](x,y)\rightarrow(-y,x)[/tex]Applying the rule to the given points. we have;
[tex]\begin{gathered} A(-5,-3)\rightarrow A^{\prime}(3,-5) \\ B(-4,0)\rightarrow B^{\prime}(0,-4) \\ C(-2,0)\rightarrow C^{\prime}(0,-2) \\ D(0,-3)\rightarrow D^{\prime}(3,0) \end{gathered}[/tex]Then the produced image was then reflected over the x-axis;
Reflection across the x-axis have the rule;
[tex](x,y)\rightarrow(x,-y)[/tex]Applying the rule to the resulting image;
[tex]\begin{gathered} A^{\prime}(3,-5)\rightarrow A^{\prime^{}}^{\prime}(3,5) \\ B^{\prime}(0,-4)\rightarrow B^{\prime}^{\prime}(0,4) \\ C^{\prime}(0,-2)\rightarrow C^{\prime^{}}^{\prime}(0,2) \\ D^{\prime}(3,0)\rightarrow D^{\prime}^{\prime}(3,0) \end{gathered}[/tex]Therefore, the coordinates of the final image is;
[tex]A^{\prime\prime}(3,5),B^{\prime\prime}(0,4),C^{\prime}^{\prime}(0,2),D^{\prime}^{\prime}(3,0)[/tex]Solve for X. Write down what type of solution the equation has. 3) [tex] \frac{10}{2x + 1} = \frac{14}{4x - 7} [/tex]
Answers
You have the following equation:
[tex]\frac{10}{2x+1}=\frac{14}{4x-7}[/tex]In order to solve for x the previous equation, multiply both sides by the LCM of the denominators, which is (2x+1)(4x-7):
[tex]\begin{gathered} (2x+1)(4x-7)\frac{10}{2x+1}=(2x+1)(4x-7)\frac{14}{4x-7} \\ (4x-7)10=(2x+1)14 \\ 40x-70=28x+14 \\ 40x-28x=14+70 \\ 12x=84 \\ x=\frac{84}{12} \\ x=7 \end{gathered}[/tex]Hence, the solution to the given equation is x = 7
EFGH is translate 5 units to the left and 2 units up.A. E(-1,-3)B. E(6,-6)C. E (-1,1)D. E(9,-3)
Answers
To translate the figure 5 units to the left and 2 up, apply the following translation to each coordinate of the figure
[tex]T_{(-5,2)}\colon(x,y)\rightarrow(x-5,y+2)[/tex]So, you have
[tex]\begin{gathered} E(4,-1)\rightarrow E^{\prime}(4-5,-1+2)\rightarrow E^{\prime}(-1,1) \\ F(0,-3)\rightarrow F^{\prime}(0-5,-3+2)\rightarrow F^{\prime}(-5,-1) \\ G(2,-4)\rightarrow G^{\prime}(2-5,-4+2)\rightarrow G^{\prime}(-3,-2) \\ H(6,-2)\rightarrow H^{\prime}(6-5,-2+2)\rightarrow H^{\prime}(1,0) \end{gathered}[/tex]Therefore, the coordinates of E' are (-1,1) and the correct answer is C. E(-1,1).