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2 years ago

There is a line that includes the point (0, 4) and has a slope of 9. What is its equation in

Mathematics

1 answer:

Artyom0805 [142]2 years ago

4 0

Answer:

y = 9x + 4

Step-by-step explanation:

The slope-intercept equation is

y = mx + b

M = slope

B = y-intercept.

From the point, we know the line intercepts y at 4. So the y-intercept is 4.

Now the slope is 9.

Now insert the numbers:

y = 9x + 4

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Analysis of an accident scene indicates a car was traveling at a velocity of 69.5 mph (31.1 m/s) along the positive x-axis at th

STatiana [176]

We can find the acceleration via

${v_f}^2-{v_i}^2=2a\Delta x$

We have

$\left(5.20\dfrac{\rm m}{\rm s}\right)^2-\left(31.1\dfrac{\rm m}{\rm s}\right)^2=2a(115\,\mathrm m)$

$\implies\boxed{a=-4.09\dfrac{\rm m}{\mathrm s^2}}$

Then by definition of average acceleration,

$a_{\rm ave}=\dfrac{v_f-v_i}t$

so that

$-4.09\dfrac{\rm m}{\mathrm s^2}=\dfrac{5.20\frac{\rm m}{\rm s}-31.1\frac{\rm m}{\rm s}}t$

$\implies\boxed{t=6.33\,\mathrm s}$

We alternatively could have found the time without knowing the acceleration. Since acceleration is constant, the average velocity is

$v_{\rm ave}=\dfrac{x_f-x_i}t=\dfrac{v_f+v_i}2$

Then

$\dfrac{115\,\rm m}t=\dfrac{5.20\frac{\rm m}{\rm s}+31.1\frac{\rm m}{\rm s}}2$

$\implies\boxed{t=6.33\,\mathrm s}$

7 0

3 years ago

Question: Antonio is working with a new geometric series generated by the equation A(n)=20(1.1)^n-1.His sister challenged him to

Mekhanik [1.2K]

Answer:

sum of 22nd = 1,428.05

sum of 23 to 40 is 932.53

Step-by-step explanation:

A(n)=20(1.1)^n-1

20 is the first term or a1

1.1 is the common ratio or r

A(22) = 20(1.1)^22-1

22nd term = 20(1.1)^21

22nd term = 148.00

sum of geometric sequence

formula

Sn = a1(1-r^n)/1-r

Sn = sum

a1 = first term

n = number of term

r = constant ratio

sum of 22nd = 1,428.05.

23 to 40 is 17 terms

Sequence: 23, 25.3, 27.83, 30.613, 33.6743, 37.04173, 40.745903 ...

The 17th term: 105.684378686

Sum of the first 17 terms: 932.528165548

socratic

miniwebtoolcomgeometricsequencecalculator

6 0

3 years ago

Paula and Kawai shared $312 in the ratio of 6:7. How much money did each person get?

Maslowich

Answer:

Paula get $\$144$ and Kawai get $\$168$ .

Step-by-step explanation:

Given: Paula and Kawai shared $\$312$ in the ratio of $6:7$ .

To find: How much money did each person get?

Solution:

We have,

Paula and Kawai shared $\$312$ in the ratio of $6:7$ .

So, let Paula get $\$6x$ and Kawai get $\$7x$ .

As per the question,

$6x+7x=312$

$\implies13x=312$

$\implies x=\frac{312}{13} =24$

Therefore, Paula get $6\times 24=\$144$ , and Kawai get $7\times 24=\$168$ .

Hence, Paula get $\$144$ and Kawai get $\$168$ .

6 0

3 years ago

A cleaner recommends mixing 1½ cup of cleaner for every 12 cups of water. What is the ratio of cleaner to water in simplest form

guapka [62]

We know that

1½ cup of cleaner-------> (1*2+1)/2-----> 3/2 cup of cleaner

the ratio of cleaner to water=(3/2)/12---> 3/(2*12)--> 3/24--> 1/8

the answer is
1/8

6 0

4 years ago

Deon finished his math assignment in 2/5 hours. Then he completed his chemistry assignment in 1/2 hours. How much more time did

ipn [44]

Answer:

Deon spent 1/10 of an hour more on chemistry than on math

Step-by-step explanation:

7 0

3 years ago