Three times a number, subtracted from 20, is equal to -7

Write a fraction greater than 1 for 2 using 3 as the denominator .

hodyreva [135]

The question is a little confusing, but a fraction that is equal to 2 using 3 as a denominator is 6/3. Any addition to the numerator will make the number larger than 2; so 7/3, 10/3, 20/3 are all greater than 2.

8 0

3 years ago

Solve the equation (If possible please show work)

deff fn [24]

Answer:

$x=-3$

Step-by-step explanation:

So we have the equation:

$-2(-x-4)+3=-7-4x$

First, distribute the left side:

$-2(-x)-2(-4)+3=-7-4x\\2x+8+3=-7-4x$

Add values on the left side:

$2x+11=-7-4x$

Add 7 to both sides. The right side cancels:

$(2x+11)+7=(-7-4x)+7\\2x+18=-4x$

Subtract 2x from both sides. The left side cancels:

$(2x+18)-2x=(-4x)-2x\\18=-6x$

Divide both sides by -6:

$(-6x)/-6=18/-6\\x=-3$

Therefore, x equals -3.

8 0

3 years ago

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A box is being created out of a 15 inch by 10 inch sheet of metal. Equal-sized squares are cutout of the corners, then the sides

ivolga24 [154]

Answer:

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box has largest volume.

Step-by-step explanation:

Given that,

A box is being created out of a 15 inches by 10 inches sheet of metal.

The length of the one side of the squares which are cut out of the each corners of the metal sheet be x.

The length of the metal box be = (15-2x) inches.

The width of the metal box be =(10-2x) inches

The height of the metal box be =x inches

Then, the volume of the metal box= length×width×height

=(15-2x)(10-2x)x cubic inches

=(150x-50x²+4x³) cubic inches

∴ V= 4x³-50x²+15x

Differentiating with respect to x

V'=12x²-100x+15

Again differentiating with respect to x

V''=24x-100

For maximum or minimum value, V'=0

12x²-100x+15=0

Apply quadratic formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ , here a=12, b= -100 and c=15

$x=\frac{-(-100)\pm\sqrt{(-100)^2-4.12.15}}{2.12}$

$\Rightarrow x=\frac{100\pm\sqrt{9280}}{2.12}$

$\Rightarrow x=0.1528,8.18$

For x= 8.18, The value of (15-2x) and (10-2x) will negative.

∴x=0.1528 .

Now, $V''|_{x=0.1528}=24(0.1528)-100$

∴At x=0.1528 inch, the volume of the metal box will be maximum.

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box has largest volume.

4 0

3 years ago

Ruth is knitting hats to sell at a local fair. The booth costs her $63 and the materials for each hat cost $10. She plans on sel

aev [14]

Answer: Ruth have to make 7 hats to break even.

Step-by-step explanation:

Break even point is a point where Cost = Revenue.

Let x be the number of hats sold.

Given: Cost of booth = $63

Each hat cost = $10

Selling price for each cost = $19

As per given,

Total cost = Cost of booth+ (Cost of each hat)(Number of hats)

= 63+10x

Total selling price = 19x

For break even,

63+10x=19x

9x=63

x=7

Hence, Ruth have to make 7 hats to break even.

7 0

3 years ago

What are the greatest commom factor of 2x2x3x5 and 2x3x3x5

butalik [34]

Answer:

$\huge \bold \purple{answer}$

The greatest common factor of 2x2x3x5 and 2x3x3x5 is 2x3x5

8 0

3 years ago

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