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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juan visited a candy store
Answer:
ok lol
Step-by-step explanation:
The figure below shows the graph of function f with domain [-1,1] and range [0,1].
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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It takes 14 pints of blueberries to make 4 jars of blueberry jam.
Answer:It takes 14 pints of blueberries to make 4 jars of blueberry jam.
Step-by-step explanation:
work out the area of this quarter circle take p2b 3.14 to and read and other digits given by a calculator
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
math
(5 points) will mark brainliest!! pls help :)
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.
A coin is tossed 4 times. What are the odds against the coin showing tails all 4 times?
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?
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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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. )
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
(1.2 times 10^9) divided by (3 times 10^5) in scientific notation
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]
write an indirect proof that a triangle cannot have 2 right angles
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
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]
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
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.
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
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
What does ± indicate when its used like 2±1?
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.
Second Graph problem! Can anybody please help me out with this? (Almost done for today) (Algebra graph problem)
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
Answer:
d. 2x^2
Step-by-step explanation
please help.. no links
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]
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
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.
Simplify the expression 4(x-5) / 2
a. 8x - 40
b. 2x -
C. 5x - 20
d. 2x - 10
HELP PLZZZZZZ
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
1 year = 365 days
1 day = 24 hours
How many years is 1,000,000 hours?
Has to be dimensional analysis
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
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?
Answer:
3/11
Step-by-step explanation:
thank you for the poits
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?
cyclist a speed is d = v × t
so you can find velocity of a and b.
then compare them both.
what's
- 5 3/4 + (-4 5/6) in simplest form
Answer:
-(127/12)
Step-by-step explanation:
-23/4 -29/6 = -254/24
-254/24 = -127/12
What is the equation of the line in slop-intercept form?
Enter your answer in the blank spots
y= __x + __
Answer:
y=2x +5
Step-by-step explanation:
so 2 goes in the first blank and 5 goes in the second
Hope this helps!❆
Rational numbers on the number line
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.
i need help! i will be giving brainliest if you actually show the work and dont troll :)
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
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
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
45 cows can graze a field in 13 days. How many cows will graze the same field in 9 days
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
PLEASEE HELPP I WILL GIVE BRAINLIEST
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
In the figure below, BD and AC are diameters of circle P.
What is the arc measure of minor arc DC in degrees?
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.
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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°