Marren has 1/4 pound of raisins. she divides the raisins into 4 servings. each serving contains

triangle MNO is an equilateral triangle with sides measuring 16 units What is the height of the triangle?

fiasKO [112]

see the attached figure to better understand the problem

we know that

The equilateral triangle has three equal sides

so

in the equilateral triangle ABC

$AB=BC=AC=16 units$

the height of the triangle is the segment BD

in the right triangle BCD

Applying the Pythagorean Theorem

$BC^{2} =BD^{2}+DC^{2}$

solve for BD

$BD^{2}=BC^{2}-DC^{2}$

substitute the values

$BD^{2}=16^{2}-8^{2}$

$BD^{2}=192$

$BD=\sqrt{192}\ units$

therefore

the answer is

the height of the triangle is $\sqrt{192}\ units$

7 0

3 years ago

Read 2 more answers

HELPPPP PLEASE ANSWER THIS CORRECTLY AND U WILL GET BRAINLIEST WHAT IS THE SOLUTION TO THIS PROBLEM

Allushta [10]

Answer:

The other equation should be y= -5/3x +3 comment

if you have any questions

Step-by-step explanation:

Brainliest?!?!?

6 0

3 years ago

Read 2 more answers

Assume that the total revenue received from the sale of x items is given by, R(x)equals34 ln (4 x plus 5 ), while the total c

katen-ka-za [31]

Answer:

63 units

Step-by-step explanation:

The profit function P(x) is given by the revenue function minus the cost function:

$P(x) = R(x) - C(x)\\P(x) = 34ln(x+5)-\frac{x}{2}$

The number of units sold 'x' for which the derivate of the profit function is zero, is the number of units that maximizes profit:

$P(x) = 34ln(x+5)-\frac{x}{2}\\P'(x) =0= \frac{34}{x+5}-\frac{1}{2}\\x+5=68\\x=63\ units$

The number of units that should be manufactured so that profit is maximum is 63 units.

5 0

3 years ago

The frequency table shows the scores from rolling a dice. Work out the median

nikitadnepr [17]

Answer:

need a little more information

Step-by-step explanation:

6 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

Marren has 1/4 pound of raisins. she divides the raisins into 4 servings. each serving contains _ pound of raisins.