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1 year ago

Solving for x - (6x -5) = 2x+6 2

Mathematics

1 answer:

allochka39001 [22]1 year ago

6 0

we have

$\frac{6x-5}{2}=2x+6$

step 1

Multiply by 2 both sides

$\begin{gathered} 6x-5=2(2x+6) \\ 6x-5=4x+12 \end{gathered}$

step 2

Group terms

$6x-4x=12+5$

Combine like terms

$2x=17$

divide by 2 both sides

$\begin{gathered} x=\frac{17}{2} \\ x=8.5 \end{gathered}$

Verify

substitute the value of x in the original expression

$\begin{gathered} \frac{6(8.5)-5}{2}=2(8.5)+6 \\ 23=23 \end{gathered}$

is ok

the value of x satisfy the equation

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A rectangular garden has length twice as great as its width. A second rectangular garden has the same width as the first garden

stiks02 [169]

Use the information to write the dimensions of each rectangle in terms of w, the width of the 1st one.

1st rectangle;
l = 2w
w = 2

2nd rectangle:
w = w
l = 2w + 4

If the area of the 2nd rectangle is 70 square meters, you will use the area formula to write an equation that you will solve using the factoring.

A = lw
70 = w(2w + 4)
70 = 2w^2 + 4w
0 = 2w^2 + 4w -70
0 = 2 (w^2 +2w - 35)
0 = 2 (w + 7) (w - 5)

To get zero, the width would need to be -7 or 5. Because it is a distance, it has to be 5 meters.

The width of both rectangles is 5 meters.

6 0

3 years ago

Air has a density of 0.001226 g/mL. What volume of air would have a mass of 1.0 lb? A. 2.7 mL B. 815.6 mL C. 37 mL D. 3.7 × 102

Andre45 [30]

Answer:

$Volume = 3.7\ * 10^2\ L$

Step-by-step explanation:

Given

$Density = 0.001226 g/mL$

$Mass = 1.0\ lb$

Required

Determine the volume of air

Density is calculated using:

$Density = \frac{Mass}{Volume}$

Substitute values for Density and Mass

$0.001226 g/mL = \frac{1.0\ lb}{Volume}$

Convert lb to grams

$0.001226 g/mL = \frac{1.0 * 453.592\ g}{Volume}$

$0.001226 g/mL = \frac{453.592\ g}{Volume}$

Solve for Volume

$Volume = \frac{453.592\ g}{0.001226 g/mL}$

$Volume = 369977.161501\ mL$

Convert mL to L

$Volume = 369977.161501\ L * 0.001$

$Volume = 369.977161501\ L$

Represent using scientific notation

$Volume = 3.69977161501\ * 10^2\ L$

Approximate

$Volume = 3.7\ * 10^2\ L$

8 0

4 years ago

Can someone please help me?:\

katrin [286]

The circumference of the top of the cake is $9.5\pi\approx29.845$ in.

It sounds like the baker is trying to line the circumference with cherriesto fit as many as possible along the border, like in the picture I've attached below.

This comes down to dividing the cake's circumference by the diameter of each cherry:

$\dfrac{9.5\pi}{0.75}\approx39.79$