The table shows the time Merrida spent driving and the number of miles she drove. She drove the same number of miles each hour.

Merrida’s Driving Time and Distance
Miles
Hours
140
4
175
5
210
6

How many miles did she travel each hour?

9514 1404 393

Answer:

  y = 1/5

Step-by-step explanation:

Divide both sides of the equation by the coefficient of the variable.

  7 = 35y

  7/35 = (35y/35)

  1/5 = 1y

  y = 1/5

_____

A number divided by itself is 1. A number multiplied by 1 is unchanged.

To get from 35y to 1y, or y, divide by 35. That gives you (35/35)y = 1y = y.

Whatever you do to one side of the equation must also be done to the other side. Dividing 7 by 35 gives 7/35 = (7/7)×(1/5) = 1/5.

Answer :

square of 5 is 25 .

Answer:

The top of the ladder is sliding down at a rate of -1.25 ft/s.

Step-by-step explanation:

From the Pythagorean Theorem:

[tex]\displaystyle a^2 + b^2 = c^2[/tex]

(Where a is the height, b is the distance between the bottom of the ladder and the wall, and c is the length of the ladder itself.)

Note that the hypotenuse c is a constant value at 26 feet. Substitute:

[tex]\displaystyle a^2 + b^2 = (26\text{ ft})^2 = 676 \text{ ft}^2[/tex]

We want to determine how fast the top of the ladder is sliding down the wall at the instant of time when the bottom of the ladder is 10 feet from the wall and sliding away from the wall at the rate of 3 ft/s.

In other words, we want to find da/dt given that b = 10 ft, and db/dt = 3 ft/s.

First, we can differentiate both sides with respect to t, where a and b are both functions of t:

[tex]\displaystyle \frac{d}{dt}\left[ a^2 + b^2\right ] = \frac{d}{dt}\left [ 676 \text{ feet}^2\right ][/tex]

Implicit differentiation yields:

[tex]\displaystyle 2a \frac{da}{dt} + 2b \frac{db}{dt} = 0[/tex]

Next, since we know that b = 10 ft, we can find a:

[tex]\displaystyle \begin{aligned} a^2 + b^2 & = 676\text{ ft}^2 \\ \\ a^2 +(10 \text{ ft})^2 & = 676\text{ ft}^2 \\ \\ a & = 24\text{ ft} \end{aligned}[/tex]

Substitute and solve for da/dt:

[tex]\displaystyle \begin{aligned} 2a \frac{da}{dt} + 2b\frac{db}{dt} & = 0 \\ \\ 2(24 \text{ ft}) \frac{da}{dt} + 2(10 \text{ ft})(3 \text{ ft/s}) & = 0 \\ \\ 48 \text{ ft} \cdot \frac{da}{dt} & = -60 \text{ ft$^2$/s} \\ \\ \frac{da}{dt} & = -1.25 \text{ ft/s} \end{aligned}[/tex]

Since the ladder is sliding down the wall, da/dt is expected to be negative.

In conclusion, the top of the ladder is sliding down at a rate of -1.25 ft/s.

Answer:

Sydney will be 154.94cm

Answer:

The answer is letter D 0,6,12,18,24

Step-by-step explanation:

hope it's can help

(explanation attached)

There were 55 questions in the test.

Answer:

55

Step-by-step explanation:

Answer:

[tex]y=\frac{7}{2} x -8[/tex]

Step-by-step explanation:

We are given that a line contains these 2 points: (4,6) and (0,-8), in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept

First, we need to find the slope of the line

The slope can be calculated using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

Even though we have 2 points, let's label their values to avoid any confusion and mistakes when calculating:

[tex]x_1=4\\y_1=6\\x_2=0\\y_2=-8[/tex]

Now substitute into the formula

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-8-6}{0-4}[/tex]

Subtract

m=[tex]\frac{-14}{-4}[/tex]

Divide

m=[tex]\frac{7}{2}[/tex]

The slope is 7/2

Here is the equation of the line so far:

[tex]y=\frac{7}{2}x + b[/tex]

We now need to find b

As the equation passes through (4,6) and (0,-8), we can use either one of them to help solve for b.

Taking (4,6) for instance:

[tex]6=\frac{7}{2}(4) + b[/tex]

Multiply

[tex]6=14 + b[/tex]

Subtract

-8 = b

The equation therefore is:

[tex]y=\frac{7}{2} x -8[/tex]

Topic: slope-intercept form

See more: https://brainly.com/question/27726094

Hope this helps you !! :)

The solution is, the slope of the line in the graph is 5/7.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

from the given graph, we get,

the line is passing through the points ( 0,0) and, (5,7).

now, we know that

slope of a line is,

m = x1 - x2 / y1 - y2

so, we have,

here,

Slope(m) = 5-0/7-0

               = 5/7

Hence, The solution is, the slope of the line in the graph is 5/7.

To learn more on slope click:

brainly.com/question/3605446

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Answer:

Step-by-step explanation:

70000

Answer:

your answer is c

Step-by-step explanation:

Testing the hypothesis in this problem which is a two-tailed test, we can conclude that there is not sufficient evidence to conclude that the mean time of installation has changed, since the p-value of the test is 0.0364 > 0.01,

At the null hypothesis, we test if the mean is of 25 minutes, that is:

[tex]H_0: \mu = 25[/tex]

At the alternative hypothesis, we test if the mean has changed, that is, if it is different than 25 minutes.

[tex]H_1: \mu \neq 25[/tex]

We have the standard deviation for the sample, thus, the t-distribution is used. The value of the test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

In this problem:

The value of the test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{26.2 - 25}{\frac{4}{\sqrt{51}}}[/tex]

[tex]t = 2.14[/tex]

Since the p-value of the test is 0.0364 > 0.01, there is not sufficient evidence to conclude that the mean time of installation has changed.

A similar problem is given at https://brainly.com/question/23777908

Answer:

[tex]54[/tex]

Step-by-step explanation:

[tex] a_1 {r}^{n - 1} \\ 2 \times {3}^{4 - 1} \\ 2 \times {3}^{3} \\ 2 \times 3 \times 3 \times 3 \\ 2 \times 9 \times 3 \\ 18 \times 3 \\ = 54[/tex]

Hope this helps you.

Let me know if you have any other questions :-):-)

Answer:

9990 is the right answer

Answer:

B. x=4

Step-by-step explanation:

Answer:

31.36cm;22.4cm

Step-by-step explanation:

hope this helps

Answer:

Answer: 31.36 cm² ; 22.4 cm

Area:

[tex]{ \rm{area = (side \times side)}} \\ { \rm{area = (5.6 \times 5.6)}} \\{ \underline{ \underline { \rm{ \: \: area = 31.36 \: {cm}^{2} \: \: }}}}[/tex]

Perimeter:

[tex]{ \rm{perimeter = (4 \times side)}} \\ { \rm{perimeter = (4 \times 5.6)}} \\ { \underline{ \underline{ \rm{ \: \: perimeter = 22.4 \: cm \: \: }}}}[/tex]

Answer:

10 and 1 fourth

Step-by-step explanation:

41 over 4 = 41/4 so you divide 41 by 4 which is 10 R1 so its 10 wholes, 1 and 4

Answer:

246

Step-by-step explanation:

2(5)^3 - 4(1)^2

250 - 4

246

Answer:

B

Step-by-step explanation:

Im pretty sure it's B  X is going by 4's 4,8,12 then y is going by 12

Answer:

pretty sure its A

Step-by-step explanation:

A is the only one with the line going threw -1 and 5

Answer: its A just got done with it

A product of 10 has a number in one's position, and another figure will be 0.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

The one number is 10.

And let the other number of two digits will be xy.

Then the product of 10 and another number will be

10 × xy = xy0

The number at ones place when the product of 10 and another number will be 0.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

Answer:

$126

Step-by-step explanation:

I divided the figure in 3 parts, 1 triangle and 2 rectangles

found the area of each figure and added all to find the total area

Answer:

Domain = (infinity, infinity) Range = (3,0)

Step-by-step explanation:

Hard to explain without giving a 15 minute lecture lol

Answer:

x=-5

Step-by-step explanation:

-5*-3=15

15-2=13

Hope it helps

Answer:

x = -5

Step-by-step explanation:

-3x-2=13

Add 2 to both sides of the equation

-3x-2+2=13+2

Simplify

-3x=15

Divide both sides of the equation by the same term

[tex]\frac{-3x}{3} =\frac{15}{-3}[/tex]

Simplify

x = -5

Answer:

7/17

Step-by-step explanation:

Answer:

4.140393356

Step-by-step explanation:

Mean = (3+4+5+7+10+12+15) / 7 = 8

Count = 7 numbers

Sum of the numbers = 56

Each number minus the mean =

(3-8=-5)(4-8=-4)(5-8=-3)(7-8=-1)(10-8=2)(12-8=4)(15-8=7)

Now square of each of these numbers:

25+16+9+1+4+16+49 = 120

Variance = 120/7 = 17.14285714

Standard deviation = square root of the variance

Sqrt 17.14285714 = 4.140393356

Answer:

Algebra =

X/4 = -5/20

Simplify :

X/4 = -1/4

Of course, Will same x/4 = -1/4

x = -1

Step-by-step explanation:

[tex]\begin{aligned}\tt\frac{x}{4}&=\tt\frac{-5}{20}\\\tt 20x&=\tt -5\times 4\\\tt 20x&=\tt -20\\\tt x&=\tt -1\end{aligned}[/tex]

Answer:

7

Step-by-step explanation:

Pine Street in x miles long.

Maple street is 3 times as long as Pine Street, so Maple street is 3x miles long.

Maple street is 21 miles long.

3x = 21

x = 7

Maple Street is 7 miles long.