Which expresstion is equivalent to 22 - 3

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:

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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Step-by-step explanation:

Movement from one place to another

Answer:

Step-by-step explanation:

Formula:

Lateral surface area = perimeter of the base × height

………………………………………………………………

perimeter of the base = 2×(1.5+3) = 9

height = 4.

then

Lateral surface area = 9 × 4 = 36

Area of two bigger rectangles

Area of two smaller rectangles

LSA

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°

To factorize something:

 ⇒ need to simplify the equation to its most basic form

Let's solve:

  [tex]2x^2+6x=2(x^2+3x)=2x(x+3)[/tex]

Thus the factorized form is ⇒ [tex]2x(x+3)[/tex]

Answer: 2x(x+3)

Hope that helps!

Answer:

Solution:

→ 2x(x + 3)

Step-by-step explanation:

Method:

→ Common factor

→ Rewrite in factored form

Answer:

2

Step-by-step explanation:

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:

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.

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°

$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:

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

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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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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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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Answer:

What is 2 raised to the power of 3?

2 x 2 x 2

= 8

Step-by-step explanation:

Hope this helps.

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:

A. [tex]y\leq \frac{1}{2}x+2[/tex]

Step-by-step explanation:

First, let's find the slope of the line, so we can eliminate some answers.

From point (0,2) we can go up 1 and over to the right 2 to the point of (2,3). Slope is rise over run so 1 over 2.

This eliminates C and D.

The last part is to recognize that y being less than the equation will result in the shaded region being below the line. If y was greater than the equation then the shaded region would be above the line.

Therefore, the correct answer would be A. [tex]y\leq \frac{1}{2}x+2[/tex].

Hope this helps! If you have questions about my work please let me know down in the comments!

Answer:

[tex]y\leq \frac{1}{2}x+2[/tex]

Step-by-step explanation:

The first part of finding our answer is finding the slope of the line. The image attached shows this.

[tex]\frac{rise}{run} = \boxed{\frac{1}{2}}[/tex]

This means the slope is [tex]\frac{1}{2}[/tex], removing the bottom 2 answer choices.

Now we have to choose between the [tex]\leq[/tex] and [tex]\geq[/tex] sign. Since the shaded area is below the line, it will be the [tex]\leq[/tex]. (If it was the [tex]\geq[/tex] sign, the shaded area would be above the line.) This marks the first answer as the correct answer.

Answer:

(4, 3)

Step-by-step explanation:

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.

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:

C. interquartile range

Step-by-step explanation:

using this to show im right

"The interquartile range (IQR) is the difference between the upper (Q3) and lower (Q1) quartiles, and describes the middle 50% of values when ordered from lowest to highest."

Hope This Helped

#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:

m=200

Step-by-step explanation:

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

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.