Answer:
Given that Elena is currently e years old and Katie is k years old. Now, nine years ago, Katie was twice as old as Elena was.
So, k - 9 = 2(e - 9)
⇒ k - 2e + 9 = 0 .............. (1)
And, in four years, Elena will be as old as Katie is now.
So, k = e + 4
⇒ k - e - 4 = 0 ............... (2)
Therefore, the equations (1) and (2) matches the conditions. (Answer)
Elena donates some money to charity whenever she earns money as a babysitter. The table shows how much money, d, she donates for different amounts of money, m, that she earns.
d 4.44 1.80 3.12 3.60 2.16
m 37 15 26 30 18
1. What percent of her income does Elena donate to charity?
%
2. Which quantity, d or m, would be the better choice for the dependent variable in an equation describing the relationship between d and m?
3. Use your answers to write and equation that relates m and d
4.44/37= 0.12
1.80/15= 0.12
3.12/26= 0.12
3.60/30= 0.12
2.16/18= 0.12
1. She donates 12% of her income to charity
2. The quantity, d, would be the better choice for the dependent variable (y) the cost of the donation, depends on her income, if her income increases, the amount donated would increase.
3. d = 0.12m
(my apologize if this is incorrect)
Answer:
Step-by-step explanation:
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The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function f of theta equals 2 times sine theta plus radical 2 period
Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length. (5 points)
Part B: If the angle was doubled, that is θ became 2θ, what are the solutions in the interval [0, 2π)? How do these compare to the original function? (5 points)
Part C: A toddler is jumping on another pogo stick whose length of its spring can be represented by the function g of theta equals 1 minus cosine squared theta plus radical 2 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal? (5 points)
Answer:
0
Step-by-step explanation:
So,0= the lengths of springs from the original pogo stick and the toddler's pogo stick are equal.
Hence, the values for different conditions were calculated with the help of trigonometric functions.
Part A
θ=kπ
Where k is an integer k=0,1,2..
Part B
θ=[tex]k\frac{\pi }{2}[/tex]
Where k is an integer k=0,1,2..
Part C
θ=kπ
Where k is an integer k=0,1,2..
What is trigonometric function?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths
Part A
Given that,
f(x)=2sinθ+[tex]\sqrt{2}[/tex]
Non compressed length = [tex]\sqrt{2}[/tex]
Then
2sinθ+[tex]\sqrt{2}[/tex]=[tex]\sqrt{2}[/tex]
2sinθ=0
sinθ=0
Therefore θ is the integer multiple of π
θ=kπ
Where k is an integer k=0,1,2..
Part B
Here angle is doubled
Then,
2sin2θ+[tex]\sqrt{2}[/tex]=[tex]\sqrt{2}[/tex]
2sin2θ=0
sin2θ=0
Here θ will be the integer multiple of [tex]\frac{\pi }{2}[/tex]
θ=[tex]k\frac{\pi }{2}[/tex]
Where k is an integer k=0,1,2..
Part C
g(x)=1-[tex]cos^{2}[/tex]θ+[tex]\sqrt{2}[/tex]
Here
f(x)=g(x)
2sinθ+[tex]\sqrt{2}[/tex]=1-[tex]cos^{2}[/tex]θ+[tex]\sqrt{2}[/tex]
2sinθ=1-[tex]cos^{2}[/tex]θ
we know that [tex]1-cos^{2}[/tex]θ=[tex]sin^{2}[/tex]θ
2sinθ=[tex]sin^{2}[/tex]θ
sinθ=0
Therefore θ is the integer multiple of π
θ=kπ
Where k is an integer k=0,1,2..
Hence, we have solved that
Part A
θ=kπ
Where k is an integer k=0,1,2..
Part B
θ=[tex]k\frac{\pi }{2}[/tex]
Where k is an integer k=0,1,2..
Part C
θ=kπ
Where k is an integer k=0,1,2..
Learn more about Trigonometric functions here
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Unit 6, Lesson 18. 6.18 Cool-Down.
A triangle has one side that is 4 centimeters long and one that is 9 centimeters long. The third side is a whole number of centimeters. What is the longest possible third side?
Answer:
12 cm
Step-by-step explanation:
You want the longest possible integer length of the third side of a triangle with sides 4 cm and 9 cm.
Triangle inequalityThe triangle inequality requires the longest side be less than the sum of the other two sides:
x < 9 cm + 4 cm
x < 13 cm
The largest integer length less than 13 cm is 12 cm.
The longest possible third side is 12 cm.
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Please answer the question of angles! Would you want to be my friend? I love animals because they are cute! I wear glasses! I love to watch Steven Universe, My little pony, and Teen Titans Go!
Answer:
These would be complementary angles.
Step-by-step explanation:
Complementary angles are angles that add up to 90 degrees.
The table below shows how long a copier took to make copies.
Answer:
Each additional copy increased the time by 8 seconds
Step-by-step explanation:
It is increased because- the amount of seconds is increasing every time an additional copy is added to the table
it is 8 because- 12 increases by 8 to get 20, and 20 increases by 8 to get 28, and 28 increases by 8 to get 36.
Jack wants to know how much water a sphere can hold with a diameter of 16 cm. Find the volume. Use 3.14 for pi.
Answer:
2143.57cm^3
Step-by-step explanation:
here we know the volume of sphere is 4/3πr^3 and the total volume of the sphere is the required capacity of the sphere to hold the water
Find the area of the irregular figure in the diagram.
Answer:
15 because there are 15 squares i counted
Step-by-step explanation:
510 boys worked for 12 days and produced 12,000 mat how many boys are needed to produce 10,000 mat in 10 days.
Answer:
1000
Step-by-step explanation:
substitute 510 with 1000 and multiply by 10 to get 10,000
o Mr. Math S. Fun is looking for his missing pair of
socks. He had 8 pairs from the beginning. 1 red pair,
3 blue pairs, 4 green pairs. He uses 7 pairs last week
and he knows he has a pair of socks remaining. He
left clues on what he used each day last week, help
him which among his socks missing?
Answer:
1/3
Step-by-step explanation:
add all of the totals including the missing pair
we now have 24
7+1 is 8
24 minus 8 is 16
24 can be split into 2 groups of 8
and we have 2/3 left. which makes our solution 1/3
Choose the model for the problem 3/4 divided by 5.
3/20
3/4
1/20
15/20
h e l p m e p l e a s e t h a n k y o u
Answer:
[tex]a)\ \frac{3}{20}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4} \div 5\\\\\frac{3}{4}*\frac{1}{5}\\\\\frac{3}{20}[/tex]
Hope this helps!
Your answer is 3/20
3/4 divided by 5 is 3/20
Hope this helps
Please help with 34. a, b, and c
help, question is below :)))
Answer:
$43 million
Step-by-step explanation:
Step 1. Turn the sentence into an equation (total = T)15.4 million = 0.36 (T)
Step 2. Solve for T15,400,000 / 0.36 = T
42,777,777.78 = T
$42.8 million ≈ $43 million (rounded)
The final answer rounded to the nearest million is $43 million. This makes sense since $15.4 was only 36% of this total. Checking our math, 36% of $43 million is $15.4 million!
Hope this helps :)
Find the unique four-digit integer n with these properties:
The last digit (the units digit) of n is 9.
The digits of n add up to 27.
Two digits of n are the same.
n is a perfect square.
Answer:
3,969
Step-by-step explanation:
If n is a perfect square, then the last digits of the prefect square must be 3 or 7 because n ends in 9.
Since n is 4 digits the number can only land between 33 and 97.
(33, 37, 43, 47, 53, 57, 63, 67, 73, 77, 83, 87, 93, 97)
squared- 1089, 1369, 1849, 2209, 2809, 3249, 3969, 4486, 5329, 5939, 6889, 7569, 8649, 9409
possible answers- 2209, 3969, 4486, 5939, 6889, 9409
2+2+0+9 = 13
3+9+6+9 = 27
4+4+8+6 = 22
5+9+3+9 = 26
6+8+8+9 = 31
9+4+0+9 = 22
Solve the inequality 5y+4 ≤ 22-y and graph the solution set on a number line. Please explain how to do it!
Answer:
y≤3
Step-by-step explanation:
5y+4≤22−y
Step 1: Simplify both sides of the inequality.
5y+4≤−y+22
Step 2: Add y to both sides.
5y+4+y≤−y+22+y
6y+4≤22
Step 3: Subtract 4 from both sides.
6y+4−4≤22−4
6y≤18
Step 4: Divide both sides by 6.
6y/6≤18/6
y≤3
Hey there!
Let's solve your inequality step-by-step.
[tex]\fbox{5y+4≤22−y}[/tex]
Step 1: Simplify both sides of the inequality.
[tex]\fbox{5y+4≤−y+22}[/tex]
Step 2: Add y to both sides.
[tex]\fbox{5y+4+y≤−y+22+y}[/tex]
[tex]\fbox{6y+4≤22}[/tex]
Step 3: Subtract 4 from both sides.
[tex]\fbox{6y+4−4≤22−4}[/tex]
[tex]\fbox{6y≤18}[/tex]
Step 4: Divide both sides by 6.
[tex]\fbox{6y/6 ≤ 18/6}[/tex]
[tex]\fbox{y≤3}[/tex]
Answer:
[tex]\fbox{y≤3}[/tex]
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An empty box is shaped like a rectangular prism. The box has a base area of 9/10 square feet and a height of 1/3 foot. How much packing material is required to fill the box?
A. 3/10 [tex]ft^{3}[/tex]
B. 1/10[tex]ft^{3}[/tex]
C. 1/3[tex]ft^{3}[/tex]
D. 2/3[tex]ft^{3}[/tex]
We need volume
Area of base=9/10ft^2Height=1/3ftSo
Volume=Area of base×Heightvolume:-
[tex]\\ \rm\rightarrowtail \dfrac{9}{10}\times \dfrac{1}{3}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{3}{10}ft^3[/tex]
Sandra bought 4 pounds of sweet potatoes for $5.36. What is the cost per pound of
the sweet potatoes?
A. $0.75
B. $1.34
C. $1.26
D. $9.36
Answer:
B. $1.34
Step-by-step explanation:
5.36 ÷ 4
=536×1/4×1/100
=536/400
=1.34
Rectangle QUAD has coordinates Q(0,0), U(0,3), A(6,3), and D(6,0). Q'U'A'D' is the image of QUAD after a dilation with center (0,0) and scale factor 6. What are the coordinates of point D'?
Answer:
Step-by-step explanation:
Since the dilation is centered at the origin, we can multiply each of the coordinates by the scale factor. This gives us that D'(36,0).
ancient bussy swag please help 2 plus 2
at a carnival a game was set up so you would spin the spinner and roll a die. the spinner had 6 equal sized sections numbered 1-6 to win the game the spinner and the die had to land on the same number. what is the probability that you would win the game?
Answer:
Step-by-step explanation:
400
i need help!!!!!!!!! how do i do this
Answer:
[tex]4^{2}[/tex]
Step-by-step explanation:
so when you multiply two numbers with the same constant, and different exponents, just add the exponents!
so it is 5 - 3 = 2
so its [tex]4^{2}[/tex]
Answer:
A) 4²
Step-by-step explanation:
[tex](4^5)(4^{-3})\\\\4(^{5-3})\\\\4^2\\\\16[/tex]
Hope this helps!
Brody earns $14 per hour for the first 40 hours worked in a week and $21 per hour for any hours over 40 that he worked. Brody earned $812 for one week. How many overtime hours did Brody work that week?
Answer:
brody worked 58 hrs
What is the value of x?
Answer:
-4
Step-by-step explanation:
vertical opposite angles are equal
110=x+114
=-4+114
Answer:
-4 the answer is -4
Which of the following rates is the best deal on a box of cereal?
options:
$3.20 for 20 ounces
$4.50 for 25 ounces
$5 for 40 ounces
$6.50 for 20 ounces
Answer:
C. $5 for 40 ounces
Step-by-step explanation:
First, we need to find the unit rate for each deal.
To do this, we divide the price of the cereal box by the unit (ounces):
1. $3.20 for 20 ounces
3.20/20 = $0.16 for each ounce
2. $4.50 for 25 ounces
4.50/25 = 0.18 for each ounce
3. $5 for 40 ounces
5/40 = 0.13 for each ounce
4. $6.50 for 20 ounces
6.50/20 = 0.33 for each ounce
As you can see, the third one is the best deal, as it is the least expensive.
Hope this helps!
Jenny is studying the growth of a particular type of plant. She is testing the effects of three growth factors: lighting, age, and temperature. Here are the levels she's testing for each.
Growth factor Levels
Lighting Low, Medium, High, Very high
Age month, months, months, months, months
Temperature , , ,
She wants to find the number of ways of combining one level from each of the growth factors. How many ways are there?
Answer:
there are so many ways
Step-by-step explanation:
such as observing day by day and checking its height with a scale everyday etc
The number of ways of combining different growth factors to form a level is 80.
What is Permutation?The act of organizing all the components of a set into some sequence or order is known as permutation. Permuting, in other words, is the act of reordering the components of a set that has previously been sorted.
A permutation is the selection of r items from a collection of n items without replacement, with the order of the items being significant.
nPr = (n!) / (n-r)!
What is a Combination?The combination is a method of picking elements from a collection in which the order of selection is irrelevant (unlike permutations).
A combination is a selection of r items from a collection of n items with no replacements and no regard for order.
nCr = (n!)/{(r!)((n-r)!)}
How do we solve the given question?We are given that Jenny is studying the growth of a particular type of plant. She is testing the effects of three growth factors: lighting, age, and temperature. Here are the levels she's testing for each.
Growth factor Levels
Lighting: Low, Medium, High, Very high.
Age: 1 month, 2 months, 3 months, 4 months, 5 months.
Temperature: 20°, 22°, 24°, 26°.
We are asked to find the number of ways in which she can combine different levels to form one level.
We first check the number of combinations for each factor and then multiply them all to get the total number of ways possible.
Lighting: 4 (∵ All the 4 levels are possible, so the combinations are 4P1 = 4).
Age: 5 (∵ All the 5 levels are possible, so the combinations are 5P1 = 5).
Temperature: 4 (∵ All the 4 levels are possible, so the combinations are 4P1 =4).
∴ Total number of ways of combining different growth factors to form a level = 4*5*4 = 80
∴ The number of ways of combining different growth factors to form a level is 80.
Learn more about permutations and combinations at
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The price of a pair of shoes is $72.00, plus 8% sales tax. What is the sales tax on this pair of shoes in dollars and cents?
A) $5.76
B) $6.56
C)$6.98
D) $7.24
Answer:
A.
Step-by-step explanation:
To find the answer, we have to do 8% of 72.
8% of 72 = 5.76
really thats all whats needed to do the problem
hope this helps :)
Answer:
A)5.76
Step-by-step explanation:
usa test prep
thank you!
56 cookies.Each cookie cost 2.95, including tax. Of the cookies she made 1/4 of them were lemon.How much money will be made if they sell the lemon cookies
1/4 of cookies
56/414cookiesCost of one cookies =2.95
Total cost
2.95(14)$41.3Answer:
$41.3
Step-by-step explanation:
Each cookie costs,
→ a = $2.95
Lemon cookies (1/4) of 56 cookies is,
→ b = 1/4 × 56
→ b = 56/4
→ [ b = 14 lemon cookies ]
The money made if she sell the lemon cookies alone will be,
→ a × b
→ 2.95 × 14
→ $41.3
Hence, the money made is $41.3.
A CD costs £12 and a T-shirt costs £15, I have £60 to spend. I buy x number of CDs and y number of T-shirts. Write;
A) An expression for the amount of money I spend.
B) An inequality showing the amount of money I spend has to be less than or the same as what I have.
-Can you plot your inequality on a pair of axis?
-Can you use the graph to find the different numbers of CDs and T-shirts I can buy?
Worth 20 points!
Answer:
A: [tex]12x+15y=60[/tex] B: [tex]12x+15y\leq 60[/tex]
Step-by-step explanation:
288 feet
75.36 feet
37.68 feet
24 feet
Answer:
37.68 feet.
Step-by-step explanation:
Circumference = diameter * π
= 12 * π
= 37.68 feet.
If line m || line n and Ð2 measures 35°, what is the measure of Ð5?
Answer:
145
Step-by-step explanation:
angle 2 = angle 3
=> angle 3 = 35
now, we have
=> 35+angle 5 = 180
=> angle 5 = 180 - 35
=> angle 5 = 145
Answer:
145°
Step-by-step explanation:
line m || line (Given)
[tex]m\angle 2 = 35\degree ......(1)[/tex] (Given)
[tex]m\angle 3 = m\angle 2 ......(2)[/tex] (vertical angles)
From equations (1) and (2)
[tex]\implies m\angle 3 = 35\degree[/tex]
[tex]m\angle 3 +m\angle 5 = 180\degree[/tex] (interior angles on the same side of transversal)
[tex] \implies 35\degree +m\angle 5 = 180\degree[/tex]
[tex] \implies m\angle 5 = 180\degree-35\degree[/tex]
[tex] \implies m\angle 5 = 145\degree[/tex]