Solve each compound inequality and graph the solutions. -2 < x - 3 < 5

Answer:

4 11/20

Step-by-step explanation:

The length of road unpaved is 7 3/10 less 2 3/4 miles  The LCD of the fractions is 20 (both 10 and 4 divide evenly into 20).

Thus, the problem becomes 7 6/20 - 2 15/20.

We have to borrow 1 from that 7 because 15/20 is larger than 6/20.  This results in

6 26/20 - 2 15/20, or

4 11/20  

The total length of the main road in Belleville is [tex]7^{(3/10)}[/tex] miles. So far, [tex]2^{3/4}[/tex] miles have been repaved, leaving [tex]7^{(3/10)}[/tex] - [tex]2^{3/4}[/tex] miles that have not been repaved.

1. The total length of the main road is given as [tex]7^{(3/10)}[/tex] miles. In mathematical notation, [tex]7^{(3/10)}[/tex] represents the cube root of 7, which is then raised to the power of 3. So, the total length of the road is the cube root of 7, and then that result is cubed.

2. The length of the repaved portion is given as [tex]2^{3/4}[/tex] miles. In mathematical notation, [tex]2^{3/4}[/tex] represents the fourth root of 2, which is then raised to the power of 3. So, the repaved length is the fourth root of 2, and then that result is cubed.

3. To find the remaining length that has not been repaved, we simply subtract the repaved length from the total length:

  Remaining length = [tex]7^{(3/10)}[/tex] - [tex]2^{3/4}[/tex]

Calculating the values, the total length is approximately 2.262 miles (rounded to three decimal places) and the repaved length is approximately 1.682 miles (rounded to three decimal places). Now, subtracting the repaved length from the total length, we get approximately 0.580 miles (rounded to three decimal places) as the length that has not been repaved.

Therefore, the remaining length that has not been repaved is approximately 0.580 miles (rounded to three decimal places).

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Answer:

1.55 × 10^24

Step-by-step explanation:

The answer is A aka 1.55 x 10 to the power of 24

Answer:

A) Sin A  + Sin B  =  1.2 Sin C  

D) Sin C =  2.5 Sin A  = 1.25 Sin B

E)  Sin A  + Sin C  =  1.75 B

Step-by-step explanation:

Here, in the given triangle ABC

Base AC = 16 units, AB  = 2 units, and BC  = 8 units

Now, by Trigonometric Functions:

[tex]\frac{Sin A}{8} = \frac{Sin B}{16} =\frac{Sin C}{20}[/tex]

Comparing first two terms, we get:

[tex]\frac{Sin A}{8} = \frac{Sin B}{16} \\\implies 2Sin A = Sin B[/tex]                 ........... (1)

Also,

[tex]\frac{Sin B}{16} = \frac{Sin C}{20} \\\implies Sin C = 1.25 Sin B[/tex]   ....... (2)

Comparing first and last  terms, we get:

[tex]\frac{Sin C}{20} = \frac{Sin A}{8} \\\implies SinC = 2.5 Sin A[/tex]      ..........  (D)

Also, Sin A  = 0.5 Sin B

So, the given statement Sin A  = 2 Sin B is FALSE

⇒ 2.5 Sin A  = 1.25 Sin B   .......... (D)

Also,  Sin B  = 2 Sin A

⇒ Sin A  + Sin B =  Sin A + 2 Sin A =  3 Sin A

Also, Sin A  = 0.4 Sin C

⇒3 Sin A = 3 x (0.4) Sin C  = 1.2 Sin C  ..

⇒Sin A  + Sin B  =  1.2 Sin C   ........ (A)

B)   Sin A  - Sin B  = 0.4 Sin C - 2 Sin A  =  0.4 Sin C - 2 (0.4 Sin C)  

= 0.4 Sin C  - 0.8 Sin C  = -0.4 Sin C

⇒Sin A  - Sin B  =  -0.4 Sin C   ........ (B)

So, the given statement is FALSE

E)   Sin A  + Sin C =  0.5 Sin B + 1.25 B =  1.75 B

⇒ Sin A  + Sin C  =  1.75 B  ....(E)

Answer:

Step-by-step explanation:

I need help

Answer:

28 girls

Step-by-step explanation:

Given girls : boys ===> 7 : 12

i.e.

fraction all children who are girls = 7 / (7 + 12) = 7 / 19

fraction all children who are boys = 12 / (7 + 12) = 12 / 19

given that there are 76 children

number of girls = fraction of all children who are girls x total number of children

= 7/19   x   76

= 28 girls

Answer:

1/2

Step-by-step explanation:

The answer would be x-2y= -4 I hope this helped!

Answer:

Midpoint of AB=(6,10) ,Midpoint of BC=(6,9) and Midpoint of CA=(-3,12)

Step-by-step explanation:

Given that the points are A(-3,13), B(15,7) and C(-3,11)​

To find the mid points :

To find midpoint of AB

Let [tex](x_1,y_1) and (x_2,y_2)[/tex] be the points A(-3,13),B(15,7) respectively

Midpoint of AB[tex]=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

[tex]=(\frac{-3+15}{2},\frac{13+7}{2})[/tex]

[tex]=(\frac{12}{2},\frac{20}{2})[/tex]

[tex]=(6,10)[/tex]

Midpoint of AB=(6,10)

To find midpoint of BC

Let [tex](x_1,y_1) and (x_2,y_2)[/tex] be the points B(15,7),C(-3,11) respectively

Midpoint of BC[tex]=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

[tex]=(\frac{15-3}{2},\frac{7+11}{2})[/tex]

[tex]=(\frac{12}{2},\frac{18}{2})[/tex]

[tex]=(6,9)[/tex]

Midpoint of BC=(6,9)

To find midpoint of CA

Let [tex](x_1,y_1) and (x_2,y_2)[/tex] be the points C(-3,11),A(-3,13),respectively

Midpoint of CA[tex]=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

[tex]=(\frac{-3-3}{2},\frac{11+13}{2})[/tex]

[tex]=(\frac{-6}{2},\frac{24}{2})[/tex]

[tex]=(-3,12)[/tex]

Midpoint of CA=(-3,12)

Therefore Midpoint of AB=(6,10) ,Midpoint of BC=(6,9) and Midpoint of CA=(-3,12)

Answer: x-intercept(6,0) & y-intercept(0,3)

Step-by-step explanation: To find the x-intercept, subsitutue zero in for y and solve for x, and vice versa to solve for y.

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

Now you know the answer as well as the formula. Hope this helps, have a BLESSED AND WONDERFUL DAY!

- Cutiepatutie ☺❀❤

Answer:

The irregular polygon is D.

Step-by-step explanation:

An irregular polygon is a shape that doesn't have all congruent sides.

Answer:

D

Step-by-step explanation:

Answer:  Y = - 4 & x = 1

Step-by-step explanation:

Systems of linear equations: We will solve this using substitution but you can use 2 more ways.

7x + 2y = -1

2x - 4y = 19

Leave X  alone first: -------------------

10x - 2y = 18

10x/10 = 18 + 2y/10

x = 9/5 + y/5

Solve for y:

7(9/5 + y/5) + 2y = -1

63/5 + 7y/5 + 2y - 1

63/5 + 7y/5 = 10y/5 = -1

63/5 + 17y/5 = -1 (-5/5)

17y/5 = -68/5 (cancel the 5)

y = -68/17

y = - 4 (Your Answer)

7x + 2(- 4) = -1

7x + (-8) = -1

7x = 7

x =   1

CHECK=

7(1) + 2(-4) = -1

7+ (-8) = -1.

-1=-1

Answer:

(1, -4).

(x = 1, y = -4).

Step-by-step explanation:

7x + 2y = -1

3x  – 4y = 19    Multiply the first equation by 2:

14x + 4y = -2     Adding:

17x = 17

x = 1.

Plug this into the second equation:

3(1) - 4y = 19

-4y =  19 - 3 = 16

y = -4.

The answer for the given polynomial by synthetic division is 3x+16+(30/(x-3)).

Step-by-step explanation:

The given polynomial is (3x^2 +7x -18) divided by (x - 3)

Take (x-3)=0, then x=3

    3  |  3        7       -18  

                    9        48

           3       16       30

step 1: write the coefficients of x^2, x and constant in first row. The divisor 3 is written separately on outside.

step 2: Write down the coefficient of x^2= 3 in the answer row as it is without any change.

step 3: Multiply each number in the answer row with the divisor and fill the answers in the second row.

step 4: The final step is to add the first row and second row. After addition, the answers are written in answer row and the last number in the answer row is the Remainder.

step 5: The remainder is written by dividing it with the divisor (x-3). The answer in the descending powers of x is 3x + 16 + (30/(x-3)).

The result of the division (3x^2 + 7x - 18) by (x - 3) using synthetic division is obtained as (3x + 16 + 30/(x - 3)).

To perform the synthetic division, the divisor (x - 3) is represented by its root '3'. Write down the coefficients from the dividend polynomial (3, 7, -18) at the top of your division setup. Write '3' to the left, leave some space, and then write down '3', '7', -18.

Then, perform the synthetic division: step one, bring the first coefficient (3) straight down. Step two, multiply this number by the root of the divisor (3), which is also 3. Write this product (9) underneath the next coefficient (7). Add these two numbers (7 + 9) to get 16. Write this number under the line. Now, repeat the previous step by multiplying 16 by the root, 3, to get 48. Write this under -18, add to get 30.

The quotient of the division is the polynomials received from the synthetic division which is 3x + 16 with a remainder of 30. So, the result of division (3x^2 + 7x - 18) by (x - 3) is (3x + 16 + 30/(x - 3)).

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Answer:

f(x) = x³ - 3x² - 10x

Step-by-step explanation:

Given that the zeros are x = - 2, x = 5 and x = 0 then the factors are

(x + 2), (x - 5) and (x - 0) = x

The polynomial is the product of it's factors, thus

f(x) = x(x + 2)(x - 5) ← expand factors using FOIL

     = x(x² - 3x - 10) ← distribute parenthesis by x

     = x³ - 3x² - 10x

Answer:

Step-by-step explanation:

x^2 - 6x - 40 = 0.....get the -40 to the other side

x^2 - 6x = 40....now take half of ur x term (6)....so its 3...then square it (3^2 = 9)...now add 9 to both sides

x^2 - 6x + 9 = 40 + 9

(x - 3)(x - 3) = 49

(x - 3)^2 = 49...take sqrt of both sides, eliminating the ^2

x - 3 = sqrt 49

x = 3 (+ - ) 7

x = 3 + 7 = 10 or x = 3 - 7 = -4

so x = 10 or x = -4

Answer:

12

Step-by-step explanation:

3[y+2]

2+2= 4

3 multiplied by 4 is 12

Answer: 12

Step-by-step explanation: Since y = +2, we simply plug a +2 in for y in the expression. So we have 3(2 + 2).

Following your order of operations, you should simplify what's inside the parentheses first so 2 + 2 simplifies to 4.

Bring down your 3 and you have 3(4) which equals 12.

Answer:

y = 5/2 , x= 7/2

Step-by-step explanation:

5x - 3y = 10…....(1)

3x + 3y = 3......(2)

solving by elimination, we subtract equation (2) from equation (1)

so, 2x = 7

dividing both sides by 2

x= 7/2

substitute x=7/2 for the value of y in equation (1)

5(7/2) - 3y = 10

multiply both sides by 2

35 - 6y = 20

rearranging

-6y = -15

dividing both sides by -6

y = 5/2

Answer:

100 boxes

Step-by-step explanation:

Divide 1,198 with 12 because if there are 1,198 paperweights and each box holds 12 then how many boxes can hold these paperweights. Answer us 100 boxes

It takes 4 years for number of daily visitors to be 800% more than the number of daily visitors in 2003

Solution:

Let the number of visitors in 2003 be 100

From 2003 onward, the number of daily visitors to a website increased by 200% every two years

Therefore, Number of visitors in 2005 is given as:

Visitors in 2005 = 100 + 200 % of 100

[tex]Visitors\ in\ 2005 = 100 + \frac{200}{100} \times 100\\[/tex]

Visitors in 2005 is 300

Similarly, in 2007, the number of visitors is given as:

Visitors in 2007 = 300 + 200 % of 300

Visitors in 2007 = 300 + 600

Visitors in 2007 = 900

Now find the percentgae increase from 2003 to 2007

[tex]\text { Percentage increase }=\frac{\text {visitors in } 2007-\text {visitors in } 2003}{\text {visitors in } 2003} \times 100[/tex]

[tex]\text{percentgae increase} = \frac{900 - 100}{100} \times 100\\\\\text{percentgae increase} = 800[/tex]

Thus it is a 800 % increase

Number of years = 2007 - 2003 = 4 years

Thus it takes 4 years for number of daily visitors to be 800% more than the number of daily visitors in 2003

If a number increases by $200\%$, then this means that $2$ times the number is added to the original number. The result is $3$ times the original number. So, the information given in the problem means that the number of daily visitors to the website tripled every two years.

For the number of daily visitors to increase by $800\%$, it must become $9$ times its original value (that's $8$ times the original number added onto the original number). This is equivalent to tripling and then tripling again.

Relative to its value in $2003$, the number of daily visitors to the website tripled by $2005$, then tripled again by $2007$. So, $\boxed{2007}$ is the year in which this number reached $800\%$ more than its value in $2003$.

Answer: 35.27 oz

The answer is: The change of 1 kg ( kilogram ) unit for a weight and mass measure equals = into 35.27 oz ( ounce ) as per its equivalent weight and mass unit type measure often used.

Approximately, 1 kilogram is equivalent to 35.3 ounces. This calculation is achieved by starting with the knowledge that 1 kilogram is 1000 grams, then converting this measurement to ounces knowing that 1 gram equals 0.0353 ounces.

The topic at hand is the conversion between weight metrics, specifically how many ounces are approximately equivalent to a kilogram. It's important to note that 1 kilogram is approximately equivalent to 35.274 ounces. Here's why:

We understand from the given information that 1 ounce is produced by a mass of 28.35 grams (abbreviated as g). Given that 1 kilogram (kg) is equal to 1000 grams, to find the equivalent of a kilogram in ounces, we need to convert 1000 grams to ounces:

Step-by-Step Calculation

So, 1 kilogram is approximately equivalent to 35.3 ounces.

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Answer:

(negative infinity, 2)

Step-by-step explanation:

The two functions are given by f(x) = x - 3 and g(x) = - 0.5x

So, (f - g)(x) = x - 3 - ( - 0.5x) = 1.5x - 3

Then, for (f - g)(x) to be negative (1.5x - 3) < 0

⇒ 1.5x < 3

⇒ x < 2

Therefore, the interval will be (negative infinity, 2) for which the function (f - g)(x) will be negative. (Answer)

Answer:

negative infinity 2

Step-by-step explanation:

just did the test

Answer:

The square root of 49 is 7. 7*7=49

Hope this helps,

:)

Answer:

Subtracting polynomials is simply subtracting the like terms

(x-2)-(6x-9)

First you want to subtract your x from 6x

x-6x= -5x

Than you would subtract -2 and -9

-2- -9=7

-2+9=7

Your final answer would be

-5x+7

Hope this helps ;)

Step-by-step explanation:

ANSWER: 182 inches

STEP-BY-STEP EXPLANATION:

Since, it is an isosceles trapezoid, then area of an isosceles triangle is given by: [tex]\frac{1 (a+b)}{2}[/tex] × h

where a and b are the two parallel sides of the triangle and h is the height of an isosceles triangle.

Now, a= 12 inches and b= 2+2+12=16 inches and h=13 inches.

[tex]\frac{1 (12+16)}{2}[/tex] × 13 = 182 inches

Answer: C

Step-by-step explanation:

to be a good graph the x axis and y axis need labeled

The graph could be misleading because it does not indicate if the free throws were made at home or away, it is missing the scale on the y-axis, and it doesn't specify if all team members are included.

The statement that best describes why this graph could be misleading is A. The graph does not indicate if the free throws were made at home or away. The graph may show higher or lower percentages for certain players based on the location of the game. For example, a player may have a higher free throw percentage when playing at home compared to playing away.

Additionally, statement C is also correct. The graph is missing the scale on the y-axis, which makes it unclear how much higher or lower the free throw percentages are for each player.

Lastly, statement D is another reason why the graph could be misleading. Without knowing if all the people on the team are included, the graph may not provide an accurate representation of the overall free throw percentages of the team.

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Answer:

Miguel traveled 0.2 mile per minute.

Step-by-step explanation:

3÷15=0.2

Speed can be interpreted from a graph's slope in a distance versus time plot. Comparing this to Molly's speed of 0.15 mile per minute, we could establish who is faster or slower. However, without the actual graph of Miguel's bicycling, we can't make a specific comparison.

This question relates to graph interpretation and the concept of speed. Here, we're trying to compare the cycling speed of Miguel and Molly. Molly's speed is given as 0.15 mile per minute. Without the graph available, we cannot definitively compare their speeds. But let's briefly explain what we'd look for.

If we had Miguel's graph, we'd specifically examine the slope of the graph. In a distance vs. time plot, speed is represented by the slope of the graph. Therefore, if the slope of Miguel's graph indicated a value higher than 0.15 mile per minute (steep slope), Miguel was going faster. Conversely, if it showed a lesser value (gentle slope), Miguel was going slower.

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At least 2,000 students are expected to pursue a Social Sciences degree at Arizona State University. The most popular degree is Business Marketing, and about 6,000 students are estimated to enroll in the top two most popular programs (Business Marketing and Social Sciences) in the fall semester.

Based on the information provided about

Arizona State University's

most popular majors and their respective percentages, you can determine the minimum number of students expected to be working towards a Social Sciences degree. The

Social Sciences

program makes up 10% of the student body. Therefore, if the enrollment is expected to reach at least 20,000 students, you can expect that at least 2,000 students (10% of 20,000) will be working towards a

Social Sciences

degree. As for the most popular degree, Business Marketing is listed as comprising 20% of the student body, making it the most popular degree. The two most popular programs, Business Marketing and Social Sciences, make up 30% of the student body. So the university might expect that at least 6,000 students (30% of 20,000) will enroll in one of the two most popular programs in the fall semester.

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Answer:

C

Step-by-step explanation:

Answer:  C ) No, Hugo forgot to multiply both sides of the first equation in step one.

Step-by-step explanation:

Answer for Question 1 is option 2  

Answer for Question 2 is option 3  

Answer for Question 3 is option 3  

Step-by-step explanation:  

For question 1 by plotting the two points we get the coordinates as (-2, 3) and (2, 1) where the x values are -2, 2 and the y values are 3, 1 respectively.  By substituting values of x in the formula given we get that equation 2 satisfies the values of y as in the graph.  

For question 2 the plotted line is split into two parts where one half is for values of x <2 and the other half is for values of x>2. By finding out the coordinates we get them as (2,-2), (1,-2.5) and (0,-3) for x<2 and by substituting the values of x in the formula we get option 3 as our answer.  

For question 3 we need to find the value of y when x=3 and the first condition is only for values greater than 3 so we take the second condition and substitute the value of x=3 and we get the value of y as 5 so the answer is option 3  

Answer:

[tex]\large \boxed{\text{39 ft}}[/tex]

Step-by-step explanation:

Let x be the distance from the foot of the ladder to the base of the building.

We have a right triangle, so we can use Pythagoras' Theorem.

[tex]\begin{array}{rcl}80^{2} + x^{2}& = & 89^{2} \\6400+ x^{2} & = & 7921\\x^{2} & = & 1521\\x & = & \sqrt{1521}\\& = &\mathbf{39}\\\end{array}\\\text{The foot of the ladder will be $\large \boxed{\textbf{39 ft}}$ from the base of the building,}[/tex]

Answer:

Step-by-step explanation:

Answer:

A customer earns one free night per 10 nights stayed.

Step-by-step explanation:

A hotel offers a reward program based on the number of nights stayed. The function f(x) represents the number of free nights earned as a function of x, the number of nights stayed.

Here, [tex]f(x) = \frac{x}{10}[/tex] ........... (1)

In the above equation if we put x = 10 nights then f(10) = 1 night.

From, the equation (1) we get that a customer earns one free night per 10 nights stayed. (Answer)

The correct option is A. a customer will earn 1 free night per 10 night stayed.

Given,

[tex]f(x)=\dfrac{x}{10}[/tex]..........equation (1) .

Since the hotel offers a reward program based on the number of nights stayed. The function [tex]f(x)[/tex] represents the number of free nights earned as a function of [tex]x[/tex], the number of nights stayed.

From equation (1), it is clear that  f(x) is the one- tenth times  of x. it means the customer will earn 1 free night per 10 night stayed.

Hence the correct option is A. a customer will earn 1 free night per 10 night stayed.

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