What is the value of the exponential expression below 161/2
A.2
B.8
C.6
D.4

Answer: 30×2n=C

Step-by-step explanation:

30$ is flat fee so no variable

2$ dollars per person so "n" (the number of people) is times 2

= the final cost (C)

Answer:

A

Step-by-step explanation:

Because the angle with measure 124 degrees and angle y are a linear pair, their values must add up to 180 degrees. Therefore, y=180-124=56 degrees. Since all of the angles in a quadrilateral add up to 360 degrees, x must be 360-56-65-125=114 degrees. This means that the correct answer is choice a. Hope this helps!

Answer:

36% ,hope this helps

Step-by-step explanation:

1) 100 - 85  = 15

2) 240 times 15 devided by:100

3) equals 36

4) 36 %

Answer: The solution is   (0,2)

Step-by-step explanation:

2x +3y = 6      We will solve the  equations using the elimination method

-5x +2y= 4     but first we need to eliminate one of the variables and we will multiply the first equation by 5 and multiply the second equation by 2 to eliminate the x variable.

5(2x + 3y) =6(5)     new equation  :  10x  +15y = 30

2(-5x + 2y) = 4(2)   new equation   ;   -10x +4y =8    

Now we have to new equations so we will eliminate the x term by adding

10x  +15y = 30

 -10x +4y =8    

       19y = 38  divide both sides by 19.

  y= 2     Now using the solution for y plot it  into one of the new equations and solve for x

10x + 15(2) = 30

10x  + 30  =  30

        -30       -30

10x = 0

x= 0

Answer:

28/36 or 7/9

Step-by-step explanation:

there are 36 possible answers

4 of them equal 5 (1+4, 2+3, 3+2, 4+1)

4 of them equal 9 (3+6, 4+5, 5+4, 6+3)

8-36 = 28

Answer:

36

Step-by-step explanation:

This is a 30, 60 90 triangle, which means that there is a ration for calculating each side.

Answer:

150°

Step-by-step explanation:

Measure of each interior angle of polygon

[tex] = \frac{(n - 2) \times 180 \degree}{n} \\ \\ = \frac{(12 - 2) \times 180 \degree}{12} \\ \\ = \frac{10 \times 180 \degree}{12} \\ \\ = 10 \times 15 \degree \\ \\ = 150 \degree[/tex]

Answer:

[tex]\large \boxed{y = x + 5; y = -x + 1}[/tex]

Step-by-step explanation:

This is an isosceles right triangle, so triangles ABD and CBD are congruent.

∠ ABD = ∠CBD = 45°

The slope of BC = tan(45°)  =  1, and

The slope of BA = tan(-45°) = -1.

1. Equation of BC

The point-slope formula for a straight line is

y - y₁ = m(x - x₁)

x₁ = -2; y₁ = 3; m = 1  

Substitute the values

[tex]\begin{array}{rcl}y - 3 & = & 1(x - (-2))\\y - 3 & = & x + 2\\y & = & x + 5\\\end{array}\\\text{The equation for the line is $\large \boxed{\mathbf{y = x + 5}}$}[/tex]

2. Equation of BA

x₁ = -2; y₁ = 3; m = -1  

Substitute the values

[tex]\begin{array}{rcl}y - 3 & = & -1(x - (-2))\\y - 3 & = & -1(x + 2)\\y - 3 & = & -x - 2\\y & = & -x +1\\\end{array}\\\text{The equation for BA is $\large \boxed{\mathbf{y = -x + 1}}$}[/tex]

An isosceles right triangle has two equal length legs and the hypotenuse side as its base

The equation of the sides of the isosceles right triangle are;

x = 0 (equation of the base)

y = 1 - x

y = x + 5

The reason for arriving at the above equations are as follows:

The given parameters of the isosceles right triangle are:

The coordinate of the vertex of the triangle = (-2, 3)

The base of the triangle, x = 0

The required parameter:

The equation of the sides of the isosceles triangle

Strategy:

Define the terms and relate the given information with the given term definitions

Solution:

The base of an isosceles triangle is the side that form the equal base angles with the two equal sides of the triangle

In an isosceles right triangle, the two equal sides of the right triangle are the legs of the right triangle, and therefore, the base of the triangle is the hypotenuse side

The base angles of an isosceles right triangle, [tex]\theta _b[/tex] = 45°

The altitude of the triangle, y = (0 - (-2) = 2

The altitude is a perpendicular bisector of the base, therefore;

[tex]tan(\theta _b) = \dfrac{Altitude}{\dfrac{1}{2} \times Base \ length }[/tex]

Therefore;

[tex]Base \ length = \dfrac{Altitude}{\dfrac{1}{2} \times tan(\theta _b)}[/tex]

We get:

[tex]\mathbf{Base \ length} = \dfrac{2}{\dfrac{1}{2} \times tan(45^{\circ})} \mathbf{= 4~}[/tex]

The coordinate of the midpoint of the base is the horizontal line from the vertex to the base, and therefore, the coordinate of the midpoint of the base is x = 0, and y = 3 = (0, 3)

The base is 4 units long and half the base length = 4/2 = 2 units

The coordinates of vertex at the base is given by adding or subtracting 2 from the y-coordinates of midpoint of the base as follows;

Vertex coordinates at the base = (0, 3 + 2) = (0, 5), and (0, 3 - 2) = (0, 1)

The slope, m₁, of the side, s₁, with endpoints (-2, 3), and (0, 1), is found as follows;

m₁ = (1 - 3)/(0 - (-2)) = -1

Therefore, the equation of the side s₁ is (y - 1) = -1·(x - 0), which gives;

y = -x + 1

The slope, m₂, of the side, s₂, with endpoints (-2, 3), and (0, 5), is found as follows;

m₂ = (5 - 3)/(0 - (-2)) = 1

Therefore, the equation of the other side s₂ is (y - 5) = 1·(x - 0), which gives;

y = x + 5

The equation of the sides are; x = 0 (given), y = 1 - x, and y = x + 5

Learn more about finding the equation of a line here:

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Answer:

T = i or -i

Step-by-step explanation:

Consider these steps:

t^2 = -1

t = √-1 or  -√-1

t =  i or -i

Answer:

£84

Step-by-step explanation:

The total cost of the dishwasher is: £372

The deposit she makes is: £36

Thus, she still has to pay the following amount:

£372 - £36 = £336

And this amount will be divided into 4 equal monthly payments. So, we must divide the amount that she still has to pay by 4.

Each one of this monthly payments will have a value of:

£336 ÷ 4 = £84

the answer is that each monthly payment will be of £84

Answer:

The area of the triange is 20 feet. beacause the area of the rectangel is 40 feet.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

To find the product of these matrices, what we need to do is to multiply whatever we have at a specific position in the first matrix by that which we have in the same position in the other matrix.

Thus, we have the following;

(1 * -2) (3 * 1)

(-2*3). (5 * 4)

(-2) (3)

(-6). (20)

This makes option A correct

Answer:

$5979

Step-by-step explanation:

8.25% = 0.0825

1.0825^11 = 2.3917

2.3917 * 2500 = 5979.25 = 5979

Answer:

x=0

Step-by-step explanation:

3x+-2=-2

Add 2 to each side

3x+-2+2=-2+2

3x = 0

Divide by 3

3x/3 = 0/3

x = 0

｡☆✼★ ━━━━━━━━━━━━━━  ☾  

320 = 3x + 16

-16 from both sides

304 = 3x

/3 on both sides

x = 304/3

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Answer:

He made 42 cookies and 30 brownies.

Step-by-step explanation:

Let c = number of cookies

Let b = number of brownies

"He made 12 more cookies than brownies."

The number of cookies is 12 more than the number of brownies.

c = b + 12

"He sold cookies for $1.50 and brownies for $2."

The money he made from selling cookies was 1.5c.

The money he made from selling brownies was 2b.

The total sales were $123

1.5c + 2b = 123

We have a system of equations.

c = b + 12

1.5c + 2b = 123

Substitute c of the second equation with b + 12

1.5(b + 12) + 2b = 123

1.5b + 18 + 2b = 123

3.5b = 105

b = 30

c = b + 12

c = 30 + 12

c = 42

He made 42 cookies and 30 brownies.

Answer:

a) 10,500 big cats

b) 13,401 big cats

c) 33 years

Step-by-step explanation:

Hi, to answer this question we have to apply an exponential growth function:  

A = P (1 + r) t  

Where:  

p = original population  

r = growing rate (decimal form; 5/100= 0.05)

t= years  

A = population after t years  

Replacing with the values given:  

a) At 2005, 1 year passed since 2004 (t=1)

A = 10,000 (1+ 0.05)^1

A = 10,500 big cats

b)

At 2010, 6 years passed since 2004 (2010-2004= 6)

A = 10,000 (1+ 0.05)^6

A = 13,401 big cats

c)

50,000 < 10,000 (1+ 0.05)^t

Solving for t:

50,000/10,000 < 1.05^t

5 < 1.05^t

log 5 < log 1.05^t

log 5 < t ( log 1.05)

log 5 / log 1.05 < t

32.9 years < t

33 years  = t

Feel free to ask for more if needed or if you did not understand something.  

Answer: 4 inches by 6 inches or 8 inches by 3 inches.

Step-by-step explanation:

The area of a rectangle is A = W*L

where L is the width and L is the lenght.

Now, the original rectangle has a measure of 8 in by 6 in.

if 8in is the lenght and 6 in is the width.

We want to divide only one of those measures in equal parts, such that when we take the product of the end results is equal to 24 in.

If we divide the lenght by half (so both parts will have the same width as this did not change), we now have that the lenght is 8in/2 = 4in and the width is 6in.

Now the area is 4in*6in = 24in, which is the area that we where looking for.

We also could cut the width in half, and get the dimensions 8 inches by 3 inches.

Answer:

B. 78.5 feet

Step-by-step explanation:

The circumference of a circle can be found using the following formula.

c=πd

We know that the diameter is 25 feet. We also know we are using 3.14 for pi.

d=25

π=3.14

Substitute these values into the formula.

c=3.14*25

Multiply the two numbers together

c=78.5

Add appropriate units. Circumference uses the same units as the diameter. The diameter is 25 feet, so the units are feet.

c=78.5 feet

The circumference of the circle is 78.5 feet, and the correct answer is B

The right answer is 78.5ft

please see the attached picture for full solution

hope it helps

good luck on your assignment

Answer:

mph or miles per hour

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

!..........................

Step-by-step explanation:

[tex](1\frac{1}{3} )(1\frac{1}{2} )(1\frac{1}{5} )\\(\frac{4}{3} )(\frac{3}{2} )(\frac{6}{5} )\\(\frac{2}{1} )(\frac{1}{1} )(\frac{6}{5} )\\\frac{12}{5}[/tex]

In the second step I made them all into simple fractions, just because that's easier.

In the third step I did a bit of cancelling to simplify everything as much as possible.

Answer:

[tex]\frac{12}{5}[/tex]

Answer:

A.) constant

Step-by-step explanation:

The graph has a horizontal line that is neither increasing nor decreasing; therefore it is constant.

The given graph is constant because the line is parallel to the x axis, option A is correct.

The equation of the given graph is y=3.

The equation y = 3 represents a horizontal line that cuts across the y-axis at a height of 3.

This line is parallel to the x-axis and remains at a constant level of y = 3 regardless of the value of x.

There is no change in the y-value as x varies, the graph is considered constant.

Hence, the graph is constant.

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Answer:

(3x +4)²

Step-by-step explanation:

I think of a number x, then i multiply it by 3, add 4 and square the result.

Representing this mathematically,

x * 3= 3x

Then add 4 which will be 3x + 4

Squaring the result would be (3x +4)².

So, if we give our unknown which is x the value of say, 3.

Substituting the value of x into that equation would be easy.

(3 (3) +4)²

= (9 + 4)²

= (11)²

=132.

Answer:

xy-xz+yz-yx+zx-zy hoped this helped a little

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

x (y-z)+y (z-x) +z ( x-y)​

Simplify the bracket

xy -xz + yz - yx + zx - zy

combine the like terms

xy - yx -xz + zx + yz - zy

= 0

Answer: Id say b

Step-by-step explanation: a would be too high and a bit too detailed. Whereas c and d will be inaccurate.

Answer:

A. Twelve thousand

Step-by-step explanation:

cant specify my sources but please hit thank it would make my day :)

The required equation is, y = 4 + x.

Hence, The correct answer would be an option (A).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Now, Jayne stopped for gas before embarking on a road trip.

There were already 4 gallons of gas in the tank.

Hence, As per the question, the required equation would be as:

⇒ y = 4 + x

Thus, This equation relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x. The total amount of gasoline in the tank, y, is equal to the number of gallons that she put in the tank, x, plus the 4 gallons that were already in the tank.

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Answer:

y = (-3/2)x - 4

Step-by-step explanation:

Recall that a line perpendicular to a given line has a slope which is the negative reciprocal of the given line.  The given line can be re-written as  -3y  = -2x + 13, or

y = (2/3)x - 13/3

and so the slope of a line perpendicular to this given line is -3/2.

Then the desired equation, in point-slope form, is

y - 5 = (-3/2)(x + 6)  (This is in point-slope form.)

Alternatively,

2y - 10 = -3(x + 6) = -3x - 18, or

2y = 10 - 3x - 18, or

2y = -3x - 8, or y = (-3/2)x - 4  (This is in slope-intercept form.)

Answer:

x=2

y=2

Step-by-step explanation:

Answer:

7.698 m

Step-by-step explanation:

From the question,

Faisal's distance to the flagpole = 30 m

angle of elevation of its top = 12.4°

angle of depression of its bottom = 2.1°

Thus, the height of the flagpole is divided into two parts. Let the upper part be represented by x and the lower part by y.

From the triangle of the upper part (elevation), we have;

tan 12.4° = [tex]\frac{x}{30}[/tex]

x = 30 × tan 12.4°

 = 30 × 0.2199

 = 6.597 m

From the triangle of the lower part (depression), we have;

tan 2.1° = [tex]\frac{y}{30}[/tex]

y = 30 × tan 2.1°

  = 30 × 0.0367

  = 1.101 m

The height of the flagpole = x + y

                                           = 6.597 + 1.101

                                           = 7.698 m

The height of the flagpole is 7.698 m.