MATHEMATICS HIGH SCHOOL

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Answers

Answer 1

Answer:

Answer:

x=11

Step-by-step explanation:

Since both angles are congruent, 2x-10=12, so x=11

Answer 2

Answer:

Answer:

×=11

Step-by-step explanation:

2x-10=12

2×=22

×=11

2(11)-10

22-10=12

Related Questions

How do I solve x/3 - x/2 =12 they are fractions I dont know ro write on on a laptop
A junior college is going to choose a Homecoming Queen, and the candidates are the Freshman Queen and the Sophomore Queen. If there are 600 freshman and 400 sophomore voters, which would be a FAIR way of conducting the vote? [Fair, in this case, means that the Freshman Queen does not have an automatic advantage.]A) Count the votes, then deduct 100 from the freshman total. B) Count the votes and the Queen with the highest total becomes Homecoming Queen. C) Count the votes, counting each sophomore ballot as 1.5 votes and each freshman ballot as 1 vote. D) Count the votes, counting each freshman ballot as 1.5 votes and each sophomore ballot as 1 vote.
Since apparently NOBODY has asked this exact question.The basket of golf balls at a miniature golf course contains 16 golf balls, of which 6 are green.What is the probability that a randomly selected golf ball will be green?
I will just give brainliest who ever answers first
The length of a rectangle is 3 inches greater than the width. A. Write a polynomial that represents the area of the rectangle.B. Find the area of the rectangle when the width is 4 inches.

HELP IN THIS PLS I'LL DIRECTLY MARK YOU BRAINLIST!!]

Answers

Answer:

24 cars

Step-by-step explanation:

By using 11 cars and AED 79.75, you can find out the cost of washing 1 car.

(AED 79.75)/(11 cars) = AED 7.25 / car

Now we divide AED 174 by AED 7.25/car to find the number of cars.

(AED 174) / [(AED 7.25)/car] = (174/7.25) cars = 24 cars

Answer: 24 cars

Antoine is on vacation with his family. They have a vacation budget of $1,400. Antoine predicts they will spend $110 each night on the hotel, $80 a day on food, and $100 a day on activities. They will also spend $120 on gasoline for the entire trip. Write an inequality to find how many nights, n, they afford to stay on vacation. What is the longest vacation they can take?

Answers

Answer:

290n + 120 ≤ 1400

4 days

Step-by-step explanation:

Given that:

Vacation budget = $1400

Cost on hotel = $110 per night

Cost on food = $80 per day

Cost on activities = $100 per day

Cost on gas = $120 for entire trip

Number of nights they can afford to stay

Let the Number of nights they can afford = n

((110 + 80 + 100) * number of nights) + 120 ≤ vacation budget

290n + 120 ≤ 1400

290n ≤ 1400 - 120

290n ≤ 1280

n ≤ 1280 / 290

n ≤ 4.4137

Hence, longest vacation they can take is 4 days

Final answer:

The family can afford up to 4 nights for their vacation, as per the inequality 290n + 120 ≤ 1400, where 'n' stands for the number of nights.

Explanation:

Let's first define the total expenses per day as the sum of the hotel costs ($110), food costs ($80), and the daily amount for activities ($100). This adds up to $290 per day. So for 'n' nights, the family will be spending $290n. In addition, there's a $120 onetime expense for gasoline. Hence, the inequality representing their spending will be: 290n + 120 ≤ 1400.

To find the longest vacation this family can afford, we simply need to solve this inequality. Pay attention as we do this: 290n ≤ 1280 (subtracting 120 from both sides), and then n ≤ 4.41 (dividing both sides by 290).

Since the number of nights 'n' should be a whole number, the family can afford up to 4 nights on their vacation.

Learn more about Vacation budgeting here:

brainly.com/question/36787192

#SPJ3

ABCD is rectangle. Find the length of each diagonal
AC=c/3
BD=4-c

Answers

Answer:

Recall the following result:

In a rectangle ABCD, the diagonals AC and BD are equal to each other, that is, AC = BD.

Consider the following statement:

$\text{AC}=(c)/(3)$ and BD =4-c

The objective is to find the length of each diagonal.

As per the result:

In a rectangle ABCD:

AC = BD

Substitute the given values:

$(c)/(3) =4-c$

Multiply both sides by 3:

$c = 3(4-c)$

Simplify:

c = 12-3c

Add 3c to both sides :

4c= 12

Divide both sides by 4;

c = 3

Then,

$\text{AC}=(3)/(3)=1$

BD=4-3 = 1

Therefore, the length of each diagonal is, 1.

The lenght of each diagonals is 1.

Allie deposited $300.00 into a new savings account that earns 13% interest compounded quarterly. How long will it take for the balance to grow to $995.00? Round your answer to the nearest month. years and months

Answers

Answer:

9 years 4 months

Step-by-step explanation:

To find out how long it will take for Allie's initial deposit of $300to grow to $995 in a savings account with a 13% annual interest rate compounded quarterly, we can use the compound interest formula:

$\boxed{\begin{array}{l}\underline{\textsf{Compound Interest Formula}}\n\nA=P\left(1+(r)/(n)\right)^(nt)\n\n\textsf{where:}\n\phantom{ww}\bullet\;\;\textsf{$A$ is the final amount.}\n\phantom{ww}\bullet\;\;\textsf{$P$ is the principal amount.}\n\phantom{ww}\bullet\;\;\textsf{$r$ is the interest rate (in decimal form).}\n\phantom{ww}\bullet\;\;\textsf{$n$ is the number of times interest is applied per year.}\n\phantom{ww}\bullet\;\;\textsf{$t$ is the time (in years).}\end{array}}$

In this case:

A = $995
P = $300
r = 13% = 0.13
n = 4 (quarterly)

Substitute the values into the formula and solve for t:

$995=300\left(1+(0.13)/(4)\right)^(4t)$

Simplify the expression inside the bracket:

$995=300\left(1.0325\right)^(4t)$

Divide both sides of the equation by 300:

$(995)/(300)=\left(1.0325\right)^(4t)$

Take natural logs (ln) of both sides of the equation:

$\ln\left((995)/(300)\right)=\ln\left(1.0325^(4t)\right)$

$\textsf{Apply the power law:} \quad \ln x^n=n \ln x$

$\ln\left((995)/(300)\right)=4t\ln\left(1.0325\right)$

Divide both sides of the equation by 4ln(1.0325) to isolate t:

$(\ln\left((995)/(300)\right))/(4\ln\left(1.0325\right))=t$

$t=(\ln\left((995)/(300)\right))/(4\ln\left(1.0325\right))$

Evaluate using a calculator:

$t=9.37184241...$

Therefore, it will take 9.37 years for the balance to grow to $995.00.

To determine the number of months, subtract 9 from the value of t and multiply by 12:

$\textsf{Months}=12(9.37184241...-9)=4.46210895...$

Therefore, it will take 9 years and 4 months (rounded to the nearest month) for the balance to grow to $995.00.

Additional comments

In the case of quarterly compounding, the interest is calculated and added to the account balance every three months (once every quarter). So, even though it will take 9 years and 4 months for the balance to reach $995.00, Allie's account will not show this exact amount at that specific time. It will show a balance of $979.61 at 9 years and 3 months, and a balance of $1,011.45 at 9 years and 6 months, so technically, the account balance will still show as $979.61 at 9 years and 4 months.

Answer:

9 years and 4 months

Step-by-step explanation:

In order to calculate the number of years and months it will take for Allie's savings account balance to grow to $995.00, we can use the following compound interest formula:

$\sf A = P\left(1 + (r)/(n)\right)^(nt)$

where:

A is the future value
P is the present value
r is the annual interest rate
n is the number of compounding periods per year
t is the number of years

We can use the following values for the variables in the formula:

P = $300.00

r = 13% = 0.13

n = 4 (compounding quarterly)

A = $995.00

Substituting value, we get

$\sf 995 = 30000\left(1 + (0.13)/(4)\right)^(4\cdot t)$

$\sf 995 = 300.00\left(1.0325\right)^(4\cdot t)$

$\sf (995)/(300)=\left(1.0325\right)^(4\cdot t)$

$\sf 3.316 = \left(1.0325\right)^(4\cdot t)$

In order to solve the exponential equation, we can take the natural log of both sides:

$\sf ln(3.316) = ln(1.0325) ^ {4t}$

Using the properties of logarithms, we can bring the exponent down in front of the log:

$\sf 4t * ln(1.0325) = ln(3.316)$

Dividing both sides by ln(1.0325), we get:

$\sf t =( ln(3.316) )/(4ln(1.0325))$

Evaluating this expression, we get:

$\sf t = 9.3702710709672$

In the nearest hundred:

$\sf t \approx 9.37$

Therefore, year = 9 year

month = 37% of 12 = 4.44≈ 4 month

So, it will take Allie 9 years and 4 months for her savings account balance to grow to $995.00.

What is one of the solutions to the following system of equations?y^2+x^2=53
y-x=5
a)(-10,-5)
b)(-7,-2)
c)(7,2)
d)(5,10)

Answers

$y^2+x^2=53 \ny-x=5 \n \n\hbox{solve the 1st equation for y:} \ny-x=5 \ny=5+x \n \n\hbox{substitute 5+x for y in the 1st equation:} \n(5+x)^2+x^2=53 \n25+10x+x^2+x^2=53 \n2x^2+10x+25-53=0 \n2x^2+10x-28=0 \n2x^2+14x-4x-28=0 \n2x(x+7)-4(x+7)=0 \n(2x-4)(x+7)=0 \n2x-4=0 \ \lor \ x+7=0 \n2x=4 \ \lor \ x=-7 \nx=2 \ \lor \ x=-7 \n \ny=5+x \ny=5+2 \ \lor \ y=5-7 \ny=7 \ \lor \ y=-2 \n \n(x,y)=(2,7) \ or \ (x,y)=(-7,-2)$

The answer is B.

11. A line segment is different from a line in that a segment hasA. only one endpoint.

B. no endpoints.

C. two endpoints.

D. an undefined length.