MATHEMATICS
HIGH SCHOOL

Answer: MNOP is similar to QRST with ratio of 5:4. That means the MP:QT ratio would also be 5:4

The length of QT would be

MP/QT = 5/4

85mm/QT=5/4

85mm*4= 5*QT

5QT= 340

QT=68mm

The length of QT would be

MP/QT = 5/4

85mm/QT=5/4

85mm*4= 5*QT

5QT= 340

QT=68mm

MIDDLE SCHOOL

Which of the following is the solution to 4|x+2|>16

Answer:

x < - 6 or x > 6

Step-by-step explanation:

Inequalities of the type | x | > a, always have solutions in the form

x < - a or x > a

given 4| x + 2 | > 16 ( divide both sides by 4 )

| x + 2 | > 4 ← in the above form, hence

x + 2 < - 4 or x + 2 > 4 ( subtract 2 from both sides of both inequalities )

x < - 6 or x > 6 ← solution

MIDDLE SCHOOL

3 similar shirts and 4 similar jackets cost $360. 1 such shirt and 3 such jackets cost $220. Find the costof each shirt.

3s + 4j = 360

1s + 3j = 220

This one we can solve using substitution, in that

s + 3j = 220 implies s = 220 - 3j (subtract 3j from each side).

Now substitute into the first equation:

3(220 - 3j) + 4j = 360. Solve for jackets.

660 - 9j + 4j = 360 [Distributive property]

660 - 5j = 360 [Add -9j + 4j]

Subtract 360 from each side, and add 5j to each side.

660 - 360 - 5j + 5j = 360 - 360 + 5j

300 = 5j

Divide each side by 5.

$60 = price of a jacket.

Three of these plus a shirt runs $220.

3(60) = 180

180 + s = 220

180 - 180 + s = 220 - 180 [Subtract 180 from each side]

s = 40

Now we double check.

3(40) + 4 (60) = 120 + 240 = 360. This satisfies the first equation.

We could check the second one too, but I'm satisfied.

1s + 3j = 220

This one we can solve using substitution, in that

s + 3j = 220 implies s = 220 - 3j (subtract 3j from each side).

Now substitute into the first equation:

3(220 - 3j) + 4j = 360. Solve for jackets.

660 - 9j + 4j = 360 [Distributive property]

660 - 5j = 360 [Add -9j + 4j]

Subtract 360 from each side, and add 5j to each side.

660 - 360 - 5j + 5j = 360 - 360 + 5j

300 = 5j

Divide each side by 5.

$60 = price of a jacket.

Three of these plus a shirt runs $220.

3(60) = 180

180 + s = 220

180 - 180 + s = 220 - 180 [Subtract 180 from each side]

s = 40

Now we double check.

3(40) + 4 (60) = 120 + 240 = 360. This satisfies the first equation.

We could check the second one too, but I'm satisfied.

HIGH SCHOOL

Which point is an x-intercept Og the quadratic function f(x) = (x-4)(x+2)?

Hi there!

To find the x-intercept of the function we need to calculate f(x) = 0.

Rule AB = 0, gives A = 0 or B = 0.

Add 4 to both sides or subtract 2 from both sides.

Hence, the solutions are:

(4, 0) & (-2, 0)

To find the x-intercept of the function we need to calculate f(x) = 0.

Rule AB = 0, gives A = 0 or B = 0.

Add 4 to both sides or subtract 2 from both sides.

Hence, the solutions are:

(4, 0) & (-2, 0)

MIDDLE SCHOOL

A circle has a radius of 5 ft, and an arc of length 7 ft is made by the intersection of the circle with a central angle. Which equation gives the measure of the central angle, q?

Answer:

B q=7/5

Step-by-step explanation:

Well Q=s/r and they said a Radius of 5 Which puts 5 at the bottom.

Then an arc length of 7 Which =S. so q=7/5

To work out the central angle, you just re-arrange the equation for the length of an arc:

Equation for length of an arc:

× × π =

We can arrange this to work out the central angle, q. But first, lets substitute in all of the values that we know:

angle = q

diameter = 5 x 2 = 10 ft

length of arc = 7

[Substitute in]

× π = (Now just rearrange for q)

= (multiply both sides by 360 to get q)

= × (now just simplify)

=

= (rounded to 3 decimal places)

______________________________

Therefore:

The equation that gives you ange q is:

= ×

and q = 80.214 when all of the values are substituted in.

MIDDLE SCHOOL

It takes Harrison 1 1/2 hours to finish his history project it takes Miles 3 2/3 hours to finish his science project. How many times as long does it take Miles to finish his science project then it takes Harrison to finish his history project

Answer: The answer is

Step-by-step explanation: Given in the question that

Time taken by Harrison to finish his history project is given by

and the time taken by Kiles to finish his science project is

Let the time taken by Miles to finish his science project be 'p' times that of the time taken by Harrison to finish his history project.

Therefore,

Thus, Miles take times more time than Harrison.

COLLEGE

The discount points are 3% which represents $2,700. The buyer down payment is 20%. What is the purchase price of the property? (Please show all steps)

Answer: The purchase price of the property is $112,500.

Step-by-step explanation:

Let the original value of property be 'x'.

Discount rate = 3%

Amount of discount = $2700

According to question, it becomes,

Rate of down payment = 20%

So, Remaining rate of payment = 100-20 = 80%

So, Purchase price of the property would be

Hence, the purchase price of the property is $112,500.

MIDDLE SCHOOL

How do you write 485,830 in word form?

485,830 is written as . . .

four hundred eighty-five thousand, eight hundred thirty

four hundred eighty-five thousand, eight hundred thirty

MIDDLE SCHOOL

Four friends went on vacation with their family over the summer. Harlin’s family drove 363 miles in 6 hours, Kevin went 435 miles in 7 hours, Shanna drove 500 miles in 8 hours, Hector drove 215 miles in 5 hours. Which family drove the fastest?

Answer:

Shanna's family

Step-by-step explanation:

d/t = r (distance/time = rate)

Harlin: 363/6 = 60.5 mph

Kevin: 435/7 = 62.14 mph

Shanna: 500/8 = 62.5 mph

Hector: 215/5 = 43 mph

MIDDLE SCHOOL

Identify the equation of a line parallel to y=3x-6 and passes through (3,5) in slope intercept form

Answer:

y = 3x - 4

Step-by-step explanation:

slope is 3

y -5 = 3 (x - 3)

y - 5 = 3x - 9

y = 3x - 4