Find the general indefinite integral. (use c for the constant of integration. )

A trapezoid has an area of 10 square units. The scale factor would be 3  to dilate the trapezoid to have an area of 90 square units.

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor.

Let the linear scale factor be k.

The area scale factor is [tex]k^2[/tex]

We'll multiply the old area (10) by the area scale factor ([tex]k^2[/tex] ) to get the area of 90 square units

[tex]10 \times k^2 = 90\\\\k^2 = \frac{90}{10} \\\\k^2 = 9\\\\k = \sqrt{9} \\\\k = 3[/tex]approximately

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Answer:

17/28

60.7%

17:28

11/28

39.3%

11:28

Difference:  [tex]\frac{3}{14}[/tex]

Explanation:

A fraction can be turned into a percent by dividing the numerator by the denominator and multiplying the result by 100%.

For example:

17/28 = 0.607

0.607 * 100% = 60.7%

A fraction can be turned into a ratio by writing it like this:

numerator:denominator

For example:

11/28

11:28

To find the difference between 2 fractions with the same denominator, simply subtract the 2 numerators.

For example:

[tex]\frac{17}{28} - \frac{11}{28}[/tex]

You subtract 11 from 17, then put the resulting 6 in the fraction with the same denominator. This results in [tex]\frac{6}{28}[/tex] which can be simplified to [tex]\frac{3}{14}[/tex].

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Step-by-step explanation:

let the big cube side be b

small cube side be s

s = 2/3 * b

bv + sv = 118.125

b^3 + 8/9 b^3= 118.125

17 b^3/8 = 118.125

b^3 = 55.58

b = 3.816in

s = 2.544in

Answer:

Step-by-step explanation:

A triangular pyramid has 6 edges, 4 vertices, and 1 base

The quadrilateral is a trapezoid and the area of the quadrilateral is 85.04 square units

The vertices are given as:

A:(-2, 3) B:(4, -6) C:(10, 2) D:(6, 8)

Next, we plot the vertices (see attachment)

From the attached graph, we can see that the quadrilateral is a trapezoid

From the plot, we have the following features:

Height: AD

Parallel sides: CD and AB

Calculate the lengths using:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

So, we have:

[tex]AD = \sqrt{(-2 -6)^2 + (3 -8)^2}[/tex]

[tex]AD = \sqrt{89}[/tex]

[tex]CD = \sqrt{(10 -6)^2 + (2 -8)^2}[/tex]

[tex]CD = \sqrt{52}[/tex]

[tex]AB = \sqrt{(-2 -4)^2 + (3 +6)^2}[/tex]

[tex]AB = \sqrt{117}[/tex]

The area is then calculated as:

Area = 0.5 * (CD + AB) * AD

This gives

Area = 0.5 * (√52 + √117) * √89

Evaluate

Area = 85.04

Hence, the area of the quadrilateral is 85.04 square units

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[tex]\text{Slope- intercept form is y =mx+c, where m is the slope and c is the y-intercept.}\\ \\\textbf{1)}\\\\~~~~~3x = -8+y\\\\\implies y = 3x +8\\\\\textbf{2)}\\\\~~~~~9=3x+3y\\\\\implies 3y= 9-3x\\\\\implies y= \dfrac 13(9-3x)\\\\\implies y= 3-x\\\\\implies y= -x+3\\\\\textbf{3)}\\\\~~~~~~4y-10 = 20x\\\\\implies 4y = 20x +10\\\\\implies 2y = 10x +5\\\\\implies y = \dfrac 12(10x +5)\\\\\implies y= 5x +\dfrac 52[/tex]

The solid was obtained by rotating the region bounded by x² = 27y, x = 0, and y = 1 about the y-axis is 42.411 cubic units.

It is the reverse of differentiation.

Consider the solid obtained by rotating the region bounded by the given curves about the y-axis.

[tex]\rm x = 3\sqrt{3y} \ or \ x^2 = 27y[/tex]

x = 0, and y = 1

Then the volume of the solid will be

[tex]\rm Volume = \int _{0}^{1} \pi x^2 dy\\\\Volume = \int _{0}^{1} \pi 27y dy\\\\Volume = 27\pi \int _{0}^{1} \ ydy\\\\Volume = 27 \pi [\dfrac{y^2}{2}] _{0}^{1}\\\\[/tex]

[tex]\rm Volume = 13.5 \times \pi \times [y^2] _{0}^{1}\\\\Volume = 13.5 \times \pi \times (1^2 - 0^2)\\\\Volume = 42.411 \ cubic \ units[/tex]

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Answer:

28 cm

Step-by-step explanation:

let the unknown side be x , then

using Pythagoras' identity in the right triangle

x² + 21² = 35²

x² + 441 = 1225 ( subtract 441 from both sides )

x² = 784 ( take square root of both sides )

x = [tex]\sqrt{784}[/tex] = 28

Answer:

the unknown side is 28

Step-by-step explanation:

[tex]a^{2} + b^{2} = c^{2} \\c = 35\\a = 21\\21^{2} + b^{2} = 35^{2}\\441 + b^{2} = 1225\\b^{2} = 1225 - 441\\b^{2} = 784\\b = \sqrt{784} \\b = 28[/tex]

Answer:

10,200

Step-by-step explanation:

P(1-r)^n

r = decimal form of the interest rate percent

n = amount of years

principal times (1 - decimal form of the interest rate percent) to the (amount of years) power

12000 (1-.05)^3

use PEMDAS

12000 times (.95)^3

12000 times .857375 =

ANSWER:

10288.5

Answer:

a) P(1 and tails) = 1/10 = .1

b) P(even and heads) = 1/5 = .2

Step-by-step explanation:

The spinner has 5 outcomes: 1-5.

The coin has 2 outcomes: Heads or Tails.

We want to find the probability of P(1 ∩ T) and P(2,4 ∩ H).

Spinning the spinner and flipping the coin are independent events; therefore, getting one outcome has no effect on the outcome of another.

For independent events, the multiplication rule is:

If we use this formula for A, we get that:

The probability of getting a 1 on the spinner is P(1) = 1/5.

The probability of getting tails on the coin toss is P(tails) = 1/2.

We can now multiply these probabilities together:

The probability of getting a 1 on the spinner and tails on the coin toss is P(1 and tails) = 1/10 or .1.

There are two even numbers between 1 and 5: 2 and 4.

The probability of getting an even number on the spinner is 2/5.

The probability of getting heads on the coin toss is 1/2.

We can multiply these probabilities together:

The probability of getting an even number on the spinner and heads on the coin toss is P(even and heads) = 1/5 or .2.

so let's say the sale price is "P", so Nicole would want to know how much will it be P discounted by 18% of P.

Well, the sale price will just be P or 100% of P, minus 18%, the discounted price will be 100% - 18% = 82%, so the discounted price will be 82% of P.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{82\% of P}}{\left( \cfrac{82}{100} \right)P}\implies \boxed{0.82}\cdot P\qquad \impliedby \textit{discounted price}[/tex]

Answer:

[tex]|-a| =a[/tex]

Step-by-step explanation:

Old coordinate (0,-1)

New coordinate (1,0)

The translation is

Verification

Image of (0,-1) is (0,1)

Image of (1,0) is (-1,0)

Answer:

(x + 1, y + 1)

Step-by-step explanation:

Translation of x-coordinate :

Translation of y-coordinate :

Hence, the points which describes the change :

Answer:

y = 1/2x + 0.5

or

y = 1/2x + 1/2

Step-by-step explanation:

y = mx + b

b is y-intercept:

when x = 0, y = 0.5 (when the line cross the vertical (y) axis of the graph)

the point is (0, 0.5) so b = 0.5

m is slope:

slope = rise / run

rise = 1

run = 2

for every 2 x values, y increase by 1

slope (m) = 1/2

Answer:

V = 36π x 14

Step-by-step explanation:

The volume of a cylinder can be found by multiplying the base area and the height. Therefore, the following equation can be written:

V = 36π x 14

Answer:

Option 4

Step-by-step explanation:

Formula for volume of a cylinder :

Volume = Base Area x Height

Hence :

⇒ V = 36π x 14

Answer:

1075

Step-by-step explanation:

Let us say pi/ is 3.14

Diameter is radius times 2, so the radius is half of 37(aka 18.5)

A = n[tex]x^{2}[/tex]

A = 3.14 x 18.5²

A = 3.14 x 342.25

A =  1074.665

snice 6 > 4

A = 1075

Answer:

34494.79

Step-by-step explanation:

round it up to the nearest cent

hope this helps

pls mark brainliest

Answer:

132 m²

Step-by-step explanation:

Split the figure into 2 parts :

Area (Triangle)

Area (Rectangle)

Area (Figure)

Answer:

A, C and D

Step-by-step explanation:

Answer:

113.1cm2

Step-by-step explanation:

looked it up

Answer:

[tex]20cm^2[/tex]

Step-by-step explanation:

We are talking of a linear scale ie 1 cm = 50 cm

So if the real yacht length is 10 meters(10,000 cm), then the model length will be 10000/50 = 200 cm

However, when talking about areas, the scale factor is different. We cannot simply divide 5m by 50

Let's say the sail height is 1 meter and the sail width is 5 meters which will give a sail area of 5 sqm.

The scaled height would be 100/50 = 2cm and scaled width will be 500/50 = 10 cm

So the area of the sail on the model will be 2 x 10 =200 square cm

In short, area of sail on model = (area of sail on real yacht( ÷ (50 x 50)

Since there are 10,000 square cm to 1 square meter we get the answer as 5 x 10000/2500 = 20 square cm

Answer:

in 2nd figure will mean greater

Answer:

its the 4th one hopes this help

s

Step-by-step explanation:

[tex]area = 24 \: {cm}^{2} [/tex]

[tex]height = 8 \: cm[/tex]

the volume of the given prism.

[tex]v = area \: of \: cross \: section \times height[/tex]

[tex]v = 24 \times 8[/tex]

[tex]v = 192 \: {cm}^{3} [/tex]

hence, the volume of the prism is 192 cubic centimeters.

Step-by-step explanation:

If you are solving for y :

[tex] \: [/tex]

[tex]x < 3y - 18[/tex]

[tex]x + 18 < 3y[/tex]

[tex] \frac{x + 18}{3} < \frac{3y}{3} [/tex]

[tex]y > \frac{3}{x} + 6[/tex]

An equation is formed of two equal expressions. The amount of 20% milk and 12% milk that is needed to be mixed is 7.5 gallons and 12.5 gallons, respectively.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the amount of 20%milk mixed be represented by x, while the amount of 12% milk mixed is represented by y. Therefore, the two-equation can be written as,

x+y=20 gallons

0.20x + 0.12y = (0.15×20)

Solve the first equation for x, therefore,

x = 20 - y

substitute the value of x in the second equation,

0.20(20-y) + 0.12y = 3

4 - 0.2y +0.12y = 3

-0.08y = -1

y = 12.5 gallons

substitute the value of y in the first equation,

x + 12.5 = 20

x = 7.5 gallons

Hence, the amount of 20% milk and 12% milk that is needed to be mixed is 7.5 gallons and 12.5 gallons, respectively.

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Answer:

area: 5×27÷2

perimeter:8+27+34

Answer: 17, 13, 9, 5, 1

Step-by-step explanation:

y=-2(-2) + 9 = 13

y=-2(0) + 9 = 9

y=-2(2) + 9 = 5

y=-2(4) + 9 = 1

Answer:

B:Similar :SAS

Step-by-step explanation:

The Angle-Side (SAS) Similarity Theorem states that  If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.

In the given triangles <B=<E= 40 °

Or,

Hence triangle ABC~ Triangle DEF by SAS similarity theorem.

Give brainliest :)

Option B is correct, by SAS postulate the triangles ABC and DEF are similar.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

ABC and DEF  are similar triangle as the corresponding angles are congruent and the corresponding sides are in proportion .

If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent.

Hence, by SAS postulate the triangles ABC and DEF are similar.

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Answer:

144

Step-by-step explanation:

In a regular decagon like the one shown in the picture each angle is 144 degrees and it all adds up to 1,440. If you want proof search up "angle of a decagon"

The equation of the line that is parallel to x = 3 and goes through (4, -3) is: x = 4).

The slopes or parallel lines are always the same.

Given the equation of a vertical line, x = 3, the slope is undefined. So also, the slope of the line that is parallel to x = 3 is undefined.

If the line passes through the point (4, -3), it means it intercepts the x-axis at x = 4.

Therefore, the equation of the line that passes through (4, -3) and is parallel to x = 3 is: x = 4.

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