Answer:
It landed at a height of 14 feet
Step-by-step explanation:
Given
[tex]y = -\frac{1}{8}x^2 +4x[/tex] --- Path of a t-shirt
[tex]3y = 2x - 14[/tex] --- height of bleachers
Required
Height when t-shirts land in bleachers
[tex]3y = 2x - 14[/tex]
Make y the subject
[tex]y = \frac{2}{3}x - \frac{14}{3}[/tex]
Substitute [tex]y = \frac{2}{3}x - \frac{14}{3}[/tex] in [tex]y = -\frac{1}{8}x^2 +4x[/tex]
[tex]\frac{2}{3}x - \frac{14}{3} = -\frac{1}{8}x^2 +4x[/tex]
Multiply through by 24
[tex]16x- 112 = -3x^2 +96x[/tex]
Express as:
[tex]3x^2 + 16x -96x- 112 = 0[/tex]
[tex]3x^2 -80x- 112 = 0[/tex]
Using a calculator:
[tex]x = 28[/tex] or [tex]x = -\frac{4}{3}[/tex]
x can not be negative:
So:
[tex]x = 28[/tex]
Substitute [tex]x = 28[/tex] in [tex]y = -\frac{1}{8}x^2 +4x[/tex] to calculate the height it landed
[tex]y = -\frac{1}{8} * 28^2 + 4 * 28[/tex]
[tex]y = 14[/tex]
Circle 1 has a center (−4, 5) and a radius of 6 cm. Circle 2 has (2, −3) and a radius of 9 cm. What transformations can be applied to Circle 1 to prove that the circles are similar? Enter your answers in the blanks. Enter the scale factor as a fraction in the simplest form.
The circles are similar because the transformation rule (___ , ___ ) can be applied to Circle 1 and then dilate it using a scale factor of ___/___
Answer:
The circles are similar because the transformation rule (+ 5 , - 6) can be applied to Circle 1 and then dilate it using a scale factor of 3/4.
Step-by-step explanation:
All the circles are similar.
That is because you can transform one circle onto another by two similarity operations: translation and dilation (scale factor).
For these two circles you have to translate the center of circle 1 to the center of circle 2, which will make that the two circles are concentric (have the same center).
The two centers are (-6,2) and (-1,- 4). To move the center (-6, 2) to (-1,4) you have to shift it 5 units to the right and 6 units down:
- 6 + 5 = - 1
2 - 6 = - 4.
After this translation, you dilate the circle with smaller radius using a scale factor equal to the ratio of the bigger radius to the smaller radius: 8/6 = 4/3.
Enter the scale factor as a fraction in simplest form. 3/4
The circles are similar because the transformation rule (+5 , - 6) can be applied to Circle 1 and then dilate it using a scale factor of 3/4.
Answer:
The circles are similar because the transformation rule ( [tex]x + 6, y - 8[/tex]) can be applied to Circle 1 and then dilate it using a scale factor of [tex]\frac{3}{2}[/tex]Step-by-step explanation:
just took the test down. proof down below
Mrs. Egan is saving money for a new television. She already has $110 in the bank. She is going to save $65 per week. Write an equation that represents Mrs. Egan's savings account
Given AB =6 and BD =8, find the value of x
Answer: x=10
Step-by-step explanation:
Find AD by making a 90 degree triangle with segments AB and BD
a=6 b= 8 c= c
[tex]a^{2}+b^{2} =c^{2}[/tex]
[tex]6^{2} +8^{2} =c^{2} \\36+64=c^{2} \\100=c^{2} \\10=c[/tex]
AD is = to 10- AD is also the radius of the circle. since x is also the radius of the circle, it is also 10
4. Find the percent of increase from 56 to 70. Round your answer
to the nearest tenth of a percent.
Answer:
25%
Step-by-step explanation:
In winter, the price of apples suddenly went up by $0.75 per pound. Sam bought 3 pounds of apples at the new price for a total of $5.88.
Write an equation to determine the original price per pound.
Find the original price per pound.
Answer:
look down
Step-by-step explanation:
sam bought 3 pounds so 0.75 multiplied with 3 is 2.25 then we subtract 5.88 by 2.25 to get the original price for 3 pounds which is 3.63. Last step we divide 3.63 by 3 to get the original price for 1 pound and the answer should be 1.21 per pound.
The final equation should be $5.88- $2.25÷3= $1.21
Write each phrase as an algebraic expression.
4. Jenny is 5 times as a old
5. Brandon spent 10 dollars more
7) A container is 1/3 full of water and 1/4 full of oil. What fraction of the container is empưy?
Answer:
[tex]Empty = \frac{5}{12}[/tex]
Step-by-step explanation:
Given
[tex]Water = \frac{1}{3}[/tex]
[tex]Oil = \frac{1}{4}[/tex]
Required
The fraction that is empty
The constituent of the water can be represented as:
[tex]Water + Oil + Empty = 1[/tex]
Make Empty the subject
[tex]Empty = 1 - Water - Oil[/tex]
Substitute values for Water and Oil
[tex]Empty = 1 - \frac{1}{3} - \frac{1}{4}[/tex]
Take LCM
[tex]Empty = \frac{12 - 4 - 3}{12}[/tex]
[tex]Empty = \frac{5}{12}[/tex]
A set of 4 chairs cost $56, or you can buy 1 chair for $16. How much less is the cost of 1 chair if you buy the set?
help please asap please
What percent of 29 is 99?
Answer:
29%
Step-by-step explanation:
29\99=0.29292929
x100=29.29292929
round to the nearest whole number
29%
I need an answer to this problem
what is the absolute value of |4x|- 12 = 4
Answer:
X = 4
Step-by-step explanation:
4 X 4 equals 16 and 16 minus twelve equals 4
Find the perimeter and area of the triangle. Show all work.
31 yd
14 yd
28 yd
Solve for the zeroes of the following function by factoring or quadratic formula f(x)=x2+10x+16
Answer:
(+2)(+8)
Step-by-step explanation:
What is 3 to the power of 9 ?
Answer:
3 to the power of 9 = 19,683
Step-by-step explanation:
3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3= 19,683
hope this is helped
if it did let me know if it was right
and mark brainlest
What is the determinant of 
Answer:
15
Step-by-step explanation:
Please see attached photo for explanation.
In the attached photo,
|H| => Determinant of H
From the calculations made as illustrated in the attached photo, the determinant of H is 15
Which step has the mistake in solving for roots?
2x^2 – 7x – 3 = 1
Step 1: 2x^2 – 7x – 4 = 0
Step 2: x^2 – 7x – 8 = 0
Step 3: (x-8)(x+1) = 0
Step 4: (x-8/4)(x+1/4) = 0
Step 5: (x-2)(4x+1) = 0
Step 6: x – 2 = 0 4x + 1 = 0
Step 7: x = 2 x = -1/4
One of these steps is incorrect. List the step that is incorrect, then finish the problem correctly.
Answer:
Step-by-step explanation:
2x² - 7x - 3 = 1
Step 1: 2x² - 7x - 4 = 0
Step 2: incorrect.
Use Quadratic Formula to solve for roots.
x = [7 ± √(7² – 4·2(-4))] / [2·2]
= [7 ± √81] / 4
= [7 ± 9] /4
= -0.5, 4
Carlos' grandmother will give him $20 plus $5 for every hour that he completes yard work. This situation can be described by an equation of the form y = mx + b, where x = the time in hours and y = the total amount of money earned. What is the value of b in this equation?
Answer: b= 20
Step-by-step explanation:
y= 5x + 20
help pleasee!!!!!!!!!!!!!!!!!!
Answer:
76 because if the two lines are parallel then x = 76
hope this helps and brainliest please
The population of a town can be modeled by the function P= 16,512(1.03)' where t'is
the number of years after 2006. What is the significance of the value 16,512?
Answer:
The answer is C
Step-by-step explanation:
An initial investment of $5,000 grows at 9% per year.
Answer:
C. f(t) = 5000(1.09)^t
Step-by-step explanation:
Compound interest formula:
F = P(1 + r)^t
Answer: C. f(t) = 5000(1.09)^t
I just need these three pretty please
Four times a number is equal to three times the quantity of one more than the number. What is the number?
a. 1
b. 2
c. 3
d. 4
e. 5
Answer:
x = 3
Step-by-step explanation:
Equation: 4x = 3(1 + x)
Distribute the 3: 4x = 3 + 3x
Subtract 3x from both sides: x = 3
Need answer to this urgently
Answer:
x=3
Step-by-step explanation:
25+134+4x+9+180
4x+168+180
4x+12
x=3
You want Brainliest help me plsss
Answer:
the slope in the equation is 5, while the slope on the graph is 2
the partial circle has a radius of 11 inches
What is the area of this figure? ANSWER ASAP
Answer:
285.1 in.²
Step-by-step explanation:
The circle is a ¾ circle.
Area of the figure = ¾(πr²)
Radius (r) = 11 in.
Plug in the value
Area = ¾(π*11²)
Area = ¾(π*121)
Area = 285.099533 ≈ 285.1 in.² (nearest tenth)
What is the greatest common factor of 15, 75, and 9
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{Factors of each number }\huge\boxed{\downarrow}\\\\\large\textsf{9: 1. 3. \& 9}\\\large\textsf{15: 1, 3, 5, \& 15}\\\large\textsf{75: 1, 3, 5, 15, 25, \75}[/tex]
[tex]\huge\text{Like terms between the factors}\\\\\bullet \large\textsf{1 \& 3}[/tex]
[tex]\huge\text{Reason for the factors of the numbers }\huge\boxed{\downarrow}\\\\\large\textsf{9: 1}\times\large\textsf{9 = \bf{9} }\& \large\textsf{ 3}\times\large\textsf{3 = \bf 9}\\\\\large\textsf{15: 1}\times\large\textsf{15 = \bf 15 }\&\large\textsf{ 3}\times\large\textsf{5 = \bf 15}\\\\\large\textsf{75: 1}\times\large\textsf{ 75 = \bf 75}, \large\textsf{ 3}\times\large\textsf{25 = \bf 75}, \& \large\textsf{ 5}\times\large\textsf{ 15 = \bf 75}[/tex]
[tex]\huge\text{BIGGEST NUMBER OUT OF THE LIKE}\\\huge\text{TERMS }\huge\boxed{\downarrow}\\\\\large\textsf{\bf 3}[/tex]
[tex]\huge\text{ANSWER }\huge\boxed{\downarrow}\\\\\large\boxed{\textsf{The GCF (Greatest Common Factor) is: \huge\boxed{\textsf3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\large\text{Amphitrite1040:)}[/tex]Please help ...........
Answer:
B
Step-by-step explanation:
PLS HELP I WILL MARK BRAINLIST!!
Answer:
C, 105
Step-by-step explanation:
45 divided by 3 is 15 so 15 x 7 = 105 minutes.
A record with a diameter of 12 inches rotates at 33 revolution per minute find the angular speed of the record in radians per second
9514 1404 393
Answer:
1.1π radians/second
Step-by-step explanation:
Each revolution is 2π radians, and there are 60 seconds in a minute. The rotation rate is ...
(33 rev/min)×(2π rad/rev)×(1 min)/(60 sec) = 66π/60 rad/sec
= 1.1π rad/sec
The angular speed is 1.1π radians per second.