What is the best estimate for the volume of the pyramid?

1). Write an equation of a line with the given slope and y-intercept.

asambeis [7]

Answers:

1) The Equation of a Line is:

$y=mx+b$ (1)

Where:

$m$ is the slope

$b$ is the y-intercept

For this problem we have a given $m=-2$ and a given $b=4$

So, we only have to substitute this values in the equation (1):

$y=-2x+4$

This is option B

2) Here we have to find the slope $m$ and the y-intercept $b$ of this equation:

$y=\frac{1}{5}x-8$

According to the explanation in the first answer related to the equation (1), the slope of this line is:

$m=\frac{1}{5}$

And its y-intercept is:

$b=-8$

This is option C

3) We have to Equations of the Line, and we are asked if these are parallel:

$y=6x+9$ (a)

$27x-3y=-81$ (b)

Equation (b) has to be written in the same form of (a), in the form $y=mx+b$ in order to be able to compare both:

$-3y=-81-27x$

$y=-\frac{1}{3}(-81-27x)$

$y=\frac{81}{3}+\frac{27}{3}x$

$y=9x+27$ (c)

There is a rule that establishes that Two lines are parallel if they have the same slope. In this case, if we compare equations (a) and (c) we find they don’t have the same slope, then they are not parallel.

4) Here we are asked to write $y=\frac{3}{5}x+4$ in a standard form with integers:

$-\frac{3}{5}x+y=4$

Multiply each side by 5:

$5(-\frac{3}{5}x+y)=5(4)$

$5(-\frac{3}{5}x)+5y=20$

$-3x+5y=20$

In this case none of the options apply, please check if the question was written correctly.

5) In this question we are asked to write an equation parallel to:

$y=2x+7$ (2)

That passes through the given point (3,11). (Notice that in the Cartesian plane the points have an x-component and a y-component)

First, remember that two Equations of the line are parallel when they have the same slope. Now that this is clear, we are going to use the equation of the slope with the given point to find the parallel equation:

Equation of the slope:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ (3)

From (2) we know the slope is 2, then we only have to substitute this value and the points in (3):

$2=\frac{y-11}{x-3}$

$2(x-3)=y-11$

$2x-6=y-11$

Finally:

$y=2x+5$

This is option B

4 0

3 years ago

True or false: the standard deviation of a set of data values is never a negative number

Anestetic [448]

True I think !! Not to sure

8 0

3 years ago

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each quadratic equation with its so

Anon25 [30]

The quadratic equations and their solutions are;

9 ± √33 /4 = 2x² - 9x + 6.

4 ± √6 /2 = 2x² - 8x + 5.

9 ± √89 /4 = 2x² - 9x - 1.

4 ± √22 /2 = 2x² - 8x - 3.

Explanation:

Any quadratic equation of the form, ax² + bx + c = 0 can be solved using the formula x = -b ± √b² - 4ac / 2a. Here a, b, and c are the coefficients of the x², x, and the numeric term respectively.

We have to solve all of the five equations to be able to match the equations with their solutions.

2x² - 8x + 5, here a = 2, b = -8, c = 5. x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(5) / 2(2) = 8 ± √64 - 40/4. 24 can also be written as 4 × 6 and √4 = 2. So x = 8 ± 2√6 / 2×2= 4±√6/2.

2x² - 10x + 3, here a = 2, b = -10, c = 3. x =-b ± √b² - 4ac / 2a =-(-10) ± √(-10)² - 4(2)(3) / 2(4) = 10 ± √100 + 24/4. 124 can also be written as 4 × 31 and √4 = 2. So x = 10 ± 2√31 / 2×2 = 5 ± √31 /2.

2x² - 8x - 3, here a = 2, b = -8, c = -3. x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(-3) / 2(2) = 8 ± √64 + 24/4. 88 can also be written as 4 × 22 and √4 = 2. So x = 8 ± 2√22 / 2×2 = 4± √22/2.
2x² - 9x - 1, here a = 2, b = -9, c = -1. x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(-1) / 2(2) = 9 ± √81 + 8/4. x = 9 ± √89 / 4.

2x² - 9x + 6, here a = 2, b = -9, c = 6. x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(6) / 2(2) = 9 ± √81 - 48/4. x = 9 ± √33 / 4 .

8 0

3 years ago

Read 2 more answers

Please help me

nikklg [1K]

Answer:

2. $1,100 in clothing sales gives Rachel a $260 paycheck

3 $.2,200 in clothing sales gives Rachel a $370 paycheck

5. $10,800 in clothing sales gives Rachel a 1,230 paycheck

Step-by-step explanation:

Here is the complete question :

Rachel works for a clothing store. She is $150 paid every week plus a 10% commission on any clothes that she sells. Which of the following is true in regards to Rachel's weekly paycheck? Chose three correct answers.

1. $100 in clothing sales gives Rachel a $250 paycheck

2. $1,100 in clothing sales gives Rachel a $260 paycheck

3 $.2,200 in clothing sales gives Rachel a $370 paycheck

4. $ 4,200 in clothing sales gives Rachel a $420 paycheck

5. $10,800 in clothing sales gives Rachel a 1,230 paycheck

6. $ 16,000 in clothing sales gives Rachel a 1,450 paycheck

The equation representing Rachel's paycheck = amount she earns every month + commission

If she makes $100 in clothing sales, her paycheck = $150 + (0.1 x 100) = $160

If she makes $1100 in clothing sales, her paycheck = $150 + (0.1 x 1100) = $260

If she makes $2200 in clothing sales, her paycheck = $150 + (0.1 x 2200) = $370

If she makes $4200 in clothing sales, her paycheck = $150 + (0.1 x 4200) = $570

If she makes $10800 in clothing sales, her paycheck = $150 + (0.1 x 10800) = $1230

If she makes $16000 in clothing sales, her paycheck = $150 + (0.1 x 16000) = $1750

thus the correct options are 2,3,5

4 0

3 years ago

Which of the following is the net of a pyramid?

Masja [62]

Answer:

The answer is A

Step-by-step explanation: a net of a pyramid will always have a square and 4 triangles around it.

4 0

3 years ago