Which of the statements about the graph of the function y = 2x are true? Check all of the boxes that apply. The domain is all real numbers x because the exponent of 2 can be any real number When the x-values increases by 1 unit, the y-value multiplies by 2. The y-intercept is (0, 1). The graph never goes below the x-axis because powers of 2 are never negative. The range is all real numbers.

Answers

Answer 1

Answer:

The correct options are 1, 2, 3 and 4.

Step-by-step explanation:

The given function is

[tex]f(x)=2^x[/tex]

The above function is defined for all the values of x.

Therefore the domain is all real numbers x because the exponent of 2 can be any real number.

⇒ The x is exponent of 2, therefore the x-values increases by 1 unit, the y-value multiplies by 2.

Put x=0, to find the y-intercept.

[tex]f(x)=2^=1[/tex]

The y-intercept is (0, 1).

The value of f(x) is always greater than 0 because powers of 2 are never negative.

[tex]f(x)>0[/tex]

The graph never goes below the x-axis because powers of 2 are never negative.

⇒Therefore the range of the function is all positive real numbers.

Therefore the correct options are 1, 2, 3 and 4.

Answer 2

The True statements about the graph of the function [tex]y =2^x[/tex] are option a), b), c) and d). Refer the below solution for better understanding.

Given :

[tex]y = 2^x[/tex]

Solution :

Domain is all real numbers x because the exponent of 2 can be any real number.

x is exponent of 2, therefore the x-values increases by 1 unit, the y-value multiplies by 2.

At [tex]x=0[/tex],

[tex]y=2^0=1[/tex]

y intercept -- (0 , 1).

y is always greater than zero because power of 2 never be negative.

Graph never goes below the x-axis because powers of 2 are never be negative.

The range of the function is all positive real numbers.

Therefore all the options are correct.

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Related Questions

If 30 people claimed that they get an average of seven hours of sleep, how many people claimed that they get at least eight hours of sleep each night? [Type your answer as a number.]

Answers

60 people claimed they they got at least eight hours of sleep.

Answer:

78 people claimed that they get at least eight hours of sleep each night.

Step-by-step explanation:

We know that 30 people claimed that they get an average of seven hours of sleep. Using the circular diagram, we find that these 30 people represent 25% of the total number of people.

According to the graph, people that get at least eight hours of sleep each night represent 65%, that is, 50% of the people sleep eight hours and 15% sleep nine or more.

Then, we use the rule of three, if 30 people represent 25% of the total, how many people would represents 65%?

[tex]x=65\%\frac{30 \ people}{25 \%} = 78 \ people[/tex]

Therefore, 78 people claimed that they get at least eight hours of sleep each night.

What is the median of the following set of data 28,45,12,34,36,19,20

Answers

Answer:

28

hope this helps

Answer:

34 is the median of the following data set.

Step-by-step explanation:

We have given a data set of values.

28,45,12,34,36,19,20

We have to find median of the given data set.

Median is defined as the middle value of the ordered data set.

Putting given data set in order , we have

12,19,20,28,34,36,45

Hence, the middle value is 28.

So, median is 34  for given data set.

Rewrite in polar form x^2 + y^2 - 6y - 8 = 0

Answers

Answer:

The correct answer option is [tex]r^2-6rsin(\theta)=8[/tex].

Step-by-step explanation:

We are given the following equation and we are to rewrite it in polar form:

[tex]x^2 + y^2 - 6y - 8 = 0[/tex]

[tex]\left \{ {{x^2+y^2=r^2} \atop {y=rsin \theta}} \right.[/tex]

Here, we need to make a perfect square trinomial:

[tex][r^2-6rsin(\theta)+[/tex] ___[tex]^2]=8[/tex]

[tex]6rsin(\theta)[/tex] ---> [tex]2 .r.3.sin \theta[/tex]

Completing the square to get:

[tex]r^2-6rsin(\theta)+[3sin(\theta)]^2-[3sin(\theta)]^2=8[/tex]

[tex][r-3sin(\theta)]^2=8+[3sin(\theta)]^2[/tex] --> [tex][r-3sin(\theta)]^2=8+9sin^2(\theta)[/tex]

[tex]r-3sin(\theta)=\sqrt{8+9sin^2(\theta)}[/tex] --> [tex]r=\sqrt{8+9sin^2(\theta)} +3sin(\theta)[/tex]

the correct answer is B. r^2=6r sin 0+8

Find last years salary if after 3% pay raise, this years salary is $34505

Answers

Answer:

     $34,505

s = --------------- = $33,500

         1.03

Step-by-step explanation:

Last year's salary was 1.00 s.

A 3% pay raise would thus amount to 0.03s.

This would equal this year's salary:  $34,505.

Thus, 1.03s = $34,505; find s, which was last year's salary.

Dividing both sides by 1.03, we get:

     $34,505

s = --------------- = $33,500

         1.03

Blake ate 2/6 of a pumpkin pie and give 3/6 of the pie to his sister. What fraction of the pumpkin pie was left?

Answers

Final answer:

After Blake ate 2/6 of a pumpkin pie and gave another 3/6 to his sister, the fraction of the pie that was left is calculated by subtracting the total part taken away (5/6) from the whole pie (1), resulting in 1/6 of the pie remaining.

Explanation:

The question asks about determining the fraction of a pumpkin pie left after Blake ate 2/6 of it and gave another 3/6 to his sister. To calculate the remaining portion of the pie, we add the fractions that were eaten and given away, and subtract that sum from the whole pie, which is represented as 1 (or 6/6, since we are working with sixths).

2/6 (eaten by Blake) + 3/6 (given to his sister) = 5/6. This means 5/6 of the pie was either eaten or given away.

To find the fraction of the pie that was left, we subtract the portion that is gone from the whole. Since 5/6 of the pie was no longer available, subtracting this from 1 (the whole pie) gives us 1 - (5/6) = 1/6. Therefore, 1/6 of the pumpkin pie was left.

Which factorization can be used to identify the real zeros of the function f(x)=-20x^2+23x-6?

Answers

Answer:

see explanation

Step-by-step explanation:

Given f(x) = - 20x² + 23x - 6

To find the zeros set f(x) = 0, that is

- 20x² + 23x - 6 = 0 ( multiply through by - 1 )

20x² - 23x + 6 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 20 × 6 = 120 and sum = - 23

The factors are - 15 and - 8

Use these factors to split the x- term

20x² - 15x - 8x + 6 = 0 ( factor the first/second and third/fourth terms )

5x(4x - 3) - 2(4x - 3) = 0 ← factor out (4x - 3)

(4x - 3)(5x - 2) = 0

Equate each factor to zero and solve for x

4x - 3 = 0 ⇒ 4x = 3 ⇒ x = [tex]\frac{3}{4}[/tex]

5x - 2 = 0 ⇒ 5x = 2 ⇒ x = [tex]\frac{2}{5}[/tex]

Answer:

-(4x - 3)(5x - 2) = 0

Step-by-step explanation:

The function f(x) = −(x + 5)(x + 1) is shown. What is the range of the function? all real numbers less than or equal to 4 all real numbers less than or equal to −3 all real numbers greater than or equal to 4 all real numbers greater than or equal to −3

Answers

all real numbers such that y is less than or equal to 4

ANSWER

all real numbers less than or equal to 4.

EXPLANATION

The given function is

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

Expand

[tex]f(x) = - ( {x}^{2} + x + 5x + 5)[/tex]

[tex]f(x) = - ( {x}^{2} + 6x + 5)[/tex]

[tex]f(x) = - {x}^{2} - 6x - 5[/tex]

a=-1,b=-6,c=-5

The x-value of the vertex is given by

a=-1,b=-6,c=-5

[tex]x = \frac{ - b}{2a} [/tex]

[tex]x = - \frac{ - 6}{2( - 1)} = - 3[/tex]

The y-value of the vertex is

[tex]f( - 3) = - ( - 3 + 5)( - 3 + 1)[/tex]

[tex]f( - 3) = - ( 2)( - 2) = 4[/tex]

Since a=-1, the function opens downwards.

The highest value is the y-value of the vertex which is 4.

Therefore the range is all real numbers less than or equal to 4.

The correct choice is A.

What are the center and radius of a circle with standard form equation (x+3) square + (y+8) square =6

Answers

Answer:

centre = (- 3, - 8), radius = [tex]\sqrt{6}[/tex]

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x + 3)² + (y + 8)² = 6 ← is in standard form

with centre = (- 3, - 8) and r = [tex]\sqrt{6}[/tex]

How do show 4/6 and 5/7 on a number line

Answers

Answer:

|-----|-----|-----|-----0-----|-----|     |------|------|------|------|------0------|-----|

0  1/6 2/6 3/6 4/6 5/6  1     0    1/7   2/7  3/7  4/7  5/7  6/7   1

Step-by-step explanation:

since 4/6 means the fourth one of the 6 spots, we can just make a number line that is split into 6 parts and find the fourth line. we do the same thing with seven to get the answers above

Final answer:

To show 4/6 and 5/7 on a number line, mark 42 equal sections between 0 and 1, and place 4/6 at the 28th mark and 5/7 at the 30th mark, as they equate to 28/42 and 30/42 respectively.

Explanation:

To show 4/6 and 5/7 on a number line, you would follow these steps:

Determine a number line with a section that includes both fractions. This might typically be between 0 and 1 if you are only dealing with fractions less than a whole.Divide this section into parts that can accommodate both denominators. For example, a common denominator for 6 and 7 is 42, since 6 * 7 = 42.Mark off 42 equal sections between 0 and 1 on your number line.Count and mark the position that corresponds to 4/6 and 5/7. To find the position of 4/6, you would count 28 sections from 0 (since 4/6 = 28/42). For 5/7, you would count 30 sections from 0 (since 5/7 = 30/42).Place a point or tick mark at these positions and label them accordingly.

Both 4/6 and 5/7 will be placed between 0 and 1 on the number line, with 4/6 slightly to the left of 5/7.

What is the value of n? Enter your Answer in the box. N=

Answers

n can be whatever number u want it to be or whatever number given because it is a variable

HELP ASSAP WILL MARK BRAINIEST!!!!!!!!

Answers

The x-intercept is -2, since the line intersects with the x-axis at (-2, 0).

The y-intercept is 1, since the line intersects with the x-axis at (0, 1).



Please consider marking this answer as Brainliest to help me advance.

Tina had $145 she spent $40 on fruit at the farmers market how to Slovenia the equation 40 + c = 145 to find the amount Tina has left

Answers

If Tina has $150 and she spent $40 on fruit at the market that means that she now has $105 left. C = 105

To help u out

Change equation to 145-40=

Subtract.

Replace c with 105 so; 40+105=145

MARKING BRAINLIEST

On Thursday night, Betsy received $34.50 in tips working as a coat checker. This is $1.75 more than the amount in tips she received on Wednesday night. How much did she receive on Wednesday night?

Answers

$34.50 - $1.75 = $32.75

she received 32.75 dollars on wednesday night

A fisherman travels 8 miles downstream with the current in the same time that he travels 3 miles upstream against the current. If the speed of the current was 5 mph what is the speed at which the fisherman travels in still water?

Answers

I also need help with this too so I'm just here to wait and see the answer

The speed is the distance covered by an object at a particular time. The speed at which the fisherman travels in still water is 11 mph.

What is speed?

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.

[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]

Let the speed of the boat be represented by x mph.

A fisherman travels 8 miles downstream with the current at the same time that he travels 3 miles upstream against the current. Also, the speed of the current was 5 mph. Therefore,

8 miles/ (x + 5)mph = 3 miles/(x - 5) mph

8x - 40 = 3x + 15

5x = 55

x = 11 mph

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Planes A and B intersect.
Which describes the intersection of plane A and line m?
line k
line n
point X
point W

Answers

I think line k I'm not sure

Answer:

Point X is the correct answer.

Step-by-step explanation:

The point X is on the line M in plane A

Select the figure obtained when rotating the figure about an axis along its largest side, and find the exact surface area of the resulting figure.

A rectangle with length 22 and width 18.

The figure obtained is a (square/cylinder/sphere)

The exact surface area is ______π.



Answers

Answer:

The figure obtained is a cylinder

The exact surface area is 1440π.

Step-by-step explanation:

* Lets study the rotation of a rectangle around one of its sides

- If the dimensions of the rectangle are length (L) and width (W)

- If we rotate the rectangle around its length (L), we will construct

 a cylinder with radius = W and height = L

- If we rotate the rectangle around its width (w), we will construct

 a cylinder with radius = L and height = W

∵ The surface area of any cylinder =

   perimeter of base × height + 2 base area

∵ The base is a circle

∴ perimeter base = 2πr and base area = πr²

∴ The surface area = 2πrh + 2πr²

* In first case:

- Surface area = 2π(W)L + 2π(w)² = 2πWL + 2πW²

* In second case:

- Surface area = 2π(L)W + 2π(L)² = 2πLW + 2πL²

* Now lats check our question:

∵ L = 22 and W = 18

- It will rotate around the largest side

∴ It will rotate around L

∴ The figure obtained is a cylinder

* From the explanation above this is the first case

∵ L = 22 and W = 18

∵ The surface area = 2πWL + 2πW²

∴ The surface area = 2 × 18 × 22 × π + 2 × (18)² × π

                                = 792π + 648π = 1440π

* The exact surface area is 1440π.

Darlene spent 20 minutes jogging and 10 minutes cycling and burned 400 calories . The next day she did 10 minutes of jogging and 20 minutes of cycling and burned 350 calories . How many calories were burned for each minute of jogging and how many for each minute of cycling

Answers

This is very spread out just to show properly but you could get it smaller haha

Final answer:

In this algebra problem, we created two equations from the problem and solved them simultaneously, finding that Darlene burns 15 calories per minute jogging and 10 calories per minute cycling.

Explanation:

This question is about working out two equations using two variables, a classic application in

algebra

. Let's call the calories burned per minute jogging as

J

, and the calories burned per minute cycling as

C

. From the information given in the question, we know that:

20J + 10C = 40010J + 20C = 350

These equations can be solved simultaneously. To make things easier, let's multiply the second equation by 2, which gives us:

20J + 40C = 700

By subtracting equation 1 from this, we get:

30C = 300

, simplifying this, we find that

C = 10 calories per minute for cycling

. Substitute C=10 into the first equation, we get:

20J + 100 = 400

, which simplifies to

J = 15 calories per minute for jogging

. Thus, Darlene burns 15 calories for each minute of jogging and 10 calories for each minute of cycling.

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The ball game begins at 2:00 p.m it takes ying 30 minutes to get to the ball park . At what time should ying leave home to get to the game before 30 minutes before it starts

Answers

Answer:

30 Mintues to get there + 30 Mintues early = 1 hour

2:00 PM - 1 hour = 1 PM

Step-by-step explanation:

Simplify the expression 43 + 2(3 − 2).

Answers

Answer:

45

Step-by-step explanation:

Simplify the following:

43 + 2 (3 - 2)

3 - 2 = 1:

43 + 2×1

2×1 = 2:

43 + 2

43 + 2 = 45:

Answer:  45

Answer:

STOP SAYING ITS 45 BECAUSE ITS NOT THE 43 IS SUPPOSED TO BE 4 TO THE POWER OF 3

Step-by-step explanation:

okay?

What is the value of x?


x =

(Secants, Tangents, and Angles)

Answers

Answer:

The value of x is [tex]58\°[/tex]

Step-by-step explanation:

we know that

The measurement of the external angle is the semi-difference of the arcs which comprises

so

In this problem

[tex]51\°=\frac{1}{2}(160\°-x\°)[/tex]

solve for x

[tex]102\°=(160\°-x\°)[/tex]

[tex]x=160\°-102\°=58\°[/tex]

Find the equation of a circle with a center at (7,2) and a point on the circle at (-2,-5).
( x - 7 )^2 + ( y - 2 )^2 = sqrt 130
( x + 7 )^2 - ( y + 2 )^2 = sqrt 130
( x - 7 )^2 + ( y - 2 )^2 = 130
( x + 7 )^2 - ( y + 2 )^2 = 130

Answers

Answer:

(x - 7)² + (y - 2)² = 130

Step-by-step explanation:

The first step is finding the length of the radius.

r² = (2 - -5)² + (7 - -2)²

    = 7² + 9²

    = 49 + 81

   = 130

The general equation of a circle is:

(x - a)² + (y - b)² = r²

Where (a, b) is the coordinate of the center and r is the radius.

∴ The equation of the required circle is;

 (x - 7)² + (y - 2)² = 130

Plz help!!!!!!!!!!!!

Answers

Answer:

rational

Step-by-step explanation:

any number that can be written as a fraction is rational, it is also a termintating decimal.

Answer:   rational

Step-by-step explanation:

[tex]\dfrac{1}{4}=0.25\\\\\text{Since the decimal terminates (ends), it is a rational number.}[/tex]

-4.1x^2+0.9x-9.8 + 1.7x^2-2.4x-1.6​

Answers

Answer:

The answer is −2.4x2−1.5x−11.4

Step-by-step explanation:

Let's simplify step-by-step.

−4.1x2+0.9x−9.8+1.7x2−2.4x−1.6

=−4.1x2+0.9x+−9.8+1.7x2+−2.4x+−1.6

Combine Like Terms:

=−4.1x2+0.9x+−9.8+1.7x2+−2.4x+−1.6

=(−4.1x2+1.7x2)+(0.9x+−2.4x)+(−9.8+−1.6)

=−2.4x2+−1.5x+−11.4

How do I find the volume

Answers

Answer:

[tex]\large\boxed{V=\dfrac{256\sqrt3}{3}\ cm^3}[/tex]

Step-by-step explanation:

The formula of a volume of a square pyramid:

[tex]V=\dfrac{1}{3}(b^2)(H)[/tex]

b - edge of a base

H - height

We have b = 8cm and the triangle 90 - 60 - 30. The sides of that triangle are in ptoportion 1 : √3 : 2 (look at the picture).

From the picture we have

[tex]a=\dfrac{b}{2}\to a=\dfrac{8}{2}\ cm=4\ cm[/tex]

Therefore

[tex]H=a\sqrt3\to H=4\sqrt3\ cm[/tex]

Substitute:

[tex]V=\dfrac{1}{3}(8^2)(4\sqrt3)=\dfrac{1}{3}(64)(4\sqrt3)=\dfrac{256\sqrt3}{3}\ cm^3[/tex]

To find the volume of any cube you need to know the length, width and height. The formula to find the volume multiplies the length by the width by the height. The good news for a cube is that the measure of each of these dimensions is exactly the same. Therefore, you can multiply the length of any side three times.

you stop for lunch at a local pizza ahop where each pizza is cut into 8 sices. would your hunger be better satisifued with one slice from a 10 inch pizza or 2 slices from a 8 inch pizza and explain why? ​

Answers

Answer:

Hello there! How are you doing? I am doing fine! I'll answer the question now.

So basically, your hunger would be satisfied with the 2 slices of 8 inches, because although one slice of 8 inches is two inches less than the 10 inch slice. But then you could add another 8 inch slice and it would make it greater and bigger than the one 10 inch slice itself. So in conclusion, the 2, 8 inch slices would be better than the 1, 10 inch slice because 16 inches is greater than 10 inches.

Hope this helped! Your welcome! I can help with other history stuff too! And byee! :)

Step-by-step explanation:

Final answer:

Two slices from an 8-inch pizza provide more pizza than one slice from a 10-inch pizza based on the calculation of the areas of the pizza slices. Therefore, your hunger would be better satisfied with the two pieces from the 8-inch pizza.

Explanation:

The subject here is a mathematical comparison of the area of different pizza sizes and the number of slices eaten. The location of a pizza can be calculated using the formula for the circle size, which is πr², where r is the radius of the pizza.

In the case of a 10-inch pizza, the radius is 5 inches (half of the diameter). So the area is π(5)² = 78.5 square inches. One slice of this pizza would be 1/8th of the total area, approximately 9.81 square inches.

For an 8-inch pizza, the radius is 4 inches. So the area is π(4)² = 50.24 square inches. Two slices of this pizza would amount to 1/4th of the total area, approximately 12.56 square inches.

So, when it comes to fulfilling your hunger at lunch, two slices of an 8-inch pizza would be more satisfying as it offers more pizza than one slice of a 10-inch pizza.

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!!!! MUCH HELP NEEDED I RAISED THE POINTS TO 22 AND WILL GIVE BRAINLIEST !!!!!

what is the 16th term in the sequence 2, 6, 18, 54, 162. . . . . . . ?




Answers

Answer:

The 16 term will be 28,697,814

Step-by-step explanation:

The pattern here is that Each number is being Multiplied by 3

Example= (2x3=6)  (6x3=18)  (18x3=54) (54x3=162) keep doing that until you get the  16th term.

Took me a while....

Hopes this helps you!

A number is chosen at random from the positive, even integers from 2 to 50. Find the probability that the number chosen is divisible by 3 or 8

Answers

Answer:

2/5

Step-by-step explanation:

it is 2/5

Probability = 12/25 or 48%.

To find the probability that a number chosen at random from the positive, even integers from 2 to 50 is divisible by 3 or 8, we need to count the number of even integers within this range that are divisible by 3 or 8, and then divide this count by the total number of even integers in the range.

First, let's find how many even integers between 2 and 50 are divisible by 3.

The even integers divisible by 3 in this range are: 6, 12, 18, 24, 30, 36, 42, 48.

Count: 8

Now, let's find how many even integers between 2 and 50 are divisible by 8.

The even integers divisible by 8 in this range are: 8, 16, 24, 32, 40, 48.

Count: 6

Notice that 24 and 48 are counted twice because they are divisible by both 3 and 8. We only want to count them once.

So, the total count of even integers between 2 and 50 that are divisible by 3 or 8 is 8 (from being divisible by 3) + 6 (from being divisible by 8) - 2 (counting 24 and 48 once) = 12.

Now, we calculate the total number of even integers between 2 and 50:

Total even integers between 2 and 50 = (50 - 2) / 2 + 1 = 25

Now, we can calculate the probability:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

            = 12 / 25

            = 0.48

So, the probability that a number chosen at random from the positive, even integers from 2 to 50 is divisible by 3 or 8 is 0.48.

-4(j+k+g) plz help using box method ​

Answers

Answer:

-4j-4k-4g

Step-by-step explanation:

What is the m∠ABC? m∠ABC = 15° m∠ABC = 45° m∠ABC = 60° m∠ABC = 75

Answers

Answer:

60 is c not d

Step-by-step explanation:

Answer:

c. m∠ABC = 60°

Step-by-step explanation:

E2020

Mai biked 6 3/4 miles today, and Noah biked 4 1/2 miles. How many times the length of Noah’s bike ride was Mai’s bike ride ?

Answers

Answer:

1.5 times.

Step-by-step explanation:

Givens:

Mai biked [tex]6\frac{3}{4} \ mi[/tex]Noah biked [tex]4\frac{1}{2} \ mi[/tex]

So, to know how many times the length of Noah's bike ride was Mai's bike ride, we can use the following equation:

[tex]6\frac{3}{4} \ mi=x(4\frac{1}{2} \ mi)\\\frac{27}{4}=\frac{9}{2}x\\ x=\frac{54}{36}=\frac{3}{2}=1.5[/tex]

Therefore, Mai biked 1.5 times more miles than Noah.

1.5 times the length of Noah’s bike ride was Mai’s bike ride.

Step-by-step explanation:

Given :

Mai Biked -

[tex]\rm 6\dfrac{3}{4} \; miles = \dfrac {27}{4} \; miles[/tex]

Noah Biked -

[tex]\rm 4\dfrac {1}{2} \; miles = \dfrac {9}{2} \; miles[/tex]

Calculation :

To find how many times the length of Noah’s bike ride was Mai’s bike ride, use below equation

[tex]\dfrac{27}{4}=x\dfrac{9}{2}[/tex]

[tex]\rm x = 1.5 \; times[/tex]

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