Formula; f(x)=x

1. x+1=

The equation of the line perpendicular to y = -²/₃x + 5 and passing through the point (6, -7) is; y = ³/₂x - 16

We want to find the equation of the line perpendicular to y = -²/₃x + 5 and passing through the point (6, -7).

Now, the slope that is perpendicular to that line is;

m = -1/(-²/₃) = 3/2

Thus;

Equation of the new line is;

y - (-7) = 3/2(x - 6)

y + 7 = 3x/2 - 9

y = ³/₂x - 16

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The population of Smalltown in 2018, using the mathematical operation of addition, was 3,554.

An addition is one of the basic mathematical operations involving combining two or more numbers or values to form a single value.

Additions are used to find the sum or total of a group of numbers.

2016 population of Smalltown = 3,187

2017 addition to the population of Smalltown = 148

The total population of Smalltown in 2017 = 3,335 (3,187 + 148)

2018 addition to the population of Smalltown = 219

The total population of Smalltown in 2018 = 3,554 (3,335 + 219)

Thus, in 2018, the total population of Smalltown was 3,554, 219 more than the population in 2017.

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The equation of the slant asymptote of the rational function is; y = 2x - 3

We want to find the equation of the slant asymptote of the rational function given as;

f(x) = (10x³ - 15x² + x - 1)/(5x² - 2)

To solve this question, we will divide the numerator by the denominator.  The result (not including the remainder) will be the equation of the slant asymptote.

We can tell the first term of the quotient will be 2x since 10x³/5x² = 2x. Thus, the answer from the given options will be either 2x − 3 or 2x − 11/5.

The easiest method to apply here is to simply multiply these options by the denominator to get;

(5x² − 2) (2x − 3) = 10x³ − 15x² − 4x + 6

(5x² − 2) (2x − 11/5) = 10x³ − 11x² − 4x + 22/5

So the answer must be 2x − 3

Thus, the equation of the slant asymptote of the rational function is; y = 2x - 3

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The area of the circle with center located at Point B (3, 1) and tangent to the y-axis is 9π units^2. The answer is E.

The area of a circle is the area enclosed by the circle. It is the product of the square of the radius and the constant π. The Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.

Area of circle = πr^2

To know the radius of a circle given its center and tangent line to it, find the distance between the the center and the point of tangency. As the radius is the distance from the center of the circle to any point in the circumference of the circle

If the circle is tangent to y-axis, then the radius is the absolute value of the x-coordinate.

r = 3 units

Using the formula for the area of a circle:

Area of circle = πr^2

Area of circle = π(3 units)^2

Area of circle = 9π units^2

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The magnitude of vector →JK is 4

And the direction of vector →JK is given by an angle 360°

For given question,

Let J(-6, -4) = (x1, y1) and

K(-10,-4) = (x2, y2)

By distance formula, the magnitude of vector is,

[tex]|\vec{JK}|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\|\vec{JK}|=\sqrt{(-10+6)^2+(-4+4)^2}\\\\ |\vec{JK}|=\sqrt{(-4)^2}\\\\ |\vec{JK}|=4[/tex]

To find the direction of the vector JK:

[tex]tan\theta=\frac{y_2-y_1}{x_2-x_1} \\\\tan\theta=\frac{-4+4}{-10+6}\\\\ tan\theta=0\\\\\theta=0^{\circ}[/tex]

However, the angle is in the fourth quadrant, so we add  360°  to obtain a positive angle.

Thus,  0° + 360° = 360°

Therefore, the magnitude of vector →JK is 4

And the direction of vector →JK is given by an angle 360°

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the answer is negative 41

A person 11 miles west and 12 miles south of the tower will not have coverage.

A circle is a closed curve that is drawn from a fixed point. This point is called the center. All points on the curve are equidistant from this center point.

The cell phone tower covers a circular area with radius 15 miles. This means that there will be coverage in all directions from center up to 15 miles.

The person is 11 miles west and 12 miles south of the tower.

Distance of person from center will be calculated using distance formula

[tex]d = \sqrt{(11^{2} + 12^{2} }[/tex]

∴ [tex]d = \sqrt{121 + 144}[/tex]

∴ [tex]d = 16.27[/tex] miles.

Since this distance is greater than the radius of circle (15 miles), the person will not have cell phone coverage.

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The coordinates of the centroid of the triangle with the given vertices X (5, 7), Y (9, -3), Z (13, 2) is (13 - 4,2) or (9, 2).

The centroid is the object's center point. The centroid of a triangle is the point where the three medians of the triangle intersect. It is also defined as the point at which all three medians intersect. A median line connects the midpoint of a side and the opposite vertex of a triangle.

The midpoint D of XY is [tex]$\left(\frac{5+9}{2}, \frac{7-3}{2}\right)$[/tex] or (7, 2).

Note that DZ is a line that connects the vertex Z and D, the midpoint of XY. The distance from D(7, 2) to Z(13, 2) is 13 - 7 or 6 units.

If P is the centroid of the triangle XYZ, then [tex]$P Z=\frac{2}{3} D Z$[/tex].

So, the centroid is [tex]$\frac{2}{3}(6)$[/tex] or 4 units to the left of Z. The coordinates of the centroid (P) are (13 - 4, 2) or (9, 2).

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Answer:

jimmy

Step-by-step explanation:

Answer: 5=10.25, 13=26.65, 19=38.95

Answer:

Step-by-step explanation:

The value of a cannot be determined because the expression is not an equation

The expression is given as:

a/2 - 3/2 + 22

The above is an expression, and not an equation

For the value of the variable a to be solved, the expression must be an equation

Equations are mathematical expressions that are represented by the equal to or equality sign i.e =

Examples of equations are:

a + b = c

y = mx + c

Ax + By = C

y = ax^2 + bx + c

y =  x

Hence, the value of a cannot be determined because the expression is not an equation

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Solving the question with the help of geometrical progression, we get that the value of this finite series is 31.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

As we know the formula for geometric progression is:

aₙ = a₁ r ⁿ⁻¹

Where , a₁ is the first term and r is the ratio , and n is the number of terms.

Here, the ratio is 4/2 = 2

Here, a₅ = 1 . 2⁵ ⁻ ¹ = 2⁴ = 16

a₄ = 1 . 2⁴ ⁻ ¹ = 2³ = 8

Now, We should calculate the value 1 + 2 + 4 + 8 + 16 = 31.

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Answer:

1⁷/15

Step-by-step explanation:

2¾(3⅜-1½)

using the rule of BODMAS

change the fractions in the bracket into improper fraction

2¾(27/8-3/2)

find LCM of the fractions in the bracket

2¾(27-12)/8

2¾(15/8)

convert the other mixed fraction to an improper fraction

11/8(15/8)= 5.15625~ 5.2

The set of statements is true; B. The number of stations airing the program increased by 82%. the equivalent expression that represents this situation is r+0.82r.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

IT is given that year ago, a radio program was aired on r stations across the country.

Also Today, the number of stations airing the radio program can be represented by the following expression; 0.82r

Therefore, the equivalent expression that represents this situation is r+0.82r

Hence, The set of statements is true; B. The number of stations airing the program increased by 82%. the equivalent expression that represents this situation is r+0.82r.

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Answer:

10 times 3.50 + 10x= f(x)

Step-by-step explanation:

35+28

f(x)= 63

The function f(x) that presents the total cost of the candy will be f(x) = 35 - 0.70x.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

Mark decided to make Christmas presents for his classmates. he bought 10lb of two types of candies: caramel candies for $2.80 per pound and chocolate candies for $3.50 a pound.

Let x be the number of pounds of caramel candies and (10 - x) be the number of pounds of chocolate candies. Then the equation is given as,

f(x) = 2.80x + 3.50(10 - x)

f(x) = 2.80x + 35 - 3.50x

f(x) = 35 - 0.70x

The function f(x) that presents the total cost of the candy will be f(x) = 35 - 0.70x.

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The simplified value of y in the equation is x = 38 + -3.5y

Simplifying

[tex](14y + -4) + (3x + 11) + (x + 21) = 180[/tex]

Reorder the terms:

[tex](-4 + 14y) + (3x + 11) + (x + 21) = 180[/tex]

Remove parenthesis around (-4 + 14y)

[tex]-4 + 14y + (3x + 11) + (x + 21) = 180[/tex]

Reorder the terms:

[tex]-4 + 14y + (11 + 3x) + (x + 21) = 180[/tex]

Remove parenthesis around (11 + 3x)

[tex]-4 + 14y + 11 + 3x + (x + 21) = 180[/tex]

Reorder the terms:

[tex]-4 + 14y + 11 + 3x + (21 + x) = 180[/tex]

Remove parenthesis around (21 + x)

[tex]-4 + 14y + 11 + 3x + 21 + x = 180[/tex]

Reorder the terms:

[tex]-4 + 11 + 21 + 3x + x + 14y = 180[/tex]

Combine like terms: -4 + 11 = 7

[tex]7 + 21 + 3x + x + 14y = 180[/tex]

Combine like terms: 7 + 21 = 28

[tex]28 + 3x + x + 14y = 180[/tex]

Combine like terms: 3x + x = 4x

[tex]28 + 4x + 14y = 180[/tex]

Solving

[tex]28 + 4x + 14y = 180[/tex]

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-28' to each side of the equation.

[tex]28 + 4x + -28 + 14y = 180 + -28[/tex]

Reorder the terms:

[tex]28 + -28 + 4x + 14y = 180 + -28[/tex]

Combine like terms: 28 + -28 = 0

[tex]0 + 4x + 14y = 180 + -28\\4x + 14y = 180 + -28[/tex]

Combine like terms: 180 + -28 = 152

[tex]4x + 14y = 152[/tex]

Add '-14y' to each side of the equation.

[tex]4x + 14y + -14y = 152 + -14y[/tex]

Combine like terms: 14y + -14y = 0

[tex]4x + 0 = 152 + -14y\\4x = 152 + -14y[/tex]

Divide each side by '4'.

[tex]x = 38 + -3.5y[/tex]

Simplifying

[tex]x = 38 + -3.5y[/tex]

Therefore, we can simplify that the value of y can be expressed as   x = 38 + -3.5y

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Solving the quadratic inequality, the solution set for x is given as follows:

x < -1 or x > 2.

For this problem, the inequality is given by:

x² - x - 2 > 0.

To graph a quadratic inequality, first we have to find the roots of the quadratic function, hence:

x² - x - 2 = 0

(x - 2)(x + 1) = 0.

Hence the roots are:

As the graph given at the end of the answer shows, any concave up quadratic function is positive to the left and to the right of the roots, hence the solution set for the inequality is:

x < -1 or x > 2.

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Based on the graph (see attachment), John's speed on each section of the walk are as follows:

Speed can be defined as the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured as meter per seconds.

Distance can be defined as the amount of ground covered (travelled) by a physical object over a specific period of time and speed, regardless of its direction, starting point or ending point.

Mathematically, speed can be calculated by using this formula;

Speed = distance/time

Based on the graph (see attachment), John's speed on each section of the walk can be calculated as follows.

For the first interval, we have:

Speed = 6/1.5

Speed = 4 km/h.

For the first interval, we have:

Speed = 6/1.5

Speed = 4 km/h.

For the second interval, we have:

Speed = 6/0

Speed = 0 km/h.

For the third interval, we have:

Speed = 6/4

Speed = 1.5 km/h.

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Answer:

A. The first mistake was made is Step 1

Step-by-step explanation:

The first mistake was in Step 1. Take a look below to see how Step 1 should've been.

4(2x +5)-(3x-4)=15

Use distributive property.

4(2x +5)-(3x-4)=15

8x+20-3x+4=15

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1 = -4(2) + 9 is an equation in slope-intercept form for the line passing through points (-2,17) and (2,1)

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope

We have been asked to write an equation in slope-intercept form for the line passing through (-2,17) and (2,1)

First we will find the slope(m)

We know that slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

For the pairs of points (-2,17) and (2,1)

⇒ m = [tex]\frac{1- 17}{2 - (-2)}[/tex]

⇒ m = [tex]\frac{-16}{4}[/tex]

⇒ m = -4

We know that the equation for slope(m) and y - intercept(b) of a line is given by :

y = mx + b

Here lets take equation 1 = -4(2) + b .Here x and y is substituted with the second two points.

⇒  1 = -4(2) + b

⇒  1 = -8 + b

⇒  b = 1 +8

⇒  b = 9

The equation in the slope intercept is as follows:-

1 = -4(2) + 9

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Answer:14.

Step-by-step explanation:

14.2 is closer to 14 than 15

Answer:

14

Step-by-step explanation:

The nearest whole number in 14.2 is 4.

Since 2 is less than 5, the 4 stays the same.

We get left with 14.

The factors of x²+19x-42 are (H) (x-2).

To find the factors:

Factors are: (x-2) and (x+21)

Therefore, factors of x²+19x-42 are (H) (x-2).

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Stand C sold their tomatoes at the least expensive price per pound that price is 2.70 per pound.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

We have to determine the price of sold tomatoes at the least expensive price per pound.

The price of sold tomatoes at stand A:

⇒ 2/(3/4) = 2/0.75  = 2.67 per pound.

The price of sold tomatoes at stand B:

⇒ 3.45/(5/4) = 3.45/1.25  = 2.76 per pound.

The price of sold tomatoes at stand C:

⇒ 14.85/(11/2) = 14.85/5.5= 2.70 per pound.

Here is the least expensive price per pound at stand C.

Hence, the stand C sold their tomatoes at the least expensive price per pound that price is 2.70 per pound.

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Each party basket will have 73 pieces of candy

Felicia has 4.5 bags of candy for her party basket

Each bag has 146 pieces of candy

She has 9 party baskets, the number of candies in each party basket can be calculated by multiplying 4.5 by 146 and dividing the result by 9

4.5 × 146/9

= 657/9

= 73

Hence there are 73 pieces of candy in each basket

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The simplification form of the given complex fraction [tex]\frac{1}{1+\frac{x}{y} }[/tex]  is equal to

(y)/ (y +x).

As given in the question,

Given complex fraction is equal to  [tex]\frac{1}{1+\frac{x}{y} }[/tex]

Simplify the given complex fraction by taking the least common multiple of the denominator,

[tex]\frac{1}{1+\frac{x}{y} }\\\\\\= \frac{1}{\frac{y+x}{y} } \\\\\\=\frac{ (1)(y)}{y+ x} \\\\= \frac{y}{y+x}[/tex]

Therefore, the simplification form of the given complex fraction [tex]\frac{1}{1+\frac{x}{y} }[/tex]  is equal to (y)/ (y +x).

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The number of people who can go to the amusement park is 3 people

89.50 = 7.75 + 27.25p

89.50 - 7.75 = 27.25p

81.75 = 27.25p

p = 81.75 / 27.25

p = 3

Therefore, the number of people who can go to the amusement park is 3 people.

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The amount of money available after x number of years is given by y = 1000(1.05)ˣ

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the amount of money after x years. Assume our initial amount is $1000, the rate is 5% (0.05) and it will only compound once per year. The equation is given by:

y = 1000(1 + 0.05)ˣ

y = 1000(1.05)ˣ

The amount of money available after x number of years is given by y = 1000(1.05)ˣ

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