Mathematics College

The original surface area of a 3D solid is 200 square units.The sides are dilated by a scale factor 3.find the surface area of the image.

Answers

Answer 1

Given:

The original surface area of the cuboid is 200 square units.

The formula for the surface area(A) of a cuboid is,

$A=2(lh+lw+hw)$

We were told the original surface area is being dilated by 3,

Therefore, all the sides of the cuboid will be increased by 3.

$\begin{gathered} A_2=2(3l\times3h+3l\times3w+3h\times3w) \\ A_2=2(9lh\times9lw+9wh) \end{gathered}$

Let us now factorize out 9 from the formula above

$A_2=9(2(lh+lw+wh))$

Recall that

$A=2(lh+lw+hw)$

Therefore,

$A_2=9A$

Also, recall that the original surface area of the cuboid is 200 square units.

$A=200\text{unit}^2$

Hence,

$A_2=9\times200unit^2=1800unit^2$

Therefore, the surface area of the dilated image is

$1800\text{unit}^2$

Related Questions

One spinner is divided into four equal parts. A second spinner is divided into five equal parts. The grid shows the possible outcomes when each spinner is spun once.
a. How many possible outcomes are there?
b. What is the probability that an outcome contains numbers that are both greater than 3?
c. Find the probability of spinning the same two numbers.

Answers

Spinners are used to illustrate probability distribution function

The number of possible outcomes is 20The probability that the outcomes are greater than 3 is 11/20The probability of spinning the same numbers is 1/5

The number of possible outcomes

This is the sample size of the distribution.

So, the number of possible outcomes is calculated as:

$n = 4 * 5$

Where 4 and 5 are the number of sections in both spinners

This gives

$n = 20$

Hence, the number of possible outcomes is 20

The probability that the outcomes are greater than 3

From the distribution, there are 11 outcomes that have a spin greater than 3.

So, the probability is:

p = 11/20

Hence, the probability that the outcomes are greater than 3 is 11/20

The probability of spinning the same numbers

From the distribution, there are 4 outcomes with the same numbers

So, the probability is:

p = 4/20

Simplify

p = 1/5

Hence, the probability of spinning the same numbers is 1/5

Answers

Answer:

56/48

Step-by-step explanation:

Multiply both sides by 8.

Answer:

56/48

Step-by-step explanation:

You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount. You only multiply or divide, never add or subtract, to get an equivalent fraction. Only divide when the top and bottom stay as whole numbers.

In this case you have a clue which is 48, correct?

Okay well 6 times 8 = 48

Then you would want to take the 8 and times it by the numerator which is 7

So 7 times 8 = 56

Hope this helpsss

How do I create and solve linear inequalities in one variable?

Answers

Answer:

The graph of a linear inequality in one variable is a number line. Use an open circle for < and > and a closed circle for ≤ and ≥. Inequalities that have the same solution are called equivalent.

Just pay to god man hole u get 100 namaste

does a debit card use a pin or a credit card, or do both?

Answers

I believe both a debit, and credit card require a pin code.

what muiltupication will give you 1600

Answers

Answer:

5 x 320

Step-by-step explanation:

5 x 320 = 1600

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Answer:

800 x 2

I saw that this was your first question. Welcome to the Brainly Community

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14
20
K
22.4
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T
32
L
Similar By:
S
Determine if the triangles are similar. If similar.state how and complete the similarity statement

Answers

The triangles JTK and KSL are not congruent. So we cannot complete a similarity statement.

what is congruent ?

In geometry, two figures are said to be congruent if they have the same shape and size. In other words, if all corresponding angles are congruent and all corresponding sides are of equal length, then the two figures are congruent.

For example, two triangles are congruent if all three pairs of corresponding angles are congruent and all three pairs of corresponding sides are of equal length. Similarly, two circles are congruent if they have the same radius.

According to the question:
To determine if the triangles JTK and KSL are similar, we need to check if their corresponding angles are congruent and their corresponding sides are in proportion.

First, we can see that angle JTK and angle KSL are congruent because they are both right angles.

Next, we can use the Pythagorean theorem to find the length of side TK:

$TK^2 = JK^2 - JT^2$

$TK^2 = 14^2 - 2^2$

$TK^2 = 192$

TK = sqrt(192)

TK = 8*sqrt(3)

Now, we can compare the ratios of the corresponding sides to see if they are equal:

JT : JK : TK = 2 : 14 : 8*sqrt(3)

KS : KL : SL = 32 : 22.4 : 15.2

We can simplify these ratios by dividing by the greatest common factor, which is 2:

JT : JK : TK = 1 : 7 : 4*sqrt(3)

KS : KL : SL = 8 : 5.6 : 3.8

We can see that these ratios are not equal. Therefore, the triangles JTK and KSL are not similar.

Since the triangles are not similar, we cannot complete a similarity statement.

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how do i solve 1-(1+.04/12)^-12x10

Answers

To solve the expression 1 - (1 + 0.04/12)^(-12x10), you can follow these steps: Step 1: Simplify the exponent. In this case, -12x10 simplifies to -120.

Step 2: Evaluate the term within the parentheses first. 0.04/12 simplifies to 0.0033333 (approximately).

Step 3: Add 1 to 0.0033333 to get 1.0033333.

Step 4: Raise 1.0033333 to the power of -120.

Step 5: Calculate the value inside the parentheses using a calculator or software. The result is approximately 0.742657.

Step 6: Subtract the value obtained in Step 5 from 1.

1 - 0.742657 = 0.257343 (approximately).

Hence, the value of the expression 1 - (1 + 0.04/12)^(-12x10) is approximately 0.257343.

It's important to follow the order of operations (PEMDAS/BODMAS) when solving mathematical expressions. In this case, the exponent is evaluated first, followed by addition and subtraction. Utilizing a calculator or software that supports exponentiation and parentheses can help simplify complex expressions and obtain accurate results efficiently.

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Please see attached picture.

Need help answering.

Answers

In the given graph, the x-intercepts are (2,0) and (6,0).

The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.

The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).

The sign of the leading coefficient is positive, since it is 1/2.

To find the equation of the quadratic function, we start by using the vertex form:

$y = a(x - h)^2 + k$

where (h, k) is the vertex. Plugging in the given vertex (4,-2), we get:

$y = a(x - 4)^2 - 2$

Next, we use the other two points to find two additional equations:

$6 = a(8 - 4)^2 - 2 (plugging in (8,6))\\0 = a(2 - 4)^2 - 2 (plugging in (2,0))$

Simplifying these equations, we get:

$6 = 16a - 2\\8a = 4 -- > a = 1/2 \\0 = 4a - 2 \\4a = 2 -- > a = 1/2 \\$

So the equation of the quadratic function is:

$y = (1/2)(x - 4)^2 - 2$

Now, we can answer the questions:

The y-intercept is the point where the graph intersects the y-axis. To find it, we set x = 0 in the equation:

$y = (1/2)(0 - 4)^2 - 2 = 6$

So the y-intercept is (0,6).

To find the x-intercepts, we set y = 0 in the equation:

$0 = (1/2)(x - 4)^2 - 2$

Simplifying, we get:

$(x - 4)^2 = 4\\ - 4 = \pm 2 \\= 2, 6$

So the x-intercepts are (2,0) and (6,0).

The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.

The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).

The sign of the leading coefficient is positive, since it is 1/2.

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What units would you use for each scenario that follows?

a. riding a bicycle
b. rainfall during a storm
c. water coming from a fire hydrant

Answers

a. miles
b. inches
c. pounds

A tank in the shape of a hemisphere has a diameter of 24 feet. If the liquid that fills the tank has a density of 92.5 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?

Answers

The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

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What are the center and radius if the equation (x-2)^2 + (y-9)^2

Answers

Step-by-step explanation:

(x-2)^2 + (y-9)^2 = r^2

this is of the form fora circle with center h,k and radius r

(x-h)^2 + (y-k)^2 = r^2

for the equation given center = 2, 9 and radius = r

use 22/7 to calculate the pelmeter of the rectangle 3cm 5cm

Answers

The Perimeter of rectangle 3cm 5cm is 16 cm.

What is rectangle ?

In geometry, a rectangle is a plane figure of four sides having four angles of 90 degree. A rectangle has different length and breadth.

Some important formulas for rectangle :

Area of rectangle = Length × BreadthPerimeter of rectangle =2 * ( length + breadth ) Diagonal of rectangle = √(length^2 + breadth^2)What is perimeter of rectangle?

Perimeter is define as the distance around all the edges of a shape. In case of rectangle perimeter is the distance of all 4 edges i.e. 2 lengths and 2 breadth .

Thus , perimeter of rectangle = ( 2 × length ) + (2 × breadth)

= 2 ( length + breadth )

In the given question,

length of rectangle = 3cm

breadth of rectangle = 5cm

therefore, perimeter of rectangle = 2(3+5) = 16cm

Hence, The Perimeter of rectangle is 16 cm.

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Consider the function f(x) = 3x + 1 and the graph of the function g(x) shown below.

A coordinate plane linear graph function shows a line intersecting Y-axis at minus 5 and X-axis at 1.5.
The graph g(x) is the graph of f(x) translated units , and g(x) =

Answers

g(x) is a translation of 6 units downwards.

How to identify the translation that generates g(x)?

Here we have the function:

y = f(x) = 3x + 1

Notice that the y-intercept of f(x) is:

f(0) = 3*0 + 1 = 1

The y-intercept of f(x) is y = 1.

Now, we know that the y-intercept of g(x) is -5. then:

g(x) = 3x - 5 = f(x) - 6

Meaning that g(x) is a translation of 6 units downwards.

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Answer:

translated 2

units up

g(x)= f(x-2)

Step-by-step explanation:

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Answers

Answer:

hi the answer is 7.3

Step-by-step explanation:

hope it helps you have a good day

Which of these relations on the set of all people are equivalence relations? Determine the properties of an equivalence relation that the others lack.
a) {(a, b) | a and b are the same age}
b) {(a, b) | a and b have the same parents}
c) {(a, b) | a and b share a common parent}
d) {(a, b) | a and b have met} e) {(a, b) | a and b speak a common language}

Answers

Relations in the options (a), (b) and (e) are the Equivalence relations as, the relations are reflexive, symmetric and transitive all.

Given, five relations as,

a) {(a, b) | a and b are the same age}

b) {(a, b) | a and b have the same parents}

c) {(a, b) | a and b share a common parent}

d) {(a, b) | a and b have met}

e) {(a, b) | a and b speak a common language}

we have to find which of them are equivalence relations

a) as, (a , a) ∈ R ∀ a hence, Reflexive.