Write the equation of a parabola that has a vertex of (-2,5.5) and passes through the point (-2.5,2.5).

Answers

Answer 1

The equation of a parabola that has a vertex of (-2, 5.5) and passes through the point (-2.5, 2.5) is  [tex]y=-12(x+2)^2+5.5[/tex]

The vertex form of the equation of a parabola is:

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

where (h, k) is the vertex of the parabola

(x, y) is the point that the parabola passes through

The vertex, (h, k) = (-2, 5.5)

The point, (x, y) = (-2.5, 2.5)

Substitute h = -2, k = 5.5, x = -2.5, and y = 2.5 into the equation to solve for a.

[tex]2.5=a(-2.5-(-2))^2+5.5\\\\2.5=a(-2.5+2)^2+5.5\\\\2.5-5.5=a(-2.5+2)^2\\\\-3=a(-0.5)^2\\\\-3=0.25a\\\\a = \frac{-3}{0.25} \\\\a = -12[/tex]

Therefore, the equation of the parabola is:

[tex]y=-12(x-(-2))^2+5.5\\\\y=-12(x+2)^2+5.5[/tex]

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Related Questions

An object is dropped from a height of 288 feet. The equation, - 16t ^ 2 + 288t = h(t) represents the height, hof the object after tseconds. How long does it take the object to the ground?

0 seconds
16 seconds
18 seconds
88 seconds

Answers

18 seconds

Step-by-step explanation:

The object will reach the ground when its height h(t) = 0. Therefore, we can write

[tex]h(t) = 288t - 16t^2 = 0 \Rightarrow 16t^2 = 288t[/tex]

Solving for t, we get

[tex]16t = 288 \Rightarrow t = 18\:\text{s}[/tex]

work out the area of this quarter circle take p2b 3.14 to and read and other digits given by a calculator ​

Answers

Answer:

Step-by-step explanation:

area of a full circle is A = πr²

so a quarter of a circle area is A = πr²/4

A = 3.142(7²)/4

A = 38.4895 cm²               picture answer

Using π =  3.14 results in

A = 3.14(7²)/4

A = 38.465 cm²                  written question answer

For comparison purposes,

Carrying the precision of π into many more significant digits results in

A = 38.484510006474...cm²

Second Graph problem! Can anybody please help me out with this? (Almost done for today) (Algebra graph problem)​

Answers

Answer:

  x = -2

Step-by-step explanation:

The expression f(x) = 1 corresponds to the point on the graph that is 1 unit above the x-axis. You can locate that horizontal line and see where it intersects the graph. That point of intersection  is 2 grid squares to the left of the y-axis, where x = -2.

  f(-2) = 1

  x = -2

10. The ordered pairs (1, 2), (2, 8), (3, 18), and (4, 32) represent a function. What is a rule that represents this function?
It also gives me these numbers:
a. 2x
b. 2x + 2
c. x^2
d. 2x^2

Answers

Answer:

d. 2x^2

Step-by-step explanation

1 year = 365 days
1 day = 24 hours
How many years is 1,000,000 hours?
Has to be dimensional analysis

Answers

Answer: 41,667

Step-by-step explanation:

1,000,000 divided by 24= 41,666.666

you should round this answer up if your question asks for that to 41,667

Rational numbers on the number line

Answers

Answers:

A = -5/4B = -0.5C = 2

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

Explanation:

The fraction -5/4 converts to -1.25 after using your calculator or long division. It represents the mixed number -1 & 1/4. So we go 1 full unit to the left to arrive at -1, then we move another 1/4 unit to the left to get to point A. That's why point A is located at -5/4 = -1.25 = -1 & 1/4.

Point B is directly midway between 0 and -1, so it must be at -0.5; you can use the midpoint formula.

Ratios:
The number of Anna's baseball cards is 3/4 the number of Patricia's cards. If Anna gives half of her cards to Patricia, what will be the ratio of Anna's cards to Patricia's cards?

Answers

Answer:

3/11

Step-by-step explanation:

thank you for the poits

write an indirect proof that a triangle cannot have 2 right angles​

Answers

The definition of a triangle is that it has three angles and their sum is 180 degrees. Two right angles each measure 90 degrees and their sun is 180 degrees. Therefore, a triangle cannot have two right angles because that would be two angles with a sum of 180 degrees, not three as required by the definition of a triangle.

what's
- 5 3/4 + (-4 5/6) in simplest form​

Answers

Answer:

-(127/12)

Step-by-step explanation:

-23/4 -29/6 = -254/24

-254/24 = -127/12

H . E . L . P

this work is due tommorow, and i have absolutely no idea what the answer is. please help me if you can !


( don’t comment for points. )

Answers

Answer:

A) 25

B) 64

Step-by-step explanation:

Hope this helps :))

Step-by-step explanation:

x= 5

a) 5² = 5×5 =25

b) (5+3)² = 8²

= 8 × 8

= 64

A coin is tossed 4 times. What are the odds against the coin showing tails all 4 times?

Answers

It’s 50/50 so maybe 2 times? IM NOT SURE SORRY

Answer:

1/16

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] * [tex]\frac{1}{2}[/tex] * [tex]\frac{1}{2}[/tex] * [tex]\frac{1}{2}[/tex]

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

You buy clothing at a sale. You buy a sweater at
7
10
of its original price of $35. Answer each question and show all your work.

a. How much money did you spend?
b. How much money did you save?
c. What fraction of the total original price did you save?

Answers

The amount that will be spent is $24.50, the amount saved will be $10.50, and the percentage saved will be 30%.

The amount that will be spent will be:

= 7/10 × $35 = $24.50

The amount that will be saved will be:

= $35 - $24.50 = $10.50

The fraction of the original price that is saved will be:

= 10.50/35 × 100

= 30%

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https://brainly.com/question/25763817

math
(5 points) will mark brainliest!! pls help :)

Answers

(tv^3)/(u^8) (you can get the answer by cancelling out the same variables in the numerator and denominator

Answer:  [tex]\frac{tv^3}{u^8}\\\\\\[/tex]

This is the fraction tv^3 all over u^8

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

Work Shown:

[tex]\frac{t^2uv^7}{tu^9v^4}\\\\\\\frac{t^2}{t}*\frac{u}{u^9}*\frac{v^7}{v^4}\\\\\\t^{2-1}*u^{1-9}*v^{7-4}\\\\\\t^{1}*u^{-8}*v^{3}\\\\\\\frac{t}{1}*\frac{1}{u^8}*\frac{v^3}{1}\\\\\\\frac{t*1*v^3}{1*u^8*1}\\\\\\\frac{tv^3}{u^8}\\\\\\[/tex]

In the third step, I used the rule (a^b)/(a^c) = a^(b-c)

To make the negative exponent turn positive, we apply the reciprocal to the base.

45 cows can graze a field in 13 days. How many cows will graze the same field in 9 days​

Answers

Answer:

65 cows

Step-by-step explanation:

Inverse rule of three

[tex]45-------13\\x -------- 9[/tex]

[tex]x=\frac{(45)(13)}{9}=585/9=65[/tex]

Hope this helps

juan visited a candy store

Answers

Answer:

ok lol

Step-by-step explanation:

What does ± indicate when its used like 2±1?​

Answers

Answer:

it is in quadratic equation meaning you use Plus or minus

Answer:

I is both the plus and minus sign so and 2+1 and subtract 2-1 both answers are the answer

Step-by-step explanation:

The plus–minus sign, ±, is a mathematical symbol with multiple meanings. In mathematics, it generally indicates a choice of exactly two possible values, one of which is obtained through addition and the other through subtraction.

The sign may also represent an inclusive range of values that a reading might have.

please help.. no links​

Answers

Use Pythagorean theorem,

[tex]29^2 = 21^2 + x^2 \\\\\implies x^2 = 29^2 -21^2 \\\\\implies x^2 = 400\\\\\implies x = \sqrt{400} = 20[/tex]

If a slingshot is used to shoot a marble straight up into the air from 2 meters above the
ground with an initial velocity of 30 meters per second, for what values of time t will the
marble be over 35 meters above the ground? (Refer to Exercise 25 in Section 2.3 for assistance
if needed.) Round your answers to two decimal places

Answers

Answer:

use this equation: GPE=mgh

Step-by-step explanation:

GPE = gravitational potential energy = J

m = mass = Kg

g = gravitational field = N/kg = world's gravitational field is 9.8N/kg

h = height = m

OMG HELP RN

Amelia had 29 sea shells. Then, she collected 10 more sea shells. After that, she gave S sea shells to her little sister. Which of the following shows how many sea shells she has currently?
A.
29 - 10 - S
B.
29 + S + 10
C.
29 + 10 - S
D.
29 + S - 10

Answers

Answer: It should be C

Step-by-step explanation: This is because since She has 29 seashells then got 10 more that would add it and since she gave some to her little sister we subtract there

Answer:

I think that it would be C 29+10-S

Step-by-step explanation:

I say this because she had 29 then got 10 which would be 29+10 and she gave S away that's 2o+10-S

(1.2 times 10^9) divided by (3 times 10^5) in scientific notation

Answers

Answer:

[tex]4x \times {10}^{3} [/tex]

Step-by-step explanation:

[tex] \frac{1.2}{3} \times \frac{ {10}^{9} }{ {10}^{5} } [/tex]

[tex]0.4 \times {10}^{9 - 5} [/tex]

[tex]0.4 \times {10}^{4} [/tex]

[tex] = 4 \times {10}^{3} [/tex]

PLEASEE HELPP I WILL GIVE BRAINLIEST

Answers

Answer:

p=0.4

Step-by-step explanation:

6(p+2.25)=15.9

6p+13.5=15.9

6p=2.4

p=0.4

6(p+2.25)=15 9/10
6p+13.5=159/10 (convert to improper frac)
6p=159/10-13.5
6p=159/10-27/2
6p=12/5

So p=2/5! :)

i need help! i will be giving brainliest if you actually show the work and dont troll :)

Answers

Answer:

you do 215 times $0.25 you get $53.75 you take that away from $3272.30 you get $3218.55 then you divide that by 215 you get $14.97 so the answer is she makes $14.97 on one pair of earrings.

Step-by-step explanation:

Plz mark brainliest

Jacob travels to the shops 5 miles from his home, then he travels to the
post office 3 miles from the shops. Afterwards he travels home. What is
the total distance Jacob traveled? What is the total displacement of
Jacob?*
Distance 8 miles : Displacement 8 Mlles

Distance 16 Miles: Displacement 0

Distance 8 Miles: Displacement 8 Miles

Distance 6 miles : Displacement 8 miles

Answers

Answer:

[tex]\huge\boxed{Distance:16mi}\\\huge\boxed{Displacement: 0mi}[/tex]

Step-by-step explanation:

Because Jacob starts and ends at his house, his total displacement is 0mi, because the distance from his house to his house is 0 mi.

Because Jacob travels 5 miles to the shops, then (N.B. I'm inferring here) in a straight line, 3 more miles to the post office, a total distance of 8 miles, then another 8 backwards, he travels a total distance of 16mi.

Hope it helps :) and let me know if you want me to elaborate.

6 Cyclist A travels 55 km in 2 hours and 20 minutes.
Cyclist B travels 135 km in 5 hours and 36 minutes.
Which cyclist is travelling faster?

Answers

cyclist a speed is d = v × t

so you can find velocity of a and b.

then compare them both.

It takes 14 pints of blueberries to make 4 jars of blueberry jam.

Answers

Answer:It takes 14 pints of blueberries to make 4 jars of blueberry jam.

Step-by-step explanation:

The figure below shows the graph of function f with domain [-1,1] and range [0,1].

Answers

The domain are the possible input while the range are the possible output

of a function.

(a) The domain = [-√2, √2], the range = [0, 2](b) The domain = [-1, 1], the range = [0, 1](c) The domain = [-1, 1], the range = [0, -1](d) The domain = [0, 2], the range = [0, 1](e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]

Reasons:

The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1

Therefore, we have;

(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2

The x-intercept of the above function are, x = √2, and x = -√2

Which gives;

The domain = [-√2, √2]

The range = [0, 2]

(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3

At the x–intercepts, we have;

-3·x² + 3 = 0

x = ±1

The domain = [-1, 1]

The maximum value of y is given at x = 0, therefore;

= -3 × 0² + 3 = 3

The range = [0, 1]

(c) y = -f(x) = -(-x² + 1) = x² - 1

At the x–intercepts, x² - 1 = 0

x = ± 1

The domain = [-1, 1]

The minimum value of y is given at x = 0, which is y = -1

The range = [0, -1]

(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x

At the x–intercepts, we have;  -x² + 2·x = 0, which gives;

(-x + 2)·x = 0

Which gives, x = 0, or x = 2

The domain = [0, 2]

The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1

y = f(1) =  -1² + 2×1 = 1

Therefore;

The range = [0, 1]

(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2

At the x–intercepts, we have;  -x² - 4·x - 2 = 0, which gives;

x = -(2 + √2) or x = x = √2 - 2

The domain = [-(2 + √2), (√2 - 2)]

The maximum value of y is given when x = -4/(2)) = -2

Which gives;

-(-2)² - 4·(-2) - 2 = 2

The range = [0, 2]

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Simplify the expression 4(x-5) / 2
a. 8x - 40
b. 2x -
C. 5x - 20
d. 2x - 10
HELP PLZZZZZZ

Answers

If you simplify it, you get 2x-10 or D

Answer:8x-40

Step-by-step explanation:

Because when we simply 4(x-5)/2

We multiply both sides by 2 because the inverse operations of division is multiplication. 2*4(x-5)*2/2 we cancel two by two then it leave us 4*2(x-5).

Next four times two is eight. So 8(x-5) we distribe eight that means eight times x and 5, 8x-40thos is the answer. Hope this help

In the figure below, BD and AC are diameters of circle P.
What is the arc measure of minor arc DC in degrees?

Answers

Answer: 19

Step-by-step explanation:

2 lines crossing create 2 pairs of equal angles. The opposite angles are the same. Same goes in a circle.

9514 1404 393

Answer:

  arc DC = 19°

Step-by-step explanation:

The acute central angles are vertical angles, so have the same measure. Vertical angles with the same measure intercept arcs with the same measure. The measure of the arc is the measure of the central angle it subtends.

Arc AB = Arc DC = 19°

Which lines are parallel? Why?
A) a || b by same side interior angles
B) c || d by same side interior angles
C) c || d by converse of corresponding angles
D) a || b by converse of same side interior angles
E) a || b by converse of corresponding angles
F) a || b by corresponding angles
G) c || d by converse of same side interior angles
H) c || d corresponding angles

Answers

9514 1404 393

Answer:

  C) c || d by converse of corresponding angles

Step-by-step explanation:

Only corresponding angles where transversal b crosses lines c and d are shown. All answer choices involving a||b or interior angles can be eliminated from consideration.

The "corresponding angle" theorem tells you corresponding angles are congruent if the lines are parallel.

The converse of that theorem tells you the lines are parallel if the corresponding angles are congruent. Here, the angles are shown congruent, so the "converse" theorem applies.

What is the equation of the line in slop-intercept form?



Enter your answer in the blank spots




y= __x + __

Answers

Answer:

y=2x +5

Step-by-step explanation:

so 2 goes in the first blank and 5 goes in the second

Hope this helps!❆

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