The surface area of a right circular cone is 20 cm. The radius of the base and the slant height are each multiplied by 5, enlarging the cone. What is the surface area of the new cone?

Answer:

Area of Parallelogram Using Diagonals ; Using Base and Height, A = b × h ; Using Trigonometry, A = ab sin (x) ; Using Diagonals, A = ½ × d1 × d2 .....

Using Diagonals: A = ½ × d1 × d2 sin (y)

Using Base and Height: A = b × h

Using Trigonometry: A = ab sin (x)

Answer:10 feet, I think

Step-by-step explanation:

Answer:

-4 acceleration

Step-by-step explanation:

: )

Evaluating the function in the values of the domain we will get some coordinate pairs. The graph of these is in the image at the end.

Here we have the function:

3x - y = 1

And we want to graph this in the domain (-3, -1, 0, 4)

To do so, we need to evaluate the function (the values of x) in the values of the domain.

Solving the equation for y we get:

y = 3x - 1

Now, when x = -3

y = 3*-3 - 1 = -10

when x = -1

y = 3*-1 - 1 = -4

when x = 0

y = 3*0 - 1 = -1

When x = 4

y = 3*4 - 1 = 11

So we have the points (-3, -10), (-1, -4),  (0, -1), (4, 11)

The graph of these points is on the image below.

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Answer:

x=38

Step-by-step explanation:

Answer:

p = 160 - 2Q

Step-by-step explanation:

To find the values of 'a' and 'b' in the demand function p = a - bQ, we can use the given information about the demand at different price levels.

We are given two data points:

When the price (p) is RS.40, the quantity demanded (Q) is 60.

When the price (p) is RS.60, the quantity demanded (Q) is 50.

Using these data points, we can set up a system of equations to solve for 'a' and 'b'.

Equation 1: RS.40 = a - b(60)

Equation 2: RS.60 = a - b(50)

Let's solve this system of equations:

From Equation 1:

40 = a - 60b (multiply both sides by -1)

From Equation 2:

60 = a - 50b

Now, we have two equations with two variables. We can solve them simultaneously using any method (substitution, elimination, or matrices). Let's use the substitution method:

Substitute the value of 'a' from Equation 1 into Equation 2:

60 = (40 + 60b) - 50b

60 = 40 + 60b - 50b

60 = 40 + 10b

10b = 60 - 40

10b = 20

b = 20/10

b = 2

Now, substitute the value of 'b' back into Equation 1 to find 'a':

40 = a - 60(2)

40 = a - 120

a = 40 + 120

a = 160

Therefore, the values of 'a' and 'b' are a = 160 and b = 2.

The demand function can now be written as:

p = 160 - 2Q

Answer:

7x+12x=82$

Step-by-step explanation:

Dalyn is selling girl scout cookies. She sold 7 boxes of thin mints (x) and 12 boxes

of tagalongs (y). If she made $82 selling cookies, write an equation that

represents the scenario. *

There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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Answer:

B and D

Step-by-step explanation:

This is because for B you do 8x9x1 which is basically 8x9 which is 72. Then, for D you do 12x3x2. Do 3x2 first and you get 6. Then, do 6x12 which is also 72. So the correct answers that will give you the volume of 72 units cube is B and D. Hope this helps!

Answer:  -7x3 + 13x2 + 9x - 12

Answer:

3(5x2+2x-4)-x7x2+2x-3)

15 x 6 + 6x -12 - x7 + x2 + 2x -3

90 + 6x - 12 - x7 + x2 + 2x -3

(6x + 2x) (+90 - 12 - 3) (-x7 + x2)

8x + 75 - x5

To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.

The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.

Therefore, the fraction of pocket money left can be written as 17/35.

The general solution to the given differential equation is:

y = (x/12) - (1/288)

How to solve the Differential Equation?

We want to solve the differential equation given as: y' - 24xy = -2x

The integrating factor is given by the exponential of the integral of the coefficient of y, which in this case is -24x. Therefore, the integrating factor is e^(-24x).

Multiplying the entire equation by the integrating factor, we get:

e^(-24x)y' - 24xe^(-24x)y = -2xe^(-24x)

The left side of the equation is the derivative of (e^(-24x)y) with respect to x:

(d/dx)(e^(-24x)y) = -2xe^(-24x)

Integrating both sides with respect to x, we have:

e^(-24x)y = ∫(-2xe^(-24x))dx

Integrating the right side, we get:

e^(-24x)y = -∫(2xe^(-24x))dx

To evaluate the integral on the right side, we can use integration by parts. Let's differentiate -2x and integrate e^(-24x):

u = -2x (differential of u = -2dx)

dv = e^(-24x) (integral of dv = -1/24e^(-24x)dx)

Using the integration by parts formula:

∫uv dx = uv - ∫v du

We can compute the integral as follows:

-∫(2xe^(-24x))dx = -[(-2x)(-1/24e^(-24x)) - ∫(-1/24e^(-24x))(-2dx)]

= -[x/12e^(-24x) + 1/12∫e^(-24x)dx]

= -[x/12e^(-24x) + 1/12(-1/24)e^(-24x)]

= -[x/12e^(-24x) - 1/(12*24)e^(-24x)]

= -[x/12e^(-24x) - 1/(288e^(-24x))]

= -[x/12 - 1/288]e^(-24x)

Substituting this back into the previous equation, we have:

e^(-24x)y = -[-(x/12 - 1/288)e^(-24x)]

Simplifying further:

e^(-24x)y = (x/12 - 1/288)e^(-24x)

Canceling out e^(-24x) on both sides:

y = x/12 - 1/288

Therefore, the general solution to the given differential equation is:

y = x/12 - 1/288

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The expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2) Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

The property of exponents that must be applied to the expression p^(1/2) to derive p as the result is the Power of a Power Property.

The Power of a Power Property states that when a power is raised to another power, the exponents are multiplied.

For instance, consider the expression p^(1/2). We can apply the Power of a Power Property to this expression as follows: p^(1/2) = (p^(1/2))^1 By applying the Power of a Power Property, the exponent (1/2) is multiplied by the exponent 1, giving a result of 1/2.

Therefore, the expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2)Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

So we have derived p as the result using the Power of a Power Property.

In summary, we must apply the Power of a Power Property to the expression p^(1/2) to derive p as the result.

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logical expression would be  z = a.b

What is logical expression?

A Boolean expression is an expression that is used in programming languages and, when evaluated, yields a Boolean value. Either true or false describes a Boolean value.

Boolean Expression z = a.b

logical expression z= a AND b

Following figure shows the truth table for a and b.

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Answer:

9834

Step-by-step explanation:

11*100*89400.

Answer:

4x-11y

Step-by-step explanation:

How to solve your question

Simplify

(6−3)−2(+4)

(6x-3y)-2(x+4y)

(6x−3y)−2(x+4y)

Distribute

(6−3)−2(+4)

(6−3)−2−8

Eliminate redundant parentheses

(6−3)−2−8

6−3−2−8

Combine like terms

6−3−2−8

4−3−8

Combine like terms

4−3−8

4−11

The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.

By multiplying each number in the ratio by 4, we get:

1.25 * 4 = 5

3.75 * 4 = 15

7.5 * 4 = 30

So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.

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Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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7x²+5x​

(9x²+8x)-(2x²+3x)

We will subtract the like terms. That means that we will subtract \(2x^{2}\) from \(9x^{2}\) and 3x from 8x.

Answer:

(1) A. 1 × 10^-4

(2)A. 8 × 10³

(3)B. 8 × 10⁷

Step-by-step explanation:

(1)

Mass of a worker Bee = 0.00011 kg

Since 1 × 10^-4 is = 1/10⁴ or 1/10000 or 0.0001 kg, Option A 1 × 10^-4 will be the correct answer

(2)

Mass of an African Elephant = 8139kg

Since 8 × 10³ is = 8 × 1000 or 8000kg, Option A 8 × 10³ will be the correct answer

(3) Mass Of a worker bee = 0.00011 kg

Mass of an African Elephant = 8139 kg

8139/0.00011 = 73,990,909.090

This value is the closest to 8 × 10⁷ or 8 × 10000000 or 80,000,000, Option B 8×10⁷ is the correct answer

The required solution to the system of equations is (x, y) = (-2, 4). Option B is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
To solve this system of equations, we can set the two expressions for y equal to each other, since they both represent the same value of y,

x + 6 = -0.5x + 3

Simplifying and solving for x, we get:

1.5x = -3

x = -2

Now that we have the value of x, we can substitute it into one of the original equations to find the value of y. Using the first equation, we have,

y = x + 6

y = -2 + 6

y = 4

Therefore, the solution to the system of equations is (x, y) = (-2, 4).

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Given:

Lenght =8.2mm , width = 3.5mm and height = 20.1

The volume of pyramid is given by,

V=1/3 (base area) (height)

As it is rectangular pyramid,

first find area of reactangle . this will be base area for pyramid.

area of reactangle=lenght * weight

Volume is,

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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The function  \(y = -\sqrt[3]{11+8x}\) can be written as the composition of functions f(x) =  -∛x and g(x) = 11+8x.

What are functions?

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Hence, a function is essentially applied to the output of another function. When two functions are combined, the output of the function inside the parentheses becomes the input of the function outside of the parenthesis.

Given a function as follows:

\(y = -\sqrt[3]{11+8x}\)

Consider two functions, f(x) and g(x).

Let f(x) = -∛x

g(x) = 11+8x

Then f(g(x) = f(11+8x) = \(-\sqrt[3]{11+8x}\)

Therefore the function  \(y = -\sqrt[3]{11+8x}\) can be written as the composition of functions f(x) =  -∛x and g(x) = 11+8x.

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The value of the number is x = 34.

Let's break down the problem and solve it step by step.

1. "Five less than twice the value of a number": This can be represented as 2x - 5, where x is the number.

2. "Three times the quantity of 4 more than 1/2 the number": This can be represented as 3 * (x/2 + 4).

According to the problem statement, the two expressions are equal. We can set up the equation as follows:

2x - 5 = 3 * (x/2 + 4)

Now, let's solve the equation:

2x - 5 = 3 * (x/2 + 4)

Distribute the 3 to both terms inside the parentheses:

2x - 5 = (3/2)x + 12

Multiply through by 2 to eliminate the fraction:

2(2x - 5) = 2((3/2)x + 12)

4x - 10 = 3x + 24

Next, let's isolate the x term by moving the constant terms to the other side of the equation:

4x - 3x = 24 + 10

Simplify:

x = 34

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7. Radius of circle P = 2       Radius of circle Q = 1

Coordinates of the point of tangency (4,2)

The equation of the tangency line is x = 4

8. AB is not a tangent. BC² ≠ AB² + AC²

9. The three radii of the circle are; CB, CF and CD

A diameter of the circle is BD

A tangent of the circle is GE

A chord of the circle is BD

A secant of the circle is AD

A point of tangency is F

7. To find the radius, identify the diameter of the circle. For the diagram, it can be said that the diameter of the circle P is 4.

The radius then is 4/2 = 2.

The radius of circle q is 2/2 = 1

You could also use the formula

Distance = sqrt((x2 - x1)² + (y2 - y1)²)

8. √4² + √12² = √160

√13 = 169

Therefore AB is not tangent. It is less than BC

9. The line that cuts the circle into two halves is the diameter. The lines than further cuts the diameter into equal parts are the radii's

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Therefore , as a result Two of a triangle's sides and the included  SAS angle are said to be congruent if they match the corresponding sides and angles of another triangle.

The Side-Angle-Side rule is applied to check the congruence of a set of triangles. The SAS rule states that a triangle is congruent if its two sides and included angles match those of another triangle.

Here,

if the first triangle's two sides and one of its included angles are equal to the second triangle's sides and one of its included angles.

Consequently, the SAS declares two triangles to be congruent. Two triangles are said to be congruent if their matching two sides and their included angles are found in a single triangle, according to the SAS theorem of congruence.

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