What is the y-intercept of the function f(x) = 2 ^x?
A.27
B.2
C. 6
D. 1

Answer:

The answer is a D. a circle

The base shape of the cylinder can only be a circle.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A cylinder is a three-dimensional shape that has two congruent parallel circular bases connected by a curved surface.

The shape of the base determines the shape of the cylinder. If the base is circular, then the cylinder is called a circular cylinder.

A non-square rectangle and a square are not circular, and thus cannot be the base shape of a cylinder.

Hence, the base shape of the cylinder can only be a circle.

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The exact solutions of the given equation in the interval are;

A: x = 0, π/2, π, ³/₂π

We are given the equation as;

sin 4x = –2sin 2x

Writing the equation in standard form gives;

sin 4x + 2sin 2x = 0

Using trigonometric Identity, substitute (sin 4x) with (2sin 2x.cos 2x) to get;

2sin 2x cos 2x + 2sin 2x = 0

Factorize to get;

2sin 2x(cos 2x + 1) = 0

A. sin 2x = 0

The unit circle will give us 3 solutions for 2x as follows;

2x = 0

Thus; x = 0

2x = π

Thus; x = π/2

2x = 2π

Thus; x = π

B. cos 2x = - 1

The unit circle gives 2 solutions for 2x as;

2x = π

Thus; x = π/2

2x = 3π

Thus; x = ³/₂π

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Complete question is;

How do you find the exact solutions of the equation sin4x = −2sin2x in the interval [0, 2π)?

The value of the translated function g(x) will be x²+1.

A function is defined as the expression that set up the relationship between the dependent variable and the independent variable.

Given that the function is f(x) = x². The function g(x) in the form of  a(x–h)²+k will be written as below,

The function is translated to the 1 unit up which means that the value of k will be equal to the positive 1.

The function is,

g(x) = a(x–h)²+k

g(x) = 1(x-0)² + 1

g(x) = x² + 1

Therefore, the value of the translated function g(x) will be x²+1.

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Answer:

A hiker walks 10 km East, then 5 km in a direction 60 degrees North of West, then 8.7 km in a direction 30 degrees South of West. Find her resultant displacement.

Since you walk 10km North then turn and walk 5km East, your displacement from where you started is approximately 11.18 km.

From the information given, we have that you walked 10 km north (which represents the vertical side of the triangle) and 5 km east Using the Pythagorean theorem, the displacement (d) can be determined  as;

[tex]d^2 = (10 km)^2 + (5 km)^2[/tex]

Find the square values, we get

d² = 100 km² + 25 km²

add the squares, we get

d² = 125 km²

Find the square root of both sides of the equation, we have;

d = 125km²

d =  11.18 km

Therefore, your displacement from where you started is approximately 11.18 km.

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1. An algebraic expression that represents each purchase is as follows:

2. Supposing that x has the same value in both expressions written above, the two algebraic expressions are not equivalent because the slope of expression A is greater than the slope of expression B.

3. The cost of a soccer ball in relation to the cost of a baseball cannot be represented by the algebraic expression 4 + 5x because it is given that the cost of a soccer ball is $15, and no number can substitute the x variable to equate the two.

An algebraic expression is a combination of terms (variables and constants) using the mathematical operations of addition, subtraction, multiplication, division, etc.

a) 15x + 4(6) = 15x + 24

b) 4(6) + 5x = 24 + 5x or 5x + 24

c) Cost of a soccer ball = $15

Cost of a baseball = $6

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Soccer balls = $15 each

Baseballs=$6 each

Sweat socks =$5 per pair

Answer:

See below

Step-by-step explanation:

You can pull  one y   and 6 n's out to start

then   4/5 = 24/30     and 5 / 6 = 25/30

and you can factor out a   -1

- y n^6 /30  ( 24  + 25 y^3n^2 )

Answer:

5.33 inches

Step-by-step explanation:

Mean is another term for average. Therefore, we add up all precipitation items from Column B and divide by the total number of items (9):

[tex]5.98+6.05+7.59+5.27+3.11+7.18+2.95+7.22+2.61=47.96[/tex]

[tex]47.96\div{9}\approx{5.33}[/tex]

Considering the definition of perpendicular line, the equation of perpendicular line is y= -1/10x + 11/5.

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

The line is y= 10x -8.

The line has a slope of  10. If you multiply the slopes of two perpendicular lines, you get –1:

10× slope perpendicular line= -1

slope perpendicular line= (-1)÷ 10

slope perpendicular line= -1/10

The perpendicular line has a form of: y= -1/10x + b

The line passes through the point (2, 2). Then:

2= -1/10× (2) + b

2= -1/5+ b

2+ 1/5= b

11/5= b

Finally, the perpendicular line is y= -1/10x + 11/5.

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Check the picture below.

In order to estimate the mean per capita income at the 90% level of confidence with an error of at most $0.42. The sample size would be 85

Information form the question

the mean income is $28

the standard deviation is known to be $5.5

the mean per capita income at the 90% level of confidence

an error of at most $0.42

This is given as from margin of error:

This is the term refers to the minimum error that is to be allowed

Margin of error, E = Zc * √(SD²/n)

n = sample size

n = SD x (Zc/E)²

SD = standard deviation

Zc = would be the critical value at 90 percent level of confidence = 1.65

plugging in the values

n = 5.5 x (1.65/0.42)²

n = 0.25 x 15.4337

n = 84.8854

n = 85

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Answer:

45

Step-by-step explanation:

the pattern adds 3 if you look at it care fully

Answer:

a^-6 or 1/a^6

Step-by-step explanation:

(a³)-²

=a^-6

=1/a^6

If they took 1 hour and 35 minutes to complete the test and finished at 1:20 they started at 11:45.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The total time of the math test Raven took was 1 hour and 35 minutes.

Now he finishes the test at 1:20.

So, One hour before the time was 12:20.

20 minutes before that was exactly 12:00 and 15 minutes before that was

11:45 so a total of 1 hour and 35 minutes.

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The inequality to find the value of x for the rectangle is 2(2x+4) < 122 and the value of x should be less than 28.5.

According to the question,

We have the following information:

The perimeter of the rectangle is less than 122.

A rectangle has a width of x and a length of x plus 4.

Now, the expressions for the width and length of the rectangle are given below:

Width = x units

Length = (x+4) units

We know that the following formula is used to find the perimeter of rectangle:

2(length+width) < 122

2(x+4+x) < 122

2(2x+4) < 122

Dividing by 2 on both sides:

2x+4 < 122/2

2x+4 < 61

Subtracting 4 from both sides:

2x < 61-4

2x < 57

Dividing by 2 on both sides:

x < 57/2

x < 28.6

Hence, the inequality to find the value of x for the rectangle is 2(2x+4) < 122 and the value of x should be less than 28.5.

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If Samuel answers 9 questions wrong, his score will be 55 points, and if he answers x questions wrong his score is:

f(x) = 100 - x*5

We know that there are 100 points available, and each question gives 5 points, then the number of questions is given by the quotient:

100/5 = 20

There are 20 questions.

So, if you answer 9 wrong, then you answer:

20 - 9 = 11  correctly

Then your score is:

11*5 = 55

Your score will be 55 points.

And again, each answer gives 5 points, so if you answer x questions wrong your score will be the linear equation:

f(x) = (20 - x)*5

f(x) = 100 - x*5

Where x is an integer between 0 and 20.

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Answer:

8.25

Step-by-step explanation:

The expression that represents the age of randy's brother is

2x.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Randy age = 8 years old

Randy's brother age = 2 x 8 = 16

Randy's sister age = 8 - 3 = 5

The expression that represents the age of randy's brother.

Let the age of Randy = x.

=  2x

= 2x

= 2 x 8

= 16 years old.

Thus,

The expression that represents the age of randy's brother is

2x.

Where x is the age of Randy.

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The last sample range in this table is missing,the missing value is 2.

Given:

The Henry family has 5 children: Abby (age 15), Brian (age 10), Colin (age 9), Deena (age 7), and Elise (age 5).

Sample(n = 2)    A, B      A, C    A, D    Α, Ε  B, C ........ D,E

Ages                 15, 10    15,9    15,7    15, 5  10,9 .......  7,5

Sample range      5          6         8       10      1  ...........  

Let x be the sample range missing.

sample range = ages difference

= Age of D - Age of E

= 7 - 5

= 2

Therefore The last sample range in this table is missing,the missing value is 2.

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Answer:

answer is 2 i did it and got it right

Step-by-step explanation:

The new temperature is given as -15°F.

A measurement unit is a unit to measure certain quantities.

For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.

To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.

Given that,

The present temperature is 0°F.

And, the drop in the temperature is 15°.

The new temperature after the drop can be found by subtracting the amount of drop from the initial temperature as follows,

0 - 15°F

=  -15°F

Hence, the new temperature after the drop is  -15°F.

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By solving a simple equation we can see that Chris earned $192.50.

We know that Chris wins $10 per hour plus the 12.5% of the total amount he solds in computers.

So, if he works 5.5 hours and sold $1,100 in computers, the amount that he earns is given by the equation:

E = $10*5.5 + $1,100*( 12.5%/100%)

E = $10*5.5 + $1,100*(0.125) = $192.50

Then we conclude that Chris earned $192.50 today.

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Annual rate of return earned when the share was sold at $50 per share is 20%

Annual rate of return earned when the share was sold at $60 per share is 40%

Annual rate of return is given by the formula

let end of the year price = eyp

let beginning of the year price = byp

= {(eyp - byp) / byp} * 100

Annual rate of return at share price of $50 per share

when there is paying of dividends the value is added to the the eyp

eyp =  50 * 100 + 2 * 100 * 5 = 6000

byp = 50 * 100 = 5000

= {(6000 - 5000) / 5000} * 100

= 20%

Annual rate of return at share price of $60 per share

eyp =  60 * 100 + 2 * 100 * 5 = 7000

byp = 50 * 100 = 5000

= {(7000 - 5000) / 5000} * 100

= 40%

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Answer:

a )

[tex]6 ( ? ) = 27[/tex]

b )

? = The amount of rice in each container.

So, 1 container = ( ? ) ounce.

6 containers have = 6 x ( ? ) ounces.

We know that 6 containers have 27 ounces so...

[tex]6 ( ? ) = 27[/tex]

[tex]? = \frac{27}{6}[/tex]

[tex]? = 4.5[/tex]

Final Answer: 4.5 ounces in each container

Hope this helps! :)

Answer:
3/2

Step-by-step explanation:

the answer is 3/2 because you take the slope by using the equation y/x. I did this problem by starting prop the point (0,-6). I then counted for how many points I went up, how many did I go to the right or left. If it went to the right it’s positive, to the left it is negative. In this case it went to the right 2 times every time it went up 3. Meaning 3/2

The equations of both trees are Tree A = 38 + 6t and Tree B = 20 + 9t and the growth interval of tree A is t < 6

From the question, we have the following parameters that can be used in our computation:

Tree A

Tree B

The height after t years is

Tree = Initial height + rate * t

So, we have

Tree A = 38 + 6t

Tree B = 20 + 9t

Recall that

Tree A = 38 + 6t

Tree B = 20 + 9t

When Tree A is taller than Tree B, we have

38 + 6t > 20 + 9t

Evaluate the like terms

-3t > -18

Divide

t < 6

Hence, the interval is t < 6

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After solving the equation of vector, the value obtained is equal to one, which shows that vectors are orthogonal.

A vector is a quantity with both magnitude and bin physics. It is often depicted by an arrow with the same direction as the amount and a length proportionate to the size of the quantity. A vector has magnitude and the direction, but no position. As soon as a vector's length remains unchanged, it is consequently untouched by movement perpendicular to itself.

In contrast to vectors, scalars are normal variables having a magnitude but no direction. Displacement, velocity, and acceleration are all vector quantities, unlike speed, time, or weight, which are scalar variables.

uw = -6 + 10- 3

uw = 1.

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Answer:

y=3x+25

Step-by-step explanation:

we need start by making slope intercept form

lets move the 12x after moving it we get

-4y=-12x+4 we need to remove the - 4 from the y so we need to divide the whole equation by - 4

we get y=3x-1

now we can create an equation to get the parallel line

y+2=3(x+9) now distribute

y+2=3x+27 and subtract the two

y=3x+25

Answer:

b

Step-by-step explanation:

The correct option is (b) The data does not contain an outlier. This means that the people at the center were all seniors around the same age.

Outlier in a data set is simply the extremely low data point or an extremely high data point compared to other points in the dataset.

It will stand out from the other values in the dataset.

The line plot shows the ages of people visiting a senior center one afternoon.

The data points are,

70, 70, 70, 75, 75, 80, 80, 85, 90, 90, 95, 95, 95, 100.

If there is an outlier in the set, it would be extremely low or high compared to other points.

But there are no such points.

So there are no outliers.

This means that people visited at the center were all seniors around the same age.

Hence the correct option is (b).

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Answer:

-1,-2,0

Step-by-step explanation:

n(2-3)

1st term=n(2-3)

substitute value

1(2-3)=-1

2nd term=2(2-3)=-2

3rd term=3(3-3)=0