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3 years ago

10

Hey science test is worth 100 points and has 25 questions there are multiple choice questions worth three points each and short

essay answers worth eight points each how many short essay questions are on the test

1 answer:

Snezhnost [94]3 years ago

6 0

Answer:

x+y=100

3x+8y=25

Step-by-step explanation:

So there are around 3 essay questions

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The volume of a pyramid that fits exactly inside a cube is 49 cubic feet. what is the volume of the cube?

8090 [49]

The volume of a pyramid is 1/3 the volume of the cube mentioned in the question since it fits exactly inside it. So multiply 49*3 = 147 cubic feet

6 0

3 years ago

Read 2 more answers

Number of emails received in one account every day from the day it was created until it was canceled:

3241004551 [841]

The answer is B. Complete information.

A sample means only part of the whole. From the day the email was created till it was cancelled is the whole population. Consider that no mails will no longer go in because it is closed so no more additional information or data will enter that category. So it would be considered as complete. If the situation were to ask from one point to another before it was cancelled it would be considered as a sample.

6 0

3 years ago

The equation of line AB is y = 2x + 4. Write an equation of a line parallel to line AB in slope-intercept form that contains poi

ale4655 [162]

Answer:

<h3>The answer is option D</h3>

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

y = 2x + 4

comparing with the above equation for a line

The slope / m = 2

Since the lines are parallel their slope are also the same

Slope of parallel line = 2

So we have

The equation of the line using point

( 3 , -2) and slope 2 is

y + 2 = 2( x - 3)

y + 2 = 2x - 6

y = 2x - 6 - 2

We have the final answer as

<h3>y = 2x - 8</h3>

Hope this helps you

7 0

3 years ago

Find the equation for the plane through the points Upper P 0 (4 comma 5 comma negative 3 )P0(4,5,−3), Upper Q 0 (1 comma 4 comm

alexira [117]

Answer:

4x -4y +z = -7

Step-by-step explanation:

The direction vector will be perpendicular to any/all vectors between the given points. It can be found, for example, using the cross product:

d = (P0Q0) × (P0R0) = (-3, -1, 8) × (-4, -3, 4)

The cross product can be computed by hand or by any of a number of calculators or web tools. Here it will be ...

d = (20, -20, 5)

These can be the coefficients of x, y, and z in the plane equation. However, the equation is better written using coefficients that are mutually prime, so we choose the direction vector to be ...

d = (4, -4, 1)

The constant C in the plane equation

d·(x, y, z) = C

will be the dot product of this direction vector (d) any any of the given points. Using R0, we find the constant to be ...

C = (4, -4, 1)·(0, 2, 1) = 4·0 +(-4)·2 +1·1 = -8+1 = -7

so, the plane equation is ...

4x -4y +z = -7

6 0

3 years ago

Suppose that we don't have a formula for g(x) but we know that g(3) = −5 and g'(x) = x2 + 7 for all x.

Leni [432]

Answer:

a)

$g(2.9) \approx -6.6$

$g(3.1) \approx -3.4$

b)

The values are too small since $g''$ is positive for both values of $x$ in. I'm speaking of the $x$ values, 2.9 and 3.1.

Step-by-step explanation:

a)

The point-slope of a line is:

$y-y_1=m(x-x_1)$

where $m$ is the slope and $(x_1,y_1)$ is a point on that line.

We want to find the equation of the tangent line of the curve $g$ at the point $(3,-5)$ on $g$ .

So we know $(x_1,y_1)=(3,-5)$ .

To find $m$ , we must calculate the derivative of $g$ at $x=3$ :

$m=g'(3)=(3)^2+7=9+7=16$ .

So the equation of the tangent line to curve $g$ at $(3,-5)$ is:

$y-(-5)=16(x-3)$ .

I'm going to solve this for $y$ .

$y-(-5)=16(x-3)$

$y+5=16(x-3)$

Subtract 5 on both sides:

$y=16(x-3)-5$

What this means is for values $x$ near $x=3$ is that:

$g(x) \approx 16(x-3)-5$ .

Let's evaluate this approximation function for $g(2.9)$ .

$g(2.9) \approx 16(2.9-3)-5$

$g(2.9) \approx 16(-.1)-5$

$g(2.9) \approx -1.6-5$

$g(2.9) \approx -6.6$

Let's evaluate this approximation function for $g(3.1)$ .

$g(3.1) \approx 16(3.1-3)-5$

$g(3.1) \approx 16(.1)-5$

$g(3.1) \approx 1.6-5$

$g(3.1) \approx -3.4$

b) To determine if these are over approximations or under approximations I will require the second derivative.

If $g''$ is positive, then it leads to underestimation (since the curve is concave up at that number).

If $g''$ is negative, then it leads to overestimation (since the curve is concave down at that number).

$g'(x)=x^2+7$

$g''(x)=2x+0$

$g''(x)=2x$

$2x$ is positive for $x>0$ .

$2x$ is negative for $x$ .

That is, $g''(2.9)>0 \text{ and } g''(3.1)>0$ .

So $2x$ is positive for both values of $x$ which means that the values we found in part (a) are underestimations.

6 0

4 years ago