Consider the function shown.
Which inequality represents the range of the function?

Answer:

y=12x+40

Step-by-step explanation:

The earnings are the initial payment per month plus the pay per hour times the number of hours.

Answer:

option b) 5 units

Answer:

5 units

Step-by-step explanation:

You use Pythagoras' theorem

3squared + 4 squared = 25

square root of 25 is 5

He buy 10 games that costs $13.

Equation, also known as a statement of equivalence between two expressions with variable- and/or number-based components. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

Given Data

John has $160 to spend on video games.

He spent $30 on a controller the rest on video games.

If each game costs $13

Equation

30 + 13g = 160

13g = 130

g = 10

He buy 10 games that costs $13.

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The answer is C:38

explanation: you multiply 8x4=32, so then you add 6 to 32

Hope this helped!

could you please re post the question clearly as right now I don't understand what this means, you can try just taking a picture of the question and attach it to your post

The values of the coefficients and constant in the quadratic function are a = 1, b = -5, and c = 6, where a and b are coefficients and c is the constant.

Given quadratic function f(x) = x² - 5x + 6.

The values of the coefficients and constant in the function are

a = 1

b = -5

c = 6

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The saved amount after selling the tank and by using the code is $21.24.

What is selling price?

The selling price is the amount in the form of extra charges which was decided by the shopkeepers for the different commodities. The cost spent by the shopkeeper for the purchase is the cost price. And for profit selling price should be more than the cost price.

According to the question, the given parameter is as written below:

The selling price of the Jellyfish tank is: $24.99

And the discount with special code is: 15 percent

The calculated money saved by using the special code is:

Discount Amount = (24.99 x 15)/100 = 3.7485

Saved money = $24.99 - $ 3.7485 = $ 21.2415 ≅ $ 21.24

Hence, the saved amount after selling the tank and by using the code is $21.24.

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Answer:

45

Step-by-step explanation:

In this picture we can see that they gave us 2 angles.

Angle V has an angle of x+83

Angle S has an angle of 4x - 53

As one of the circle thermoses in mathematics said when there is an angle in the center of the circle, the angle at the circumference is half the angle at the center, which means we could create and equation such that:

angle of angle V = 2 times the angle of angle S

x + 83 = 2(4x - 53)

x + 83 = 8x - 106

189 = 7x

27 = x

Since we know x = 27, we can substitute into the equation angle of S to find what is the angle of TSU:

4x - 53

= 4(27) - 53

= 108 - 53

= 45

Answer:

<TSU = 55°

Step-by-step explanation:

We know that,

Angle at the circumference of a circle is twice the angle at the centre.

Therefore,

2 × <UST = <UVT

Given that,

< UVT = x + 83

< TSU = 4x - 53

Accordingly, we can make an expression like this.

[tex] \sf2 × <UST = <UVT[/tex]

[tex] \sf2(4x - 53) = x + 83 \\ [/tex]

And now solve the above expression and find the value of x.

Let us solve it now.

[tex] \sf8x - 106 = x + 83 \\ \sf8x - x = 106 + 83 \\ \sf7x = 189 \\ \sf \: x = 27[/tex]

And now, according to the question they've asked us to find the value of <TSU.

As we mentioned earlier, they've given that, <TSU = 4x - 53.

So, to find the value of Angle TSU, we have to replace x with 27 and find the value of angle TSU.

Let us solve it now

[tex] \sf \: <TSU = 4x - 53 \\ \sf \: <TSU = 4 \times 27 - 53 \\ \sf \: <TSU = 108 - 53 \\ \sf \: <TSU = 55 \degree[/tex]

Answer:

205

Step-by-step explanation:

we first enter the desired number equaling the equation, so 21. then we enter the first term and find the common difference, in this case it's going up by 9. then we take the desired term, subtract 1 and we end up with 205 as the 21st term.

21 = 25 + 9 (21 - 1)

The slope of the line is -1.

A line's slope is defined as the ratio of the change in y coordinate to the change in x coordinate.

Now the given points are : (-4,6) and (-1,3)

We know that the slope of a line is given by :

[tex]m=\frac{y_2-y_1}{x_2-x_1}.[/tex]

Now we can put the values of the points to get the slope as

[tex]m=\frac{3-6}{-1-(-4)}\\\\[/tex]

or , m = -1

Hence the slope of the line is -1

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The system of equations has two solutions, that is (4, 2).

Given,

There is a system of equations:

Equation 1: 2x + 4y = 16

Equation 2: (1/2)x - 2y = 4

The solution to the system of equations = (4, 2)

Lets check for the solution:

The equations are in the form of,

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

Here,

a₁ = 2 , a₂ = 1/2

b₁ = 4 , b₂ = 2

c₁ = 16 , c₂ = 4

Now we know that,

a₁/a₂ = b₁/b₂ = c₁/c₂

So,

a₁/a₂ = 2 / (1/2) = 4/1 = 4

b₁/b₂ = 4/2 = 2

c₁/c₂ = 16/4 = 4

Therefore, the system of equations has two solutions, that is (4, 2).

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Answer:

0

Step-by-step explanation:

7 is not in the sample space, meaning it is impossible. Therefore, the probability is 0.

If an experiment with a random outcome is repeated a large number of​ times, the empirical probability of an event is likely to be close to the true probability. This mathematical theorem is called​ The Law of Large Numbers.

The Law of Large Numbers states that on the off chance that a test with an irregular result is repeated a huge number of​ times, the empirical probability of an event is likely to be near the true probability. The bigger the number of​ redundancies, the closer together these probabilities are likely to be.The law of large numbers does not ensure that a given test, particularly a little test, will reflect the genuine population characteristics or that a test that does not reflect the genuine population will be adjusted by a subsequent sample. The law of large numbers demonstrates a greater test will speak to a population mean, whereas the central tendency theorem states a greater test will speak to a population's distribution.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

Scale factor: 1 : 8

Scale drawing:

A = 2 cm²

Object:

A = ?

Step 02:

A = 2 cm² * (8 / 1) = 16cm²

The expression in factored form for x² 13 x + 42 will be (x + 6)(x + 7).

It should be noted that an expression is simony used in Mathematics to show the relationship between the variables that are expressed.

In this case, the expression in factored form for x² 13 x + 42 will be:

x² + 13x + 42

x² + 6x + 7x + 42

x(x + 6) + 7(x + 6)

(x + 6)(x + 7)

The expression is (x + 6)(x + 7).

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Answer:

Green

Verde = green

Answer:

Total width of the gate in cm is equal to=> 109.9+89.4=199.3 cm

Step-by-step explanation:

GIVEN-

A gate is made out of 7 panels of wood, each of which is 15.7 cm wide. between the panels, there is a gap of 14.9 cm

THIS IS AN EASY SUMMATION PROBLEM-

FOR ONE PANEL WIDTH =15.7

FOR 7 PANEL'S WIDTH =15.7*7=109.9;

NOW, between the 7 panels, 6 gaps create

one gap =14.9 cm

six gap =14.9 * 6 =89.4 cm

so, the total width of the gate in cm is equal to=> 109.9+89.4=199.3 cm

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Answer:

D

Step-by-step explanation:

[tex]2x-12y=24 \\ \\ x-6y=12 \\ \\ 6y-x=-12 \\ \\ 6y=x-12 \\ \\ y=\frac{1}{6}x-2[/tex]

The slopes of the lines are neither the same nor are they negative reciprocals, so the answer is D.

The graph of the inequality 7< f has been plotted.

The given inequality is 7 < f

The inequality states that the the relationship between two numbers. The relationships are greater than, greater than or equal to , less than, less than or equal to, equal to. These are the commonly used relationship between the two number in the inequality.

Here the inequality is 7 < f

The value of f is greater than 7

Plot the inequality in the graph

At the point 7 we use a small circle to represents the term greater than, if it was greater than or equal to we use a dot at that point

Hence, the graph of the inequality 7< f has been plotted

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The two solutions of the quadratic function are 0.58 and -1.1.

The solution of a quadratic equation can be obtained using the substitution method or formula method.

The solution of the given quadratic function is determined as follows;

f(x) = 8x² + 4x - 5

0 =  8x² + 4x - 5

The formula method of a quadratic function is given as;

[tex]x = \frac{-b \ \ \pm \ \sqrt{b^2 - 4ac} }{2a}[/tex]

from the above equation, a = 8, b = 4, c = -5

[tex]x = \frac{-4 \ \ \pm \ \sqrt{4^2 - 4(8\times -5)} }{2a}\\\\x = \frac{-4 \ \ \pm \ \sqrt{16 + 160} }{2(8)}\\\\[/tex]

x = 0.58 or -1.1

Thus, the function has two solutions, a negative and positive solution.

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An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices.

10. In the given figure,

l ║m

(3x - 29)° + (8y + 17)° = 180° [Because they are linear pairs]

⇒ 3x -29 + 8y + 17 = 180

⇒ 3x + 8y - 12 = 180

⇒ 3x + 8y = 192 ............ (1)

Now,

8y + 17 = 6x -7 [Alternate interior angles]

⇒ 6x - 8y = 24 ..............(2)

On adding (1) and (2),

(3x + 8y) + (6x - 8y) = 192 + 24

simplifying the above equation, we get

⇒9x = 216

⇒ x = 216/9 = 24

⇒ x = 24

Now, 6x - 8y = 24

⇒ 8y = 6(24) - 24

⇒ y = (144 - 24)/8

⇒ y = 120/8 = 15

So, x = 24 and y = 15

11. In this given figure,

l ║m

7x - 23 = 49 + 3x ...... (Alternate interior angles)

⇒ 7x - 3x = 49+23

⇒ 4x = 72

⇒ x = 18

11y -1 = 3x [Alternate exterior angles]

⇒ 11y - 1 = 3 x 18

⇒ 11y = 54 + 1

⇒ 11y = 55

⇒ y = 5

Therefore, the value of x = 18 and y = 5

12. 11. In this given figure,

l ║m

3x - 4 = 5x - 38 [Alternate interior angles]

⇒ 5x - 3x = 38 - 4

⇒ 2x = 34

⇒ x = 17

7y - 20 + 5x - 38 + 90° = 180° [Angle sum property of a triangle]

⇒ 7y - 20 + 85 - 38 + 90 = 180

⇒ 7y + 117 = 180

simplifying the above equation, we get

⇒ 7y = 180 - 117

⇒ 7y = 63

⇒ y = 63/7 = 9

Therefore, the value of x = 17 and y = 9

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Answer:

x = 4

The two interior angles are

14x + 6 = 14 x 4 + 6 = 62°

16x + 4 = 16 x 4 + 4 = 68°

Step-by-step explanation:

The exterior angle of a triangle is the sum of the interior angles:

Here the exterior angle is 130° and the interior angles are
16x + 4 and 14x + 6

So 16x + 4 + 14x + 6 = 130

Gathering like terms and simplifying:
16x + 14x + 4 + 6 =  130

30x + 10 = 130

30x = 120           (subtract 10 from both sides)

x = 4

The two interior angles are

14x + 6 = 14 x 4 + 6 = 62°

16x + 4 = 16 x 4 + 4 = 68°

[tex] - 2y = 8 - 3x \\ \frac{ - 2y}{ - 2} = \frac{8}{ - 2} - \frac{3x}{ - 2} \\ y = \frac{3}{2} x - 4[/tex]

AS WE SEE IN THE EQUATION ABOVE THE GRADIENT IS

[tex] \frac{3}{2} [/tex]

IT MEANS THE GRADIENT OF THE NEW EQUATION IS ALSO

[tex] \frac{3}{2} [/tex]

NOW GIVEN THE POINTS WE CAN USE THE KNOWNS TO GET THE VALUE OF C IN THE NEW EQUATION.

[tex] - 3 = \frac{3}{2} (6) + c \\ - 3 = 9 + c \\ - 3 - 9 = c \\ c = - 12[/tex]

[tex]y = \frac{3}{2} x - 12[/tex]

After thoroughly calculating the equation, we conclude that x⁴ + 4x³ - 6x² - 2x + 25  is the simplified form of 3/x - 1 - 4x - 1/x + 1 = x² +(5/x)²- 1 - 5

When the top and bottom of a fraction are the same size and still whole numbers, the fraction is said to be in its simplest form or simplified form.

Using 2/4 as an example, 1/2 can be written.

Simplify a fraction by multiplying its top and bottom by the biggest number that will divide them both exactly (they must stay whole numbers). the outcome will be what we call the simplified form.

We have been asked to simply the equation

3/x - 1 - 4x - 1/x + 1 = x² +(5/x)²- 1 - 5

⇒ 3/x - 4x - 1/x + 6 = x² +(5/x)²

⇒ 2/x - 4x + 6 = x² +(5/x)²

⇒ 2/x - 4x²/x + 6x/x = x² +(5/x)²

⇒ (2 - 4x² + 6x)/x = x² +(5/x)²

Multiplying x to both side

⇒ 2 - 4x² + 6x = x² +(5/x)² × x

⇒ 2 - 4x² + 6x = x³ + 25/x

​⇒  x³ + 4x² - 2 = 6x - 25/x

​⇒ x³ + 4x² - 2 = 6x²/x - 25/x

​⇒ x³ + 4x² - 2 = (6x²- 25)/x

Multiplying x to both side

​⇒ (x³ + 4x² - 2) x = 6x²- 25

​⇒ ​x⁴ + 4x³ - 2x = 6x²- 25

​⇒ x⁴ + 4x³ - 6x² - 2x + 25

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If A is in the interior of NFL. If m/NFA = 5x+10, m/AFL = 30-2x, and m/NFL = 58°, the value of x would be 6

It is important to note that the formula for determining the sum of interior angles of a shape is expressed as;

(n-2) 180

Where 'n' is the number of sides

From the information given, we have that the shape has 3 sides, so we have

(3 -2)180

180°

Give the angles as;

Equate the angles to m/NFL, we have

5x+10 + 30-2x = 58

Now, collect like terms

5x - 2x = 58 - 40

Subtract like terms

3x = 18

Make 'x' the subject by dividing both sides by 3, we have

x = 18/3

x = 6

Thus, the value of 'x' is 3

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Answer:

x = 10

Step-by-step explanation:

55 = 5x + 5  Subtract 5 from both sides of the equation

50 = 5x  Divide both sides by 5

10 = x

Answer:10

Step-by-step explanation:- 5 on both sides then you get 50=5x 50/5=10