What is the y-value of the vertex of the function f(x)=-(x-3)(x+11)?

Answer:

a = 7/2

Step-by-step explanation:

2x - y - 5 = 0

2x = y + 5

y = 2x - 5

m = -1/2

y - 5 = -1/2(x - (-2))

y - 5 = -1/2(x + 2)

y - 5 = -x/2 - 1

y = -x/2 + 4

a = -1/2 + 4

a = 7/2

Answer:

7,497.50 OR, 7,497 &1/2 in fraction form

Step-by-step explanation:

I got this answer by dividing 14,995 by 2 and got $7,497.50 hope this helps you mark as brailiest if best answer if any questions comment on this question below!! ThNks !!

Answer:

7,497.50

Step-by-step explanation:

Answer: Line slopes:

m1= 3/2 defined by points (5,3) and (7,6)

m2= -2/3 defined by points (7,6) and (4,8)

m3 = 3/2 defined by points (4,8) and (2,5)

m4 = -2/3 defined by points (2,5) and (5,3)

All comply the orthogonal slopes rule (90º)

Step-by-step explanation:

As those 4 point define a polygon, to check is that polygon is a rectangle, you need to compare the slopes of the lines defined by the 4 points and check that accomplish the following rule:

m1 = -(1/m2). this shows that the slopes are intersected in 90º angle.

Final answer:

By calculating the dot products of the direction vectors for adjacent sides, all of which are zero, and checking the distances of opposite sides, which are equal, we prove that the given quadrilateral is a rectangle.

Explanation:

To prove that a quadrilateral with given vertices is a rectangle, we must show that the quadrilateral has four right angles and opposite sides are equal. A right angle exists between two sides if the dot product of their direction vectors is zero, as this indicates perpendicularity. Equal length of opposite sides can be shown by the distance formula. We are given the vertices of the quadrilateral: (2,5), (4,8), (7,6), and (5,3).

Calculate the direction vectors of adjacent sides:

AB: (4-2, 8-5) = (2,3)

BC: (7-4, 6-8) = (3,-2)

CD: (7-5, 6-3) = (2,3)

DA: (2-5, 5-3) = (-3,2)

Check the dot products of the direction vectors of adjacent sides to confirm right angles:

AB · BC = (2)(3) + (3)(-2) = 6 - 6 = 0

BC · CD = (3)(2) + (-2)(3) = 6 - 6 = 0

CD · DA = (2)(-3) + (3)(2) = -6 + 6 = 0

DA · AB = (-3)(2) + (2)(3) = -6 + 6 = 0

Use the distance formula to confirm equal lengths of opposite sides:

AB = √((4-2)² + (8-5)²) = √(13)

CD = √((7-5)² + (6-3)²) = √(13)

BC = √((7-4)² + (6-8)²) = √(13)

DA = √((2-5)² + (5-3)²) = √(13)

Since all adjacent sides are perpendicular and opposite sides are of equal length, the quadrilateral is a rectangle.

Answer:

x = - 3 is extraneous

Step-by-step explanation:

Given

[tex]\sqrt{x+7}[/tex] - 1 = x  ( add 1 to both sides )

[tex]\sqrt{x+7}[/tex] = x + 1 ( square both sides )

x + 7 = (x + 1)² ← distribute right side

x + 7 = x² + 2x + 1 ( subtract x + 7 from both sides )

0 = x² + x - 6 ← in standard form

0 = (x + 3)(x - 2) ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 2 = 0 ⇒ x = 2

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions.

x = - 3 : [tex]\sqrt{-3+7}[/tex] - 1 = [tex]\sqrt{4}[/tex] - 1 = 2 - 1 = 1 ≠ - 3

x = 2 : [tex]\sqrt{2+7}[/tex] - 1  = [tex]\sqrt{9}[/tex] - 1 = 3 - 1 = 2

x = 2 is a solution and x = - 3 is extraneous

Good morning ☕️

____________________

Step-by-step explanation:

Look at the photo below for the answer.

:)

Answer:

Input

Independent variable

Step-by-step explanation:

we know that

Independent variables, are the values that can be changed or controlled in a given model or equation

Dependent variables, are the values that result from the independent variables

we have the function

[tex]d(t)=50t[/tex]

In this problem

The function d(t) represent the dependent variable or the output

The variable t represent the independent variable or input

Answer:

input and independet variable                                        

Step-by-step explanation:

[tex]\huge\boxed{\text{A.}\ x=-3}[/tex]

Start by subtracting [tex]2x[/tex] from both sides of the equation. Our goal is to isolate the variable. [tex]5+4x=-7[/tex]

Now, subtract [tex]5[/tex] on both sides. [tex]4x=-12[/tex]

Finally, divide both sides by [tex]4[/tex]. [tex]x=\boxed{-3}[/tex]

Answer:

A. x = -3

Step-by-step explanation:

5 + 6x = 2x - 7

5 + 7 = 2x - 6x

12 = -4x

12/-4 = x

-3 = x

Answer:

240 liters

Step-by-step explanation:

because the tank holds 240 liters so if it's full then it will be the same

In the tank, there are 240 liters of water, as mentioned in the given condition. Option A is correct.

Given that

A tank holds 240 liters of water.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
As mentioned in the condition the tank can hold 240 liters of water, so as of the given data when the tank is full there can only be 240 liters of water.

Thus, In the tank, there are 240 liters of water, as mentioned in the given condition. Option A is correct.

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Answer:

Step-by-step explanation:

Answer:

the new height will be:

d.168 inches

Answer:

168 inches

Step-by-step explanation:

Answer:

5x^2 − 2x

Step-by-step explanation:

Let's simplify step-by-step.

=3x + 6x^2 + − 5x + − x^2

Combine Like Terms:

=3x + 6x^2 + − 5x + − x^2

=( 6x^2 + − x^2 ) + ( 3x + − 5x )

= 5x^2 + − 2x

Answer:

5x^2 − 2x

hope this helps!!

Answer:

it will take 80 minutes

Step-by-step explanation:

Total no.of rows=10

Time taken to plant 3 rows = 24 min

So,find time taken for planting 1 row

which is =24/3=8min

total time taken to plant 10 rows=8×10=80min

so it takes 80 min to plant 10 rows

It takes 8 minutes to plant one row of the garden and therefore to plant all 10 rows, it will take a total of 80 minutes.

This question is asking for the total time it would take to plant a garden with 10 rows of vegetables if it took 24 minutes to plant the first 3 rows. First, we need to understand how long it takes to plant one row. To find this out, we divide the total amount of time (24 minutes) by the number of rows planted in that time (3 rows). This gives us how long it takes to plant one row: 24 minutes ÷ 3 rows = 8 minutes per row. Now that we know this, we can work out how long it would take to plant all 10 rows. We do this by multiplying the time it takes to plant one row (8 minutes) by the total number of rows we need to plant (10 rows). This gives us the total time: 8 minutes per row x 10 rows = 80 minutes. So, it would take 80 minutes to plant all 10 rows of the garden.

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First, 12.6 times 9 is 113.4. So withouth the space, that is how long the busses are. Then you do 2meters times 8 is 16 meters between the busses. 113.4+16 equals 129.4, the final answer.

Answer:  The total length from the front of the first bus to the end of the last bus is 129.4 meters.

Step-by-step explanation:

Hi, to answer this question we have to multiply:

The number of buses by the length of each one

The number of spaces between buses by the length of each space.

Since there is no space in front of the first bus and behind the last bus, there are 8 spaces in between.

Feel free to ask for more if needed or if you did not understand something.  

Answer:

no. it is not because 0.6 is a decimal

The other number could be 6. The GCF of 6 and 24 is 6, and 6 is less than 30.

Answer:

1/9

Step-by-step explanation:

multiple the two top numbers then multiple the bottom numbers which equals 2/18 and in other forms is 1/9

Answer:

x = 10

Step-by-step explanation:

collect like terms, so add 5 to both sides: 2x = 20

divide both sides by 2 to get the value of x: x = 10

Answer:

x=10

Step-by-step explanation:

first, add 5 to both sides. the -5 and +5 cancel out, and 15 + 6 is 20. 2x=20. now divide 2 on both sides. the 2s cancel out and 20/2 is 10, so x=10.

Answer:

[tex]2^3(2^4)=2^{3+4}=2^7=2(2)(2)(2)(2)(2)(2)[/tex]

Step-by-step explanation:

You can write 2 as a factor of [tex]2^3 \times 2^4[/tex] 7 times

The given expression can be written mathematically as:

[tex]2^3 \times 2^4[/tex]

We can simplify the expression by using the rule of indices shown below:

[tex]a^b \times a^b = a^{b+c}[/tex]

Applying the rule above to the given expression:

[tex]2^3 \times 2^4\\\\2^{3+4}\\\\2^7[/tex]

Therefore [tex]2^3 \times 2^4 = 2^7[/tex]

You can write 2 as a factor of [tex]2^3 \times 2^4[/tex] 7 times

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Answer:

8ft.

Step-by-step explanation: If you are finding he area, 2 times 4 equals 8, so the answer would be 8 feet.

Answer:

-12

Step-by-step explanation:

3(x-4)+2x^2

when x =5 , sub 5 into x

3(5-4)+2(5)-(5)^2

=15-12+10-25

=-12

Answer:

Step-by-step explanation:

3(x-4)+2x-x^2 first you should eliminate the parentheses

3x-12+2x-x^2 now replace x for 5

3(5)-12+2(5)-(5)^2

15-12+10-25

-12

Answer:

60 cm

Step-by-step explanation:

Parallelogram ABCD is shown in attached diagram. The diagonals of the parallelogram bisect each other, so

AE = EC

BE = ED

Ib DE = 3y + 6 cm, BE = 5y - 10 cm, then

[tex]3y+6=5y-10\\ \\3y-5y=-10-6\\ \\-2y=-16\\ \\2y=16\\ \\y=8\ cm[/tex]

Now, EC = 2y + 4, so

[tex]EC=2\cdot 8+4=16+4=20\ cm[/tex]

Since AE = EC, then AE = 20 cm

The brace that connects points B and D has the length

[tex]BD=BE+ED=3y+6+5y-10=8y-4=8\cdot 8-4=64-4=60\ cm[/tex]

The brace that connects points A and C has the length

[tex]AC=AE+EC=20+20=40\ cm[/tex]

Answer:

60cm

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

d=1/2

Step-by-step explanation:

9(8d-5)+13=12d-2

1) Use the distributive property:

72d-45+13=12d-2

2) Combine alike terms:

72d-32=12d-2

3) Add 32 to both sides:

72d=12d+30

4) Subtract 12d on both sides:

60d=30

5) Divide both sides by 60:

d=30/60

6) Simplify 30/60 to 1/2

Answer:

25.

Step-by-step explanation:

2/3 of 300 is 200

1/4 of 300 is 75

Answer:

25

Step-by-step explanation:

2/3 of 300 is 200  

1/4 of 300 is 75

Answer:

For points :  (2, 12) and (6, 11)

, option A. is correct.

For points : (6, –1) and (–3, –1), option B. is correct

Step-by-step explanation:

We are given points in both the questions and we need to find the slope.

Slope refers to steepness of curve .It is basically change in y with change in x.

For two points [tex]P\left ( x_1,y_1 \right )\,,\,Q\left ( x_2,y_2 \right )[/tex], slope of line PQ is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

For points : (2, 12) and (6, 11)

Let [tex]P\left ( x_1,y_1 \right )=(2, 12)\,,\,Q\left ( x_2,y_2 \right )=(6, 11)[/tex],

Slope is [tex]\frac{11-12}{6-2}=\frac{-1}{4}[/tex] i.e, - 1 over 4

So, option A. is correct.

For points : (6, –1) and (–3, –1)

Let [tex]P\left ( x_1,y_1 \right )=(6, -1)\,,\,Q\left ( x_2,y_2 \right )=(-3, -1)[/tex]

Slope is [tex]\frac{-1+1}{-3-6}=\frac{0}{-9}=0[/tex]

So, option B. is correct

The required slope of the lines with the given coordinates are as follow,

For first line option A. -1/4

For second line option B.0.

For the first set of coordinates of the line,

Points  are (2, 12) and (6, 11)

let (x₁ , y₁ ) = (2, 12 )

( x₂ , y₂ ) = (6, 11 )

Slope of the line for the two coordinates (x₁ , y₁ ) = (2, 12 ) and

( x₂ , y₂ ) = (6, 11 ) is equal to

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substitute the value ,

m = ( 11 - 12 ) / ( 6 - 2 )

   = -1 / 4

For the second set of coordinates of the line,

Points  are (6, -1) and (-3, -1)

let (x₁ , y₁ ) = (6, -1 )

( x₂ , y₂ ) = (-3, -1 )

Slope of the line for the two coordinates (x₁ , y₁ ) = (6, -1 ) and

( x₂ , y₂ ) = (-3, -1 ) is equal to

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substitute the value ,

m = ( -1 - (-1) ) / ( -3 - 6 )

   =0 / -9

   = 0

Therefore, slope of the lines are option A. -1/4 and option B.0.

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Answer:

number of servings = 5 servings

Explanation:

We are given that each serving is 3/10 of a pint. To know the number of servings of 1.5 pints, we will simply use cross multiplication as follows:

1 serving ....................> 3/10 pint

?? servings ................> 1.5 pints

number of servings = (1.5*1) / (3/10)

number of servings = 5 servings

Hope this helps :)

Answer:

11/2-3/4

11-6/2=5/2

Step-by-step explanation:

Answer:

x = - 7, x = 1

Step-by-step explanation:

Given

x² + 6x = 7

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(3)x + 9 = 7 + 9

(x + 3)² = 16 ( take the square root of both sides )

x + 3 = ± [tex]\sqrt{16}[/tex] = ± 4 ( subtract 3 from both sides )

x = - 3 ± 4

x = - 3 - 4 = - 7

x = - 3 + 4 = 1

Solution set = { - 7, 1 }

88.6 as a mixed number is 14 2/3

Answer:

4700

Step-by-step explanation:

4 thousands = 4000

7 hundreds = 700

Add those numbers together and you get 4700

Hope this helps

-615

I'm assuming you meant this. (6*7) - (3^2) *(9+4^3)

(42) - (3^2) * (9+4^3)

(42) - (9) * (9+4^3)

(42) - (9) * (9+64)

(42) - (9) * (73)

42 - 657

-615

Hope this helps!

Answer:

divide it using a calculator

Answer:

Step-by-step explanation:

0.65 is your answer