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3 years ago

8. Find the slope-intercept form for the equation of the

Mathematics

1 answer:

sashaice [31]3 years ago

6 0

Answer:

$y=\frac{1}{9}x$

Step-by-step explanation:

We are given that the lines passes trough the points (-9, -1) and (0,0).

(0,0) is the origin.

Slope is: $m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{0-(-1)}{0-(-9)} =\boxed{\frac{1}{9}}$

The slope is one-ninth.

Since the lines passes at the origin, it's y-intercept is 'zero'. We do not write zeros in slope-intercept equations, to the equation of the line should be:

$y=\frac{1}{9}x$

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A certain marathon has had a wheelchair division since 1977. An interested fan wondered who is faster: the men's marathon winn

Dimas [21]

Answer:

A. The distribution of sample means of the differences will be approximately normal if there are at least 30 years of data in the sample and/or if the population of differences in winning times for all years is normal.

Step-by-step explanation:

In other to perform a valid paired test, one of the conditions required is that, data for both groups must be approximately normal. To attain normality, the population distribution for the groups must be normal or based on the central limit theorem, the sample size must be large enough, usually n > 30. Hence, once either of the two conditions are met, the paired sample will be valid.

8 0

3 years ago

Find solution to the system of linear equations. 5x1 + x2 = 0 , 25x1 + 5x2 = 0

Zigmanuir [339]

Answer:

the system of equation has infinite solution

Step-by-step explanation:

$5x_1 + x_2 = 0$ , $25x_1 + 5x_2 = 0$

Solve the first equation for x_2

Subtract 5x1 on both sides

$5x_1 + x_2 = 0$

$x_2 =-5x_1$

Now substitute -5x1 on second equation

$25x_1 + 5x_2 = 0$

$25x_1 + 5(-5x_1)= 0$

$25x_1-25x_1= 0$

0=0

So the system of equation has infinite solution

5 0

3 years ago

Read 2 more answers

Two poles are connected by a wire that is also connected to the ground. The first pole is 18 ft tall and the second pole is 24 f

9966 [12]

Answer:

72 feet from the shorter pole

Step-by-step explanation:

The anchor point that minimizes the total wire length is one that divides the distance between the poles in the same proportion as the pole heights. That is, the two created triangles will be similar.

The shorter pole height as a fraction of the total pole height is ...

18/(18+24) = 3/7

so the anchor distance from the shorter pole as a fraction of the total distance between poles will be the same:

d/168 = 3/7

d = 168·(3/7) = 72

The wire should be anchored 72 feet from the 18 ft pole.

_____

Comment on the problem

This is equivalent to asking, "where do I place a mirror on the ground so I can see the top of the other pole by looking in the mirror from the top of one pole?" Such a question is answered by reflecting one pole across the plane of the ground and drawing a straight line from its image location to the top of the other pole. Where the line intersects the plane of the ground is where the mirror (or anchor point) should be placed. The "similar triangle" description above is essentially the same approach.

Alternatively, you can write an equation for the length (L) of the wire as a function of the location of the anchor point:

L = √(18²+x²) + √(24² +(168-x)²)

and then differentiate with respect to x and find the value that makes the derivative zero. That seems much more complicated and error-prone, but it gives the same answer.

7 0

3 years ago

In the digram GH bisects FGI what is the answer for C.

zhannawk [14.2K]

The line GH bisects The triangle FGI meaning it divides it into two equal parts (that is the definition if bisection); therefore, the angles FGH and HGI are equal:

$3x-2=4x-13$

Now let us add 2 to both sides gives

$3x=4x-11$

subtracting 4x from both sides gives

$-x=-11$ $x=11.$

Hence, x = 11.

The measure of FGH is

$3x-2=3(11)-2=31$

(B)

The measure of HGI is

$4x-13=4(11)-13=31$

(C)

The measure of FGI is the sum of HGI and FGH:

$\begin{gathered} \text{FGI}=\text{HGI}+\text{FGH}=31+31 \\ FGI=62^o \end{gathered}$

7 0

1 year ago

A stockbroker has money in three accounts. The interest rates on the three accounts are 10 % 10%, 11 % 11%, and 12 % 12%. If she

leva [86]

Answer: he invested $200 at 10%, $400 at 11% and $600 at 12%

Step-by-step explanation:

Let x represent the amount invested in the account earning 10% interest.

Let y represent the amount invested in the account earning 11% interest.

Let z represent the amount invested in the account earning 12% interest.

If she has twice as much money invested at 11 % as she does in 10 %, it means that

y = 2x

If she has three times as much at

12 % as she has at 10 %, it means that

z = 3x

The interest from the first account is

x × 0.1 × 1 = 0.1x

The interest from the second account is

y × 0.11 × 1 = 0.11y

The interest from the third account is

z × 0.12 × 1 = 0.12z

If the total interest for the year is $136, it means that

0.1x + 0.11y + 0.12z = 136 - - - - - - - - 1

Substituting y = 2x and z = 3x into equation 1, it becomes

0.1x + 0.11(2x) + 0.12(3x) = 136

0.1x + 0.22x + 0.36x = 136

0.68x = 136

x = 136/0.68 = 200

y = 2x = 2 × 200

y = $400

z = 3x = 3 × 200

z = $600

4 0

3 years ago