2
Find the equation of a parabola with a vertex at (2, 4) and a known point at (-5, 2).
f (x) =

Answers

Answer 1

Answer:

           f(x) =  -²/₄₉(x - 2)² + 4

Step-by-step explanation:

The vertex form of an equation of the parabola:  

                                                         f(x) = a(x - p)² + q

vertex is (2, 4)  so  p = 2,  q = 4

so:

   f(x) = a(x - 2)² + 4

the parabola goes through the point (-5, 2) so  x=-5,  f(x)=2

  2 = a(-5-2)² + 4

  - 2 = a(49)

    a = -²/₄₉

Therefore the equation of the parabola in vertex form:

f(x) = -²/₄₉(x - 2)² + 4


Related Questions

Write an equation of the line passing through point P(4,−6) that is perpendicular to the line y=−3.

x=

Answers

Answer:

ummm im sorry i will answer in the comments

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

if you plot y= -3 and the point (4,-6) you will see that the only answer can be x=4

Find the missing number in this sequence
1,0,1,1,0,1,_,1,0,1,1,1,1,0...

Answers

Answer- 1
Explanation- it start with a single 1 then two 1s then it would have to be three 1s then four 1s

Hope this helps :)

If it costs 13 dollars for 9 books, how much does 1 book cost?

Answers

Answer:

1.4444444444444

Step-by-step explanation:

Hope this helps

Answer:

$1.44

Step-by-step explanation:

Your ratio is 13 dollars PER 9 books.

Turn it into a fraction: 13/9

Then divide.

We get 1.444... which can be rounded to 1.44

-1 TIMES the ABSOLUTE VALUE of -24 =
will give brainliest !!!!!

Answers

Answer:

-24

Step-by-step explanation:

absolute value of -24 would make it +24

-1 times 24 is -24

Answer: -24

Step-by-step explanation:

The absolute value of a number is how far away the said number is from zero, so -24's would be 24.

24 x -1 = -24

Is it possible to have more than one (x,y)(x,y) pair that is a solution to both equations? Explain or show your reasoning

Here are the two equations:
Equation 1: 6x+4y=34
Equation 2: 5x-27=15

Answers

Answer with step-by-step explanation:

Yes, it is possible to have more that one (x,y) pair because of the distributive property.

6x + 4y = 34. If this is the case, we have to find 2 numbers that sum up to 34.

x = 3y = 4

5x - 27 = 15. If we are going to calculate this equation, you need to reverse the equation. 15 + 27 = 42 = 5x. If 42 = 5x, we have to divide 42 by 5, which is 8.4

Hope this helped! (brainliest please)

The high school decided to buy new uniforms for the girls' and boys' basketball teams. They plan to buy 35 uniforms with a total cost of $1,235. The store offers discounts based on the number of items the school buys, as shown. What will the discounted price be for the high school?​

Answers

Answer:

1049.75

Step-by-step explanation:

take 15% off of 1235 or 1235 divided by 15%

The discount will be 15% and the discounted price is $1049. 75

What is discount?

A discount is a price reduction you offer a customer. There are also other methods that you can use to attract customers.

Given:

price for 35 uniforms = 1235

as, there is 15% discount for the items 25- 49 items.

So, there is 15% discount for 35 uniforms

Thus, the discounted price is

=1235 (1- 15%)

=1235 (1- 0.15)

=1235 x 0.85

= $1049. 75

Hence, the discounted price is $1049. 75.

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What is the value of x, rounded to one decimal place?

Answers

Answer:

x ≈ 5.9

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 2.7² = 6.5²

x² + 7.29 = 42.25 ( subtract 7.29 from both sides )

x² = 34.96 ( take the square root of both sides )

x = [tex]\sqrt{34.96}[/tex] ≈ 5.9 ( to 1 dec. place )

I need help ASAP ... what’s is the position of A on the number line

Answers

Answer:

[tex]2 \frac{2}{5}[/tex]

Step-by-step explanation:

Each number is split into fifth the a is on the second line so it is [tex]2 \frac{2}{5}[/tex].

Solve the equation -3(c - 1) +7c =27

Answers

Answer:

c=6

Step-by-step explanation:

u simplify  it and u get

4c+3=27

4c=24

c=6

Answer:

c= 6

Step-by-step explanation:

We can use distributive property to solve the answer.

-3(c-1)+7c= 27

-3c+3+7c

4c+3= 27

    -3   -3

4c= 24

c= 6

Hope this helps!

what is the slope of the line that goes through (-5,5) and (5,-7)

Answers

Answer:

-1/5

Step-by-step explanation:

slope formula:

m = y₂ - y₁ / x₂ - x₁

Two points are given:

(-5, -5) (5, -7)

m = -7 - (-5) / 5 - (-5)

m = -2 / 10

m = -1/5

Answer

The answer is 0

here is a picture explanation

Step-by-step explanation:

The ratio between earths actual diameter and it’s scaled diameter can be used to find the scaled diameter of the other planets. Earths diameter of 12,756 kilometers is scaled to 3.5 centimeters as shown in the table. Now let’s find the scaled diameter of Mars as an example. Using the calculations shown, Mars diameter of 6,792 would be scaled to 1.9 centimeters. Use this same process to complete the table with the scaled diameters of the other planets. Round each answer to the tenths place.

Answers

Answer:

Mercury 1.3, Venus 3.3, Jupiter 39.2, Saturn 33.1, Uranus 14, Neptune 13.6

Step-by-step explanation:

The scaled diameter of each planet is:

Mercury - 1.3 cm

Venus - 3.3 cm

Jupiter - 39.2 cm

Saturn - 33.1 cm

Uranus - 14 cm

Neptune - 13.6 cm

Given,

The ratio between the earth's actual diameter and its scaled diameter can be used to find the scaled diameter of the other planets.

Earth's diameter of 12,756 kilometers is scaled to 3.5 centimeters as shown in the table.

Using the calculations shown, Mars's diameter of 6,792 would be scaled to 1.9 centimeters.

Use this same process to complete the table with the scaled diameters of the other planets.

Round each answer to the tenths place.

What does it mean to be in proportion?

If two given ratios are equal we say that the ratios are in proportion.

Example:

1/2 and 4/8 are in proportion.

- 1/2

- 4/8 = 1/2

We have,

Earths diameter = 12,756 km

It is scaled to 3.5 cm

The ratio is:

= 12,756 km /3.5 cm

Since each planet is in proportion with each planet.

We have,

Let the scaled diameter be d.

- Mercury d

12,756 / 3.5 = 4879 / d

d =  (4879 x 3.5) / 12756

d = 1.3 cm

- Venus d

12,756 / 3.5 = 12104 / d

d = (12104 x 3.5) / 12756

d = 3.3 cm

- Jupiter d

12,756 / 3.5 = 142984 / d

d = (142984 x 3.5) / 12756

d = 39.2 cm

- Saturn d

12,756 / 3.5 = 120,536 / d

d = (120536. x3.5) / 12756

d = 33.1 cm

- Uranus d

12,756 / 3.5 = 51118 / d

d = (51118 x 3.5) / 12756

d = 14 cm

- Neptune d

12,756 / 3.5 = 49, 528 / d

d = (49528 x 3.5) / 12756

d = 13.6 cm

Thus the scaled diameter of each planet is:

Mercury - 1.3 cm

Venus - 3.3 cm

Jupiter - 39.2 cm

Saturn - 33.1 cm

Uranus - 14 cm

Neptune - 13.6 cm

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Why is -2.2 x (-3.7) = -8.14 wrong ?? I need a reason to see why it’s wrong

Answers

it is a positive integer because there are 2 negatives. when you are multiplying or dividing negatives, it always makes a positive

If side AB is parallel to side DC, how are side A'B' and side D'C' related? Explain.

Answers

Side A’B’ and D’C’ are related because they are both parallel which I think means that they would be the same length

Carmelita Delpon is a social worker. The annual cost of Carmelita's family
health insurance is $10,019.40. The company pays 66% of the cost. How
much does she pay weekly for medical insurance? *
$125.78
$95.11
$65.51
$35.52

Answers

Answer:

the answer would be 65.51 hope it helps

Step-by-step explanation:

can someone help! i’m giving brainliest to the person person that’s right :)

Answers

Answer:

3.0 is your answer

Step-by-step explanation:

10 minutes per mile. Constant Speed.

A = bh; A = 16, h = 8
B=
Help please and thank you

Answers

Answer:

b has to be 2

Step-by-step explanation:

if a equals 16

h equals 8

then b would have to be 2 because 8x2 is 16

Answer:

B=2

Step-by-step explanation:

If A equals 16 after multiplying b and h together and h is 8 then b would be 2 since 8 times 2 is 16.    

50°
25°
12x-3
Find the x

Answers

Answer:

X=9

Step-by-step explanation:

We want to first understand that a triangle will always be 180°. Next, we want to look at both where 25° and 12x-3 are. If we look closely we can see that they are the vertical angles of the interior angles of the triangle. To solve this algebraically we have to basically add all the angles (including 12x-3) to solve for x.

Adding all the angles together would look like this: 25+50+12x-3. Next, add up all like terms to get 12x+72=180. You want to get x by itself by subtracting by 72 on both sides to get 12x=108. Isolate x by dividing by 12 on each side which results in x=9

Someone help me please!

Answers

Answer:

Ok: X = 9

Step-by-step explanation:

We have

3x + (15x + 18) = 180

or

18x+18 = 180

or

18(x+1) = 180

or

x + 1  = 180/18

or

x + 1 = 10

or x = 9.

Answer:

9

Step-by-step explanation:

3x+15x+18=180

-18.             -18

3x+15x=162

18x=162

/18.    /18

x=9

What are the values of x and y if this equation is true?

22(x + yi) + (28 + 4i) 72 – 62i

Answers

Answer:

x = 2

y = -3

Step-by-step explanation:

The given equation is,

22(x + yi) + (28 + 4i) = 72 - 62i

By solving this equation further,

22x + 22yi + 28 + 4i = 72 - 62i

(22x + 28) + (22y + 4)i = 72 - 62i

Now both the sides of the equation is in the form of complex number,

By comparing real and imaginary parts given on both the sides,

22x + 28 = 72

22x = 72 - 28

22x = 44

x = 2

22y + 4 = -62

22y = -62 - 4

22y = -66

y = -3

Therefore, x = 2 and y = -3 are the values for which the given equation is true.

Rewrite each of these statements so that negations appear only within predicates (that is, so that no negation is outside a quantifier or an expression involving logical connectives). a) ¬∃y∃xP (x, y) b) ¬∀x∃yP (x, y) c) ¬∃y(Q(y) ∧ ∀x¬R(x, y)) d) ¬∃y(∃xR(x, y) ∨ ∀xS(x, y)) e) ¬∃y(∀x∃zT (x, y, z) ∨ ∃x∀zU (x, y, z))

Answers

Answer:

Follows are the solution to the given point:

Step-by-step explanation:

In point a:

¬∃y∃xP (x, y)  

∀x∀y(>P(x,y))  

In point b:

¬∀x∃yP (x, y)

 ∃x∀y  ¬P(x,y)

In point c:

¬∃y(Q(y) ∧ ∀x¬R(x, y)) [tex]\equiv[/tex]  ∀y(> Q(y) V ∀ ¬ (¬R(x,y)))

∀y(¬Q(Y)) V ∃xR(x,y) )

In point d:

¬∃y(∃xR(x, y) ∨ ∀xS(x, y))  

∀y(∀x>R(x,y)) [tex]\wedge[/tex] ∃x>s(x,y))

In point e:

¬∃y(∀x∃zT (x, y, z) ∨ ∃x∀zU (x, y, z))

∀y(∃x ∀z)>T(x,y,z) [tex]\wedge[/tex] ∀x ∃z> V (x,y,z))  

Solve the system of equations without graphing. Explain or show your reasoning.

{2y=x−4
{4x+3y=5

Answers

Answer:

(2, -1)

Step-by-step explanation:

We can subtract x from both sides from the first equation, then multiply the first equation by 4, so it's easier to solve later:

-4x+8y = -16

4x+3y = 5

Then, we can add the 2 equations, so the x cancels out:

11y = -11

y=-1

Now, we can plug y as -1 to any of the equations above:

4x+3*(-1)=5

4x=8

x=2

Therefore, the solution to these 2 equations are (2, -1)

The value of the variables 'x' and 'y' will be 2 and negative 1, respectively.

What is the solution to the equation?

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of equations is given below.

x = 2y + 4             ...1

4x + 3y = 5          ...2

From equations 1 and 2, then we have

4(2y + 4) + 3y = 5

8y + 16 + 3y = 5

11y = - 11

y = -1

Then the value of 'x' is given as,

x = 2 (-1) + 4

x = - 2 + 4

x = 2

The value of the variables 'x' and 'y' will be 2 and negative 1, respectively.

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Solve the inequality. Q No. 1

-2(x - 5) < -x + 3

Answers

Answer:

x>7

Step-by-step explanation:

-2(x - 5) < -x + 3

-2x + 10 < -x + 3

-2x + x < 3 - 10

-x < -7

-x / -1 < -7 / -1

x > 7

Answer:

X < 7

Step-by-step explanation:

Do these ratios form a proportion?
16 bikes: 20 cars
36 bikes : 45 cars

Answers

Answer:

I think no. Maybe , it's right but I think the answer is no.


If 9 x 158 = 1,422, then

Answers

Is there more to the question?

Answer:

1422/ 9 = 158

1422/158 = 9

158*9=1422

Step-by-step explanation:


Estimate 135 to the nearest integer.

Answers

Answer:

Approx. 12

Step-by-step explanation:

The square root of 135 is 11.61895. Rounded to the nearest whole number (integer), it is 12.

Kim writes an estimate for the number 0.00436 as 4x10^3. Explain why this cannot be correct

Answers

Answer:

4x10^-3

Step-by-step explanation:

because it was in a deciaml, it has to be negative

The given estimate is not correct. The correct estimate will be 4.36 × [tex]10^{-3}[/tex].

It is given that Kim writes an estimate for number 0.00436 as 4 × 10 ³.

We have to find whether it is correct or not and why ?

What do you mean by decimal fraction ?

A decimal fraction is a number in which the denominator is a multiple of 10 i.e., 10, 100, 1000. etc.

As per the question ;

The decimal number given is 0.00436.

To represent the number in the form of power of 10 , we need to move the decimal 3 places towards right.

and

We know if we move decimal 3 places towards right we need to multiply the resulted number by 10 to the power -3 , i.e., [tex]10^{-3}[/tex]

So,

The correct estimate will be ;

= 4.36 × [tex]10^{-3}[/tex]

Thus , the given estimate is not correct. The correct estimate will be 4.36 × [tex]10^{-3}[/tex].

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What is the value of x?

Answers

Answer:

x=70

Step-by-step explanation

[tex]\\180-45=135\\\\135=2x-5\\add5\\140=2x\\divide2\\x=70[/tex]

<3

Red

Answer:

x=70

Step-by-step explanation:

45+ (2x-5)=180 ....... as they are same side interior angles.

2x+40=180

2x=140

x=70

hope i helped !!! :)

( if it is right, pls give brainiest)

Rewrite in simplest terms: -7(2u-6v)-7v-3(10v+u)

Answers

Answer:

-11u-65v

Step-by-step explanation:

1) Pemdas

-7(2u-6v)-7v-3(10v+u)

-14u-42v-7v-30v+3u

2)Combine Like Terms

-14u-3u        -42v-7v-30v

3) Solve

-11u-65v

5/3=50/t Solving proportion

Answers

the answer is t = 30

Answer:

T=30

Step-by-step explanation:

5t=3*50

5t=150        

divide 5

t=30

Simplify 8 over negative 3 divided by negative 4 over 9 . (5 points)
-8
-6
6
8

Answers

Answer:

6

Step-by-step explanation:

(8/3) / (-4/9)

when dividing fractions you use the acronym k.c.f (keep change flip)

keep the first fraction

change the operation (divide to multiply)

flip the other fraction

(8/-3) x (9/4)

after re-writing your expression, you want to solve

do this by multiplying both numerators by each other and same with the denominators

(-8x9) / (3x-4)

then you get a new fraction,

-72/-12

simplify,

-72/-12 = 6 (multiplying/dividing 2 negatives will always give you a positive)

Answer:

6

Step-by-step explanation:

6

Did on test hope it helps

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