Using proportions, it is found that the signed number -15 represents the team's total loss of yards on the 3 plays.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, in one play, the team lost 5 years, that is, the amount is -5. What is the amount on three plays? The rule of three is given by:
1 play - -5 yards
3 plays - n yards
Applying cross multiplication:
n = 3 x (-5) = -15.
The signed number -15 represents the team's total loss of yards on the 3 plays.
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Find the volume of the prism or compound shape.
The volume of the compound shape, that is the object formed by two hemispheres and a right cylinder is 66π in³.
How to determine the volume of the compound shape
The volume is the space occupied by an object. The volume of the compound shape equals the sum of the individual volumes, that is, of each part, which are represented by two hemispheres and a right cylinder.
Now we proceed to determine the volume of the compound shape (V), in cubic inches, by apply the following calculation:
V = (4/3) · π · (3 in)³ + π · (3 in)² · (10 in)
V = 66π in³
The volume of the compound shape, that is the object formed by two hemispheres and a right cylinder is 66π in³. [tex]\blacksquare[/tex]
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How do u solve this equation? I’m struggling with it.
2a+3c=61
3a+5c=96
Answer:
a=17
c=9
Step-by-step explanation:
balls
Answer:
c=9 and a=17
Step-by-step explanation:
1. 2a+3c=61
2. 3a+5c=96
the LCM between 2 and 3 is 6 so
equation 1 *3
3.6a+9c+183
equation 2*2
4. 6a+10c=192
equation 3 - equation 4
5. -c=-9
c=9
substitute c into equation 1 or 2 to find a
3a+5(9)=96
3a+45=96
3a=51
a=17
The graph of this system of equations is which of the following?
2x + y = 6
6x + 3y = 18
Overlapping lines
Parallel lines
Intersecting lines
A curve intersecting with a line
Answer:
They are the same line. It means that they are overlapping line.
Answer:
Overlapping
Step-by-step explanation:
Divide every term of the second equation, it would be 2x + y = 6, which is the same as the first equation.
(1+sint)/(cost)-(cost)/(1-sint)
[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{\cos(t)}{1-\sin(t)}[/tex]
Multiply through the second term by [tex]1+\sin(t)[/tex] :
[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{\cos(t)}{1-\sin(t)}\cdot\dfrac{1+\sin(t)}{1+\sin(t)}[/tex]
[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{\cos(t)(1+\sin(t))}{1-\sin^2(t)}[/tex]
Recall that [tex]\cos^2(x)+\sin^2(x)=1[/tex] for all x :
[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{\cos(t)(1+\sin(t))}{\cos^2(t)}[/tex]
If [tex]\cos(t)\neq0[/tex], we can cancel a factor of it in the second fraction.
[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{1+\sin(t)}{\cos(t)}[/tex]
and this simplifies to
[tex]\dfrac{(1+\sin(t))-(1+\sin(t))}{\cos(t)} = \boxed{0}[/tex]
PLEASE SOMEONE HELP!!
Is 336 − –5,083 positive or negative?
Answer:
positive
Step-by-step explanation:
if you subtract a negative number, it’s the same as adding a positive number. If you add 2 positive numbers, you get a positive number, so the expression is positive.
based on the diagram given, find the value of x and y
Answer:
x = 6 , y = 2
Step-by-step explanation:
81x + 10 = 5y + 486 ............ (1)
9x + 40 = 20y + 54 ............ (2)
(1) × 4 - (2)
315x = 1890
x = 6 -------> (2)
9(6) + 40 = 20y + 54
20y = 94 - 54
y = 2
The length of the escalator is 36 ft and the
vertical height it rises is 9 ft. what is the angle
of elevation?
a. 90
b. 75. 52
c. 14. 48
d. 14. 04
Answer:
sin θ = 9 / 36 = 1/4
θ = 14.48 deg (ans C)
דיי יוטורסם
$9000 is invested at 8% compounded quarterly. In how many years will the account have grown to $14,500?
Round your answer to the nearest tenth of a year
Bella is typing a 400 word essay. She types 50 words in 2 minutes.
Enter an equation in the form of y=mx+b, that represents the number of words (y) remaining to type after x minutes.
Answer:
[tex]y=25x[/tex]
Step-by-step explanation:
If Bella types 50 words in 2 minutes, we can divide 50 by 2 to see how many words she types in 1 minute.
[tex]50/2=25[/tex]
So, Bella types 25 words per minute. When she first began writing her essay, she did not have words to start with, so there is no y-intercept ([tex]b[/tex]).
Therefore, the equation that represents this relation is [tex]y=25x[/tex].
Solving the equation
We can divide 400 by 25 to determine how many minutes it would take her to finish her essay.
[tex]\frac{400}{25} =16[/tex]
Therefore, it will take her 16 minutes to complete her essay.
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Roger has a rope that is 3 feet long.He needs to cut it into 12 equal length pieces.How many feet loń should each piece of the rope be?
Answer:
0.25
Step-by-step explanation:
3/12 is 0.25
3 divided by 12 when simplified or reduced
The fraction 3/12 is equal to the exact decimal number.
1.5 = 0.25 + g
solve the equation and find the value of the variable
Answer:
its easy it should be 1.25 or well that the answer I got
The point B is at the centre of the circle. The points P and Q are on the circumference of the circle. Calculate the area of the shaded sector. Take it to be 3.142 in your working. Give your final answer to 1 decimal place.
Answer: 24.7 square cm
Step-by-step explanation:
given data 4,x,9,5,2,7 find x if the mode is 4
Answer:
x = 4
Step-by-step explanation:
This is because the definition of mode is the number that appears the most or is the popular of the numbers in the data set.
This could be any number since each number is listed once, but the requirements/directions say the mode is 4 so you need another 4 in order to have a mode of 4.
Peter is saving to buy a new skateboard. He deposits the same amount each week into his savings account. How much money does he save each week?
Week Money in Savings Account
0 $12.00
1 $17.75
2 $23.50
3 $29.25
PLS HELP ME ILL GIVE YOU BRAINIEST
If f(x)=3x^6+4x^3-4, then what is the remainder when f(x) is divided by x+1?
Answer:
-5
f(-1) would be the remainder
PLEASE HELP ME????
THank you ! :)
you can replace the m with 14 to get an equation of: 52+14=66
Find the perimeter of the composite figure using pi
Answer:
(3 +1.5π) ft ≈ 7.71 ft
Step-by-step explanation:
We see a semicircle, not a "composite figure." The perimeter of the semicircle is the sum of the length of the arc and the length of the straight edge:
P = (1/2)πd +d . . . where d is the diameter and πd is the full circumference
P = d(1 +π/2)
P ≈ (3 ft)(1 +1.57) = 7.71 ft . . . . . using 3.14 for π
The perimeter of the figure is about 7.71 feet.
__
In terms of pi, the perimeter is ...
P = (3 +1.5π) ft
Can someone help???????
Answer:
8x-3y-24
Step-by-step explanation:
[tex] \frac{3}{4} y = 2x - 6 \\ \\ \\ 3y = 4(2x - 6) \\ \\ 3y = 8x - 24 \\ \\ 8x - 3y - 24 = 0 \\ \\ \\ is \: the \: required \: equation[/tex]
Find the length of the third side. If necessary, round to the nearest tenth
Pythagorean Theorem (Rounding)
Find c.
Write your answer in simplest radical form.
Answer:
c = 3.46
Step-by-step explanation:
use tangent to find c
2 tan 60 = c
firstly label the sides
let me know if you need further explanation on how I got my answer
what would you do to solve the system: y=x+3 and y=x^2+x-6
18
p.7 Central Angles and Inscribed Angles
#4 What is the measure, in degrees, of arc JKI ?
4) MJKI
80°
K
mJKI =
degrees
Answer:
280°
Step-by-step explanation:
There are 360° in a circle. you are given an arc that is 80°.
To find the arc JKI, subtract 80 from 360.
360 - 80 = 280°
Please help me on this equation
3 3/4 ÷ 5/7 =
Answer:
5 1/4
Step-by-step explanation:
3 3/4 / ( 5/7) =
15/4 / ( 5/7) =
15/4 * 7/5 =
(15*7) / (4*5 )
105 / 20 = 5 1/4
Answer:
5.25
Step-by-step explanation:
Turn mixed number into a improper fraction.
Divide fraction by 20.
It doesn’t matter if 5 1/4, or 21/4 or 5.25., they all equal the same.
You want to save for retirement. assuming you are now 25 years old and you want to retire at age 50, you have 25 years to watch your investment grow. you decide to invest in the stock market, which has earned about 13% per year over the past 80 years and is expected to continue at this rate. you decide to invest $1,000 today. required: how much do you expect to have in 25 years?
Answer:
4250
Step-by-step explanation:
0.13 = 13%
1000×0.13=130
130×25= 3250 + 1000 = 4250
What I did:
You have to turn the percent to a decimal first
Then multiply the decimal by the first investment amount (1000)
then multiply that by the years that you have before retirement
You add that amount plus the 1000 you have started with
Which temperature during the week is farther from 0? Explain how you decided this using absolute value
Answer:
The farthest temperature from zero during the week is 5 °F because it's absolute value, 5, is the highest out of all the other numbers.
Step-by-step explanation:
Determine the equation of the line shown in the graph:
10
-8 -6 -4 -2.
-
I
y = -1
y = 0
Ox=-1
X=0
Answer:
X=-1
Step-by-step explanation:
As you can see the line is not intercepting at y also
Identify the solution to the system of equations
{x=-2y-6 -3x-7y=18
Answer:
(- 6, 0 )
Step-by-step explanation:
x = -2y - 6 → (1)
- 3x - 7y = 18 → (2)
substitute x = - 2y - 6 into (2)
- 3(- 2y - 6) - 7y = 18 ← distribute parenthesis and simplify left side
6y + 18 - 7y = 18
- y + 18 = 18 ( subtract 18 from both sides )
- y = 0 , then
y = 0
substitute y = 0 into (1)
x = - 2(0) - 6 = 0 - 6 = - 6
solution is (- 6, 0 )
Answer:
(x, y) = (-6, 0)
Step-by-step explanation:
A system of equations is easily solved using a graphing calculator. The attached shows the solution to be ...
(x, y) = (-6, 0)
__
The first equation gives a convenient expression for substituting for x in the second equation:
-3(-2y -6) -7y = 18
18 -y = 18 . . . . . . . . simplify
y = 0 . . . . . . . . add y-18
x = -2(0) -6 = -6
The solution by substitution is (x, y) = (-6, 0).
Consider the number 9,953.
Is this number divisible by 2, 3, 4, 5, 9, or 10? Provide justification for
each number without using a calculator.
Hint: If a number is not divisible by 2, then what other numbers is it
also not divisible by?
Write your answer in complete sentences.
Answer:
No for all of them
Step-by-step explanation:
2 --> not even
3 --> of the sum of the numbers are not divisible by three
4 --> the last two digits are not equal to a multiple of four
5 --> the last digit is not ending with 0 or 5
9 --> the sum of the digits is not equal to a multiple of nine
10 --> the last number is not zero
