Which expressions are equivalent to
5
12
⋅
5
8

Answer:

1/4

Step-by-step explanation:

[tex] \frac{3}5 \div x = \frac{12}{5} \\ \\ \frac{3}{5 } \times \frac{1}{x} = \frac{12}{5} \\ \\ \frac{3}{5x} = \frac{12}{5} \\ \\ x = \frac{3 \times 5}{12 \times 5} \\ \\ x = \frac{1}{4} [/tex]

Step-by-step explanation:

y=42

x=90

Since the triangle has the hypotenuse as the diameter of the circle, the angle opposite the hypotenuse which is x is equal to 90 degrees.

Whenever there is a triangle with the corner of the triangle touching the side of the triangle, the distance between the two legs of the triangle on the circle is 2 times the angle of the corner that is touching. So 21(2)=42

Hope this helps :)

Answer:

Step-by-step explanation:

Let the number of students is x, then the number of parents is 4x

Total number of people is 50:

Solve for x:

There are 10 students

Answer:

10 students

Step-by-step explanation:

First find the sum of the ratio:

1 + 4 = 5

Number of students = [tex]\frac{number in ratio}{sum of ratio}[/tex] × total

= [tex]\frac{1}{5}[/tex] × 50

= 10

∴ 10 out of 50 are students.

( The rest are parents; 50-10=40parents )

The answer is true.

(+)(+)= +

(-)(-)= +

(-)(+)= -

Answer:

1. A = 64 cm²

2. A = 240 yd²

3. A = 220.5 cm²

4. A = 193.4 m²

Step-by-step explanation:

1. We want to split this figure into two rectangles. We know the top figure is a rectangle because a rectangle has four right angles. For the bottom rectangle, because the sides are all perpendicular, all of the angles are also right angles.

Because they're rectangles, opposite sides are congruent. So now you can find the measures of the sides.

Refer to the image below for the rest.

Don't forget to add up the two areas for the total area of the whole figure.

2. We want to split this figure into a triangle and a rectangle.

Because the bottom figure has four right angles, we know that it's a rectangle. Therefore, its side measures are 24, 24, 8, and 8 because opposite sides of a rectangle are congruent.

For the triangle, because the sum of the triangle's base and two other segments is 24, we can use 24 - (6 + 6) = base. So the triangle base is 12.

Do this same thing to find the height of the triangle.

Refer to the image below for the rest.

Don't forget to add up the two areas for the total area of the whole figure.

3. We want to split this figure into a triangle and semicircle.

We're already given that the height is 15 and part of the base is 8, but there is no way to assume that the other part of the base is also 8. Remember, it's not to scale.

We know that this is a semicircle because there is a diameter present (a segment that intersects the center of the circle). This means that all radii of the circle are congruent, so the two radii present are both 8.

Because of Reflexive Property, the other part of the triangle base is now proven to also be 8.

Refer to the image below for the rest.

Don't forget to add up the two areas for the total area of the whole figure.

4. We want to split this figure into a rectangle and semicircle.

For the rectangle, because the sides are all perpendicular, all of the angles are also right angles. So we can prove that it is a rectangle.

Because this is a rectangle, opposite sides are congruent. So we have the sides of 15, 7, 15, and 7.

We know that this is a semicircle because there is a diameter present (a segment that intersects the center of the circle). This means that all radii of the circle are congruent.

Because of Reflexive Property, we know that the diameter of the circle is 15. The radius is half the diameter, meaning all radii are 1/2 (15), or 7.5.

Refer to the image below for the rest.

Don't forget to add up the two areas for the total area of the whole figure.

Answer:

(3x²+4y)(3x²-4y)

Step-by-step explanation:

"difference in two squares" is the formula where a²-b²=(a-b)(a+b)

So we need to apply that formula to [tex]9x^{4}[/tex]-16y², where [tex]9x^{4}[/tex] is a and 16y² is b

First, we need to find the two factors, when squared, equal [tex]9x^{4}[/tex] and 16y²

let's start with [tex]9x^{4}[/tex]

9 is 3 squared; [tex]x^{4}[/tex] is x² squared

let's try 3x² as a factor

To double check, we can square it

(3x²)²

apply the Laws of Exponents; square 3 and multiply the power by 2

when you solve, the answer will be [tex]9x^{4}[/tex]

So it works

now let's find the factor for 16y²

16 is 4 squared, and y² is y squared

so let's try 4y

(4y)²

apply the Laws of Exponents; square 4 and multiply the power by 2

the result is 16y²

Also works!

Now let's apply the formula; as said above, [tex]9x^{4}[/tex] is a and 16y² is b

so: [tex]9x^{4}[/tex]-16y²=(3x²+4y)(3x²-4y)

we can even double check this:

multiply the 2 binomials; apply FOIL

[tex]9x^{4}[/tex]-12x²y+12x²y-16y²

the 2 12x²y's cancel out

and the result is

[tex]9x^{4}[/tex]-16y²

Hope this helps!

The fraction [tex]\frac{20}{2}[/tex] is 10 as a whole number.

A fraction is a mathematical expression that represents a part or a division of a whole. It is used to represent numbers that are not whole numbers or integers. A fraction consists of two components:

1. Numerator: The numerator is the number on the top of the fraction. It represents the quantity or part of the whole being considered.

2. Denominator: The denominator is the number at the bottom of the fraction. It represents the total number of equal parts into which the whole is divided.

Given the fraction [tex]\frac{20}{2}[/tex],

divide numerator and denominator by 2,

[tex]\frac{20\div 2}{2\div 2}[/tex] = [tex]\frac{10}{1}[/tex] = 10.

So, [tex]\frac{20}{2}[/tex] = 10

Learn more about Fraction here:

https://brainly.com/question/10354322

#SPJ6

Answer: [tex]160.28\ cm^2[/tex]

Step-by-step explanation:

Given

diameter of cone [tex]d=12\ cm[/tex]

radius is [tex]r=\frac{d}{2}=6\ cm[/tex]

The slant height of the cone [tex]l=85\ mm\approx 8.5\ cm[/tex]

The surface area of a cone is

[tex]\Rightarrow A=\pi rl[/tex]

Substitute the value

[tex]\Rightarrow A=\frac{22}{7}\times 6\times 8.5=160.28\ cm^2[/tex]

Answer:

x = 3

Step-by-step explanation:

The 2 lines intersect at (3, - 2 ) with x = 3

Answer:

x=4.5

Step-by-step explanation:

The sum of all the angles in a square=360°

20(4.5)=90

90×4=360

Answer:

[tex]\displaystyle \cos(\alpha+\beta)=\frac{3\sqrt{22}-\sqrt{371}}{40}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \cos(\alpha)=\frac{\sqrt{11}}{8}\text{ and } \sin(\beta)=\frac{\sqrt7}{5}[/tex]

Where both α and β are in QI.

And we want to find cos(α + β).

First, let's determine the side lengths for each angle.

For α, we are given that its cosine is √(11)/8.

And since cosine is the ratio of the adjacent side to the hypotenuse, the adjacent side to α is √11 and the hypotenuse is 8.

Therefore, the opposite side will be:

[tex]o=\sqrt{8^2-(\sqrt{11})^2}=\sqrt{53}[/tex]

Hence, for α, the adjacent side is √11, the opposite side is √53, and the hypotenuse is 8.

Likewise, for β, we are given that its sine is √7/5.

And since sine is the ratio of the opposite side to the hypotenuse, the adjacent side of β is:

[tex]a=\sqrt{5^2-(\sqrt{7})^2}=\sqrt{18}=3\sqrt{2}[/tex]

In summary:

For α, the adjacent is √11, the opposite is √53, and the hypotenuse is 8.

For β, the adjacent is 3√2, the opposite is √7, and the hypotenuse is 5.

Using an angle addition identity, we can rewrite our expression as:

[tex]\cos(\alpha+\beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)[/tex]

And since both α and β are in QI, all trig ratios will be positive.

Using the above information, we can substitute in the following values:

[tex]\displaystyle \cos(\alpha +\beta)=\Big(\frac{\sqrt{11}}{8}\Big)\Big(\frac{3\sqrt2}{5}\Big)-\Big(\frac{\sqrt{53}}{8}\Big)\Big(\frac{\sqrt7}{5}\Big)[/tex]

Finally, simplify:

[tex]\displaystyle \cos(\alpha +\beta)=\frac{3\sqrt{22}}{40}-\frac{\sqrt{371}}{40}=\frac{3\sqrt{22}-\sqrt{371}}{40}\approx -0.1298[/tex]

Answer:

9

Step-by-step explanation:

let the number be n then 3 times the sum of 2 and the number is

3(n + 2) = 4n - 3 ( 3 less than 4 times the number )

3n + 6 = 4n - 3 ( subtract 3n from both sides )

6 = n - 3 ( add 3 to both sides )

9 = n

That is the number is 9

Answer:

D because you going up to the surface

Answer:

its c

Step-by-step explanation:

Answer:

the answer it's not correct because you have to put the 6x

Step-by-step explanation:

if you do not put an x after you put the number it would you would get it wrong

Answer:

The perimeter of a rectangular field is 100 meters

Step-by-step explanation:

The given data of the rectangular field are;

The unit cost of levelling the rectangular field, U[tex]_c[/tex] = 50/m²

The total cost of levelling the field, T[tex]_c[/tex] = 30,000

The length to breadth ratio of the field, L:B = 3:2

Where;

L = The length of the field

B= The breadth of the field

From the given data of the field, we have;

The area of the field, A = T[tex]_c[/tex]/U[tex]_c[/tex]

∴ A = 30,000/(50/m²) = 600 m²

The area of the field, A = 600 m²

The formula for the area of a rectangle, A = Length, L × Breadth, B

A = L × B

We are given that the length to breadth ratio of the field, L:B = 3:2

∴ L/B = 3/2

L = (3/2) × B

The area of the rectangular field, A = L × B

∴ The area of the rectangular field, A = (3/2) × B × B = (3/2) × B²

A = (3/2) × B²

From the calculation for the cost of levelling the field, we have, A = 600 m²

∴ A = (3/2) × B²

A = 600 m²

By transitive property, we have;

(3/2) × B² = 600 m²

B² = (2/3) × 600 m² = 400 m²

B = √(400 m²) = 20 m

The breadth of the field, B = 20 m

From L = (3/2) × B, we have;

L = (3/2) × B

∴ L = (3/2) × 20 m = 30 m

∴ The  length of the field, L = 30 m

The perimeter, 'P', of a rectangle given the length, 'L' and breadth, 'B', is given as follows;

The perimeter of a rectangle, P = 2·L + 2·B

Therefore, for the rectangular field, we have;

P = 2 × 30 m + 2 × 20 m = 60 m + 40 m = 100 m

The perimeter of a rectangular field, P = 100 m.

Answer:

4√2 ÷ 3√5

4*1.32 /3*2.23= 5.28/6.69

Answer:

yes

Step-by-step explanation:

if my eyes are good then yes

Answer:

23,084-9,567= 13,517 so he will have to pay $13,517

Answer:

x = 65

Step-by-step explanation:

Answer:

x=20

Step-by-step explanation:

80+30+70=180, so 70+x = 90 so x =20

Answer:

6^(2/3)

Step-by-step explanation:

exponent fraction rule

Answer:

the first one, 6^2/3

Step-by-step explanation:

Answer:

55 lbs of $0.40 and 45 lbs of $1.40  

Step-by-step explanation:

Let's say that we have two buckets, one that weighs x pounds and the candies in it are $0.40 per pound and another that weighs 100-x pounds (because we know the two added together must be 100 pounds) and the candies in it are $1.40 per pound.

There is a third bucket that is made when you combine the two, it weighs 100 pounds and the candies in it are $0.85. Multiply the cents per pound by the pounds of the candy for each bucket and you get this equation:

0.4 * x + 1.4 (100-x) = 0.85 * 100

Solve!

0.4x + 140 - 1.4x = 85

-x + 140 = 85

-x = -55

x = 55

From this we get that 100 - x = 45.

So, the answer is 55 lbs of $0.40 and 45 lbs of $1.40

Answer:

slope = [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 9) and (x₂, y₂ ) = (- 2, 8)

m = [tex]\frac{8-9}{-2-3}[/tex] = [tex]\frac{-1}{-5}[/tex] = [tex]\frac{1}{5}[/tex]

Answer:

The area of the shape is 89m²

Step-by-step explanation:

You need to subtract the area of the empty triangle from the area of the rectangle.

The rectangle's area is 13m × 8m = 104m²

The triangle's area is (6m × (13 - 8)m) / 2 = (6 × 5) / 2 m² = 15m²

Subtract the triangle's area from the rectangle:

104m² - 15m²

= 89m²

Answer:

-7

Step-by-step explanation:

[tex] - 3(n + 4) = 9 \\ \\ - 3n - 12 = 9 \\ \\ - 3n = 12 + 9 \\ \\ - 3n = 21 \\ \\ n = \frac{ - 21}{3} \\ \\ n = - 7[/tex]

Answer:

D

Step-by-step explanation:

"Turn around phrase" just means that you are subtracting the last number minus the first number. Subtracting the negative number is written as -(-34.7)

Answer:

7.85+8.22 = 16.07

Step-by-step explanation:

ok let's do it this way

7+8=15 ok and

80+20 is 100 so 1 dollar

and 5 and 2 are 7 so 1 dollar and 7 cents

now 15+1 is 16 and the 7 cents is 16.07

Answer:

The ratio of milk to chocolate syrup is 3 to 1.

There are 2 tablespoons of chocolate syrup to 6 cups of milk.

There are 4 tablespoons of chocolate syrup to 8 frozen bananas to 12 cups of milk

Step-by-step explanation:

Answer:

3 cups of milk =2 frozen banana and 1 tablespoon of chocolate syrup

1 cups of milk =2:3frozen banana and 1:3 tablespoon of chocolate syrup

2cups of milk =2*2/3=4:3 frozen banana and 1*2/3=2:3 tablespoon of chocolate syrup

4cups of milk =2*4/3=8:3 frozen banana and 1*4/3=4:3tablespoon of chocolate syrup

10cups of milk =10*2/3=5:3frozen banana and 1*10/3=10:3tablespoon of chocolate syrup