4 and 1 over 7 divided by 2 over 3
(Ignore messy writing I rush myself)

The function f(x)=1+|2x-5| in piecewise form without using absolute values will be f₁ = 4, f₂ = 2 and  a = 5/2.

Given that,

f(x) = 1 + |2x - 5|

And,

f(x) = {f₁       x < a

         {f₂      x ≥ a

Now,

We have,

f(x) = 1 + |2x - 5|

And,

By definition of absolute value,

|x| = {x        x ≥ 0

       {-x       x < 0

And,

Given the absolute value,

|2x - 5|

Solve for x,

i.e.

2x - 5 = 0

We get,

x = 5/2 = 2.5

i.e.

a = 5/2

i.e.

For all values greater than x = 5/2, 2x - 5 is positive,

And,

For all values less than x = 5/2, 2x - 5 is negative.

So,

|x| = {x        x ≥ 5/2

       {-x       x < 5/2

i.e.

|2x - 5| = {2x - 5        x ≥ 5/2

              {-(2x - 5)       x < 5/2

Now,

f(1) = 1 + |2(1) - 5|

We get,

f₁ = 4

And,

f(2) = 1 + |2(2) - 5|

We get,

f₂ = 2

Hence we can say that the function f(x)=1+|2x-5| in piecewise form without using absolute values will be f₁ = 4, f₂ = 2 and  a = 5/2.

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Answer:

She could have planted 250 seeds on Wednesday

The total change in temperature, in degrees Fahrenheit, for the package of food is 50°F

The initial temperature of the package of food as given in the question is -15°F

At noon, the temperature of the package of food was changed to 35° F

We need to find out the total change in temperature which is

Temperature of food package at noon - The initial temperature of the package of food

By substituting the values given in question we get

                       = 35° - (-15° F)

Which is a simple integer problem

                      = 35 - (-15)

                     = 35 + 15

                     =   50 F

Hence, the total change in temperature, in degrees Fahrenheit, for the package of food is 50° F

An integer is the range 0, a wonderful natural number or a poor integer with a minus signal. The poor numbers are the additive inverses of the corresponding advantageous numbers. in the language of arithmetic,

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Answer:

7 - y

Step-by-step explanation:

The sum of -7 and y: -7 + y

The opposite of the sum: -(-7 + y) = 7 - y

The floating-point literal that correctly represents the scientific notation value: 2.3 x 10^7 will be A. 2.3e^7.

It should be noted that scientific notation simply means. way that's used to express numbers that are either too large or too small to be written in decimal form.

Therefore, it should be noted that the floating-point literal that correctly represents the scientific notation value: 2.3 x 10^7 will be:

= 2.3 × 20^7

= 2.3 × e^7

= 2.3e7

The correct option is A.

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Which floating-point literal correctly represents the scientific notation value: 2.3 x 10^7?

a. 2.3e^7

b. 2.3 × 10e^7

c. 2.3e × 10^7

d. 2.3 × e^7

Common ratio= 1/2, Next two term= 1/16, 1/32

This is a geometric sequence since there is a common ratio between each term.

i.e.,

the common ratio (r) = [tex]\frac{1/2}{1}[/tex] = [tex]\frac{1/4}{1/2}[/tex]

                                  = 1/2

We can write the formula for general term of the series as

[tex]a_{n}[/tex] = a[tex](\frac{1}{2})^{n-1}[/tex]

If the further sequence does continue in the same way then the whole infinite sequence indicated is a geometric series.

So we have

[tex]a_{2}[/tex] =(1) [tex](\frac{1}{2} )^{2-1}[/tex]= 1/2

[tex]a_{3}[/tex] = 1× [tex](\frac{1}{2} )^{3-1}[/tex]= 1/4

[tex]a_{4}[/tex] = 1× [tex](\frac{1}{2} )^{4-1}[/tex]= 1/8

[tex]a_{5}[/tex] = 1× [tex](\frac{1}{2} )^{5-1}[/tex]= 1/16

[tex]a_{6}[/tex] = 1× [tex](\frac{1}{2} )^{6-1}[/tex]= 1/32

......

Therefore the sequence is in the same series, and we get the next two terms of the sequence which are 1/16, 1/32

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Answer:

-4/3

Step-by-step explanation:

[tex] \frac{6 - ( - 2)}{ - 2 - 4} = - \frac{8}{6} = - \frac{4}{3} [/tex]

The two terms of each arithmetic sequence [tex]a_{4}[/tex] = 8 [tex]a_{7}[/tex] = 20 are d = 4 and a = -4.

[tex]a_{4}[/tex] = 8

8 = a +3d.............1

[tex]a_{7}[/tex] = 20

20 = a + 6d...........2

equating equation 1 and 2

8 = a +3d

20 = a + 6d

d = 12/3

d = 4...............3

from equation 3

8 = a + 12

a = -4

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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A cell phone tower is 173.21 feet high.

Consider the following diagram

Let AB be the height of tower, C be the position of Jen.

Jen walks 50 feet from the tower, and finds the angle of elevation from her position to the top of the tower to be 60°

An angle ACB be an angle of elevation.

⇒ ∠ACB = 60°

And AC = 50 ft

We need to find the distance AB.

Consider tangent of angle ACB.

⇒ tan(60) = AB / BC

⇒ 1.7321 = AB / 100

⇒ AB = 1.7321 × 100

⇒ AB = 173.2 feet

Therefore, a cell phone tower is 173.21 feet high.

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According to the question, the given expression can be simplified with the help of factors.

Given expression = [tex]-2\sqrt{-45}-3\sqrt{125}[/tex]

Do the factors of 45 as well as 125 and take the common things out from the square root:

Required expression = [tex]-2(3)\sqrt{-5}-3(5)\sqrt{-5}= -21i\sqrt{5}[/tex]

In the theory of complex number, [tex]i^{2} = -1[/tex] is already defined.

Hence, the answer for the given expression is [tex]-21i\sqrt{5}[/tex].

What is simplification?

Simplification is the process to make the expression as simple for the calculation. That means, to calculate the solution of a complex expression.

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Answer:(x+3)(x-5)

Step-by-step explanation:(x^2-5x)+(3x-15)

x(x-5)+3(x-5)

(x+3)(x-5)

Answer:

$26.22

Step-by-step explanation:

Stuart's bank account balance (before) : $ - 51.41

Profit/Loss : + $ 77.63

Therefore:

-  $  5  1  .  4  1

+

   $ 7  7  .  6  3

_____________

  $ 2  6  .  2  2

Therefore, Stuart has $26.22 in his bank account at the end of the month assuming there are no other other transactions.

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The length of the line segment XY which was bisected at point M is;

1) 32

2) 6

1) From the given line segments, it is clear that XM is congruent to YM since M bisects XY. Thus;

XM = YM and XM + YM = XY

We are given that;

XM = 3x + 1

YM = 8x - 24

Thus;

3x + 1 = 8x - 24

8x - 3x = 1 + 24

5x = 25

x = 25/5

x = 5

Thus;

XM = 3(5) + 1 = 16

YM = 8(5) - 24 = 16

XY = 16 + 16 = 32

2) From the given line segments, it is clear that XM is congruent to YM since M bisects XY. Thus;

XM = YM and XM + YM = XY

We are given that;

XM = 5x + 8

YM = 9x + 12

Thus;

5x + 8 = 9x + 12

9x - 5x = 8 - 12

4x = -4

x = -1

XM = 5(-1) + 8 = 3

YM = 9(-1) + 12 = 3

XY = 6

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Answer:

a=25

b=40

Step-by-step explanation:

We can get two equations from these statements

1.a+b=65

2.a<b

therefore 2a=10+b

and 2a-10=b

substitute into original equation

a+(2a-10)=65

3a=75

a=25

b=65-25

=40

volume of the largest sample is 7 times the volume of the smallest sample.

A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum.

given:

The volume of the largest sample is 7/8 gallon.

The volume of smallest sample is is 1/8 gallon.

So,

volume of the largest sample/volume of the smallest sample

=7/8 / 1/8

=7/8 * 8/1

=7

Hence, volume of the largest sample is 7 times the volume of the smallest sample.

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The value of the given expression (5/3)(3x - 6) - (6 - 4x) at x = 5 is 29.

According to the given question.

We have an expression (5/3)(3x - 6) - (6 - 4x).

So, the value of the given expression (5/3)(3x - 6) - (6 - 4x) at x = 5 is given by

(5/3)(3x - 6) - (6 - 4x)

= 5x - 10 - (6 - 4x)               (by distributive rule)

= 5x - 10 - 6 + 4x

= 9x - 16

= 9(5) - 16                 (at x = 5)

= 29

Hence, the value of the given expression (5/3)(3x - 6) - (6 - 4x) at x = 5 is 29.

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Answer:

55 minutes

Step-by-step explanation:

→ Work out long it will take to get to 7:00

7:00 - 6:10 = 50 minutes

→ Work out how much extra time after 7:00

7:05 - 7:00 = 5 minutes

→ Add the 2 answers together

50 + 5 = 55 minutes

Answer: $4490

Step-by-step explanation:

30×48=1440

 1440+(50×61)

The total percentage they travelled when Jai fell asleep is 35%.

In mathematics, a percentage is a ratio or value that is expressed as a fraction of 100. The Latin term "per centum," which means "by a hundred," is the source of the English word "percent." The sign "%" stands for percentage. We apply the percentage method to determine the portion of a whole expressed in terms of 100. Use the percentage formula to convert a number to a fraction of 100.

The total length of trip was 740 miles.

Jai travelled before they fell asleep  = 259 miles

Therefore the percentage of total trip travelled before Jai fell asleep =

= [tex]\frac{259}{740}\times100[/tex]

= 35 %

So by 35% of the total trip, they travelled when Jai fell asleep.

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Answer:

61

Step-by-step explanation:

5•5+36

(5)(5)+36

=25+36

=61

Based on the calculations below, the amount of tuition per year is $36,000 while the amount of the increase in tuition each year is $1,000.

Note: There are two questions in this question as follows:

1. How much is tuition per year?

2. By how much will tuition increase each year?

We can calculate the tuition per year and the increase in the tuition each year as below:

Number of semesters in a year = 2

Tuition in each semester = $18,000

Increase in the tuition per semester = $500

Using the above information, we can proceed as follows:

Tuition per year = Tuition in each semester * Number of semesters in a year = $18,000 = $36,000

Increase in the tuition each year =  Increase in the tuition per semester * Number of semesters in a year = $500 * 2 = $1,000

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Answer:

$0.15 per ounce

Step-by-step explanation:

Take the total price and divide by the ounces to get the price per ounce. 3.60/24 equals 0.15

The inequality that models the situation is:

$50 + $25*x < $175

Where x is the number of lessons that the student can take.

We know that Mr. Bass charges $25 per class plus a fixed fee of $50.

Then if a student takes x classes, the cost is given by the expression:

$50 + $25*x

And we know that this needs to be smaller than $175, then we can write the inequality:

$50 + $25*x < $175

Now we can solve this for x:

$25*x < $175 - $50

$25*x < $125

x < $125/$25

x < 5

So the student needs to take less than 5 classes.

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Answer:

11, 15, 19, 23 = An+4

23,19,15,11=An-4

The inequality given by (x/3) + 5 ≥ 1/6 has the solution x ≥ -29/2 or [-29/2 , +∞).

Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.

To solve an inequality is to find the values of x such that when we substitute that number for x we have a true statement.

Given the inequality (x/3) + 5 ≥ 1/6, subtract 5 from both sides.

(x/3) + 5 - 5 ≥ 1/6 - 5

x/3 ≥ -29/6

Multiply both sides by 3.

3(x/3) ≥ 3(-29/6)

x ≥ -29/2

To check, let x = -29/2

x = -29/2 ≥ -29/2

Substitute this value to the inequality.

(x/3) + 5 ≥ 1/6

(-29/2)/3 + 5 ≥ 1/6

1/6 ≥ 1/6

let x = -14,

x = -14 ≥ -29/2

Substitute this value to the inequality.

(x/3) + 5 ≥ 1/6

-14/3 + 5 ≥ 1/6

1/3 ≥ 1/6

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Answer:

8,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Step-by-step explanation:

8(10^42)

Parenthesis is the multipication sign  btw

Answer:

The graph on the screen is

Step-by-step explanation:

Good luck with your studies!

The equation of line in slope intercept form which passes through (-1, -5) and (4, -2) will be y = [tex]\frac{3}{5}[/tex] x .

What is the slope intercept form of a line ?

The equation of a straight line in the form y = mx + c is known as the slope intercept form, where m denotes the slope and c denotes the y-intercept of a line.

It is given that line is passing through (x1 , y1) and (x2 , y2) that is ,  (-1, -5) and (4, -2).

Let's find out the value of slope first.

We know that , slope (m) = (y2-y1) / (x2-x1)

⇒ m = [(-2-(-5)] / [4 - (-1)]

⇒ m = 3 / 5

Now we will use the slope to find the y-intercept.

∵ y = mx + c

where , c is the y-intercept.

(-2 -(-5)) = (3/5) × (4-(-1)) + c

3 = [ (3/5) × 5 ] + c

3 = 3 + c

c = 0

Now ; we will write the equation in slope intercept form that is ;

y = mx + c

or

y = [tex]\frac{3}{5}[/tex] × x + 0

or

y = [tex]\frac{3}{5}[/tex] x

Therefore , the equation of line in slope intercept form which passes through (-1, -5) and (4, -2) will be y = [tex]\frac{3}{5}[/tex] x .

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The final answer in scientific notation is 4 × 10⁰.

Firstly writing both dividend and divisor in scientific notation.

Dividend = 32 × 10⁻²²

Divisor = 8 × 10⁻²²

Now  performing division to find the quotient.

Quotient = Dividend ÷ Divisor

Quotient = 32 × 10⁻²² ÷ 8 × 10⁻²²

As per the known rule of exponents, aˣ ÷ aⁿ = aˣ⁻ⁿ

Quotient = (32 ÷ 8) × 10⁻²² ⁻ ⁽⁻²²⁾

Dividing the base numbers

Quotient = 4 × 10⁻²²⁺²²

Performing subtraction on exponents

Quotient = 4 × 10⁰

Also, as per the known fact, a⁰ = 1. So, the final answer is 4 and in scientific notation the final answer is 4 × 10⁰.

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