9/12 devided by 2/12

Answer:

[tex](f+g)(x) = -8x-6[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]\displaystyle f(x) = -5x - 4 \text{ and } g(x) = -3x - 2[/tex]

And we want to find:

[tex](f+g)(x)[/tex]

Recall that this is equivalent to:

[tex]\displaystyle (f+g)(x) = f(x) + g(x)[/tex]

Substitute and simplify:

[tex]\displaystyle \begin{aligned} (f+g)(x) &= (-5x-4)+(-3x-2) \\ \\ &= -8x-6 \end{aligned}[/tex]

In conclusion:

[tex](f+g)(x) = -8x-6[/tex]

Answer:

8.7

Step-by-step explanation:

Calculate the area of the triangle by using sine.

Area of Triangle

[tex]A = \frac{1}{2} \times \text{side} \times \text{side} \times \sin{\theta}[/tex]

θ ... included angle between the two sides

We already have two sides a and another side which is congruent to a, making it isosceles triangle. But we don't have the included angle. The angle we need is the vertex angle of the isosceles triangle. Angle B is one of the base angles (two base angles are congruent) and it measures 70°.

Recall that angles in any triangle add up to 180°.

base angle + base angle + vertex angle = 180°

70° + 70° + vertex angle = 180°

vertex angle = 40°

Now we have all the information to use the formula!

[tex]A = \frac{1}{2} \times \text{side} \times \text{side} \times \sin{\theta}[/tex]

[tex]A = \frac{1}{2} \times 5.2 \text{ cm} \times 5.2 \text{ cm} \times \sin{40^\circ}[/tex]

[tex]A = 13.52 \text{ cm}^2 \times \sin{40^\circ}[/tex]

[tex]A \approx 8.6904 \text{ cm}^2[/tex]

Rounded to 1 DP:

[tex]A = 8.7 \text{ cm}^2[/tex]

Answer:

0.375x^2

Step-by-step explanation:

(-1.5x)(-0.25x)  

= (-1.5)(0.25)(x)(x)

= 0.375x^2

At 3:30 pm

the minute hand was at 6 and hour hand was in between 3 and 4

At 4 pm

the minute hand is at 12 and hour hand is at 4

Total numbers travelled by minute hand

Total degrees turn

Answer: 78

Step-by-step explanation:

6(4+9)

use foil to distribute the 6 to the 4 and 9

6×4 + 6×9

24 + 54

⇒ 78

Answer:

[tex]\text{P(green)} =\frac{45}{139}[/tex]

Step-by-step explanation:

The total number of candies is :

= 42+45+20+32

= 139

Then

we have 45 green out of 139 candies.

Then

[tex]\text{P(green)} =\frac{45}{139}[/tex]

Note : 45/139 is already simplified.

[tex]Rational \: numbers \: can \: be \: written \: in \: the \: form \: of \: \frac{a}{b} \\ 2.3 = \frac{23}{10} = > answer[/tex]

Hope this helps :)

Answer:

C. 3rd one Fraction 10/24

Step-by-step explanation:

3/4 - 2/6 = 0.41 or = 10/24 or it could be equal to 5/12​ are 10/24, 15/36, 20/48 and 25/60 or as Decimal 0.41

Step-by-step explanation:

Hope This Helped

Based on the given table, the maximum temperature in the year was 22°C and the minimum was -12°C. It is colder when the temperature is -7°C.

The temperatures between -7°C and 7 °C are :-6, -4, 0, 1, and 6.

During the year, the highest recorded temperature was 22°C in the month of July. The lowest temperature was -12°C in the month of Janaury.

The lower the temperature, the colder it is. This is why -7°C is colder than 7°C.

The temperatures between -7°C and 7°C are temperatures that are higher than -7°C but lower than 7°C. These are:

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Arc length = 4.28 cm.

Arc length is the distance between two points along a section of a curve.

circumference of a circle of radius r is C = 2πr,

and central angle = 360 degrees.  

circumference = 28 cm.  

28 cm =2πr

28= 2*3.14*r

28= 6.28*r

r= 4.46 cm.  

Arc length, s = r[tex]\theta[/tex]

[tex]\theta[/tex] =55 degrees,

s = 4.28 cm.

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Answer:

2 1/6

Step-by-step explanation:

The answer is 2 1/6 because you should start by adding 3 1/2 + 2 1/3. This equals 5 5/6 feet. You should then subtract 8 - 5 5/6 because you are figuring out how much is left. When you subtract 8 - 5 5/6, you get 2 1/6. So 2 1/6 feet of the board is left.

Hope this helps!

Answer:

A.) 20

Step-by-step explanation:

According to the bar graph, in February, the store sold 50 computers. In September, it seems like the store sold 30 computers. Therefore, if 50 - 30 = 20, the store sold 20 more computers in February than in September.

Answer:

A) 20

Step-by-step explanation:

Computers sold in Feb: 50

Computers sold in Sept: 30

50 - 30 = 20

Answer:

C

Step-by-step explanation:

Option C is correct, the polygon in c option is the next step in the series

A polygon is a plane figure made up of line segments connected to form a closed polygonal chain.

In the first step we can see a triangle

The triangle has three sides

In the second step there is a rectangle which has four sides

The third step has pentagon which has five sides

So in next step the polygon should have six sides

Hexagon is the next step in the series

Hence, option C is correct, the polygon in c option is the next step in the series

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Answer:

24 units ^2

Step-by-step explanation:

The base runs from 3 to 7 so the base is 7-3 = 4 units

The height runs from 2 to 8  so the height is 8-2 = 6 units

The area is

A = bh

   = 6*4 = 24 units ^2

The surface area of the stool is 3629.84 square cm

The radius is given as:

r = 34.2

The surface area is calculated using:

A = πr^2

So, we have:

A = 3.14 * 34^2

Evaluate

A = 3629.84

Hence, the surface area of the stool is 3629.84 square cm

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Answer: (-2, 1)

Step-by-step explanation:

The 1st value in a pair is x, the 2nd is y.

▪︎ (-2, 1)

1 = 2(-2)+5

1 = -4+5

1 = 1 ✅

▪︎ (-1, 4)

4 = 2(-1)+5

4 = -2 + 5

4 = 3❌

▪︎ (1, 6)

6 = 2*1+5

6 = 2 + 5

6 = 7❌

▪︎ (3, 10)

10 = 2*3+5

10 = 6 + 5

10 = 11❌

[tex]|\Omega|=10^2=100\\|A|=2\cdot3=6\\\\P(A)=\dfrac{6}{100}=6\%[/tex]

Yes

Functions are relations that express a rule between the x-values and the y-values.

What Makes a Function

Functions are types of relations, specifically, where the x-values do not repeat. This means that each x-value has exactly one y-value. So, if the x-values do not repeat in a relation, then it must be a function.

How To Find a Function From Coordinates

In the question, we are given 4 different coordinate points. The points have 4 x-values, none of which repeat. This means that the relationship must be a function.

To find a function from points, all you need to do is check that the x-values do not repeat.

How To Find a Function From a Graph

If you are given a continuous graph, another way to figure out if it is the vertical line test. The vertical line test is when you draw vertical lines across the graph. If you are able to draw a vertical line everywhere on the graph without the line intersecting with the graph more than once, then it is a function. However, if the line intersects with the graph more than once at any point, then it is not a function.

Using the Vertical Line Test, the graph does not represent a function is  ellipse, the third graph.

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function. It is done by visually examining the number of intersections of the curve with vertical lines.

Any vertical line in the x y plane must intersect the graph of a function at most once.

In the given graphs, the graph of a function intersects the y axis twice. So, it is not a function.

From the given graphs, the third graph which is of ellipse crosses the vertical line twice.

Thus, the graph does not represent a function is ellipse.

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Answer: 0.388

8 continuing so draw a line over the eights.

The chemical need to be added to the tank is  16000 cubic cm

The volume is the total capacity of a container.

Total volume of tank = 80,000 cubic centimeters of water

Chemical volume =  5 cubic centimeters

Chemical needed = = 80,000 /5 = 16000 cubic cm is needed.

Thus,  16000 cubic cm chemical is needed.

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Answer:

  n² -3

Step-by-step explanation:

The square of a number is found by multiplying it by itself. The square of a number in an algebraic expression is shown using an exponent of 2. For a number represented by n, the square of the number is n².

3 less than a number is found by subtracting 3 from the number. Equivalently, it is found by adding -3 to the number. The addition can be done in any order. For a number represented by n, 3 less than the number is either of ...

  -3 +n

  n -3

__

The expression for "3 less than the square of a number" is ...

  n² -3 . . . . . where n represents the number

It can also be written ...

  -3 +n²

We generally prefer the first form, with variable exponents decreasing left-to-right.

Answer:

1) 19³=6859

2) 16² =256

3) 15³ =3375

4) 20² =400

5) 10³ =1000

Step-by-step explanation:

using your calculator to (square = number times itself) or (cube = number times itself times itself again)

Answer:

x = 2 or -2

Step-by-step explanation:

This is a regular hexagon

To find the value of x we will have to find the sum of interior angles first and to do that:

(n-2)*180 (n is the number of angles)

(6-2)*180 = 720 is the sum of all six angles

since this is a regular hexagon, all angles has equal measures so

720/6 = 120 now

30x^2 = 120 divide both sides by 30

x^2 = 4 find the root of both sides

x = 2 or -2

the equation's squared variable is the "x", namely x², so we're looking at a vertical parabola, and thus its axis of symmetry will be a vertical line that runs through its vertex, so

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+5} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 4}{2(1)}~~~~ ,~~~~ 5-\cfrac{ (4)^2}{4(1)}\right) \implies \left( - \cfrac{ 4 }{ 2 }~~,~~5 - \cfrac{ 16 }{ 4 } \right)\implies (\stackrel{x}{-2}~~,~~1) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{axis of symmetry}}{x=-2}~\hfill[/tex]

Check the picture below.

Answer:

-2.6112

Step-by-step explanation:

= 0.510 (3+0.2) x -1.6

= 0.510 x 3.2 x -1.6

= -2.6112

hence answer is -2.6112.

Applying the circle theorems, we have:

4. y = 120°

x = 45°

5. x = 90°

y = 32°

6. x = 40°

y = 20°

7. x = 116°

y = 98°

8. x = 100°

y = 60°

9. x = 54°

y = 75°

The angle formed outside a circle by the intersection of two secants equals half the positive difference of the measures of the intercepted arcs, based on the angle of intersecting secants theorem.

The angle formed when two chords of a circle intersect, equals the half the sum of the measures of the intercepted arcs, based on the angle of intersecting chords theorem.

4. y = 360 - 95 - 30 - 115 = 120°

x = 1/2(120 - 30) [angle of intersecting secants theorem]

x = 45°

5. x = 90° [based on the tangent theorem]

y = 180 - 90 - 58 [triangle sum theorem]

y = 32°

6. x = 360 - 160 - 160 [central angle theorem]

x = 40°

y = 1/2(40) [inscribed angle theorem]

y = 20°

7. x = 180 - 2(32)

x = 116°

y = 1/2[132 + 2(32)] [angle of intersecting chords theorem]

y = 98°

8. x = 180 - 80 [opposite angles of an inscribed quadrilateral are supplementary]

x = 100°

y = 1/2[(2(80) - 90) + 50] [inscribed angle theorem]

y = 1/2[70 + 50]

y = 60°

9. 40 = 1/2(134 - x) [angle of intersecting secants theorem]

2(40) = 134 - x

80 = 134 - x

80 - 134 = - x

-54 = -x

x = 54°

y = 360 - 134 - 54 - 97

y = 75°

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An expression is defined as a set of numbers, variables, and mathematical operations. The coefficients for the binomial expansion of (p+q)⁶ are 1, 6, 15, and 20.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expansion of the given binomial (p+q)⁶ can be done as shown below,

(p+q)⁶ = p⁶ + 6p⁵q + 15p⁴q² + 20p³q³ + 15p²q⁴ + 6pq⁵ + q⁶

Hence, the coefficients for the binomial expansion of (p+q)⁶ is 1, 6, 15, and 20.

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