Find the value of y.
Iog 2 32 =y
Ο
Ο
OC. 6
Ο
D.
7

Step-by-step explanation:

[tex] \because \: {a}^{m} . {a}^{n} = {a}^{m + n} \\ \therefore \: {4}^{8} . {4}^{2} = {4}^{8 + 2} = {4}^{10} \\ \\ \because \: ({a}^{m})^{n} = {a}^{m \times n} \\ \therefore \:({2}^{4})^{5} = {2}^{4 \times 5} = {2}^{20} \\ \\ {5}^{6} = 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 15625[/tex]

The solution are:

To solve for each variable using the properties of exponents, we can use the following steps:

Identify the base and exponent in each expression.

Use the properties of exponents to simplify the expressions.

Solve for the variable.

4^8 •4² = 4^a

Identify the base and exponent in each expression:

Base: 4

Exponent: 8 in the first expression, 2 in the second expression, and a in the third expression

Use the properties of exponents to simplify the expressions:

4^8 •4² = 4^(8+2) = 4^10

Solve for the variable:

4^a = 4^10

a = 10

(2^4)^5 = 2^b

Identify the base and exponent in each expression:

Base: 2

Exponent: 4 in the first expression, 5 in the second expression, and b in the third expression

Use the properties of exponents to simplify the expressions:

(2^4)^5 = 2^(4*5) = 2^20

Solve for the variable:

2^b = 2^20

b = 20

5^6

Identify the base and exponent:

Base: 5

Exponent: 6

Simplify the expression:

5^6 = 5*5*5*5*5*5 = 15625

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Answer:

13

Step-by-step explanation:

If they are equal to each other, than angle DF is the same as angle AC, and angle AC is 13, so DF must be 13

Answer:

y=(x+6)

2

−6

Step-by-step explanation:

Step-by-step explanation:

Factor using the perfect square rule.

( 1 + 6 x ) 2

Answer:

(1+6x)^2

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Given:

Height of cylinder = 6 inches

Volume of cylinder = 60π in³

To find:

The area of the cross section.

Solution:

Volume of cylinder:

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

[tex]\pi r^2h=60\pi[/tex]

Cancel the common factor π on both sides.

[tex]r^2h=60[/tex]

Substitute h = 6.

[tex]r^2\times 6=60[/tex]

Divide by 6 on both sides, we get

[tex]r^2=10[/tex]

Taking square root on both sides.

[tex]r=\sqrt{10}[/tex] inch

Area of cross section = [tex]\pi r^2[/tex]

                                   [tex]=\pi (\sqrt{10} )^2[/tex]    

                                   [tex]=10 \pi[/tex] in²

The area of the cross section is 10π in².

Answer:

The answer is 56 cm2

Step-by-step explanation:

You have to multiply the height times the base then divide that answer by two.

8x14= 112

112/2= 56

Answer:

Step-by-step explanation: Area = 1/2 b.h

= 1/2 8cm.14cm

= 1/2 112 Square cm

= 112/2

= 56 Square cm.

Answer:

22

Step-by-step explanation:

If x=2 and y=4

7•4 - 3•2

28-6

So the answer is 22

Answer:

Hence the length of line segment BA as 98 units

Step-by-step explanation:

Given:

BA as tangent to circle ,DB as secant which intersect at point C at circle

Length BC= 55 and CD=120

To Find:

Length of line segment AB.

Solution:

This follows the relationship between tangent and secant  in circle terms as:

Consider as figure such that ,

AB as tangent , DB as secant C be point at circle

So secant total distance = DB=BC+CD =55+120=175

Using formula as ,

[tex]AB^2=BC(BC+CD)[/tex]

We have to find AB

Here BC=55 and CD=120

[tex]AB^2=55(120+55)[/tex]

[tex]AB^2=55(175)[/tex]

[tex]AB^2=9625[/tex]

[tex]AB=98.10[/tex]

So nearest unit for length will be 98

Hence the length of line segment BA as 98 units

Answer:

98 units

Step-by-step explanation:

edge

Each bottle of shampoo contains 10.5 ounces. The formula for the total volume of shampoo (y) in terms of the number of bottles (x) is y = 10.5x.

Let's denote the amount of shampoo in each bottle as b (in ounces). Since there are 12 bottles of shampoo, the total volume of shampoo in ounces (y) is given by the product of the number of bottles (x) and the amount in each bottle (b). So, the equation is:

y = x * b

The problem states that the case of 12 bottles holds a total of 126 ounces. This can be expressed as:

126 = 12 * b

Now, we can solve for b by dividing both sides of the equation by 12:

b = 126 / 12

Simplifying:

b = 10.5

So, each bottle of shampoo contains 10.5 ounces.

Therefore, the formula for the total volume of shampoo (y) in terms of the number of bottles (x) is:

y = 10.5x

Answer:

Step-by-step explanation:

it is A

Answer:

No. If standards differ at different sports stadiums, that makes the game unfair for one team or the other. A win at one stadium could be a loss at another. To make the game fair, all facilities should be equal.

Step-by-step explanation:

The unique dimensions and characteristics of each baseball stadium, known as park factors, can impact whether a hit becomes a home run. Although it might seem unfair, it's the same for all teams and is part of the game's complexity. Not only the player's skill but also their knowledge of the park's attributes can influence the outcome of the game.

The different sizes and features of baseball stadiums, known as park factors, can impact game dynamics, including whether a hit results in a home run. This is part of the sport's complexity and challenge, as players must adapt their strategies for different venues. It might seem unfair, but it's the same for all teams as they each host and visit various stadiums throughout the season.

In some parks, for example, the distance from home plate to the outfield wall is less, which could make it easier for a hit to become a home run. In contrast, larger parks or those at higher altitudes, where the air is thinner and ball travels further, might be tougher to score a home run.

All these make baseball a fascinating sport, where not only the player's skill but also nuanced aspects like knowledge of the park play an essential role in the outcome of the game. Thus, by definition, a home run is still a successful hit, but where that hit ends up can depend on numerous variables, including the park's attributes.

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The area in square millimeters of the triangle outlined on the origami figure is 441 square millimeters.

In Mathematics and Geometry, the area of a triangle can be calculated by using the following mathematical equation (formula):

Area of triangle = 1/2 × b × h

Where:

Conversion:

7 cm to mm = 7 × 10

7 cm to mm = 70 mm.

1.26 cm to mm = 1.26 × 10

1.26 cm to mm = 12.6

By substituting the given side lengths into the formula for the area of a triangle, we have the following;

Area of triangle = 1/2 × b × h

Area of triangle = 1/2 × 70 × 12.6

Area of triangle = 35 × 12.6

Area of triangle = 441 square millimeters.

I think I would be 30% maybe... I could be wrong

Answer:

27%

Step-by-step explanation:

First get the decrease

Decrease = $23500 - $17155

= $6345

Percentage decrease = decrease/initial price x 100%

That’s

$6345/$23500 x 100%

0.27 x 100%

27%

The percentage decrease in the price of the car is 27%

Answer: (1) The least number of meals is 26 (2) She loses 150 if she caters no meal in one week. (3) Her profit would be 2,650 if she caters for 50 meals in one week

Step-by-step explanation: The weekly profit is given as a quadratic equation which is;

P = 2x² -44x - 150

We begin by solving for the value of x.

When 2x² -44x - 150 = 0

Divide all through by 2

x² - 22x - 150 = 0

By factorization,

(x - 25) (x + 3) = 0

(x -25) = 0 OR (x + 3) = 0

When x - 25 = 0

x = 25

When x + 3 = 0

x = -3

What this implies is that when Amelia caters for 25 meals in a week, her profit is calculated as follows

P = 2x² - 44x -150

P = 2(25)² - 44(25) - 150

P = 2(625) - 1100 - 150

P = 1250 - 1100 - 150

P = 0

(1) Therefore she must cater for at least 26 meals before she can begin to make any profit.

(2) She loses 150 if she caters no meal in one week.

This can be calculated as follows;

When x = 0,

P = 2x² - 44x - 150

P = 2(0)² - 44(0) - 150

P = 0 - 0 -150

P = -150

(3) When she caters 50 meals her profit becomes 2,650

P = 2x² - 44x - 150

P = 2(50)² - 44(50) - 150

P = 2(2500) - 2200 - 150

P = 5000 - 2200 - 150

P = 2650

1) The least number of meals Amelia needs to cater in order to begin making a profit is 25.

2) Amelia loses $150 if she caters no meals in a week.

3) For catering 50 meals, Amelia's profit is $2650.

1) To find the least number of meals Amelia needs to cater in order to begin making a profit, we need to determine when her profit, P, becomes positive. In other words, we need to solve the quadratic equation 2x^2 - 44x - 150 = 0 for x. This equation can be factored as (2x + 6)(x - 25) = 0. Therefore, x = -3 or x = 25. Since the number of meals cannot be negative, the least number of meals Amelia needs to cater in order to begin making a profit is 25.

2) If Amelia caters no meals one week, the profit, P, is given by P = 2(0)^2 - 44(0) - 150. Simplifying this equation, we get P = -150. Therefore, Amelia loses $150 if she caters no meals in a week.

3) To find Amelia's profit for catering 50 meals, we substitute x = 50 into the profit equation P = 2x^2 - 44x - 150. Plugging in x = 50, we get P = 2(50)^2 - 44(50) - 150 = 5000 - 2200 - 150 = $2650.

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Answer:

p=2

Step-by-step explanation:

9(p - 4) = -18

Divide each side by 9

9/9(p - 4) = -18/9

p-4 = -2

Add 4 to each side

p-4+4 = -2+4

p = 2

Answer:

see below

Step-by-step explanation:

m/n = 1/7

Using cross products

7m = n

This is a direct proportion

Answer:

5n

Step-by-step explanation:

The result of n x 5 is equal to 5 times the value of n.

The equation 'n x 5' represents the product of a number n and 5. The result can be positive or negative based on the value and sign of n. Also, parenthesis placement in expressions greatly affects the outcome due to the order of operations.

Understanding the Multiplication of Numbers and Order of Operations

The equation n x 5 indicates that a number n is being multiplied by 5. The results of this product will depend on the value of n and whether n is positive, negative, or zero. For example, if n is positive, like 2, then the product is also positive: 2 x 5 = 10. If n is negative, like -3, the result is negative: (-3) x 5 = -15. It's important to remember that when two positive numbers multiply, the answer has a positive sign, and when two negative numbers multiply, the result is also positive. However, if the two numbers have opposite signs, the answer will have a negative sign.

Furthermore, the placement of parentheses can affect the result of mathematical expressions. For instance, 2 + (3 x 5) is not the same as (2 + 3) x 5 due to the order of operations. In the first expression, multiplication is performed first, resulting in 17, whereas the second expression results in 25.

Understanding the rules of multiplication, including the signs of the numbers involved and the order of operations, is essential for solving equations and expressions correctly.

Answer:

In (3x)^2, you are squaring both the 3 and the x:

9x^2

in 3x^2, you are squaring just the x:

3x^2

Answer:

(3x)^2=9x^2

(3x^2)=3x^2

Step-by-step explanation:

The difference between the two is that

(3x)^2 means the square applied to both the 3 and the x to give 9x^2

But on the other side

(3x^2) means that the square only applies to x without involving 3 which gives 3x^2

So there is difference between them

Answer:

i think disagree ._.

Answer:

D

Step-by-step explanation:

Answer:

Option C: Multiply 15 ft by 12 in/1 ft and 2.54 cm/1 in

Step-by-step explanation:

to convert feet to centimeter, we first convert to inches and from iches to centimeter

1 feet = 12 inches and 1 inches = 2.54 cm

∴ 15 feet = 180 inches and 180 inches = 457.2

This means to convert from feet to centimeter

Multiply 15 ft by 12 in/1 ft and 2.54 cm/1 in

Answer:

[tex]\sqrt{38}[/tex]

Step-by-step explanation:

Given that:

The 3 demensions of the right rectangular prism measures 5 centimeters by 3 centimeters by  2 centimeters.

Because we do not know which one is the height, the length and the width of the box, so we assume them (it does not affect the length of the interior

diagonal )

To find the length of the interior  diagonal of the prism, we use the following formula:

d = [tex]\sqrt{l^{2} +w^{2} +h^{2} }[/tex] = [tex]\sqrt{5^{2} +3^{2} + 2^{2} } = \sqrt{38}[/tex]  

Hope it will find you well.

Answer

38 or about 6.16

Answer:

A=6

Total base area is 12

A=96

Total surface area is 108

Answer:

Step-by-step explanation:

A=6

There are two bases, so total base area is 12

A= 96

The total surface area is 108

Answer:

659.4 cm^2

Step-by-step explanation:

The area of the curved surface of the cone = πrL

=  π*7*16

= 3.14 * 112

= 351.68 cm^2,

Surface area of the hemisphere = 2 π r^2

= 2*3.14*7^2

= 307.72 cm^2.

Total area = 351.68 + 307.72

= 659.4 cm^2.

Answer:

Everything in -> [x]

(RS) [(RU)] = [(RT)] (RV)

(16) [(6)] = [(8+VT)] (8)

VT = [4]

Step-by-step explanation:

I just did the assignment, you're welcome.

Answer:

(RS) [(RU)] = [(RT)] (RV)

(16) [(6)] = [(8+VT)] (8)

VT = [4]

Step-by-step explanation:

Here mi amor

jk

Lol

Answer:

58 should be the answer

Step-by-step explanation:

<CBD is 90 and <BDC is 32 as well since its the same as angle <BDA and 180 in every triangle so 180-90-32=58.

Answer:

They both contain circles or its either they both are nets.

Step-by-step explanation:

Answer:

Time taken to reach maximum height=4.69 seconds

Maximum Height=371.56feet

Step-by-step explanation:

Given the height function of the pumpkin:

[Tex]h = -16t^2 + 150t + 20[/tex]

The pumpkin reaches it's maximum height at its axis of symmetry.

Therefore, we determine its equation of symmetry.

The equation of symmetry:

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

a=-16, b=150.

Therefore:

[Tex]t=-\frac{150}{2*-16}=4.6875[/tex]

The pumpkin reaches maximum height after 4.6875 seconds.

At t=4.6875

[Tex]h = -16(4.6875)^2 + 150(4.6875)+ 20\\=371.5625\approx 371.56 \:feet[/tex]

The pumpkin's maximum height is 371.56 feet.