The daily cost of hiring an Algebra tutor, y, for x hours can modeled using a linear function. The tutor charges a fixed traveling fee of $10, plus $30 per hour. The tutor will work for a maximum of 4 hours in one day. For one day of work, what is the domain of the function for this situation?

Answer:

(2d +3d) + 3-12 equals to 5d - 9

Step-by-step explanation:

you try collecting like terms

Answer:

[tex]5d-9[/tex]

Step-by-step explanation:

Given the following question:

[tex](2d + 3) + (3d-12)[/tex]

To find the answer remove the parentheses, group like terms, and solve by using inverse of operations.

[tex](2d + 3) + (3d-12)[/tex]
[tex]2d+3+3d-12[/tex]
[tex]2d+3d+3-12[/tex]
[tex]3-12=-9[/tex]
[tex]2d+3d+-9[/tex]
[tex]2d+3d=5d[/tex]
[tex]5d-9[/tex]

Your answer is "5d - 9."

Hope this helps.

Answer:

Option (5)

Step-by-step explanation:

Lina's speed during the first part of the trip = s miles per hour

If she travels initial 80 miles on this trip with this speed, time taken to cover the distance [tex]t_1=\frac{\text{Distance}}{\text{Speed}}=\frac{80}{s}[/tex] hours

Now speed at which she traveled remaining 50 miles = (s + 10) miles per hour

So the time spent to cover this distance  [tex]t_2=\frac{50}{s+10}[/tex] hours

Total time for the complete trip = [tex]t_1+t_2[/tex] = [tex]\frac{80}{s}+\frac{50}{s+10}[/tex]

= [tex]\frac{80(s+10)+50s}{s(s+10)}[/tex]

= [tex]\frac{80s+800+50s}{s(s+10)}[/tex]

= [tex]\frac{130s+800}{s(s+10)}[/tex]

Therefore, Option (5) will be the answer.

Option C is correct. The expressions that represent the total time of her trip in hours is [tex]t_1 + t_2 = \frac{80}{s} +\frac{50}{s+10} \\[/tex]

Let the speed travelled during the first part of the trip be "s"

The formula for calculating the distance is expressed as:

[tex]distance=speed\times time[/tex]

For the first part of the journey:

distance = 80miles

time = t₁

Speed = s

Substitute the given parameters into the formula:

[tex]80 = st_1\\t_1=\frac{80}{s}[/tex]........................................... 1

For the second part of the trip;

Distance travelled = 5 miles

speed = s + 10 (10miles/hour faster than the first part of the trip)

time = t₂

Get the time  t₂

[tex]50=(s+10)t_2\\t_2=\frac{50}{s+10}[/tex]

Adding both times taken to get the total time of her trip in hours.

[tex]t_1 + t_2 = \frac{80}{s} +\frac{50}{s+10} \\[/tex]

Hence the expression that represent the total time of her trip in hours is [tex]t_1 + t_2 = \frac{80}{s} +\frac{50}{s+10} \\[/tex]

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Hey there!

Option answer: C

----------------------------------------------------------------

As all of the bundles have the same content inside, so assuming that there is x number of Fiction books and y number of Non-fiction books in each bundle.

Let n be the total number of bundles that my team can send.

There are 64 Fiction books, so

nx=64 ...(i)

Or x=64/n ...(ii)

also, there are 48 Non-Fiction books, so

ny=48 ...(iii)

Or y=48/n ...(iv)

Observing that the numbers x, y, and n are counting numbers and from equations (i) and (iii), n is the common factor of 64 and 48.

The possible common factors of 64 and 48 are,

n=1,2,4,8, and 16.

So, my team can send 1,2,3,4,8 or 16 bundles of books.

Now, from equations (ii) and (iv),

For n=1:

x=64/1=64

y=48/1=48

So, for 1 bundle the number of Fiction and Non-fictions books are 64 and 48 respectively.

For n=2:

x=64/2=32

y=48/2=48

So, for 2 bundles, the number of Fiction and Non-fictions books are 32 and 24 respectively.

For n=4:

x=64/4=16

y=48/4=12

So, for 4 bundles, the number of Fiction and Non-fictions books are 16 and 12 respectively.

For n=8:

x=64/8=8

y=48/8=6

So, for 8 bundles, the number of Fiction and Non-fictions books are 8 and 6 respectively.

For n=16:

x=64/16=4

y=48/16=3

So, for 16 bundles, the number of Fiction and Non-fictions books are 4 and 3 respectively.

Answer:

-5/2

Step-by-step explanation:

Slope intercept form = y=mx+b

M=Slope

B=y-intercept

Answer:

-5/2 is the slope

Step-by-step explanation:

the form that it is currently in is slope intercept form

( y= mx+b ) m is the is the slope and x is a variable. -5 is the y intercept.

Line B has a positive slope and a positive y-intercept because crosses the y-axis above the origin.

As per the shown graph,

In line A, we move from left to right along the line, and the y-values decrease. This means line A has a negative slope.

In line B, we move from left to right along the line, and the y-values increase. This means line B has a positive slope.

Similarly, line C has a positive slope.

Here, lines A and B cross the y-axis above the origin (positive y-intercept)

Thus, line B has a positive slope and a positive y-intercept.

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Cylinder volume = base area x height

                            = pi x r² x h

d = 7 yd => r = 7:2 = 3,5 yd

and h = 4 yd

to be calculed

V = 3,14 x 3,5² x 4

Answer:

Step-by-step explanation:

Given sequence

This is a GP with

Formula for nth term is:

Answer: 1/4

Step-by-step explanation:

Hope this helps

The 0.25 is equivalent to 1/4, where the numerator is 1 and the denominator is 4.

The fraction that is equal to 0.25 is 1/4. To understand this, examine the decimal representation of 0.25. The decimal point separates the whole number part from the fractional part. In 0.25, the digit 2 is in the tenths place, and the digit 5 is in the hundredths place. As a fraction, the number 2 in the tenths place can be written as 2/10, and the number 5 in the hundredths place written as 5/100. Simplifying these fractions, find that 2/10 reduces to 1/5 and 5/100 reduces to 1/20.

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Answer:

a = 9 + b - c → D

Step-by-step explanation:

To cancel the square root of one side of an equation square the two sides

Examples:

If [tex]\sqrt{x}[/tex] = 5, to find x square the two sides to cancel the square root

([tex]\sqrt{x}[/tex] )² = (5)², then x = 25

If [tex]\sqrt{a+b}[/tex] = 7, to find a + b square the two sides to cancel the square root

([tex]\sqrt{a+b}[/tex] )² = (7)², then a + b = 49

Now let us solve the question

To solve it for a square the two sides then keep a on the left side and move b, c to the other side

∵ [tex]\sqrt{a-b+c}[/tex] = 3

→ Square the two sides to cancel the square root

∴ ([tex]\sqrt{a-b+c}[/tex])² = (3)²

∴ a - b + c = 9

→ Add b to both sides to move b from the left side to the right side

∴ a - b + b + c = 9 + b

∴ a + c = 9 + b

→ Subtract c from both sides to move c from the left side to the right side

∴ a + c - c = 9 + b - c

∴ a = 9 + b - c

Answer:

The two triangles are not congruent.

Step-by-step explanation:

If two right triangles are drawn with a line as hypotenuse, the two triangles are not congruent. Because as per RHS congruency ie Right Angle - Hypotenuse - Side : right angle, hypotenuse & also one other side equality is needed for congruence. Given case doesn't satisfy the last 'other side equality' condition.

Answer:

h

Step-by-step explanation:

Answer:

(j-8)years is the answer to the question

The time taken for the light to reach earth will be 3.6 ×10⁴ hours. The quantity of time that an activity or a condition continues to exist. is known as the time period.

The amount of time that an action or a state continues to exist. is the time period. Depending on the nature of the activity or situation under consideration, it might be measured in seconds or millions of years.

The given data in the problem is;

v is the speed of ultraviolet light= 3 ×10⁸ m/sec

d is the distance covered by the light= 4×10¹³ Km=4× 10¹⁶m

The  time taken by the light to reach the surface of the earth will be;

[tex]\rm d = v\times t \\\\ \rm t= \frac{d}{v} \\\\ \rm t= \frac{4\times 10^{16}}{3\times 10^8} \\\\ \rm t= 1.33 \times 10^{8} \ sec[/tex]

In one hour there are 3600 seconds so the time period in the hours is found as;

[tex]\rm t= 1.33 \times 10^8 \times \frac{1}{3600} \\\\ \rm t=3.6 \times 10^4\ hours[/tex]

Hence the time taken for the light to reach earth will be 3.6 ×10⁴ hours.

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Answer:

C. 3. 7 × 104 hours

Step-by-step explanation:

Answer:

Skewed left

is

61.5

58

13

Step-by-step explanation:

The missing statements are skewed left, Outlier, score and scores; range; scores.

1. This distribution of test scores is skewed left.

  The distribution is skewed left because the tail of the boxplot extends to the left, indicating that there are more lower scores in the dataset.

2. The test score of 23 is an outlier.

  The value 23 is an outlier since it lies outside the whiskers of the boxplot. An outlier is a data point that is significantly different from the rest of the data.

3. The median test score is 61.5.

The median is the value that separates the data into two equal halves. Since the line divides the box at 61.8, the median is 61.5.

4. The range of all the test scores is

=  81 - 23

= 58.

The range of the middle 50 percent is the difference between the upper quartile and the lower quartile, which is given as (73 - 60) = 13.

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Answer: D.) 7, 21, 35, 35, 21, 7

Step-by-step explanation:

For pascal triangle :

Row 1: 1,

Row 2: 1, 1.

Row 3: 1, 2, 1.

Row 4: 1, 3, 3, 1.

Row 5: 1, 4, 6, 4, 1.

Row 6: 1, 5, 10, 10, 5, 1.

Row 6: 1, 6, 15, 20, 15, 6, 1.

Row 7: 1, blank, blank, blank, blank, blank, blank, 1

To obtain values for any row :

Digit 1 is plaved at both extremes ; and each two successive digit in the previous row is added to obtain the numbers in that row.

For row 7:

After placing 1 at both extremes ;

Each two successive digits in row 6 are summed up;

Row 6: 1, 6, 15, 20, 15, 6, 1.

(1 + 6) = 7;

(6 + 15) = 21

(15 + 20) = 35

(20 + 15) = 35

(15 + 6) = 21

(6 + 1) = 7.

Hence,

Row 7 = 1, 7, 21, 35, 35, 21, 7, 1

Answer:

xy - 3

Step-by-step explanation:

Product of x and y = xy

Required number = xy - 3

Answer:cycle-3

Step-by-step explanation:

Answer:

x=8.2

Step-by-step explanation:

First, figure out which trig function you are going to use.

In this problem you are dealing with the opposite side to the angle and the hypotenuse, and if you remember SOH CAH TOA, this requires sine.

sin (55) =opposite/hypotenuse

sin (55) =x/10

multiply both sides by 10 to get 10 * sin (55) = x

10 * sin (55) = 8.2

Answer:

64π Inches squared

Step-by-step explanation:

A=πr^2

Half of 16 is 8

r=8

A=π8^2

A=64π

Answer:

B the range of f (-00,-4)

Answer:

A and D

Step-by-step explanation:

A is correct as x must be any real number to yield a proper f(x) value.

B is incorrect, as a value of x=0 would mean f(x) = 0 which is outside the listed range.

C is incorrect as the equation is a quadratic (highest exponent is ^2) which forms a parabola shape on a graph and therefore does not infinitely decrease.

D is correct. To find a maximum or turning point, we can take the derivative of the function and set it to 0, as the slope at any turning point will always be 0:

f'(x) = -8x

0 = -8x

x = 0

So, the maximum occurs where x=0

f(x) = -4x^2

f(x) = -4(0)^2

f(x) = 0

This means the y-value is also 0, meaning that (0,0) is our maximum.

E is incorrect. Since the maximum is only just on the x-axis (0,0) it only touches the x-axis once so it only has one x-intercept.

Hope this helped!

Answer:

I THINK ITS 20 BUT I AM NOT SURE

Answer:

A. Line of reflection is a perpendicular bisector

B. 90 degree angles, equal lines

C. Pre-image an image are on the same circle.

Step-by-step explanation:

I hope this helped you in any way possible. :)

Solution (1):

[tex]0 > -2 + \dfrac{b}{7}[/tex]

[tex]0 + 2 > \dfrac{b}{7}[/tex]

[tex]2 > \dfrac{b}{7}[/tex]

[tex]2 \times 7 > b[/tex]

[tex]\boxed{\bold{14 > b}}[/tex]

Solution (2):

[tex]\dfrac{v}{14} - 2 < -3[/tex]

[tex]\dfrac{v}{14} < -3 + 2[/tex]

[tex]\dfrac{v}{14} < -1[/tex]

[tex]v < -1 \times 14[/tex]

[tex]\boxed{\bold{v < -14}}[/tex]

Solution (3):

[tex]13 < \dfrac{n}{4}+ 9[/tex]

[tex]13 - 9 < \dfrac{n}{4}[/tex]

[tex]4 < \dfrac{n}{4}[/tex]

[tex]4 \times 4 < n[/tex]

[tex]\boxed{\bold{16 < n}}[/tex]

Solution (4):

[tex]138 > -6+9n[/tex]

[tex]138 + 6 > 9n[/tex]

[tex]144 > 9n[/tex]

[tex]\dfrac{144 }{9} > \dfrac{9n}{9}[/tex]

[tex]\boxed{\bold{16 > n}}[/tex]

Solution (5):

[tex]-9 + \dfrac{x}{2} > -14[/tex]

[tex]\dfrac{x}{2} > -14 + 9[/tex]

[tex]\dfrac{x}{2} > -5[/tex]

[tex]x > -5 \times 2[/tex]

[tex]\boxed{\bold{x > -10}}[/tex]

Solution (6):

[tex]-6 > -9 + \dfrac{k}{4}[/tex]

[tex]-6 + 9 > \dfrac{k}{4}[/tex]

[tex]3 > \dfrac{k}{4}[/tex]

[tex]3 \times 4 > k[/tex]

[tex]\boxed{\bold{12 > k}}[/tex]

Solution (7):

[tex]-11 > \dfrac{a}{2} -2[/tex]

[tex]-11 + 2 > \dfrac{a}{2}[/tex]

[tex]9 > \dfrac{a}{2}[/tex]

[tex]-9 \times 2 > a[/tex]

[tex]\boxed{\bold{-18 > a}}[/tex]

Answer:

4.24 hours

Step-by-step explanation:

Irina can paint 1/9 of a room in 1 hour since she can paint a room in 9 hours. 1/9x, where x is the number of hours she works and 1/9 of a room per hour is her speed, would be her part of the calculation.

Paulo can paint 1/8 of a room in 1 hour since he can paint an entire room in 8 hours. 1/8x, where x is the number of hours he works and 1/8 of a room per hour is his speed, would be his part of the equation.

1/9x + 1/8x = 1 (Irina's portion of the room plus Paulo's portion of the room equals one complete room) would be the equation.

Look for a denominator that has the same value as the numerator. Both 9 and 8 split evenly into 72 as the initial number. We multiply the top of 1/9 by 8 to convert the fraction and get 8/72x because 9*8 = 72. We multiply the top of 1/8 by 9 to convert the fraction and get 9/72x because 8*9 = 72. We have 8/72x+9/72x=1 currently.

17/72x=1

÷ both sides by 17/72:

17/72x ÷ 17/72 = 1÷17/72

∴ x=1/1 * 72/17

∴ x=72/17= 4.24

Answer:

see graph

Step-by-step explanation:

Answer:

The first transformation occurs when we add a constant d to the parent function \displaystyle f\left(x\right)={b}^{x}f(x)=b

​x

​​ , giving us a vertical shift d units in the same direction as the sign. For example, if we begin by graphing a parent function, \displaystyle f\left(x\right)={2}^{x}f(x)=2

​x

​​ , we can then graph two vertical shifts alongside it, using \displaystyle d=3d=3: the upward shift, \displaystyle g\left(x\right)={2}^{x}+3g(x)=2

​x

​​ +3 and the downward shift, \displaystyle h\left(x\right)={2}^{x}-3h(x)=2

​x

​​ −3. Both vertical shifts are shown in Figure 5.

Graph of three functions, g(x) = 2^x+3 in blue with an asymptote at y=3, f(x) = 2^x in orange with an asymptote at y=0, and h(x)=2^x-3 with an asymptote at y=-3. Note that each functions’ transformations are described in the text.

Figure 5

Observe the results of shifting \displaystyle f\left(x\right)={2}^{x}f(x)=2

​x

​​  vertically:

The domain, \displaystyle \left(-\infty ,\infty \right)(−∞,∞) remains unchanged.

When the function is shifted up 3 units to \displaystyle g\left(x\right)={2}^{x}+3g(x)=2

​x

​​ +3:

The y-intercept shifts up 3 units to \displaystyle \left(0,4\right)(0,4).

The asymptote shifts up 3 units to \displaystyle y=3y=3.

The range becomes \displaystyle \left(3,\infty \right)(3,∞).

When the function is shifted down 3 units to \displaystyle h\left(x\right)={2}^{x}-3h(x)=2

​x

​​ −3:

The y-intercept shifts down 3 units to \displaystyle \left(0,-2\right)(0,−2).

The asymptote also shifts down 3 units to \displaystyle y=-3y=−3.

The range becomes \displaystyle \left(-3,\infty \right)(−3,∞).

Graphing a Horizontal Shift

The next transformation occurs when we add a constant c to the input of the parent function \displaystyle f\left(x\right)={b}^{x}f(x)=b

​x

​​ , giving us a horizontal shift c units in the opposite direction of the sign. For example, if we begin by graphing the parent function \displaystyle f\left(x\right)={2}^{x}f(x)=2

​x

​​ , we can then graph two horizontal shifts alongside it, using \displaystyle c=3c=3: the shift left, \displaystyle g\left(x\right)={2}^{x+3}g(x)=2

​x+3

​​ , and the shift right, \displaystyle h\left(x\right)={2}^{x - 3}h(x)=2

​x−3

​​ . Both horizontal shifts are shown in Figure 6.

Graph of three functions, g(x) = 2^(x+3) in blue, f(x) = 2^x in orange, and h(x)=2^(x-3). Each functions’ asymptotes are at y=0Note that each functions’ transformations are described in the text.

Figure 6

Observe the results of shifting \displaystyle f\left(x\right)={2}^{x}f(x)=2

​x

​​  horizontally:

The domain, \displaystyle \left(-\infty ,\infty \right)(−∞,∞), remains unchanged.

The asymptote, \displaystyle y=0y=0, remains unchanged.

The y-intercept shifts such that:

When the function is shifted left 3 units to \displaystyle g\left(x\right)={2}^{x+3}g(x)=2

​x+3

​​ , the y-intercept becomes \displaystyle \left(0,8\right)(0,8). This is because \displaystyle {2}^{x+3}=\left(8\right){2}^{x}2

​x+3

​​ =(8)2

​x

​​ , so the initial value of the function is 8.

When the function is shifted right 3 units to \displaystyle h\left(x\right)={2}^{x - 3}h(x)=2

​x−3

​​ , the y-intercept becomes \displaystyle \left(0,\frac{1}{8}\right)(0,

​8

​

​1

​​ ). Again, see that \displaystyle {2}^{x - 3}=\left(\frac{1}{8}\right){2}^{x}2

​x−3

​​ =(

​8

​

​1

​​ )2

​x

​​ , so the initial value of the function is \displaystyle \frac{1}{8}

​8

​

​1

​​ .

A GENERAL NOTE: SHIFTS OF THE PARENT FUNCTION \DISPLAYSTYLE F\LEFT(X\RIGHT)={B}^{X}F(X)=B

​X

​​

For any constants c and d, the function \displaystyle f\left(x\right)={b}^{x+c}+df(x)=b

​x+c

​​ +d shifts the parent function \displaystyle f\left(x\right)={b}^{x}f(x)=b

​x

​​

vertically d units, in the same direction of the sign of d.

horizontally c units, in the opposite direction of the sign of c.

The y-intercept becomes \displaystyle \left(0,{b}^{c}+d\right)(0,b

​c

​​ +d).

The horizontal asymptote becomes y = d.

The range becomes \displaystyle \left(d,\infty \right)(d,∞).

The domain, \displaystyle \left(-\infty ,\infty \right)(−∞,∞), remains unchanged.

HOW TO: GIVEN AN EXPONENTIAL FUNCTION WITH THE FORM \DISPLAYSTYLE F\LEFT(X\RIGHT)={B}^{X+C}+DF(X)=B

​X+C

​​ +D, GRAPH THE TRANSLATION.

Draw the horizontal asymptote y = d.

Identify the shift as \displaystyle \left(-c,d\right)(−c,d). Shift the graph of \displaystyle f\left(x\right)={b}^{x}f(x)=b

​x

​​  left c units if c is positive, and right \displaystyle cc units if c is negative.

Shift the graph of \displaystyle f\left(x\right)={b}^{x}f(x)=b

​x

​​  up d units if d is positive, and down d units if d is negative.

State the domain, \displaystyle \left(-\infty ,\infty \right)(−∞,∞), the range, \displaystyle \left(d,\infty \right)(d,∞), and the horizontal asymptote \displaystyle y=dy=d.

Step-by-step explanation:

Answer:

well if a is 12 it means that would become 144/12. simplified to a whole number is 12. so 12-2.4 would = 9.6

Step-by-step explanation:

Answer:

9.6

[tex]12^{2}[/tex]/12 cancels out

12-2.4=9.6

Mr Green: [tex]4(3a+1+2b) = 12a + 4 + 8b[/tex]

Mrs Green: [tex]6(5a-a)+4(2+4b)=6*4a + 8 + 16b = 24a +16b + 8[/tex]

Keith: [tex]4(2+4b+6a) = 8 + 16b + 24a=24a+16b + 8[/tex]

Kevin: [tex]4(6a+2)+8b + 2 = 24a + 8 + 8b + 2 = 24a + 8b + 10[/tex]

Thus Mrs Green and Keith has the expression that is equivalent to

'24a + 16b + 8'

Hope that helps!

Answer:

F (x) = 1,6

Step-by-step explanation:

my answer is due to the reason that it is one of the three options and it should only in a way make sense that it is the right answer

Answer: The two numbers are 39 and 41

==================================================

Work Shown:

x = some odd number

x+2 = next odd number

eg: x = 3 and x+2 = 3+2 = 5

Add up those two expressions, set the sum equal to 80, and solve for x

(x) + (x+2) = 80

2x+2 = 80

2(x+1) = 80

x+1 = 80/2

x+1 = 40

x = 40-1

x = 39

----------

Another way to solve is to do this

2x+2 = 80

2x = 80-2

2x = 78

x = 78/2

x = 39

-----------

Either way, the solution is x = 39 which means the next odd number up is x+2 = 39+2 = 41

To check the answer, add up the two values

39+41 = 80

This confirms we have the right answer.