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Answer:

Angle is measured in degrees (°) and radians. It is formed between the two adjacent sides of a polygon. Every polygon has different sides and different numbers of angles. The formula to find the angles in degrees is useful in geometry and trigonometry. It is essential to understand other concepts of mathematics, such as arc, a central angle of the circle, etc.  

A full circle = 360°

A straight line = 180°

A semicircle= 180°

A Quarter circle = 90°

Given: Hypotenuse = 12

Perpendicular = 6

The trigonometry function to calculate the angle is given by:

sinA = 6/12

A = 30°

Answer:

Step-by-step explanation:

Steps

1] On the right, put brackets around the 1st 2 terms.

y = (x^2 + 2x) - 6

2] Divide the second term's coefficient by 2 and square the result.

2/2 = 1

3] Square the result

1^2 = 1

4] Add that inside the brackets

y = (x^2 + 2x + 1) - 6

5] Subtract 1 outside the brackets. The original equation is still there.

y = (x^2 + 2x + 1) - 6 - 1

y = (x^2 + 2x + 1) - 7

6] What is inside the brackets is a perfect square.

y = (x + 1)^2 - 7

Answer D

Answer:12

Step-by-step explanation:

Peter's age = x

John's age = y

y=2x

after 8 years = y+8=y+x+2

=(y-y)+8-2=x

=6=x

y=2(6)=12

The z score corresponding to the sample is -6.25

The formula for calculating the z-score is expressed as

z = x- μ/σ

Given the following parameters

x = 22 (sample size)

Mean  μ = 72

standard deviation σ = 8

Substitute

z = 22-72/8

z = -50/8

z = -6.25

Hence the z score corresponding to the sample is -6.25

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Based on the dataset given, the first quartile is 38.75, and the third quartile is 45.25. This interquartile range is 6.5. The lower fence is 29 and the upper fence is 55.

Order the sets:

31, 38, 39, 40, 41, 45, 45, 45,46, 58

First quartile position:

= 1(10 + 1) / 4

= 2.75th position

= 38 + 0.75 x (39 - 38)

= 38.75

Third quartile:

= 3(10 + 1) / 4

= 8.25th position

= 45 + 0.25 x (46-45)

= 45.25

Interquartile range:

= 45.25 - 38.75

= 6.5

Upper fence:

= 45.25 + (1.5 x 6.5)

= 55

Lower fence:

= 38.75 - (1.5 x 6.5)

= 29

59 is an outlier.

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The regression equation is y =  3.002 + 0.5x and the scatterplot is illustrated.

It should be noted that a scatterplot simply means a type of data that shows the relationship between two numerical variables.

From the information, summation is X is 99, summation Y is 82.5, summation XY is 797.47, and summation X² is 1001.

Now the value of a will be:

= 82.5 - 1001 - 99 - 797.47/(11.1001 - 99²)

= 3.002

b = (11 × 797.47 - 99 × 82.5)/11.1001 - 99²

= 0.5

The regression equation will be:

y = a + bx.

y = 3.002 + 0.5x

There's positive linear correlation between x and y.

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The simplified expression for the area of the rectangular table is Three-halves x squared, 3x²/2

Since the carpenter built a square table with side length x.  Next, he will build a rectangular table by tripling one side and halving the other.

To find the area of the rectangular table, we know that Area, A = LW where

Now, since the length of the square is x, and the rectangular table has one side of the square tripled and halving the other side .

So,

let

So, the area of the rectangular table A = LW

= x/2 × 3x

= 3x²/2

So, the simplified expression for the area of the rectangular table is Three-halves x squared, 3x²/2

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The coefficients in the expression are -1 and 9

The expression is given as:

-x^2 + 9x

In an expression ax, the coefficient is a.

Using the above as a guide, we have:

-x^2 + 9x

The coefficients in the above expression are -1 and 9

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The probability of a meerkat living smaller than 16.1 years exists at 99.85%.

The empirical rule notes that for a normal distribution most of the data lose within three standard deviations (σ) of the mean (µ). That exists 68% of the data lose within the first standard deviation (µ ± σ), 95% loses within the first two standard deviations (µ ± 2σ), and 99.7% declines within the first three standard deviations (µ ± 3σ).

68% declines within (10.4 ± 1.9). 68% declines within 8.5 years to 12.3 years.

95% declines within (10.4 ± 2[tex]*[/tex]1.9). 95% declines within 6.6 years to 14.2 years.

99.7% declines within (10.4 ± 3 [tex]*[/tex]1.9). 68% declines within 4.7 years to 16.1 years.

Probability of a meerkat living less than 16.1 years

= 100% - (100% - 99.7%)/2

= 100% - 0.15%

= 99.85%

Therefore, the probability of a meerkat living less than 16.1 years exists at 99.85%.

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If no less than 100000 packets must be packed each week, the minimum number of packets needed to be packed each day for the remaining days is 21250.

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

There are 6 days from Monday to Saturday. The factory is closed on Tuesday and 15000 packets were packed on Monday. If no less than 100000 packet must be packed, hence:

4x + 15000 ≥ 100000

x ≥ 21250

If no less than 100000 packets must be packed each week, the minimum number of packets needed to be packed each day for the remaining days is 21250.

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The electricity that is used, on average, by a security system in 2 years is 4.3Kw.

The average power consumption of the security system given is 2.7 watt.

(a) Electricity consumption in 2 years

in KW-h = (24*365*2.7)/1000 = 4.304 KWh

(b) As per US data CO2 emissions = 0.99 pound per kilowatt-h.

Hence here CO2 emissions = 4.3 × 0.99 = 4.2610 pounds / KW-h.

= 4.3 pound / KW-h.

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hi,  

smallest value is 8.  

x^2 will always be a positive number regardless of the value of  x.

the smallest value for a positive number is 0, therefore x^2 +8 will never be smaller than 8

Answer:

[tex]\huge\boxed{\sf x =6,\ y = 42}[/tex]

Step-by-step explanation:

Let the numbers be x and y

x + y = 48 --------(1)

y = 7x -------------(2)

Put Eq. (2) in (1)

x + 7x = 48

8x = 48

Divide 8 to both sides

x = 48/8

Put x = 6 in Eq. (2)

y = 7 (6)

[tex]\rule[225]{225}{2}[/tex]

Assume a is the 1st number and b is the 2nd number, a + b = 48

b = 7a (the second number is seven times the first number​)

a = a

So, equation: a + 7a = 48

a + 7a = 48

8a = 48

a = 6

To find b = 7 (6) = 42

Hope it helps!

[tex]4x + 18 = 7x - 21 \\ 18 + 21 = 7x - 4x \\ 39 = 3x \\ x = \frac{39}{3} = 13 [/tex]

Answer:

300

Step-by-step explanation:

30+30+w+x+y+z = 360 (all angles round a point add up to 360)

Simplifying :

60 + w+x+y+z = 360

Subtracting 60 from both sides :

w+x+y+z = 300

Hope this helped and brainliest ?

Sum of entire angle=360°

so

The number of stone pavers needed to go round the patio is 3.

The first step is to determine the perimeter of the concrete patio.

Perimeter : 12 + 12 + 14 = 38 feet

Number of stone pavers needed to go round the patio : perimeter of the patio / length of each stone paver

38 / 14 = 3

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The missing side in the given triangle is x = √193 km

The Pythagoras theorem is expressed as;

x^2 = a^2 + b^2

where

x is the longest side

Substitute the given side

x^2 = 12^2 + 7^2

x^2 = 144 + 49

x = √193 km

Hence the missing side in the given triangle is x = √193 km

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Answer:

a) [tex]f(x) = x + 3[/tex]

b) [tex]f(x) = -x - 5[/tex]

c) [tex]f(x) = 2x + 6[/tex]

Step-by-step explanation:

To determine the equation of a straight line, we need two things:

1. two known points (coordinates) on the line, used to calculate the gradient

2. the y-intercept of the line (the y-coordinate of the point at which the line crosses the y-axis)

Then we can use the equation:

[tex]\boxed {f(x) = ax + q}[/tex]

where a is the gradient and q is the y-intercept, to determine the equation of the line.

a) known points: (0, 3), (-4, -1)

y-intercept: 3

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

             ⇒ [tex]\frac{3 - (-1)}{0 - (-4)}[/tex]

             ⇒ [tex]\bf 1[/tex]

∴ a = 1 , q = 3

∴ equation:

[tex]{f(x) = ax + q}[/tex]

[tex]f(x) = 1x + 3[/tex]

⇒ [tex]\bf f(x) = x + 3[/tex]

b) known points: (-7, 2) , (0, -5)

y-intercept = -5

gradient = [tex]\frac{2 - (-5)}{-7 - 0}[/tex]

             ⇒ [tex]\bf -1[/tex]

∴ equation:

[tex]f(x) = -1x + (-5)[/tex]

⇒ [tex]\bf f(x) = -x - 5[/tex]

c) known points: (-3, 0), (0, 6)

y-intercept = 6

gradient = [tex]\frac{6 - 0}{0 - (-3)}[/tex]

             ⇒ [tex]\bf 2[/tex]

∴ equation:

[tex]\bf f(x) = 2x + 6[/tex]

The amount of water left is 4/10 gallons

Fractions are written as a ratio of two integers

Given the following parameters

Amount of gallon bought = 8/10 gallons

Amount he drank = 4/10

Determine the amount left

Amount left = 8/10 -4/10

Amount left = 4/10 gallons

Hence the amount of water left is 4/10 gallons

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Answer:

(12 + n/3) = 2n + 1

Step-by-step explanation:

(12 + n/3) = 2n + 1

36 + n = 6n + 3

33 = 5n

n = 33/5

The value of CE = 18.3

According to the statement

Here we have given the value of tangents AE = 8 and BC = 3

we have to find the value of CE and

It is given that AE is the tangent to the circle.

Now we make a equation to find the CE then

(8)^2 = 3(x+3)

In this equation the value of AE is 8. and

In this x is the value of CE and BC have value 3.

And the total value of BE becomes the 3(x+3) and 3 is the parts by which  BE is formed.

Then solve the equation

64= 3x +9

3x = 64-9

x = 18.3

So, The value of CE = 18.3

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Answer:

[tex](-\infty, -1) \cup (0, \infty)[/tex]

Step-by-step explanation:

The function is decreasing if, as x increases, the value of the function (y) gets smaller.  This means as you read the graph from left-to-right, the function is decreasing if the graph is falling.

From -infinity to -1, the graph is falling, then the graph rises (f is increasing) until x =0, then the graph falls again from x = 0 to infinity.

The probability that a student attended the game, given that the student is from North Beach is 0.65.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that a student attended the game, given that the student is from North Beach = number of North beach students that attended the game / total number of students who attended the game

110 / 170 = 0.65

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The attached line is a parallel line that goes through C and parallel to AB

Parallel lines are lines on the same plane that have the same slope, they do not intersect even when they are extended indefinitely

From the question, we have the following points and line:

The following steps would create the parallel line that goes through C and parallel to AB

See attachment for the parallel line that goes through C and parallel to AB

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The quantity reported an equivalent net percentage change of 28 percent.

In this problem we must determine the simple percentage change equivalent to two consecutive percentual changes. The formula that describes the situation is:

1 + r/100 = (1 - 60/100) · (1 + 80/100)

1 + r/100 = 72/100

r/100 = - 28/100

r = - 28

The quantity reported an equivalent net percentage change of 28 percent.

The statement is incomplete. Complete form is presented below:

A quantity is changing. At first it descreased by 60 percent and it increased by 80 percent. What is net change of the quantity in percentage?

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Answer:

ΔABC ≅ ΔEDF

Step-by-step explanation:

Triangle ABC is congruent to triangle EDF because they're the same size.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex] \sf\triangle ABC \cong \triangle DEF[/tex]

For checking congruency, we need to follow a proper order when choosing the triangle. because each triangle name is unique in itself.

So, According to Triangle ABC, we need to find the triangle with first two letters That resembles AB, that is :

and next should be :

[tex] \qquad \large \sf {Conclusion} : [/tex]

so, now we got the sense for naming, therefore the answer will be :

[tex] \sf\triangle ABC \cong \triangle DEF[/tex]

The actual roots of f(x) are -4 and 3

The function is given as:

f(x) = 2x^2 + 2x – 24.

Expand the function

f(x) = 2x^2 + 8x- 6x – 24.

Factorize the function

f(x) = 2x(x + 4) - 6(x + 4)

Factor out x + 4

f(x) = (x + 4)(2x - 6)

Set to 0

(x + 4)(2x - 6) = 0

Solve for x

x = -4 and 2x = 6

This gives

x = -4 and x = 3

Hence, the actual roots of f(x) are -4 and 3

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Answer:

A

Step-by-step explanation:

Got 100 on test

The transcribe expression is the expression of the equation in words.

The expression can be transcribe as follows;

1. st  = s multiply by t

2. 6 / t - 4 = 6 divided by t minus 4

3. 20 + t² = 20 plus t squared.

4. 50 - x = 50 minus x

5. x - y² = x minus y squared.

6. 24 / 12 + 12 = 24 divided by 12 plus 12

7. xy - 16 = x multiply by y minus 16

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Answer:

2633.88

Step-by-step explanation:

Pe^rt

2200*e^.06*3