Write the equation of each parabola in vertex form

Write The Equation Of Each Parabola In Vertex Form

Answers

Answer 1

Answer: 9. y=[tex](x+4)^2-3[/tex]

10. y=[tex]-(x-5)^2+5[/tex]

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

12. y=[tex]x^2-3[/tex]  or y=[tex](x-0)^2-3[/tex]

Step-by-step explanation:


Related Questions

Using Pythagoras' Theorem please solve it.​

Answers

[tex] \huge\underline\mathcal{Answer \: - }[/tex]

Pythagoras theorem states that the square of hypotenuse equals the sum of square of other two sides.

therefore ,

[tex](25) {}^{2} = (x + 3) {}^{2} + 4 { }^{2} (x + 2) {}^{2} \\ \\ \longrightarrow \: 625 = x {}^{2} + 9 + 6x + 16(x {}^{2} + 4 + 4x) \\ \\ \longrightarrow \: 625 = x {}^{2} + 9 + 6x + 16x {}^{2} + 64x + 64 \\ \\ \longrightarrow \: 625 = 17x {}^{2} + 70x + 73 \\ \\ \longrightarrow \: 17x {}^{2} + 70x + 73 - 625 = 0 \\ \\ \longrightarrow \: 17x {}^{2} + 70x - 552 = 0[/tex]

now using quadratic formula ,

[tex]x = \frac{ - b \: \pm \: \sqrt{b {}^{2} - 4ac} }{2a} \\ [/tex]

here , a = 17 , b = 70 , c = -552

substituting the values in the equation above ,

[tex]x = \frac{70 \: \pm \: \sqrt{70 {}^{2} - 4(17)( - 552)} }{2 \times 17} \\ [/tex]

after simplifying we get ,

[tex]\boxed{x = 4} \: \: or \:\boxed{ x = \frac{ - 138}{7} } \\ [/tex]

since length can't be negative , therefore the other value will be neglected and hence ,

[tex]\boxed{value \: of \: x \: = \: 4 \: cm}[/tex]

hope helpful ;-;

Answer:   x = 4

======================================================

Work Shown:

As you mentioned, we'll use Pythagoras' Theorem aka Pythagorean Theorem.

[tex]a^2+b^2 = c^2\\\\(x+3)^2+(4(x+2))^2 = 25^2\\\\(x+3)^2+16(x+2)^2 = 625\\\\(x^2+6x+9)+16(x^2+4x+4) = 625\\\\x^2+6x+9+16x^2+64x+64 = 625\\\\17x^2+70x+73 = 625\\\\17x^2+70x+73-625 = 0\\\\17x^2+70x-552 = 0\\\\[/tex]

Next, we'll use the quadratic formula with a = 17, b = 70, c = -552.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-70\pm\sqrt{(70)^2-4(17)(-552)}}{2(17)}\\\\x = \frac{-70\pm\sqrt{42436}}{34}\\\\x = \frac{-70\pm206}{34}\\\\x = \frac{-70+206}{34} \ \text{ or } \ x = \frac{-70-206}{34}\\\\x = \frac{136}{34} \ \text{ or } \ x = \frac{-276}{34}\\\\x = 4 \ \text{ or } \ x \approx -8.1176\\\\[/tex]

Ignore the negative x value solution. The sides (x+3) and 4(x+2) will be negative values if we plugged in x = -8.1176, but negative side lengths do not make sense.

This makes x = 4 the only possible solution.

----------------

If x = 4, then,

vertical leg = x+3 = 4+3 = 7horizontal leg = 4(x+2) = 4*(4+2) = 4*6 = 24

This is a 7-24-25 right triangle.

We can confirm this using the pythagorean theorem

[tex]a^2+b^2 = c^2\\\\7^2+24^2 = 25^2\\\\49+576 = 625\\\\625 = 625 \ \ \ \checkmark[/tex]

Choose the statements that are true about a cube with side length 1 unit.
It has a volume of 6 cubic units.
It has a volume of 1 cubic unit.
It has a volume of 3 cubic units.
It is called a "one block."
It can be used to measure volume.
It is called a "unit cube."

Answers

The answer to the mentioned statement are :

first statement is WRONG

the second statement is RIGHT

The third statement is also WRONG

the fourth statement is RIGHT

fifth statement is RIGHT

sixth statement is WRONG

The side of the given cube is 1 unit.

This means that the Length= Breadth = Height = 1 unit because it is cube

This means that the volume can be described as

( side ) ³

that is 1 × 1 × 1 = 1 cubic unit

thus the first statement is WRONG

However the second statement is RIGHT

The third statement is also WRONG

since it is a cube whose volume is 1 cubic unit

thus we can say that it is one block

Thus the fourth statement is RIGHT

fifth statement is RIGHT

sixth statement is WRONG

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what is 0.4111111… as a fraction

Answers

So there is a method to do this problem
Take 0.41111... as x
Thus 10x = 4.11111... and 100x= 41.1111...

=> 100x - 10x = 41.1111... - 4.111111
=> 90x=37
=> x= 37/90
=> 0.4111... = 37/90

please help need this asap!!!!! PLEASE SOMEONE ANSWER I WILL GIVE EXTRA POINTS!!!

Answers

The area of the circles are as follows:

254.34 km²1962.5 mm²379.94 m² 907.46 cm²

How to find area of a circle?

The area of a circle can be found as follows;

area of a circle = πr²

where

r = radius

Therefore,

a.

area of the circle = πr²

diameter = 18km

r = 18 / 2

r = 9 km

Hence,

area of the circle = πr²

area of the circle = 3.14 × 9²

area of the circle = 254.34 km²

b.

area of the circle = 3.14 × 25²

area of the circle = 3.14 × 625

area of the circle = 1962.5 mm²

c.

area of the circle = 3.14 × 11²

area of the circle = 3.14 × 121

area of the circle = 379.94 m²

d.

area of the circle = 3.14 × 17²

area of the circle = 3.14 × 289

area of the circle = 907.46 cm²

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A 100ml tub of ice cream costs £1.50. Work out how much 500ml tub of ice cream would cost.

Answers

Answer:

Answer: 7.5 or 7 1/2.

If x is a positive integer, this expression is equivalent to what?

Answers

Given:

[tex]\text{ Th expression is }4x^{\frac{1}{2}},\text{ x is a positive integer.}[/tex]

Required:

Which option is equivalent?

Explanation:

The equivalent for is

[tex]\begin{gathered} =4x^{\frac{1}{2}} \\ =4\sqrt{x} \end{gathered}[/tex]

Answer:

Option B is correct answer.

0.8-2x=-1.4

Solve for x

Answers

Answer:

x= -0.3

Step-by-step explanation:

0.8-2x=1.4 Set up equation

-2x=1.4-0.8  Put Like terms together

-2x=0.6       Subtract like terms

x=0.6/-2     Divide

x=-0.3        Answer

Of 85 entries in the parade, 19 were
marching bands. How many entries were
not marching bands?

Answers

The answer is 66. Do 85-19 to get the answer

please help me solve this

Answers

It is to be noted that:

The current total bid for Empire design is $3,060,000The current total bid for Build-EM-UP-CO is $ 3,120,000.

What is a bid?

Bidding is an individual or business's offer to establish a price for a product or service or a demand that something be done. Bidding is a method of determining the price or worth of something. Bidding may be done by a person who is influenced by a product or service in a given setting.

The calculations are given as follows:

Given:
Proposal of Empire design:

$30000 x b

$ 60000/ I beam

Proposal of Build-EM-UP-CO.

$32000 x b

$ 40000/ I beam

Empire Design

Since b = 9ft; and number of I beams = 6, Hence

Total bid = (300,000 * 9) + (60,000 * 6)

= $3,060,000

Build-EM-UP-CO.

Recall that b = 9ft; and number of I beams = 6, Hence

Total Bid = (320,000 * 9) + (40,000 * 6)
Therefore,
Total bid = $3,120,000.

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Full Question:

For full details of the question, see the attached image

Please help me find out what 758x92 is

Answers

Answer:69736

Step-by-step explanation:

69,736

is the answer

Express each phrase as a rate and unit rate.
(Round your answer to the nearest hundredth.)
1) 7 calculators cost $120.00

Answers

Answer:

$100.00

Step-by-step explanation:

5 and above ex: 150 =200 140=100 under 5 keep the first letter then turn the other numbers into 0's 5 and above make the first number go up one then turn the rest of the numbers in to 0's

"-2+8" > "-2" heeeeelpp

Answers

Answer: Yes this equation means 6 is greater than -2, making this a true statement if that was what you're asking for.

3 movie tickets cost $36. At this rate, what is the cost per ticket?​

Answers

The cost per ticket is $12!

Answer:

12

Step-by-step explanation:

36 divided by 3 is 12

Which system is responsible for carrying this oxygen to the muscles?

Answers

Answer:

The circulatory system

Step-by-step explanation:

Is this math? lol

:]

find the area. please explain how to get it​

Answers

Answer:

Step-by-step explanation:
(the small double lines like = means that the length of those sides are all same)
So, if one length is considered as x
     the other two will also be x
      we see that the length of one side is given which is 27
      to find x
      x + x + x = 27
        3x = 27
    so, x = 27/3
          x = 9m

(the small vertical single line means that those sides are equal)
so if one side is y, the other two are also y
so , y + y+ y = 30
       3y = 30
       y = 10m

If we imagine the stairs to be made of small rectangles of length 10m and base 9m , finding area will be easier.
we will see that there are 9 rectangles in total
area of rectangle = length x base
so, area of 1 rectangle = 9x10
                                       = 90
[tex]m^{2}[/tex]
so area of 9 identical rectangles = 9 x 90
                                                      = 810 [tex]m^{2}[/tex]

What is the answer to f(2)=

Answers

the answer is 2f

Re-order terms so constants are on the left

f×2=2f

(Can anyone answer this please? I need it ASAP!!) A2B3C4 (in hexadecimal) - 3F2E1D (in hexadecimal) = ______________

Answers

The hexadecimal value from the operation is 6385A7

Hexadecimal Numbers

To solve this problem, we have to subtract the hexadecimal numbers from one another.

In doing so, we would subtract 3F2E1D from A2B3C4.

This would give us,

[tex]A2B3C4 - 3F2E1D = 6385A7[/tex]

The value of the expression is 6385A7.

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NAME
DATE
PERIC
Lesson 3: More about Constant of Proportionality
Cool Down: Fish Tank
Mai is filling her fish tank. Water flows into the tank at a constant rate. Complete the table
as you answer the questions.
1.
How many gallons of water will be in the fish tank after 3 minutes? Explain your
reasoning.
2.
How long will it take to fill the tank with 40 gallons of water? Explain your reasoning
3. What is the constant of proportionality?

Answers

The ratio of one variable quantity to another that is always constant and to which it is proportional is known as the constant of proportionality then the constant of proportionality exists r = 1.6.

What is meant by constant of proportionality?

The ratio of one variable quantity to another that is always constant and to which it is proportional is known as the constant of proportionality.

Given

x            y

0.5.     0.8

1.         1.6

3.        4.8

25.       40

To estimate the constant of proportionality uses the following formula:

y = r x

Where r is the constant of proportionality;

Simplify the value of r, we get

r = y/x

Substitute the values of x = 0.5 and y = 0.8, in the above equation then

r = 0.8/0.5

r = 1.6

When x = 1 ; y = 1.6

r = 1.6/1

r = 1.6

When x = 3; y = 4.8

r = 4.8/3

r = 1.6

When x = 25 ; y = 40

r = 40/25

r = 1.6

The value of r exists constant.

Therefore, the constant of proportionality exists r = 1.6.

The complete question is:

Mai is filling her fish tank. Water flows into the tank at a constant rate. Complete the table and answer the question below.

time (minutes) water (gallons)

0.5 0.8

1

3

40

What is the constant of proportionality?

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please show work out


find the dimension of A34×b41 matrix]

Answers

A34 should represent either a square matrix with number of columns=number of rows =34 or the 4th element in the 3rd row in the matrix A [which is not possible in the given matrix since each row has only 3 elements]

The dimension of a matrix is given as (the number of rows it has, say a) x (the number of columns it has, say b) [read as a by b].. The given matrix has 4 rows and 3 columns, so its dimension is 4x3.

For a matrix A of dimension axb to be multiplied with a matrix B of dimension cxd, the number of columns of matrix A should be equal to the number of rows of matrix B, that is b = c should be satisfied. In this case both matrices are of the same dimension 2x3 but 3 (number of columns in first matrix) is not equal to 2 (number of rows in second matirx). So these matrices cannot be multiplied as their dimensions do not match.

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Find the equation of the line that contains the point (-1,-6) and is parallel to the line 4x + 7y=11. Write the equation in slope-intercept form, if possible.
answer box to complete your choice.

Answers

Answer:

y = -4/7x - 46/7

Step-by-step explanation:

4x+7y=11

7y=11-4x

y=-4/7x + 11/7

Slope or parallel line: -4/7

Point=(-1,-6)

y+6 = -4/7(x+1)

y = -4/7x - 46/7

:]

In the figure ZX = 2x + 1 YW = 3x - 1 and YX = 1, find perimeter of VYZ

Answers

The perimeter of triangle VYZ is 12 units.

How to find the perimeter of a triangle?

The perimeter of a triangle is the sum of the whole sides of the triangle.

In other words, the perimeter of a triangle is the total distance covered by its boundaries or the sides.

Therefore,

perimeter of ΔVYZ = VY + ZY + ZV

Therefore,

VY  =  ZY = ZV = XW

Hence,

YW = YX + XW

Therefore,

XW = YW - YX

YW  = 3x - 1

YX = 1

Hence,

XW = 3x - 1 - 1

XW = 3x - 2

Therefore,

perimeter of ΔVYZ = 3x - 2 + 3x - 2 + 3x - 2

perimeter of ΔVYZ = 9x - 6

ZX = YW

2x + 1 = 3x - 1

2x - 3x = - 1 - 1

-x = -2

x = 2

Therefore,

perimeter of ΔVYZ = 9(2) - 6

perimeter of ΔVYZ = 18 - 6

perimeter of ΔVYZ = 12 units

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A =
h(a + b)/2 solve for b

Answers

Answer: b = (−ah+2a)/h

Step-by-step explanation:

Step 1: Flip the equation.

Step 2: Add (-1)/2ah to both sides.

Step 3: Divide both sides by h/2.

The answer is B= 2A/H-a

Which numbers I have to put in the boxes

Answers

where’s the problem

Question 5Which of the following is equivalent to (2 – 2) (x - 1)

Answers

[tex]\begin{gathered} (x-2)(x-1)=x^2-x-2x+2=x^2-3x+2 \\ \end{gathered}[/tex]

Question
Solve 2y−18x=−26 for y.

Answers

Answer:

-26

Step-by-step explanation:

What is the equation of the line that passes through the point (−3,1) and has a slope of −3?

Answers

y=-3x-8
step-by-step explanation:
see image (also use some of my explanation from my previous answer)

What is the solution set of the following equation?
-8x + x + 15 = -7x + 12

a. Ø
b. {all reals}
c. {1/7}

Answers

Answer:

A

Step-by-step explanation:

(-8x  +  x) + 15  = -7x +12

   -7x    +15 = -7x + 12

      15 = 12          There are no solutions

A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment of $456. What was the simple interest rate of the bonds?

Answers

5.7%

Explanaton:

let amount invested = Principal = $8000

time = 1 year

rate = ?

Interest = $456

To get the rate, we'll apply simple interest formula:

[tex]\begin{gathered} I\text{ = PRT} \\ I\text{ = interest, P = principal, R = rate, T = time} \end{gathered}[/tex][tex]\begin{gathered} 456\text{ = 8000}\times R\times1 \\ 456\text{ = 8000R} \\ \text{divide both sides by 8000:} \\ \frac{456}{8000}\text{ =}\frac{8000R}{8000} \\ \\ R\text{ = 0.057} \\ In\text{ percent, rate = 0.057}\times100 \\ \text{Rate = 5.7\%} \end{gathered}[/tex]

Hence, the simple rate of the bonds is 5.7%

You invested $101 and received $106.05 after one year. What was the interest rate?

Answers

The rate of interest was 5%.

The rate of interest and simple interest can be related through the formula -

S.I. = PRT/100, where S.I. stands for simple interest, P stands for principal, R stands for rate of interest and T stands for time.

Amount = Principal + Interest

Interest = 106.05 - 101

Performing subtraction on Right Hand Side of the equation

Interest = $5.05

Rate of interest = (5.05×100)/(101×1)

Performing multiplication in numerator and denominator

Rate of interest = 505/101

Performing division

Rate of interest = 5

Therefore, to earn $106.05 from $101 in one year, the rate of interest should be 5%.

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Which is larger, 52 or 33?​

Answers

Answer:

52

Step-by-step explanation:

52 is a bigger number than 33?

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