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3 years ago

7

Miyu has 36 grapes to share with her friends. She wants to make sure each friend gets an equal number of grapes. Which size grou

p of friends makes it impossible for Miyu to share her grapes equally?

1 answer:

MrRa [10]3 years ago

4 0

If there is a group of 5 friends she can't share her grapes evenly.

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Mikes plumbing charges 68 for coming to your house and 17 per hour for labor if I paid him 357, how many hours, h, was mike at m

Roman55 [17]

Answer:

b. $68 + 17h = 357$

f. 17 hours

Step-by-step explanation:

Charges for coming to my house = $68 (this will be the constant of the equation)

Amount charged per hour labor = $17

hours = h

Total amount paid to Mike = 357

The equation that represents this situation can be expressed as:

$68 + 17h = 357$

Solve for h

$68 + 17h - 68 = 357 - 68$ (subtraction property of equality)

$17h = 289$

$\frac{17h}{17} = \frac{289}{17}$ (division property of equality)

$h = 17$

Mike was in my house for 17 hours.

5 0

3 years ago

(3x+4)^2=14 what are the solutions?

kherson [118]

$\bf (3x+4)^2=14\implies \sqrt{(3x+4)^2}=\pm\sqrt{14}\implies 3x+4=\pm\sqrt{14}
\\\\\\
3x=\pm \sqrt{14}-4\implies x=\cfrac{\pm \sqrt{14}-4}{3}\implies x=
\begin{cases}
\cfrac{\sqrt{14}-4}{3}\\\\
\cfrac{- \sqrt{14}-4}{3}
\end{cases}$

7 0

3 years ago

A fence must be built to enclose a rectangular area of 45 comma 000 ftsquared. Fencing material costs $ 3 per foot for the two s

Tatiana [17]

Answer:

150 feet by 300 feet.

Step-by-step explanation:

The fence is to enclose a rectangular area of 45,000 ft squared.

If the dimensions of the rectangle are x and y

Area of a rectangle = xy

xy=45000
$x=\frac{45000}{y}$

Perimeter of the Rectangle =2x+2y

Fencing material costs $ 3 per foot for the two sides facing north and south and $6 per foot for the other two sides.

Cost of Fencing, C=$(6*2x+3*2y)=$(12x+6y)

Substitute $x=\frac{45000}{y}$ into the Cost to get C(y)

C=12x+6y

$C(y)=12(\frac{45000}{y})+6y\\C(y)=\frac{540000+6y^2}{y}$

The value at which the cost is least expensive is at the minimum point of C(y), when the derivative is zero.

$C^{'}(y)=\dfrac{6y^2-540000}{y^2}$

$\dfrac{6y^2-540000}{y^2}=0\\6y^2-540000=0\\6y^2=540000\\y^2=\frac{540000}{6} =90000\\y=\sqrt{90000}=300$

Recall,

$x=\frac{45000}{y}=\frac{45000}{300}=150$

Since x=150, y=300

The dimensions that will be least expensive to build is 150 feet by 300 feet.

6 0

3 years ago

Last year the manager of a health care facility served 36,500 dinners. The manager estimates an increase of 5% in the number of

EastWind [94]

Answer:

38,325 dinners.

Step-by-step explanation:

We have been given that last year the manager of a health care facility served 36,500 dinners. The manager estimates an increase of 5% in the number of dinners to be served next year.

The estimated number of dinners next year would be 36,500 plus 5% of 36,500.

$36,500+(\frac{5}{100}\times 36,500)$

$36,500+(0.05\times 36,500)$

$36,500+1,825$

$38,325$

Therefore, 38,325 dinners will be served next year.

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3 years ago

Solve the inequality below.<br> 10x – 4 < 6x

AnnZ [28]

Answer:

x<1

Step-by-step explanation:

7 0

3 years ago

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