a history book weights 24 oz more than a math book. the marh book is 75% the weight of the history book. how much does each book weight

Answer:

  23.20°

Step-by-step explanation:

All three sides of this right triangle are given, so the acute angle of interest can be found using any of the inverse trig functions.

The tangent of the angle is the ratio of opposite and adjacent sides:

  Tan = Opposite/Adjacent

Here, that means ...

  tan(α) = 3/7

To find the value of α, we need to use the inverse tangent function, also called the arctangent function.

  α = arctan(3/7) ≈ 23.19859°

  α≈ 23.20°

Answer:

x = 45°

Step-by-step explanation:

Vertical Angle Theorem

When two straight lines intersect, they form two pairs of angles.  The vertically opposite (non-adjacent) angles are congruent (equal).

From inspection of the given diagram, the straight line with points C and D and the straight line with points F and G intersect at point E.

Therefore, angles ∠FEC and ∠DEG are vertically opposite, and so they are equal.

From inspection of the diagram:

Therefore:

⇒ ∠FEC =∠DEG

⇒  x = 45°

Answer:

.38

Step-by-step explanation:

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

5/13

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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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:

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:

x=1,2,3,4 y=3,7,11,15

firstly find d such that d=7-3=4

afunction f(x)= 3+4(x-1)

and x= 1,2,3,4 y=3,9,27,81

y=x²

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:

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: Then the graph of the function f(x) will change shifting vertically down (because the negative sign in 4) by 4 tons.

Answer:

d

Step-by-step expladnation:

Answer:

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

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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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:

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 %

7 evaluates the expression a2 + b.

option a.7 is the correct choice which evaluates the given expression.

Given values are a = 2 and b =3

the given expression is = a2 + b

To evaluate an expression, we first replace the variable with the given number, then we use the order of operations to simplify the expression.

Substitute these value in the given expression.

=2 × 2 ₊ 3

=7

Every time we replace the variables with its values  we get the answer as 7. The other options present does not satisfy the equation.

For ex: 25 , we don't get this number when we substitute the given values in the expression. 10 is also not what we get when we solve the expression. Likewise other options are also invalid.

Hence we get the answer as 7.

Your question is incomplete. Please find the missing content here.

Which of the following choices will evaluate the expression a2 + b when a = 2 and b = 3?

a. 7

b. 10

c. 25

d. None of these choices are correct

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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:

Step-by-step explanation:

5 + 1 = 6 units

90 : 6 = 15 (one unit)

15 * 5 = 75°

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 equivalent form of the  compound inequality  are −2x − 8 < -44 and −2x − 8 ≥ −4

Inequality are expression not separated by an equal sign. Given the compound inequality

−44 > −2x − 8 ≥ −48?

Add 8 to all the sides

−44 + 8> −2x − 8+8 ≥ −48 + 8

−36 > −2x  ≥ −40

This can be also be written as

−44 > −2x − 8 and −2x − 8 ≥ −48

Changing the sides will change the sign to have

−2x − 8 < -44 and −2x − 8 ≥ −48

Hence the equivalent form of the  compound inequality  are −2x − 8 < -44 and −2x − 8 ≥ −4

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Answer: $201.81

Step-by-step explanation:

The total amount of faux fur required is [tex]6(3.1)=18.6[/tex] square yards.

Multiplying this by $10.85 per square yard, we get the total cost is [tex](18.6)(10.85)=\$201.81[/tex]

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

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: 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]

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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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 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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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