how to find the scale factor of two
similar shapes​

Should be 160 chairs

To determine the total number of chairs in the restaurant, multiply the count of tables with 2 chairs (20 tables) by 2, and those with 4 chairs (30 tables) by 4, and sum the two products to get a total of 160 chairs.

To calculate the total number of chairs in the restaurant, we first need to find out how many tables are there with 2 chairs and how many with 4 chairs. Since 40% of the tables have 2 chairs, we multiply 40% (or 0.4) by the total number of tables (50) to find the number of tables with 2 chairs, which equals to 20 tables.

The remaining 60% of the tables have 4 chairs, so we multiply 60% (or 0.6) by the total number of tables (50) to find the number of tables with 4 chairs, which equals to 30 tables.

To find the total number of chairs, we multiply the number of tables with 2 chairs (20) by 2 and the number of tables with 4 chairs (30) by 4, then we add the two results together:

Tables with 2 chairs: 20 tables imes 2 chairs/table = 40 chairs

Tables with 4 chairs: 30 tables imes 4 chairs/table = 120 chairs

So, the total number of chairs in the restaurant is:

40 chairs + 120 chairs = 160 chairs

Answer:

Options B,C,E are true.

Step-by-step explanation:

It has been given in the question ∠ACD is supplementary to ∠ACE and ∠BCD

∠ACD ≅ ∠BCE

Option A. ∠ACE is supplementary to ∠BCD

False. They are not lying on a point of straight line.

∠ACE + ∠BCD ≠180°

Option B. ∠BCE is supplementary to ∠ACE

Since ∠ACD + ∠ACE = 180° [Given]

and ∠ACD ≅ ∠BCE [Given]

Therefore, ∠BCE + ∠ACE = 180°

TRUE.

Option C. ∠BCD is supplementary to ∠BCE

Since ∠ACD + ∠BCD = 180°[Given]

and ∠ACD ≅ ∠BCE [Given]

So ∠BCE + ∠BCD = 180°

TRUE.

Option D. ∠ACE ≅ ∠BCE

Since ∠ACD + ∠ACE = 180°

And ∠ACD + ∠BCD = 180°

This is clear from these equations that ∠ACE is supplementary to ∠BCD.

FALSE :

Option E. ∠BCD is congruent to ∠ACE

As we have already proved in option D. ∠BCD ≅ ∠ACE

TRUE

Therefore, Options B, C, E are TRUE

Answer:

The volume of the prism = 300 units³

Step-by-step explanation:

* Lets study the triangular prism

- The triangular prism has 6 faces

- Two right triangular bases

- Four rectangular side faces

- The volume of the prism = area of its base × its height (altitude)

* Now lets solve the problem

∵ The base is a right triangle with a hypotenuse of 13 units and

   a leg of 12 units

∵ The area of the right triangle = 1/2 × leg1 × leg2

- You can find the length of other leg by using Pythagoras theorem

∵ (hypotenuse)² = (leg1)² + (leg2)²

∵ hypotenuse = 13 units

∵ leg1 = 12 units

∴ (13)² = (12)² + (leg2)²

∴ 169 = 144 +  (leg2)² ⇒ subtract 144 from both sides

∴ 25 =  (leg2)² ⇒ take √ for both sides

∴ leg2 = 5 units

- The area of the right triangle = 1/2 × leg1 × leg2

∴ The area of the base = 1/2 × 12 × 5 = 30 units²

∴ The volume of the prism = 30 × 10 = 300 units³

Answer:

7 ft bRo

Step-by-step explanation:

wow i took 21 and divided it by three and i got SEVEN

how old are you like four

The height of the flat screen TV can be calculated by dividing the given area (21 square feet) by the given width (3 feet). This gives us a height of 7 feet.

In this problem, we are given the area of the flat screen TV and the width. The area of a rectangle is calculated by multiplying the width and the height, so to find the height, we can divide the area by the width.

Let's denote the height as 'h'. So, the formula will be: Width times height = Area of the screen, or in our case, 3 feet times h = 21 square feet. Solving this equation gives us h = 21 ÷ 3 = 7 feet.

So, the height of the TV is 7 feet.

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Answer:

there are no answers it is false just did it

Step-by-step explanation:

ANSWER

The second term is 7.

EXPLANATION

The given sequence has it's first term to be:

[tex]t_1 = 3[/tex]

The recursive definition is :

[tex]t_{n+1}=2t_n+n[/tex]

To find the second term , we substitute n=1,

to obtain,

[tex]t_{1+1}=2t_1+1[/tex]

This implies that:

[tex]t_{2}=2t_1+1[/tex]

[tex]t_{2}=2(3)+1[/tex]

Simplify:

[tex]t_{2}=6+1[/tex]

[tex]t_{2} = 7[/tex]

Answer:

The second term of the sequence is 7 ⇒ the 2nd answer

Step-by-step explanation:

* Lets revise the recursive formula

1. Determine if the sequence is arithmetic (Do you add, or subtract, the

  same amount from one term to the next?)

2. Find the common difference. (The number you add or subtract.)

3. Create a recursive formula by stating the first term, and then stating

   the formula to be the previous term plus the common difference.

   a1 = first term;

   an+1= an + d

- Where:

# a1 = the first term in the sequence

# an = the nth term in the sequence  

# an+1 = the term after the nth term  

# n = the term number

# d = the common difference.

* Now lets solve the problem

∵ The recursive definition is tn+1 = 2 tn + n and t1 = 3

- Lets find the 2nd term

∵ t1 = 3

∵ tn+1 = 2 tn + n

* To find the second term put n = 1

∴ t2 = 2 (3) + 1

∴ t2 = 6 + 1 = 7

∴ t2 = 7

* The second term of the sequence is 7

Answer:

see explanation

Step-by-step explanation:

Note that the sum of the coefficients of g(x)

1 + 2 - 3 = 0

Hence x = 1 is a root of g(x) and (x - 1) is a factor

Note the sum of the coefficients of f(x)

1 - 3 - 13 + 15 = 0

hence x = 1 is a root of f(x) and (x - 1) is a factor

Since (x - 1) is a factor of both

Then f(x) is also divisible by x² + 2x - 3

Answer:

2 miles.

Step-by-step explanation:

Answer:5

Step-by-step explanation:

To solve the expression 2 + 3x16 - 2x21 - 3, we apply the order of operations rule (PEMDAS) without any parentheses or exponents to handle. The expression simplifies to 5.

The student is asking to solve a mathematical expression using the correct order of operations. The proper order to solve math expressions is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This rule is often remembered by the acronym PEMDAS.

Let's solve the expression step by step:

First calculate any operations inside parentheses. In the given problem, there are none.

Next, perform all multiplication and division operations from left to right. 3x16 equals 48, and 2x21 equals 42.

Subtract and add from left to right. So, 2 + 48 - 42 - 3 = 5.

Therefore, the expression

2 + 3x16 - 2x21 - 3= 5

.

Answer:

4

Step-by-step explanation:

-5+9=4

Definition of average rate of change a function g(x) over an interval [a,b]:

[tex]A = \dfrac{g(b)-g(a)}{b-a}[/tex]

Substitute your function and your interval:

[tex]A = \dfrac{(3^6-6)-(3^0-6)}{3-0} = \dfrac{3^6-6-3^0+6}{3} = \dfrac{3^6-1}{3} = \dfrac{728}{3}[/tex]

The average rate of change of the function gx) = 3(2x) - 6 over the interval [0,3] is calculated as (g(3) - g(0)) / (3 - 0) which equals to 6.

The average rate of change of a function over an interval [a,b] is defined as:

(g(b) - g(a)) / (b - a)

Here, the function g(x) = 3(2x) - 6, and the interval is [0,3]. Let's calculate g(3) and g(0).

g(3) = 3(2*3) - 6 = 12

g(0) = 3(2*0) - 6 = -6

Now, apply these values to the average rate of change formula:

(g(3) - g(0)) / (3 - 0) = (12 - (-6)) / 3 = 18 / 3 = 6.

So, the average rate of change of the function g(x) over the interval [0,3] is 6.

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The answer is -12 and 9. You have to factor the equation first. Once you do this, than you can set each problem equal to zero and solve. I hope this helps.

Answer:

1

Step-by-step explanation:

In each set, there is a difference of 1 between the two x's.

I just did it its 2 4 and 8 i think

Answer:

x = 14

Step-by-step explanation:

3(x + 3) - 2x = 23

3x + 9 - 2x = 23

x + 9 = 23

x = 14

ANSWER

The discriminant is 49.

EXPLANATION

The given quadratic equation is:

[tex]0 =2{x}^{2} + 3x - 5[/tex]

We can rewrite this as

[tex]2{x}^{2} + 3x - 5 = 0[/tex]

Comparing this to

[tex]a{x}^{2} + bx + c = 0[/tex]

We have a=2,b=3, c=-5.

The discriminant is given by:

[tex]D = {b}^{2} - 4ac[/tex]

We plug in the values to get:

[tex]D = {3}^{2} - 4(2)( - 5)[/tex]

[tex]D =9 + 40[/tex]

[tex]D = 49[/tex]

Answer:

D IS THE ANSWER (49)

Step-by-step explanation:

Answer:

A. 0.5

B. 4.5

C. 1.5

D. 0.5

Step-by-step explanation:

y varies inversely with x can be written as:

y = k/x

where k is constant of variation.

1. value of A

x=A, y = 9 and k = 4.5 (given)

y = k/x

9 = 4.5/A

=> A = 4.5/9

=> A=0.5

2. Value of B

x =1, y= B, k = 4.5

y = k/x

B = 4.5/1

B= 4.5

3. Value of C

x=C, y=3. k=4.5

y = k/x

3 = 4.5/C

3C = 4.5

C = 4.5/3

C = 1.5

4. Value of D

x= 9, y=D, k=4.5

y = k/x

D = 4.5/9

D = 0.5

Answer:

[tex]A=0.5[/tex]

[tex]B=4.5[/tex]

[tex]C=1.5[/tex]

[tex]D=0.5[/tex]

Step-by-step explanation:

The form an the equation of inverse variation is:

[tex]y=\frac{k}{x}[/tex]

Being "k" the constant of variation.

Since we know "k" and we have the values given in the table, we can find the missing values:

To find A we need to substitute the [tex]y=9[/tex], the value of "k" and [tex]x=A[/tex] into the equation and solve for "A":

[tex]9=\frac{4.5}{A}[/tex]

[tex]A=\frac{4.5}{9}=0.5[/tex]

To find B we need to substitute the [tex]x=1[/tex], the value of "k" and [tex]y=B[/tex] into the equation:

[tex]B=\frac{4.5}{1}=4.5[/tex]

To find C we need to substitute the [tex]y=3[/tex], the value of "k" and [tex]x=C[/tex] into the equation and solve for "C":

[tex]3=\frac{4.5}{C}[/tex]

[tex]C=\frac{4.5}{3}=1.5[/tex]

To find D we need to substitute the [tex]x=9[/tex], the value of "k" and [tex]y=D[/tex] into the equation:

[tex]D=\frac{4.5}{9}=0.5[/tex]

Answer:

Population will be approx 1606300.

Step-by-step explanation:

Given that a city’s population is about 763,000 and is increasing at an annual rate of 1.5%. Now we need to predict the population of the city in 50 years.

We can use growth formula

[tex]A=P\left(1+r\right)^t[/tex]

Where P=763000

rate r=1.5% = 0.015

time t = 50 years

Plug these values into above formula

[tex]A=763000\left(1+0.015\right)^{50}[/tex]

[tex]A=763000\left(1.015\right)^{50}[/tex]

[tex]A=763000\left(2.10524242061\right)[/tex]

[tex]A=1606299.96692[/tex]

Hence population will be approx 1606300.

Therefore, the predicted population of the city in 50 years is approximately [tex]$1,586,997$[/tex].

To predict the population of the city in 50 years, we can use the formula for compound interest, where the principal is the initial population, the interest rate is the annual growth rate, and the time is 50 years.

Given:

- Initial population = 763,000

- Annual growth rate = 1.5% = 0.015

Step 1: Calculate the total growth factor after 50 years using the compound interest formula.

Growth factor = [tex](1 + r)^_t[/tex]

Growth factor =[tex](1 + 0.015)^_{50}[/tex]

Growth factor = [tex]$1.015^{50} = 2.079$[/tex]

Step 2: Calculate the final population by multiplying the initial population with the growth factor.

Final population = Initial population × Growth factor

Final population = 763,000 × 2.079

Final population = [tex]$1,586,997$[/tex]

Answer: SECOND OPTION

Step-by-step explanation:

The area of a parallelogram can be calculated with this formula:

[tex]A=bh[/tex]

Where "b" is the of one base and "h" is the height.

You can observe in the figure that "b" and "h" are:

[tex]b=AB=4\sqrt{2}ft\\\\h=AX=3ft[/tex]

Then, substituting these values into the formula, you get that the area of the given parallelogram is:

[tex]A=(4\sqrt{2}ft)(3ft)\\\\A=12\sqrt{2}ft^2[/tex]

This matches with the second option.

Answer:

12√2 sq. ft.

Step-by-step explanation:

Hope this helps.

Answer:

[tex]\frac{1}{4}[/tex] of the books in the book store are mystery fiction books.

Step-by-step explanation:

Let x represent all the books in the books store.

Then, the fraction of books that are fiction books is [tex]\frac{3}{4}x[/tex]

We have that; [tex]\frac{1}{3}[/tex] of the fiction books are mystery books.

The fraction of the books at the  bookstore that are mystery fiction  books is [tex]\frac{1}{3}\times \frac{3}{4}x=\frac{1}{4}x[/tex].

Therefore [tex]\frac{1}{4}[/tex] of the books in the bookstore are mystery fiction books.

Answer:

1/4

Step-by-step explanation:

Answer:

A. 15%

Step-by-step explanation:

percent change = (new number - old number)/(old number) * 100%

The new number is the increased area, 25,587.5 sq yd, and the old number is the original area, 22,250 sq yd.

percent change = (25,587.5 sq yd - 22,250 sq yd)/(22,250 sq yd) * 100%

percent change = (3,337.5 sq yd)/(22,250 sq yd) * 100%

percent change = 0.15 * 100%

percent change = 15%

Since the percent change is a positive number, it is a percent increase.

The percent increase was 15%.

Answer: A. 15%

The student's question relates to the point P with the polar coordinates (3, -π/3). Polar coordinates are not unique, so we can find all coordinates of point P by adding multiples of 2π to the angle part of the coordinate, that is, (3, -π/3 + 2πn) where n is an integer.

The polar coordinates system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from the origin (point O) and an angle measured anti-clockwise from an arbitrary direction, usually the x-axis.

Each point is represented by the ordered pair (r, θ). Our point P has the polar coordinates (3, -π/3). However, polar coordinates are not unique for a given point. To find all polar coordinate pairs for point P, we add multiples of 2π to the angle part of the coordinate pair, as a complete revolution is 2π in radians. Therefore, alternative polar coordinate pairs for point P would include (3, -π/3 + 2πn) where n is an integer.

Examples include:

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Answer:

x = 34; y = 14

Step-by-step explanation:

Step 1: Make the equations

x + y = 48

x - y = 20

Step 2: Solve the equations

x + y = 48

x - y = 20

2x = 68

x = 34

34 + y = 48

y = 14

Answer: [tex]V=11.775\ in^3[/tex]

Step-by-step explanation:

You need to use the formula for calculate the volume of a cone. This is:

[tex]V=\frac{1}{3}\pi r^2h[/tex]

Where "r" is the radius and "h" is the height.

You know that the diameter of the cone-shaped paperweight is 3 inches. Then, you need to divide the diameter by 2 to find the radius:

[tex]r=\frac{3in}{2}\\\\r=1.5\ in[/tex]

Now you know that:

[tex]r=1.5\ in\\h=5\ in\\\pi=3.14[/tex]

Substituting these values into the formula [tex]V=\frac{1}{3}\pi r^2h[/tex], you get that the volume of the  paperweight is:

[tex]V=\frac{1}{3}(3.14)(1.5\ in)^2(5\ in)[/tex]

[tex]V=11.775\ in^3[/tex]

The volume of the paperweight will be 11.76 cubic inches.

Let d be the diameter of the base circle and h be the height of the cone.

Then the volume of the cone will be

V = 1/12 x πd² x h

The cone-shaped paperweight has a diameter of 3 inches and a height of 5 inches.

Then the volume of the paperweight will be

V = 1/12 x π(3)² x 5

V = 1/12 x 3.14 x 9 x 5

V = 11.76 cubic inches

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Answer:divide the diameter by 2 and plug the values for volume, pi, and radius into the formula for volume of a cylinder. Next, square the radius and multiply the values together. Then, divide both sides by 200.96 for the answer, remembering to include the appropriate unit of measurement

Step-by-step explanation:

Finding A Diameter Of A Cylinder Is Easy.

If You Know The Radius, Multiply The Radius By 2 To get Your Diameter,

Have A Great Day!

Answer:

14

Step-by-step explanation:

2k - 1 is linear, so this is an arithmetic series.  The sum of an arithmetic series is:

S = (n/2) (a₁ + an)

Here:

S = 196

a₁ = 2(1) - 1 = 1

an = 2n - 1

Solving:

196 = (n/2) (1 + 2n - 1)

196 = (n/2) (2n)

196 = n²

n = 14

Answer:

2 reals and 2 rationals.

Step-by-step explanation:

The discriminate gives

b^2 - 4*a*c

b = -7

a = 5

c = 2

(-7)^2 - 4(5)(2)

49 - 40

9

Taking the square root gives you +/-3

The discriminate tells you that there are 2 roots, both real and both rational

x = [(-7) +/- 3  ]/2*5

x = (- 7 - 3)/10 = - 1

x = (- 7 + 3)/10 = -0.4

Answer:

[tex]\frac{\tan 60\degree}{\cos45 \degree}= \sqrt{6}[/tex]

Step-by-step explanation:

We want to evaluate

[tex]\frac{\tan 60\degree}{\cos45 \degree}[/tex]

We use special angles or the unit circle to obtain;

[tex]\frac{\tan 60\degree}{\cos45 \degree}=\frac{\sqrt{3}}{\frac{\sqrt{2}}{2}}[/tex]

This implies that;

[tex]\frac{\tan 60\degree}{\cos45 \degree}=\sqrt{3}\div \frac{\sqrt{2}}{2}[/tex]

[tex]\frac{\tan 60\degree}{\cos45 \degree}=\sqrt{3}\times \sqrt{2}[/tex]

[tex]\frac{\tan 60\degree}{\cos45 \degree}= \sqrt{6}[/tex]

Answer:

[tex]\sqrt{6}[/tex].

Step-by-step explanation:

[tex]\frac{tan(60)}{cos(45)}[/tex]

[tex]= \frac{\frac{sin(60)}{cos(60)}}{cos(45)}[/tex]

[tex]= \frac{sin(60)}{cos(60)*cos(45)}[/tex]

[tex]= \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}*\frac{\sqrt{2}}{2}}[/tex]

[tex]= \frac{\frac{\sqrt{3}}{2}}{\frac{\sqrt{2}}{4}}[/tex]

[tex]= \frac{4\sqrt{3}}{2\sqrt{2}}[/tex]

[tex]= \frac{2\sqrt{3}}{\sqrt{2}}[/tex]

[tex]= \frac{2\sqrt{3}\sqrt{2}}{2}[/tex]

[tex]=\sqrt{3}\sqrt{2}[/tex]

[tex]=\sqrt{6}[/tex].

186-140=46/2=23 weeks -2/23=slope

Answer:

Equation is W = -2t+186

It will take 23 weeks to achieve the goal.

Slope = -2 pounds per week

Step-by-step explanation:

Here  current Weight  is 186 pounds

and her goal is to weigh 140 pounds

she can safely lose 2 pounds per week which is the slope

for t =0 , W =186 pounds  (Y intercept )

    slope = 2 pounds per week

since its decreasing therefore its negative

W = -2t+186 is the equation

To achieve the desired goal W = 140

plugging W = 140 and solving for t

140 = -2t+186

2t = 186-140

2t = 46

t = 23

It will take 23 weeks to achieve the goal.

Slope = -2 pounds per week

Answer:

Option  C) 70%

Step-by-step explanation:

we know that

To determine the percentage of games played that won, divide the number of games won by the total number of games played.

so

[tex]P=14/20=0.70[/tex]

Convert to percentage (multiply by 100)

[tex]0.70*100=70\%[/tex]