Find the missing length.

The equation of the line passing through the point (5, - 3) that is parallel to 5x + 7y = 9 will be 5x + 7y - 4 = 0.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The equation of the line is given below.

5x + 7y = 9

The equation of the line that is parallel to the line is given as,

5x + 7y + d = 0

The line is passing through (5, -3). Then we have

5(5) + 7(-3) + d = 0

25 - 21 + d = 0

4 + d = 0

d = - 4

The equation of the line passing through the point (5, - 3) that is parallel to 5x + 7y = 9 will be 5x + 7y - 4 = 0.

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The product of 12 and a number and then the product multiplied by itself 7 times is (12n)^7.

In Mathematics, an algebraic expression is a mathematical equation that can be used for showing the relationship which exist between two (2) or more variables, numerical quantities, as well as in conjunction with different mathematical operations.

Additionally, a coefficient simply refers to a constant numerical value (number or numeral) that written before the variable in any algebraic expression.

Assuming the variable n represents the unknown numerical value (number), we would translate the word problem into an algebraic expression as follows;

The product of 12 and a number = 12 × n = 12n

Since the product is multiplied by itself 7 times, we have the following algebraic expression;

Algebraic expression = (12n)^7

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Answer:

Out of 50 students in a class, 40% are girls, meaning there are 50 x 40% = 20 girls in the class.

And the number of boys is 50 - 20 = 30 students.

If 30% of the girls wear spectacles, that means 30/100 x 20 = 6 girls wear spectacles.

And the number of girls not wearing spectacles is 20 - 6 = 14.

So the total number of girls wearing spectacles is 6, and the number of boys is 30, and the number of girls not wearing spectacles is 14.

Answer:

Step-by-step explanation:

a PERSON SHOULD SPEND AT LEAST 35 DOLLARS A WEEK ON COFFEE

The standard deviation of the sampling distribution of sample means will be 0.6667.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

Given information

μ= 38 and σ = 6; n = 81

The standard deviation of the sampling distribution is given as,

⇒ 6 / √81

⇒ 6 / 9

⇒ 0.6667

The standard deviation of the sampling distribution of sample means will be 0.6667.

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Answer:

Step-by-step explanation:

Answer:

1. The volume of water in the tank in cubic yards can be calculated by multiplying the length, width, and depth of the tank in feet by the conversion factor of 0.037037 yds3/ft3:

87 ft x 36 ft x 15 ft x 0.037037 yds3/ft3 = 997.78 yds3

2. To treat the water, the aquarium must purchase 998 bags of salt, as 1.1 yds3 of water requires one bag of salt.

3. The aquarium must pay $4,835.30 for the salt to treat the water in the new shark tank. This is calculated by multiplying the number of bags of salt (998) by the cost of one bag of salt ($4.85).

The simplified ratio of miles to gallons is 14:1. The solution has been obtained by using the concept of ratios.

What are ratios?

A ratio is a comparison or condensed version of two identical values. The reciprocity of this relationship tells us how many times one quantity is equal to the other. To put it simply, a ratio is a number that can be used to represent one thing as a percentage of another.

We are given the distance to be 189 miles and the volume of gas 13[tex]\frac{1}{2}[/tex] gallons.

So, in order to find the ratio of miles to gallons, we need to divide 189 miles onto 13[tex]\frac{1}{2}[/tex] gallons of gas.

We get

189/13.5 = 14

Hence, the ratio of miles to gallons is 14:1.

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F(x)=1/(x+3)(x-7) is the rational functions which is graphed.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;

In a graphic, these vertical asymptotes are given by dashed vertical lines.

An example is a value of x for which the denominator of the function is 0.

In this graphic:

Dashed vertical lines at: x=-3, x=7 , thus, for x+3 and x-7 the denominator is zero.

Thus, the function graphed is:

F(x)=1/(x+3)(x-7)

Hence, F(x)=1/(x+3)(x-7) is the rational functions which is graphed.

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Answer: Yes, there is an outlier of 45, This means that one person's age was 45, which is 25 years younger than the next closest age.

Hope this helps! :)

Step-by-step explanation:

Answer:

D

GIVE HIME BRAINLIEST

Step-by-step explanation:

The velocity of the ball when it returns to the ground is -8 m/s

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The distance of a ball thrown upward is given by:

h(t) = -2t² + 12t - 10

The ball hits ground when h(t) = 0, hence:

-2t² + 12t - 10 = 0

t = 5 or 1

The velocity (V) of the ball is:

V = dh/dt

V = (d/dt)(-2t² + 12t - 10) = -4t + 12

V = -4t + 12

The ball hits ground when t = 5 or 1 s, hence:

V(1) = -4(1) + 12 = 8 m/s

V(5) = -4(5) + 12 = -8

The velocity on the ground is -8 m/s

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Answer:

C is irrational--6 is not a perfect square.

The next two numbers on the number pattern are given as follows:

A 12.2, 12.9.

To obtain the next two points on the number pattern, first we must identify what is the pattern.

The pattern is given as follows:

The final term is 6.1, which is obtained after the addition of 0.7 to 5.4. Double 6.1 is obtained multiplying the number by 2, as follows:

2 x 6.1 = 12.2.

Then the number obtained after 0.7 is added to 12.2 is given as follows:

0.7 + 12.2 = 12.9.

Meaning that the correct option to complete the number pattern is given by option A.

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The two lines L1 and L2 are parallel

For two lines to be parallel the slope must be equal, hence we calculate the slope of the two lines

The slope, m of the linear function L1 is calculated using the points (–2, 9) and (1, 3)

m = (y₀ - y₁) / (x₀ - x₁)

m = (9 - 3) / (-2 - 1)

m = (6) / (-3)

m = -2

The slope, m of the linear function L2 is calculated using the points (–4, 10) and (3, –4)

m = (y₀ - y₁) / (x₀ - x₁)

m = (10 + 4) / (-4 - 3)

m = (14) / (-7)

m = -2

The lines are parallel

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The coordinates of the endpoint P2 in the line segment are (- 4, 8).

In this problem we have the coordinates of an endpoint in a line segment and the midpoint of that segment, that is, the point in the line segment that partitions it into two parts of equal length. The formula needed to find the coordinates of the missing endpoint is:

0.5 · P1(x, y) + 0.5 · P2(x, y) = M(x, y)

Where:

If we know that P1(x, y) = (- 6, 4) and M(x, y) = (- 5, 6), then the coordinates of the other endpoint are:

0.5 · P1(x, y) + 0.5 · P2(x, y) = M(x, y)

0.5 · (- 6, 4) + 0.5 · P2(x, y) = (- 5, 6)

(- 3, 2) + 0.5 · P2(x, y) = (- 5, 6)

2 · (- 3, 2) + P2(x, y) = 2 · (- 5, 6)

(- 6, 4) + P2(x, y) = (- 10, 12)

P2(x, y) = (- 10, 12) - (- 6, 4)

P2(x, y) = (- 4, 8)

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The radius of a circle that has a circumference of 16 is given by 8/π

The formula for the circumference of a circle is C = 2πr

Where,

r = the radius and

C = the circumference

From

C = 2πr

r = C / 2π

When C = 16

r = 16 / 2π

r = 8/π

In conclusion, the radius of the circle is 8/π

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The values of Radius PQ if PQ = 24 and OR = 5. is 13 and The radius if PQ has length 24 and 9 units aways from center is 15 .

What is area of circle ?

Area of circle can be defined as  product of pi and square of radius.

Given,

In the chord PQ of O , point R is choosen so that OR is perpendicular to PQ.

The radius if PQ = 24 and OR = 5.

r = [tex]\sqrt{(24/2)^2 +5^2 }[/tex]

r = [tex]\sqrt{144+25}[/tex]

r = [tex]\sqrt{169}[/tex]

r = 13.

The radius if PQ has length 24 and 9 units aways from center.

radius  = [tex]\sqrt{(24/2)^2 + 9^2}[/tex]

= [tex]\sqrt{(12)^2 + 9^2}[/tex]

= [tex]\sqrt{144+81}[/tex]

= [tex]\sqrt{225}[/tex]

r = 15 .

The far from PQ from the center if it has length 16 and the circle has radius 10 is

PQ = [tex]\sqrt{10^2 - (16/2)^2}[/tex]

PQ = [tex]\sqrt{100-64}[/tex]

PQ = [tex]\sqrt{36}[/tex]

PQ = 6

The value of OR if PQ has length 6[tex]\sqrt{5}[/tex] and radius 9 .

OR = [tex]\sqrt{(9^2) - (3\sqrt{5})^2 }[/tex]

OR = [tex]\sqrt{81-45}[/tex]

OR = [tex]\sqrt{36}[/tex]

OR = 6 .

The value of OP .

OP = [tex]\sqrt{QR^2 + OR^2 }[/tex]

OP = [tex]\sqrt{(2\sqrt{3})^2 + (2\sqrt{2})^2 }[/tex]

OP = [tex]\sqrt{12+8}[/tex]

OP = 2[tex]\sqrt{5}[/tex]

Hence, the values of Radius PQ if PQ = 24 and OR = 5 is 13 and The radius if PQ has length 24 and 9 units aways from center is 15 .

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Answer: Pictures below show intersection point on the graph.

Step-by-step explanation:

The equation for the function shown in the graph is y = sin(x + π/2).

The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilize the sine function.

Given a graph of a sine function,

which shows the amplitude of 1,

and value of x-intercept is π/2, when y is 0, x is π/2

the equation for sine is

y = a sin(bx)

where a is the amplitude = 1

b is π

y = sin(x),

but given x-intercept π/2,

so, y = sin(x + π/2)

Hence option A is correct.

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This means that, in addition to what the employee contributes, the employer will match up to 6% of an employee's total compensation to his or her 401k account.

Employee compensation is the total remuneration that an organisation pays to an employee in exchange for the work that employee performed during the accounting period, whether that payment is made in cash or in kind. Taxes less subsidies on production include those due or owed on goods or services produced as outputs as well as other taxes or subsidies on production, such as those due on labour, equipment, buildings, or other assets used in production.

Employee compensation consists of two main parts:

(a) Salary and wages paid in cash or kind;

(b) Social insurance contributions that employers are required to pay, including contributions to social security programmes, actual social contributions to other employment-related social insurance programmes, and imputed social contributions to those same programmes.

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a) 5-5 is a numerical expression

b) c-5 is a variable expression where, variable is c

c) 8÷x+9 is a variable expression where, variable is x

d) 100·6 is a numerical expression

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The perimeter of polygon ABC = 67.4

The perimeter of polygon PQRS = 78.8

The perimeter of a polygon is calculated by adding the lengths of all sides of the polygon together.

The Two-Tangent Theorem states that if two tangents are drawn to a circle from the same external point, then the tangents are congruent (have the same length).

Perimeter of polygon ABC = AB + BC + AC

AB = 10.5 + (23.2 - 11.2) = 22.5 [based on the Two-Tangent Theorem]

BC = 23.2

AC = 10.5 + 11.2 = 21.7

Perimeter of polygon ABC = 22.5 + 23.2 + 21.7 = 67.4

Perimeter of polygon PQRS = PQ + QR + RS + PS

PQ = 25

PS = 21.8

QR = 13 + 4.6 = 17.6

RS = 4.6  + 9.8 = 14.4

Perimeter of polygon PQRS = 25 + 21.8 + 17.6 + 14.4 = 78.8

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A function is an equation with one solution to every value of x for the variable y. A input of a specific type is paired with exactly 1 output by a function.

Quantities and their modifications, equations and surrounding structures, locations of forms and forms themselves are all included in the field of mathematics. The term "function" describes the connection between a group of inputs, of which each has a corresponding output. A function is an association between inputs and outcomes in which each input results in a single, unique output. Functions are typically denoted by the letter f. (x). The input is just a variable x. There are four primary categories of functionality available. depending on the following elements: on.

Given:

A function is an equation with one solution to every value of x for the variable y.

Each argument of a specific type is paired with absolutely one output by a function. Typically, functions are named f(x) or g instead of y. (x). When x equals 2, as directed by f(2), we should choose the value of given function.

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Points are (0,0) and (2,8).

What is the gradient?

The vector field f's value at a point p in the vector calculus is the "direction and rate of fastest increase" for a scalar-valued differentiable function f with many variables.

Here, we have

Given: y = 4x

The number in front of the x is the gradient (slope). This number represents the amount of up or down for a given amount of long.

If the number in front of the x (coefficient) is positive the 'slope' goes up. If the coefficient is negative it means the 'slope' is down.

Now, substitute any value you chose into x, multiply it by 4 and you have your value for y

Let x = 0,

y = 4(0) = 0

So this can be our first point on the graph.

(x₁, y₁) ⇒ (0,0)

Let x = 2

y = 4(2) = 8

So this can be our second point on the graph.

(x₂, y₂) ⇒ (2,8)

Now, we draw a line through them extending it to the edges of the axis.

Hence, Points are (0,0) and (2,8).

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f(x) and g(x) are inverses using composition

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

To confirm the inverse relationship using composition.

For valid inverse f(g(x)) must be equal to g(f(x))

f(x) = ∛(x) + 13; g(x) = (x - 13)³:

f(g(x)) = f((x - 13)³)

f(g(x)) = ∛((x - 13)³) + 13

f(g(x)) = x - 13 + 13

f(g(x)) = x

g(f(x)) = g(∛(x) + 13)

g(f(x)) =  (∛(x) + 13 - 13)³

g(f(x)) =  (∛(x))³
g(f(x)) =  x

Since f(g(x)) = g(f(x)) then f(x) and g(x) are inverse

f(x) = x³ + 1; g(x) = ∛(x - 1):

f(x) = x³ + 1; g(x) = ∛(x - 1)

f(g(x)) = f(∛(x - 1))

f(g(x)) =  (∛(x - 1))³ + 1

f(g(x)) =  x - 1 + 1

f(g(x)) =  x

g(f(x)) = g(x³ + 1)

g(f(x)) = ∛((x³ + 1) - 1)

g(f(x)) = ∛(x³)

g(f(x)) = x

Since f(g(x)) = g(f(x)) then f(x) and g(x) are inverse

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Answer:

the expression "square root of 1+3a/25" makes sense for all values of a that are greater than or equal to -8.333.

Step-by-step explanation:

The square root of a number is only defined for non-negative values of that number. Therefore, for the expression "square root of 1+3a/25" to make sense, the value inside the square root must be non-negative.

1+3a/25 >= 0

This inequality can be rearranged to get the values of a for which the expression makes sense.

3a/25 >= -1

3a >= -25

a >= -25*3/3

a >= -25/3

a >= -8.333

Therefore, the expression "square root of 1+3a/25" makes sense for all values of a that are greater than or equal to -8.333.

The compound inequality for the graph given is  -2 < x < 5.

When a compound inequality is graphed such that there is an open circle instead of a filled - in circle over a number, then it means that x is either greater than this value, or less than this value. In other words, x is not equal to this value.

The circles over - 2 and 5 are not filled in which means that x is greater or less than - 2 and 5.

x is less than 5 because the arrow goes from 5 to infinity and x is greater than - 2 for the same reason.

The compound inequality is therefore:

-2 < x < 5

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