SOMEONE HELP ME!! Please I have like 5 minutes!!

Can you solve this? I need help. I don't understand.

ZanzabumX [31]

Answer:

2 sqrt(5) OR 4.5

Step-by-step explanation:

You have to know Pythagorean theorem to solve this question.

a^2 + b^2 = c^2

To use this theorem you have to have a right triangle. There are two right triangles in your image. The lower (larger) one has two sides labeled, so you can use Pythagorean thm to find the third side. There's a short cut, bc some right triangles have easy-to-memorize lengths of the sides. 3-4-5 is one of these number sets. A multiple of this is 6-8-10. We could've solved:

b^2 + 8^2 = 10^2

But it would've come out the same. The unlabeled side is 6.

We can use the 6 and the 4 on the smaller right triangle and use the Pythagorean thm again to solve for x.

4^2 + x^2 = 6^2

16 + x^2 = 36 subtract 16 from both sides.

x^2 = 20

Take the square root of both sides.

sqrt (x^2) = sqrt 20

x = 2 sqrt(5) which is approximately 4.472.

2 sqrt(5) is an exact answer if that is what they are asking for. 4.472 is an approximation to the nearest thousandth. It would be 4.47 to the nearest hundredth or 4.5 to the nearest tenth.

8 0

2 years ago

A glass is 4/7 full. Then 70 cm³ orange juice is poured in. The glass is now 3/4 full.

Nataly_w [17]

Answer:

The volume of the glass is 217.8 cm³

Step-by-step explanation:

If the glass were initially 4/7 full, that means 3/7 of the volume is still available to hold more juice.

Let v represent the volume of the glass.

Then (3/7)v + 70 cm³ = (3/4)v.

We need to solve this for v.

Here the LCD is 28. Thus,

(3/7)v + 70 cm³ = (3/4)v → (12/28)v + 70 cm³ = (21/28)v.

Subtracting (12/28)v from both sides, we get:

70 cm³ = (9/28)v.

We can isolate v by mult. both sides by the inverse of 9/28, which is 28/9:

(28/9)(70 cm³) = v

The volume of the glass is 217.8 cm³

3 0

3 years ago

Read 2 more answers

PLEASE SOLVE I DESPERATELY NEED HELP!!! Solve the system of equations by graphing.

Anon25 [30]

Answer:

The steps will be :

1. Draw both equations into the graph.

2. Look for the coordinates where they intersect(curve and line crosses each other). So the coordinates will be (-2,0) and (3,5).

3. The x-value of the coordinates will the solution to the equations.

4. Therefore, the answer will be -2 and 3.

4 0

3 years ago

A family is purchasing a house and needs to finance a $195,000 mortgage from the bank with an annual percentage rate (APR) of 5.

N76 [4]

The monthly payment amount is $860.25.

Step-by-step explanation:

Step 1; The bank offers an amount of $195,000 with an APR of 5.3%. This means that the family must pay 5.3% of the $195,000 every year for 30 years. To calculate we must determine how much 5.3% of $195,000 is. To do that we make 5.3% a fraction by dividing it by 100 and multiplying it with the amount.

5.3% of $195,000 = $\frac{5.3}{100}$ × $195,000 = 0.053 × $195,000 = $10,335 per year.

Payment owed for 30 years = Payment owed a year × 30

= $10,335 per year × 30 = $310,050 for 30 years.

Step 2; To find the monthly payments we need to know how many months are in a 30 year period. Months in 30 years = 30 × 12 months = 360 months. The monthly payment is, therefore, payment owed in 30 years divided by the months in that 30 year period.

Monthly payment = $10,335 / 360 = $ 861.25.

So the family must pay a monthly payment of $861.25 for 30 years.

4 0

2 years ago

Match the numerical expressions to their simplest forms.

Aloiza [94]

Answer:

$(a^6b^1^2)^\frac{1}{3}$ = $a^2b^4$

$\frac{(a^5b^3)^\frac{1}{2}}{(ab)^-^\frac{1}{2}}$ = $a^3b^2$

$(\frac{a^5}{a^-^3b^-^4})^\frac{1}{4}$ = $a^2b$

$(\frac{a^3}{ab^-^6})^\frac{1}{2}$ = $ab^3$

Step-by-step explanation:

Simplify each of the expressions:

1

$(a^6b^1^2)^\frac{1}{3}$

Distribute the exponent. Multiply the exponent of the term outside of the parenthesis by the exponents of the variable.

$(a^6b^1^2)^\frac{1}{3}$

$a^6^*^\frac{1}{3}b^1^2^*^\frac{1}{3}$

Simplify,

$a^2b^4$

2

Use a similar technique to solve this problem. Remember, a fractional exponent is the same as a radical, if the denominator is (2), then the operation is taking the square root of the number.

$\frac{(a^5b^3)^\frac{1}{2}}{(ab)^-^\frac{1}{2}}$

Rewrite as square roots:

$\frac{\sqrt{a^5b^3}}{\sqrt{(ab)}^-^1}$

A negative exponent indicates one needs to take the reciprocal of the number. Apply this here:

$\frac{\sqrt{a^5b^3}}{\frac{1}{\sqrt{ab}}}$

Simplify,

$\sqrt{a^5b^3}*\sqrt{ab}$

Since both numbers are under a radical, one can rewrite them such that they are under the same radical,

$\sqrt{a^5b^3*ab}$

Simplify,

$\sqrt{a^6b^4}$

Since this operation is taking the square root, divide the exponents in half to do this operation:

$a^3b^2$

3

$(\frac{a^5}{a^-^3b^-^4})^\frac{1}{4}$

Simplify, to simplify the expression in the numerator and the denominator, the base must be the same. Remember, the base is the number that is being raised to the exponent. One subtracts the exponent of the number in the denominator from the exponent of the like base in the numerator. This only works if all terms in both the numerator and the denominator have the operation of multiplication between them:

$(\frac{a^8}{b^-^4})^\frac{1}{4}$

Bring the negative exponent to the numerator. Change the sign of the exponent and rewrite it in the numerator,

$(a^8b^4)^\frac{1}{4}$

This expression to the power of the one forth. This is the same as taking the quartic root of the expression. Rewrite the expression with such,

$\sqrt[4]{a^8b^4}$

SImplify, divide the exponents by (4) to simulate taking the quartic root,

$a^2b$

4

$(\frac{a^3}{ab^-^6})^\frac{1}{2}$

Using all of the rules mentioned above, simplify the fraction. The only operation happening between the numbers in both the numerator and the denominator is multiplication. Therefore, one can subtract the exponents of the terms with the like base. The term in the denomaintor can be rewritten in the numerator with its exponent times negative (1).

$(a^3^-^1b^(^-^6^*^(^-^1^)^))^\frac{1}{2}$

$(a^2b^6)^\frac{1}{2}$

Rewrite to the half-power as a square root,

$\sqrt{a^2b^6}$

Simplify, divide all of the exponents by (2),

$ab^3$

7 0

3 years ago