When you multiply a number by 12 and subtract the product from 360, the difference is 216. Find the number.

Answer:

sin C = cos A

Step-by-step explanation:

sinC = opp/hyp

=12/13

cosA = adj/hyp

12/13

The range of the function at domain {-2, -1, and 0} will be { 12 , 3 and 0}.

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given that:-

The range for the given domain: {-2, -1, and 0} and the function is y = 3x².

The range will be the value of y at each given value of the domain.

Domain: { -2, -1, 0 }

y  =  3x²

At x = -2  →  y = 3 ( -2)² = 12

At x = -1   →  y = 3 (-1)²   = 3

At x = 0   →  y = 3 (0)    = 0

Therefore range of the function at domain {-2, -1, and 0} will be { 12 , 3 and 0}.

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If Five hundred ten of 650 high school students said that pizza was their favorite food. The margin of error is 0.0322.

Given:

Sample proportion=Five hundred ten=510

Sample size=650

Hence:

Margin of error=z×√p×(1-p)/n

Margin of error=2√510/650× (1-510/650)÷650

Margin of error=2√0.78461538×(1-0.78461538)÷650

Margin of error=2√0.78461538×0.21538462÷650

Margin of error=2√0.168994085÷650

Margin of error=2√0.0002599909

Margin of error=0.0322

Therefore the correct option is D.

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Answer:

B

Step-by-step explanation:

using the addition identity for sine

sin(A + B) = sinAcosB + cosAsinB

using the sine and cosine ratios in the right triangle

sinABC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{4}{5}[/tex]

cosABC = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{3}{5}[/tex]

using the exact values

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , cos60° = [tex]\frac{1}{2}[/tex]

Then

sin(ABC + 60)

= sinABC cos60 + cosABC sin60

= ( [tex]\frac{4}{5}[/tex] × [tex]\frac{1}{2}[/tex] ) + ([tex]\frac{3}{5}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] )

= [tex]\frac{4}{10}[/tex] + [tex]\frac{3}{10}[/tex] [tex]\sqrt{3}[/tex]

= [tex]\frac{2}{5}[/tex] + [tex]\frac{3}{10}[/tex] [tex]\sqrt{3}[/tex]

sin<ABc

cos<ABC

Now

The set A satisfying the given inequality is A = (-[tex]\infty[/tex], -10].

Following are some facts which are true for an inequality relation:

[tex]\frac{5x-2}{8} - \frac{3x-5}{10} &\ge& x+y\\\\\Rightarrow\;\; \frac{13}{40}x + \frac{1}{4}&\ge& x+y\\\\\Rightarrow\;\;\;\;\;\; -\frac{27}{40}x &\ge & y - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\;\; -x &\ge & \frac{40}{27}\left( y-\frac{1}{4} \right).\hspace{1cm}(1)[/tex]

Since y ∈ B, -2 ≤ y ≤ 7. So,

[tex]\;\;\;\;\;\;\;\,-2 - \frac{1}{4}\; \le\; y - \frac{1}{4} \;\le\; 7 - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\; -\frac{9}{4}\; \le\; y - \frac{1}{4} \;\le\; \frac{27}{4}\\\\\Rightarrow\;\;\; -\frac{9}{4}\cdot \frac{40}{27} \;\le\; \frac{40}{27} \left( y-\frac{1}{4} \right) \;\le \;\frac{27}{4}\cdot \frac{40}{27}\\\\\Rightarrow\;\;\;\;\;\;\;\; -\frac{10}{3} \;\le\; \frac{40}{27}\left( y - \frac{1}{4} \right)\; \le\; 10.[/tex]

The set {-x | inequality (1) holds ∀ y ∈ B} is [10, [tex]\infty[/tex]) i.e.

10 ≤ -x ≤ [tex]\infty[/tex].

Multiplying -1 throughout gives

-10 ≥ x ≥ -[tex]\infty[/tex].

x, thus, lies in the range A = (-[tex]\mathbf{\infty}[/tex], -10}.

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Disclaimer: The question was incomplete. Please find the full content below.

Find the set A such that for x ∈ A

[tex]\frac{5x - 2}{8} - \frac{3x - 5}{10} \ge x + y[/tex]

∀y ∈ B = {y ∈ R | -2 ≤ y ≤ 7}.

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Answer:

x = 6

Step-by-step explanation:

.16x + 2 * .02 = (x + 2) * .17
.16x + .4 = .17x + .34
.06 = .01x
6 = x

Answer:

1, 17, 33, 49

Step-by-step explanation:

given the first term is 1 then the next 3 terms are

1 + d, 1 + 2d, 1 + 3d ( d is the common difference )

the sum of the first 4 terms is 100 , then

1 + 1 + d + 1 + 2d + 1 + 3d = 100 , that is

4 + 6d = 100 ( subtract 4 from both sides )

6d = 96 ( divide both sides by 6 )

d = 16

1 + d = 1 + 16 = 17

1 + 2d = 1 + 2(16) = 1 + 32 = 33

1 + 3d = 1 + 3(16) = 1 + 48 = 49

the first 4 terms are

1, 17, 33, 49

Answer:

see the file attached!!!!

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:A. \:\: 10[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } = 102[/tex]

[ subtract 2 from both sides ]

[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } - 2 = 102 - 2[/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } - \bigg( 2 \sdot x \sdot \cfrac{1}{x} \bigg)= 100[/tex]

[ 2 can written like that, as they cancel out each other ]

Apply Identity [ a² + b² -2ab = (a - b)² ]

[tex]\qquad \tt \rightarrow \: \bigg (x - \cfrac{1}{x} \bigg) {}^{2} = 100[/tex]

[tex]\qquad \tt \rightarrow \: x - \cfrac{1}{x} {}^{} = \sqrt{100}[/tex]

[tex]\qquad \tt \rightarrow \: x - \cfrac{1}{x} {}^{} = 10[/tex]

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Answer:

The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer.

y-intercept: (0,50)

Slope: 45

Answer:

[tex]|{\sf XY}| = 10\; {\rm cm}[/tex].

Step-by-step explanation:

Refer to the diagram attached. The dashed segment attached to [tex]\!{\sf Z}[/tex] points to the north. Rotating this segment clockwise with point [tex]{\sf Z}\!\![/tex] as the fixed center of rotation would eventually align this segment with the one between point [tex]\!\!{\sf Z}[/tex] and point [tex]\!\!{\sf X}[/tex]. The bearing of point [tex]{\sf X}[/tex] from point [tex]{\sf Z}[/tex] is the size of the angle between these two line segments when measured in the clockwise direction.

Subtract the bearing of [tex]{\sf Y}[/tex] from [tex]{\sf Z}[/tex] from the bearing of [tex]{\sf X}[/tex] from [tex]{\sf Z}[/tex] to find the measure of the angle [tex]\angle {\sf YZX}[/tex]:

[tex]\begin{aligned}\angle {\sf YZX} &= 135^{\circ} - 45^{\circ} \\ &= 90^{\circ}\end{aligned}[/tex].

Thus, triangle [tex]\triangle {\sf YZX}[/tex] is a right triangle ([tex]90^{\circ}[/tex]) with segment [tex]{\sf YX}[/tex] as the hypotenuse. It is given that [tex]|{\sf XZ}| = 6\; {\rm cm}[/tex] whereas [tex]|{\sf ZY}| = 6\; {\rm cm}[/tex]. Thus, by Pythagorean's Theorem:

[tex]\begin{aligned}|{\sf ZY}| &= \sqrt{|{\sf ZX}|^{2} + |{\sf ZY}|^{2}} \\ &= \sqrt{(8\; {\rm cm})^{2} + (6\; {\rm cm})^{2}} \\ &= 10\; {\rm cm}\end{aligned}[/tex].

Step-by-step explanation:

please mark me as brainlest

The simplified form of the expression has a numerator (x + 9)(2x + 1) and the denominator (x + 7) and the expression doesn't exist at (x = 9).

The given expression is:

= [(3x² - 27x)/(2x² + 13x - 7)]/(3x/4x² - 1)

Firstly, factorize the expression 4x² - 1.

4x² - 1 = (2x - 1)(2x + 1)

Then, factorize 2x² + 13x - 7.

2x² + 13x - 7 = 2x² + 14x - x - 7

2x(x + 7) - 1(x + 7)

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

Then, factorize the equation 3x² - 27x.

3x² - 27x = 3x(x - 9)

The factorized terms will be substituted into the equation. This will be:

= [3x(x - 9)/(2x - 1)(x + 7)] / 3x[(2x - 1)(2x + 1)]

= (x + 9)(2x + 1)/(x + 7)

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We write the equation in the form of directional.

y -1 = 6x               ⇔    y = 6x + 1

y - 1 = 3x              ⇔    y = 3x + 1

y - 7 = 2x - 6         ⇔    y = 2x - 6 + 7

                                    y = 2x + 1

y - 7 = x - 2           ⇔    y = x - 2 + 7

                                    y = x + 5

Equations cleverly arranged .

Point Q = (0,1)  

b factor , not only fits the last equation

In the drawing have engraved points Q and R are tangent linear function appropriate to that point . This graphics solution . y = 3x + 1

Answer b

We check choice by the system of equations , where substitute wartoćsi points Q and R to the model equations linear function

The result of equations confirmed our choice Answer b

Answer:

y = x/2 -3

Step-by-step explanation:

x - 2y = 6

Slope intercept form is y = mx+b  where m is the slope and b is the y intercept

We need to solve for y

Subtract x from each side

x-2y-x = -x+6

-2y = -x+6

Divide each side by -2

-2y/-2 = -x/-2 +6/-2

y = x/2 -3

The slope intercept form is

y = x/2 -3

Answer: slope intercept form is

y = x/2 -3

Step-by-step explanation:

hope this helps ; )

Answer: two units to the left, four units down and reflected across the y axis

The cost of renting a community center for x guest is given as y = 10x + 100

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

The standard linear equation is in the form:

y = mx + b

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

Let y represent the cost of renting a community center for x guest. Hence:

y = 10x + 100

The cost of renting a community center for x guest is given as y = 10x + 100

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Answer:

6

Step-by-step explanation:

Mean no. of runs per game =

= Total no. of runs/ total no. of games

= 9+8+4+0+7+6+4+5+9+8 / 10

= 60 / 10

= 6

Step-by-step explanation:

since the two angles from a straight line, they make a linear pair and linear pairs are supplementery. by the angle addition postulate, you can determine that the two angles sum to 180. substituting the one angle mearsure that you are guven and using a bit of simple arithmetic and the subtraction property of equality, you can determine that the other angle,angle YXZ, is 45 degrees. I hope this is helpful

A function assigns the values. The function g(x) can be written as g(x) = -3x + 12.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function f(x)=-x, now since a transformed function g(x) is produced by shifting the function 4 units upwards and vertical stretch by a factor of 3. Therefore, g(x) can be written as,

Vertical Shift by 4 units,

f(x)+4

Vertical stretch by a factor of 3

g(x) = 3(f(x) + 4)

g(x) = -3x + 12

Hence, the function g(x) can be written as g(x) = -3x + 12.

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Answer: none

Step-by-step explanation:

If we put a=0 and b=-4.05 then the expression 4a+4b becomes -16.2 and when we put a=-4.05 and b=0 then the expression becomes -16.2.

Given  2 (a + b) = -8.1

Because no relationship between a and b is given so we can put any value of one variable to determine the value of another variable.

If we put a=0 in 2(a+b) =-8.1 then b=-4.05

If we put b=0 then a =-4.05.

We need to put these values in 4a+4b

when a=0 b=-4.05

4a+4b=4*0+4*-4.5

=-16.2

when b=0 and a=-4.05

4a+4b=4*-4.05+4*0

=-16.2

Hence for a=0,b=-4.5 the value of 4a+4b equals -16.2 and for a=-4.05 and b=0 the function equals -16.2.

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Their speed in terms of square feet per minute is 3/10 square feet per minute.

We know that the speed formula is the rate at which an object travels a given distance. Speed is defined as the distance traveled by a body in a given amount of time. Speed in the SI is measured in m/s.

Given that the distance = 1/5 square feet.

The time = 2/3 minute.

Speed = distance/time = (1/5)/(2/3) = (1/5)*(3/2) = 3/10

Therefore, we can conclude that their speed in terms of square feet per minute is 3/10 square feet per minute.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

Expression in scientific notation :

[tex]\qquad \tt \rightarrow \:3.45 × {10}^{-4} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 0.000345[/tex]

[tex]\qquad \tt \rightarrow \: 0.000345 \times \cfrac{10000}{10000} [/tex]

[tex]\qquad \tt \rightarrow \: (0.000345 \times 10000) \times \cfrac{1}{10000} [/tex]

[tex]\qquad \tt \rightarrow \: 3.45 \times \cfrac{1}{10 {}^{4} } [/tex]

[tex]\qquad \tt \rightarrow \: 3.45 \times{10 {}^{ - 4} } [/tex]

[tex] \textsf{Correct option - D} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

3.45 x 10-4

Step-by-step explanation:

The graph of the equation is shown in the attached picture which is a straight line.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have a graph of a equation:

y + 2 = (x+2)

or

y = x

The above equation is a linear equation or straight line equation the slope of the equation is 1.

m = 1

The y-intercept of the equation is 0.

We can plot the equation y = x by using the slope and y-intercept.

Thus, the graph of the equation is shown in the attached picture which is a straight line.

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Answer:

Step-by-step explanation:

To calculate a+1/a, we first need to calculate for a.

a = 7 - 4 * [tex]\sqrt[2]{3}[/tex]

square root of 3 = 1.73

a = 7 - 4 * 1.73

a = 7 - 6.9

a = 0.1

0.1 + 1 / 0.1 = 0.1 + 10 = 10.1

Now, in case 4 wasn't being multiplied with the square root of 3, and instead, it was four root of 3, I am gonna do the calculations again:

a = 7 - [tex]\sqrt[4]{3}[/tex]

a = 7 - 1.31

a = 5.69

5.69 + 1 / 5.69 = 5.69 + 0.17 = 5.86

Hope I Helped!

Using the continuity concept, as the value of the function has to be equal to the limit, it is found that the value of k is of k = -4.

A function is said to be continuous at x = a if, and only if:

[tex]\lim_{x \rightarrow a} f(x) = f(a)[/tex]

In this problem, we have to check at x = -2, hence:

[tex]\lim_{x \rightarrow -2} f(x) = f(-2)[/tex]

[tex]k = \lim_{x \rightarrow -2} f(x)[/tex]

For the limit, we have to check the lateral conditions, hence:

[tex]\lim_{x \rightarrow -2} f(x) = \lim_{x \rightarrow -2} \frac{x^2 - 4}{x + 2} = \lim_{x \rightarrow -2} \frac{(x - 2)(x + 2)}{x + 2} = \lim_{x \rightarrow -2} x - 2 = -2 -2 = -4[/tex]

Hence, from the continuity condition, k = -4.

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Answer:

Step-by-step explanation:

1)   = f(x - a) + b

Coordinate change

(x, y) → (x + a, y + b)

2) RFy(x, y) = f(-x)

Coordinate change

(x, y) → (-x, y)

3) RFx(x, y) = -f(x)

Coordinate change

(x, y) → (-y, x)

4) RCCW90(x, y) = f⁻¹(-x)

Coordinate change

(x, y) → (-y, x)

5) RCCW180(x, y) = -(f(-x))

Coordinate change

(x, y) → (-x, -y)

6) A 270 degrees counterclockwise rotation gives;

RCCW270(x, y) = -(f⁻¹(x))

Coordinate change

(x, y) → (y, -x)

Step-by-step explanation:

1) Horizontal translation a units right = f(x - a)

The vertical translation b units up = f(x) + b

Therefore, we get;  = f(x - a) + b

The coordinate change

(x, y) → (x + a, y + b)

2) A reflection across the y-axis = RFy(x, y) = f(-x)

The coordinate change

(x, y) → (-x, y)

3) A reflection across the x-axis gives RFx(x, y) → (x, -y)

Therefore, in function notation, we get;

RFx(x, y) = -f(x)

4) A 90 degrees rotation counterclockwise, we get RotCCW90(x, y) → (-y, x)

In function notation RotCCW90(x, y) = INVf(-x) = f⁻¹(-x)

5) A 180 degrees counterclockwise rotation about the origin gives;

(x, y) → (-x, -y)

Therefore, we get;

In function notation RotCCW180(x, y)  = -(f(-x))

6) A 270 degrees counterclockwise rotation gives RotCCW270(x, y) → (y, -x)

In function notation RotCCW270(x, y) = -(f⁻¹(x))

[tex] \frac{ - 3}{5} \\ [/tex]

because , in the third quadrant , the value of cos is negative. Moreover , we can find the third side of the triangle using Pythagoras theorem.

then ,

[tex] \cos(\theta) = \frac{base}{hypotenuse} \\ \\ \dashrightarrow \: \cos(\theta) = \frac{ - 3}{5} [/tex]

hope helpful.

The answer is cos 0 = -3/5

Given :

tan 0 = 4/3 and is in the 3rd quadrant

this implies that both the perpendicular and base are negative.

Perpendicular = -4

Base = -3

Hypotenuse = [tex]\sqrt{(perpendicular)^{2} + (base)^{2} }[/tex]

Hypotenuse = [tex]\sqrt{(-4)^{2} + (-3)^{2} }[/tex]

Hypotenuse = [tex]\sqrt{25} = 5[/tex]

cos 0 = [tex]\frac{Base}{Hypotenuse}[/tex]

cos 0 = -3/5

Therefore, cos 0 = -3/5

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Answer:

A function is when each input has exactly one output

Step-by-step explanation:

Each input can only have one output, but an output can have multiple inputs.