Find the missing side of this right triangle.
X

8

16
VI?]
X =
Enter the number that belongs in the green box.

Answer:

a. D. f⁻¹(x) = x - 21, for all x

b. f(f ⁻¹(x)) = f(x - 21) = x and f ⁻¹(f(x)) = f ⁻¹(x + 21) = x

Step-by-step explanation:

See attached picture.

The required answers are:

a. The inverse of the function is f1(x) = x - 21

b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.

a. To find the inverse function of f(x) = x + 21, we can interchange x and y and solve for y:

x = y + 21

Now, let's solve for y:

y = x - 21

Therefore, the equation for f1(x), the inverse function, is f1(x) = x - 21.

b. To verify that the equation is correct, we need to show that f(f(x)) = x and f¯¹ (f(x)) = x.

First, let's calculate f(f(x)):

f(f(x)) = f(x + 21) = (x + 21) + 21 = x + 42

Since f(f(x)) = x + 42, we can see that f(f(x)) is not equal to x. Therefore, f(f(x)) ≠ x.

Now, let's calculate f¯¹(f(x)):

f¯¹(f(x)) = f¯¹(x + 21) = (x + 21) - 21 = x

Since f¯¹(f(x)) = x, we can see that f¯¹(f(x)) is equal to x.

Thus, we have verified that the equation for the inverse function, f1(x) = x - 21, is correct by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.

Therefore, the required answers are:

a. The inverse of the function is f1(x) = x - 21

b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.

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The volume of the given cone.

[tex]\large\boxed{Formula:V= \frac{1}{3}\pi{r}^{2}h}[/tex]

[tex]\large\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}[/tex]

Let's solve!

Substitute the values according to the formula.

[tex]V= \frac{1}{3}×3.14×{3}^{2}×8[/tex]

[tex]\large\boxed{V= 75.36 \: {yd}^{3}}[/tex]

Therefore, the volume of the given cone is 75.36 cubic yards.

The gallon of water required by Dakota to fill the pool will be given as:-

V(x) = 2x⁶ + 10x⁴.

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

Given that:-

The function which will represent the gallons of water will be:-

As it is given in the question the pool is of a rectangular shape so the volume of the pool will be calculated as:-

V = Area of the rectangular part x depth

V = ( 2x⁴ + 10x ²) ( x² )

V = 2x⁶ + 10x⁴.

Since the amount of the water will be equal to the volume of the pool so the function for the gallons will be given as;-

V (x) = 2x⁶ + 10x⁴.

Therefore gallon of water required by Dakota to fill the pool will be given as:-V(x) = 2x⁶ + 10x⁴.

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Answer:

e

Step-by-step explanation:

According to Angle Sum Property :

∠A + ∠B + ∠C = 180°

============================================================

Given :

⇒ ∠A = 50°

⇒ ∠B = 32°

===========================================================

Solving :

⇒ 50° + 32° + ∠C = 180°

⇒ ∠C + 82° = 180°

⇒ ∠C = 98°

#1

Volume

#2

Radius=10/2=5cm

Volume

#3

Volume

#4

#5

radius=8/2=4

Volume

Answer:

1)  314 cm³

2)  523.33 cm³

3)  87.92 in³

4)  11 cm

5)  502.4 cm³

Step-by-step explanation:

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 5^2 \cdot 4\\& = 3.14 \cdot 25 \cdot 4\\& = 3.14 \cdot 100\\& = 314 \: \sf cm^3\end{aligned}[/tex]

[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3\quad\textsf{(where r is the radius)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume} & =\dfrac{4}{3} \cdot 3.14 \cdot 5^3 \\& =\dfrac{4}{3} \cdot 3.14 \cdot 125 \\& =\dfrac{500}{3} \cdot 3.14 \\& = 523.33\: \sf cm^3\:(2\:dp)\end{aligned}[/tex]

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 2^2 \cdot 7\\& = 3.14 \cdot 4 \cdot 7\\& = 3.14 \cdot 28\\& = 87.92\: \sf in^3\end{aligned}[/tex]

[tex]\textsf{Volume of a square pyramid}=\sf \dfrac{1}{3} a^2h \quad\textsf{(where a is the base edge and h is the height)}[/tex][tex]\textsf{Area of base of square pyramid}=\sf a^2 \quad\textsf{(where a is the base edge)}[/tex]

Given:

[tex]\implies 81=a^2[/tex]

[tex]\implies a=\sqrt{81}[/tex]

[tex]\implies a=9\: \sf cm[/tex]

Substitute the given values into the formula and solve for h:

[tex]\begin{aligned}\implies \textsf{297} & =\dfrac{1}{3} \cdot 9^2 \cdot h\\\\297 & =\dfrac{81}{3} h\\\\891 & =81 h\\\\h & = 11 \: \sf cm\end{aligned}[/tex]

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 4^2 \cdot 10\\& = 3.14 \cdot 16 \cdot 10\\& = 3.14 \cdot 160\\& = 502.4\: \sf cm^3\end{aligned}[/tex]

Answer:

[tex]x = 39[/tex]

Step-by-step explanation:

Based on the given conditions, write: [tex]x=\frac{13}{1-\frac{2}{3}}[/tex]

Find common denominator and write numerators above common denominator: [tex]x=\frac{\frac{13}{3-2} }{3}[/tex]

Calculate the sum or difference: [tex]x=\frac{\frac{13}{1} }{3}[/tex]

Divide the fraction by multiplying its reciprocal: [tex]x=13*3[/tex]

Calculate the product or quotient: [tex]x=39[/tex]

Answer: [tex]x=39[/tex]

Answer:

£19.50

Step-by-step explanation:

let x be the original price , then

[tex]\frac{2}{3}[/tex] x = 13 ( multiply both sides by 3 to clear the fraction )

2x = 39 ( divide both sides by 2 )

x = 19.5

original price of game was £19.50

Answer:

5.6

Step-by-step explanation:

If you add all the numbers together then divide it by 15 you would get 5.6

Answer:

5:1

Step-by-step explanation:

Originally the ratio is 20:4

but then it is simplified to 10:2

then 5:1

Exponential model best represents the data is [tex]f(x)= 3(0.2)^{x}[/tex]

A symbol written above and to the right of a mathematical expression to indicate the operation of raising to a power.

The given table values satisfied the fourth function.

If we put one by one all the values of x given in a table we get the corresponding value of f(x).

like, if we put -2 we get f(x)= 75 closer to 71

Hence, Exponential model best represents the data is [tex]f(x)= 3(0.2)^{x}[/tex]

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The pie chart below depicts a housewife's expenditures for a certain day.

A map wherein the round is split into segments, each one representing a percentage of the total.

The data below show the expenditure of a housewife for a particular day

Item amount

Rice - 120

Yam - 100

Beans - 140

Vegetable - 140

Meat - 180

Sugar - 40

Palm oil - 60

The pie chart is given below.

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Answer:

  D.  (CPCTC)

Step-by-step explanation:

Your proof that the triangles are congruent is complete at the 4th step. In Step 5, you are asked to draw a conclusion about corresponding angles in those congruent triangles.

__

Two geometric objects are congruent if they are identical in size and shape by any measure. If they are not labeled, you cannot tell them apart. Every measure of one is identical to the corresponding measure of the other. The location and orientation of congruent figures does not affect their congruence. You can move them, rotate them, flip them over, and they remain congruent.

This property, "corresponding parts of congruent triangles are congruent," is abbreviated "CPCTC." Once you have demonstrated objects are congruent, you can use this fact to relate measures of the objects that may not have been part of the demonstration.

general

We generally work with plane geometric figures that are polygons or have well-defined curved edges. Polygon figures are comprised of straight sides of fixed length. At each vertex, where sides meet, an angle is formed. Corresponding sides form corresponding angles.

The sides are generally named by the vertices at either end. The angles may be named by the vertex where it is located, or by the names of the sides that make it up.

In triangle ABC, for example, the vertices have labels A, B, and C. The sides are AB, AC, and BC. And the angles are A, B, and C, or BAC, ABC, ACB. (The vertex of the angle is the middle letter.)

To prove polygons are congruent, you must show corresponding angles are congruent, and corresponding sides are congruent. Generally, the number of sides will put constraints on the size of the angles. (A 6-sided polygon will have 6 angles that total 720°, for example.)

triangles

When the polygon is a triangle, the constraints on side lengths and angles generally mean there are shortcuts to proving congruence. The postulates that tell you what these are have been given mnemonic abbreviations. When we say, "angle" or "side" in this context, we are referring to congruent corresponding angles in the two triangles, or congruent corresponding sides.

These can also be applied to right triangles, where one angle is known to be 90°. In addition, there is a theorem that only applies to right triangles:

your proof

The triangles in your figure have a side marked with a single hash mark. This means those corresponding sides in the two triangles are congruent to each other.

There is an angle marked with two (2) arcs in each triangle. This marking means those corresponding angles are congruent. Likewise for the angles marked with three (3) arcs. You will notice the 3-arc angle, 2-arc angle, and 1-hash mark side are in the same order in the two triangles. This means the AAS congruence postulate applies, as is claimed on line 4 of your proof.

As you have seen, we only need to show some parts of a triangle are congruent in order to show all parts of the triangle are congruent. When we make a claim about corresponding parts that weren't an explicit part of the proof, we are essentially relying on the definition of congruent polygons. For triangles, that definition is summarized by the abbreviation CPCTC.

Line 5 of your 2-column proof is making a claim about corresponding angles of the triangle. That claim is supported by CPCTC.

_____

Additional comment

Choices A and C refer to congruence postulates, as discussed above. Those have no relation to the claim regarding angles ACB and XZY.

The "corresponding angles theorem" tells you corresponding angles are congruent where a transversal crosses parallel lines. It has no relation to the angles in this problem.

Answer:

Step-by-step explanation:

To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.

Answer:

(4, 3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

           [tex]\sf (\sqrt{x+1}) + (\sqrt{x-1})[/tex]

[tex]\sf\dfrac{\sqrt{x+1} +\sqrt{x-1}}{\sqrt{x+1}-\sqrt{x-1}} = \dfrac{(\sqrt{x+1} +\sqrt{x-1})(\sqrt{x+1} +\sqrt{x-1})}{(\sqrt{x+1} -\sqrt{x-1})(\sqrt{x+1} +\sqrt{x-1})}\\[/tex]

           When doing so, in the numerator, we get in the form of the identity (a +b)² and in the denominator a² - b²

                            [tex]\sf =\dfrac{(\sqrt{x+1} +\sqrt{x-1})^2}{(\sqrt{x+1})^2 - (\sqrt{x-1})^2}\\\\=\dfrac{(\sqrt{x+1})^2+(\sqrt{x-1})^2+2*\sqrt{x+1}*\sqrt{x-1}}{x + 1 - (x - 1)}\\\\=\dfrac{x+1 +x -1 + 2*\sqrt{(x+1)(x-1)}}{x + 1 - x + 1}\\\\=\dfrac{x+ x + 1 - 1 +2\sqrt{x^2-y^2}}{x-x+1+1}\\\\=\dfrac{2x+2\sqrt{x^2-y^2}}{2}\\\\= \dfrac{2x}{2}+\dfrac{2\sqrt{x^2-y^2}}{2}\\\\=x + \sqrt{x^2-y^2}[/tex]

Answer:

m=200

Step-by-step explanation:

percent means 100,so we duvude 300:by 100 then m=200

Answer:

What is 2 raised to the power of 3?

2 x 2 x 2

= 8

Step-by-step explanation:

Hope this helps.

Step-by-step explanation:

Movement from one place to another

Answer:

2

Step-by-step explanation:

Considerando la ecuación lineal, cuando se requiere 50 unidades, el precio será $22.

Una ecuación lineal o línea se puede expresar en la forma y = mx + b.

dónde

Conociendo dos puntos (x1, y1) y (x2, y2) de una recta, se puede calcular la pendiente m de dicha recta mediante la siguiente expresión:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Sustituyendo el valor de la pendiente m y el valor de uno de los puntos en la expresión de una ecuación lineal, y = mx + b, se obtiene el valor de la ordenada al origen b.

En este caso, siendo la ecuación lineal Precio=m× cantidad + b, sabes que los clientes demandarán 60 unidades de un producto cuando el precio es de $24 por unidad, y 40 unidades cuando el precio es de $20 cada una. Esto es:

Entonces, la pendiente m es calculada mediante la siguiente expresión:

[tex]m=\frac{20-24}{40-60}[/tex]

Resolviendo:

m= 0.2

Entonces, considerando el valor de la pendiente m y el punto 1, el valor de la ordenada al origen b se calcula como:

24 = 0.2× 60 + b

24 = 12 + b

24 -12= b

12= b

Entonces. la relación entre la cantidad de unidades y precio es Precio=0.2×cantidad + 12

Entonces, cuando se requiere 50 unidades, el precio será calculado como:

Precio=0.2×50 + 12

Resolviendo:

Precio= 22

Finalmente, cuando se requiere 50 unidades, el precio será $22.

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Answer:

280°

Step-by-step explanation:

using the relationship

π radians = 180° , then substituting gives

[tex]\frac{14\pi }{9}[/tex] = [tex]\frac{14(180)}{9}[/tex] = 14 × 20 = 280°

Answer:

She spent 17/30 of her money and still has 13/30 of her money

Step-by-step explanation:

The first step to solve is to find a common denominator. The common denominator of this problem is 30. So 1/6 turns into 5/30, and 2/5 becomes 12/30. Then you add them together to get 17/30. If you subtract 17 from 30 you will get your answers.

$8.80 because 2.20*3 is 6.60+2.20 is 8.80

Answer:

Step-by-step explanation:

Lilly= 2.20$ spent

Friend= 2.20$ x 3= 6.60$ spent

6.60$+2.20$=

8.80$ total spent together

Answer:

I think the answer is $244.65 im not completely sure if this is the right answer so correct me if im wrong

Answer:

His bank account now has 352 dollars in it.

Step-by-step explanation:

55+364-67=352

Answer:

$352

Step-by-step explanation:

1st balance: $55

amount deposited: $364

total: $55+$364=$419

amount withdrawed: $67

amount left in account: $419-$67=$352

ans=$352

Answer:

4

Step-by-step explanation:

Because i divided 4 2/3 by 22 1/6 = 4.75 and for full sheets it would be 4

Hope This Helped

Answer:

12.6

Step-by-step explanation:

4.2×3=12.6

I hope this answer can help you

Answer:

1.4 kg

Step-by-step explanation:

Given :

⇒ Watermelon (Peter) = 3 × Papaya (Paul)

⇒ Watermelon (Peter) = 4.2 kg

=============================================================

Solving :

⇒ 4.2 = 3 × Papaya (Paul)

⇒ Papaya (Paul) = 1.4 kg

Therefore the mass of the papaya is 1.4 kg.