To solve this problem, set up equations based on the given information. M = C - 5 and M - 7 = (C - 7) / 2. Solve the system of equations to find Maura's age (19).
Explanation:To solve this problem, we can set up equations based on the given information. Let's let M represent Maura's age and C represent Cara's age.
The first clue tells us that Maura is 5 years younger than Cara, so we can write the equation M = C - 5.
The second clue tells us that seven years ago, Maura was half as old as Cara. So seven years ago, Maura's age was M - 7 and Cara's age was C - 7. We can write the equation M - 7 = (C - 7) / 2.
Now we can solve this system of equations to find Maura's age. Substituting the value of M from the first equation into the second equation, we get (C - 5) - 7 = (C - 7) / 2. Simplifying and solving for C, we find that Cara's current age is 24. Substituting this value back into the first equation, we find that Maura's current age is 19.
1. The center of a circle is located at (5, −5) . The radius of the circle is 3.
What is the equation of the circle in general form?
x^2+y^2+10x−10y+47=0
x^2+y^2+10x−10y+41=0
x^2+y^2−10x+10y+47=0
x^2+y^2−10x+10y+41=0
2.The standard form of the equation of a circle is (x−5)2+(y−6)2=1.
What is the general form of the equation?
x^2+y^2−10x−12y−62=0
x^2+y^2+10x+12y+62=0
x^2+y^2−10x−12y+60=0
x^2+y^2+10x+12y+60=0
which choice is equivalent to the expression below?
√- 20
A. -20i
B. 2i √5
C. -2 √5
D. 2 √5i
E. 20i,
What is the sum of the first 7 terms of the series −4+8−16+32−... ?
Enter your answer in the box.
we have that
−4+8−16+32−.....
a1=-2*(-2)-----> -4
a2=-4*(-2)-----> +8
a3=+8*(-2)-----> -16
a4=-16*(-2)----> +32
a5=+32*(-2)----> -64
a6=-64*(-2)-----> +128
a7=+128*(-2)-----> -256
The sum of the first 7 terms of the series is
[a1+a2+a3+a4+a5+a6+a7]-----> [-4+8-16+32-64+128-256]-------> -172
Jay took out a small-business loan for 210,000. The terms of the loan are 5% annual interest for four years.
Jay will pay back $_____ by the end of the four years.
Show your work.
A. 420,000
B.252,000
C. 168,000
D. 42,000
I will assume that this is a simple interest. In this problem, you are asked to find the future value of the loan at the end of four years.
The formula in finding the future value of the loan is:
F = P (1 + rt)
Where F = future value of the loan
P = principal amount of the loan
r = simple interest rate
t = time in years
Substituting the amounts given in the problem:
F = 210,000 (1 + 5%x4)
= 210,000 (1.2)
= 252,000
Therefore, Jay will pay back $252,000 by the end of four years.
What is the value of c such that x2 + 10x + c is a perfect square trinomial?
The value of c that makes x² + 10x + c a perfect square trinomial is c = 25.
What value of c makes the equation a perfect square trinomial?Given the equation in the question:
x² + 10x + c
A perfect square trinomial is of the form (ax² + bx + c), and it can be factored into (px + q)², where p and q are constants.
To find the value of c such that x² + 10x + c is a perfect square trinomial, we need to factor it as (px + q)².
Note that, the coefficient of x in the given trinomial is 10, so 2pq must equal 10.
Also, the coefficient of x² is 1, so p² must equal 1.
Hence, we have:
2pq = 10
p² = 1
From equation (2), we know that p could be either 1 or -1, after taking the square of both sides:
If p = 1, from equation (1) we have:
2pq = 10
2(1)q = 10
2q = 10
q = 10/2
q = 5
So, if p = 1 and q = 5, the perfect square trinomial is (x + 5)².
Let's expand to check:
(x + 5)² = x² + 10x + 25
Therefore, the value of c is 25.
Learn more about perfect square trinomials here: https://brainly.com/question/30594377
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Miriam ahorró durante toda la semana $14.00.El sabado se gasto 1/7 de esa cantidad y el domingo 5/8, ¿Que cantidad gastó en total durante esos dos días?
What is the area of a circle whose radius is 5 ft? 5π ft² 10π ft² 20π ft² 25π ft²
Answer:
The area of the circle is equal to [tex]25 \pi\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The area of circle is equal to
[tex]A=\pi r^{2}[/tex]
where
r is the radius of the circle
In this problem we have
[tex]r=5\ ft[/tex]
substitute
[tex]A=\pi (5^{2})=25 \pi\ ft^{2}[/tex]
The area of a circle with a radius of 5 ft is equal to 25π ft² which is calculated using the formula A = πr². Below step-by-step calculation helps in understanding how to apply the formula correctly.
To find the area of a circle whose radius is 5 ft, we use the formula for the area of a circle: [tex]A = \pi r^2[/tex].
Step 1: Identify the radius (r) of the circle
[tex]r=5 \text{ ft}[/tex]Step 2: Plug the radius value into the formula
[tex]A &= \pi (5 \text{ ft})^2[/tex]Step 3: Square the radius
[tex](5 \text{ ft})^2 = 25 \text{ ft}^2[/tex]Step 4: Multiply this result by π (pi)
[tex]A = \pi \times 25 \text{ ft}^2[/tex]which gives [tex]A = 25 \pi \text{ ft}^2[/tex].
Therefore, the area of a circle with a radius of 5 ft is 25π ft².
What number should be placed in the box to help complete the division calculation?
Dimitri is helping to plan the school talent show. Each performer for the talent show has 6 66 minutes for his or her performance, which includes transition time between performances. If the introduction for the talent show is 24 minutes long and the entire show, including the introduction, will last 1 5 0 150150 minutes, how many different performances can the talent show accommodate? Choose 1 answer: (Choice A) A 2 1 2121 (Choice B) B 2 4 2424 (Choice C) C 2 5 2525 (Choice D) D 2 9 29
Which graph could be the graph of f(x)=|x-h|+k if h and k are both positive?
Quick! Need the answer, will give brainiest
The junior class has 50 students. Twenty-five students take only french, 15 take only Latin, and 10 take both. If a student is chosen at random from the class, what is the probability that the student takes latin?
A.)1
B.)1/2
C.)
1/4
Answer: B ) [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given: The number of students in junior class n(S)= 50
The number of students take only Latin n(L-F)= 15
The number of students take only French n(F-L)=25
The number of students take both = n(F∩L)=10
The number of students take Latin n(L)=n(L-F)+n(F∩L)=15+10=25
Therefore, the probability that the student takes Latin is given by :-
[tex]\text{Probability(Latin)}=\frac{\text{number of students take latin}}{\text{Total students}}\\\\=\frac{25}{50}=\frac{1}{2}[/tex]
Worker A earns $9.50 per widget produced, produces 7 widgets per day, and works 5 hours per day. Worker B earns $8.80 per widget produced, produces 9 widgets per day, and works 8 hours per day. Which of these statements is true?
APEX confirmed
Answer: worker B earns more per day than worker A but less per hour that worker A
Mark's father travels 463 miles every month for his job. How many miles does he travel in 8 months?
Which of these following debts could possibly be forgiven under chapter 7 bankruptcy?
A. A mortgage
B. A student loan
C. Alimony
D. Child support
Answer:
A. A mortgage
Step-by-step explanation:
The chapter 7 of bankrupcy states that the person that owes the money should have his/her posessions taken away and by selling them repay the creditors, even if the sum of the belongings does not cover up for the whole amount that the person owes, this means that a mortgage is forgiven, but the house or the property is taken away and sold in an auction in order for the creditor to recover some of the money lost.
Please help asap!!! 12 points
I need help with this as well
Do two triangles with the same base and height have the same area
Explain why (√10)^3d is equivalent to (10^d)^3/2
You deposit $2200 Into three separate bank accounts for each pay 3% annual interest. How much interest does each account earn after 6 years?
Final answer:
Each of the three separate bank accounts with $2200 deposited at an annual interest rate of 3% will earn $396 in interest after 6 years.
Explanation:
The question asks about the amount of interest earned after 6 years on three separate bank accounts that each have a deposit of $2200 and an annual interest rate of 3%. To calculate the interest for each account, we can use the formula for simple interest, which is I = PRT, where I is the interest, P is the principal amount ($2200), R is the annual interest rate (0.03), and T is the time in years (6).
The interest for each account is calculated as follows:
I = PRT = $2200 × 0.03 × 6 = $396.
Therefore, each account earns $396 in interest after 6 years.
Each account earns [tex]\( \$396 \)[/tex] in interest after 6 years.
To calculate the interest earned on each account after 6 years, we'll use the formula for simple interest:
[tex]\[ \text{Simple Interest} = P \times r \times t \][/tex]
Where:
- P is the principal amount (the initial deposit)
- r is the annual interest rate (as a decimal)
- t is the time the money is invested or borrowed for, in years
Given:
- [tex]\( P = \$2200 \)[/tex] (the deposit into each account)
- [tex]\( r = 0.03 \)[/tex] (3% annual interest rate as a decimal)
- [tex]\( t = 6 \)[/tex] years (the time period)
Let's calculate the interest earned on each account using the formula.
[tex]\[ \text{Interest} = \$2200 \times 0.03 \times 6 \][/tex]
[tex]\[ \text{Interest} = \$2200 \times 0.18 \][/tex]
[tex]\[ \text{Interest} = \$396 \][/tex]
Find n (write in simplest radical form)
1. A ball is dropped from a height of 225 feet. The ball’s height y (in feet) after t seconds can be modeled by y = 225-16t2 . After how many seconds does the ball hit the ground?
GIVING BRAINLIEST TO THE FIRST RIGHT ANSWER!!!!
The following is the correct way to show the product for 0.453 × 8.1:
True
False
Answer:
true
Step-by-step explanation:
To show the variation in a set of data, you could calculate the
Answer:
range
Step-by-step explanation:
apex
To show the variation in a set of data, we can use the standard deviation as a tool.
What is Data variability?Data variability also known as spread or dispersion, refers to how spread out a set of data is. Variability gives users a way to describe how much data sets vary and allows users to use statistics to compare their data to other sets of data.
Given is variation in a set of data.
To show the variation in a set of data, we can use the standard deviation which provides a numerical measure of the overall amount of variation in a data set, and can be used to determine whether a particular data value is close to or far from the mean.
Therefore, to show the variation in a set of data, we can use the standard deviation as a tool.
To solve more questions on standard deviation, visit the link below-
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The supply and demand curves reflect data for a specific brand of sunglasses. Which circumstance best explains the shift of the demand curve from D to D1?
a. An ad campaign highlights the sustainable resources used to make the sunglasses.
b. Consumer reports indicate that the sunglasses break easily.
c. Fuel costs increase, making it more costly to produce the sunglasses.
d. Tax incentives encourage the producer to hire more workers.
Since there is a decrease in quantity and supply the answer would be Consumer reports indicate that the sunglasses break easily.
Answer "A" is definitely wrong
solve for x: 7/8-1/x=3/4
x = 1
x = 2
x = 4
x = 8
9514 1404 393
Answer:
x = 8
Step-by-step explanation:
[tex]\dfrac{7}{8}-\dfrac{1}{x}=\dfrac{3}{4}\\\\7x-8=6x\qquad\text{multiply by $8x$ to clear fractions}\\\\\boxed{x=8}\qquad\text{add $8-6x$}[/tex]
__
If you don't mind dealing with fractions, you can add 1/x -3/4 to get ...
7/8 -3/4 = 1/x
1/8 = 1/x . . . . . . . simplify
x = 8 . . . . . . . . . . take reciprocals; equivalently, multiply by 8x.
Your revenue is 32456 your gross margin is 23487 your operating expenses are 8123 your profit is
To compute for your profit, you just have to deduct your operating expenses to your gross margin. The gross margin is already the gross profit you have earned which is computed by deducting cost of goods sold to the revenue.
23,487 (gross margin) – 8,123 (operating expenses) = 15,364 (profit)
What is the area of the circle if XY = 5.4 mm?
the answer would be 7.29π mm² because what you would do is
you would first divide 5.4 by two in order to get what the radius is
then you would multiply 2.7 times 2.7 in order to get 7.29
the reason that this is correct is because you have to make sure that you plug in the right values in the formula
The park ranger stocks the children fishing pond keeping a ratio of 4 sunfish to 3 perch if he puts 300 sunfish into the pond how many perch should be put into the pond
Which of the following is the solution to the equation x + 8.6 = 36.2?
10.4
17.2
27.6
44.8
The answer is 27.6 because 36.2-8.6 is 27.6