A bookcase has a mass of 20 kilograms. A book in the bookcase has a mass of 500 grams.
How many books of the same mass would it take to equal the mass of the bookcase?
Enter your answer in the box.

Answer:

[tex] = > {x}^{2} + {y}^{2} + 6x - 14y + 49 = 0[/tex]

Step-by-step explanation:

From the graph we can see that

Diameter = 6 units

=> Radius = 3 units and centre is at (-3,7)

=> Equation is Circle with centre (-3,7) and radius of 3 units will be

[tex] = > {(x + 3)}^{2} + {(y - 7)}^{2} = {3}^{2} [/tex]

[tex] = > ( {x}^{2} + 6x + 9) + ( {y}^{2} - 14y + 49) = 9[/tex]

[tex] = > {x}^{2} + {y}^{2} + 6x - 14y + 49 = 0[/tex]

The circumference of the circle is 72cm.

[tex]Arc length = 2\pi r(\frac{x}{360} )[/tex]

where

r is the radius of the circle

x is the central angle of the arc

Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. It is calculated as

circumference of the circle = 2πr

According to the given question we have

central angle of the arc, x = 15 degrees

Arc length = 3 cm

Let r be the radius of the given circle.

Then,

Arc length = 2πr[tex](\frac{15}{360} )[/tex]

⇒ 3 ×[tex]\frac{360}{15}[/tex]  = circumference of the circle   ( circumference or circle =2πr)

⇒ circumference of the circle = 72 cm

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The probability the next customer pays using a debit card based on the last three weeks is 30% or 0.3.

This is the chance or likelood for an event to occur. For example, if in a city it has snowed every year on December 25th, there is a high probability it will snow this year and in the next years.

Total of a specific outcome/ total of outcomes

Based on this, let's calculate the probability the next customer pays using the debit card:

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Answer:

Step-by-step explanation:

4x + 4y = -37

2x + 5y = -17

we are told to use elimination ,   instead of substitution,

meaning get rid of the x or y  in one of the equations.

Part C :   let's multiply (2x + 5y = -17 ) *  (-2)  so we get

-4x - 10y = 34    , then add

4x + 4y = -37

0x -6y = -3      now we have only one variable ,  y

because both sides have a minus sign, we can just drop it

6y = 3   ( divide both sides by 6)

y = 3/6

Part B : y = 1/2    we now know y

plug in the y value into  1st equation.

4x + 4(1/2) = -37

now solve for x

4x + 2 = -37

4x = -39

Part A :  x = - 39/4

Answer:

4.55 or 4.7 depending on how you round

Step-by-step explanation:

3 1/2=3.5

1 1/3= 1.3

3.5x1.3=4.55

The distance between Casey and the base of the lighthouse is 49 ft.

The angle of elevation refers to the angle formed by the straight horizontal line and an object. The crosshair of an observer is usually above the horizontal. 

The angle of depression is the angle formed by the horizontal and a downward angle to an object. The crosshair of an observer is usually above below the horizontal.

The distance between Casey and the base of the lighthouse can be determined by using the tangent of trigonometry.

(TOA)

[tex]\mathbf{tan \theta = \dfrac{opp}{adj}}[/tex]

[tex]\mathbf{tan \ 58 = \dfrac{78}{x}}[/tex]

[tex]\mathbf{x= \dfrac{78}{1.6003}}[/tex]

x ≅ 49 ft

The height of the goal post can be determined by using the tangent of trigonometry.

[tex]\mathbf{tan \theta = \dfrac{opp}{adj}}[/tex]

[tex]\mathbf{tan 17 = \dfrac{x}{131}}[/tex]

x = (tan 17) × 131

x = 0.3057 × 131

x ≅ 40 ft

The horizontal distance between Zack and the water fountain is calculated by using the tangent of trigonometry.

[tex]\mathbf{tan \theta = \dfrac{opp}{adj}}[/tex]

[tex]\mathbf{tan \ 28 = \dfrac{75}{x}}[/tex]

[tex]\mathbf{x = \dfrac{75}{0.5317}}[/tex]

x = 141 ft

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The length of the repel line using one of the 3 trigonometry ratios will be 186.78 feet.

From the information given, Peyton is walking her dog, Willow, on a local trail and the dog falls 153 feet down a ravine.

The length will be calculated thus:

Cos 35° = 153/AC.

AC = 153/cos 35°

AC = 153/0.819

AC = 186.78 feet.

Therefore, the length is 186.78 feet.

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Answer: 125

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

220-110

110/2=55

Answer:

2 units

Step-by-step explanation:

Answer:

The answer is 2 units

Step-by-step explanation:

[tex]16x^2-25\\\\=(4x)^2-5^2\\\\=(4x+5)(4x-5)[/tex]

Answer:

~150.8

Step-by-step explanation:

surface area of a cylinder=2 pi r h + 2 pi r²

[tex]\large{\boxed{\mathfrak\pink{\fcolorbox{pink}{pink}{Answer:-}}}}[/tex]

→ POINTS TO BE NOTED

nd, to find Surface area of cylinder there is one formula

[tex] \pink{ \boxed{ \sf2 \pi \: r(h + r)}}[/tex]

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★Here

★ Let's solve:-

[tex] \sf \: ↦2 \pi \times 3(5 + 3) \\ \sf \:↦ 2\pi \times 15 + 9 \\ \sf \:↦ 2\pi \times 24 \\ \sf \: ↦48\pi\:cm²[/tex]

[tex]\purple{\rule{15mm}{2.9pt}} \red{\rule18mm{2.5pt}}\orange{ \rule18mm{2.5pt}}[/tex]

Hence;

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Answer:

1.12 ≤ x ≤ 34.18

Step-by-step explanation:

This constraint ensures that the number of tires produced, represented by x, falls within the range where the production costs, represented by C(x), are below $75,000.

Answer:

c.) 36

Step-by-step explanation:

The triangle was reduced by 36 inches

Answer:

THE ANSWER IS “your net worth”

Step-by-step explanation:

Answer:

-3+15i

Step-by-step explanation:

Apply complex arithmetic rule: [tex]\left(a+bi\right)\left(c+di\right)=\left(ac-bd\right)+\left(ad+bc\right)i[/tex]

[tex]\left(-3\cdot \:3-3\left(-2\right)\right)+\left(-3\left(-2\right)+3\cdot \:3\right)i[/tex]

-3 * 3 -3 (-2) = -3

[tex]-3+15i[/tex]

Answer:

4 5/6 or 29/6

Step-by-step explanation:

Conversion a mixed number 8 1/

4

to a improper fraction: 8 1/4 = 8 1/

4

= 8 · 4 + 1/

4

= 32 + 1/

4

= 33/

4

To find a new numerator:

a) Multiply the whole number 8 by the denominator 4. Whole number 8 equally 8 * 4/

4

= 32/

4

b) Add the answer from previous step 32 to the numerator 1. New numerator is 32 + 1 = 33

c) Write a previous answer (new numerator 33) over the denominator 4.

Eight and one quarter is thirty-three quarters

Conversion a mixed number 3 5/

12

to a improper fraction: 3 5/12 = 3 5/

12

= 3 · 12 + 5/

12

= 36 + 5/

12

= 41/

12

To find a new numerator:

a) Multiply the whole number 3 by the denominator 12. Whole number 3 equally 3 * 12/

12

= 36/

12

b) Add the answer from previous step 36 to the numerator 5. New numerator is 36 + 5 = 41

c) Write a previous answer (new numerator 41) over the denominator 12.

Three and five twelfths is forty-one twelfths

Subtract: 33/

4

- 41/

12

= 33 · 3/

4 · 3

- 41/

12

= 99/

12

- 41/

12

= 99 - 41/

12

= 58/

12

= 2 · 29/

2 · 6

= 29/

6

Answer:

The answer is D. x=-1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Divide both sides by 10.

2. Add 4 to both sides.

3. Subtract 10x from both sides.

4. Divide both sides by -8.

The answer is D.

Answer:

a = 2a(- 1)

Step-by-step explanation:

I have done the maths

Answer:

t=15

Step-by-step explanation:

t/3 + 3/3 = 6

combine fractions w/ common denominator:

t+3/3 = 6

multiply both sides by denominator (3):

note: the two threes from 3 x t+3/3 cancel each other out

t+3=3x6

t+3=18

subtract 3 from both sides and you get 15

t=15

hope this helps :)

The required kite is flying at a height of approximately 45.02 meters to the nearest tenth of a meter.

To find the height at which the kite is flying, we can use trigonometry, specifically the tangent function. The tangent of the angle of elevation (42 degrees) is the ratio of the height (h) of the kite to the distance from Cynthia to the kite (50 meters).

The formula for the tangent of an angle is:

[tex]tan(angle) = opposite/adjacent[/tex]

In this case, the angle is 42 degrees, the opposite side is the height of the kite (h), and the adjacent side is the length of the string (50 meters).

[tex]tan(42^o) = h / 50[/tex]

To find the height (h), we can rearrange the equation:

[tex]h = 50 * tan(42^o)[/tex]

Now, let's calculate the height:

[tex]h =50 * tan(42^o)[/tex]

h ≈ 50 meters * 0.9004
h ≈ 45.02 meters (rounded to two decimal places)

So, the kite is flying at a height of approximately 45.02 meters to the nearest tenth of a meter.

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Answer:

x=−1 and y=−1

Step-by-step explanation:

Solve by substitution

x−y=0;2x+3y=−5

Step: Solve x−y=0 for x:

x−y+y=0+y(Add y to both sides)

x=y

Step: Substitute yfor x in 2x+3y=−5:

2x+3y=−5

2y+3y=−5

5y=−5(Simplify both sides of the equation)

5y/5=−5/5 (Divide both sides by 5)

y=−1

Step: Substitute−1 for y in x=y:

x=y

x=−1

Answer:

x=−1 and y=−1

The solution to the system is x = -1.8 and y = -1.8.

A group of two or more equations that must be solved simultaneously make up a system of equations. There are many unknown variables in a system of equations, and each equation in the system depicts the relationship between those variables.

A set of variable values that satisfy every equation in a system of equations is the solution to the system of equations.

To solve this system of equations graphically, we can plot the two equations on a coordinate plane and find the point where they intersect, which represents the solution to the system.

a) To plot the equation x - y = 0, we can rearrange it to y = x and plot the line passing through the origin and the point (1, 1), as shown below:

Graph of the line y = x passing through the origin and the point (1, 1).

To plot the equation 2x + 3y = -5, we can rearrange it to y = (-2/3)x - 5/3 and plot the line passing through the points (-2, 1) and (1/3, -5/3), as shown below:

Graph of the line y = (-2/3)x - 5/3 passing through the points (-2, 1) and (1/3, -5/3).

b) The point where the two lines intersect is the solution to the system. From the graph, we can see that this point is approximately (-1.8, -1.8).

Therefore, the solution to the system is x = -1.8 and y = -1.8.

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Answer: Since the arc length is given (4 ) and the radius is given (6), the central angle  can be found

Arc Length = theta * r

4 pi = theta * 6 Divide by 6

4 pi / 6 = theta

theta = (2/3) pi

Step-by-step explanation:

Answer:

-5=0

Step-by-step explanation:

g(4)=8-8-5=-5 you substitute 4 into x

-5=0

Step-by-step explanation:

in my opinion

total area = the width × the length

= (3x-4)(-8x+2)

= -24x²+6x+32x -8

= -24x² + 38x -8

Answer:

x^2+2x-6, or C

Step-by-step explanation:

We want to combine the values of both f(x) and g(x) into one equation.

We could write this as 2x+1+x^2-7

Simplified- x^2+2x-6, or C

Answer:

35

Step-by-step explanation:

5*³√8-（-4）*√16+9=5*2+4*4+9=35

[tex](x - 4) {}^{2} + (y - 1) {}^{2} = r {}^{2} [/tex]

passes through ( 4 , -4 )

[tex](4 - 4) {}^{2} + ( - 4 - 1) {}^{2} = r {}^{2} [/tex]

[tex]r {}^{2} = ( - 5) {}^{2} [/tex]

[tex]r {}^{2} = 25[/tex]

[tex]r = \sqrt{25} = 5[/tex]

Your radius is 5 units

[tex]c = 2\pi \: r \\ c = 2 \times 3.14 \times 5 \\ c = 31.4[/tex]

Place your center at the point x=4 and y=1

Then take your radius 5 units by going straight down left right or up by 5 units

AND DRAW