The door on a model building is 2 inches tall. The door on the actual building is 8 feet tall.
What was the scale used?
01:24

The value of 'x' is 10°

We have that supplementary angles sum up to 180

M∠A = (6x +4)° and m∠B = (10x + 16)°.

Then,

6x + 4 + 10x + 16 = 180

Collect like terms

16x + 20 = 180

16x = 180 - 20

16x = 160

x = 160/ 16

x = 10°

Thus, the value of 'x' is 10°

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Step-by-step explanation:

გჰჰბფჯ არ არის დაწერეთ პირველი კომენტარი არ არის დაწერეთ პირველი კომენტარი არ არის დაწერეთ პირველი

The sentence indicates that the increase in the value of a coin collection was exponential as such increase was continuous and constant in time. (Correct choice: A)

Exponential functions are trascendent expressions, these are, expressions that cannot be described algebraically, that are defined by the following expressions:

[tex]f(x) = a \cdot \left(1+ \frac {r}{100}\right)^{x}[/tex]     (1)

Where:

Exponential functions are used to represent constant continuous increases or decreases in terms of the independent variable. The sentence indicates that the increase in the value of a coin collection was exponential as such increase was continuous and constant in time. (Correct choice: A)

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Step-by-step explanation:

a probability is always the number of desired cases over the number of total possible cases.

in this situation the number of total cases is 7 : days of the week.

the 3 probabilities just differ based on the number of desired cases.

P(Monday) : there is only one desired case out of the 7 possible ones. so, the probability is

1/7 = 0.142857143...

P(starts with S) : 2 desired cases (Saturday and Sunday).

so the probability is

2/7 = 0.285714286...

P(Monday or starts with S) : 3 desired cases (Monday, Saturday, Sunday).

so the probability is

3/7 = 0.428571429...

The probability that a randomly selected riverside high school student is in twelfth grade is 0.4

The complete question is in the attached image

From the image, we have:

The probability is then calculated as:

P = 200/500

Divide

P = 0.4

Hence, the probability that a randomly selected riverside high school student is in twelfth grade is 0.4

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Answer:

the answer is C

Step-by-step explanation:

The polynomial which is equivalent to fog(x) is 2/x + 1.

A polynomial is a type of expression. An expression is a mathematical statement without an equal-to sign (=).

Here,

given functions are;

f(x) = x + 1   ;     g(x) =  2/x

Now, we need to compose fog(x) from the given function;

fog(x)  =   f ( g(x) )

          =  f( 2/x)

          = 2/x + 1

Thus, the polynomial which is equivalent to fog(x) is 2/x + 1.

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Answer:

overfishing

Step-by-step explanation:

I'm not completely sure but i think it's overfishing because it has more to relate to the food chain which would be most likely to lead to a shortage

Answer:

1/36

Step-by-step explanation:

Rolling a 1 the first time has an 1/6 chance and rolling a 4 has an 1/6 chance the 2nd time.

1/6 * 1/6 = 1/36 chance.

Answer:

btyivh

he was so much for your support of school and I have a great day of school and I have a great day of school and I have a great day of school

The solution points to the system graph are (–2,–4) and (4,8). Therefore, option A is correct.

We need to find the solution to the given function.

The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be at the point where the two lines intersect.

From the given graph we can see that the two functions are intersecting at (–2,–4) and (4,8).

The solution points to the system graph are (–2,–4) and (4,8). Therefore, option A is correct.

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The y-intercept of the continuous function in the table is (0, –6)

To determine the y-intercept coordinate, we must understand the y-intercept is a point on a graph where the line passes through the y-axis at x = 0.

With the above information in mind, we can easily obtain the y-intercept coordinate as follow:

From the the two columns given in the question, the value of y when x = 0 is -6.

Thus, the y-intercept coordinate is (0, -6)

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(a) [tex]\sin(-194^{\circ})=-\sin 194^{\circ}=-(-\sin 14^{\circ})=\sin 14^{\circ}[/tex]

(b) [tex]\cos 481^{\circ}=\cos 121^{\circ}=-\cos 59^{\circ}[/tex]

(c) [tex]\tan 185^{\circ}=\tan 5^{\circ}[/tex]

(d) [tex]\sin 331^{\circ}=\sin(-29^{\circ})=-\sin 29^{\circ}[/tex]

The amount he would invest today to have enough money in ten years if the investment offers an interest rate of 6.0% compounded monthly is $13740.79

The formula for calculating the compound interest is given as:

A = P(1+r/n)^nt

Given the following parameters

25000 = P(1+0.06/12)^12(10)

25000 = P(1+0.005)^120

25000 = P (1.005)^120

25000 = 1.8194P

P =  25000/1.8194

P = $13740.79

Hence the amount he would invest today to have enough money in ten years if the investment offers an interest rate of 6.0% compounded monthly is $13740.79

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Answer:

No

Step-by-step explanation:

[tex]300 \times .9 \times 1.1 = 297[/tex]

The statements A, B, D, and E are defined.

When we multiply matrices, the number of columns of the 1st matrix must equal the number of rows of the 2nd matrix.

When we add or subtract matrices, the number of rows and columns must be the same.

A) If C is 7x3 and A is 3x2, that means C has 3 columns and A has 3 rows. So C * A is defined.

B) When you transpose a matrix, the number of rows and columns are switched. So C^T has 3 rows and 7 columns. So C^T is defined.

C) B has 2 columns and C has 7 rows, so B * C is not defined.

D) Because A and B have the same number of rows and columns, we can add them. So A + B is defined.

E) B^T has 2 rows and 3 columns, and C^T has 3 rows and 7 columns. So B^T has the same number of columns as the number of rows as C^T. So B^T * C^T is defined.

F) C and A have different numbers of rows and columns, so C-A is not defined.

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Answer:

d

Step-by-step expladnation:

The factors of the trinomial to the given quadratic expression are (x+1) and (x-4)

Given the quadratic equation below

f(x) = x^2 - 3x - 4

Factorize

f(x) = x^2 - 4x + x - 4 = 0
f(x) = x(x - 4) + 1(x - 4) = 0
(x+1)(x-4) = 0

Hence the factors of the trinomial to the given quadratic expression are (x+1) and (x-4)

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Answer:

6.5 %

Step-by-step explanation:

Full commission would then be   2 * 3152.50 = 6305

Full commission percentage of sale is then:

6305 / 97000   * 100 % = 6.5 %

To achieve his goal of paying off $430,000 in 10 years, Rob Herndon needs to make $34,186.97 at 5% compounded annually.

A future value refers to a value on a future date based on an assumed growth rate of interest over time.

The future value can be determined using the FV formula or table.

We can also compute the future value using an online finance calculator as follows:

N (# of periods) = 10 years

I/Y (Interest per year) = 5%

PV (Present Value) = $0

FV (Future Value) = $430,000

Results:

PMT = $34,186.97

Sum of all periodic payments = $341,869.70

Total Interest= $88,130.30

Thus, for Rob Herndon to achieve his goal of paying off $430,000 in 10 years, he needs to make $34,186.97 at 5% compounded annually.

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Considering the box-and-whisker plot, it is found that:

a) 25% of the students scored less than 60.

b) 25% of the students received a score greater than 85.

A box and whisker plot shows three things:

From the plot given in the graph, we have that:

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Answer:

.38

Step-by-step explanation:

sin is the opposite side from angle T over the hypotenuse.

5/13

Answer: 49/9

Step-by-step explanation:

[tex]2=3\sqrt{4x}-12\\\\14=3\sqrt{4x}\\\\\frac{14}{3}=\sqrt{4x}\\\\4x=\frac{196}{9}\\\\x=\frac{196}{36}\\\\x=\frac{49}{9}[/tex]

Answer:

write three methods of writing set. Give one example of each method.

Answer:

$1.20 per dozen eggs, $1.68 per dozen oranges

Step-by-step explanation:

Let x=cost of one dozen eggs and y=cost of one dozen oranges.

3x + 2y = 6.96------>3x + 2y = 6.96

2x + y = 4.08-------->4x + 2y = 8.16

---------------------

x = 1.20

4(1.20) + 2y = 8.16

4.80 + 2y = 8.16

2y = 3.36

y = 1.68

Answer:

The cost of one dozen of egg is 1.2

The cost of one dozen of orange is 1.68

Step-by-step explanation:

The solution is in the image

The values of x in x²-x-2=0​ are x = 2 or -1

The equation is given as:

x²-x-2=0​

Add 2 to both sides

x² - x = 2

Take the coefficient of x

k = -1

Divide by 2

k/2 = -1/2

Square both sides

(k/2)² = 1/4

Add 1/4 to both sides of x² - x = 2

x² - x + 1/4= 2 + 1/4

Evaluate

x² - x + 1/4= 9/4

Express as perfect square

(x - 1/2)² = 9/4

Take the square roots

x - 1/2 = ±3/2

This gives

x = 1/2 ±3/2

Evaluate

x = 2 or -1

Hence, the values of x in x²-x-2=0​ are x = 2 or -1

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Answer: plug in the coordinates for x and y

Step-by-step explanation:

take a look at my work if you still need some help

Answer:

28

Step-by-step explanation:

The diagram shows a square, and it is known that all side lengths for a square are equal. We can use these information on hand and write the following equation to find the side length:

7x + 3 = 5x + 8 transfer like terms to the same side of the equation

7x - 5x = 8 - 3 add/subtract

2x = 5 divide both sides by 2

x = 2.5 to find a side length simply replace x with 2.5

5x + 8 = 5*(2.5) + 8

5*(2.5) + 8 = 28

Answer:

4$

Step-by-step explanation:
The ratio between the $5.80 spent for 58 text messages is $0.10. This means that each text message sent is $0.10. So you just multiply $0.10 and 40 text messages to find that it costs $4 to send 40 messages.

Answer:

4.  Horizontal shrink by a factor of ¹/₅

5.  Left 5, Up 5

6.  Right 5, Down 5

Step-by-step explanation:

Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]

Identify the transformations that take the parent function to the given function.

Question 4

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=(5x)^3[/tex]

Comparing the parent function with the given function, we can see that the x-value of the parent function has been multiplied by 5.

Therefore, the transformation is:

[tex]y=f(5x) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{5}[/tex]

As a > 1, the transformation visually is a compression in the x-direction, so we can also say:  Horizontal shrink by a factor of ¹/₅

Question 5

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=(x+5)^3+5[/tex]

Comparing the parent function with the given function, we can see that there are a series of transformations:

Step 1

5 has been added to the x-value of the parent function.

[tex]f(x+5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units left}[/tex]

Step 2

5 has then been added to function.

[tex]f(x+5)+5 \implies f(x+5) \: \textsf{translated}\:5\:\textsf{units up}[/tex]

Transformation:  Left 5, Up 5

Question 6

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=(x-5)^3-5[/tex]

Comparing the parent function with the given function, we can see that there are a series of transformations:

Step 1

5 has been subtracted from the x-value of the parent function.

[tex]f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}[/tex]

Step 2

5 has then been subtracted from function.

[tex]f(x-5)-5 \implies f(x-5) \: \textsf{translated}\:5\:\textsf{units down}[/tex]

Transformation:  Right 5, Down 5

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Answer:

4) Horizontal shrink by a factor of 1/5

5) Left 5, Up 5

6) Right 5, Down 5

Explanation:

Main parent function: f(x) = x^3

4.) f(x) = (5x)^3

Comparing it with f(ax) which gives horizontal compression when a > 1 or horizontal stretch when 0 < |a| < 1 by a factor of 1/a

The function has been compressed horizontally by a factor of 1/5.

5.) f(x) = (x+5)^3 + 5

Comparing with f(x + c) + d, gives function moved c units left, d units up.

The function has moved 5 units left and 5 units up.

6.) f(x) = (x-5)^3 - 5

Comparing with f(x - c) - d, gives function moved c units right, d units down.

The function has moved 5 units right, 5 units down.

The length of the flagpole is x - 5  yards

The complete question is in the image

The area of the flagpole is given as:

Area = x^2 - 10x + 25

Expand the expression

Area = x^2 - 5x -5x + 25

Factorize the expression

Area = (x - 5)(x - 5)

Express as squares

Area =(x - 5)^2

The area of a square is

Area = Length^2

So, we have:

Length = x - 5

Hence, the length of the flagpole is x - 5  yards

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