Here is a prism.
Its face is made from 6 identical squares
with side length 2 cm.
Work out the volume of the prism.

Height 2cm
Width 12 cm

Answer:

Answer:

a) $7.50

Step-by-step explanation:

The total cost of $85.50 includes a 5% discount, so 95% of what price is $85.50?

[tex].95x = 85.50[/tex]

[tex]x = 90[/tex]

So the original price is $90. Divide this by 12, obtaining $7.50.

Answer:

a)$7.5

Step-by-step explanation:

Solution:

Let X represents socks

Given,

Selling price (SP) of 12x=$85.50

Discount precent (d%)=5%

So,

SP=(100-d)% of MP. [this formula really exist believe it or not]

85.50= (100-5)/100 ×MP

or, 85.50×100 =95×MP

or, 8550/95=MP

So,MP=$90

Now At last ,

cost of 1 shocks before discount is 90/12

which is $7.50 ans√

Answer:

x⊥a

Step-by-step explanation:

If we draw this out, we see that x is perpendicular to a as well.

Answer:

The two triangles in group A are similar because two angles of one are congruent to two angles of the other.

The two triangles in group A are similar because two angles of one are congruent to two angles of the other.

The two triangles in group B are not similar. The ratio of the short sides of the two triangles is 10:4 or 2.5:1, and that is the same ratio as the two sides 24 and 9.6.

However, using the fact that an angle bisector in a triangle divides the opposite side into two segments in the same ratio as the lengths of the two sides that include the angle, the length of the third side of the left triangle can be found to be about 25.12; and 9.25 times 2.5 is not close to 25.12.

b. In group A, the third side of the first triangle, by the Pythagorean Theorem, is sqrt(306).

The scale factor between the two triangles is 3:5, so the length of the third side of the second triangle is 15*(5/3) = 25.

In both triangles, the third angle measure is 31 degrees, since the sum of the three angles is 180.

c. The scale factor, again, is 3:5 which means the ratio of the areas of the two triangles is 3²:5² or 9:25.

d. The first triangle can be carried onto the second with the following transformations:

(1) dilate by a factor of 5/3 to make it the same size;

(2) rotate 90 degrees counterclockwise;

(3) translate so the hypotenuses of the two triangles are the same line segment; and

(4) reflect on the hypotenuse.

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If the top is 8 feet above the ground and ladder is 5 feet away from bottom of wall then the angle between ladder and house is 58°.

Given top is 8 feet above the ground, ladder is 5 feet away from bottom of the wall.

Trigonometric ratios are the ratios of the sides of a right angled triangle. sin is the ratio of perpendicular and hypotenuse , cos is the ratio of base and hypotenuse, tan is the ratio of perpendicular and base, cosec is the ratio of hypotenuse and perpendicular, sec is the ratio of hypotenuse and base, cot is the ratio of base and perpendicular.

Here we use tan d where d is the angle between ladder and wall of the house.

tan d= P/B

tan d=8/5

tan d=1.6

[tex]d=tan^{-1} 1.6[/tex]

d=57.99

After rounding off it will be 58°.

Hence the angle between ladder and house is 58°.

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Answer:

[tex]y=\frac{96}{x}[/tex]

Step-by-step explanation:

So when x and y, vary inversely, it means that the product of x and y will remain constant such that: [tex]xy=c[/tex]. This means that the function can be defined as [tex]y=\frac{c}{x}[/tex] by dividing both sides by x. In this case x=12, and y=8, this means the constant is equal to 12 * 8 which is 96. So we have the equation:  [tex]xy = 96[/tex], which can be defined as [tex]y=\frac{96}{x}[/tex]

Answer:

300 meters per minute

Step-by-step explanation:

Step 1

Determine the fraction of the total distance for each part of the race.

Given:

1st part of race = 4/9 of total distance

2nd part of race = 2/5 of remaining distance

Step 2

Determine the distance of the third part of the race.

Given:

time = 15 minutes

speed = 300 meters per minute

Step 3

If the third part of the race (which is 1/3 of the total distance) is 4500m, then the distance of the whole race is:

Step 4

Determine the distance of the 1st part of the race:

Step 5

Determine the speed of the 1st part of the race:

Given:

time = 20 minutes

distance = 6000 m

Answer:

[tex]14^{2}[/tex]

Step-by-step explanation:

14*14

14 is the base.  We are multiplying 14 two times.  Two would be the exponent

14 ^2

The input and output table for the linear function y = 3x is (-2, -6), (-1, -3), (0, 0), (1, 3) and (2, 6).

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the linear function y = 3x:

When x = -2; y = 3(-2) = -6

When x = -1; y = 3(-1) = -3

When x = 0; y = 3(0) = 0

When x = 1; y = 3(1) = 3

When x = 2; y = 3(2) = 6

The input and output table for the linear function y = 3x is (-2, -6), (-1, -3), (0, 0), (1, 3) and (2, 6).

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Answer: ( -6/ 6/ 9

Step-by-step explanation:

The fabric mill produce 1,807,845 meters of fabric in 365 days.

A fabric mill produces 4953 meters of fabric in a day.

operations and interpretations to function to make function simple or more understandable called simplify and the process is called simplification.

We have 4953 meter of fabric in a day.
So for 365 days
fabric = 4953 x 365
= 1,807,845

Thus, the fabric mill produce 1,807,845 meters of fabric in 365 days.

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Applying the vertical angles theorem, the measure of VU is determined as: 64°.

If two angles lie directly opposite each other, they are vertical nagles and are therefore equal.

13x = 15x - 8 [vertical angles theorem]

13x - 15x = - 8

-2x = -8

x = 4

Let y represent m(VU). Since m(RV) = m(VU), therefore:

13x + 2y = 180 [angles on a straight line]

Plug in the value of x

13(4) + 2y = 180

52 + 2y = 180

2y = 180 - 52

2y = 128

y = 64°

m(VU) = 64°.

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The slosh-out water is 29.9 cubic cm.

Volume is defined as the space covered by any solid body in the three-dimensional plane. For the cylinder, the parameters are height and radius.

The volume of the cone is calculated as:-

V = ⅓r^2h

V = ⅓r^2h

V = ⅓(3.5)^2(7)

V = ⅓(12.25)(7)

V = 1/3(85.75)

V = 85.75/3

1/3 cup of water is sloshed out:

Sloshed water = (85.75/3 )/3

Sloshed water = 29.9 cubic cm

Therefore, the sloshed-out water is 29.9 cubic cm.

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Answer:

-9w^2-90w

Step-by-step explanation:

You just use the distributive property and watch the negatives and positives.

[tex]\huge\boxed{-9w^2-90w}[/tex]

Distribute [tex]-9w[/tex] to both [tex]w[/tex] and [tex]10[/tex] as shown in the attached image. Then, just simplify the terms with multiplication.

[tex](-9w)\cdot w+(-9w)\cdot10\\\boxed{-9w^2-90w}[/tex]

Answer: A 1/2 ^4

Step-by-step explanation:

Answer:

a)1/2^4

Step-by-step explanation:

First solve 2^-4.

Use negative power rule: x^-a = 1/xa

⇒ 1/2^4

Simplify 2^4 to 16

⇒ 1/16

Just evaluate the other options.

The first one is correct.

Here's why:

⇒ Simplify 2^4 to 16.

⇒ 1/16

They have the same steps, therefore making Option A correct.

Note: This is the longer way, there is a easier way of dealing with these types of problems. Example: Without using a calculator problem.

The simplest way to factor polynomials is to use the greatest common factor.

It should be noted that the polynomial simply means the expression of more than two algebraic terms.

In this case, the simplest way to factor polynomials is to use the greatest common factor. This simply had to do with the largest factor that the numbers share.

Other methods that can be utilized include the grouping method, the sum of the difference in cubes and in two squares.

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Answer:

vertex = (2, 64 )

Step-by-step explanation:

given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

f(x) = - 16x² + 64x ← is in standard form

with a = - 16, b = 64, c = 0 , then

x = - [tex]\frac{64}{-32}[/tex] = 2

substitute x = 2 into f(x) for corresponding y- coordinate

f(2) = - 16(2)² + 64(2) = - 16(4) + 128 = - 64 + 128 = 64

vertex = (2, 64 )

Answer:

The inverse of the function f(x) = 64x³ - 1 is [tex]\frac{\sqrt[3]{x+1}}{4}[/tex]

Step-by-step explanation:

First replace x with y.

[tex]x=64y^3-1[/tex]

Then solve for y.

[tex]y^3=\frac{x+1}{64}[/tex]

Cube root both sides.

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

Hence, the inverse is [tex]\frac{\sqrt[3]{x+1}}{4}[/tex]

The dimensions of the enlarged rectangular picture is 15 x 10 inches.

When the  dimensions of the enlarged rectangular picture is enlarged by a scale factor of 5, it means that the dimensions would be five times larger what they were initially.

New dimensions : (3 x 5) x (2 x 5)

15 x 10 inches

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Answer:

I’m just adding so you can mark brainliest

Step-by-step explanation:

The way to construct the equation in a graph is illustrated.

Converting the equation in slope-intercept form

2x-3y= -18

-3y= -2x-18

-3y= -(2x+18)

3y=2x+18

y=(2x+18)/3

And for equation 2

y= -5-3x

The points can be calculated by putting negative and positive values of x in both equations.

The graph is attached as a picture.

As we can see from the graph that two lines intersect at (-3,4) so it is the solution of the given system of linear equations.

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Answer:

f(x)

Step-by-step explanation:

This question isn't to difficult, since all you need to know is: [tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]. If the you're not quite sure why this is true, I'll try to express this in another way. [tex](\frac{a}{b})^x=\frac{a}{b}*\frac{a}{b}*\frac{a}{b}...\text{ x amount of times}[/tex], and as you may know when multiplying fractions, you simply multiply the numerators by the numerators and the denominators by the denominators, this means that you can simplify it to: [tex]\frac{a*a*a...\text{ x amount of times}}{b*b*b...\text{ x amount of times}}[/tex] this is literally what an exponent is which is why you can distribute the exponent as such: [tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]. The next thing you need to know is that: [tex]1^x=1[/tex] for any real number. This is you can express this as: [tex]1*1*1...\text{ x amount of times} = 1[/tex], since 1 times 1 times 1, will always remain 1. You may think this will not apply for rational exponents, but it still does since: [tex]1^{\frac{a}{b}}=\sqrt[b]{1}^a[/tex], and no matter what b is, it's going to be 1. The square root of 1, is 1..., the cube root of 1 is 1.... This is because the very definition of a radical is what number times times it self index amount of times is equal to the number under the radical, and no matter how many times you multiply 1, you're going to get 1. If that's a bit confusing what I'm saying is: [tex]\sqrt[n]{b}\implies\text{?}^n=b[/tex].

Anyways hopefully you understand that, if not I'm sorry if I went a bit overboard trying to explain it. Anyways all you need to really know is that: [tex](\frac{1}{3})^x=\frac{1^x}{3^x}=\frac{1}{3^x}[/tex]. So this means as x increases, all you're really doing is increasing the denominator which is decreasing the number. The f function has an integer as a base, so the function will overall be increasing. This is not true for g(x) since as x increases the y-value decreases. So this means that f(x) has a faster rate. This is because the g(x) has a horizontal asymptote, since as x approaches infinity, g(x) approaches 0, since the denominator is increasing towards infinity. So the rate of change will be slowing down as x increases, since there is only so much the g(x) can change, since it has a horizontal asymptote. This is not true for f(x) as it has no horizontal asymptote and just goes towards infinity. So the f(x) has a faster rate.

Option 3. The effect that it has when there are exceptions to the overall trend between two variable is that It is irrelevant to the relationship.

This is used in statistics to show that there is the existence of two variables that are positively correlated.

These two variables would then have a positive slope trend line. Hence the answer to the question is option 3.

What effect does it have when there are exceptions to the overall trend in a relationship between two variables?

O It increases the relationship

O It decreases the relationship

O It is irrelevant to the relationship.

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The approximate arc length from the task content is; Choice C; 0.785 units.

Since the arc length is given mathematically by the formular;

Arc length = (A/360) × 2πr

Hence, since A = π/4 = 18/4 = 45.

Hence; Arc Length = (45/360) × 2 × 3.14 ×1

Arc length = 6.28/8 = 0.785 units.

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If we make appropriate equation then we can find that there are 21 people and animals belong to the circus.

Given The number of acrobats and ballerinas, minus the number of clowns, is one fewer than the number of dogs. Double the combined number of acrobats and ballerinas is five more than three times the number of clowns.

We have to find total people and animals belong to the circus.

An equation is relationship between variables that are expressed in equal to form. It is solved to find the variables in equal to form Equations of two variables look like ax+ by=c.

let the number of acrobats be x, ballerinas be y, clowns be z, clowns be u.

According to given information in question the equations are:

x+ y-z=u-1-----------------------1

2(x+ y)=3z+5-------------------2

u=z+1----------------------------3

Put the value of u from 3 in 1

x+y- z=z+1-1

x+y-2z=0

from 2

z=2x+2y-5/3

put the value of z in x+y-2z=0

x+y-2(2x+2y-5/3)=0

-x-y+10=0

x+ y=10-------------------------4

put put the value of x+y=10 in 1

10-z=u-1

u+z=11-----------------------------5

solving 3

u-z=1------------------------6

Now add 5&6

u+z+u-z=11+12

2u=12

u=6

Put the value of u in 6

6-z=1

z=5

From above we get x+y=10, u=6, z=5

Add all three we get the total number of people and animals belong to circus.

x+y+u+z=10+6+5

=21

Hence there are total 21 people and animals belong to the circus.

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Answer:

32 km / hr

Step-by-step explanation:

930 to 1015 is   45 min =   .75 hr

24 km / .75 hr = 32 km /hr

Answer:

$2,000

Step-by-step explanation:

7,440/3.72

Answer:

∠ ACB = 128° and ∠ABC = 32°

Step-by-step explanation:

∠ ADC = ∠ CAD (base angles theorem)

∠ ACD = 82° (angles in a triangle add to 180°)

∠ ACB = 128° (angles around a point add to 360°)

∠ ABC = 32° (angles in a triangle add to 180°)

Answer:

Option (2)

Step-by-step explanation:

The angle opposite the shortest side is the smallest and the angle opposite the longest side is the largest.

Since m is greater than or equal to 6, we know that:

2m+3 > m+8 > m-3

Answer:

Step-by-step explanation:

-4 [tex]\leq[/tex] x [tex]\leq[/tex] 6

x = {-4,-3,-2,-1,0,1,2,3,4,5,6}

Hope I helped...