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3 years ago

What is the slope of this line?

Mathematics

2 answers:

IrinaVladis [17]3 years ago

5 0

Answer:

M=6/7 (M= six over seven)

Step-by-step explanation:

shusha [124]3 years ago

5 0

Answer:

$\boxed{\sf{-3}}$

Step-by-step explanation:

You can solve this problem by using the slope formula to find the slope of the line.

<u>Slope formula:</u>

$\sf{\dfrac{Y_2-Y_1}{X_2-X_1}=\dfrac{RISE}{RUN}}$

y2=(-2)

y1=10

x2=(-5)

x1=(-9)

Rewrite the problem down and then solve it.

$\sf{\dfrac{(-2)-10}{(-5)-(-9)} }=\dfrac{-2-10}{-5+9}=\dfrac{-12}{4}$

Divide by 4 as well.

$\sf{\dfrac{-12\div4}{4\div4}=\dfrac{-3}{1}=\boxed{\sf{-3}}}$

Therefore, the slope is -3.

I hope this helps! Let me know if my answer is wrong or not.

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a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to the curve at the given point.

xxMikexx [17]

Answer:

y = 13*( -x/9 + 1/5)

Step-by-step explanation:

Given:

- The curve has an equation as follows:

$44 = 5x^2 + 3xy + 3y^2$

Find:

a. Verify that the given point (2,2) lies on the curve.

b. Determine an equation of the line tangent to the curve at the given point.

Solution:

- To verify whether the point lies on the given curve we will substitute the coordinates of the point into the equation as follows:

44 = 5*(2)^2 + 3*(2)(2) + 3*(2)^2

44 = 20 + 12 + 12

44 = 44 ......Hence proven.

- The equation of the line tangent to the curve is expressed as a linear function as follows:

y = m*x + C

Where, m is the gradient of the line.

C is the y-intercept.

m = Δy / Δx = dy/dx

- We will take the derivative of the given curve with respect to x as follows:

$0 = 10x + 3*( y + xy' ) + 6y*y'\\\\-10x - 3y = y' ( 3x + 6y)\\\\ y' = - \frac{10x + 3y}{3x + 6y}$

- Evaluate y' at the point (2,2) we get:

y' = - ( 10(2) + 3(2) ) / ( 3(2) + 6(2) )

y' = - ( 26 ) / (18)

y'= m = - 13/9

- To evaluate C, we will use the point (2,2) for linear expression above with m as follows:

y = -13*x/9 + C

2 =-13*(2)/9 + C

C = 13 / 5

- The equation of the tangent is as follows:

y = 13*( -x/9 + 1/5)

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3 years ago

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Hoochie [10]

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3 years ago

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UkoKoshka [18]

Answer:

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5 0

3 years ago

In a study of parents' perceptions of their children's size, researchers asked parents to estimate their youngest child's height

tatyana61 [14]

Answer:

Test statistic t=6.505

P-value=0

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that parents tend to underestimate their youngest child's size.

Then, the null and alternative hypothesis are:

$H_0: \mu=0\\\\H_a:\mu> 0$

The significance level is assumed to be 0.05.

The sample has a size n=39.

The sample mean is M=7.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=7.2.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{7.2}{\sqrt{39}}=1.153$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{7.5-0}{1.153}=\dfrac{7.5}{1.153}=6.505$

The degrees of freedom for this sample size are:

$df=n-1=39-1=38$

This test is a right-tailed test, with 38 degrees of freedom and t=6.505, so the P-value for this test is calculated as (using a t-table):

$P-value=P(t>6.505)=0$

As the P-value (0) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that parents tend to underestimate their youngest child's size.

5 0

3 years ago

Someone plz help me :(

kondaur [170]

Answer:

the answer is 9 mark me brainlest

Step-by-step explanation:

A P E X

7 0

3 years ago