The table gives the numbers of teachers and students in grades 6 to 8 at Earhart Middle School. Grade Teachers Students 6 1 25 7 2 50 8 3 75 Which teacher-to-student ratio maintains the proportional relationship described in the table?

Final answer:

The equation of the line that is parallel to 2x+3y=3 and passes through the point (3, −4) is y = −(2/3)x − 2. We found this by first converting the given line into slope-intercept form to find the slope, and then using the point-slope form with the given point.

Explanation:

To find the equation of the line that is parallel to 2x+3y=3 and passes through the point (3, −4), we first need to determine the slope of the given line. The equation of a line in slope-intercept form is y = mx + b, where m represents the slope. We can rewrite the given equation in slope-intercept form by isolating y:

2x + 3y = 3

3y = −2x + 3

y = −(2/3)x + 1

This shows that the slope (m) of the given line is −(2/3). Since parallel lines have the same slope, the slope of the new line will also be −(2/3). Now we use the point-slope form of a line which is y − y1 = m(x − x1), where (x1,y1) is a point on the line. Plugging in the given point (3, −4) and the slope −(2/3), we get:

y − (−4) = −(2/3)(x − 3)

Distributing the slope on the right side and moving −4 to the other side gives us the final equation:

y = −(2/3)x + 2 + −4

y = −(2/3)x − 2

This is the equation of the line that is parallel to 2x+3y=3 and passes through the point (3, −4).

Answer:

[tex]x=4[/tex]

Step-by-step explanation:

We have been given an image of two right triangles and we asked to find the value of x.

First of all , we will find the length of segment RT using sine.

[tex]\text{Sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

Upon substituting our given values in above formula we will get,

[tex]\text{Sin}(60^{\circ})=\frac{2\sqrt{3}}{RT}[/tex]

[tex]RT=\frac{2\sqrt{3}}{\text{Sin}(60^{\circ})}[/tex]

[tex]RT=\frac{2\sqrt{3}}{\frac{\sqrt{3}}{2}}[/tex]

[tex]RT=\frac{2\sqrt{3}}{\sqrt{3}}\times 2[/tex]

[tex]RT=2\times 2[/tex]

[tex]RT=4[/tex]

Now we know that length of segment RT and angle QRT of triangle QRT, so we will use tangent to find the length of segment QR (x) as:

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

[tex]\text{tan}(45^{\circ})=\frac{x}{4}[/tex]

Multiplying both sides of our equation by 4 we will get,

[tex]\text{tan}(45^{\circ})*4=\frac{x}{4}*4[/tex]

[tex]\text{tan}(45^{\circ})*4=x[/tex]

Substituting [tex]\text{tan}(45^{\circ})=1[/tex] we will get,

[tex]1*4=x[/tex]

[tex]4=x[/tex]

Therefore, the value of x is 4 units.

Answer:

Option B. $170.10

Step-by-step explanation:

Gail bought groceries worth = $165.00

She gets rebate of taxes on the amount = $80.00

She has to pay tax on = 165 - 80 = $85.00

In her state sales tax are = 6%

So her tax on groceries  = 6% of 85 = 0.06 × 85 = $5.10

Now she paid total amount = 165 + 5.10 = $170.10

Gail paid $170.10 for the groceries, including sale tax

Option B. $170.10

690-6 = 684

690+6 = 696

 the answer is A

use the slope intercept equation to find the slope and the y intercept

y = mx-b

m = slope

b = y intercept

m is the number before the x so -3 is the slope

 and -1 is the y intercept

 so a point on the graph would be the y intercept at (0,-1)

Answer:

1/20

Step-by-step explanation:

1/4*1/5=1/20

Answer: The value of c must be 36 to make it perfect square trinomial.

Explanation:

A standard perfect square trinomial is [tex]x^2+2ax+a^2=(x+a)^2[/tex] where [tex]a^2[/tex] is the constant term.

Given trinomial [tex]x^2-12x+c=x^2+2(-6)a+c[/tex]

On comparing with standard perfect square trinomial we get a=-6

Therefore the constant term c=[tex]a^2=(-6)^2=36[/tex]

Such that the trinomial becomes [tex]x^2-12x+36=x^2+2(-6)x+(-6)^2=(x-6)^2[/tex] a perfect square trinomial.

Hence the value of c for the given trinomial must be 36 to make it perfect square trinomial.

Answer:

a

Step-by-step explanation:

Answer:

it takes 30 hours for Jamie to equal Lisa's earnings

Step-by-step explanation:

Lisa earns $8.10 an hour and worked 40 hours.

Total amount Lisa earns = rate times hours

Total amount Lisa earns =[tex]8.10 \cdot 40=324[/tex]

Jamie earns $10.80 an hour

LEt 'n' be the number of hours Jamie works

Total amount Jamie earns =[tex]10.80 \cdot n=10.80n[/tex]

we need to find out 'n' when Jamie earnings is equal to Lisa earnings

[tex]10.80n= 324[/tex]

Divide by 10.80 on both sides

n= 30

So it takes 30 hours for Jamie to equal Lisa's earnings

Scott's gross income in 4 weeks, rounded to the nearest cent, is $1887.20.

Calculate Scott's daily earnings:

  Scott earns $16.85 per hour, and he works for 7 hours per day.

  Daily earnings = $16.85/hour × 7 hours = $117.95

Calculate Scott's weekly earnings:

  Scott works 4 days per week.

  Weekly earnings = Daily earnings × Number of days worked per week

                  = $117.95/day × 4 days/week

                  = $471.80

Calculate Scott's gross income for 4 weeks:

  Scott works for 4 weeks.

  Gross income for 4 weeks = Weekly earnings × Number of weeks

                            = $471.80/week × 4 weeks

                            = $1887.20

However, we need to ensure the precision of the final answer. As currency involves cents, it's important to round appropriately.

Since we're dealing with money, we'll round to the nearest cent.

After rounding, the gross income for 4 weeks is $1887.20.

12 days

12X24= 288 HRS

288X60=17280 MINS

17280X60=1036800 SECONDS

The correct option is [tex]\boxed{\bf option A}[/tex] i.e, [tex]\boxed{\bf 129\text{ cm}}[/tex].

Further explanation:

A circle is the set of all points on a plane whose distance from a fixed point is constant.

There are infinite points on the circle and distance of these points from the center of circle is always constant.

The distance from the center of the circle to any point on the circle is called as radius of the circle.

The circumference is the length of the circle and the formula of the circumference [tex]C[/tex] for the circle is as follows:

[tex]\boxed{C=2\pi r}[/tex]  …… (1)

Here, [tex]r[/tex] is the radius of the circle and the value of [tex]\pi[/tex] is approximately equal to [tex]3.14[/tex].

The formula of the circumference for circle is terms of diameter is as follows:

[tex]\boxed{C=d\pi}[/tex]

Here, [tex]d[/tex] is the diameter of the circle.

The relationship between diameter and the radius is as follows:

[tex]\boxed{d=2r}[/tex].

From attached Figure 1 it is observed that the radius of the circle is [tex]20.5\text{ cm}[/tex].

Substitute [tex]r=20.5[/tex] in the equation (1) to obtain the value of circumference [tex]C[/tex] as follows:

[tex]\begin{aligned}C&=2\pi r\\&=2\cdot 3.14 \cdot 20.5\\&=128.74\\ &\approx129\end{aligned}[/tex]

Therefore, the circumference of the circle is [tex]\boxed{\bf 129\text{\bf cm}}[/tex].

Thus, the correct option is [tex]\boxed{\bf option A}[/tex].

Learn more:

1. Learn more about circle https://brainly.com/question/1952668

2. Learn more about radius of circle https://brainly.com/question/1506955

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Circle

Keywords:  Circle, radius of a circle, point, distance, diameter, circumference, d=2r, C=2pir, 129. centimeter, locus of circle, approximate, value, shown below.

Final answer:

To find the value of 10 times the big number minus 6 times the small number, we need to solve a system of equations. The solution to the system is x = 2 and y = 11, so the value of 10y - 6x is 98.

Explanation:

To find the value of 10 times the big number minus 6 times the small number, we need to solve the system of equations:

4x + 3y = 41 (equation 1)

2x + y = 15 (equation 2)

We can first solve equation 2 for y by subtracting 2x from both sides: y = 15 - 2x. Now we can substitute this value of y into equation 1:

4x + 3(15 - 2x) = 41

Simplifying, we get: 4x + 45 - 6x = 41

Combining like terms, we have: -2x + 45 = 41

Subtracting 45 from both sides, we get: -2x = -4

Dividing both sides by -2, we get: x = 2

Now we can substitute this value of x back into equation 2 to solve for y:

2(2) + y = 15

Simplifying, we get: 4 + y = 15

Subtracting 4 from both sides, we get: y = 11

Finally, we can calculate 10 times the big number minus 6 times the small number:

10y - 6x = 10(11) - 6(2) = 110 - 12 = 98

Answer:

Options A and Option E.

Step-by-step explanation:

A line has a slope of -4/5. Now a line perpendicular to this line will have the slope as [tex]m_{1}.m_{2}=-1[/tex]

Therefore [tex]m_{2}=-\frac{1}{m_{1}}=\frac{1}{\frac{4}{5} }=\frac{5}{4}[/tex]

Now we will find the slope with the help of points given in the options if they lie on the perpendicular line.

A). [tex]m=\frac{5-0}{2+2}=\frac{5}{4}[/tex]

B). [tex]m=\frac{-5-5}{4+4}=\frac{-10}{8}=-\frac{5}{4}[/tex]

C). [tex]m=\frac{0-4}{2+3}=-\frac{4}{5}[/tex]

D). [tex]m=\frac{-5+1}{6-1}=\frac{-4}{5}=-\frac{4}{5}[/tex]

E). [tex]m=\frac{9+1}{10-2}=\frac{10}{8}=\frac{5}{4}[/tex]

Options A and E are the correct options.

Answer:

paying a price to keep Mowgli alive would b ur answer

Step-by-step explanation:

Answer:

[tex]x= +-\frac{7}{4}[/tex]

Step-by-step explanation:

[tex]16x^2= 49[/tex]

Solve the equation for x

To solve the equation , we need to isolate x

To get x alone , we need to remove the numbers attached with x

To remove 16 we divide both sides by 16

[tex]x^2 = \frac{49}{16}[/tex]

Now to remove square from x we take square root on both sides

[tex]\sqrt{x^2} = \sqrt{\frac{49}{16}}[/tex]

square root (49) = 7

square root (16)= 4

So , [tex]x= +-\frac{7}{4}[/tex]

When we take square root we include +-