if cos theta =3/4 find sec theta

Answer:

Step-by-step explanation:

The slope of a line can not be found between two points with the same x-coordinate, as division by zero is undefined. Hence, the line defined by the points (-2,10) and (-2,-15) is a vertical line and has no slope.

The y-intercept of a line is the point at which the line intersects the y-axis, i.e., the value of y when x=0. A vertical line does not intersect the y-axis, hence it has no y-intercept.

Since the line has no slope or y-intercept, its equation can not be written in the standard form of y = mx + b, where m is the slope and b is the y-intercept. Instead, the equation of the line can be written as x = constant, where constant is the x-coordinate of the points on the line, i.e., x = -2.

The function is continuous only if m = 7.

If the function is continue, then the value of the function needs to be the same one in both pieces of the function when we evaluate in x = -2

That means that:

f(-2) = f(-2)  (trivially)

Replacing the two pieces of the function we will get:

m*(-2) - 6 = (-2)^2 + 10*(-2) - 4

now we can solve that equation for m.

-2m - 6 = 4 -20 - 4

-2m = -20 + 6 = -14

m = -14/-2 = 7

m = 7

that is the value of m.

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Answer: The answer is 12x-3

the equation 4x + 5x^2 -7x in standard form will be 5x² -3x and The value of a, b, and c will be 5, -3, and 0

ax²+bx+c=0, with a not, equals 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given a quadratic equation  4x + 5x^2 -7x

From the Standard form of a quadratic equation:

ax²+bx+c=0

In our case,

=>  4x + 5x^2 -7x

=> 5x² -3x

Comparing both equations we get the:

z = 5

b = -3

and c = 0

Therefore,  the equation 4x + 5x^2 -7x in standard form will be 5x² -3x and The value of a, b, and c will be 5, -3, and 0.

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The transformation from the function f(x)=1/x to g(x)=1/5x can be achieved by multiplying the input value x by 5.

f(x)=1/x becomes g(x)=1/(5x) after the transformation

A mathematical transformation is a function that maps one set of values (input) to another set of values (output) based on a set of rules or operations. Transformations can be used to manipulate geometric figures, to change coordinate systems, to map one image to another, and more. Common examples of mathematical transformations include translation, rotation, scaling, and reflection.

It could then be concluded that the transformation is achieved by multiplying the input value x by 5.

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The complete question goes thus:

Describe the f(x)=1/x to g(x)=1/5x transformation

The area of the square pyramid with the height of the triangular faces of 10 inches and the side length of the square base of 4 inches is 96 square inches. The correct option is therefore;

B. 96 in²

The surface area is the area or extent covered by the outer faces or boundary enclosures of the figure.

The description of the shape in the figure = Square pyramid

Side length of the square base of the square pyramid = 4 inches

Base length of the triangular slant faces = Side length of the square base = 4 inches

Height of the triangular faces = 10 inches

The surface area of the square pyramid is therefore;

Sum of the area of the four triangular faces + Area of the square base

Area of one triangular face = (1/2) × 4 × 10 = 20

Area of the square base = 4 × 4 = 16

The total surface area of the square pyramid is therefore;

A = 4 × 20 in² + 16 in² = 96 in²

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The sum of given polynomial is x⁴+x³+4x²-5x-8.

Addition of Algebraic Expressions is the process of collecting like terms and adding them. Identify and add the coefficients of like terms and sum them to find the final expression of given problems.

The given polynomials are x⁴-3x + 1, 4x²-2x+8, and x³-9.

Here, x⁴-3x + 1+4x²-2x+8+x³-9

= x⁴+x³+4x²-3x-2x-9+1

= x⁴+x³+4x²-5x-8

Therefore, the sum of given polynomial is x⁴+x³+4x²-5x-8.

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"Your question is incomplete, probably the complete question/missing part is:"

Add the following polynomials, then place the answer in the proper location on the grid. Write your answer in descending powers of x.

x⁴-3x + 1, 4x²-2x+8, and x³-9

The true statement is "viet's car can uses 13 gallons of gas for every miles it travels.

The correct answer choice is option B.

Julio's car:

m = k × g

Where,

m = miles traveled

g = gallons of gas used

m = k × g

300 = k × 12

300 = 12k

divide both sides by 12

k = 300/12

k = 12

So,

m = 12g

Viet's car:

m=13g

Therefore, the correct statement is viet's car uses 13 gallons of gas for every mile.

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Step-by-step explanation:

please make me brainalist and keep smiling

1) In geometry, the coordinate is used as to write the equations of lines as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

2) By showing that the opposite sides of the quadrilateral are congruent.

3) To prove the figure is a rhombus you must verify that all sides are the same length.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

1) Let two points on the line are (x₁ , y₁) and (x₂, y₂).

Then, The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

2) We know that;

Opposite angles in a quadrilateral are congruent, and Parallel lines have congruent corresponding angles.

Hence, In coordinate geometry, By showing that the opposite sides of the quadrilateral are congruent.

3) In coordinate geometry, To prove that it is a rhombus, remember that the definition of a rhombus is a quadrilateral with four congruent sides. Therefore, to prove it is a rhombus you must verify that all sides are the same length.

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Answer:

The equation to represent Frederick's account balance after t years is:

A = 1050 * (1 + (0.051/365))^(365t)

Where A is the account balance and t is the number of years.

On December 31 of each year, the quick ratio is 1.6. According to the above computation, the quick ratio is improving.

A good fast ratio is often anything greater than 1 or 1:1. If the ratio is 1:1, the company's liquid assets and current liabilities are equal in amount. A greater ratio means the business could more than cover its current liabilities.

For the present year

Current liabilities minus Quick Assets is the Quick Ratio.

= ($1,000 + $1,200 + $800) ÷ $1,875

= $3,000 ÷ $1,875

= 1.6

Current liabilities minus Quick Assets is the Quick Ratio.

=($1,140 + $1,400 + $910) ÷ $2,300

= $3,450 ÷ $2,300

= 1.5

b. according to the above computation, the quick ratio is improving.

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The option that shows a proportional relationship is selling 94 cars in 1 year (option D)

Two numbers or elements are said to be proportional if they have the same ratio. In this case, the ratio is 24 cars every 3 months, which can be simplified as 8 cars per month.

Based on this ratio, the option that is proportional is selling 96 cars in a year because this will means 96 cars in 12 months and 96/12= 8, which shows the ratio is the same.

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On a coordinate plane, a vector has origin (0, 0) and terminal point (3, 2). The magnitude of the vector is 5

The magnitude of a vector can be calculated using the distance formula, which is the square root of the sum of the squares of the differences of the x and y components. In this case, the x component is 3 and the y component is 2, so the magnitude can be calculated as follows:

√(3^2 + 2^2) = √(9 + 4) = √(13) = 5

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Answer:

its D

Step-by-step explanation:

on edge

Answer:

[tex]3 {x}^{4} - 6 {x}^{3} - 21 {x}^{2} - 2x + 8[/tex]

Step-by-step explanation:

One root being i, an imaginary number is throwing me off.. but I can give it a shot if youd like.

So a coefficient is the number Infront of the X. so for 6X^2, the coefficient is 6.

It says the Leading Coefficient is 3. The one option for that is 3x^4, so that will be the in the first blank.

The exponents now (the little numbers) start with 4 and go down 1 after each block. Which means the last two blocks will have no little numbers since it would be 1 and 0. Those don't need exponents.

For the block after the 21x^2, we have two choices. Either 6x or 2x

For the last block we have two choices also.

8 or 24

To find if it's 6x or 2x...

Its showing roots of -2, i, and 4 with multiplicity of 1, which means

x^2-4x+2x+8

x^2-2x+8

We have 2x and 8

Those must be the other two blocks

Answer:

70 parking spaces were full.

Step-by-step explanation:

To calculate this, multiply the total number of parking spaces (100) by the percentage of the lot being used (70%):

100 * 0.70 = 70

The the vertices of reflected square, Q'R'S'T are Q' = (3, 1), R' = (-8, -2), S' = (-7, -7) and T' = (-2, -6)

A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

Given that, a square QRST with vertices Q(-3, 1), R(8, -2), S(7, -7) and T(2, -6)

is reflected across y-axis, to form Q'R'S'T we need to find the vertices of reflected square.

We know that, rule of reflection over y-axis,

(x, y) → (-x, y)

Q' = (3, 1)

R' = (-8, -2)

S' = (-7, -7)

T' = (-2, -6)

Hence, the the vertices of reflected square, Q'R'S'T are Q' = (3, 1), R' = (-8, -2), S' = (-7, -7) and T' = (-2, -6)

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Answer:

(7x+3)

Step-by-step explanation:

The Imaginary part is [tex]& \frac{-5 \sqrt{3}-2}{4}[/tex]

[tex]& \frac{5+2 i}{-1+\sqrt{3} i} \times \frac{-1-\sqrt{3} i}{-1-\sqrt{3} i} \\[/tex]

[tex]& =\frac{-5-5 \sqrt{3} i-2 i+2 \sqrt{3}}{4} \\[/tex]

[tex]& =\frac{-5+2 \sqrt{3}}{4}+i\left(\frac{-5 \sqrt{3}-2}{4}\right) \\[/tex]

Imaginary part

[tex]& \frac{-5 \sqrt{3}-2}{4}[/tex]

The complete question is,

Find the imaginary part of 5+2i/-1+√3i

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The complex number -i5 has -i5 as its imaginary component.

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Add a phrase to the shape's perimeter to get the side length that is missing.The total length of all of a shape's sides makes up the shape's perimeter.

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The missing side length of perimeter of the figure is 15 feet is 5.

To get the length of the missing side, subtract the perimeter from the total of the known sides. Advice: Consider it. The whole and one component are both known. You deduct the known portion from the total to determine the missing component.

Since there are two of each side length, it is easy to do this by simply adding the length and breadth and multiplying the result by two. The perimeter formula is defined as

perimeter=(length + width)2.

or

add all sides

4 + 3+ 3+ x = 15

10 +x = 15

x = 15 -10 = 5

x = 5

The missing side length of perimeter of the figure is 15 feet is

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The other equation in the form y = mx + b is y = x + 3

From the question, we have the following parameters that can be used in our computation:

y = -3x + 5

y = mx + b has a slope of 1

So, we have

y = x + b

The point where the graphs of two equations intersect has y-coordinate 2.

So, we have

3x + 5 = 2

x + b = 2

Eliminate x

So, we have

3b - 5 = 6 - 2

Evaluate

3b = 9

So, we have

b = 3

hence, the equation is y = x + 3

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Answer:

the total number of employees needed is 35 cashiers + 100 floor assistants = 135 employees.

Step-by-step explanation:

Answer:

If AP and DQ are altitudes, AP= 6, DQ = 10, and DE = 12, then AB = 8.

Step-by-step explanation:

The subject pronoun requested would be they and in Spanish would be "ellas".

In the Spanish language, there are two feminine pronouns that are often used as subjects in sentences, these pronouns are:

Ella - This is a singular pronoun equivalent to she

Ellas - This is a plural pronoun equivalent to "they", but again it is exclusively used for feminine nouns such as a group of women.

Based on this, the pronoun you are looking for is the pronoun "ellas", here is an example of how to use it: Ellas son amables.

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Answer:

2,6,7,8,9 because if doubled it should equal more than ten

The solution of the system of equations is (8, 11).

We know that one of the equations of the system is:

y = x + 3

And the other line passes through the points (3, 1) and (4, 3), then the slope of that line is:

a = (3 - 1)/(4 - 3) = 2

So the line is something like:

y = 2*x + b

To find the value of b, the y-intercept, we can replace the values of one of the points.

I will use (3, 1)

1 = 2*3 + b

1 = 6 + b

1 - 6 = b

-5 = b

So the other line is y = 2x - 5

Then the system of equations is:

y = x + 3

y = 2x - 5

Now we can solve the system:

x + 3 =2x - 5

3 + 5 = 2x -x

8  =x

The x-value of the solution is 8, then the only option that can be correct is.

(8, 11)

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a) The double-declining-balance rate is 0.5 or 50%.

b) The double-declining-balance depreciation for the first year is $53800.

What is depreciation?

Depreciation is an accounting procedure that allows a business to distribute an asset's cost over the course of its useful life. In other words, it keeps track of how an asset's value decreases over time. In order to better align an asset's productivity in use to its operating costs over time, businesses depreciate assets on their financial statements and for tax purposes.

The formula of the double-declining-balance rate is 2 × (1/useful life)

Given that the building acquired at the beginning of the year at a cost of $107,600 has an estimated residual value of $4,300 and an estimated useful life of 4 years.

The double-declining-balance rate is

= 2 × (1/4)

= 0.5

= 50%

The double-declining-balance depreciation for the first year is

$107,600 ×  50%

= $107,600 × (1/2)

= $53800

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The solution for the given equation is 15. Therefore, Nico, Raj and Sandra are correct.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 2/5 (5+x)=8

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Method 1:

Now, 2(5+x)=40

5+x=20

x=15

Method 2:

Multiply 5/2 on both the sides of an equation, we get

2/5 (5+x)×5/2 =8×5/2

5+x=20

x=15

Therefore, Nico, Raj and Sandra are correct.

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"Your question is incomplete, probably the complete question/missing part is:"

Nico, Aditi, Erick, Raj, and Sandra are solving the equation.

Two-fifths (5 + x) = 8

Each student begins to solve the problem as shown.

Nico

Aditi

Erick

Two-fifths (5 + x) = 8. (Five-halves) two-fifths (5 + x) = 8 (five-halves)

Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8

Two-fifths (5 + x) = 8. Two-fifths (5 + x) minus 5 = 8 minus 5

Raj

Sandra

Two-fifths (5 + x) = 8. (one-half) two-fifths (5 + x) = 8 (one-half)

Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8

Which students are correct in their approach to solving the problem? Select three options.

Nico

Aditi

Erick

Raj

Sandra

Answer:

D. The average rates of change of f and g cannot be determined from the given information.

Step-by-step explanation:

To determine the average rate of change of a function, we need the equation of the function. Since the equation of g is not given, we cannot determine the average rate of change of g and compare it with the average rate of change of f. Hence, option D is the correct answer.

The value of function for f'(2) is 0.22.

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

Given that, f(x)= √(x+3) at the specific point x=2.

f'(2)= [tex]\lim_{h \to \ 0}[/tex]((f(2+h)-f(2))/h)

Find the derivative using the chain and power rules.

[tex]f(x)=(x+3)^{\frac{1}{2} }[/tex]

f'(x) = [tex]\frac{1}{2(x+3)^{\frac{1}{2} }}[/tex]

f'(2)=  [tex]\frac{1}{2(2+3)^{\frac{1}{2} }}[/tex]

f'(2)=  [tex]\frac{1}{2(2+3)^{\frac{1}{2} }}[/tex]

f'(2)= 1/2√5

f'(2)= 1/4.47

f'(2)= 0.22

Therefore, the value of function for f'(2) is 0.22.

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