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3 years ago

What is the equation of the line with a y-intercept of 4 and a point (8,8)?

Mathematics

1 answer:

Nookie1986 [14]3 years ago

7 0

Answer:

The equation of the line with a y-intercept of 4 and a point (8,8) is $y=\frac{1}{2} *x+4$

Step-by-step explanation:

A linear equation can be expressed in the form

y = m * x + b

where x and y are coordinates of a point, m is the slope and b is the y-intercept. Since this equation describes a line in terms of its slope and its y-intercept, this equation is said to be in its slope-intercept form.

Graphically this equation represents a line.

In this case, you know:

The point (x,y)=(8,8)
Y-intercept= 4

Replacing:

8=m*8 +4

Solving:

8-4=m*8

4=m*8

4÷8= m

$m=\frac{1}{2}$

Then, the equation of the line with a y-intercept of 4 and a point (8,8) is $y=\frac{1}{2} *x+4$

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If = 80°, and m∠BED = 25°, what is ? 55° 30° 65° 20°

Tomtit [17]

The complete question in the attached figure

we know that
The measure of the external angle is the semidifference of the arcs that it covers.
so
m∠BED =(1/2)*[mAC-mBD]-------> solve for mBD
mBD=mAC-2m∠BED
mBD=80-2*25--------> mBD=30°

the answer is
mBD=30°

5 0

3 years ago

Some transportation experts claim that it is the variability of speeds, rather than the level of speeds, that is a critical fact

scZoUnD [109]

Answer:

Explained below.

Step-by-step explanation:

The claim made by an expert is that driving conditions are dangerous if the variance of speeds exceeds 75 (mph)².

(1)

The hypothesis for both the test can be defined as:

H₀: The variance of speeds does not exceeds 75 (mph)², i.e. σ² ≤ 75.

Hₐ: The variance of speeds exceeds 75 (mph)², i.e. σ² > 75.

(2)

A Chi-square test will be used to perform the test.

The significance level of the test is, α = 0.05.

The degrees of freedom of the test is,

df = n - 1 = 55 - 1 = 54

Compute the critical value as follows:

$\chi^{2}_{\alpha, (n-1)}=\chi^{2}_{0.05, 54}=72.153$

Decision rule:

If the test statistic value is more than the critical value then the null hypothesis will be rejected and vice-versa.

(3)

Compute the test statistic as follows:

$\chi^{2}=\frac{(n-1)\times s^{2}}{\sigma^{2}}$

$=\frac{(55-1)\times 94.7}{75}\\\\=68.184$

The test statistic value is, 68.184.

Decision:

$cal.\chi^{2}=68.184$

The null hypothesis will not be rejected at 5% level of significance.

Conclusion:

The variance of speeds does not exceeds 75 (mph)². Thus, concluding that driving conditions are not dangerous on this highway.

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3 years ago

The circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm. (a) Use differentials to estimate the ma

andreev551 [17]

The maximum error in the calculated surface area is 24.19cm² and the relative error is 0.0132.

Given that the circumference of a sphere is 76cm and error is 0.5cm.

The formula of the surface area of a sphere is A=4πr².

Differentiate both sides with respect to r and get

dA÷dr=2×4πr

dA÷dr=8πr

dA=8πr×dr

The circumference of a sphere is C=2πr.

From above the find the value of r is

r=C÷(2π)

By using the error in circumference relation to error in radius by:

Differentiate both sides with respect to r as

dr÷dr=dC÷(2πdr)

1=dC÷(2πdr)

dr=dC÷(2π)

The maximum error in surface area is simplified as:

Substitute the value of dr in dA as

dA=8πr×(dC÷(2π))

Cancel π from both numerator and denominator and simplify it

dA=4rdC

Substitute the value of r=C÷(2π) in above and get

dA=4dC×(C÷2π)

dA=(2CdC)÷π

Here, C=76cm and dC=0.5cm.

Substitute this in above as

dA=(2×76×0.5)÷π

dA=76÷π

dA=24.19cm².

Find relative error as the relative error is between the value of the Area and the maximum error, therefore:

$\begin{aligned}\frac{dA}{A}&=\frac{8\pi rdr}{4\pi r^2}\\ \frac{dA}{A}&=\frac{2dr}{r}\end$

As above its found that r=C÷(2π) and r=dC÷(2π).

Substitute this in the above

$\begin{aligned}\frac{dA}{A}&=\frac{\frac{2dC}{2\pi}}{\frac{C}{2\pi}}\\ &=\frac{2dC}{C}\\ &=\frac{2\times 0.5}{76}\\ &=0.0132\end$

Hence, the maximum error in the calculated surface area with the circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm is 24.19cm² and the relative error is 0.0132.

Learn about relative error from here brainly.com/question/13106593

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2 years ago

Original price $60 makeup 15% retail price is

lara31 [8.8K]

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4 years ago

What is the equation of the line with a y-intercept of 4 and a point (8,8)? ​

What is the equation of the line with a y-intercept of 4 and a point (8,8)?