What is the absolute value of these respective values?
18 and -91

Answer:

x=6

Step-by-step explanation:

10-5x=3(x-4)-2(x+7)

Distribute

10-5x=3x-12-2x14

Combine like terms

10-5x = x-26

add 5x to each side

10-5x+5x = x+5x-26

10 = 6x-26

Add 26 to each side

10+26 = 6x-26+26

36 = 6x

Divide by 6

36/6 = 6x/6

6 =x

Answer:

\(10-5x=3\left(x-4\right)-2\left(x+7\right)\)

\(3\left(x-4\right)-2\left(x+7\right)\)

combine like terms:-

\(=3x-12-2x-14\)

\(3x-2x=x\)

\(=x-12-14\)

Subtract -12 -14

\(=x-26\)

\(10-5x=x-26\)

Subtract 10 from both sides:-

\(-5x=x-36\)

Now, subtract x from both sides:-

\(-5x-x=x-36-x\)

\(-6x=-36\)

Divide both sides by -6:-

\(\frac{-6x}{-6}=\frac{-36}{-6}\)

\(x=6\)

OAmalOHopeO

Answer:

9.5 < x < 15

Step-by-step explanation:

The possible values of x for the given problem lies in  (-infinity, -1.33) ∪ (9.5, 15).

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

Given that,

The sides of the triangle are as follows,

CD = x - 4,  DE = 3x + 21 and  CE = 6x - 13.

There can be three cases for the given problem.

Case 1,

The longest side of the triangle is CE = 6x - 13.

Since the sum of the two sides of a triangle is always greater than the longest one, the following inequality can be written for the given triangle,

6x - 13 < x - 4 + 3x + 21

=> 6x - 13 < 4x + 17

=> 6x - 4x < 17 + 13

=> 2x < 30

=> x < 15

Case 2,

The longest side of the triangle is DE = 3x + 21.

Since the sum of the two sides of a triangle is always greater than the longest one, the following inequality can be written for the given triangle,

3x + 21 < 6x - 13 + x - 4

=> 3x + 21 < 7x - 17

=> 7x - 3x > 21 + 17

=> x > 38/4

=> x > 9.5

Case 3,

The longest side of the triangle is CD = x - 4.

Since the sum of the two sides of a triangle is always greater than the longest one, the following inequality can be written for the given triangle,

x - 4 < 3x + 21 + 6x - 13

=>  x - 4 < 9x + 8

=> x - 9x > 8 + 4

=> x < -1.33

Thus, the range of the values of x is intersection of x < 15, x > 9.5 and  x < -1.33, which is equivalent to (-infinity, -1.33) ∪ (9.5, 15).

Hence, the range of possible values of x lies in the interval (-infinity, -1.33) ∪ (9.5, 15).

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Answer:

(5 - (-1)) or 6

Step-by-step explanation:

Substitute the variables

= (x - y)

=(5 - (-1))

= 6

Hope this was simple enough for you to understand!

Answer:

D. 28

Step-by-step explanation:

We are given the following polynomial function:

\(F(x) = x^2 - 2x - 7\)

Find F(-5).

This is the value of F for which \(x = -5\). So

\(F(-5) = (-5)^2 - 2(-5) - 7 = 25 + 10 - 7 = 28\)

28, which means that the correct answer is given by option D.

9514 1404 393

Answer:

Step-by-step explanation:

The figure and its image are symmetrical about the origin, so the following three transformations are equivalent:

  1. reflection across the origin

  2. rotation 180° about the origin

  3. reflection across both x- and y-axes, in either order

__

The figure itself has left-right symmetry, so only one reflection is necessary to map the figure to its image: reflection across a horizontal line. Following that reflection, the image can be put into place by an appropriate translation. One such pair of transformations is ...

  4. reflection across the x-axis and translation 6 units right, in either order

Answer:

Its A

Step-by-step explanation:

ez

Answer:

A

Step-by-step explanation:

y= -3x + 7

Answer:

the answer is A) 59, 681

Step-by-step explanation:

all you have to do is subtract

so 95,216 - 35,535= 59,681

hope i helped

-lvr

Answer:

Right angle

Step-by-step explanation:

It is because ANGLE QMS from the given figure denote 90 ° and right angle means 90°.

Answer:

42, 41, 123

Step-by-step explanation:

3, 2, 6, 5, 15, 14

- 1 x3. - 1. x3. - 1

you just gotta look for the pattern thats the same in the sequence so the next three numbers would be x3, then - 1 then x3 again onto the numbers.

Answer:

The next three numbers are 42, 41, and 123

Step-by-step explanation:

3 - 1 = 2

2 * 3 = 6

6 - 1 = 5

5 * 3 = 15

15 - 1 = 14

The pattern is subtracting one and then multiplying by three.

14 * 3 = 42

42 - 1 = 41

41 * 3 = 123

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:

\(12 * 0.25 = 3\)

Ratio refers to the quantitative relationship between two or more quantities, expressing the proportion of one quantity to the other(s). It is typically expressed as a fraction, where the numerator represents one quantity, and the denominator represents the other quantity.

For example, the ratio of the number of boys to the number of girls in a class of 30 students might be expressed as 2:3, which means there are 20 girls and 10 boys in the class. Similarly, the ratio of the length to the width of a rectangle might be expressed as 4:3, indicating that the length is four times greater than the width.

The ratio of sheep to horses is 4:1, which means that for every 4 sheep on the farm, there is 1 horse. We can also say that the total ratio of sheep and horses on the farm is 4+1=5.

To express the relationship between the chickens and the sheep, we need to use the fact that there are 32 chickens and 12 sheep on the farm. We can write this as a ratio:

\(chickens : sheep = 32 : 12\)

We can simplify this ratio by dividing both sides by 4:

\(chickens: sheep = 8: 3\)

This means that for every 8 chickens on the farm, there are 3 sheep.

To determine the number of horses on the farm, we can use the fact that the total ratio of sheep and horses is 5. We know that the ratio of sheep to horses is 4:1, so we can write:

\(sheep : horses = 4 : 1\)

We can simplify this ratio by dividing both sides by 4:

\(sheep : horses = 1 : 0.25\)

This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:

\(12 * 0.25 = 3\)

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Answer:

The answer is 275 students.

Step-by-step explanation:

In 75 students, 33 students attend.

So the ratio is 33/75.

so multiply with 625.

625 x 33/75 = 275

Using the principle of proportional relationship, the amount of weight lost by hedgedog in 120 days is 3.6 oz

Proportional relationships are defined thus :

Taking a piar of points :

-0.24 = 8k

Divide both sides by 8

(-0.24/8) = k

k = - 0.03

Hence, hedgedog loses weight at a rate of - 0.03 oz per day.

The amount of weight lost in 120 days :

The proportional relationship = y = - 0.03x

Substitute x into the equation

y = -0.03(120)

y = - 3.6 oz

Therefore, the amount of weight lost in 120 days is 3.6 oz.

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Answer:

Step-by-step explanation:

\((a^2-1)x^2+(a-1)x+a^2-4a+3=0\\\\Calculate\ and\ identify\ the\ polynomials\\\\\Longleftrightarrow\ a^2x^2-x^2+ax-x+a^2-4a+3=0\\\\\Longleftrightarrow\ a^2x^2+ax+a^2-4a+3=x^2+x+0\\\\\Longleftrightarrow\ \left\{\begin{array}{ccc}a^2&=&1\\a&=&1\\a^2-4a+3&=&0\\\end{array} \right.\\\\\Longleftrightarrow\ \left\{\begin{array}{ccc}(a-1)(a+1)&=&0\\a-1&=&0\\(a-1)(a-3)&=&0\\\end{array} \right.\\\\\\We\ must\ exclude\ a=-1\ and\ a=3\ (not\ solution)\\\Longrightarrow\ a=1\\\)

The median, mean, range and mode will be 6, 5.4, 9 and 7.

What is median?

The median is the middle number in the data set when the data set is written from least to greatest.

The median is the number in the middle when arranged in an ascending order. The numbers will be:

0, 3, 4, 6, 6, 7, 7, 7, 9.

The median is 6.

The range is the difference between the highest and lowest number which is: = 9 - 0 = 9

The mode is the number that appears most which is 7.

The mean will be the average which will be:

= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.

= 49/9

= 5.4

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The surface area of the vase is 168.4 square inches.

What is a cylinder?

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

The surface area of the cylindrical vase can be found using the formula SA = B + Ph, where B is the area of the base, P is the perimeter of the base, and h is the height of the vase. Since the vase has a circular base, the area of the base can be found using the formula for the area of a circle: B = πr², where r is the radius of the base.

The diameter of the vase is 4.3 inches, so the radius is half of that, or 2.15 inches. The area of the base is therefore:

B = πr² = 3.14 * (2.15)² ≈ 14.46 square inches.

The perimeter of the base is the circumference of the circle, which can be found using the formula C = 2πr:

P = 2πr = 2 * 3.14 * 2.15 ≈ 13.53 inches.

Now we can use the formula SA = B + Ph to find the surface area of the vase:

SA = B + Ph = 14.46 + 13.53 * 11 ≈ 168.39 square inches.

Rounding to the nearest tenth of a square inch, the surface area of the vase is approximately 168.4 square inches.

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The average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

To determine the average rate of change of the school's enrollment during the given time period, we can use the formula:

Average rate of change = (Change in enrollment) / (Change in time)

The change in enrollment is calculated by subtracting the initial enrollment from the final enrollment, while the change in time is calculated by subtracting the initial year from the final year.

Given that in 2004 there were 975 students enrolled and in 2009 there were 730 students enrolled, we can calculate the change in enrollment:

Change in enrollment = 730 - 975 = -245 students

The change in time can be calculated as:

Change in time = 2009 - 2004 = 5 years

Now we can calculate the average rate of change:

Average rate of change = (-245 students) / (5 years) = -49 students per year

Therefore, the average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

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Answer:

C

Step-by-step explanation:

subtract 5 from both sides

Answer:

d. h = 11.3 ft

Step-by-step explanation:

volume of cone = \(\frac{1}{3}\)r²\(\pi\)h

r = 4 feet

Put in your values:

\(\frac{1}{3}\)(4)²(3.14)h = 189 ft³

16(3.14)h = 567

50.24h = 567

h = \(\frac{567}{50.27}\) = 11.3

The height of the cone is h = 11.3 feet

In geometry,  a cone is a three-dimensional shape formed by joining a set of line segments from a common point called apex to all the points of the base which is a circle.

Height of the cone is distance from apex to the center of the circular base.

Volume of a cone is defined as the total capacity of the cone and the formula for the same is given by,

V = \(\frac{1\\}{3}\)πr²h

Here, V = 189 ft³, r = 4 ft, π = 3.14

Substituting these values in formula for the volume,

189 = \(\frac{1}{3}\) × 3.14 × 4² × h

189 = \(\frac{50.24}{3}\)h

h = 189 × 3 / 50.24

h = 11.285 ≈ 11.3

Hence the height of the cone with radius 4 ft and volume 189 ft³ to the nearest tenth of a foot is 11.3 ft.

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f= the original amount of people, a steady growth throughout the years

t=time

In 1955 the population was 12 thousand. Compared to the current population of 12.36 thousand, the population then was roughly 77%.

A function assigns the values.  The population of the town in 1955 was 12 thousand people, and the percent increase in population from year to year was 3%.

A function assigns the value of each element of one set to the other specific element of another set.

The function that gives the population of the town is given, therefore, the following can be written,

Since the year 1955 the value of t=0. Therefore, The population of the town in 1955 was 12 thousand.

The percentage increase in population from year to year is 3%.

Hence, The population of the town in 1955 was 12 thousand people, and the percent increase in population from year to year was 3%.

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Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to group things that can actually be factored. You dont want to group -7x^3 and -9 because that would just be a mess and wouldnt give you the right answer.

\((-7x^3+21x^2)+(3x-9)\\-7x^2(x-3)+3(x-3)\\(-7x^2+3)(x-3)\)

Answer: is A

Step-by-step explanation:

the total area of the two triangles as shwon in the image is 70 in²

Area can be defined as the total portion occuppied by a plane fiqure.

To calculate the total area of the two triangles, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

Similarly,

Where:

Substitute these values into equation 2

Therefore, the total area of the two triangles is 40+30 = 70 in².

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Answer:

a. – 4 or –3

b. –4 or –2

c. 4 or –3

d. 7 or 4

Step-by-step explanation:

To factorize the above expression, multiply the first and last term together, then find two factors of the result such that their sum will result to the middle term of the expression.

Now, we shall give the answers to the question.

a. x² + 7x + 12 = 0

x² + 3x + 4x + 12 = 0

Factorise

x(x + 3) + 4(x + 3) = 0

(x + 4)(x + 3) = 0

x + 4 = 0 or x + 3 = 0

x = 0 – 4 or x = 0 – 3

x = – 4 or –3

Therefore, the roots of the equation are – 4 or –3

b. t² + 6t + 8 = 0

t² + 2t + 4t + 8 = 0

Factorise

t(t + 2) + 4(t + 2) = 0

(t + 4)(t + 2) = 0

t + 4 = 0 or t + 2 = 0

t = 0 – 4 or t = 0 – 2

t = –4 or –2

Therefore, the roots of the equation are –4 or –2

c. 2n² – 2n – 24 = 0

Divide through by 2

n² – n – 12 = 0

n² + 3n – 4n – 12 = 0

Factorise

n(n + 3) – 4(n + 3) = 0

(n – 4)(n + 3) = 0

n – 4 = 0 or n + 3 = 0

n = 0 + 4 or n = 0 – 3

n = 4 or n = –3

Therefore, the roots of the equation are 4 or –3

d. y² – 11y + 28 = 0

y² – 4y – 7y + 28 = 0

Factorise

y(y – 4) – 7(y – 4) = 0

(y – 7)(y – 4) = 0

y – 7 = 0 or y – 4 = 0

y = 0 + 7 or y = 0 + 4

y = 7 or 4

Therefore, the roots of the equation are 7 or 4.

Answer:

i think the answer is option 1           3

Step-by-step explanation:

i say this bc 3/4 times 4 is 3

hope this helps

if this is the correct answer plz mark brainliest.

Answer:

998.

Step-by-step explanation:

Just get rid of the negative sign

Answer:

This should 998 I guess

Step-by-step explanation:

Minus the negative signs