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Alenkinab [10]
3 years ago
13

Help me please!!!!!!

Mathematics
1 answer:
lara [203]3 years ago
4 0

Answer:

a. b=2

b. b = 2a

c. a = \frac{1}{2}b\\

d. b = 10

Step-by-step explanation:

Gradient is just another similar term for slope l, m, and it can be calculated by m = \frac{y_2 -y_1}{x_2 -x_1}\\ where x_n and 1y_n is the xy-coordinates of point n

We let (0,0) be point 1 and (a,b) be point 2, we can then write the equation:

m = \frac{b -0}{a -0}\\ m = \frac{b}{a}.

It also says that the points are with a gradient of 2 so m = 2. We can then write the equation:

2 = \frac{b}{a}\\

Finding bIf a = 1:

2 = \frac{b}{a} \\ 2 = \frac{b}{1} \\ 2 = b \\ b = 2

Writing an expression for b in terms of a.

2 = \frac{b}{a} \\ \frac{b}{a} = 2 \\ \frac{b}{a} \times a = 2 \times a \\ b = 2a

Writing an expression for a in terms of b

2 = \frac{b}{a} \\ \frac{b}{a} = 2 \\ \frac{a}{b} = \frac{1}{2} \\ \frac{a}{b} \times b = \frac{1}{2} \times b \\ a = \frac{1}{2}b

Finding b if a = 5

2 = \frac{b}{a} \\ 2 = \frac{b}{5} \\ \frac{b}{5} = 2 \\ \frac{b}{5} \times 5 = 2 \times 5 \\ b = 10

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Please i want to know how to find slope intercepts
algol [13]

Answer:

Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula.

Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.

Step-by-step explanation:

The general formula is y = mx +b.

m = slope.

b = y-intercept of the line  

8 0
3 years ago
Russel wants to buy three ties and a belt and must spend no more that $80. The belt costs $28.50. If three ties are the same pri
docker41 [41]

Answer:

About $17.16

Step-by-step explanation:

$80-$28.50= 51.5

Then you divide that by 3 (for the 3 ties)

7 0
3 years ago
1<br> 4<br> Joey enlarged a 3-inch by 5-inch photograph on a copy machine. He enlarged it four times. The table below<br> shows
lozanna [386]

Answer:

3) 5.4

Step-by-step explanation:

Given two points (x1, f(x1)) and (x2, f(x2)), the average rate of change is computed as follows:

[f(x2) - f(x1)]/[x2 - x1]

From the original photograph to the fourth enlargement, the points are (0, 15) and (4, 36.6). Replacing into the equation we get:

[36.6 - 15]/[4 - 0] = 5.4

4 0
3 years ago
Oceanside bike rental shop charges fourteen dollars plus nine dollars an hour for renting a bike . Jason paid fifty-nine dollars
Dafna11 [192]

he payed 58 dollars to rent a bike for two hours because 40+9=49 & 49+9=58

5 0
3 years ago
In a survey, the planning value for the population proportion is . How large a sample should be taken to provide a confidence in
tatuchka [14]

Answer:

n=350

Step-by-step explanation:

Notation and definitions

n random sample taken  (variable of interest)

\hat p=0.35 estimated proportion  (value assumed)

p true population proportion

Confidence =0.95 or 95% (value assumed)

Me=0.05 (value assumed)

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.05 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.586  

And rounded up we have that n=350

4 0
3 years ago
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