What is the first step when rewriting y = –4x2 + 2x – 7 in the form y = a(x – h)2 + k?
2 must be factored from 2x – 7
–4 must be factored from –4x2 + 2x
x must be factored from –4x2 + 2x
–4 must be factored from –4x2 – 7

Answer:

y = [tex]\frac{3}{2}[/tex] x + 7

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y - 8 = - [tex]\frac{2}{3}[/tex] (x + 5) ← is in point- slope form

with m = - [tex]\frac{2}{3}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{3} }[/tex] = [tex]\frac{3}{2}[/tex]

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept ) , then

y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

to find c substitute (- 6, - 2 ) into the partial equation

- 2 = - 9 + c ⇒ c = - 2 + 9 = 7

y = [tex]\frac{3}{2}[/tex] x + 7 ← equation of line K

The equation of the perpendicular line in the slope-intercept form will be y = (3/2)x + 7.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given as,

y - 8 = -2/3(x+5)

The equation of the line that is perpendicular to the line y - 8 = -2/3(x+5) is given as,

y = 3/2x + c

The line is passing through (-6, -2), then we have

-2 = 3/2(-6) + c

-2 = -9 + c

c = 7

The equation of the perpendicular line in the slope-intercept form will be y = (3/2)x + 7.

More about the equation of a perpendicular line link is given below.

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Answer:

1.9998 inches = radius

Step-by-step explanation:

V=(4/3)πr³

33.5 = (4/3)πx³

33.5 * 3/4 = (4/3)πx³(3/4)

25.125 / π = (πx³) / π

[tex]\sqrt[3]{7.998}[/tex] = [tex]\sqrt[3]{x^3}[/tex]

1.9998 = x

to check what type of conic it may be, we first check the squared variables, their coefficents and sign.

in this case 2x² and 5y² are both positive, that means we have either an ellipse or a circle.

if the coefficients are equal, boinggggg! we have a circle, or if you wish an ellipse with equal axes.

if the coefficients are different, like in this case, we have an ellipse.

Answer:

photo

Step-by-step explanation:

Answer:

x < 10

Step-by-step explanation:

the dot isn't colored in, meaning that x could not equal 10, and the graph goes left, meaning that x is less than 10.

Answer:

x<10

Step-by-step explanation:

Since the inequality doesn't have the circle filled in it is not a less than or equal to and since this is on the 10 this would be x<10

Answer:

Answer for 1

3. 21,356 x one half

Answer for 2

1. A and C

Step-by-step explanation:

Hello there!

In order to solve this inequality, we should first use the distributive property:-

3(a-4)≥4(a+5)

3a-12≥4a+20

Now, add 12 to both sides:-

3a≥4a+32

Subtract 4a from both sides:-

3a-4a≥32

-a≥32

Divide both sides by -1:-

a≤-32

The inequality sign changed because we divided both sides by a negative number.

[tex]\mathcal{NOTE:-}[/tex]

I hope everything is clear; however, if you need any explanation or clarification, don't hesitate to let me know, and I will comment or edit my answer. Good luck and have a great rest of your day! :)

The volume of 3 of shipping containers 267.75 cubic yards.

We need to find the volume of one shipping container and then multiply it by 3 to find the volume of three shipping containers.
Find the volume of one shipping container.
Volume = Base Area × Height
Volume = 25.5 square yards × 3.5 yards
Calculate the volume.
Volume = 89.25 cubic yards
Find the volume of three shipping containers.
Total Volume = Volume × Number of Containers
Total Volume = 89.25 cubic yards × 3
Calculate the total volume.
Total Volume = 267.75 cubic yards.

For similar question on volume.

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     You commented that part of the instruction included "If the theorem cannot be applied, explain the reason."

     The theorem cannot be applied. Since this is not a right triangle, we cannot solve using the Pythagorean Theorem unless we are given a height. If we have the height of this triangle, then we can break it into two different right triangles and solve.

What is a right triangle? A right triangle is a triangle that has an angle measurement of 90 degrees.

       In summary, this is an isosceles triangle and the Pythagorean Theorem only applies to right triangles.

Answer:

Step-by-step explanation:

Answer A represents an exponential equation; see below for a demo.

In Answer A we have (1, 3), (2, 3²), (3,3³)

Answer: 12

Step-by-step explanation:

Start with 90/10 which gets you 9

Then add 3 and 9 which is 12

Answer:

12

Step-by-step explanation:

Order of operations says to do the division first

90/10 = 9

Then add the rest

9+3 = 12

Answer:

90 degrees

Step-by-step explanation:

a triangles angles add up to 180

this means that you can add all the angles together and get 180

you can first add 30 and 60 and then subtract the sum from 180

30 + 60 = 90

180 - 90 = 90

the last angle is 90 degrees

Hey ! there

Answer:

Step-by-step explanation:

In the question we are given with two angles of the triangles that are 30° and 60° . And we are asked to find the third angle of triangle .

For solving this question we must have knowledge of angle sum property which says that the sum of all the angles which are present inside the triangle ( interior angles ) is equal to 180°.

Solution : -

As we know that ,

So ,

[tex] \longmapsto \qquad \: 30° + 60° + x° = 180°[/tex]

Step 1 : Adding 30° and 60° :

[tex] \longmapsto \qquad \:90° + x° = 180° [/tex]

Step 2 : Subtracting 90° from both sides :

[tex] \longmapsto \qquad \: \cancel{90°} - \cancel{90 ° } + x° = 180° - 90° \: [/tex]

On further calculations , We get :

[tex] \longmapsto \qquad \: \blue{\underline{\boxed{\frak{x° = 90°}}}}[/tex]

Verifying : -

Now we are verifying our answer by adding all the angles of triangle and equating them with 180° because of angle sum property. So ,

Therefore, our solution is correct .

Answer:

N/a^3/2

Step-by-step explanation:

loga(N/X)=3/2

N/X= a^3/2

X= N/a^3/2

Step-by-step explanation:

When subtracting logarithms with the same base, it is equivalent to combining them into one logarithm, then dividing the arguments inside:

[tex] log_{a}(n) - log_{a}(x) = log_{a}( \frac{n}{x} ) [/tex]

Then use the formula:

[tex] log_{a}( \frac{n}{x} ) = \frac{3}{2} [/tex]

[tex]{a}^{ \frac{3}{2} } = \frac{n}{x} [/tex]

[tex]x = n {a}^{ - \frac{3}{2} } [/tex]

Answer:

50% or 0.5

Step-by-step explanation:

Based on the given conditions, formulate: (5+11-2)÷28

Calculate the sum or difference: 16-2/28

Calculate the sum or difference: 14/28

Cross out the common factor: 1/2

get the result: 50% or 0.5

Answer: 50% or 0.5

The proportional relationship between (0,0) and (4,11) represents a direct variation

The equation that represents the graph is  y = 11x/4

The points on the graph are given as:

(x,y) = (0,0) and (4,11)

The equation of the graph is then calculated using:

y = (y₁/x₁) * x

This gives

y = (11/4) * x

Evaluate

y = 11x/4

Hence, the equation that represents the graph is  y = 11x/4

Read more about proportional relationships at:

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Answer:

Below.

Step-by-step explanation:

1 / secA+tanA =  1 / [1/cosA+sinA/cosA))]

= 1/ [(1 + sinA)/cosA]

= cosA/(1+sinA)

Now check if this is identical to 1-sinA/cosA:

1-sinA/cosA = cosA/(1+sinA)

Cross multiply:

(1-sinA)(1+sinA) = cos^2A

1 - sin^2A = cos^2A

sin^2A + cos^2A = 1  

This is a known idenity.

So the original identity is true.

Answer:

204, there is no remainder.

Step-by-step explanation:

Answer: 204 Rem 2

Step-by-step explanation: Use long division

Answer:

-2/3  is greater than  -0.8

Step-by-step explanation:

-2/3 when made into a decimal is about -0.67

This is greater than -0.8 because -0.67 covers less area when put into a visual.

Answer:

Convert -0.8 into a fraction or -2/3 into a decimal;

-2/3 in decimal form = -0.666...

Compare the two decimals;

-0.8 __ -0.666...

-0.8 < -0.666..., so -2/3 is greater.

Answer:

13πr/60 units

Step-by-step explanation:

Formula

Solving

The number of rotations for the new wheel will be  1,056 rotations

Let the initial circumference be 50 rotations  (assumed)

If the number of rotations of the circumference of the tires were increased by 20%, then the new circumference will be:

Ne circumference = 1.2 * 50 = 60

number of rotations for the new wheel = 63360/60
number of rotations for the new wheel = 1,056 rotations

Hence the number of rotations for the new wheel will be  1,056 rotations

Learn more on circumference here: https://brainly.com/question/20489969

Answer:

y=-2

Step-by-step explanation:

2x-2x=0

7y-8y=-y

4-2=2

-Y=2

Y=-2

Answer:

97 1/3 or 97.3333

Step-by-step explanation:

multiply 2 2/3 by 36 1/2

:)

Answer:

I got you with Question 3 and 4 my guy.

3) He would need 12 and it would cost 50k

4) 9% payments: $563.24, 7% payments: $494.75. Monthly savings: $69.49, 9% total repaid: $2022,764.90 , 7% total repaid: $148,423.63 , Savings: $54,341.27

The Tom will need to bring to the closing $54,341.27

He would need 12 and it would cost 50k.

We have given that,

Tom buys a condominium for $42,600.

He makes a down payment of 15% and pays these closing costs to survey $225.

The meaning down payment is a part of the full price paid at the time of purchase or delivery with the balance to be paid later.

Inspection, $110; mortgage fee, $852; legal fees, $450; title insurance, $286

9% payments: $563.24

7% payments: $494.75.

Monthly savings: $69.49

9% total repaid: $2022,764.90  

7% total repaid: $148,423.63

Savings: $54,341.27

To learn more about the savings visit:

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Step-by-step explanation:

side of square = 10

area of square = side² = 10² = 100 cm²

P.S : ARE YOU SURE THE OPTIONS ARE CORRECT ???

Answer:

A dollar is a whole amount and is written to the left of the decimal.

...

In 1 dollar there are 100 cents and we write them after a period:

1 cent of a dollar is written $0.01.

10 cents of a dollar is written $0.10.

1 dollar and 1 cent is written $1.01.

1 dollar and 10 cents is written $1.10.

Money Is a Special Decimal

All money is a decimal value with two places. You will see examples including $1.25, $65.98, and $26.34. No matter how big the value gets, you can only have two decimal places. One cent is 0.01.

Answer:

$292.00

Step-by-step explanation:

Total amount collected= number of people×amount per each person

total amount= 73×$4.00

Total amount collected=$292.00

Answer:

$292

Step-by-step explanation:

its really easy, you just multiply 73 to 4

Answer:

5.735

pythagorian theorem is a^2 + B^2 = c^2

C is the longest side of the right triangle

Answer:

its 10

Step-by-step explanation:

The reason its 10 is because it shows more 10 then any number

Length: 44 metre

Here given,

length = L

breadth = 12 metre

perimeter = 112 metre

Answer:

71.98

[tex]d=2\sqrt{ \frac{A}{\pi }} = 2 * \sqrt{\frac{4069.44}{\pi }}[/tex] ≈ 71.98175 rounded to hundred-thousandths