5 tan x -3 = 1 solve this equation for 0° ≤ x ≤ 360° make a sketch of the graph and indicate all the solutions. ​

Answer:

L = 1/2x

Step-by-step explanation:

The perimeter of a rectangle is the sum of all four sides. In this case, the perimeter is represented by the expression 3 1/2x + 18.

Since the perimeter of a rectangle is the sum of the lengths of all four sides, so, if we know the perimeter and one side's length, we can find the length of the other side.

We can use the expression 3 1/2x + 18 to find the length of the rectangle.

Let's assume that the length of the rectangle is represented by the variable L and the width is represented by the variable W.

So we know that the perimeter of the rectangle is represented by the expression 3 1/2x + 18 and the perimeter of a rectangle is 2(L + W)

So we can write the equation

2(L + W) = 3 1/2x + 18

Expanding the left side of the equation:

2L + 2W = 3 1/2x + 18

Now we know that one of the sides of the rectangle is 1/2x so

L = 1/2x

Therefore, the expression that represents the length of the rectangle is 1/2x

The savings before he purchased the radio is

A percentage is a figure or ratio that can be stated as a fraction of 100.

If we need to determine the percentage of the given number, we divide the number by its whole number and multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".

Given cost of radio = $109.65

and $109.65 is 43% of his savings,

let saving be  x

according to conditions,

43% of x = 109.65

43x/100 = 109.65

43x = 109.65 × 100

x = 10965/43

x = $255

Hence the saving of George is $255.

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The amount of discount in dollars is 28.17

To find the amount of the discount, we need to multiply the original price by the percentage that was discounted.

Discount = Original Price x (Discount Percentage/100)

Discount = 46.95 x (60/100) = 28.17

So, the amount of discount in dollars is 28.17

The simplified value of the equation is w = -1.

To simplify means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.

Given equation w/4 + 11/12 = 1/2 - w/6

the equation is written as,

w/4 + w/6 = 1/2 - 11/12

solving by LCM

(3w + 2w)/12 = (6 - 11)/12

5w = -5

w = -5/5

w = -1

Therefore the value of w is -1.

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The mass per cup for the objects will be 320g and 272g respectively.

What is mass?

Mass simply means the weight that an object contains.

The mass of a teapot and 4 cups is 1,280 grams. The mass per cup will be:

= Mass / Number of cups

= 1280 / 4

= 320g

The mass of the same teapot and 10 cups is 2,720 grams. The mass per cup will be: = 2720 / 10 = 272g

Hence, the mass per cup for the objects will be 320g and 272g respectively.

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Complete questions:

The mass of a teapot and 4 cups is 1,280 grams. The mass of the same teapot and 10 cups is 2,720 grams. Each cup has the same mass. What is the mass?

The fraction is 0.001545/5 =0.00309/1 .

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

2 in² and 5 yd²

now,

1 inch =0.0278yard

so, we get,

2in^2=0.001545 yd^2

i.e. 0.001545/5

=0.00309/1

hence, The fraction is 0.001545/5 =0.00309/1 .

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Answer: -32

Step-by-step explanation:

The domain and range of the function y = 1/2 - 1 lies on  (-∞, ∞)

The collection of all input values (sometimes referred to as independent variables) for which a function is defined and yields a valid output is known as the domain of the function. It is the collection of all possible values that can be entered into a function.

All real numbers, for instance, fall inside the domain of the function        f(x) = x², since any real number may be squared to yield an accurate result.

On the other hand, a function's range is the collection of all feasible output values (also known as the function's dependent variable) that it can generate. It is the collection of all outcomes that the function is capable of producing.

For instance, since squaring real numbers makes the range of the function f(x) = x² all non-negative values.

It's vital to remember that not all functions have the same range or are defined for all conceivable input values. For instance, because the square root function x is not defined for negative numbers, all real numbers that are not negative fall within its domain.

In conclusion, the collection of all input values for which a function is defined and yields a valid output is known as the domain of the function. The collection of all potential output values that a function may produce is known as its range.

In the given function;

y = 1/2x - 1

The domain of this function is (-∞, ∞)

The range of the function f(x) = 1/2x - 1 is (-∞, ∞)

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Answer: Shayla's method for determining whether a graph of a relation is a function is not completely accurate. While it is true that a function can only have one y-intercept, the converse is not necessarily true. A graph can have exactly one y-intercept and still not be a function.

For example, a vertical line has exactly one y-intercept, but it does not define a function because the same value of x can have multiple y-values.

It is also important to note that a graph can be a function even if it does not intersect the y-axis at all.

A more accurate way to determine whether a graph represents a function is to use the vertical line test. This test states that if a vertical line can be drawn through the graph such that it intersects the graph in more than one point, then the graph does not represent a function. If a vertical line can be drawn through the graph such that it intersects the graph in exactly one point, then the graph represents a function.

Step-by-step explanation:

Step-by-step explanation:

"average" or "mean value" are calculated by adding all data points up and dividing that sum by the number of data points.

e.g. if you eat 1 popsicle today, ate 2 popsicles yesterday and 3 the day before, you have 3 data points : 3, 2, 1.

in my example you had

(3 + 2 + 1)/3 = 6/3 = 2 popsicles every day on average.

the same principle here.

you have 2 days points. and your average score is

(88 + 93)/2 = 181/2 = 90.5

Given vertices:

Plot the points (see attached).

AC is the base of the triangle:

Add BD, the height. It will help to find the length of the other two sides and the area:

Find AB and BC using Pythagorean:

Perimeter: 7 + 5.7 + 5 = 15.7 units

Area: 1/2*7*4 = 14 units²

Given vertices:

Plot the points (see attached).

As we see this is a rectangle.

Find two adjacent sides using distance equation:

Perimeter: 2(4.1 + 8.2) = 2(12.3) = 24.6 units

Area: √17 * 2√17 = 2*17 = 34 units²

Answer:

11.  Perimeter:  17.7 units

11.  Area:  14 square units

12.  Perimeter:  24.7 units

12.  Area:  34 square units

Step-by-step explanation:

Given vertices of the polygon:

Plot the given points in the coordinate plane (see attachment 1).

From inspection, we can see that the polygon is a triangle with the following dimensions:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

The length of AC is 7 units.

To find the length of AB and BC, use the distance formula.

[tex]\begin{aligned}AB&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(2-(-2))^2+(5-1)^2}\\&=\sqrt{(4)^2+(4)^2}\\&=\sqrt{16+16}\\&=\sqrt{32}\\&=4\sqrt{2}\;\sf units\end{aligned}[/tex]

[tex]\begin{aligned}BC&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(5-2)^2+(1-5)^2}\\&=\sqrt{(3)^2+(-4)^2}\\&=\sqrt{9+16}\\&=\sqrt{25}\\&=5\;\sf units\end{aligned}[/tex]

Therefore:

[tex]\begin{aligned}\textsf{Perimeter}&=AB+BC+AC\\&=4\sqrt{2}+5+7\\&=12+4\sqrt{2}\\&=17.6568542...\\&=17.7\;\sf units\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Area}&=\dfrac{1}{2}\cdot 7\cdot 4\\\\&=\dfrac{7}{2} \cdot 4\\\\&=\dfrac{28}{2}\\\\&=14\;\sf square\;units\end{aligned}[/tex]

Given vertices of the polygon:

Plot the given points in the coordinate plane (see attachment 2).

From inspection, we can see that the polygon is a rectangle.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

Since AB = DC and BC = AD, find the length of AB and BC using the distance formula.

[tex]\begin{aligned}AB&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(1-(-3))^2+(6-5)^2}\\&=\sqrt{(4)^2+(1)^2}\\&=\sqrt{16+1}\\&=\sqrt{17}\;\sf units\end{aligned}[/tex]

[tex]\begin{aligned}BC&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(3-1)^2+(-2-6)^2}\\&=\sqrt{(2)^2+(-8)^2}\\&=\sqrt{4+64}\\&=\sqrt{68}\\&=2\sqrt{17}\;\sf units\end{aligned}[/tex]

Therefore:

[tex]\begin{aligned}\textsf{Perimeter}&=AB+BC+CD+AD\\&=2(AB+BC)\\&=2(\sqrt{17}+2\sqrt{17})\\&=2(3\sqrt{17})\\&=6\sqrt{17}\\&=24.7386337...\\&=24.7\;\sf units\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Area}&=AB\cdot BC\\&=\sqrt{17} \cdot 2\sqrt{17}\\&=34\;\sf square\;units\end{aligned}[/tex]

Answer:

this statement is true .............

Answer:

OK the so the answer is this,

A - Irregular - It is an irregular polygon as the sides and angles are unequal.

B - Neither - As circle is not a polygon.

C - Irregular - Again, it is an irregular for the same reason.

D - Regular - Sides and angles are equal

E - Regular - Equilateral triangle

Answer:

The annual passenger revenue of the rail transport corporation was $930 million when:

R = 930

-20|t-15| + 1,010 = 930

-20|t-15| = 80

|t-15| = 4

So, we can see that t-15 = 4 and t-15 = -4 both lead to an annual revenue of $930 million dollars.

To find the values of t, we add 15 to both sides of the equation:

t-15 = 4 => t = 19

t-15 = -4 => t = 11

So, the years where the passenger revenue was $930 million are:

2011

2019

A kitten who is just born is predicted to weigh 4.05 ounces and its weight is predicted to increase by 0.4 ounces. Then the correct option is B.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Information was gathered on the weight, in ounces, of cats for the initial three months after birth. A line of fit was drawn through the dispersed plot and had the condition w = 4.05 + 0.4d, where w is the heaviness of the cat in ounces and d is the age of the little cat in days.

A kitten who is just born is predicted to weigh 4.05 ounces and its weight is predicted to increase by 0.4 ounces. Then the correct option is B.

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Answer:

Hi!

0 is basically inverse 0

any integer Inverse change the function

Therefore, the three consecutive odd integers that add up to 93 are 33, 35, and 37.

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Answer:

The area is 48 feet^2

Step-by-step explanation:

The area of a triangle can be calculated with the following formula:

area=1/2(base)(height)

Substitute in the numbers and find the answer.

a=(0.5)(6)(16)=48

The distance from Earth to the Sun is 396 times larger than the distance from the Earth to the moon.

Scientific notation.

This is a mode of expressing large numbers of great power. Its helps in the simple expression of numbers so that some arithmetic operations can be performed as required.

In the given question, we have;

distance from Earth to the Sun = 1.47 X 10^11 meters

and

distance from Earth to moon = 3.71 X 10^8 meters

Thus,

to determine by how much is the distance between the Earth and Sun greater than that between the Earth and moon;

n = distance from Earth to the Sun/ distance from the Earth to the moon

  = 1.47 X 10^11/ 3.71 X 10^8

  = 3.962 x 10^2

n = 396

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Answer:

Step-by-step explanation:

a. To minimize the average cost, we need to find the value of x that minimizes the cost function C(x) = x² - 40x + 500.

This is the same as finding the minimum value of the parabola represented by the function. The vertex of the parabola is the point at which the parabola reaches its minimum or maximum value. The vertex form of a parabola is given by C(x) = a(x - h)² + k, where (h, k) is the vertex.

By comparing the given function with the vertex form of a parabola, we can find the vertex:

C(x) = x² - 40x + 500

= a(x - h)² + k

= (x - h)² + k

The x-coordinate of the vertex h = 40/2 = 20

So the minimum average cost occurs when 20 televisions are made per week.

b. To find the minimum average cost, we need to substitute the value of x = 20 into the cost function:

C(x) = x² - 40x + 500

= 20² - 40*20 + 500

= 400 - 800 + 500

= 100

So the minimum average cost is $100 per television.

If the average cost is $200 per television, we can set C(x) = 200 and solve for x:

200 = x² - 40x + 500

0 = x² - 40x + 300

This is a quadratic equation that can be solved by factoring or by using the quadratic formula.

we can factor it as

0 = (x-50)(x-6)

x = 50 or x = 6

The number of televisions made per week if the average cost is $200 per television is 50 or 6. Since 50 is much higher than 20, the minimum average cost, it is not physically possible to make 50 televisions with the average cost of $200 per television. So the answer is 6 televisions per week.

Therefore , the solution of purchased so that the consumer has an equal amount of each LCM if hot dogs are packaged with 10 dogs per pack .

"Sandwich rolls or hot dog buns are typically sold in packs of eight because the buns are baked in clusters of four in pans designed to hold eight rolls." Because hot dogs are sold by the pound and store-bought standard-sized hot dogs weigh 1.6 ounces,

Here,

purchased so that the consumer has an equal amount of

each if hot dogs are packaged with 10 dogs per pack and hot dog buns are packaged with 8 buns per pack  LCM is 40.

hot dog buns are packaged with 8 buns per pack  LCM is 40. 4 packages of hot dogs and 5 packages of buns are required.

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Answer: We can set up a system of equations to solve this problem. Let x be the number of quarters and y be the number of nickels. We know that:

x + y = 20 (the total number of coins)

0.25x + 0.05y = 4.20 (the total value of the coins in dollars)

We can use the first equation to solve for one variable in terms of the other, and then substitute that into the second equation to get a single equation with one variable.

For example:

x = 20 - y

0.25(20-y) + 0.05y = 4.20

5-0.25y + 0.05y = 4.20

5= 4.20

y = 20 - 5

y = 15

x = 20 - 15

x = 5

So Jada has 5 quarters and 15 nickels in her pocket.

Step-by-step explanation:

The table that represents the equation and the graph is

(-1, 7.5). (1, 4.5), (3, -1.5), and (5, 1.5)

This can be found by tracing the points on the graph or substituting into the equation

The equation is 3x − 2y = 12, rearranging will result to 1.5x - 6 = y

substituting the values of x into y = 1.5x - 6

for x = -1, y = 1.5 * -1 - 6 = -7.5

for x = 1, y = 1.5 * 1 - 6 = -4.5

for x = 3, y = 1.5 * 3 - 6 = -1.5

for x = 5, y = 1.5 * 5 - 6 = 1.5

Hence the third option while counting from top id the correct option

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The ordered pairs for the equation 3x - 2y = 12 is (-1, -7.5), (1, -4.5), (3, -1.5) and (5, 1.5)

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

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept.

Given the equation:

3x - 2y = 12

2y = 3x - 12

y = (3/2)x - 6

When x = -1; y = (3/2)(-1) - 6 = -7.5

When x = 1; y = (3/2)(1) - 6 = -4.5

When x = 3; y = (3/2)(3) - 6 = -1.5

When x = 5; y = (3/2)(5) - 6 = 1.5

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Answer: the answer is $13

Step-by-step explantion

To show work subtract 25 from all the answer so it would be:

The system of inequalties on the graph is:

x  + 4y ≤ 15

y ≥ 0

First, we can see a solid line at y = 0 and we have the region above that line shaded, so one of the inequalities is:

y ≥ 0.

The other inequality is a solid line with a negative slope and the shaded region is below the line.

The only option that has these characteristics is:

x  + 4y ≤ 15

4y ≤ - x + 15

y ≤ (-1/4)x + 15/4

Then the system of inequalities is:

x  + 4y ≤ 15

y ≥ 0

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Answer:

Step-by-step explanation:

The simplified expression as a product of polynomials is given as follows:

(c - d)(p + 1).

The expression for this problem is defined as follows:

p(c - d) + c - d.

The expression can be defined as an addition in which the terms are given as follows:

The common factor to both of the terms of the addition is given as follows:

(c - d).

The quotients of each term relative to the common factor are given as follows:

Hence the simplified expression is given as follows:

(c - d)(p + 1).

(the plus sign for p + 1 is because the expression is an addition and not a subtraction).

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