Using linear functions, it is found that 4 movies would cause the two plans to have an equal monthly cost.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For the functions in this problem, we have that:
The fixed cost is the intercept.The cost per movie is the slope.Hence the cost functions are given as follows:
C1(x) = 22 + x.C2(x) = 14 + 3x.The costs will be the same when:
C1(x) = C2(x).
Hence:
22 + x = 14 + 3x
2x = 8
x = 4.
4 movies would cause the two plans to have an equal monthly cost.
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two investments totaling $28,000 produce annual income of $1435. One investment yields 9% per year, while the other yields 2% per year. How much is invested at each rate
The investment amount at 9% rate is $12500 and the investment
amount at 2% rate is $15500
What is mathematical expression?
A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Let x be the amount invested at 9% rate.
And (28000−x) be the amount invested at 2% rate.
The total annual income is $1435
Let us find the amount invested at 9% rate:
x9%+2%(28000−x)=1435
9%+2%(28000−x)=1435
0.09x+0.02(28000−x)=1435
0.09x+560−0.02x=1435
0.09x−0.02x=1435−560
0.07x=875
x=875/0.07
x=12500
Let us find the investment amount at 2% rate:
⇒28000−x
⇒28000−12500
⇒15500
Therefore, the investment amount at 9% rate is $12500 and the investment amount at 2% rate is $15500.
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What is the distance between "-17" and "-6"
Answer:
11
Step-by-step explanation:
Answer:
11
Step-by-step explanation
17
-6
=11
A list of needed materials calls for one five-pound pack of deck screws. You have three leftover packs. Two of them are 1/4 full, and the third pack is 1/3 full. Expressed as a fraction, what part of a full 5-pound pack of nails do you have?
Based on the fact that there are three leftover packs, the part of the 5-pound pack of nails that you have is 5/6
What part of the pack do you have?To find the part of the full 5-pound pack of nails that you have, you need to add up all the fractions of the leftovers that you have.
The part of the full 5-pound pack that you have is:
= 1/4 + 1/ 4 + 1/3
= 3/12 + 3/12 + 4/12
= 10/12
In the simplest term, this is:
= 5/6
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77. What is the circumference of the larger circle
shown above in terms of x?
A. 10 π x
B. 10 π +x
C. 10 π +2x
D. 10π+ 2πx
[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=5+x \end{cases}\implies C=2\pi (5+x)\implies C=10\pi +2\pi x[/tex]
HELP WITH THIS MATH QUESTION PLEASE! I WILL GIVE BRAINLYEST!!
Determine if each sequence below is arithmetic or not.
a. 200, 40, 8
b. -6,-3,0, 3
c. Danielles parents have offered her a way to earn her allowance each week. She would get paid $30 each week. Does the amount of money Danielle has earned on the nth week represent an arithmetic sequence?
d. The price of a stock on day n of the year
Answer:
I think the answer would be the letter b
Solve for c.
a=11+4b−4c
Answer:
c = -a/4 + b + 11/4
Step-by-step explanation:
Solve for c:
a = -4 c + 4 b + 11
a = -4 c + 4 b + 11 is equivalent to -4 c + 4 b + 11 = a:
-4 c + 4 b + 11 = a
Subtract 4 b + 11 from both sides:
-4 c = a + (-4 b - 11)
Divide both sides by -4:
Answer: c = -a/4 + b + 11/4
2. Find and simplify the product of f and g *
given the functions f (x)
; g(x) = -²
=
x+2
(2 Points)
The product of the functions f(x) and g(x), where the functions f(x) = [tex]x+2[/tex] and g(x) = [tex]-x^{2}[/tex] is
As per the given question statement, we are supposed to find and simplify the product of the functions f(x) and g(x), where the functions f(x) = [tex]x+2[/tex]and g(x) = [tex]-x^{2}[/tex].
Let's assume [tex]m(x)[/tex] be the product of the functions [tex]f(x)[/tex] and [tex]g(x)[/tex]
So, [tex]m(x) = f(x) * g(x)\\m(x)= (x+2)*(-x^{2} )\\m(x)=-x^{3} -2x^{2}[/tex]
Therefore the product of the functions f(x) and g(x), where the functions f(x) = [tex]x+2[/tex]and g(x) = [tex]-x^{2}[/tex] is [tex]m(x)=-x^{3} -2x^{2}[/tex]
This question is a classic example of how to solve functions using different mathematical operations and using the concept of algebraic expressions.
Algebraic Expressions: An algebraic symbol or set of symbols that includes one or more integers, variables, and arithmetic operations.To learn more about algebraic expressions, click on the link given below:
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Simplify 4.5p(2 − 0.2p).
A.9p − 0.9p2
B. 9p − 0.2p2
C. 9 − 0.2p2
D.9 − 0.9p2
show your work
The simplified form of 4.5p (2 - 0.2p) is option A 9p - 0.9p²
Given,
The expression: 4.5p (2 - 0.2p)
We have to simplify the expression:
Simplification:A mathematical expression is simplified when it is replaced with a simpler, typically shorter, equivalent statement.
Difference between simplification and solving:They are different in a way that extends the distinction between expressions and equations. Either equations or expressions can be simplified. Making the math language simpler entails shortening it. Finding the value or values that make the equation, or math sentence, true, is the process of solving.
That is,
4.5p (2 - 0.2p)
Open the bracket and do the multiplication:
(4.5p × 2) - (4.5p × 0.2p)
= 9p - 0.9p²
That is, the simplified form of the expression 4.5p (2 - 0.2p) is 9p - 0.9p².
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Mayerlin wants to ride her bicycle 56 miles this week. She has already ridden 8 miles.
If she rides for 6 more days, what is the average number of miles she would have to
ride each day to meet her goal?
Please help!
if in the next 6 days she rides an average of 8 miles per day, she will meet her goal.
What is the average number of miles she would have to ride each day to meet her goal?We know that Mayerlin wants to ride her bicycle for 56 miles this week, and she already has ridden 8 miles, so the distance left is:
56mi - 8mi = 48mi
Now, to find the average distance that she needs to ride each day in order to meet her goal, we need to take the quotient between the distance left and the number days that she has left (6 days), then we will get:
D = 48mi/6 = 8mi
This means that if in the next 6 days she rides an average of 8 miles per day, she will meet her goal.
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Brody's age is 3 years less than twice Trinity's age? The sum of their ages is 30.
Answer: Brody's Age is 19 and Trinity's age is 11
Step-by-step explanation:
x = Trinity's age
2x-3= Brody's age
The sum of the ages is 30, so
x + (2x-3) = 30
3x - 3 = 30
add 3 to both sides 30 turns into 33 so,
3x = 33
divide by 3 both sides
x = 11 which is trinity's age and plug x into 2x - 3 which is 19 so that's Brody's age.
PLEASE HELP !?!????!?
Answer: Supplementary Angles
Step-by-step explanation:
Supplementary angles are a pair of angles whose sum is 180°. 45° and 135° add up to 180°. Therefore, the answer is supplementary angles.
How much it’s 27+ 0.185
Answer:
27.185
Step-by-step explanation:
ASAP Please help and thank you!
Charles, age 45, would like to determine how much life insurance to purchase using the human life value approach. He assumes his average annual earnings will remain at $40,000. Of this amount, $20,912 is available annually for the support of his family. Charles will generate this income for 24 more years and he believes that 5.37 percent is the appropriate interest (discount) rate. What is Charles' human life value? (Round your answer to 2 decimal places)
Using it's formula, it is found that Charles' human life value is of $26,951.39.
What is the human life value formula?The human life value formula(HLV) is given by the following multiplication:
HLV = Annual Expenses x Number of Years x Interest Rate.
For this problem, we have that:
$20,912 is available annually for the support of his family, hence the annual expenses are of $20,912.Charles will generate this income for 24 more years, hence the number of years is of 24.As stated in the problem, the interest rate is of 5.37%, hence, as a decimal, is of 0.0537.Hence, applying the formula, we have that Charles' human life value is found as follows:
HLV = 20912 x 24 x 0.0537
HLV = $26,951.39.
Charles' human life value is of $26,951.39.
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A train is going on a journey. First it travels east for 50 kilometers. Then it turns north and travels for 22 kilometers. Next it goes west for 50 kilometers. Finally, it travels south for a certain number of kilometers. At the end of its journey it is back at its original location. How many kilometers did it travel in the southward direction?
Answer:
Answer would be 22 km at southward direction.
Answer = 22km
Step-by-step explanation:
As it started from the point O.
* Goes 50 to East direction
* Goes 22 to North direction
* Goes 50 to West direction
* And the it travels back to the starting point when it turn to south direction. It traveled 22 km to southward direction.
> Total kilometers the train traveled is 144 kilometers.
I hope you get this right.
[tex]\left|16x\right|\le 8[/tex]
Please help me with this, and thank you.
Answer:
-1/2 ≤ x ≤ 1/2 or x∈ [- 1/2, 1/2]Step-by-step explanation:
|16x| ≤ 8|16x/16| ≤ 8/16|x| ≤ 1/2x ≤ 1/2 or x ≥ - 1/2Combination of two inequalities above:
-1/2 ≤ x ≤ 1/2Or interval notation:
x∈ [- 1/2, 1/2]Write an inequality that represents the graph. An inequality that represents the graph is -1 on a number line
a .
The inequality of the number line is x > -1
What is a number line?A number line is a vertical or horizontal line that has endpoints and it is used to represent numbers at a constant interval
From the number line in the question, we can see that:
How to determine the inequality?From the question, we have
Point = -1
Assume the following
The endpoint of the circle on the number line is an open circleThe arrow points to the rightAs a general rule, open circles implies that the number at that endpoint is not included part of the solution set.
This means that the inequality of the number line is x > -1
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The vertical position y (in feet) of a rock t seconds after it was dropped from a cliff is given by the formula y equals short dash -16 t squared plus 4 t plus 380. The base of the cliff corresponds to y = 0. After how many seconds will the rock hit the ground at the base of the cliff?
The seconds that it will take the rock hit the ground at the base of the cliff is 5 seconds
How to calculate the value?Based on the information given, it should be noted that the expression given is:
y = -16t² + 4t +380
We have to divide through by 4. Therefore,
y = -4t² + t + 95
y = -4t² + 20t - 19t + 95
y = -4t(t - 5) - 19(t - 5)
t - 5 = 0
t = 0 + 5
t = 5
The time taken will be 5 seconds.
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Find the odd one out 1.234,
123.4 hundredths,
1234 thousandths,
12.34,
123 hundredths and 4 thousandths
The decimal odd one out is: 123 hundredths and 4 thousandths.
What are decimals?The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values.
Decimal notation is the term used to describe the method of representing numbers in the decimal system.
Given: 1.234 is a decimal.123.4 hundredths, 1234 thousandths and 12.34 are all different forms of the given decimal. But 123 hundredths and 4 thousandths is not.
This is due to the fact that in the other selections, it is written in decimal format or is finished, but in the fourth or final option, it is purposefully not written in decimals. It is hence the outlier.
Hence, The decimal odd one out is: 123 hundredths and 4 thousandths.
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Evaluate 3x - 7 when x = 4
Answer:
5
Step-by-step explanation:
3x-7
=3×4-7
=12-7
=5..........
Hey I need help please help
The slope of the linear function shown in the graph is of 2, as:
Run = 2.Slope = rise/run = 4/2 = 2.What is a linear function?A linear function is modeled according to the following rule:
y = mx + b
In which:
m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For this problem, we want to find the slope given two points of the function, which are (2,4).
For the calculation, we have that:
The rise is the change in y.The run is the change in x.Hence:
The rise is of 4 - 0 = 4.The run is of 2 - 0 = 2.The slope is of 4/2 = 2.More can be learned about linear functions at https://brainly.com/question/24808124
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Construct a parallelogram PQRS such that PQ = 8.1 cm, QR = 6.9 cm and the diagonal QS = 10.4 cm. Measure and write down the length of the diagonal PR.
Answer:
10.4 it is the correct answer please mark me as a brainlist
Gwen has loyalty card for a store that gives her a discount of 5% off the marked price of items. Office Chair $800, Acer Laptop $4580.
(a) How much will she pay if she bought the two items above?
(b) The store buys the chairs at $1 530 for two. Show whether the store made a profit on the one chair from Gwen’s Purchase.
The length of a rectangle is twice the width. The area of the rectangle is 94 square units. Notice that you can divide the rectangle into two squares with equal area. How can you estimate the side length of each square? Estimate the length and width of the rectangle.
Answer: w=[tex]\sqrt{47}[/tex], l=2[tex]\sqrt{47}[/tex]
Step-by-step explanation:
A=area of rectangle
A=l*w
A=2w*w
94=2w*w
w*w=47
w=[tex]\sqrt{47}[/tex] ==> width of rectangle and side length of square
94=l*w
94=l*[tex]\sqrt{47}[/tex]
l=[tex]\frac{94}{\sqrt{47} }[/tex]
l=[tex]\frac{94\sqrt{47} }{47 }[/tex]
l=2[tex]\sqrt{47}[/tex]
Use the figure for Items 2 and 3. Lines PS and TR intersect at point Q.
Applying the vertical angles theorem and the linear pair theorem, the measure of angle PQV is calculated as: 53°.
How to Apply the Linear Pair Theorem?The linear pair theorem states that when two angles form a linear pair, the sum of both angles of the linear pair would be equal to 180 degrees.
What is the Vertical Angles Theorem?Two angles that are a vertical pair, have a measure that is equal to each other, based on the vertical angles theorem. That is, they are congruent angles.
m<RQS + m<PQT = 180 degrees [linear pair theorem]
Substitute
(2m + 4)° + (3m + 1)° = 180°
Solve of the value of m
2m + 4 + 3m + 1 = 180
Add like terms together
2m + 3m + 4 + 1 = 180
5m + 5 = 180
5m + 5 - 5 = 180 - 5
5m = 175
5m/5 = 175/5
m = 35
m<PQR = 3m + 1 [vertical angles theorem]
Plug in the value of m
m<PQR = 3(35) + 1
m<PQR = 105 + 1
m<PQR = 106°
m<PQV = 1/2(m<PQR)
m<PQV = 1/2(106)
m<PQV = 53°
Thus, applying the vertical angles theorem and the linear pair theorem, the measure of angle PQV is calculated as: 53°.
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Answer:
The answer is 74
Step-by-step explanation:
Bryan ran 100 meters in 14.5 seconds. How long did he take to run 5 meters?
Answer: 0.725 seconds
Step-by-step explanation:
5 meters*14.5 seconds/100 meters=
5*14.5/100=
72.5/100=0.725 seconds
For the month of December, a checking account has a balance of $500 for 12 days, $1250 for 12 days, $1150 for 3 days, and $600 for 4 days. What is the average balance for December?
Answer:
$866.13
Step-by-step explanation:
to get an average, you add up all the factors then divide them by how many there are. I added 500 12 times to 1250 12 times to 1150 3 times and 600 4 times.
aka (500*12)+(1250*12)+1150+1150+1150+600+600+600
then i divided by 31 because 12+12+3+4=31. giving the average $866.13.
Use the hundredth grids below to answer the questions. The first two hundredth grids show Sophia's work. The second two hundredth grids show Aiden's work.
This image shows Sophia's work. One whole 10-by-10 grid and 2 columns and 5 squares on a second grid are shaded blue. On the second grid, the remaining 5 squares in the third column, 3 more columns, and 5 more squares are shaded brown.
This image shows Aiden's work. One whole 10-by-10 grid and 2 columns and 5 squares on a second grid are shaded blue. On the second grid, 4 squares in the third column are shaded brown.
Part A
Which student correctly models the problem 1.25 + 0.4. Type your answer in the box.
Sophia
Part B
What is the correct answer for 1.25 + 0.4?
1.65
Part C
Explain the errors made by the incorrect student. Refer back to the models and use equations to support your explanation.
Answer:
Aiden got the question wrong because he added four squares instead of four columns. Aiden confused 0.4 with 0.04, using 4 ones instead of 4 tens.
Im sorry if this is confusing i hope it helped :)
Please help! 10 points. If u don’t know the answer don’t answer please!
Answer: The answer is C
Step-by-step explanation: Bro I'm in 8th grade rn and I know the answer XD my IQ is 137 :)
Answer:b
Step-by-step explanation:becuase -2x times 6x = -12x
then your done with that part so then multiply 7x7 and that's 49 so its
-12x+49
One number is 14 less than another. If their sum is increased by seven, the result is 85. Find the numbers.
Answer: 32, 46
Step-by-step explanation:
a=number 1. b=number 2
a=b-14
a+b+7=85
b-14+b+7=85
b+b-14+7=85
2b-7=85
2b=92
b=46
a=46-14
a=32
Answer:
Step-by-step explanation:
the equation to find this is
x+(x+14)+7=85
first minus the 7
X+(x+14)+7-7= 85-7
x+(x+14)=78
78÷2 = 39
42+36
Select all the products that are equivalent to 1/6
A. −3/4⋅(−2/9)⋅1/2
B. −3/2⋅(−2/9)⋅1/2
C. −1/2⋅(−2/3)⋅1/2
D. 1/2⋅(−2/9)⋅1/2
E. 1/2⋅(−5/6)⋅(−2/5)
B, C, and E are the products equivalent to 1/6
We have been given five different products and we have to find out which of them are equivalent to 1/6. So,
(-3/4)*(-2/9)*(1/2) => 6/72 => 1/12(-3/2)*(-2/9)*(1/2) => 6/36 => 1/6(-1/2)*(-2/3)*(1/2) => 2/12 => 1/6(1/2)*(-2/9)*(1/2) => -2/36 => -1/18(1/2)*(-5/6)*(-2/5) => 10/60 => 1/6Here we observe that the product of B, C, and E after solving them is equivalent to 1/6 whereas, the product of A and D is 1/12 and -1/18 respectively.
Hence, We get that the product for the numbers
(-3/2)*(-2/9)*(1/2), (-1/2))*(-2/3)*(1/2), and (1/2)*(-5/6)*(-2/5)Which are Options B, C, and E equivalent to 1/6
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