Write the prime factorization of 685 using exponent and explain how you got that answer?

The water level of a lake fell by 1 1/4 in. during a 1 1/2 week long drought what is the average rate at which the water level c

Luda [366]

Answer:

$\frac{5}{6}$ inches per week

Step-by-step explanation:

This is a very simple ratio problem. Basically,

<em>If $1\frac{1}{4}$ inches in $1\frac{1}{2}$ week, then HOW MANY INCHES (let it be x) in 1 week???</em>

<em />

We set up two ratios and cross multiply and solve for x:

$\frac{1\frac{1}{4}}{1\frac{1}{2}}=\frac{x}{1}\\1\frac{1}{4}*1=1\frac{1}{2}*x\\1\frac{1}{4}=1\frac{1}{2}x\\x=\frac{1\frac{1}{4}}{1\frac{1}{2}}\\x=\frac{\frac{5}{4}}{\frac{3}{2}}\\x=\frac{5}{4}*\frac{2}{3}\\x=\frac{5}{6}$

So average rate at which the water level changed every week is 5/6 inches per week.

4 0

3 years ago

A given line has the equation 10x + 2y = −2.

worty [1.4K]

The equation is $\boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }$

<h3>Further explanation </h3>

This case asking the end result in the form of a slope-intercept.

<u>Step-1: find out the gradient. </u>

10x + 2y = -2

We isolate the y variable on the left side. Subtract both sides by 10x, we get:

2y = - 10x - 2

Divide both sides by two

y = -5x -1

The slope-intercept form is $\boxed{ \ y = mx + c \ }$ , with the coefficient m as a gradient. Therefore, the gradient is m = -5.

If you want a shortcut to find a gradient from the standard form, implement this:

$\boxed{ \ ax + by = k \rightarrow m = - \frac{a}{b} \ }$

10x + 2y = −2 ⇒ a = 10, b = 2

$\boxed{m = - \frac{10}{2} \rightarrow m = -5}$

<u>Step-2:</u> the conditions of the two parallel lines

The gradient of parallel lines is the same $\boxed{ \ m_1 = m_2 \ }$ . So $\boxed{m_1 = m_2 = -5}.$

<u>Final step:</u> figure out the equation, in slope-intercept form, of the parallel line to the given line and passes through the point (0, 12)

We use the point-slope form.

$\boxed{ \ \boxed{ \ y - y_1 = m(x - x_1)} \ }$

Given that

m = -5
(x₁, y₁) = (0, 12)

y - 12 = - 5(x - 0)

y - 12 = - 5x

After adding both sides by 12, the results is $\boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }$

<u>Alternative steps </u>

Substitutes m = -5 and (0, 12) to slope-intercept form $\boxed{ \ y = mx + c \ }$

12 = -5(0) + c

Constant c is 12 then arrange the slope-intercept form.

Similar results as above, i.e. $\boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }$

$\boxed{Standard \ form: ax + by = c, with \ a > 0}$

$\boxed{Point-slope \ form: y - y_1 = m(x - x_1)}$

$\boxed{Slope-intercept \ form: y = mx + k}$

<h3>Learn more </h3>

A similar problem brainly.com/question/10704388
Investigate the relationship between two lines brainly.com/question/3238013
Write the line equation from the graph brainly.com/question/2564656

Keywords: given line, the equation, slope-intercept form, standard form, point-slope, gradien, parallel, perpendicular, passes, through the point, constant

7 0

3 years ago

Read 2 more answers

Dana needs 300 pickets for her colorful picket fence. She wants equal amounts of each of her 4 selected colors. She already has

Pavlova-9 [17]

Dana would need 75 pickets of each color to have an equal amount.

75x4=300

She would need 43 more red pickets to equal 75. (32+43=75)

49 more green pickets to equal 75 (26+49=75)

66 more yellow pickets to equal 75 (9+66=75)

75 blue pickets to equal 75. (0+75=75)

7 0

3 years ago

Read 2 more answers

An ice cream store sells 28 flavors of ice cream. Determine the number of 4 dip sundaes.

weeeeeb [17]

Answer:

$20,475\ ways$

Step-by-step explanation:

we know that

<u><em>Combinations</em></u> are a way to calculate the total outcomes of an event where order of the outcomes does not matter.

To calculate combinations, we will use the formula

$C(n,r)=\frac{n!}{r!(n-r)!}$

where

n represents the total number of items

r represents the number of items being chosen at a time.

In this problem

$n=28\\r=4$

substitute

$C(28,4)=\frac{28!}{4!(28-4)!}\\\\C(28,4)=\frac{28!}{4!(24)!}$

simplify

$C(28,4)=\frac{(28)(27)(26)(25)(24!)}{4!(24)!}$

$C(28,4)=\frac{(28)(27)(26)(25)}{(4)(3)(2)(1)}$

$C(28,4)=20,475\ ways$

6 0

3 years ago

Which is more economical: purchasing the economy size of a detergent at 6 kilograms for $6.15 or purchasing the regular size at

Ad libitum [116K]

Answer:

n, they will drive from Fort Worth to San Antonio, a distance of 229 miles, to visit his grandparents. On the way back, Mike reverses his trip and travels from San Antonio to Dallas through Forth Worth. Write one equation to show the distance traveled from Dallas to San Antonio, and a second equation to show the distance traveled from San Antonio to Dallas. What do you notice about the distance traveled each w

Step-by-step explanation:

n, they will drive from Fort Worth to San Antonio, a distance of 229 miles, to visit his grandparents. On the way back, Mike reverses his trip and travels from San Antonio to Dallas through Forth Worth. Write one equation to show the distance traveled from Dallas to San Antonio, and a second equation to show the distance traveled from San Antonio to Dallas. What do you notice about the distance traveled each w

4 0

2 years ago