Answer:
a) The vertex of the graph is [tex](h,k) = (0, 31)[/tex], b) [tex]a = -16[/tex], c) The equation of the parabola is [tex]f(t) = -16\cdot t^{2}+31[/tex].
Step-by-step explanation:
a) The tennis ball experiments a free fall, that is, an uniform accelerated motion due to gravity and in which effects from Earth's rotation and air viscocity are negligible. The height of the ball in time is represented by a second order polynomial. Hence, the vertex of the parabola is the initial point highlighted in graph.
The vertex of the graph is [tex](h,k) = (0, 31)[/tex].
b) If we know that [tex](h,k) = (0, 31)[/tex], [tex]f(t) = a\cdot (t-h)^{2} + k[/tex] and [tex](t,f(t)) = (1,15)[/tex], then the value of [tex]a[/tex] is:
[tex]f(t) = a\cdot (t-h)^{2} + k[/tex]
[tex]15 = a\cdot (1-0)^{2}+31[/tex]
[tex]15 = a\cdot 1 + 31[/tex]
[tex]a = 15-31[/tex]
[tex]a = -16[/tex]
c) The equation of the parabola is [tex]f(t) = -16\cdot t^{2}+31[/tex].
Gina earns an hourly rate of $8.94 for a 40-hour week. She receives
double-time (2 times the hourly rate) for any weekend work. This week
she worked his regular 40 hours plus 10 hours on Saturday. Calculate her
gross pay.
Answer: $536.40
Step-by-step explanation:
8.94 * 2 = 17.88
8.94(40) + 17.88(10)
357.60 + 178.80 = $536.40
Jake paid $28.00 for admission to the county fair and bought 12 tickets to play games. If he spent a total of $64, what is the cost, x, of one ticket? Write and Solve an Equation.
Answer:
64 - 28 = 36
36 divided by 12 = 3
one ticket is 3 $
pls help me with all of them ill give 81 points
Answer:
1. No
2. Yes
3. [tex]\sqrt{80}[/tex]
4. x=8
Step-by-step explanation:
1.
6^2+8^2
=36+64=100
9^2=81
100≠81
No
2.
5^2+12^2
=25+144
=169
13^2=169
169=169
Yes
3.
x^2=4^2+8^2
x^2=16+64
x^2=80
x=[tex]\sqrt{80}[/tex]
4.
x^2+6^2=10^2
x^2+36=100
x^2=64
x=[tex]\sqrt{64}[/tex]=8
help me...................
Answer:
A. 4
Step-by-step explanation:
The answer to this question is option A. which is 4. This is because for every value of 5 or above, we round up to the next digit. For option B and C, those values are either 5 or above. This means that choosing those values would give a new value of 74.16, not 74.15 as the answer is showing.
CAN SOMEONE PLEASE HELP
Answer:
99°
Step-by-step explanation:
Triangle=180°
Given, 41+40=81
180-81
Answer:
99°
Step-by-step explanation:
Sum of angles in a triangle is supplementary,
x + 41° + 40° = 180°
x + 91° = 180°
x = ( 180 - 91 )
x = 99°
a publisher for a promising new novel figures fixed costs overhead, advances, promotion, copy editing, type setting and so on at $57,000 and variable costs printing, paper, binding, shipping at $2.90 for each book produced. If the book is sold to distributors for $10 each, how many must be sold to break even?
Answer:
$2.90 for each book produced. If the book is sold to distributors for $10 each, how many must be sold to break even?
Step-by-step explanation:
. citizen of the represented state
classes
3. Jeff, Lorri, and Dan had a race.
In how many different ways
could they come in first, second,
and third?
Answer:
6 different ways.
Step-by-step explanation:
(1) Jeff, Lorri, Dan
(2) Jeff, Dan, Lorri
(3) Lorri, Jeff, Dan
(4) Lorri, Dan, Jeff
(5) Dan, Jeff, Lorri
(6) Dan, Lorri, Jeff
A social studies quiz has 4 true-or-false questions. The following list shows the possibilities for a student's responses to these questions. TTTT, TTTF, TTFT, TTFF, TFTT, TFTF, TFFT, TFFF, FTTT, FTTF, FTFT, FTFF, FFTT, FFTF, FFFT, FFFF How many outcomes include 2 true and 2 false answers?
Answer:
The answer is there are six outcomes
Step-by-step explanation:
TTFF, TFTF, TFFT, FTTF, FTFT,
FFTT
The probability of getting outcomes including 2 true and 2 false answers is 3/8.
The given sample space is {TTTT, TTTF, TTFT, TTFF, TFTT, TFTF, TFFT, TFFF, FTTT, FTTF, FTFT, FTFF, FFTT, FFTF, FFFT, FFFF}
We need to find how many outcomes include 2 true and 2 false answers.
What is the formula to find the probability of an event?The formula to find the probability of an event is P(E)=Number of favourable outcomes/Total number of outcomes.
Now, the number of favourable outcomes=6 and = the total number of outcomes=16.
So, P(E)=6/16=3/8
Therefore, the probability of getting outcomes including 2 true and 2 false answers is 3/8.
To learn more about the probability visit:
https://brainly.com/question/11234923.
#SPJ2
HELP PLS
find the value of x
Answer:
x = 5
Step-by-step explanation:
These angles are supplementary so:
9x + 12x + 75 = 180
21x + 75 = 180
21x = 180 - 75
21x = 105
x = 5
Rewrite each fraction with a denominator of 24.
3/8 and 7/6
Answer:
3/8=9/24
7/6=28/24
Step-by-step explanation:
[tex]\frac{3}{8}\cdot \frac{3}{3}=\frac{9}{24}[/tex]
[tex]\frac{7}{6}\cdot \frac{4}{4}=\frac{28}{24}[/tex]
If it takes 2 pounds of batter to make 5 sheets of cookies ,how many pounds of batter will it take to make 27 sheets of cookies?
Answer:
6666666
Step-by-step explanation:
6
Answer:
12 pounds of batter
Step-by-step explanation:
27/5 =5.4
change 5.4 to 6
6 x 2 =12
12 pounds of batter
Liz has two pieces of string; one 18cm long, the other 24cm long. She wants to cut them
up to make pieces of string that are all the same length with no string left over. What is the
greatest length she can make the pieces of string?
Answer:
6cm
Step-by-step explanation:
length of the longest string=24
length of the shortest string=18.
for both string to have the same length,
24-x=18
x=24-18
=6cm
Which of the given values is a solution to the equation −8d+2=−40d+2?
Answer: d=0
Step-by-step explanation:
-8d+2=-40d+2
Add 40d to both sides
32d+2=2
Then isolate the 32d by subtracting 2 from the right side.
32d=0
Divide both sides by 32 and get
d=0
What is the range of the set of data points given below? 175 159 180 172 163 166 170 162 175 157 178 160
Answer:
Range = highest observation - lowest observation
180-157 = 23
Answer:
Hi! The answer to your question is 23
Step-by-step explanation:
☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
Rosa is making a poster that has a rainbow as part of the design. Using a compass she draws a semicircle with a radius of 18 cm. She draws another semicircle that has a radius of 12 cm as shown. What is the area of the shaded part of the rainbow?
Answer:
282.7 cm²
Step-by-step explanation:
Hello There!
To find the area of the shaded area we are going to want to find the area of the whole semi circle and subtract it by the area of the smaller semi circle
To find the area of a semicircle we use this formula
[tex]A=\frac{\pi r^2}{2}[/tex]
where r = radius
For the large semi circle
The radius of the larger semi circle is 18 cm so we plug in 18 into r in the formula
So..
[tex]A=\frac{\pi 18^2}{2} \\18^2=324\\324\pi =1017.87602\\\frac{1017.87602}{2} =508.9380099[/tex]
So the area of the whole semi circle is 508.9380099 cm²
Now to find the area of the smaller semi circle
The radius for the smaller semi circle is 12 cm so we plug in 12 into r in the formula
[tex]A=\frac{12^2\pi }{2} \\12^2=144\\144\pi =452.3893421\\\frac{452.3893421}{2} =226.1946711[/tex]
so the area of the smaller semi circle is 226.1946711cm²
Finally we want to subtract the area of the smaller semi circle from the area of the whole semi circle
508.9380099 - 226.1946711 = 282.7433388
Finally we want to round to the nearest tenth and we get that the area of the rainbow is 282.7 cm²
HELP MEEEEEEE PLEASE
Answer:
14m
Step-by-step explanation:
The expression that shows the number of coupon books:
14*m = 14m
Answer:
14m
Step-by-step explanation:
they say the members are represented by M, and the members sold 14 coupon we can't say it is m + 14 so the answer is 14m
A figure is shown.
8x
7x
44.4°
What is the measure, in degrees, of the highlighted angle?
We know that the sum of a straight line is 180° . So here there are 3 angles in a straight line . And the sum is 180° . So that ,
[tex]\tt\to Sum_{(angles \ of \ a \ straight \ line)}= 180^o \\\\\tt \to 7x + 8x + 44.4^o = 180^o \\\\\tt\to 15x = 180^o - 44.4^o \\\\\tt\to 15x = 135.6^o \\\\\tt\to x =\dfrac{135.6^o}{15}\\\\\tt\to \boxed{\orange{\tt x = 9.04^{\circ} \approx 9^{\circ} }}[/tex]
So the measure of angle that is highlighted will be 8x = 8(9) = 72°
Answer:
72.32degrees
x is 9.04
Step-by-step explanation:
7×9.04=63.28
8×9.04=72.32
44.4+63.28+72.32=180
Select all names that apply to this figure
Answer:
Quadrilateral and Parallelogram. There is not enough information given to determine the rest of the shapes.
The number of people I don’t know amusement park triples every hour. This morning, there were 20 people at the muse meant park when it opened. Now, there are 4860 people have them use meant park. Write an equation to represent the number of hours the amusement park has been open.
Answer:
equation is y=20(3)^x
Step-by-step explanation:
example:
Solve for x over the integers:
20 (3)^x = 4860
Divide both sides by 20:
3^x = 243
243 = 3^5:
3^x = 3^5
Equate exponents of 3 on both sides:
Answer:
x = 5 hours open with 4860 guest
URGENT I'll give you stars, brainliest answer, or slide into ur dms for this answer pls9^(x2)=y in log form
Answer:
log ( 28 )
13 √ 25
log
( 1/ 2 )
Step-by-step explanation:
To solve this, we will use this property of logarithms:
If x= a ^ y
then log an (x) = y, where a is the base
So if e^9 = y , or y = e^9
then log e (y) = 9
NB: log e (y) is also referred to as the natural log of y, or ln y.
So it can also be written as:
Answer: ln y = 9, or log e (y) = 9
Work out the surface area of this solid prism.

The diagram is not drawn to scale.
Christopher sold his dinette set for $245 through an online site, which charged him 9% of the selling price as commission. what is the commission?
Answer:
$22.05
Step-by-step explanation:
If a product has a sales commission, then one must divide the commission percent by (100) to convert the percent to a decimal. Then multiply the result by the price of the product to find the amount of money that will be given as a commission.
Applying this knowledge to the given problem, one must divide (9%) by (100) to convert to decimal form,
9% / 100 = 0.09
Now multiply the result by the price of the product (245) to find the amount given away in commission,
0.09 * 245 = 22.05
Zrób rysunek pomocniczy i oblicz miary kątów w sześciu trójkątach, które otrzymasz wykreślając dwusieczne kątów trójkąta. Kąt ABC wynosi 620 , kąt ACB wynosi 1020 .
Answer:
Zrób rysunek pomocniczy i oblicz miary kątów w sześciu trójkątach, które otrzymasz wykreślając dwusieczne kątów trójkąta. Kąt ABC wynosi 620 , kąt ACB wynosi 1020 .
Step-by-step explanation:
please please help i will mark u brill
please fast i need it right know !!!!!
Answer:
yes
Step-by-step explanation:
8d+54=150
8*12+54
96+54
150
There are 50 pieces of candy and 15 gum balls what is the ratio
You are testing the claim that the mean GPA of night students is different from the mea GPA of day students. You sample 20 night students, and the sample mean GPA is 2.84 with a standard mean GPA is 2.55 with a standard deviation of 0.45. Test the claim using a 1% level of significance. Assume the population standard deviations are unequal and that GPAs are normally distributed. Give answer to at least 4 decimal places. What are the correct hypotheses
Answer:
As the calculated value of z does not lie in the critical region the null hypothesis is accepted that the GPA mean of the night students is the same as the GPA mean of the day students.
Step-by-step explanation:
Here n= 20
Sample mean GPA = x`= 2.84
Standard mean GPA = u= 2.55
Standard deviation = s= 0.45.
Level of Significance.= ∝ = 0.01
The hypothesis are formulated as
H0: u1=u2 i.e the GPA of night students is same as the mean GPA of day students
against the claim
Ha: u1≠u2
i.e the GPA of night students is different from the mea GPA of day students
For two tailed test the critical value is z ≥ z∝/2= ± 2.58
The test statistic
Z= x`-u/s/√n
z= 2.84-2.55/0.45/√20
z= 0.1441
As the calculated value of z does not lie in the critical region the null hypothesis is accepted that the GPA mean of the night students is the same as the GPA mean of the day students.
Solve 96 = 2w^2, where w is a real number. Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas. If there is no solution, click on No solution.
Answer:
Step-by-step explanation:
96 = 2w²
48 = w²
√48 = w
√(16)(3) = w
± 4√3 = w
± 6.93
w = 6.93, -6.93
NEED HELP FAST‼️ WILL MARK B‼️‼️‼️
Triangle ABC has the following coordinates. A(6,-6), B(3,-3) and C(6,-3). What are the
coordinates of triangle A'B'C' if it is dilated with a scale factor of 4 with the origin as the center of
dilation?
Answer:
4×6=24,4×-6=-24,4×3=12,4×-3=-12,4×
6=24,4×-3=-12
$
1. Una esfera de latón de 3 pies
cúbicos a 22°C se expuso al calor hasta alcanzar una temperatura de
66°C. ¿Cuál será su nuevo volumen'si el coeficiente de dilatación lineal del latón es de 18x1095
Answer:
Tell in english plss
Step-by-step explanation:
i dont understangd okk
This grid shows where a squirrel hid different nuts which ordered pair shows wheee the squirrel hid the acorns
2,8
2,10
8,2
8,8