julie spends$5.62 at the store. michael apends 5 times as much as julie. jeremy spends $6.72 more than michal. how much does each person spend.
please help.
the longer leg of a right triangle is 3m longer than the shorter leg. the hypotenuse is 6m longer than the shorter leg. find the side lengths of the triangle
Final answer:
Using the Pythagorean theorem, we find that the side lengths of the right triangle are 9m for the shorter leg, 12m for the longer leg, and 15m for the hypotenuse.
Explanation:
We are asked to find the side lengths of a right triangle, with the condition that the longer leg is 3m longer than the shorter leg, and the hypotenuse is 6m longer than the shorter leg. We can name the shorter leg 'x'. Therefore, the longer leg will be 'x + 3' and the hypotenuse will be 'x + 6'. According to the Pythagorean theorem (a² + b² = c²), we can set up the equation x² + (x + 3)² = (x + 6)².
First, we expand the equations: x² + (x² + 6x + 9) = (x² + 12x + 36).
Combining like terms, we get 2x² + 6x + 9 = x² + 12x + 36. Simplifying further, we get x² - 6x - 27 = 0.
This is a quadratic equation that can be factored as (x - 9)(x + 3) = 0, which gives us the solutions x = 9 and x = -3. Since a side length cannot be negative, we discard the negative value.
Thus, the lengths of the sides of the triangle are: shorter leg x = 9m, longer leg x + 3 = 12m, and hypotenuse x + 6 = 15m.
you can afford a $800 per mpnth mortgage payment .youve found a 30 year loan at 8%interest.
A. How bit of a lone can you afford?
B How much total money will you pat the loan company?
C How much of that is interest?
thanks for your help!!!
The total interest paid for a mortgage at 8% interest rate with a $800 monthly payment.
A. To find the maximum loan amount you can afford:
Calculate the monthly payment using the formula: $800 = P * [r(1 + r)^n] / [(1 + r)^n - 1], where P = Loan amount, r = monthly interest rate, and n = number of payments.Substitute the values: r = 8% / 12, n = 30 years * 12 months, and solve for P to find the maximum loan amount.B. Total payment over 30 years = Monthly payment * 12 months * 30 years.
C. Total interest paid = Total payment - Loan amount.
3÷3912.00 carry to the hundreth
The price, s, of a mountain bike at Speed Cycling is $290 less than twice the price, d, of the same bike at Downhill Racing. The difference in price between the bike at Speed Cycling and Downhill Racing is $304. Which system of equations can be used to determine the price of the bike at each store?
s - 2d = -290
s - d = -304
2s - d = 290
s - d = -304
2s - 2d = 290
s - d = -304
s - 2d = -290
s - d = 304
The system of equations that can be used to determine the price of the mountain bike at each store is:
s - 2d = -290
s - d = 304
Let's determine the correct system of equations to find the prices of the mountain bike at Speed Cycling (s) and Downhill Racing (d).
Given:
The price at Speed Cycling (s) is $290 less than twice the price at Downhill Racing (d). This can be expressed as s = 2d - 290.
The price difference between Speed Cycling and Downhill Racing is $304. This can be expressed as s - d = 304.
Now, we have the two equations:
s = 2d - 290
s - d = 304
These equations form a system that can be used to determine the prices of the bike at each store.
To solve for s and d, you can use the method of substitution or elimination. By substituting the value of s from the first equation into the second equation, you can find the prices of the bike at each store:
Substitute s from the first equation into the second equation:
(2d - 290) - d = 304
Now, solve for d:
d - 290 = 304
Add 290 to both sides:
d = 304 + 290
d = 594
Now that you've found the price at Downhill Racing (d), you can find the price at Speed Cycling (s) by using the first equation:
s = 2d - 290
s = 2 * 594 - 290
s = 1188 - 290
s = 898
So, the price of the mountain bike at Downhill Racing (d) is $594, and the price at Speed Cycling (s) is $898.
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what are the steps to solve a^2+6a+9/a-10?
The value of the expression at a - 10 = 0 is 169.
We have,
Expression:
a² + 6a + 9 _________(1)
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
From the expression a - 10 = 0.
Find the value of a.
a = 10
Now,
Substituting a = 10 in (1).
a² + 6a + 9
Simplify the expression.
10² + 6 x 10 + 9
100 + 60 + 9
Add the like terms in the expression.
100 + 69
169
Thus,
The value of the expression at a - 10 = 0 is 169.
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The complete question:
what are the steps to solve a^2 + 6a + 9 when a - 10 = 0.
Help me understand this MATH problem...MR.LARSON IS PLANNING THE SEATING FOR A SCHOOL RECITAL. HE NEEDS TO RESERVE 1/3 OF THE SEATS FOR STUDENTS AND 1/6 OF THE SAETS FOR PARENTS.
A. AFTER RESEVING SEATS FOR STUDENTS AND PARENTS, WHAT FRACTION OF THE SEATS IN THE AUDITORIUM ARE LEFT?
B. MR.LARSON's PRINCIPAL TELLS HIM THAT HE ALSO NEEDS TO RESREVE 1/8 OF THE SEATS FOR TEACHERS AND SCHOOL OFFICIALS. THE REMAINDER CAN BE USED FOR OPEN SEATING. WHAT FRACTION OF THE SEATS ARE NOW LEFT FOR OPEN SEATING?
C. LATER, MR.LARSON's PRINCIPAL SAYS HE SHOULD RESERVE 1/4 OF THE SAETS FOR STDENTS FROM OTHER MIDDLE SCHOOLS. ARE THERE ENOUGH SEATS LEFT? IF NOT, EXPLAIN WHY NOT; OTHERWISE, STATE WHAT FRACTION OF THE SEATS WILL BE AVAILABLE FOR OPEN SEATING.
The lottery in an extremely small state consists of picking two different numbers from 1 to 10. Ten Ping-Pong balls numbered 1 through 10 are dropped into a fish bowl, and two are selected at random. Suppose you bet on 2 and 9. What is the probability that you won the lottery?
To win the lottery by betting on numbers 2 and 9, the combined probability is calculated by multiplying the individual probabilities of drawing each number. The probability of drawing number 2 is 1/10, and subsequently drawing number 9 is 1/9, resulting in a combined probability of 1/90.
Explanation:The question asks about the probability of winning a lottery by correctly guessing two specific numbers out of ten. To determine this probability, we must consider the two stages of the lottery separately. Initially, any one of the ten balls can be drawn, so the probability of drawing the first number you bet on, which is 2 in this case, is 1/10. Once the first ball is chosen, it is not replaced, meaning the second selection will be made from the remaining nine balls. Therefore, the probability of drawing the second number you bet on, number 9, after having already drawn number 2, is 1/9. We use the product rule because we need the outcome of drawing both numbers.
Using the product rule, the combined probability of drawing both numbers in the correct order is calculated by multiplying the probabilities of each individual event. Therefore, the combined probability is (1/10) x (1/9), which simplifies to 1/90. This is the probability of winning the lottery by betting on numbers 2 and 9.
A coffee company has found that the marginal cost, in dollars per pound, of the coffee it roasts is represented by the function below, where x is the number of pounds of coffee roasted. Find the total cost of roasting 110 lb of coffee, disregarding any fixed costs.
C'(x)=- 0.018x+ 4.75, for x less than or equal to 200
The total cost of roasting 110 lb of coffee is $765.
How to solve Cost Function?Based on the given function, the marginal cost of roasting x pounds of coffee is:
C'(x) = -0.018x + 4.75 for x ≤ 200.
To find the total cost of roasting 110 lb of coffee, we need to integrate the marginal cost function to get the total cost function C(x), and then evaluate C(110).
However, since we are disregarding any fixed costs, we can assume that the total cost function is simply the integral of the marginal cost function.
Integrating C'(x) = -0.018x + 4.75 with respect to x, we get:
C(x) = -0.009x² + 4.75x + C
where C is the constant of integration. Since we are disregarding any fixed costs, we can assume that C = 0.
Therefore, the total cost of roasting 110 lb of coffee is:
C(110) = -0.009(110)² + 4.75(110) = 765
The total cost of roasting 110 lb of coffee is $765.
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Final answer:
To find the total cost of roasting 110 lb of coffee, integrate the marginal cost function C'(x) = -0.018x + 4.75 over the range of x values. Substitute 110 for x in the total cost function to find the total cost.
Explanation:
To find the total cost of roasting 110 lb of coffee, we need to integrate the marginal cost function over the desired range of x values. The marginal cost function is given by C'(x) = -0.018x + 4.75. Integrating this function will give us the total cost function C(x).
Integrating C'(x) gives C(x) = -0.009x^2 + 4.75x + C, where C is the constant of integration. Since we are disregarding any fixed costs, we can ignore the constant term C.
Now we can substitute 110 for x in the total cost function to find the total cost of roasting 110 lb of coffee: C(110) = -0.009(110)^2 + 4.75(110) = -108.9 + 522.5 = $413.6.
What is the slope of the line whose equation is 2x−4y=102x−4y=10 ?
Answer:
That's the correct answer!!
Step-by-step explanation:
Write the ratio 8:20 in the simplest form
Express the decimal 2.39 as a percent
The percent of the decimal 2.39 can be expressed as 239%.
What is the percent of the decimal 2.39?To express the decimal 2.39 as a percent, we need to multiply it by 100. This is because a percent is a fraction out of 100.
To do this, we can write 2.39 as 2.39/1 and multiply it by 100/1:
(2.39/1) * (100/1) = 239/1
Therefore, 2.39 as a percent is 239%.
To understand this concept further, let's break it down:
The number 2.39 represents 2 whole units and 0.39 of another unit. When we convert it to a percent, we are essentially comparing it to 100 units.
We can think of the decimal point as moving two places to the right when we multiply by 100. So, 2.39 becomes 239.
Finally, we add the percent symbol (%) to indicate that the value is a percentage.
Therefore, the decimal 2.39 can be expressed in percent as 239%.
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over a 2 hr time period a snail moved 50in how much is that in yards
A box contains 17 transistors, 3 of which are defective. If 3 are selected at random, find the probability that
a. All are defective.
b. None are defective.
The 21st century version of Let’s Make a Deal has five doors instead of three. Two doors have cars behind them and the other three doors have mules. What percentage of doors have cars behind them?
Final answer:
There is a 40% chance that one of the five doors will have a car behind it as there are two doors with cars and five doors in total.
Explanation:
To find the percentage of doors that have cars behind them in the 21st century version of Let’s Make a Deal with five doors, we can use a simple ratio. Since two out of the five doors have cars behind them, we can set up the ratio as 2 cars to 5 total doors.
The calculation for the percentage would be: (Number of doors with cars / Total number of doors) × 100. Plugging in the numbers gives us:
(2 / 5) × 100 = 40%
Therefore, the percentage of doors with cars behind them is 40%.
write an expression for the total cost of the three types of tickets and show your work: $8.75, $6.50, $6.50
To find the total cost of three types of tickets priced at $8.75, $6.50, and $6.50, add the prices together, resulting in a total cost of $21.75.
Explanation:To write an expression for the total cost of purchasing three types of tickets with prices $8.75, $6.50, and $6.50, you need to add these values together. Here is the step-by-step process of calculating the total cost:
Identify the cost of each type of ticket: Ticket 1 costs $8.75, and Tickets 2 and 3 each cost $6.50.Add the cost of the three tickets together: $8.75 + $6.50 + $6.50.Calculate the total cost: $8.75 + $6.50 + $6.50 = $21.75.The expression for the total cost of the three tickets is $21.75.
To find the total cost of the three types of tickets, you sum the individual costs to get a total of $21.75.
Explanation:To write an expression for the total cost of the three types of tickets, we sum up the cost of each ticket. The three types of tickets cost $8.75, $6.50, and $6.50 each. Therefore, the expression for the total cost is:
Total Cost = $8.75 + $6.50 + $6.50
To calculate the total cost, we add these prices together:
$8.75 + $6.50 = $15.25
$15.25 + $6.50 = $21.75
So, the total cost of the three tickets is $21.75.
43. Cost of Natural Gas In April 2009, Peoples Energy had the following rate schedule for natural gas usage in single- family residences:
Monthly service charge $15.95 Per therm service charge
1st 50 therms $0.33606/therm
Over 50 therms $0.10580/therm
Gas charge $0.3940/therm
(a) What is the charge for using 50 therms in a month?
(b) What is the charge for using 500 therms in a month?
(c) Develop a model that relates the monthly charge C for
x therms of gas.
(d) Graph the function found in part (c).
Source: Peoples Energy, Chicago, Illinois, 2009
The charge for using 50 therms is $16.803, while the charge for using 500 therms is $64.413. The model that relates the monthly charge for x therms of gas can be computed using specific conditions. Graphing the function will result in a piecewise linear graph with different slopes for different ranges of therms.
Explanation:To find the charge for using 50 therms in a month, we can use the rate schedule provided. The charge for the first 50 therms is $0.33606 per therm. So, the charge for using 50 therms would be 50 x $0.33606 = $16.803.
For using 500 therms in a month, we need to consider both the charge for the first 50 therms and the charge for the additional therms. The charge for the first 50 therms is $0.33606 per therm, and for the additional therms (450 therms), the charge is $0.10580 per therm. So, the total charge would be (50 x $0.33606) + (450 x $0.10580) = $16.803 + $47.610 = $64.413.
The model that relates the monthly charge for x therms of gas can be represented as follows:
C(x) = $15.95 + ($0.33606 x therms) if x ≤ 50
C(x) = $15.95 + ($0.33606 x 50) + ($0.10580 x (therms-50)) if x > 50
Graphing this function will result in a piecewise linear graph with a slope of $0.33606 for the first 50 therms and a slope of $0.10580 for any additional therms beyond 50.
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How do i find the cost per pound?
which capital letter appears to have parallel line segments?
A.D
B.L
C.N
D.T
You are purchasing office supplies. Because of the volume of your orders your company receives 15% off all purchases. You buy a case of paper for $24.95 and a toner refill at $35.99. You find discontinued ink for $49.95 at 50% off. The local sales tax is 4.5%. What do you spend
Find the inverse of the given function h(x)=log(x)
Wich symbols makes -3/4 -11/12 a true sentence
The mathematical symbol that makes the expression -3/4 -11/12 true is subtraction.
The student is likely asking which mathematical symbol (operation) would make the expression -3/4 -11/12 a true sentence. The symbols that could apply are addition (+), subtraction (-), multiplication (x), or division (). To determine which symbol makes the sentence true, one would typically compare the result of applying each operation to the numeric values given.
For example, to test addition:
-3/4 + (-11/12) = (-9/12) + (-11/12) = -20/12 = -5/3
To test subtraction:
-3/4 - (-11/12) = (-9/12) - (-11/12) = 2/12 = 1/6
Therefore, subtraction makes the original expression a true one, because subtracting a negative is the same as adding the positive equivalent, which would simplify to an expression that equals 1/6.
I need help on how to solve this equation C+(4-3c)-2=0 stp by step
A total of 304 tickets were sold for the school play. They were either adult or student tickets. The number of student tickets were sold was three times the number of the adult tickets sold. How many adult tickets were sold?
76 adult tickets were sold.
Explanation:Let's assume the number of adult tickets sold is x. Since the number of student tickets sold was three times the number of adult tickets sold, we can represent it as 3x.
According to the problem, the total number of tickets sold was 304. So, we can write the equation:
x + 3x = 304
Combining like terms, we get:
4x = 304
Divide both sides by 4:
x = 76
Therefore, 76 adult tickets were sold.
Jackie deposited $315 into a bank account that earned 1.5% simple interest each year.
If no money was deposited into or withdrawn from the account, how much money was in the account after 3 years?
Round your answer to the nearest cent.
need in six minutes or less
Three people have a median age of 30 and a mean age of 36. The range of ages is 20 . How old is each person?
Gabrielle is 10 years younger than Mikhail. The sum of their ages is 56 . What is Mikhail's age?
Explain how you can use the basic moves of algebra to transform the equation 5x-3y=12 into 0=12-5x+3y
Lindsay draws a right triangle and adds the measures of the right angle and one acute angle. Which is a possible sum of the two angles?
Answer:
[tex]90< \gamma< 180[/tex]
Step-by-step explanation:
An acute angle is an angle that measures more than 0º and less than 90º. And a right angle is an angle that measures exactly 90º. Thus:
Let:
[tex]\alpha = Right\hspace{3}angle=90^{\circ}\\\beta= Acute\hspace{3}angle\hspace{10}0^{\circ}<\beta<90^{\circ}\\\gamma= Sum\hspace{3} of\hspace{3} the\hspace{3} two\hspace{3} angles =\alpha +\beta[/tex]
So, in this sense, the sum of the two angles can´t be equal or greater than 180º, since [tex]\beta<90^{\circ}[/tex] , also it has to be at least greater than 90º since [tex]\beta>0^{\circ}[/tex]
Therefore the sum of the two angles is:
[tex]90^{\circ}< \gamma< 180^{\circ}[/tex]
In another words, the sum is greater than 90º and less than 180º
If g(x) = 4x - 4^x, what is the value of g(3/2)?
To calculate g(3/2) for the function g(x) = 4x - 4^x, we first multiply 4 by 3/2 to get 6, then calculate 4 raised to the power of 3/2 to get 8, and subtract the latter from the former to obtain the final result of -2.
Explanation:To find the value of g(3/2) for the function g(x) = 4x - 4x, we simply substitute x with 3/2. The calculation involves two parts: multiplying 4 by 3/2, and then raising 4 to the power of 3/2.
For the first part, 4 multiplied by 3/2 equals 6.For the second part, 4 raised to the power of 3/2 is the square root of 4 cubed, which equals the square root of 64, giving us 8.Finally, subtract the second part from the first to get g(3/2) = 6 - 8, which equals -2.Therefore, the value of g(3/2) is -2.
If [tex]g(x) = 4x - 4^x[/tex], what is the value of g(3/2) is -2.
To find the value of g(3/2), you need to substitute x = 3/2 into the given function [tex]g(x) = 4x - 4^x.[/tex]
g(3/2) = [tex]4(3/2) - 4^\frac{3}{2}[/tex]
Now, let's simplify this expression:
[tex]g(3/2) = 6 - 4^\frac{3}{2}[/tex]
The value of 4^(3/2) is the square root of 4 cubed, which is [tex]2^3[/tex] = 8. Therefore:
g(3/2) = 6 - 8
Now, subtract 8 from 6:
g(3/2) = -2
So, the value of g(3/2) is -2.