Find the value of the trigonometric ratio, tan C.

Answer:

6 Units squared.

Look at file for explanation.

Answer:

the equation of the line in slope-intercept form is;

[tex]y=8x-26[/tex]

Step-by-step explanation:

First use the formula for the slope of the segment that joins the two given points:

[tex]slope=\frac{y_2-y_1}{x_2-x_1} =\frac{6-(-2)}{4-3}=\frac{8}{1} =8[/tex]

now that we have the slope, we can use the point-slope form of a line to find the line with slope 8 that passes through any of the given points, for example through (3, -2):

[tex]y-y_0=m\,(x-x_0)\\y-(-2)=8\,(x-3)\\y+2=8\,(x-3)\\y=8x-24-2\\y=8x-26[/tex]

Answer:

7x+10 cm

Step-by-step explanation:

To find the perimeter add up all the sides

There are 5 sides

3x+ 5+ 2x+2x+5

Combine like terms

3x+2x+2x   +5+5

7x + 10

The perimeter is 7x+10 cm

Answer:

\frac{2\cot \left(-240^{\circ \:}\right)\cos \left(-1050^{\circ \:}\right)-\cot ^2\left(50^{\circ \:}\right)}{\sec ^2\left(40^{\circ \:}\right)}

Step-by-step explanation:

ok

Answer:

Pythagorean Theorem: a² + b² = c² should be used.

Step-by-step explanation:

51² + b² = 60²

b² = 60² - 51²

b = 3√111

b = 31.607

Pythagorean Theorem is used to find any missing side of a right triangle if 2 other sides are present.

Answer:

Pythagoras theorem

EXPLANATION

HYPOTHENUS SQUARE =OPPOSITE SQUARE + ADJACENT SQUARE

i.e 60^2= 51^2+x^2

i.e 3600=2601+x^2

collecting like terms we have

3600-2601=x^2

999=x^2

√999=x

x=31.6

Answer:

B) 2775.9

Step-by-step explanation:

The missing options are:

A) 578

B) 2775.9

C) 134.591

D) 31.757

The digit 5 is in the tenths in 4.59. This means that its value is 0.5. A value 10 times greater is 10*0.5 = 5, that is, a 5 in the ones, like in 2775.9.

Step-by-step explanation:

45X + 2000 = Y

Where X = Number of units

Y = Total Cost

The total cost of producing x units for which the fixed costs are $2500 and the cost per unit is $40 is  T(x) = 40x + 2500.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The total cost of producing x units for which the fixed costs are $2500 and the cost per unit is $40.

Assuming total cost to be T.

∴ T(x) = 40x + 2500.

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Answer:

x = 3

Inverse matrix:

[tex]A^{-1} = \begin{pmatrix} \frac{1}{9} & \frac{2}{9} \\ \frac{1}{3} & -\frac{1}{3} \end{pmatrix} \quad[/tex]

Step-by-step explanation:

Determinant: ad - bc

a = 3, b = 2, c = 3, d = -1

3 * (-1) - (2 * x) = -9

-3 - 2x = -9

-2x = -6

x = 3

For matrix

[tex]A = \begin{pmatrix}a & b\\c & d\end{pmatrix} \quad[/tex]

the inverse is

[tex]A^{-1} = \dfrac{1}{ad - bc}\begin{pmatrix}d & -b \\-c & a\end{pmatrix}\quad[/tex]

Here we have: det = -9

a = 3, b = 2, c = 3, d = -1

Inverse matrix:

[tex]A^{-1} = \dfrac{1}{-9}\begin{pmatrix} -1 & -2 \\ -3 & 3 \end{pmatrix}\quad[/tex]

[tex]A^{-1} = \begin{pmatrix} \frac{-1}{-9} & \frac{-2}{-9} \\\frac{-3}{-9} & \frac{3}{-9}\end{pmatrix} \quad[/tex]

[tex]A^{-1} = \begin{pmatrix} \frac{1}{9} & \frac{2}{9} \\\frac{1}{3} & -\frac{1}{3}\end{pmatrix}\quad[/tex]

Answer:

7 packages

Step-by-step explanation:

Total number of saplings = 15 + 20 = 35

Number of saplings per package = 5

Number of packages = Total saplings ÷ Number of saplings per package

                                   = 35 ÷ 5

                                     = 7

Answer:

7

Step-by-step explanation:

Answer:

840 female students

Step-by-step explanation:

The total percentage of students is 100%, so, the percentage of female  students = 100% - 47.5%

=52.5%

Multiply the total no. of students by the percentage to get the no. of female students.

1600 x 52.5%

= 840 female students

You can also obtain the same answer by first multiplying the male percentage to find the no. of male students, then subtracting it from the total 1600.

Answer:

The expressions are not equivalent.

Step-by-step explanation:

The answers would be 196 and 193 for t = 8

The answers would be 76  and 73 for t = 3

Answer:

1. -0.66666666666667

2. -1

3. 1.333

4. 1.5

Answer:

A

Step-by-step explanation:

The zeroes of the function are the x values when f(x) = 0 so we can write:

0 = x² + x - 30

0 = (x + 6)(x - 5) (To factor this we need to find 2 numbers that have a sum of 1 and a product of -30; these numbers are 6 and -5)

x + 6 = 0 or x - 5 = 0 (Use Zero Product Property)

x = -6, 5

Hey there! :)

Answer:

A. x = -6 and x = 5.

Step-by-step explanation:

Given:

f(x) = x² + x - 30

Factor the equation by finding two numbers that sum up to 1 and multiply into -30. We get:

-5, 6

Use these to express this quadratic function in factored form:

f(x) = (x - 5) (x + 6)

Set each factor equal to 0 to solve for the zeros of the equation:

0 = x - 5

x = 5

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

0 = x + 6

x = -6

Therefore, the correct answer is A. x = -6 and x = 5.

Hey there! :)

Answer:

m∠θ = 69°.

Step-by-step explanation:

If sin (21°) = 0.36 and cos θ = 0.36, the two angles are complementary because the sine and cosine values are equivalent. Therefore:

90 - 21 = 69°.

The correct answer is D) m∠θ = 69°.

Answer:

125.6 cubed inches

Step-by-step explanation:

1. 3.14(2)^2(10) - Multiply 3.14 with 2 squared and 10.

2. First find out what is 2 squared, which is 4. Then, multiply 4 with 3.14, which is 12.56.

3. Now, multiply 12.56 with 10 or just move the decimal point one place to the right, which gives you 125.6 cubed inches.

Answer:

radius

Step-by-step explanation:

That "fixed distance" is the 'radius' of the circle.

Hey there! :)

Answer:

Choice B.

Step-by-step explanation:

Since h(x) equals (g o f)(x):

f(x) is substituted for x in the equation g(x). We can go through the answer choices and choose the most suitable choice by substitution:

A. f(x) = x, g(x) = x/ x + 1

(g o f)(x) = x / x + 1. This is incorrect.

B. f(x) = x², g(x) = x / x + 1

(g o f)(x) = x² / x² + 1. This matches h(x), so this is correct.

C. f(x) = x + 1, g(x) = 1/x²

(g o f)(x) = 1/(x² + 2x + 1). This is incorrect.

D. f(x) = x + 1, g(x) = x²

(g o f)(x) = x² + 2x + 1. This is incorrect.

Therefore, B is the correct answer.

Answer:

25/18

Step-by-step explanation:

Additive inverse of a number X is the number which when is added to X =0

ex: additive inverse of 2 is -2 since 2 +(-2)=0

Multiplicative inverse of a number N is the number which when multiplied by N gives 1

ex: multiplicative inverse of 6/7 is 7/6

6/7*7/6=1

Ex of reciprocal is

5/9 & 9/5

7/6 & 6/7

Additive inverse of -5/6=5/6

Multiplicative inverse of 4/12 is 12/4

Reciprocal of 9/5 is 5/9

(5/6)*(12/4)*(5/9)=25/18

Answer:

(5/6)*(12/4)*(5/9)=25/18

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

There are 3 + 3 + 6 = 12 marbles in the bag and 12 * 12 = 144 ways to choose two marbles when replacing. There are 3 * 6 = 18 ways to choose a red marble and then a blue marble so the probability is 18 / 144 = 1 / 8.

Answer:

WHAT

Step-by-step explanation:

Answer:

5/3

Step-by-step explanation:

it should be y/x

you can count 5 up and 3 over

Answer:

8/5

Step-by-step explanation:

You can use the formula [tex]\frac{y_{1}-y_{2}}{x_{1}-x_{2}}[/tex] with a pair of points [tex](x_{1},y_{1})[/tex][tex](x_{2},y_{2})[/tex]. We can use points (1,4) and (-4,-4). Plugging in the equation we get (4-(-4))/(1-(-4)), which simplifies to 8/5, which is the slope.

Answer:

As x increases, the rate of change of f(x) exceeds the rate of change of g(x).

Step-by-step explanation:

Hope this helps :)

Answer:

The second box plot best represents the data

Answer:

$7

Step-by-step explanation:

So since he gets $28 in one month and there are 4 weeks in a month, -->

28/4 = 7 so, $7

Step-by-step explanation:

f(x) =  y

so f(4.999) = -5 when x = 4.999

f(5)= undefined because open circles means > or < with out the line underneath that means equal to

f(5.0001)= 7 when x=5.0001

f(9)= 7 when x=9 because the closed circle means ≥ or ≤ or equal to

Answer:

see attached

Answer:

B) 128.3 square yards

Step-by-step explanation:

A = (n/360 deg)(pi)r^2

where n = central angle of sector.

A = (75/360)(3.14159)(14 yd)^2

A = 128.3 yd^2

Answer:

B. 128.3 yards

Step-by-step explanation:

Area of a Sector Formula: A = ∅/360πr²

Simply plug in our variables:

A = 75/360(π)(14)²

A = 5π/24(196

A = 128.3

Answer:

[tex]\boxed{OptionA}[/tex]

Step-by-step explanation:

More than always indicates "ADDITION". So the mathematical operation is "+".

Answer:

A. +

Step-by-step explanation:

The key word in the phrase is "more than"

That signifies an increase of value which is addition's main function

If the number that was represented in the phrase is x, then we could write out an equation

x=q+15

Answer: C

Step-by-step explanation: With inverse equations, you switch y and x (y=f(x)) and undo/reverse the steps towards x.

1. Multiply by 3

2. Add 2

Equation by itself

0. x

1. 3(x)

2. 3(x+2)

The inverse of the given function is f⁻¹(x) = 3(x + 2).

The inverse function of a function f(x) in mathematics is a function that reverses the operation of f(x).

The given function in the question:

f(x) = (x/3) - 2

f(x) + 2 = x/3

x + 2 = f⁻¹(x)/3

f⁻¹(x) = 3(x + 2)

Hence, the inverse of the given function is f⁻¹(x) = 3(x + 2).

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Answer:

20 units

Step-by-step explanation:

The perimeter of a rectangle is

P = 2(l+w)

P = 2( 3x+2 + 4x)

Adding like terms

P = 2( 7x+2)

We know the perimeter is 74 units

74 = 2 ( 7x+2)

Divide by 2

74/2 = 2/2 (7x+2)

37 = 7x+2

Subtract 2 from each side

37-2 = 7x+2-2

35 = 7x

Divide by 7

35/7 = 7x/7

5 =x

We want to find the length RS = PQ = 4x

RS = 4x = 4*5 = 20