Given:
The kiddie pool is 7 feet long. The adult swimming pool is 42 feet long.
To find:
How many times as long as the kiddie pool is the adult swimming pool?
Solution:
Let adult swimming pool is x times the kiddie swimming pool.
[tex]42=x\times 7[/tex]
[tex]42=7x[/tex]
Divide both sides by 7.
[tex]\dfrac{42}{7}=\dfrac{7x}{7}[/tex]
[tex]6=x[/tex]
Therefore, adult swimming pool is 6 times the kiddie swimming pool.
g)
(Sin 5A - Sin 7A - Sin 4A + Sin 8A)÷
(Cos 4A - Cos 5A - Cos 8A + Cos 7A)=
Cot 6A
We use a similar strategy as in your previous question. Rewrite:
sin(5x) = sin(6x - x) = sin(6x) cos(x) - cos(6x) sin(x)
sin(7x) = sin(6x + x) = sin(6x) cos(x) + cos(6x) sin(x)
→ sin(5x) - sin(7x) = -2 cos(6x) sin(x)
sin(4x) = sin(6x - 2x) = sin(6x) cos(2x) - cos(6x) sin(2x)
sin(8x) = sin(6x + 2x) = sin(6x) cos(2x) + cos(6x) sin(2x)
→ sin(8x) - sin(4x) = 2 cos(6x) sin(2x)
cos(5x) = cos(6x - x) = cos(6x) cos(x) + sin(6x) sin(x)
cos(7x) = cos(6x + x) = cos(6x) cos(x) - sin(6x) sin(x)
→ cos(7x) - cos(5x) = -2 sin(6x) sin(x)
cos(4x) = cos(6x - 2x) = cos(6x) cos(2x) + sin(6x) sin(2x)
cos(8x) = cos(6x + 2x) = cos(6x) cos(2x) - sin(6x) sin(2x)
→ cos(4x) - cos(8x) = 2 sin(6x) sin(2x)
Then
(sin(5x) - sin(7x) - sin(4x) + sin(8x)) / (cos(4x) - cos(5x) - cos(8x) + cos(7x))
= (2 cos(6x) sin(2x) - 2 cos(6x) sin(x)) / (2 sin(6x) sin(2x) - 2 sin(6x) sin(x))
= (2 cos(6x) (sin(2x) - sin(x))) / (2 sin(6x) (sin(2x) - sin(x)))
= cos(6x) / sin(6x)
= cot(6x)
QED
You rent an apartment that costs $1800 per month during the first year, but the rent is set to go up 9.5% per year. Write a recursive formula to show what the rent is during the nth year of living in the apartment.
Answer:
Step-by-step explanation:
You rent an apartment that costs \$1800$1800 per month during the first year, but the rent is set to go up \$160$160 per year. What would be the monthly rent during the 9th year of living in the apartment?
\text{Write out the first 3 terms:}
Write out the first 3 terms:
a_1=1800\leftarrow \text{rent in 1st year}
a
1
=1800←rent in 1st year
a_2=1960\leftarrow \text{rent in 2nd year}
a
2
=1960←rent in 2nd year
a_3=2120\leftarrow \text{rent in 3rd year}
a
3
=2120←rent in 3rd year
\text{Arithmetic Sequence: }d=160
Arithmetic Sequence: d=160
The common difference
\text{Explicit Formula: }
Explicit Formula:
a_n=
a
n
=
\,\,a_1+(n-1)d
a
1
+(n−1)d
a_{\color{green}{9}}=
a
9
=
\,\,1800+(\color{green}{9}-1)(160)
1800+(9−1)(160)
a_{9}=
a
9
=
\,\,3080
3080
[tex]\sqrt[3]{250} -\sqrt[3]{54}[/tex]
help plzz
Answer:
exact form: 2 ^3√2
Step-by-step explanation:
A large company put out an advertisement in a magazine for a job
opening. The first day the magazine was published the company got 90
responses, but the responses were declining by 10% each day.
Assuming the pattern continued, how many total responses would the
company get over the course of the first 19 days after the magazine was
published, to the nearest whole number?
Answer:
C(19)=12 responses
Step-by-step explanation:
Exponential Decay Function
The exponential function is frequently used to model natural growing or decaying processes, where the change is proportional to the actual quantity.
An exponential decaying function can be expressed as follows:
[tex]C(t)=C_o\cdot(1-r)^t[/tex]
Where:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the decaying rate, expressed in decimal
The company puts out an advertisement for a job opening. Initially, the company got 90 responses to the advertisement. Each day, the responses declined by 10%.
This is an example where the decay model can be used to calculate the responses to the advertisement at the day t.
The initial value is Co=90, the decaying rate is r=10% = 0.10. The model is written as:
[tex]C(t)=90\cdot(1-0.1)^t[/tex]
Calculating:
[tex]C(t)=90\cdot(0.9)^t[/tex]
We are required to calculate the number of responses at day t=19, thus:
[tex]C(19)=90\cdot(0.9)^{19}[/tex]
C(19)=12 responses
Find the length of AC
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex] \cot(A) = \frac{AC}{BC} \\ [/tex]
[tex] \cot(60°) = \frac{AC}{8 \sqrt{3} } \\ [/tex]
[tex] \frac{1}{ \sqrt{3} } = \frac{AC}{8 \sqrt{3} } \\ [/tex]
[tex] \frac{AC}{8 \sqrt{ 3} } = \frac{1}{ \sqrt{3} } \\ [/tex]
Multiply sides by 8√3
[tex]8 \sqrt{3} \times \frac{AC}{8 \sqrt{3} } = 8 \sqrt{3} \times \frac{ 1 }{ \sqrt{3} } \\ [/tex]
[tex]AC = 8[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
We want to factor the following expression: (x+7)^2+2y(x+7)+y^2 which patter can we use to factor the espression? U and V are either constant integers or single-variable expressions.
A. (U+V)^2 or (U-V)^2
B. (U+V)(U-V)
C. We can’t use any of the patterns.
Answer:
A. (U+V)^2 or (U-V)^2
Step-by-step explanation:
Tell me which if these two tables are functions or not and why
X + 8 = -15
What does x= ???
Answer: x=−23
Step-by-step explanation:
Let's solve your equation step-by-step.
x+8=−15
Step 1: Subtract 8 from both sides.
x+8−8=−15−8
x=−23
a number was subtracted from 7 and that difference was the divided by 2. after which the quotient was multiplied by 4. this product was 4. what was the difference
Answer:
Difference is 9-7 = 2
Given number is 9
Step-by-step explanation:
Assume;
Given number is x
So,
Subtracted from 7;
x - 7
Divided by 2
(x-7)/2
Multiplied by 4
[(x-7)/2]4
Product was 4
[(x-7)/2]4 = 4
x-7 = 2
x = 9
Given number is 9
Difference is 9-7 = 2
Who is most likely to be in favor of protectionist policies? A. A government that wants to contain the cost of public services B. A producer who is concerned about training workers C. A consumer who wants to pay lower prices D. A factory worker who is concerned about keeping a job
Answer:
A. A government that wants to contain the cost of public services
Step-by-step explanation:
what is the value of x in the function f(x)=3/2x-4 when f(x)=5?
Answer:
3.5
Step-by-step explanation:
3/2(5) - 4
= 1.5(5) - 4
= 7.5 - 4
= 3.5
Hope this helped!
Anyone know this one ??
Answer:
C- 1/2 squash per month
Have a Good one!
please help!!
My age today is
three times what it
will be three years
from now
minus three times
what my age was three
years ago.
How old am I?
Find the slope of the line that goes through the points (0, 9) and (-2, -4).
Answer:
I think it is 13 over 2
Step-by-step explanation:
Priya noticed in the last activity that between the 2 triangles, you only need to know 4 angles to show that they are similar. She wondered which fourth angle would work to prove that triangle RST is similar to triangle EFG. Draw a sketch of the triangle. Then pick one angle measurement that would prove the triangles are similar. Explain to Pyria why knowing that angle would be enough.
Answer:
Please find attached a drawing of the triangles ΔRST and EFG showing the angles
The angle on ΔEFG that would prove the triangles are similar is ∠F = 25°
Step-by-step explanation:
In order to prove that two triangles are similar, two known angles of each the triangles need to be shown to be equal
Given that triangle ∠R and ∠S of triangle ΔRST are 95° and 25°, respectively, and that ∠E of ΔEFG is given as 90°, then the corresponding angle on ΔEFG to angle ∠S = 25° which is ∠F should also be 25°
Therefore, the angle on ΔEFG that would prove the triangles are similar is ∠F = 25°.
Consider the equation and its solution.
8(x-2) = 64
8x-18-84
8x = 80
X=10
Which property is used in the last step to find thatx-10?
distributive property
addition property of equality
subtraction property of equality
division property of equality
Answer:
division property of equality
Step-by-step explanation:
The property used in the last step to find x = 10 in the expression is the division property of equality.
8(x-2) = 64
8x-18 = 84
8x = 80
x = 10
In 8x = 80 ;
Division property of equality was used to find the value of x.
The property states that when we divide both sides by a non-zero value, the two sides remains the same.
2
Select the correct answer.
Simplify the following expression.
Answer:
The answered would be 1/64 since it's simplified
Answer:
I think the exact form is 1/64
A recipe for giant soap bubbles uses 1/2 cup dishwashing liquid and 4 1/2 cups of water. How many cups of water will be used with 1 1/2 cups of dishwashing liquid?
A. 5 1/2
B. 6
C. 9
D. 13 1/2.
Answer: D. 13 1/2.
Step-by-step explanation:
1/2*3= 1 1/2 cups of dishwashing liquid.
4 1/2*3= 13 1/2 cups of water will be used with 1 1/2 cups of dishwashing liquid.
Explain how to use the distributive property to find the product (3) 4 1/5
Answer:
[tex]\frac{63}{5}[/tex]
Step-by-step explanation:
Given expression:
(3) 4[tex]\frac{1}{5}[/tex]
The distributive law is mostly applied to multiplication and division which helps to expand a parentheses;
4[tex]\frac{1}{5}[/tex] can be written as [tex]\frac{21}{5}[/tex]
Now;
(3) [tex]\frac{21}{5}[/tex]
With distributive property, we simply multiply the two terms;
3 x [tex]\frac{21}{5}[/tex] = [tex]\frac{63}{5}[/tex]
Answer:
Rewrite 3 ( 4 1 /5 ) as 3 ( 4 + 1 5 ) . Distribute the 3 to get 3(4) + 3 ( 1 /5 ) . Multiply to get 12 + 3 /5 . Then add to get 12 3 /5
Step-by-step explanation:
GIVING BRAINLIEST AFTER TWO ANSWERS ARE GIVEN!!! WILL CHOOSE THE BEST ONE!!!
Answer:
D
Step-by-step explanation:
Answer:5
Step-by-step explanation:
hihihi
What is the image of (6,5) under a counterclockwise
rotation of 180°?
Answer:
(-6, -5)
Step-by-step explanation:
For a rotation of 180 degrees no matter the direction, you just flip the sign. In (6, 5) both are positive so you just change them to a negative.
quadrilateral ABCD is inscribed in circle E. the m<A=152 find m<C
Answer:
The angle for C is 28°.
Step-by-step explanation:
In a cyclic quadrilateral, opposite angles are supplementary which means that both angles add up will be 180° :
∠A + ∠C = 180°
152° + ∠C = 180°
∠C = 180° - 152°
∠C = 28°
Answer:
B. 28
Step-by-step explanation:
The answer above me is right, I used their answer on my question earlier and I ended up getting the question right. Hope this helps!
Is the relation a function?
(9,-8) (12, 7) (1, 13) (-9, 3) (4, 0)
Yes
No
No answer text provided.
O No answer text provided.
460divided by 9 estimated would be 50
Answer:
it would be 51
Step-by-step explanation:
460 divided by 9 is 51.111...
so the estimated result would be 51 since 51.111... rounds down to 51
i need help to solve please
Step-by-step explanation:
3x+13+8x+14=180-109
11x+27=71
11x=44
x=4
I NEED HELP PLEASE!!!
IM BEGGING YOU PLEASE!!
Answer:
B. - 3.5
Step-by-step explanation:
10.99 / 3.14 = 3.5 rounded to the nearest tenth.
This is easy to do, just divide the circumference by 3.14 and that's the radius.
(BTW i love ur shikamaru profile pic uwu)
If a point is randomly chosen on the regular hexagon shown, what is the probability that it will be in a green section of the figure?
1/6
1/3
1/2
3/4
Answer:
1/2
Step-by-step explanation:
i just took the test on usatestprep
Answer:
1/2
Step-by-step explanation:
Look at the student work shown below.
Simplify: 6t(5s + 7).
(6t)(5s) + 7
30st + 7
Did the student correctly simplify the expression? If “yes,” explain the steps the student followed. If “no,” explain what the student did wrong and what should have been done. 20 points. WILL MARK THE BRIANLIEST!!!! PLS HURRY!! ANY WRONG ANSWERS WILL BE FLAGGED.
Answer:
NO WRONG (6T)(5S)+7 IS WRONG YOU ARE SOPOSED TO ADD THAT 6+5=11 11+7=18 18 DIVIDED BY 7=2.5
Step-by-step explanation:
SORRY FO CAPLOCK THAT HOW I TYPE SIR
Find x. Round your answer to the nearest tenth of a degree.
Answer:
If x is the corner mostly and you said round it to the nearest tenth , rounding 9 to the nearest tenth would be 10 and same for 15.
Step-by-step explanation:
what is 250 to 400 in percentage
Answer:
60%
Step-by-step explanation:
:))))))
step 1 Address the formula, input parameters & values
Formula :
Increase
Initial Value
x 100 = Percent Increase (%)
Initial Value X = 250 & New Value Y = 400
Increase = (Y - X)
(400 - 250)
250
x 100 = ?
step 2 Apply the values in the percentage increase {(Y - X)/X x 100} formula
=(400 - 250)
250
x 100
=150
250
x 100
= 60%
(400 - 250)
250 x 100 = 60%
60 percent increase (%↑) or raise from 250 is 400 or 160% of 250 is 400
Answer:
62.5%
Step-by-step explanation:
Divide 250 by 400 to get 0.625. Then, multiply by 100 to get the percentage, 62.5%.