Answers for a) $53.2, b) z = 10x+0.07y and c) y =300
What is an equation?The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, a car rental company charges $7 a day and 9 a mile to rent one of its cars, then the cost z, in dollars, to rent a car for 2 days and drive y miles can be found from the equation
z = 7x + 0.09y
a) x = 4, y = 280
z = 7*4 + 280*0.09
z = 53.2
Therefore, the cost to rent a car for 4 days and drive it for 280 miles is $53.2
b) The equation that gives the cost z
z = 10x+0.07y
c) When the costs are equal, then,
10*2+0.07y = 7*2+0.09y
20+0.07y = 14+0.09y
0.02y = 6
y = 300
Therefore, the cost of renting the cars from each of the two companies will be equal when y = 300 miles.
Hence, Answers for a) $53.2, b) z = 10x+0.07y and c) y =300
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2+2+2+2+2+2+2+2+2+0+0+0+0+0+0
Answer:
18
Step-by-step explanation:
18
step by step explanation: you literally add them up
What is the moment of inertia of a 1. 5-kg-rod that rotates about its center? the length of the rod is 1. 8 m.
the moment of inertia is [tex]0.405 kgm^{2}[/tex] .
Given :
mass of rod (m) = 1.5kg
length of rod (l) = 1.8m
formula :
We know that moment of inertia of rod about it's center is
[tex]I = ml^{2}/12[/tex]
I = (1.5)*(1.8*1.8)/12
I = 1.5*3.24/12
I = 4.86/12
I = 0.405 [tex]kgm^{2}[/tex]
hence, the moment of inertia of rod about its center is 0.405 [tex]kgm^{2}[/tex].
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The moment of inertia of the given condition is 0.405 kgm².
Given that,
Mass of the rod = 1.5 kg
Length of the rod = 1.8 m
A thin rod with mass M and length L has an axis running through its center, and the formula for its inertial momentum is given by,
I = ML²/12
I = 1.5*(1.8)²/12
I = 0.405 kgm²
Hence, the moment of inertia of the given condition is 0.405 kgm².
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A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power. What is the smallest possible sum for this series?
The smallest possible sum for this series is 20736 = 12^4.
Given:
A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power.
S = a + (a+2) + (a+4) + ... + (a+2*287) = 288(a+(a+574))/2 = 288(a+287)
288 = 2^5 * 3^2
smallest value of (a+287) that will make S = 288(a+287) a perfect fourth power is:
a + 287 = 2^3 * 3^2 = 72
a = −215
Smallest sum = 288*72 = 20736 = 12^4
Smallest odd integer in series = −215
−215 + −213 + −211 + ... + −1 + 1 + 3 + ... + 213 + 215 + ... + 359
= 20736 = 12^4.
Therefore the smallest possible sum for this series is 20736 = 12^4.
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Find the quotient of
4 2/3 divided by 2 2/5
Give your answer as a mixed number in its simplest form
Answer:
1 17/18
Step-by-step explanation:
4 2/3 / 2 2/5 =
= 14/3 / 12/5
= 14/3 × 5/12
= 70/36
= 35/18
= 1 17/18
4 2/3 divided by 2 2/5 results to 35/18.
What is Division?In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed.
Given:
4 2/3 divided by 2 2/5
So, 14/3 divided by 12/5
= 14/ 3 x 5/ 12
= 7/3 x 5/6
= 35/ 18
Hence, 4 2/3 divided by 2 2/5 results to 35/18.
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I need help with this question
Two companies offer Janeen a sales position. Company A pays $4,000 per month plus $400 per car sold. Company B pays $3,750 per month plus $450 per car sold. Which equation could be used to determine the number of cars sold in a month, x, that would result in the same total income from each company?
Answer:
4000 + 400x = 3750 + 450x
Step-by-step explanation:
The number of cars where the offer would be equal is 5 cars.
4000 + 400x = 3750 + 450x Subtract 400x from both sides of the equation
4000 = 3750 + 50x Subtract 3750 from both sides of the equation
250 = 50x Divide both sides by 50
5 = x
If you sell less than 5 cars a month, take job A. If you sell more than 5 cars a month, take job B.
can someone help
p(n)=2n; find p(-1) work must be shown
The solution for p(-2) in the function when the function p(n) = 2n is -2
How to determine the solution for p(-1) in the function?From the question, we have the following equation that can be used in our computation:
p(n)=2n
To make the equation legible, we need to rewrite it
So, we have the following representation
p(n) = 2n
Also from the question, we have
p(-1)
This means that the value of n is -1, and we calculate p(n) when n = -1
Substitute the known values in the above equation, so, we have the following representation
p(-1) = 2 * -1
So, we have the following equation
p(-1) = 2 * -1
There is no constant to add or subtract to both sides of the equation
So, we have the following representation
p(-1) = -2
Hence, the solution is -2
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nple
If a pyramid has a square base with side lengths and height h, which
formula represents the volume of the pyramid?
Since the base of the pyramid is a square, the area of the base is
Abase = SXS = 5².
The volume of a pyramid is one-third the product of base area and
height, so the volume of this pyramid is
Key Term
Cavalieri's principle is applicable to all three-dimensional shapes, including
and
Cavalieri's principle implies that a tilted cone (or pyramid) has exactly the same
as an upright cone (or pyramid) with same base and
height.
The formulas for the volumes of a cone and a pyramid are applicable even if their shapes are not upright.
Summary
What is the relationship between the volume of a rectangular prism and a pyramid with the same base area
and height?
Copyright © 2019 Edmentum Inc. All Rights Reserved
Using mensuration we know that the volume of the square-based pyramid is (1/3)(x^2h) cubic units.
What is mensuration?The subject of mathematics known as mensuration is concerned with measuring geometric shapes and their various characteristics, such as length, volume, shape, surface area, lateral surface area, etc. In fundamental mathematics, learn about mensuration.Example 1: Calculate the size of a square with a 5 cm side. 5 x 5 Equals 25 when the values are substituted. The square's area is 25 square centimeters as a result.So, if 'B' is the base and 'h' is the height of the pyramid, its volume is V = (1/3) (Bh) cubic units.
Imagine a square pyramid whose base is a square of length 'x'. Then the base area will be: B = x^2So the volume of the square-based pyramid is (1/3)(x^2h) cubic units.Therefore, using mensuration we know that the volume of the square-based pyramid is (1/3)(x^2h) cubic units.
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The coordinates of the vertices of Triangle PQR are P(2, 5), Q (-6,5), and R (-2, 1). Determine
whether PQR is a right triangle. Show your work.
Answer:
PQR is a right triangle
Step-by-step explanation:
slope of the line that contains PQ = 0
Because the line is parallel to x axis
slope of the line that contains QR
(5-1)/(-6+2) = 4/-4 = -1
slope of the line that contains PR
(1-5)/(-2-2) = -4/-4 = 1
PR and QR are perpendicular so the triangle is right
Please help!!!
Write the compound inequality for the graph.
Answer:
-8 < x ≤ 0
Step-by-step explanation:Let's remember what open and closed circle mean:
Open Circle:
Less than ( < ) / Greater than ( > )
Closed Circle:
Greater than or equal to ( ≥ ) / Less than or equal to ( ≤ )
Now, let's review this graph:
Let's call this unknown value 'x'
Reading the graph left to right:
x is greater than -8, but is less than or equal to (Remember!! Closed circle!)
We can right this as:
-8 < x ≤ 0
And that is our answer! If your problem wants a different variable (y, z, q, etc) just put that in place of 'x'
Let me know if this helped!
Which of the following statements are TRUE? Select ALL that apply.
A. When dilating a figure with a scale factor greater than 1, the new figure will be further from the center of dilation.
B. When dilating a line, the new line will be parallel to the original line.
C. When dilating a figure with a scale factor less than 1, the new figure will be closer to the center of dilation.
D. When dilating a figure with a scale factor less than 1, the new figure will be further from the center of dilation.
How do you graph g(x)= -3x
(Algebra 1 Honors)
Put different values of x in the function and find values of g(x). Then plot the points on a graph.
What is a graph?Graphing a function involves tracing the curve on a coordinate plane that corresponds to the function. Every point on the curve will satisfy the function equation if the curve (or graph) reflects the function.
The given function is
g(x) = - 3x
Put x = - 3
g(x) = -3(-3)
g(x) = 9
Put x = - 2
g(x) = -3 (-2)
g(x) = 6
Put x = - 1
g(x) = -3 (-1)
g(x) = 3
Put x = 1
g(x) = - 3 (1)
g(x) = - 3
Put x = 2
g(x) = -3 (2)
g(x) = - 6
Plot the points on a graph, and keep the values of x on the x-axis and g(x) on the y-axis.
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At the Jackson Zoo, 1/2 of the animals are primates. Of the primates, 1/2 are monkeys. What fraction of the animals at the Jackson Zoo are monkeys?
The fraction 1/4th of the animals at the Jackson Zoo are monkeys.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
At the Jackson Zoo, 1/2 of the animals are primates
So if x is the total animals in that zoo, total primates are x/2.
Now out of them, 1/2 are monkeys i.e 1/2 of x/2
= x/4.
Hence 1/4 th fraction of the animals at the Jackson Zoo are monkeys.
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Work out an estimate for the mean time some people spent mowing their lawn
The mean time some people spent mowing their lawn is 1.01
Mean
Mean refers the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Given,
Here we have the table of data.
Now, we need to estimate for the mean time some people spent mowing their lawn.
According to the given problem, the mean is calculated for each time interval, then we get,
For the time period 0 ≤ t < 10, then the mean is,
=> 3/(3 + 11 + 14 + 2)
=> 3/30
=> 0.1
For the time period 10 ≤ t < 20, then the mean is,
=> 11/(3 + 11 + 14 + 2)
=> 11/30
=> 0.37
For the time period 20 ≤ t < 40, then the mean is,
=> 14/(3 + 11 + 14 + 2)
=> 14/30
=> 0.47
For the time period 40 ≤ t < 60, then the mean is,
=> 2/(3 + 11 + 14 + 2)
=> 2/30
=> 0.07
So, the mean time is obtained by adding the values,
=> (0.1 + 0.37 + 0.47 + 0.07)
=> 1.01
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Can I have help with this one pls
Answer:
[tex]r = \dfrac{a}{b - pcos( \theta)} \\ \\ r \times (b - pcos( \theta)) = \dfrac{a}{ \cancel{b - pcos( \theta)}} \times \cancel{b - pcos( \theta)} \\ \\ a = r \times (b - pcos( \theta) \\ \\ a = rb - rpcos( \theta)[/tex]
11 ) (−11,−11) with slope 5 5
Slope-intercept form:
y= 8/5x+3
Point-slope form:
y+5= 8/5 • (x+5)
Find the exact value of the following if 0 ≤ x ≤pi/2 and 0 ≤ y ≤ pi/2
sin(x - y) if cos x = 3/5 and sin y = 24/25
The value of trigonometric function sin(x-y) = -44/125
Given ,
cos x = 3/5
sin y = 24/25
Sin( x - y) = sin(x)cos(y) - sin(y)cos(x)
substituting the values,
=> sin(x)cos(y) - sin(y)cos(x)
=> sin(x)cos(y) - (24/25)(3/5) ------(1)
As we know ,
sin(x) = √(1 - cos²x)
sin x = √(1 - (3/5)²)
=> sin x = √1 -9/25
=> sin x = √16/25
=> sin x = 4/5
Again ,
cos y = √(1 - sin²y)
=> cos y = √(1 - (24/25)²
=> cos y = √1 - 576/625
=> cos y = √49/625
=> cos y = 7/25
Substituting the values of sin x and cos y in equation (1)
=> sin(x - y) = (4/5)(7/25) - (24/25)(3/5)
=> sin(x - y) = (28 / 125) - (72 / 125)
=> sin(x - y) = -44/125
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Pocahontas weighs 8.5 kg. Her brother is 3 times as heavy. How
31
4
much does her brother weigh?
Your answer is in bold below!
8.5 x 3 = 25.5
Answer: Her brother is 25.5 kg.
Step-by-step explanation:
If her brother is 3 times as heavy, we need to multiply 8.5 kg by 3.
8.5 kg times 3 is 25.5 kg.
If you roll a four-sided die and a six-sided die, which roll totals (2, 3, ..., 10) have the lowest probability? (Enter your answers as a comma- separated list.) 2,3,4
For rolling four-sided die and a six-sided die, six-sided die have the lowest probability.
Define the word probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.As per the state question-
Sample space for four-sided die = (1, 2, 3, 4).
Sample space for six-sided die = (1, 2, 3, 4, 5, 6).
The each outcome for the four-sided die will be 1/4 .
The each outcome for the six-sided die will be 1/6.
1/6 < 1/4
Thus, six-sided die have the lowest probability.
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PLEASE HELP WILL GIVE BRAINLYEST IF YOU REMIND ME AND FOR THE CORRECT ANSWER!
Answer:
3 times .. just multiply
Michael and Imani go out to eat for lunch.
Part A
If their food and beverages cost $25.30 and there is an 8% meals tax, how much is the bill? Enter your answer to the nearest cent.
$
Part B
After adding a tip, the total lunch cost was $32.24. What percentage tip did they give? Enter your answer to the nearest percentage.
%
Part A:
After adding the meals tax we get the total bill as $27.32
Part B:
After adding the tip the total lunch cost was 432.24, hence the percentage of tip he gave is 18%
Tax
Meal plus tax = 25.3 + 8/100 * 25.3
Meal plus tax = 25.3 + 2.024 Round later. Find the total.
Meal plus tax = 27.324
Meal plus tax = 27.32 rounded to the nearest cent.
Tip
Total cost = $32.242
tip = 32.242 - 27.324
percentage of tip= 4.918
= 18%
Hence we get the required answers.
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If the ratio of a £40 is one to 4, how much will each person get?
Solve the system.
2x + y = −3 −2y = 6 + 4x
Write each equation in slope-intercept form.
The given equations, 2x + y = -3 and -2y = 6 + 4x, written in slope-intercept form is y = -2x - 3
Writing equations in slope-intercept formFrom the question, we are to write the equations in slope-intercept form.
The given equations are
2x + y = -3
and
-2y = 6 + 4x
The slope-intercept form of the equation of a line is
y = mx + b
Where m is the slope
and b is the y-intercept
Writing 2x + y = -3 in slope-intercept form
2x + y = -3
Subtract 2x from both sides of the equation
2x - 2x + y = -3 - 2x
y = -3 - 2x
y = -2x - 3
Writing -2y = 6 + 4x in slope-intercept form
-2y = 6 + 4x
Divide through by -2
-2y/-2 = 6/-2 + 4x/-2
y = -3 - 2x
y = -2x - 3
Hence, the equation is y = -2x -3
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PLEASE I NEED THIS SUPER FAST
What is the area of a rectangle with side lengths of 6/8 meter and 4/10 meter
enter your answer as a fraction in simplest form
The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is,
Area of rectangle = 6/8 meter × 4/10 meter
= 24 / 80 meters²
= 6 /20 meters²
= 0.3 meters²
Hence, The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is 0.3 meters².
Which theorem or postulate justifies this statement?
/8 = /10
O linear pair postulate
O alternate exterior angles theorem
O vertical angles theorem
O alternate interior angles theorem
O corresponding angles postulate
Answer: 3)
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Please help!!! 10 points!! The total price of 3 pencils and 1 protractor at $3 was 4 times the total price of 1 pencil and 1 eraser at $0.60. What is the price of 1 pencil?
Step-by-step explanation:
The total price of 3 pencils and 1 protractor at $3 was 4 times the total price of 1 pencil and 1 eraser at $0.60. What is the price of 1 pencil?
when pencil = p
3p + 3 = 4(p + 0.6)
expand right side:
3p + 3 = 4p + 2.4
subtract 3 from both sides:
3p + 3 - 3 = 4p + 2.4 - 3
3p = 4p -0.6
subtract 4p from both sides:
3p - 4p = 4p -0.6 - 4p
-p = -0.6
divide both sides by -1:
(-p)/-1 = (-0.6)/-1
p = 0.6
so each pencil costs $0.60
It takes 2 cups of water to cook 1 rice
Answer: About 1 to 1.5 ratio. You would use one cup rice to 1.5 cup water.
Step-by-step explanation:
hi please help me im having trouble
Answer:
Your answer will be 7
Answer:
7
Step-by-step explanation:
i know
Find a polynomial function of degree 3 with the given numbers as zeros. Assume that the leading coefficient is 1.
-2,5,6
Answer:
[tex]f(x)=x^3-9x^2+8x+60[/tex]
Step-by-step explanation:
The zeros of a function are the x-values when f(x) = 0.
Factor Theorem
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
If the zeros of the polynomial are -2, 5 and 6 then (x + 2), (x - 5) and (x - 6) are factors of the polynomial.
Therefore, the polynomial in factored form is:
[tex]f(x)=a(x+2)(x-5)(x-6)[/tex]
where a is the leading coefficient.
Given a = 1:
[tex]f(x)=(x+2)(x-5)(x-6)[/tex]
Expand the parentheses to express the polynomial in standard form:
[tex]f(x)=(x+2)(x-5)(x-6)[/tex]
[tex]f(x)=(x^2-3x-10)(x-6)[/tex]
[tex]f(x)=x^3-6x^2-3x^2+18x-10x+60[/tex]
[tex]f(x)=x^3-9x^2+8x+60[/tex]
How do I answer the question?
The value of n for the given exponential function is 5/2.
Exponential function:
Exponential function means the function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
Given,
Here we have the exponential function (√7)⁵ = 7ⁿ
Now, we need to find the value of n.
Based on the rule of exponent, we have written the square as 1/2, like the following,
√7 = [tex]7^{\frac{1}{2}}[/tex]
So, when we apply these on the given expression then we get,
(√7)⁵ = [tex](7^{\frac{1}{2}})^5[/tex]
Now, we have to multiply both values on the power then we get,
=> [tex](7^{\frac{5}{2}})[/tex]
When we equate this with the RHS, then we get the value of n as,
[tex]= > (7^{\frac{5}{2}})=7^n[/tex]
Therefore, the value of n is 5/2.
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