The volume of a rectangular prism is (x^3-3x^2 +5x-3) and the area of its base is (x^2-2) if the volume of a rectangular prism is the product of its base area and height what is the height of the prism?

A)x-3 + 7x-9/x^2-2
B) x-3 + 7x-9/x^3 -3x^2+5x -3
C) x-3 + 7x +3 /x^2-2
D)x-3 + 7x+3/x^3-3x^2 +5x-3

Answer:

1. .21

2. .79

Step-by-step explanation:

1. 103/490

2. 387/490

Answer:

120 [tex]cm^{3}[/tex]

Step-by-step explanation:

6 x 5 x 4 =120

Answer:

120 cm^3

Step-by-step explanation:

volume = length * width * height

volume = 6 cm * 5 cm * 4 cm

volume = 120 cm^3

Answer:

Its C

hope this helps!!

The correct answer is A .)1

Answer:

261.67 [tex]ft^{3}[/tex]

Step-by-step explanation:

The formula is 1/3 [tex]\pi r^{2}h[/tex]

Answer:

261.67 ft^3

Step-by-step explanation:

mark me brainy plz!

Answer:

Step-by-step explanation:

For this case we have the following equation of the second degree:

[tex]7x ^ 2 = 9 + x[/tex]

Rewriting:

[tex]7x ^ 2-x-9 = 0[/tex]

The solutions will be given by the following equation:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

We have to:

[tex]a = 7\\b = -1\\c = -9[/tex]

Substituting the values:

[tex]x = \frac {- (- 1) \pm \sqrt {(- 1) ^ 2-4 (7) (- 9)}} {2 (7)}\\x = \frac {1 \pm \sqrt {(- 1) ^ 2 + 4 (7) (9)}} {2 (7)}[/tex]

Answer:

Option D

Answer:

30 boxes

Step-by-step explanation:

~ You begin with the bottom row, which has 10 boxes.

~ You do 10 - 2 to get the number of boxes in the next layer, which is 8.

~ You then take 8 - 2, which is 6 for the next layer up.

~ Take 6 - 2, which is 4 for the next layer up.

~ Take away another two: 4 - 2 is 2.

~ When you take 2 away from 2, you get 0, so you have no more boxes.

~ Then, you add all the different amounts of boxes for each layer:

-> 10 + 8 + 6 + 4 + 2

-> Group smaller numbers together to get two bigger ones:

-> 18 + 12

= 30

Answer:

Step-by-step explanation:

A is correct answer

Step-by-step explanation:

[tex]a)\ 12:18:36=\dfrac{12}{6}:\dfrac{18}{6}:\dfrac{36}{6}=2:3:6\\\\b)\ 320:480=32:48=\dfrac{32}{16}:\dfrac{48}{16}=2:3\\\\c)\ 16mm:480=\dfrac{16mm}{16}:\dfrac{480}{16}=1mm:30[/tex]

To simplify the given ratios, find the greatest common divisor (GCD) and divide all terms by the GCD. The simplified ratios are 2:3:6, 2:3, and 1:30. Refer to the solution for more details.

To simplify ratios, we divide both sides by their greatest common divisor (GCD).

a) 12:18:36

Find the GCD of 12, 18, and 36. It is 6.

Divide each number by 6:

The simplified ratio is 2:3:6.

b) 320:480

Find the GCD of 320 and 480. It is 160.

Divide both numbers by 160:

The simplified ratio is 2:3.

c) 16mm:480

Find the GCD of 16 and 480. It is 16.

Divide both numbers by 16:

The simplified ratio is 1mm:30. However, if there is no importance to specify units, simply 1:30 would be enough.

Answer : True

Explanation : It is according to distance formula.

The answer is True -Apex

4xk = 4K 4x4= 16 +4K + 7k = 16+ 11k ( I would double check me

Answer:

Step-by-step explanation:

The slope-intercept form y = mx + b

m - slope

b - y-intercept → (0, b)

We have the equation

y - 2x = -3              add 2x to both sides

y = 2x - 3

slope m = 2

y-intercept b = -3

We need two points to draw a graph of this linear function.

One is y-intercept (0, -3). The second one is calculated by choosing any value of x and put it to the equation:

for x = 2 → y = 2(2) - 3 = 4 - 3 = 1 → (2, 1).

Answer:

y = [tex]-\frac{1}{3} x[/tex] + 2

Step-by-step explanation:

The slope of the line that has an x intercept of (2,0) and y-intercept of (0,-6) is:

Slope(s) = Change in y ÷ change in x

s = [tex]\frac{0 - -6}{2 - 0}[/tex] = 3

The slope of the perpendicular line to this line with slope of 3 has to have a slope of -1 ÷ 3 = [tex]-\frac{1}{3}[/tex]

Reason: The product of slopes of lines perpendicular to each other have to be -1

So the slope of the perpendicular line that passes through (-6,4) is [tex]-\frac{1}{3}[/tex]

As mentioned earlier, we derive a slope of a line by dividing the change in y by the change in x

Taking another point (x,y) on the line,

[tex]-\frac{1}{3}[/tex] = [tex]\frac{y - 4}{x - -6}[/tex]

[tex]-\frac{1}{3}[/tex] = [tex]\frac{y - 4}{x + 6}[/tex]

y - 4 = [tex]-\frac{1}{3}[/tex]x - 2

y = [tex]-\frac{1}{3}[/tex]x + 2

To find the slope-intercept equation of a line that passes through a given point and is perpendicular to another line, we can determine the slope of the given line and use it to find the equation.

To find the slope-intercept equation of a line, we need to know the slope and the y-intercept. Since the line that this problem is referring to is perpendicular to a line with an x-intercept of 2 and a y-intercept of -6, we can determine the slope of the line we are looking for by taking the negative reciprocal of the slope of the given line.

The slope of the given line is found using the formula: slope = (y2 - y1) / (x2 - x1)

Once we have the slope, we can use the point-slope form of a linear equation to find the equation of the line that passes through (-6,4) and has the determined slope. Finally, we can rearrange the equation to obtain the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.

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Answer:

y = f(x) = a + bx

Step-by-step explanation:

independent variable = x

dependent variable =y

Answer:A linear function is a straight line which is just a linear function with the equation y=mx+b

Step-by-step explanation:

Answer:

Triangle (scalene)

Step-by-step explanation:

Polygon is a closed figure.

The names of polygons depends on the number of sides. Some common polygons are:

3 sides - triangle

4 sides - quadrilateral

5 sides - pentagon

6 sides - hexagon

Triangle and Quadrilaterals have their own types as well.

The points G, H , and I are shown in the attached image. As you can see, it creates a 3-sided figure, which is a triangle.

Note: Since all 3 sides have different length, we call it a "scalene triangle"

Answer:

0.5

Step-by-step explanation:

Given that height of 7 year old children are normally distributed with mean =49 inches and std deviation = 2inches

Brenda is 50 inches tall

This means her X score is 50

To convert this X score to Z score we use the formula given below

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Here we know all the values of x, mu and sigma

Just substitute

Z score

=[tex]\frac{50-49}{2} =\frac{1}{2} \\=0.5[/tex]

Thus Z score of Brenda is 0.5

Answer:

0.5

Step-by-step explanation:

Answer:

length×width

Step-by-step explanation:

Multiplying the length of a rectangle by the width will always give you the area. If one value is missing replace it with x.

Length x width should give you the answer your needing

Answer:

A. Use straightedge to connect vertex B to right-most vertex of the equilateral triangle.

Step-by-step explanation:

The process is to create a bisector of angle ABC... so it means cutting angle at vertex/summit B in half.

Drawing a line from the vertex B to the right-most vertex of the equilateral triangle will deliver you the bisector.

The only answer choice that includes vertex B is the answer A, all other answers are dealing with vertex A and C... which will not help you to draw the bisector or angle ABC.

Answer:

Option A is right

Step-by-step explanation:

Given in the picture is an angle B formed by line segments AB and BC

To construct bisector of angle B

First with centre at B a circle is drawn which meets AB and BC at D and E respectively. With same radius equal to DE and centres of D and E two circles are drawn which intersect at the right most point.

The next step is join B to the rightmost vertex of equilateral triangles

This will be the angle bisector of angle ABC

Hence option A is right

Answer:

146cm^2

Step-by-step explanation:

Area of trapezoid:

(4+14)/2*10=90

Area of triangle:

(14*8)/2=56

90+56=146

For this case we have a figure composed of a trapezoid and a triangle.

By definition we have that the area of a trapezoid is given by:

[tex]A = \frac {(B + b) * h} {2}[/tex]

Where:

B: It's the biggest side

b: It is the minor side

h: It's the height.

So:

[tex]A = \frac {(14 + 4) * 10} {2}\\A = 90 \ cm ^ 2[/tex]

For its part, the area of a triangle is:

[tex]A = \frac {b * h} {2}[/tex]

Where:

b: It's the base

h: It's the height

[tex]A = \frac {14 * (18-10)} {2}\\A = \frac {14 * 8} {2}\\A = \frac {14 * 8} {2}\\A = 56 \ cm ^ 2[/tex]

Thus, the total area is the sum of the two areas:

[tex]146 \ cm ^ 2[/tex]

ANswer:

[tex]146 \ cm ^ 2[/tex]

Answer:

270,000

Step-by-step explanation:

So, you have a number of people (15) that can stand comfortably within a certain area (5x8 ft = 40 sq feet).  And you need to find out how many people can fit in the whole park area.

First step is to find out how big the park is, in square feet, so we can then evaluate the number of people that we can fit in.

You had the right number for calculating the area of the park:

A = 400 yards x 200 yards = 1,200 feet x 600 feet = 720,000 sq feet

Now, how many people can we fit in there?  Let's use a simple cross-multiplication (x being the number of people fitting in the whole park, what we are looking for):

[tex]\frac{x}{720 000} = \frac{15}{40}[/tex]

By isolating x, we have x = (720,000 * 15) / 40 = 10,800,000 / 40 = 270,000

So, the park could accommodate 270,000 people.

That is of course if there are no trees, no benches, no kids playground or any other infrastructure in the park.

Answer:

Minimum balance account requires an amount of money to left in it all times in order to avoid fees.

Step-by-step explanation:

We have "many types of account" available in the banking sectors. As per the convenience of the customer, they opt from them. The minimum balance account is the type of account in which the customer has to maintain a standard amount prescribed by the bank in his account, failing to maintain it will lead to the gathering of fine or fee.

Answer:

Minimum Balance account.

Step-by-step explanation:

A minimum balance account is an account type that requires a minimum balance as set by the bank, at all times, in order to waive maintenance fees.

Failing this, certain amount is charged when money is deposited in that account. It can range from few dollars to 500 dollars in some banks.

Answer:

[tex]\frac{1}{5}\frac{in}{miles}[/tex]

Step-by-step explanation:

we know that

The original scale of the map is

[tex]\frac{2}{30}\frac{in}{miles}=\frac{1}{15}\frac{in}{miles}[/tex]

If the map is enlarged to 3 times its size

then

the new scale will be

[tex]\frac{2*3}{30}\frac{in}{miles}=\frac{6}{30}=\frac{1}{5}\frac{in}{miles}[/tex]

The scale of the original map is 2 inches to 30 miles. After enlarging the map 3 times, the new scale will be 1 inch to 15 miles, as 6 inches on the enlarged map would represent 90 miles.

The question is asking to determine the scale of a map after it has been enlarged. The original map scale is such that 2 inches represent 30 miles. If the map is enlarged 3 times its original size, each inch on the original map would now be represented by 3 inches on the enlarged map. Therefore, the 2 inches that originally represented 30 miles would now be stretched out to 6 inches on the enlarged map.

We can determine the new scale setting up a proportion:

We know the distances must remain consistent, so we set up the proportion:

By cross-multiplication, we find that:

The scale of the enlarged map will therefore be 1 inch representing 15 miles, as we can conclude from 6 inches representing 90 miles.

Answer:

B - +4.

Step-by-step explanation:

The person does not get 4.5 yards.

1/4, -1/4, and -4 do not work as well because negative numbers express loss, and not gain, and the person does not get any fractions.

Answer:

I believe the answer is B. +4

Step-by-step explanation:

Answer:

[tex]h=15.73\ in[/tex]

Step-by-step explanation:

we know that

The volume of a cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]V=1,000\ in^{3}[/tex]

[tex]r=9/2=4.5\ in[/tex] ----> the radius is half the diameter

substitute and solve for h

[tex]1,000=(3.14)(4.5)^{2} h[/tex]

[tex]h=1,000/[(3.14)(4.5)^{2}][/tex]

[tex]h=15.73\ in[/tex]

Answer:

r = 11 in V =968 pi in3

Step-by-step explanation:

got it right on edge

The answer is A. $18,600 because $620,000 × 3% = $18,600

Answer:

D) 72

Step-by-step explanation:

The way to find the area of this figure easily is to break it down in regular shapes we know.  You can then see it as two horizontal rectangles on top and bottom, measuring 6 x 4 each, then a vertical rectangle in the middle measuring 4 x 6.

So, overall, we have 3 similar rectangles measuring 4x6 or 6x4... which are equivalent.

The area of each of those 3 rectangles is 24 units (6x4).

Since we have 3 of those: 3 * 24 = 72.

[tex]x=-10, y=5\Longrightarrow\boxed{-10, 5}[/tex]

Answer:

The area of two pieces is [tex]51.28\ in^{2}[/tex]

Step-by-step explanation:

step 1

Find the area of the circle (large pizza)

The area is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=14/2=7\ in[/tex] ----> the radius is half the diameter

assume

[tex]\pi =3.14[/tex]

substitute

[tex]A=(3.14)(7)^{2}[/tex]

[tex]A=153.86\ in^{2}[/tex]

step 2

Divide the area into 6 pieces

[tex]153.86/6=25.64\ in^{2}[/tex]

step 3

Find the area of two pieces

[tex]25.64*2=51.28\ in^{2}[/tex]

rationalized form means that the number shoudnlt be a decimal that has never ending digits.

hope this answer to your question :)

Answer:

The center is (-5,1)

and

the radius is 3

Step-by-step explanation:

The given equation of the circle is

[tex](x+5)^2+(y-1)^2=9[/tex]

We can rewrite this equation in the form;

[tex](x-h)^2+(y-1)^2=r^2[/tex]

This implies that;

[tex](x--5)^2+(y-1)^2=3^2[/tex]

When we compare, we get;

(h,k)=(-5,1) which is the center and r=3 the radius.

The answer is:

The center of the circle is located on the point (-5,1) and the radius is equal to 3 units.

To determine the center and the radius of a circle from its equation, we need to look for "h" and "k", being "h" the x-coordinate of the center and "k" the y-coordinate the center, then, calculate the radius.

Since we are given the ordinary equation of the circle, we can find the radius and the center directly.

The ordinary equation is:

[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]

Where,

h is the x-coordinate of the center

y is the y-coordinate of the center

r is the radius.

So, we are given the circle:

[tex](x+5)^{2} +(y-1)^{2} =9[/tex]

Which is also equal to:

[tex](x-(-5))^{2} +(y-(1))^{2} =9[/tex]

Where,

[tex]h=-5\\k=1[/tex]

[tex]r^{2}=9\\\sqrt{r^{2}}=\sqrt{9} \\r=3units[/tex]

Hence, the center of the circle is located on the point (-5,1) and the radius is equal to 3 units.

Have a nice day!

Anwer:

1/7^2

explantion:

The expression equivalent to 7^3 • 7-^5 is 1 / 7^2.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now the given expression is,

7^3 • 7-^5

Now using the exponential property,

n^a . n^b = n^(a+b)

Therefore, we can write as,

7^3 • 7-^5 = 7^(3-5)

Solving we get,

7^3 • 7-^5 = 7^-2

Since, n^-a = 1/n^a

⇒7^-2 = 1 / 7^2

Therefore, we can write

7^3 • 7-^5 = 1 / 7²

this is the required equivalent expression.

Thus, the expression equivalent to 7^3 • 7-^5 is 1 / 7^2.

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