Sketch the Graph for each equation y= | 3x + 5 |

Answer:

great!

Step-by-step explanation:

how about you?

The volume of the rectangular tank is:

V = l × w × h = 40 cm × 30 cm × 35 cm = 42,000 cm³

The initial volume of water in the tank is:

V1 = l × w × h1 = 40 cm × 30 cm × 15 cm = 18,000 cm³

When 4800 cm³ of water is poured into the tank, the new volume of water becomes:

V2 = V1 + 4800 cm³ = 18,000 cm³ + 4800 cm³ = 23,800 cm³

Let's assume that the new water height is h2 cm. We can use the formula for the volume of a rectangular tank to find the new height:

V = l × w × h2

h2 = V / (l × w) = (23,800 cm³) / (40 cm × 30 cm) ≈ 19.83 cm

Therefore, the new height of the water in the tank is approximately 19.83 cm.

The volume of a solid formed by revolving the region bounded above by the line is (932π/15)

To use the disk method, we need to integrate over the axis of revolution, which is the y-axis in this case. We can break the solid into vertical disks of thickness dy.

The radius of each disk is given by the distance between the y-axis and the curve \(x = y^2 - 1\). So the radius is:

\(r = y^2 - 1\)

The height of each disk is the difference between the y-coordinate of the top curve y = 3 and the y-coordinate of the bottom curve y = 1. So the height is:

h = 3 - 1 = 2

The volume of each disk is then:

\(dV = \pi r^2h dy\)

Substituting r and h, we have:

\(dV = \pi (y^2 - 1)^2 (2) dy\)

To find the total volume, we integrate over the range of y from 1 to 3:

\(V = \int_{1}^{3} \pi(y^2 - 1)^2 (2) dy\)

This integral can be simplified by expanding the squared term:

\(V = \int_{1}^{3} \pi (y^4 - 2y^2 + 1) (2) dyV = 2\pi \int_{1}^{3}(y^4 - 2y^2 + 1) dyV = 2\pi [(1/5)y^5 - (2/3)y^3 + y]^3_1\)

V = \(2\pi [(1/5)(3^5 - 1^5) - (2/3)(3^3 - 1^3) + (3 - 1)]\)

V = 2π [(1/5)(242) - (2/3)(26) + 2]

V = 2π [(242/5) - (52/3) + 2]

V = 2π [(726/15) - (260/15) + 30/15]

V = 2π [(466/15)]

V = (932π/15)

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Note: The full question is

Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines. y = 1, y = 3, x = y^2 - 1.

When value of x is given as 3 then according to the said proportional relationship y will be  13.15.

We are given that y and x have a proportional relationship, and y = 9 when x = 2. This means that there is a constant of proportionality, k, such that y = kx.

We can use the information given to find the value of k:

y = kx

9 = k(2)

k = 9/2

Now that we know the value of k, we can use it to find the value of y when x = 3:

y = kx

y = (9/2) * 3

y = 13.5

So the value of y when x = 3 is 13.5

A ratio is a way of comparing two or more values or quantities. It is a mathematical expression that shows the relationship between different values, typically by using the symbol ":" to separate the values. For example, if we have three apples and two oranges, we can express the relationship between the apples and oranges as a ratio 3:2. Ratios can also be written as fractions, in this case the ratio 3:2 can be written as 3/2.

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Solution

Given that:

Total number of messages sent is 96

Let the number of messages Yoko sent be x

=> Austin will send x - 6 (since austin sent 6 fewer messages)

=> Tom will send 3(x - 6) (since Tom sent 3 times as many messages)

Since they make a total of 96

Hence, Yoko sent: 24 messages

Austin sent: 24 - 6 = 18 messages

Tom sent: 3(18) = 54 messanges

Number of text messages Yoko sent: 24 messages

Number of text messages Austin sent: 18 messages

Number of text messages Tom sent:​ 54 messanges

Answer:

50(5π + 6) cm²

Step-by-step explanation:

TSA of figure = 1/2 of TSA(Cylinder) + Area of rectangle

= 1/2 of 2πr(h+r) + 20*15

= πr(h+r) + 300

= 10π(15+10) + 300

= 250π + 300 cm²

or 50(5π + 6) cm²

Answer:

Step-by-step explanation:

1)  DE = 6/sin63 = 6.7

DF = 6/tan63 = 3.1

m∠E = 180 - 90 - 63 = 27°

2)  tan30 = 1/√3 = UV / (27√10)

UV = (27√10) / √3 · (√3/√3) = (27√30) / 3 = 9√30

3)  cosV = 3/8

cos⁻¹(3/8) = 68

m∠V = 68°

Answer: The initial value is 12,000 and it represents the price of the baseball card at the time of purchase.

Explanation: I just looked at the beginning of the graph, surprisingly I got it right.

Initial value is 12,000 and it represents the price of the baseball card at the time of purchase.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

The function C(t) is represented on the following graph, where C represents the value of the card, and t is time in years since the card was purchased.

We need to find the initial value and we have to select the statement which is true.

The initial value is 0 and it represents the lowest value of the card.

The initial value is 10 and it represents the amount of time it takes for the card to increase in value.

The initial value is 12,000 and it represents the price of the card when it was new.

Among the given statements, the 4th statement is true based on the graph.

Hence initial value is 12,000 and it represents the price of the baseball card at the time of purchase.

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The value of distance AB is 187.5 units

Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other.

sine rule can be expressed as;

a/sinA = b/sinB = c/sinC

The opposite side to angle A is BC

the opposite side to angle C is AB

therefore;

A = 180-( 117 +24)

A = 180- 141

A = 39°

290/sin 39 = x/ sin24

xsin39 = 290 × sin24

0.629x = 117.95

x = 117.95/0.629

x = 187.5

therefore the distance AB is 187.5

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Answer:

x=8. You plug 8 in for x.

7+12(8)=103

7+96=103

Step-by-step explanation:

7+12x=103

or 12x=103-7

x=96/12=8

to check it 8 is needed.

7+12×8=103

Answer:

B and D

Step-by-step explanation:

they both make srnse to me

The required percentage of individuals is 66.07%.

What is percentage?

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

The required data from the given table is as follows,

The total number of individuals is 112.

The number of individuals who ride Ferris wheel but not roller coaster is 74.

As per the question the percentage can be found as below,

Required percent = (The required number ÷ Total number) × 100

                              = (74 ÷ 112) × 100%

                               = 66.07%

Hence, the percentage of the individuals rode the Ferris wheel and did not ride the roller coaster is  66.07%.

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The perimeter of the figure is 4(π + 9)ft.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

Given is a 2 - D figure as shown in the figure attached.

We can write the perimeter as -

P = P{rectangle} + P{semicircle}

P = 2(10 + 8) + (4π)

P =  (4π) + (36)

P = 4(π + 9)

Therefore, the perimeter of the figure is 4(π + 9)ft.

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Answer:

\( \sqrt[4]{ {x}^{3} } \)

Step-by-step explanation:

\( \sqrt{x} \times \sqrt[4]{x} \\ = {x}^{ \frac{1}{2} } \times {x}^{ \frac{1}{4} } \\ = {x}^{ \frac{1}{2} + \frac{1}{4} } \\ = {x}^{ \frac{3}{4} } \\ = \sqrt[4]{ {x}^{3} } \)

The angle sum property of a triangle and the angle formed between a tangent and a radius of a circle indicates.

m∠ADC = 58°

A tangent to a circle is a straight line which touches the circumference of a circle at only one point.

The vertical angles theorem indicates that we get;

∠1 ≅ ∠2

Therefore; m∠1 = m∠2

The tangent to a circle indicates that we get;

The angle formed at vertex B and Q are 90 degrees angles and the triangles ABP and AQP are right triangles, which indicates that the acute angles of each of the right triangles are complementary, therefore;

m∠1 + 26° = 90°

m∠1 = 90° - 26° = 64°

Therefore, m∠2 = m∠1 = 64°

m∠2 = m∠CAD = 64°

The segments AC and AD are radial lengths therefore, the triangle ΔACD is an isosceles triangle.

m∠ADC ≅ m∠ACD (Base angles of an isosceles triangle)

The angles ∠ADC and ∠ACD are therefore;

m∠CAD + m∠ADC + m∠ACD = 180° (Angle sum property of a triangle)

m∠CAD + m∠ADC + m∠ADC = 180°

m∠CAD + 2 × m∠ADC = 180°

64° + 2 × m∠ADC = 180°

m∠ADC = (180° - 64°)/2 = 58°

m∠ADC = 58°

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Recall the inverse function theorem. If \(f\) is invertible and differentiable in all the right places, then

\(f^{-1}\bigg(f(x)\bigg) = x \\\\ ~~~~~~~~ \implies \left(f^{-1}\right)'\bigg(f(x)\bigg) f'(x) = 1 \\\\ ~~~~~~~~ \implies \left(f^{-1}\right)'\bigg(f(x)\bigg) = \dfrac1{f'(x)} \\\\ ~~~~~~~~ \implies \left(f^{-1}\right)'(x) = \dfrac1{f'\left(f^{-1}(x)\right)} \\\\ ~~~~~~~~ \implies \left(f^{-1}\right)'(-4) = \dfrac1{f'\left(f^{-1}(-4)\right)}\)

Solve for \(x\) such that \(f(x)=-4\).

\(x^3 + 2x - 1 = -4 \\\\ x^3 + 2x + 3 = 0 \\\\ (x + 1) (x^2 - x + 3) = 0\)

\(x^2-x+3=0\) has non-real solutions, so we're left with

\(x+1 = 0 \implies x = -1\)

Then we have

\(f(-1) = -4 \implies f^{-1}(-4) = -1 \implies \left(f^{-1}\right)' (-4) = \dfrac1{f'(-1)} = \boxed{\dfrac15}\)

since

\(f(x) = x^3 + 2x - 1 \implies f'(x) = 3x^2 + 2 \implies f'(-1)=5\)

Answer:

y = 1/x+2 + 3

Step-by-step explanation:

x = -2

y = 3

Answer:

  13,551,737

Step-by-step explanation:

You want the sum of the first 13 terms of the geometric sequence with first term 17, and successive terms 51, 153, ....

The common ratio is found by dividing a sequence term by the one before it:

  r = 51/17 = 3

The common ratio is 3.

The index of the 13th term of the sequence is n = 13.

The sum of n terms of a geometric sequence with first term a1 and common ratio r is ...

  Sn = a1·(r^n -1)/(r -1)

For a1 = 17, r = 3, and n = 13, the sum is ...

  \(S_{13}=17\cdot\dfrac{3^{13}-1}{3-1}=17\cdot\dfrac{1594322}{2}=\boxed{13,\!551,\!737}\)

The equations that can be used to find the lengths of the legs of the triangle are as follows:

The equation that can be used to find the length of the leg of the right triangle uses Pythagoras theorem,

Therefore,

c²  = a² + b²

where

Therefore,

10²  = (x + 2)² + x²

100 = (x + 2)² + x²

Therefore, using the area of a triangle,

area of a triangle  = 1 / 2 bh

where

Therefore,

area of the triangle = 1 / 2 × (x + 2)(x)

24 = 0.5 × (x + 2)(x)

24 = x² + 2x / 2

cross multiply

48 = x² + 2x

x² + 2x - 48 = 0

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The roof top would be 0. At 12 seconds the ball is at -225.6, which would be the ground so the building would be 225.6 meters tall.

The highest positive value is 81.6, so this is the highest the ball goes up.

The value changes from a positive to a negative between 8 and 10, which means that would be around the time it is the same height as the building.

The answers would be:

The first and third choices

I'll be referring to each of these numbers as x and y.

x + y = 4

(x^2) + (y^2) - 3(x)(y) = 76

x = 4 - y

(4 - y)^2 + (y^2) - 3(4 - y)(y) = 76

(4 - y)(4 - y) + y^2 - (3y)(4 - y) = 76

16 - 4y - 4y + y^2 + y^2 - 12y + 3y^2 = 76

16 - 20y + 5y^2 = 76

5y^2 - 20y - 60 = 0

y^2 - 4y - 12y = 0

(y - 6)(y + 2) = 0

y = 6 or -2

x = 4 - 6 = -2

x = 4 - - 2 = 6

As you can see, we got the same numbers for both x and y, -2 and 6. Therefore, the two numbers are -2 and 6. But, we can check our work to ensure that the answer is correct.

x = -2

y = 6

6 - 2 = 4

4 = 4

(-2)^2 + (6^2) - 3(-2)(6) = 76

4 + 36 - 3(-12) = 76

40 + 36 = 76

76 = 76

Hope this helps!

Answer:

X and y = -2 or 6

Step-by-step explanation:

Answer:

x < -5

Step-by-step explanation:

-2(5x+1) >48

-10x-2 > 48

-10x-2+2 > 48+2

-10x > 50

p.s : when dividing by a negative number with inequalities, change the sign, i.e. < would then be >....

therefore:

x < -5

The ending inventory using LIFO is $920.

The ending inventory using FIFO is $1,472.

LIFO means last in first out. It means that it is the last purchased inventory that is the first to be sold. Ending inventory would consist of first purchased inventory.

23 x $40 = $920

FIFO means first in, first out. It means that it is the first purchased inventory that is the first to be sold. Ending inventory would consist of last purchased items in inventory.

23 x $64 = $1,472

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Answer:

the anser is d

Step-by-step explanation:

Answer:

b) 7x² - 12x√14 + 72

Step-by-step explanation:

Let's solve the problem,

→ (x√7 - 3√8)(x√7 - 3√8)

→ (x√7 - 3√8)²

→ 7x² - 12x√14 + 72

Hence, option (b) is correct.

Answer:

1.15

Step-by-step explanation:

26.50-1.73= 24.77

Each book was 5.33 and since there was 4 of them:

5.33 x 4 = 21.32

We subtract from the original answer

24.77- 21.32 = 3.45

3.45/3 = 1.15

Hope this makes sense

The interest Raymond will pay this month is $54.98

What does APR mean?

APR means annual percentage rate, which means that since we are computing monthly interest, the annual rate which is the whole 12 months needs to be divided by 12 to ascertain the equivalent monthly interest rate

monthly interest=21.99%/12

What is the monthly interest amount in dollars?

The monthly interest amount in dollars is determined as the monthly interest rate multiplied by the credit card balance at the end of the month

monthly interest=$3,000*21.99%/12

monthly interest=$54.98

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Answer:

  x = 17

Step-by-step explanation:

In order to make any sense of this problem, we must assume the lines that look parallel are parallel. With that assumption, the two marked angles are supplementary:

  61° +7x° = 180°

  7x = 119 . . . . . . . subtract 61°, divide by °

  x = 17 . . . . . . . . divide by 7

Answer:

E. p - 7 + 7 = 22 + 7

Step-by-step explanation:

p - 7 + 7 = 22 + 7 ( -7 + 7 = 0)

p = 22 + 7

p - 7 = 22//

z =(2-√-116)/-20=1/-10+i/10√ 29 = -0.1000-0.5385i

z =(2+√-116)/-20=1/-10-i/10√ 29 = -0.1000+0.5385i

Step-by-step explanation: