a) Graph the following: f(x) = 3(x + 1)2 H10 9 8 7 커 6 5 or 4 3 2 1 10 -9 -8 -2 - 1 2 3 6 8 9 -2 -4 -5 -6 -7 -8 -9 10+ Clear All Draw: b) Use the graph to identify the vertex vertex is c) Use the graph to identify the axis of symmetry Axis of symmetry. x =
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According to the equation of the function we can say that it comes from the parent function
[tex]y=x^2[/tex]since it is added 1 unit inside the parentheses it means that the function is shifted 1 unit to the left.
Also since it is multiplied by 3 it means that the function is compressed by 3.
The vertex is going to be at (-1,0)
and the axis of symmetry at x=-1
Related Questions
A museum opened at 8:00 am. In the first hour, 125 people purchased admission tickets. In the second hour, 20% more people purchased admission tickets than in the first hour. Each admission ticket cost $9.50. How much money did the museum make on total ticket sales in the first two hours?
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we must calculate the people who bought the ticket
we must add the people of the first hour together with the people of the second hour
if in the second hour there were 20% more people it means that they were 120% in the second hour
so the sum of the first hour and second hour is
[tex]\begin{gathered} 125+(125\times\frac{120}{100}) \\ \\ 125+(150)=275 \end{gathered}[/tex]the total number of people in the first two hours was 275
now multiply the number of people by the cost of ticket to find the total
[tex]275\times9.50=2612.50[/tex]the total money was $2,612.50
8. Darrin was asked to simplify √72 and arrived at the solution 2√18. Is this solution completely simplified? Explain why or why not. Include your work to justify your response.
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No
[tex]6\sqrt[]{2}[/tex]Explanation
Step 1
let the given expression
[tex]\sqrt[]{72}[/tex]the firs thing to do is to get the prime factors of 72, so
a) prime factors
[tex]\begin{gathered} 72=2\cdot2\cdot2\cdot3\cdot3 \\ \text{hence} \\ 72=2^33^2 \\ 72=2\cdot2^2\cdot3^2 \end{gathered}[/tex]Step 2
now we know that:
[tex]\begin{gathered} \sqrt[n]{a^n}\text{ =a} \\ \text{and} \\ \sqrt[]{ab}=\sqrt[]{a}\cdot\sqrt[]{b} \end{gathered}[/tex]so
[tex]\begin{gathered} \sqrt[]{72}=\sqrt[]{2\cdot2^2\cdot3^2} \\ \sqrt[]{72}=\sqrt[]{2}\sqrt[]{2^2}\sqrt[]{3^2} \\ \sqrt[]{72}=2\cdot3\sqrt[]{2} \\ \sqrt[]{72}=6\sqrt[]{2} \end{gathered}[/tex]therefotre:
Darrin was wrong because his expression was not totally simplified, the full simplification is
[tex]6\sqrt[]{2}[/tex]I hope this helps you
at the beginning of his science experiment mob solution has the temperature of -2 during the experiment the change in the solution temperature was -6 what is Bob spinal temperature
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at the beginning of his science experiment mob solution has the temperature of -2 during the experiment the change in the solution temperature was -6 what is Bob spinal temperature
we know that
Th initial temperature was
T1=-2
T2-T1=-6
so
substitute the value of T1 in the expression above
T2-(-2)=-6
Solve for T2
T2+2=-6
T2=-6-2
T2=-8
therefore
The final temperature was -8
we have that
T1 ------> initial temperature
T2 ----> final temperature
The 17 boys in the class represent 65% of the students in class
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There are 17 boys in the class which represents 65% of the students in class.
To find the missing amount, we need to use the rule of three.
If 17 boys --------- 65%
Then
x boys --------- 100%
Where x=(17*100)/65
x = 26.15
Hence, there are 26 students in class.
Consider the following loan. Complete parts (a)-(C) below.An individual borrowed $63,000 at an APR of 7%, which will be paid off with monthly payments of $445 for 25 years.The amount borrowed is $ 63,000, the annual interest rate is 7%, the number of payments per year is 12, and the payment amount is $ 445.b. How many total payments does the loan require? What is the total amount paid over the full term of the loan?There are ?? payments toward the loan and the total amount paid is ??
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Answer:
Explanation:
b)From the question, we have it that there are 12 payments in a year and this goes on for 25 years
The number of repayments is:
[tex]\text{ 25}\times12=\text{ }300[/tex]Now, to get the total amount paid, we have to multiply the number of repayments by the payment per repayment:
[tex]\text{ 300}\times\text{ 445 = \$133,500}[/tex]c) of the total amount paid, we want to get the value paid towards the principal and the amount paid as interest
The loan value is $63,000 and the total amount repaid is $133,500
The amount paid as interest is the difference between the amount paid and the amount borrowed:
[tex]\text{ interest = \$133,500 - \$63,000 = \$70,500}[/tex]We have the percentage as:
[tex]\begin{gathered} \frac{63000}{133500}\text{ = 47.2\% } \\ \text{This is the percentage paid towards principal} \\ \text{Percentage towards interest is 100 - 47.2 = 52.8 \%} \end{gathered}[/tex]What is 25% of 120? Use any strategy to help you.
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Which statement is true about the graph of the line 8x+3y=0It is a vertical lineIt is a horizontal lineIt passes through (8,3)It passes through the origin
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Vertical ine is in the form
x = a where a is a number
Horizontal line is in the fomr
y = b, where b is a number
Clearly the equatin isn't a vertical or hirzontal line.
Now, 3rd and 4th hoice evaluate:
(8,3) --- point it passes
let's plug in:
8x + 3y
8(8) + 3(3) = 0 ??? NO!!
T
This choice is not right.
Now, 4th choice:
passes through origin (0,0)
8x + 3y = 0
Now plugging in:
8(0) + 3(0)
= 0
So, this is correct.
It passes through the origin
If point Pis 3/8 of the distance from A to B, then point P partitions the line segment from A to B into aratio.
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We can start by drawing the segment:
We know that AP is 3/8 of the distance AB.
We then know that:
[tex]PB=AB-AP=AB-\frac{3}{8}AB=(1-\frac{3}{8})AB=\frac{5}{8}AB[/tex]Then, the ratio between the two segments become:
[tex]\frac{AP}{PB}=\frac{\frac{3}{8}AB}{\frac{5}{8}AB}=\frac{3}{8}\cdot\frac{8}{5}=\frac{3}{5}[/tex]The ratio AP/PB is 3/5.
(If we express this as PB/AP the ratio would be 5/3).
3. The numbers are measurements of radius, diameter, and circumference of circles A and B.Circle Ais smaller than circle B. Which number belongs to which quantity? 2.5, 5, 7,6, 15.2,15.7,47.7
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on a piece of paper graph y
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To answer this question, we need to follow the next steps.
1. This is an inequality, and there is a line that we need to represent it.
2. The line is y = x - 1.
3. We need to graph the line. For this, we can graph it using the x- and the y-intercept of the line.
[The x-intercept is the point where the line passes through the x-axis, and it is represented as (a, 0) - see that the value for y = 0. Likewise, the y-intercept is the point where the line passes through the y-axis, (0, b) - see that the value for x at this point is x = 0.]
4. Finding the x- and the y-intercepts:
Finding the x-intercept[tex]y=x-1\Rightarrow0=x-1\Rightarrow x=1[/tex]Therefore, the x-intercept is (1, 0).
Finding the y-intercept[tex]y=x-1\Rightarrow x=0\Rightarrow y=0-1\Rightarrow y=-1[/tex]Therefore, the y-intercept is (0, -1).
5. Finding the line equation
With these two points, (1, 0) and (0, -1), we need to label these points so we can apply the two-point form of the line as follows:
(1, 0) ---> x1 = 1, y1 = 0.
(0, -1) ---> x2 = 0, y2 = -1.
The two-point form of the line is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Substituting the corresponding values for x1, y1, x2, and y2, we have:
[tex]y-0=\frac{-1-0}{0-1}(x-1)\Rightarrow y=\frac{-1}{-1}(x-1)\Rightarrow y=x-1[/tex]We were able to prove that the values are correct since we found the same line equation. Therefore, with those two points, we can graph the line.
6. Reference point to graph the inequality
Now, we need to use a reference point to see where the shaded area corresponding to the inequality is. We can choose the reference point (0, 0).
If we substitute the corresponding values for x = 0, and y = 0 in the inequality, we have:
[tex]yThe previous result is NOT TRUE: 0 is greater than -1. Therefore, the inequality must be in the other part of the line, and not the point (0,0) is. Additionally, we have that the values must be less than, <, which means the line must be graph as a dotted line.Thus, we can graph the inequality as follows:
In summary, we can see above the graph of the inequality y < x - 1. We needed to find the x- and y-intercepts to find the line. After testing the reference point (0,0), we realized that the shaded area that corresponds to the inequality must be on the other side of the line - the other side of the line where the point (0, 0) is not. We needed to graph a dotted line since the values must be less, <, - and not equal to, in the inequality.
Find the vertex and foci hyperbola y^2-x^2 = 81
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Solution:
The standard equation of a hyperbola is expressed as
[tex]\begin{gathered} \frac{\left(y-k\right)^2}{a^2}-\frac{\left(x-h\right)^2}{b^2}=1\text{ ---- equation 1} \\ \text{where} \\ (h,\text{ k) is the coordinate of its center} \\ a\text{ is the axis} \\ b\text{ is the conjugate axis} \end{gathered}[/tex]Given the equation of the hyperbola to be
[tex]y^2-x^2=81\text{ ---- equation 2}[/tex]Express equation 2 in a similar form as equation 1.
Thus,
[tex]\begin{gathered} y^2-x^2=81 \\ \text{divide both sides of the equation by 81} \\ \frac{y^2-x^2}{81}=\frac{81}{81} \\ \Rightarrow\frac{y^2}{9^2}-\frac{x^2}{9^2}=1\text{ ---- equation 3} \end{gathered}[/tex]In comparison with equation 1, we can conclude that
[tex]\begin{gathered} a=9 \\ b=9 \end{gathered}[/tex]Vertices of the hyperbola:
The vertices of the hyperbola are expressed as
[tex]\mleft(h,k+a\mright),\: \mleft(h,k-a\mright)[/tex]where
[tex]h=0[/tex]The vertices of the hyperbola are evaluated to be
[tex]\begin{gathered} (h,\: k+a)\Rightarrow(0,\text{ 0+9)=(0, 9)} \\ (h,\: k-a)\Rightarrow(0,0-9)=(0,-9) \end{gathered}[/tex]Hence, the vertices of the hyperbola are
[tex](0,9),\text{ (0, -9)}[/tex]Foci of the hyperbola:
The foci of the hyperbola are expressed as
[tex]\begin{gathered} \mleft(h,k+c\mright),\: \mleft(h,k-c\mright) \\ \text{where c }\mathrm{\: }is\: the\text{ distance from the center (h,k) to a focus} \\ c\text{ is evaluated as } \\ c=\sqrt{a^2+b^2} \end{gathered}[/tex]Evaluating c gives
[tex]\begin{gathered} c=\sqrt{a^2+b^2} \\ =\sqrt[]{9^2+9^2} \\ =\sqrt[]{81+81} \\ =\sqrt[]{162} \\ c=9\sqrt[]{2} \end{gathered}[/tex]Thus, the foci are evaluated as
[tex]\begin{gathered} (h,k+c)\Rightarrow(0,\text{ 0+9}\sqrt[]{2})=(0,9\sqrt[]{2}) \\ (h,k-c)\Rightarrow(0,\text{ 0-9}\sqrt[]{2})=(0,-9\sqrt[]{2)} \end{gathered}[/tex]Hence, the foci of the hyperbola are
[tex]\mleft(0,\: 9\sqrt{2}\mright),\: \mleft(0,\: -9\sqrt{2}\mright)[/tex]Hello, I need some help on a question like the one down below.A survey of 1,175 tourists visiting Orlando was taken. Of those surveyed:251 tourists had visited LEGOLAND294 tourists had visited Universal Studios54 tourists had visited both the Magic Kingdom and LEGOLAND80 tourists had visited both the Magic Kingdom and Universal Studios99 tourists had visited both LEGOLAND and Universal Studios38 tourists had visited all three theme parks72 tourists did not visit any of these theme parksHow many tourists only visited the Magic Kingdom (of these three)?
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raise v to the 7th power,then find the difference of the result and w
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Given:
Raise v to the 7th power, then find the difference of the result and w.
To find the expression:
According to the statement,
When we raise v to the 7th power, the result is,
[tex]v^7[/tex]After that, the difference of the result and w is,
[tex]v^7-w[/tex]Hence, the answer is,
[tex]v^7-w[/tex]Which of the following statements must be true about this diagrarn? Check allthat applyA. The degree measure of 24 equals the sum of the degreemeasures of 21 and 22.B. The degree measure of 24 equals the sum of the degreemeasures of 22 and 23.C. The degree measure of 23 equals the sum of the degreemeasures of 21 and 22D. m24 is greater than m22,O E m23 is greater than m22Em24 is greater than m21
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In the given triangle we have the following:
A. The sum of the inner angles of a triangle is always equal to 180, that is:
[tex]\angle1+\angle2+\angle3=180[/tex]From this, we can solve for the sum of angles 1 and 2 and we get:
[tex]\angle1+\angle2=180-\angle3[/tex]Now, we also know that angles 3 and 4 are supplementary angles and therefore their sum is 180 degrees, that is:
[tex]\angle4+\angle3=180[/tex]Solving for angle 4:
[tex]\angle4=180-\angle3[/tex]Equating both results we get:
[tex]\angle1+\angle2=\angle4[/tex]Therefore, it is true that angle 4 is the sum of angles 1 and 2.
B. We have that the sum of angles 2 and 3 is:
[tex]\angle2+\angle3=180-\angle1[/tex]If this were equal to angle 4 we would have:
[tex]\begin{gathered} \angle4=180-\angle1 \\ \angle4+\angle1=180 \end{gathered}[/tex]B
Use Heron's Formula, that is, the area of a triangle is A= s(s-a)(s-b)(s-c), where the(a+b+c) to find the area of the triangle with sidetriangle contains sides a, b and c andlengths: a = 6.2, b = 7.5, C = 4.9.18.4 square units23.3 square units15.1 square units28.5 square units
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Heron's formula is given as
[tex]A\text{ =}\sqrt[]{s(s-a)(s-b)(s-c)}[/tex]and
[tex]s\text{ =}\frac{1}{2}(a+b+c)[/tex]we are given that
[tex]a=6.2,\text{ b = 7.5 and c = 4.9}[/tex]First, we find the value of s using the formula
[tex]\begin{gathered} s\text{ = }\frac{1}{2}(6.2\text{ + 7.5 + 4.9)} \\ s\text{ = }\frac{18.6}{2} \\ s\text{ = 9.3} \end{gathered}[/tex]next, we substitute values of a, b, c, and s to get the area
[tex]\begin{gathered} A\text{ = }\sqrt[]{s(s-a)(s-b)(s-c)} \\ A\text{ = }\sqrt[]{9.3(9.3-\text{ 6.2)(9.3 - 7.5)(9.3 - 4.9) }} \\ A\text{ = }\sqrt[]{9.3\text{ }\times3.1\times\text{ 1.8 }\times\text{ 4.4}} \\ A\text{ = }\sqrt[]{228.33} \\ A\text{ = 15.1 square units} \end{gathered}[/tex]Therefore,
Area of triangle = 15.1 square units
LUAEWhat are the solutions of the equation |2x - 2 = 8?O A. 3 and 5B. -3 and 3OC. –3 and 5D. -5 and 3E. -5 and 5
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The solución would be
[tex]\begin{gathered} 2x-2=8 \\ 2x=8+2 \\ x=\frac{10}{2} \\ x=5 \end{gathered}[/tex]and
[tex]\begin{gathered} 2x-2=-8 \\ 2x-2=-8+2 \\ 2x=-6 \\ x=-\frac{6}{2} \\ x=-3 \end{gathered}[/tex]The solution would be -3 and 5
A manufacturer produces a commodity where the length of the commodity has approximately normaldistribution with a mean of 15.7 inches and standard deviation of 1.4 inches. If a sample of 45 items are chosenat random, what is the probability the sample's mean length is greater than 15.7 inches? Round answer to fourdecimal places
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Given:
- The Mean:
[tex]\mu=15.7in[/tex]- The Standard Deviation:
[tex]\sigma=1.4in[/tex]- And the sample:
[tex]n=45[/tex]You need to find:
[tex]P(\mu^{\prime}>15.7)[/tex]Where this the Sample Mean:
[tex]\mu^{\prime}[/tex]Therefore, you need to use the formula to find the z-statistics:
[tex]z=\frac{\mu^{\prime}-\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex]Knowing that:
[tex]\mu^{\prime}=15.7in[/tex]You can substitute values into the formula and evaluate:
[tex]z=\frac{15.7-15.7}{\frac{1.4}{\sqrt[]{45}}}=\frac{0}{\frac{1.4}{\sqrt[]{45}}}=0[/tex]Now you need to look for the probability of that value of "z" in the table of Right-Tail Normal Standard Deviation. This is:
[tex]P(\mu^{\prime}>15.7)=0.5[/tex]Hence, the answer is:
[tex]P(\mu^{\prime}>15.7)=0.5[/tex]You live in a city where the East-West streets are named using letters of the alphabet and the North-South avenues are named using numbers. The streets and avenues are arranged in grids – the streets are perpendicular to the avenues. You live on F street a half mile east of 2nd Avenue. Your friend lives on the same street a half mile west of 2nd Avenue. Both of you decide to meet at the neighborhood market at the end of 2nd Avenue directly north of F street. If both of you leave your houses at the same time, who will get to the market first?
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Let's see that between the three points you can draw an equilateral triangle since the distance between you and your friend from the second avenue is the same and the streets are perpendicular to each other (besides that they form a grid). Since both must travel the same distance and neither is supposed to be faster than the other. Your friend and you will arrive at the market at the same time.
Solve the equation by multiplying both sides by the LCD.
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EXPLANATION :
From the problem, we have the equation :
[tex]x=2+\frac{15}{x}[/tex]Multiply both sides by x :
[tex]\begin{gathered} x(x)=x(2+\frac{15}{x}) \\ \\ x^2=2x+15 \\ x^2-2x-15=0 \\ \\ \text{ Factor completely :} \\ (x-5)(x+3)=0 \end{gathered}[/tex]Equate both factors to 0 :
x - 5 = 0
x = 5
x + 3 = 0
x = -3
ANSWER :
The solution is (-3, 5)
Kevin earned $80. Out of his earnings, he spent $685 on shopping, $512 on food, and $225 for taxi. Find the remaining amount.
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SOLUTION
To get the remaining amount, we subtract all the other cost from the amount he earned.
This means, the remaining amount becomes
[tex]80-\frac{68}{5}-\frac{51}{2}-\frac{22}{5}[/tex]This becomes
[tex]\begin{gathered} \frac{80}{1}-\frac{68}{5}-\frac{51}{2}-\frac{22}{5} \\ \\ \text{LCM of the denominators = 10 } \\ \\ \frac{800-136-255-44}{10} \\ \\ \frac{365}{10} \\ \\ =\frac{73}{2}\text{ dollars} \end{gathered}[/tex]im not good at graphs please help.
Use the graph below to answer the following questions. In each case, carefully explain your reasoning and justify your answer.
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Part (a)
The graph is continuous at x = 0 because we have a connected curve at this point. There are no jumps or gaps at x = 0.
=====================================================
Part (b)
The graph is NOT differentiable at x = 0 because of the sharp point. There isn't a smooth transition from one tangent slope to the other. If you were to apply the derivative to y = |x|, then you'll find the graph of y' = |x|/x has a jump discontinuity at x = 0.
=====================================================
Part (c)
The graph is NOT continuous at x = 1 because of the open hole here. Think of it as a pothole in the ground that you can't drive over. We consider this a removable discontinuity since we basically pulled exactly one point from the graph to toss away. The graph is continuous everywhere else but x = 1.
=====================================================
Part (d)
The graph is NOT differentiable at x = 1 because we need continuity as one of the conditions. But unfortunately as mentioned in part (c), the graph isn't continuous at x = 1.
If a portion isn't continuous, then it's certainly not differentiable. Think of the "differentiable" building block dependent on the "continuous" building block as a foundation. This is because the differentiability of a function depends on a limiting value based on whether f(x) exists at that location.
As mentioned earlier, just because something is continuous, it doesn't automatically lead to differentiability. See part (b).
But luckily, if you know something is differentiable at a certain spot, then it must be continuous there as well.
=====================================================
Summary of the answers:
(a) Continuous (b) Not differentiable(c) Not continuous(d) Not differentiableLet me know if you have any questions.
Solve 1/3x -3/4 = 5/12
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We have to solve this equation:
[tex]\frac{1}{3}x-\frac{3}{4}=\frac{5}{12}[/tex]We can multiply the fractions when needed to make them have the same denominator.
Then, we can solve this as:
[tex]\begin{gathered} \frac{1}{3}x-\frac{3}{4}=\frac{5}{12} \\ \frac{1}{3}x=\frac{5}{12}+\frac{3}{4} \\ \frac{1}{3}x=\frac{5}{12}+\frac{3}{4}\cdot\frac{3}{3} \\ \frac{1}{3}x=\frac{5}{12}+\frac{9}{12} \\ \frac{1}{3}x=\frac{14}{12} \\ x=3\cdot\frac{14}{12} \\ x=\frac{14}{4} \\ x=\frac{7}{2} \end{gathered}[/tex]Answer: x = 7/2
please help me solve this(i promise to give you a good review)
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We will have the following:
First, we remember that the tangent for an angle in a right triangle is composed of the opposite side divided by the adjacent side, so:
Tan(B):
[tex]tan(B)=\frac{36}{27}=\frac{4}{3}\approx1.3333[/tex]Tan(A):
[tex]tan(A)=\frac{27}{36}=\frac{3}{4}=0.7500[/tex]Given the 2 points, find the slope: (2,3) (8,6).
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Answer:
0.5
Explanation:
Given the 2 points: (2,3) and (8,6)
[tex]\begin{gathered} \text{Slope}=\frac{\text{Change in y}}{\text{Change in x}} \\ =\frac{6-3}{8-2} \\ =\frac{3}{6} \\ =0.5 \end{gathered}[/tex]The slope of the line joining the two points is 0.5
Solve the system of equations by the substitution method. y=2x+9y=5x+10
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
y=2x+9 eq. 1
y=5x+10 eq. 2
y = ?
x = ?
Step 02:
substitution method
eq.1 in eq.2
2x+9=5x+10
2x - 5x = 10 - 9
-3x = 1
x = 1 / (-3)
x = - 1 / 3
x in eq. 1
y=2(-1/3) + 9
[tex]\begin{gathered} y\text{ = 2}\cdot(\frac{-1}{3})+9 \\ y=\frac{-2}{3}+9 \\ y=\frac{-2+27}{3}=\frac{25}{3} \end{gathered}[/tex]The answer is:
x = - 1 /3
y = 25 / 3
The Congruent Supplements Theorem states:If two angles are supplements of the same angle orof congruent angles, then the angles are congruent.Prove the Congruent Supplements Theorem.Given the diagram below and the following statements:• QEM CAX.Prove that ZMEHE XAB.
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EXPLANATION
The Congruent Supplements Theorem states that if two angles are supplements of the same angle (or congruent angles), then the two angles are congruent.
Given the statements
m< QEM + m< MEH = m
The reasons are:
Transitive property of the congruency
Are the following two slopes going to make lines that are parallel, perpendicular, or neither?m=-4/1m=1/4
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We are given the slopes of two lines.
[tex]m_1=-\frac{4}{1}\quad \text{and}\quad m_2=\frac{1}{4}[/tex]Recall that two lines are said to be parallel if they have equal slopes.
Since the given slopes are not equal then we know that they are not parallel.
Recall that two lines are said to perpendicular if their slopes are negative reciprocal of each other.
[tex]m_1=-\frac{1}{m_2}[/tex]For the given case, we see that the given slopes are indeed negative reciprocal of each other.
Therefore, the two lines with the given slopes are perpendicular.
In the graph, g (x) is transformation of the parent function f (x)=x³. The graph below shows f as a solid blue line and g as a dotted red line. which equation describes g (x)A) g (x)=2(-x-1)³-3B) g (x)=-2(x+1)³-3C) g (x)=2(-x+1)³-3D) g (x)=2(-x+1)³+3
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we have the following:
• We can discard option b, since the value is -3, and not + 3
,• and that for when it is 1, it is equal to -3, what is raised to 3 must be 0, and the only option for 0 is the following
[tex]-x+1=-1+1=0[/tex]therefore, the answer is the opcion C.
[tex]g(x)=2\mleft(-x+1\mright)^3-3[/tex]The length of a rectangular prism is described with the expression4x-2y4 units, the width is described with the expression 1.5x2y-3 units and the height is described with the expression 3xy-1 Which of thefollowing can be used to describe the volume of the prism?
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B
1) GIven the following information we can write out:
The Volume of a Rectangular Prism is equal to
[tex]V=a\cdot b\cdot c[/tex]2) Plugging into them the given dimensions we can state, expanding the factors:
[tex]\begin{gathered} V=4x^{-2}y^4\cdot1.5x^2y^{-3}\cdot3xy^{-1} \\ V\text{ =18}x^{-2+2+1}y^{4-3-1} \\ V=18x^{}y^{4-4} \\ V=18xy^0 \\ V=18x \end{gathered}[/tex]Note that we applied the exponent's rule to operate them.
3) Hence, the volume of that rectangular prism is 18x cubic units
There is a raffle with 100 tickets. One ticket will win a $700 prize, one ticket will win a $510 prize, one ticket will win a $490 prize, and the remaining tickets will win nothing. If you have a ticket, what is the expected payoff?
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ANSWER
[tex]\text{\$17}[/tex]EXPLANATION
We want to find the expected payoff.
To do this, we have to first find the probability of winning each prize:
=> 1 ticket out of 100 will win $700 prize. The probability of winning this prize is:
[tex]P(700)=\frac{1}{100}[/tex]=> 1 ticket out of 100 will win $510 prize. The probability of winning this prize is:
[tex]P(510)=\frac{1}{100}[/tex]=> 1 ticket out of 100 will win $490 prize. The probability of winning this prize is:
[tex]P(490)=\frac{1}{100}[/tex]=> The remaining tickets (97) will win nothing ($0). The probability of winning $0 is:
[tex]P(0)=\frac{97}{100}[/tex]The expected value is the sum of the product of each possible outcome and its corresponding probability:
[tex]\begin{gathered} E(X)=\Sigma\mleft\lbrace X\cdot P(X\mright)\} \\ \Rightarrow E(X)=(\frac{1}{100}\cdot700)+(\frac{1}{100}\cdot510)+(\frac{1}{100}\cdot490)+(\frac{97}{100}\cdot0) \\ E(X)=7+5.10+4.90+0 \\ E(X)=\text{ \$17} \end{gathered}[/tex]That is the expected payoff.