Given a function where one x-intercept of a parabola is (-4,0), what will be the new x-intercept if h is increased by 6?

Answers

Answer 1

(2, 0) would be the new x - intercept.

The equation of a parabola can be written in vertex form as:

y = a(x - h)² + k

Here, h represents the x-coordinate of the vertex. The x-intercepts of the parabola are the points where the parabola crosses the x-axis (i.e., where y = 0).

Given that one x-intercept is at (-4, 0), we know that x-intercepts are symmetrically located around the vertex. If the vertex's x-coordinate h is increased by 6, the entire parabola shifts horizontally to the right by 6 units.

Since the x-intercept is affected by the shift in the vertex:

Before the shift: one of the x-intercepts is at -4.

After the shift by h, the new x-intercept will be located 6 units to the right of the original intercept.

Therefore, the new x-intercept will be at:

-4 + 6 = 2


Related Questions

Please help it would be apreacated

What is the name of the line of reflection for the pair of figures?

Enter your answer in the box.

Line ___

Answers

Hi!

Answer - Line R

Well refraction is the bending of something. I choose r because it may have refraction because of the 2 rectangles at the end of both sides.

Hope This Helps!

[tex]<b><u>HEY THERE !![/tex]

CORRECT ANSWER:- LINE' t '

HOPE IT HELPED YOU.

A survey was sent to GCA students asking the question "Who is your favorite teacher?" (Just FYI - Mrs. Parker received the most votes) What type of data was collected? Question 1 options: Quantitative Qualitative Continuous Discrete Question 2 (1 point) Question 2 Unsaved A survey was sent to GCA students asking the question "On a scale of 1 to 5, with 1 being the lowest and 5 being the highest, how would you rate your AMDM teacher?" The data collected was Question 2 options: Quantitative Qualitative Continuous redundant since every student rated their AMDM teacher as a 5. Question 3 (1 point) Question 3 Unsaved You decided to attend the GCA outing at Stone Mountain. Before you left for the park, you entered the park address into a GPS/Traffic app on your phone. The app told you that Stone Mountain was 47.6 miles from your house. 47.6 miles is an example of... Question 3 options: Qualitative, continuous data Quantitative, discrete data Qualitative, discrete data Quantitative, continuous data Question 4 (1 point) Question 4 Unsaved While you were at the Stone Mountain outing, you played a game of corn hole. You counted the number times you tossed the beanbag into the hole. The number of times you were able to sink the beanbag is an example of.... Question 4 options: Qualitative, continuous data Quantitative, discrete data Qualitative, discrete data Quantitative, continuous data Question 5 (1 point) Question 5 Unsaved You recorded the time you left Stone Mountain and the time you arrived home. You calculated time it took you get home was 57.28 minutes. 57.28 minutes is an example of.... Question 5 options: Qualitative, continuous data Quantitative, discrete data Qualitative, discrete data Quantitative, continuous data

Answers

1. Qualitative

2. Quantitative

3. Quantitative, continuous data

4. Quantitative, discrete data

5. Quantitative, continuous data

A toy jeep is 12 1/2 inches long while an actual Jeep measures 18 3/4 ft long what is the value of the ratio length of a toy Jeep to the length of a actual Jeep

Answers

The length of toy jeep = [tex]12 \frac{1}{2}[/tex]

= [tex]\frac{25}{2}[/tex] inches

The length of actual Jeep = [tex]18 \frac{3}{4}[/tex] feet

We have to find the ratio length of a toy jeep to the length of actual jeep.

Firstly, we will make the dimensions of the both the given lengths same.

As 1 foot = 12 inches

[tex]18 \frac{3}{4}[/tex] feet = [tex]18 \frac{3}{4} \times 12[/tex] inches

=[tex]\frac{75 \times 12}{4}[/tex]

= 225 inches

So, the ratio length of toy jeep to actual jeep

= [tex]\frac{25}{2} \div 225[/tex]

= [tex]\frac{25}{2} \times \frac{1}{225}[/tex]

= [tex]\frac{1}{18}[/tex]

= 1:18

So, the ratio length of a toy Jeep to the length of a actual Jeep is 1:18.

Length of toy jeep = [tex]12\frac{1}{2}=\frac{25}{2}[/tex] inches

Length of actual jeep = [tex]18\frac{3}{4}=\frac{75}{4}[/tex] feet

Now to find the ratio between the two, we must convert both of them in same units. So, lets convert the actual jeep length in feet to inches.

1 feet = 12 inches.

So, [tex]\frac{75}{4}[/tex] feet = [tex]\frac{75}{4}\times12=225[/tex] inches

Ratio of length of toy jeep to actual jeep will be =

[tex]\frac{\frac{25}{2}}{225}[/tex]

[tex]\frac{25}{2\times225}[/tex]

[tex]\frac{25}{450}[/tex] = [tex]\frac{5}{90}[/tex]

ratio is : [tex]\frac{1}{18}[/tex] or 1:18


What steps would you take to construct an angle bisector? How many arcs would you make?

Answers

The steps are as follows:

1. Put the compass at one point on the vertex of the angle and draw an arc that intersects both sides of the angle.

2. Now, draw an arc from each of these points of intersection, in such a way that the arcs intersect in the interior of the angle. Keep the compass open in the same amount throughout this step.

3. Now, draw a ray/line from the vertex of the angle to the intersection point of the two arcs drawn during step 2.

How many arcs would you make? We will draw 3 arcs.

The estimated insurance loss from a hurricane was ​$18.218.2 billion. This was ​$12.412.4 billion more than the loss from a tsunami three years later. What was the estimated insurance loss from the​ tsunami?

Answers

Answer:

If you are asking about the difference between the two, the difference is $5,805.80

Step-by-step explanation:


A party host is making identical party bags for guests using 44 bottles of bubbles, 89 stickers, and 55 pencils. What is the greatest number of identical party bags the host can make with the least amount of items leftover? Describe the contents of each bag.

Answers

Answer: 11 party bags with 1 sticker leftover

Each bag contains 4 bubbles, 8 stickers, and 5 pencils.

Step-by-step explanation:

Find the GCF of 44 (bubbles), 89 (stickers), and 55 (pencils)

44: 2 x 2 x 11

89: prime so choose 88 with 1 leftover

88: 2 x 2 x 2 x 11

55: 5 x 11

GCF = 11

Disregard the GCF to see how many of that item should go in each bag.

Bubbles: 2 x 2

Stickers: 2 x 2 x 2

Pencils: 5



what the value of tge expression 30+(6÷3)+(3+4)

Answers

Remember to follow PEMDAS (Parenthesis, Exponents (and roots), Multiplication, Division, Addition, Subtraction)

First, solve the parenthesis

30 + (6/3) + (3 + 4)

30 + 2 + 7

Next, simplify. Combine like terms

30 + 2 + 7 = 39

39 is your answer

~Rise Above the Ordinary

Hello there!

Hint⇒⇒⇒⇒⇒⇒ You had to used PEMDAS.

P-Parenthesis

E-Exponents

M-Multiply

D-Divide

A-Add

S-Subtract

Explanation:

↓↓↓↓↓↓↓↓↓↓↓↓↓

[tex]30+(6/3)+(3+4)[/tex]

First you had to calculate with parenthesis first.

[tex](6/3)=2[/tex]

[tex]30+2+(3+4)[/tex]

Then you can calculate with parenthesis again.

[tex](3+4)=7[/tex]

[tex]30+2+7[/tex]

You had to add and subtract from left to right.

[tex]30+2+7=39[/tex]

[tex]=39[/tex]

Answer⇒⇒⇒⇒39

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

A cement bridge post is 24 inches square and 15 feet 9 inches in length. If the cement weighs 145 pounds per cubic foot, how much does one bridge post weigh? A. 9,280 pounds B. 9,222 pounds C. 9,135 pounds D. 8,700 pounds

Answers

Answer:

The answer is option (C), One cement bridge post weighs 9,135 pounds

Step-by-step explanation:

Step 1: Get the total volume of a cement bridge post

The cement bridge post is in the shape of a cuboid, therefor the volume of the cement bridge post can be expressed as;

Volume of cement bridge post=Base area×Length

where;

Base area=(24^2) inches square

1 foot=12 inches

Convert 24 inches to foot=24/12=2^2=4 feet²

Length=15 feet and 9 inches

1 foot=12 inches

Convert 9 inches to foot=9/12=0.75 feet

Total length=(15+0.75)=15.75 feet

replacing;

Volume of cement bridge post=(4×15.75)=63 cubic feet

Volume of cement bridge post=63 cubic feet

Step 2: Get the total weight of the cement bridge post

Total weight of the cement bridge post=Weight per cubic foot×total volume of the cement bridge post

where;

Weight per cubic foot=145 pounds per cubic foot

Total volume of the cement bridge post=63 cubic feet

replacing;

Total weight of the cement bridge post=(145×63)=9,135 pounds

One cement bridge post weighs 9,135 pounds

Find the system determinant of the given matrix. [2, 4] [3,-9]

Answers

[tex]\left[\begin{array}{ccc}2&4\\3&-9\end{array}\right]\\\\\det\left[\begin{array}{ccc}2&4\\3&-9\end{array}\right]=(2)(-9)-(4)(3)=-18-12=-30[/tex]

Answer:

-30 will be the determinant.

Step-by-step explanation:

We have to find the system determinant of the given matrix

[tex]\begin{bmatrix}2 & 4\\ 3 & -9\end{bmatrix}[/tex]

Determinant will be = 2(-9) - (4 × 3)

                                 = -18 -12

                                = -30

Therefore, as per given options by you in the comments.

option A is the answer.

What graph represents the inequality y≥2−2x?


Answers

[tex]y\geq2-2x\\\\\text{Let's the line}\ y=2-2x\\\\for\ x=0\to y=2-2(0)=2\to(0,\ 2)\\for\ x=1\to y=2-2(1)=0\to(1,\ 0)[/tex]

[tex]\text{draw a line and shade above the line}\\\\\text{Look at the picture}[/tex]

Answer:

Graph is attached below

Step-by-step explanation:

To graph the given inequality , replace the inequality sign by = sign

y≥2−2x

y=2−2x

Now make a table , assume some random number for x and find out y

x         y=2-2x

0          2

1           0

2          -2

Now graph all the points (0,2) (1,0) (2,-2)

Now we do shading. For shading use test point (0,0)

plug in 0 for x and 0 for y

[tex]y\geq 2-2x[/tex]

[tex]0\geq 2-2(0)[/tex]

[tex]0\geq 2[/tex] is false

So shade the region that does not contain (0,0)

The graph is attached below

Using the formula r=d/t, where d is the didtance in miles, r is the rate, and t is the time in hours,at which rate must you travel to cover 185 miles in 2.5 hours

Answers

The rate of speed would be 74 mph

solve.

14n + 6p - 8n = 18p for n

Answers

[tex]14n+6p-8n=18p\ \ \ \ |\text{subtract 6p from both sides}\\\\14n-8n=12p\\\\6n=12p\ \ \ \ |\text{divide both sides by 6}\\\\\boxed{n=2p}[/tex]

The correct solution for this equation is n = 2p.

I hope this helped! :)

For y = 3x - 2x2 +5x3, show how to find the value for y, when x = 3. Show your work

Answers

thereeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answer:

y= 126

Step-by-step explanation:

The given equation is: y= 3x-2x^2+5x^3

Substituting the value x=3 in the above equation,we get

   y= 3(3)-2(3)^2+5(3)^3

⇒y= 9-2(9)+5(27)

⇒y= 9-18+135

⇒y= 126

Explain why a vertical line is said to have undefined slope or no slope.

Answers

A vertical linehas undefined slope because all points on the line have the same x-coordinate.

What is the justification for each step in the solution of the equation?

23x−13=2(x+2) Given
2x−1=6(x+2)
2x−1=6x+12 Distributive Property
2x=6x+13
−4x=13 Addition or Subtraction Property of Equality
x=−134

Answers

For this case we have the following equation:

[tex]\frac{2}{3}x-\frac{1}{3}= 2 (x + 2)\\[/tex]

If we multiply both sides of the equation by 3 we get:

[tex]2x-1 = 6 (x + 2)[/tex] ---> Multiplication Property of Equality

Applying the distributive property we have:

[tex]2x-1 = 6x + 12[/tex] ---> Distributive Property

Adding 1 on both sides of equality we have:

[tex]2x-1 + 1 = 6x + 12 + 1\\[/tex]

[tex]2x = 6x + 13[/tex] ---> Addition Property of Equality

Subtracting [tex]6x[/tex] on both sides we have:

[tex]-6x + 2x = 6x-6x + 13\\[/tex]

[tex]-4x = 13[/tex] ---> Subtraction Property of Equality

Finally, dividing by -4 on both sides we have:

[tex]\frac{-4x}{-4}= \frac{13}{-4}\\[/tex]

[tex]x = -\frac{13}{4}[/tex]---> Division Property of Equality


if f(x)=2x and g(x)=1/x, what is the domain of (fg)(x)

Answers

Answer is All real No.s

Answer: all real #s except x=0

Step-by-step explanation:

Edge 2022

Five cats each ate 1/4 cup of cat food. How much food did the five cats eat?

Answers

Answer:  Five cats ate 1 and a quarter of cat food.


Step-by-step explanation

Given:-

Cat food ate by one cat = 1/4 cup

Cat food ate by five cats =[tex]5\times \frac{1}{4} \text{ [Multiplying both sides with 5 ]}\\\\=\frac{5}{4}=\frac{4+1}{4}=\frac{4}{4}+\frac{1}{4}=1+\frac{1}{4}[/tex]=1 and 1/4 cup.

Therefore cat food ate by five cats = 1 and a quarter of cup.[ here a quarter =1/4]

Which of the following equations correctly describes the graphed line?




y = 2/3x - 2


y = -2/3x - 2


y = 2/3x + 2


y = -2/3x + 2

Answers

y = - [tex]\frac{2}{3}[/tex] x - 2

the equation of a line in ' slope - intercept form ' is

y = mx + c ( m is the slope and c the y- intercept ) calculate m using the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0 , - 2 ) and (x₂ , y₂ ) = A( 6 , - 6 )

m = [tex]\frac{- 6+ 2}{6 - 0}[/tex] = [tex]\frac{-4}{6}[/tex] = - [tex]\frac{2}{3}[/tex]

y -intercept c = - 2 ( from graph )

y = - [tex]\frac{2}{3}[/tex] x - 2


Cristoble used synthetic division to divide the polynomial f(x) by x + 3, as shown on the table. What is the value of f(−3) ? −3 2 33 36 A synthetic division setup with respective columns containing the following numbers column 1 containing -3 as the divisor, column 2 containing 2, blank and 2, column 3 containing negative 5, negative 6, negative 11, and column 4 containing 3, 33, 36.There is a line above the numbers 2, negative 11 and 36.

Answers

Answer:

Remainder is 36.

Step-by-step explanation:

We are given that f(x) is divided by x+3 using synthetic division, and  we are given with table attached in the image.

In synthetic division, first row represents the coefficients of dividend. From the given table, dividend is f(x)=[tex]2x^{2}-5x+3[/tex] and  since f(x) is divided by x+3, divisor is -3.

First two numbers of last row represents coefficients of quotient and last most number of third row is remainder.

And we can write f(x) as (x+3)(2x-11)+36.

Hence remainder is 36 , when f(x) is divided by x+3.

Answer:

36

Step-by-step explanation:

this i believe is the settup u were describing

A bag of marbles contains 7 red, 5 blue, 4 red, and 2 yellow marbles. Jon selects a marble, replaces it, then selects another marble. What is the probability that Jon selects a red marble and then a yellow marble?

Question 2 options:

about 0.778 or 77.8%


0.5 or 50%


about 0.043 or 4.3%


0.25 or 25%

Answers

[tex]|\Omega|=18^2=324\\|A|=7\cdot2=14\\\\P(A)=\dfrac{14}{324}=\dfrac{7}{162}\approx0.043(=4.3\%)[/tex]

First, we find the total number of marbles.

We add up the red, blue, and yellow marbles:

The number of red marbles is 7 + 4 which equals to 11.

The number of blue marbles is 5.

The number of yellow marbles is 2.

To find the total number, we add these numbers together: 11 (red) + 5 (blue) + 2 (yellow) = 18. So, the total number of marbles is 18.

Second, we find the probability of each event - that is, picking a red marble and then a yellow marble.

Probability is the number of desired outcomes divided by the total number of possible outcomes.

The probability of picking a red marble, denoted as P(red) is the number of red marbles divided by the total number of marbles. So, P(red) = 11 / 18 which is about 0.611 or 61.1%.

The probability of picking a yellow marble, denoted as P(yellow) is the number of yellow marbles divided by the total number of marbles. So, P(yellow) = 2 / 18 which is about 0.111 or 11.1%.

Finally, we can find the answer to our question: What is the probability that Jon selects a red marble and then a yellow marble?

Because these are independent events (selecting a red marble does not affect the chance of selecting a yellow marble next), we can use the multiplication rule of probability to find the overall probability.

The multiplication rule states that the probability of two independent events both happening is the product of their individual probabilities. So the probability of picking a red marble and then a yellow marble, denoted as P(red and yellow), is P(red) * P(yellow).

P(red and yellow) = P(red) * P(yellow) = 0.611 * 0.111 which results in about 0.0679 or 6.8%.

So, the closest option is about 0.043 or 4.3% which seems to be incorrect as our calculated probability is different. There might be a mistake in the question or the provided options.

A jet ski depreciates at 11% of its original value each year. If the jet ski was $8,000 as it’s time of purchase, what is the value of the jet ski after 5 years

Answers

f(x) = 8000 - (8000)(0.11)x

     = 8000 - 880x

f(5) = 8000 - 880(5)

     = 8000 - 4400

     = 3600

Answer: $3,600

Answer:

$4467.25

Step-by-step explanation:

We have been given that a jet ski depreciates at 11% of its original value each year. The jet ski was $8,000 as it’s time of purchase.

We will exponential decay function to solve our given problem.

[tex]y=a\cdot(1-r)^x[/tex], where,

a = Initial value,

r = Decay rate in decimal form.

[tex]r=\frac{11}{100}=0.11[/tex]

[tex]y=\$8,000\cdot(1-0.11)^5[/tex]

[tex]y=\$8,000\cdot(0.89)^5[/tex]

[tex]y=\$8,000\cdot 0.5584059449[/tex]

[tex]y=\$4467.2475592[/tex]

[tex]y\approx \$4467.25[/tex]

Therefore, the value of ski jet after 5 years would be $4467.25.

△ABC is mapped to △A′B′C′ using the rule (x, y)→(−x, −y) followed by (x, y)→(x, −y) .



Which statement correctly describes the relationship between △ABC and △A′B′C′ ?


A. △ABC is congruent to △A′B′C′ because the rules represent a reflection followed by a rotation, which is a sequence of rigid motions.

B. △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.

C. △ABC is not congruent to △A′B′C′ because the rules do not represent a sequence of rigid motions.

D. △ABC is congruent to △A′B′C′ because the rules represent a reflection followed by a reflection, which is a sequence of rigid motions.

Answers

Answer:

B. △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.

Step-by-step explanation:

I just took the test, good luck! Have a wonderful day! :)

Transformation involves changing the position of a shape.

The correct statement is: (b) △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.

The transformation rule is given as:

[tex]\mathbf{(x,y) \to (-x,-y)}[/tex], then:

[tex]\mathbf{(x,y) \to (x,-y)}[/tex]

The first transformation [tex]\mathbf{(x,y) \to (-x,-y)}[/tex] is 180 degrees rotation across the originThe second transformation [tex]\mathbf{(x,y) \to (x,-y)}[/tex] is a reflection across the x-axis

Rotation and reflection are both rigid transformation.

Hence, the correct option is (b):

Read more about rotation and reflection at:

https://brainly.com/question/15577335

Sam initially invested $4,500 into a savings account that offers an interest rate of 3% each year. He wants to determine the number of years, t, for which the account will have less than or equal to $7,020.

Answers

Every year, Sam will have 103% of the amount from the previous year.

[tex]p\%=\dfrac{p}{100}\\\\103\%=\dfrac{103}{100}=1.03[/tex]

After the first year:

[tex]1.03\cdot\$4,500[/tex]

After the second year:

[tex]1.03\cdot1.03\cdot\$4,500=\$4,500(1.03)^2[/tex]

After the t-th year:

[tex]\$4,500(1.03)^t[/tex]

Therefore we have the inequality:

[tex]\$4,500(1.03)^t\leq\$7,020\ \ \ \ |\text{divide both sides by \$4,500}\\\\(1.03)^t\leq1.56\\\\(1.03)^{15}\approx15.56\\\\\text{therefore}\ t\leq15[/tex]

Answer: t ≤ 15.

25 Points! Pre-Calc help? Will award brainliest.

Find the solution set of the given equation for 0 ≤ x ≤ 2π.

-tanA = -1

A. pi/4, 3pi/4
B. pi4/, 5pi/4
C. 3pi/4, 5pi/4
D. 3pi/4, 7pi/4

Answers

The answer is B. If you look at a graph of -tan (which is cot), the places the graph crosses -1 are at pi/4 plus kpi. If you add pi to pi/4, you get 5pi/4, and these two answers are in B only.

Im adding an answer so the other guy that gave an answer gets his points.

Hayley begins solving this problem by combining like terms. 3x + 5x = 10 Which problem begins the same way? A) 5x = 20 Eliminate B) 2(x + 5) = 20 C) x 4 = 30 D) 4x ? 2x = 10

Answers

Answer:

In a linear equation  of one variable there are two terms terms containing variable and constant.

Variable means term containing x,y,z which act as variables. and constant means any rational number . In higher classes you can include real number also.

The given equation is 3x + 5x = 10

So, the solution out of four options is A) 5x = 20.

Here variable is on one side of equation and constant on other side.

But Option (D) looks absolutely correct if we replace ? by either + sign or Negative (-) sign.




Answer:

D. [tex]4x-2x=10[/tex]

Step-by-step explanation:

We have been give an equation [tex]3x+5x=10[/tex]. The equation is solved by combining like terms. We are asked to choose the equation that an be solved by combining the like terms.

Let us check our given choices one by one.

A. [tex]5x=20[/tex]

We can see that equation A will be solved by dividing 20 by 5, therefore, option A is not correct choice.

B. [tex]2(x+5)=20[/tex]

We can see that equation B will be solved by dividing 20 by 5 and then subtracting 5, therefore, option B is not correct choice.

C. [tex]\frac{x}{4}=20[/tex]

We can see that equation C will be solved by multiplying 20 by 4, therefore, option C is not correct choice.

D. [tex]4x-2x=10[/tex]

We can see that equation D will be solved by combining like terms, therefore, option D is correct choice.

What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit? A.24.8 units B.27.8 units C.28.5 units D.30.9 units

Answers

The answer is B I hope I helped

Answer:

the answer is B.28.7 hope i helped you learn something new

Step-by-step explanatio

What value of x makes the equation 3x-(7+4x)=2(5x-4)+1 true

Answers

x = 0

distribute parenthesis on both sides of the equation and simplify

3x - 7 - 4x = 10x - 8 + 1

- x - 7 = 10x - 7 ( subtract 10x from both sides )

- 11x - 7 = - 7 ( add 7 to both sides )

- 11x = 0 ( divide both sides by - 11 )

x = 0


Which correctly describes the point of discontinuity of the function?

Answers

A real-valued univariate function f=f(x) has a jump discontinuity at a point [tex]x_0[/tex] in its domain provided that

[tex]\lim \limits_{x\to x_0^-}f(x)=A_1[/tex]

and

[tex]\lim \limits_{x\to x_0^+}f(x)=A_2[/tex]

both exist and that [tex]A_1\neq A_2.[/tex]

As you can see at x=-3,

[tex]\lim \limits_{x\to -3^-}f(x)=6,[/tex] [tex]\lim \limits_{x\to -3^+}f(x)=9[/tex] and [tex]6\neq 9.[/tex]

Therefore, there is a jump discontinuity at x=-3.

Answer: correct choice is A.

What are the values of m and n in the matrix addition below?

Answers

ANSWER

The correct answer is [tex]m=45,n=12[/tex].

EXPLANATION

We were given the matrix equation;

[tex]\left[\begin{array}{cc}n-1&6\\-19&m+3\end{array}\right] +\left[\begin{array}{cc}-1&0\\16&-8\end{array}\right] =\left[\begin{array}{cc}10&6\\-3&40\end{array}\right][/tex].


We must first simplify the Left Hand Side of the equation by adding corresponding entries.


[tex]\left[\begin{array}{cc}n-1+-1&6+0\\-19+16&m+3-8\end{array}\right]=\left[\begin{array}{cc}10&6\\-3&40\end{array}\right][/tex].


That is;


[tex]\left[\begin{array}{cc}n-2&6\\-3&m-5\end{array}\right]=\left[\begin{array}{cc}10&6\\-3&40\end{array}\right][/tex].

Since the two matrices are equal, their corresponding entries are also equal. we equate corresponding entries and solve for m and n.


This implies that;


[tex]n-2=10[/tex]


We got this equation from row one-column one entry of both matrices.


[tex]n=12[/tex]


Also, the row three-column three entries of both matrices will give us the equation;


[tex]m-5=40[/tex]


[tex]m=45[/tex]


Hence the correct answer is [tex]m=45,n=12[/tex].


The correct option is option 2






What is the equation of the following graph in vertex form?
Courtesy of Texas Instruments (2 points)


y = (x - 3)2 - 1

y = (x + 3)2 - 1

y = (x - 4)2 - 2

y = (x - 4)2 + 8

Answers

For this case we have:

The equation in vertex form of the parabola is given by:

[tex]y = a (x-h) ^ 2 + k\\[/tex]

The vertex is (h, k) and is given by the highest or lowest point of the parabola, in this case it is observed that it is [tex](h, k) = (- 3, -1)\\[/tex]

Thus, the equation is given by:

[tex]y = a (x - (- 3)) ^ 2 + (- 1)\\\\y = a (x + 3) ^ 2-1\\[/tex]

We look for the value of a, substituting a point of the parabola in the equation in the form of vertex, we will take the point [tex](x, y) = (0,8)\\[/tex]

Substituting we have:

[tex]8 = a (0 - (- 3)) ^ 2 + (- 1)\\\\8 = a (0 + 3) ^ 2-1\\\\8 = a (3) ^ 2-1\\[/tex]

[tex]8 = 9a-1\\\\8 + 1 = 9a\\\\9 = 9a\\[/tex]

[tex]a = \frac{9}{9}\\\\a = 1\\[/tex]

Thus, the equation of the parabola is given by:

[tex]y = (x + 3) ^ 2-1\\[/tex]

Answer:

[tex]y = (x + 3) ^ 2-1[/tex]

Answer:

 

y = (x + 3)2 - 1

Step-by-step explanation:

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