2. The area of the base of the cone is 64π cm2 and the altitude is 6 cm. Calculate the cone: (a) the length of the constituent;(b) the area of the lateral area of the cone; c) the volume.

Answers

Answer 1

Answer: We have to calculate the (i) volume and (ii) the surface area of the cone:

[tex]\begin{gathered} A=\pi r^2+\pi rl\rightarrow(1) \\ \\ V=\pi r^2\frac{h}{3}\rightarrow(2) \end{gathered}[/tex]

The formula (1) is for the lateral surface of the cone and the formula (2) is for the volume of the cone, the unknowns are determined as follows:

[tex]\begin{gathered} r=\sqrt{\frac{64\pi}{\pi}}=8cm \\ \\ r=8cm \\ \\ l=\sqrt{r^2+h^2}=\sqrt{(8cm)^2+(6cm)^2} \\ \\ l=\sqrt{100}=10 \\ \\ l=10 \end{gathered}[/tex]

Therefore the volume and the lateral surface area is calculated as follows:

[tex]\begin{gathered} \begin{equation*} A=\pi r^2+\pi rl \end{equation*} \\ \\ A=\pi(8)^2+\pi(8)(10) \\ \\ A=144\pi cm^2\Rightarrow(x) \\ \\ \begin{equation*} V=\pi r^2\frac{h}{3} \end{equation*} \\ \\ V=\pi(8cm)^2\frac{6cm}{3} \\ \\ V=128\pi cm^3\Rightarrow(y) \end{gathered}[/tex]

Therefore x and y are the answers.


Related Questions

David has a coin collection. He keeps 9 of the coins in his box, which is 2% of the collection. How many total coins are in his collection?

Answers

Answer:  450

Work Shown:

x = total number of coins

2% of x = 0.02x = 9 coins in the box

0.02x = 9

x = 9/0.02

x = 450 coins total

2(3x+6)-96=6(2x-4)-56Which value of x makes the equation true?A. X=-2B. x=-2/3C. x=2D. x=3

Answers

Given equation:

[tex]2(3x+6)-96=6(2x-4)-56[/tex]

Solve the equation to find the value of x,

[tex]\begin{gathered} 2(3x+6)-96=6(2x-4)-56 \\ 2(3x)+2(6)-96=6(2x)-6(4)-56 \\ 6x+12-96=12x-24-56 \\ 6x-84=12x-80 \\ -84+80=12x-6x \\ -4=6x \\ x=\frac{-4}{6} \\ x=-\frac{2}{3} \end{gathered}[/tex]

Hence, x=-2/3

Answer: option B) is correct

Answer:

2(3×+6) is 96 _6 by (2×4=5) with A.X

Need help please with this

Answers

Answer: It would be Answer D

Step-by-step explanation: He Subtracted from both sides in an incorrect order

What does the fundamental theorem of algebra state about the equation 2x2−x+2 = 0?Question 5 options:The fundamental theorem of algebra tells you that the equation will have two complex roots since the leading coefficient of the equation is 2. The roots arex = 1 ± i7.−−√The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are x = 1 ± i7.−−√The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots arex = 1±i15√4.The fundamental theorem of algebra tells you that the equation will have two complex roots since the leading coefficient of the equation is 2. The roots arex = 1±i15√4.

Answers

Given

Equation

[tex]2x^2-x+2=0[/tex]

Procedure

The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are

[tex]x=\frac{1}{4}\pm\frac{\sqrt[]{15}}{4}[/tex]

The discriminant b^2 - 4ac < 0

so, there are two complex roots.

For the function f(x), = 10 (√x + 9), find f-¹(x).

Answers

The inverse of the function f(x) = 10 (√x + 9) is  f⁻¹(x) = (x - 90)² / 100

Given,

The function, f(x) = 10 (√x + 9)

We have to find the inverse of the function, f⁻¹(x)

Here,

f(x) = 10 (√x + 9)

f(x) = 10√x + 90

Replace f(x) with y.

y = 10√x + 90

Swap x with y;

x = 10√y + 90

Solve for y

That is,

x = 10√y + 90

x - 90 = 10√y

(x - 90) / 10 = √y

Square both sides

((x - 90) / 10)² = √y²

(x - 90)² / 100 = y

Replace y with f⁻¹(x)

That is,

f⁻¹(x) = (x - 90)² / 100

Therefore,

The inverse for the function  f(x) = 10 (√x + 9) is  f⁻¹(x) = (x - 90)² / 100

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The measure of two complementary angles are in ratio 2:3. What is the measure of the smaller angle

Answers

ANSWER

36°

EXPLANATION

Let a and b be the measures of the two angles. We know that they are complementary, so their measures add up to 90°. Also, we know that the quotient between their measures is 2/3,

[tex]\begin{gathered} a+b=90 \\ \frac{a}{b}=\frac{2}{3} \end{gathered}[/tex]

Solve the second equation for a,

[tex]a=\frac{2}{3}b[/tex]

Replace a with this expression in the first equation,

[tex]\frac{2}{3}b+b=90[/tex]

Add like terms,

[tex]\frac{5}{3}b=90[/tex]

Solving for b,

[tex]b=90\cdot\frac{3}{5}=54[/tex]

So the other angle is,

[tex]a=\frac{2}{3}b=\frac{2}{3}\cdot54=36[/tex]

Hence, the measure of the smaller angle is 36°.

27 is The same as the product of four and a number

Answers

Answer:

6.75

Step-by-step explanation:

6.75x4 = 27 so if this is what was meant by this then heres your answer

hope this helped

have a good day ^^

The field inside a running track is made up of a rectangle 84.39 m long and 73 m wide, together with a half-circle at each end. The running lanes are 9.76 m Wide all the way around.What is the area of the running track that goes around the field? Round to the nearest square meter.

Answers

To find the area of the running track that goes around the field, we need to follow the formula:

area of running track = outside area - inside area

1. Outside Area:

outside area = area of rectangle + 2× area of the semi- circle

= 92.52× 84.39 + π × 46.26² = 14527.32m²

2. Inside Area:

inside area = area of rectangle + 2× area of the semi- circle

= 73 × 84.39 + π × 36.5² = 10343.74m²

So, area of running track = 14527.32 m² - 10343.74m² = 4183.58m² 4184m²

Assume that AGHI ALMN. Which of the following congruence statements
are correct? Check all that apply.
A. ZN=21
B. ZL 41
C. ME ZH
☐ D. GH = LM
E. IG= LM
F. IH NM

Answers

The following congruence statements a, b, e, f are correct.


What is congruence in a triangle?

Triangle congruence: If all three corresponding sides and all three corresponding angles seem to be equal in size, two triangles are said to be congruent.

When two triangles are congruent, their sides and corresponding angles are identical.

Therefore, if GHI is congruent to LMN, then GH =LM, HI=MN and GI=LN, and also angle G=angle L, Angle H=angle M, while angle I = angle N, therefore the correct answers is f) ∠M= ∠H, (a) GH = LM b) ∠L=∠G. and e)IH=NM.


Therefore, option a, b, e, f are correct.
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How many 1/4 pound hamburgers could be made from 5 1/2 pounds of hamburger meat?

Answers

Given:

Total amount of hamburger meat = 5½ pounds

Let's find how many ¼ pound hamburgers could be made from 5½ pounds of hamburger meat.

To find how many pound hamburger could be made divide 5½ by ¼.

Thus, we have:

[tex]5\frac{1}{2}\div\frac{1}{4}[/tex]

To perform the division, take the following steps:

Step 1:

Convert the mixed fraction to improper fraction

[tex]\frac{11}{2}\div\frac{1}{4}[/tex]

Step 2:

Flip the fraction on the right and change the division symbol to multiplication

[tex]\begin{gathered} \frac{11}{2}\ast\frac{4}{1} \\ \\ =\frac{11\ast4}{2\ast1} \\ \\ =\frac{44}{2} \\ \\ =22 \end{gathered}[/tex]

Therefore, 22 of ¼ pound of hamburger could be made from 5½ pounds of hamburger meat.

ANSWER:

22

Converting between fractions, decimals, and percentsUse the definition of the word percent to write each percent as a fraction and then as a decimal.

Answers

Answer:

See below for the completed table

Explanation:

A percentage is a number or ratio written as a fraction of 100. It is usually denoted using the symbol %.

To convert from percentage to fraction, divide the percentage by 100.

[tex]25\%=\frac{25}{100}[/tex]

You can then convert the fraction to a decimal where:

[tex]\frac{25}{100}=0.25\text{ (In decimal form)}[/tex]

Using the method described above, we calculate for the other values on the table:

[tex]\begin{gathered} 50\%=\frac{50}{100}=0.5 \\ 100\%=\frac{100}{100}=1 \\ 1\%=\frac{1}{100}=0.01 \\ 37.5\%=\frac{37.5}{100}=0.375 \\ 110\%=\frac{110}{100}=1.1 \\ \frac{1}{2}\%=\frac{0.5}{100}=0.005 \end{gathered}[/tex]

The completed table is attached below.

Given that Kelsey has already made 10 pendants how many additional pendants must she make and sell to make a profit of 50 dollars?

Answers

Part a: Kelsey should make 36 pendants

Part b: Kelsey needs to make 26 more pendants

Rent of the booth at the craft fair = $200

The material cost of each pendant = is $7.80

The selling cost of each pendant = is $13.50

Let Kelsey make x number of pendants

Formulating the inequality equation we get:

Selling cost of each pendant*Number of pendants >= Rent of the booth + Material cost of each pendant*Number of pendants

= 13.50x >= 200 + 7.80x

Solving the inequality we get:

13.50x >=200+7.80x

5.70x >= 200

x >= 35.08

So, she should make a total of 36 pendants

Considering that she has already made 10 pendants. She needs 26 more pendants.

Although a part of your question is missing, you might refer to this full question: Kelsey makes pendants that she would like to sell at an upcoming craft fair. She must pay $200 to rent a booth at the craft fair. The materials for each pendant cost $7.80, and she plans to sell each pendant for $13.50. To make a profit, she must make more money than she spends. Kelsey has already made 10 pendants. Part A: Write and solve an inequality to show how many pendants Kelsey should make. Show the steps of your solutions. Part B: Given that Kelsey has already made 10 pendants, how many additional pendants must she make and sell to make a profit?

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The quotient of 134 and z is the same as 374

Answers

We will ahve the following:

[tex]\frac{134}{z}=374[/tex]

Bob's Golf Palace had a set of 10 golf clubs that were marked on sale for $840. This was a discount of 10% off the original selling price.Step 2 of 4: If the golf clubs cost Bob's Golf Palace $390, what was their profit? Follow the problem-solving process and round youranswer to the nearest cent, if necessary.

Answers

Consider that the Bob's Golf Palace bought the set of golf clubs by $390.

Moreover, take into account that the golf clubs were markes on sale for $840.

The profit is only the difference between the marked on sale and the money Bob's Golf Palace payed:

$840 - $390 = $450

Hence, the profit was $450

1/2 ^1/2 please show the steps

Answers

The value of  [tex](\frac{1}{2} )^{\frac{1}{2} }[/tex] is 0.707.

1÷2 = 0.5

Given, [tex](\frac{1}{2} )^{\frac{1}{2} }[/tex]

Could be written like, [tex](0.5)^{0.5}[/tex] or √(1 ÷ 2) or √(0.5)

So the value of √(0.5) is 0.707.

Another way is to factorize each integer as the product of its primes using the square root prime factorization method. Follow these methods to find the square root of a certain number using prime factorization:

Step 1: Divide the supplied integer by its decimal equivalent.

Step 2: If the connected components are identical, a pair is generated.

Step 3: Choose one of the pair members for her.

Step 4: Multiply the prime numbers you got by picking one from each pair.

Step 5: This product is the square root of the specified number.

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A flower garden is shaped like a circle. Its diameter is . A ring-shaped path goes around the garden. The width of the path is .The gardener is going to cover the path with sand. If one bag of sand can cover , how many bags of sand does the gardener need? Note that sand comes only by the bag, so the number of bags must be a whole number. (Use the value for .)

Answers

The number sand bags required are 84 approximately.

Given, we have:

Diameter of garden = 38 yd

Width of path = 5 yd

Diameter of garden with path = 38 + 2 x 5 = 48 yd

We need to find area of path.

Area of path = Area of garden with path - area of garden

Area of path = π × 48²/4 - π × 38²/4

Area of path = 7234.56/4 - 4534.16/4

Area of path = 1808.64 - 1133.54

Area of path = 675.1 yd²

Area covered by one sand bag = 8 yd²

Number of sand bags required =  Area of path/Area covered by one sand bag

=675.1/8

= 84.38 ≈ 84

Number of sand bags needed = 84

Therefore, number of sand bags required are 84.

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Question Solve for d. d³ = 27

Answers

Answer:

d = 3

Step-by-step explanation:

I took different numbers, like 1 and 2, and multiplied them to themselves 3 times, for example, 2 x 2 x 2, but since that answer was wrong, I decided to try a different number, which was 3 and that was correct.

Premises:
If I'm a student, then I go to school. If I go to school, then I learn.
Conclusion:
If I'm a student, then I learn.
This is an example of the Law of
?

Answers

Answer:

it's wh question I think

A and B are sets of real numbers defined as follows.A = {x|x≤ 2}XB = {x|x < 7}Write A UB and An B using interval notation.If the set is empty, write 0.

Answers

The given sets are

[tex]\begin{gathered} A=\lbrace x:x,x\leq2\rbrace \\ \\ B=\lbrace x:x,x<7\rbrace \end{gathered}[/tex]

That means A is all real numbers from 2 to negative infinity, and B is all real numbers between 7 and positive infinity

[tex]\begin{gathered} A=(-\infty,2] \\ \\ B=(7,\infty) \end{gathered}[/tex]

Then we can find the union and intersection

[tex]\begin{gathered} A\cup B=(-\infty,2]\cup(7,\infty) \\ OR \\ A\cup B=(-\infty,\infty)-(2,7] \end{gathered}[/tex]

I will draw a sketch to show you the intersection

We can see that there is NO intersection between A and B, then

[tex]\begin{gathered} A\cap B=\lbrace\rbrace \\ A\cap B=0 \end{gathered}[/tex]

n
4 Which expression is equivalent to 8.508 ÷ 70.9?
A 8.508 709
B 85.08 709
C 850.8 709
D 8,508 709
5 What is the value of 0.5 ÷ 0.8? Show your work.

Answers

Answer:

a because 8.508

Step-by-step explanation:

0.625 so it easy 0.5:0.8

In order to earn extra money during the summer, Trevor is working as a house painter. The
amount of money he earns depends on the number of houses he paints.
m = the amount of money Trevor earns
h = the number of houses Trevor paints
Which of the variables is independent and which is dependent?
h is the independent variable and m is the
dependent variable
m is the independent variable and h is the
dependent variable
Submit

Answers

The correct answer to this question is that m is the dependent variable and h is the independent variable.

The amount of money Trevor earns can be formulated in the form of linear equation. A Linear equation is the one which can be expressed in the form of y = ax + b where y is dependent, and x is independent variable whereas a, b are coefficients. According to question amount of money Trevor earns will depend on the number of houses he paints. If m is the amount of money Trevor earns and h is the number of houses Trevor paints. This can be formulated as

m = hx + b and in this expression, m is dependent variable and h is independent variable as his earning will depend on the number of houses he paints.

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A population doubles every 27 years. Assuming exponential growth find the following:help find continuous growth rate (a) The annual growth rate: 2.6(b) The continuous growth rate is____% per year help (numbers)

Answers

Given,

A population doubles every 27 years.

a. Let initial population be 1 and after 27 years it becomes 2.

Considering r as the rate of annuall growth we have,

[tex]\begin{gathered} 1(1+r)^{27}=2 \\ \Rightarrow27\ln (1+r)=\ln 2 \\ \Rightarrow\ln (1+r_{})=\frac{0.693}{27} \\ \Rightarrow1+r=1.0257 \\ \Rightarrow r=0.026 \end{gathered}[/tex]

Thus annual growth rate is 2.6%

b. For continuous growth,

[tex]\begin{gathered} 1(e^{27x})=2 \\ \Rightarrow27x=0.693 \\ \Rightarrow x=0.025 \end{gathered}[/tex]

The continuous growth rate is _2.5___% per year

Use four rectangles to estimate the area between the graph of the function f(x) = V3x + 5 and the x-axis on the interval[0, 4] using the left endpoints of the subintervals as the sample points. Round any intermediate calculations, if needed, to noless than six decimal places, and round your final answer to three decimal places.

Answers

Answer:

  12.123

Step-by-step explanation:

You want the area under the curve f(x) = √(3x+5) on the interval [0, 4] estimated using the left sum and four subintervals.

Riemann sum

When the interval [0, 4] is divided into four equal parts, each has unit width. That means the area of the rectangle defined by the curve and the interval width will be equal to the value of the curve at the left end of the interval.

The area we want is the sum ...

  f(0) +f(1) +f(2) +f(3)

As the attachment shows, that sum is ...

  area ≈ 12.123 . . . square units

__

Additional comment

The table values in the attachment are rounded to 7 decimal places. Trailing zeros are not shown. Actual values used have 12 significant digits, as the total shows.

Such a sum is called a Riemann sum, named for a German mathematician. Four such sums are commonly used, and further refinements are possible. Those are the left sum (as here), the right sum, the midpoint sum, and a sum using a trapezoidal approximation of the rectangle area.

For left, right, and midpoint sums, n function values are required for n subintervals. When the trapezoidal approximation is used, n+1 function values are required.

From a group of 6 people, you randomly select 5 of them.

What is the probability that they are the 5 oldest people in the group?

Give your answer as a fraction

Answers

The probability that they are the 5 oldest people in the group is 1/6.

Given that we have a group of 6 people, and we randomly select 5 of them.

We need to find the probability that they are the 5 oldest people in the group.

The total number of ways to select 5 people from a group of 6 people is given by 6C5 which is equal to 6.

This means that there are only 6 possible outcomes when we randomly select 5 people from a group of 6 people.

We know that the 5 oldest people in the group can be selected only in one way.

So, the number of favorable outcomes is 1.

Hence, the probability of selecting the 5 oldest people from the group when 5 people are randomly selected is: Probability = favorable outcomes/total outcomes Probability = 1/6

Therefore, the probability that they are the 5 oldest people in the group is 1/6.

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Calculate the distance between the points L=(1, -8) and C=(9, -3) in the coordinate plane.
Round your answer to the nearest hundredth.
kintett. 41
Distance:

Answers

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ L(\stackrel{x_1}{1}~,~\stackrel{y_1}{-8})\qquad C(\stackrel{x_2}{9}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ LC=\sqrt{(~~9 - 1~~)^2 + (~~-3 - (-8)~~)^2} \implies LC=\sqrt{(9 -1)^2 + (-3 +8)^2} \\\\\\ LC=\sqrt{( 8 )^2 + ( 5 )^2} \implies LC=\sqrt{ 64 + 25 } \implies LC=\sqrt{ 89 }\implies LC\approx 9.43[/tex]

What is the area of the shaded triangle?The area of the shaded triangle is in. 2

Answers

The area of the shaded triangle is equal to:

[tex]A=\frac{1}{2}bh[/tex]

the base of the shaded triangle is 4 in and the height is 5 in, then:

[tex]\begin{gathered} A=\frac{1}{2}(4)(5) \\ =\frac{1}{2}\cdot20 \\ =10 \end{gathered}[/tex]

Therefore the shaded area is 10 squared inches.

Can you please help? I think it is ODD. Do you agree?

Answers

Given,

The function is:

[tex]f(x)=x+\frac{12}{x}[/tex]

Taking x = -x then,

[tex]\begin{gathered} f(-x)=-x+\frac{12}{-x} \\ =-x-\frac{12}{x} \\ =-(x+\frac{12}{x}) \\ =-f(x) \end{gathered}[/tex]

The function is odd.

Divide using synthetic division. Write down the answer as a polynomial.x^3-5x^2-2x+24=0; (x+2)

Answers

we are given the following polynomial:

[tex]x^3-5x^2-2x+24=0[/tex]

we are asked to use synthetic division by:

[tex]x+2[/tex]

first we need to find the root of "x + 2":

[tex]\begin{gathered} x+2=0 \\ x=-2 \end{gathered}[/tex]

Now we do the synthetic division using the following array:

[tex]\begin{bmatrix}{1} & {-5} & {-2} \\ {\square} & {\square} & {\square} \\ {\square} & {\square} & {\square}\end{bmatrix}\begin{bmatrix}{24} & {} & {} \\ {\square} & {} & {} \\ {\square} & {} & {}\end{bmatrix}\begin{cases}-2 \\ \square \\ \square\end{cases}[/tex]

Now we lower the first coefficient and multiply it by -2 and add that to the second coefficient:

[tex]\begin{bmatrix}{1} & {-5} & {-2} \\ {\square} & {-2} & {\square} \\ {1} & {-7} & {\square}\end{bmatrix}\begin{bmatrix}{24} & {} & {} \\ {\square} & {} & {} \\ {\square} & {} & {}\end{bmatrix}\begin{cases}-2 \\ \square \\ \square\end{cases}[/tex]

Now we repeat the previous step. We multiply -7 by -2 and add that to the next coefficient:

[tex]\begin{bmatrix}{1} & {-5} & {-2} \\ {\square} & {-2} & {14} \\ {1} & {-7} & {12}\end{bmatrix}\begin{bmatrix}{24} & {} & {} \\ {\square} & {} & {} \\ {\square} & {} & {}\end{bmatrix}\begin{cases}-2 \\ \square \\ \square\end{cases}[/tex]

Now we repeat the previous step. we multiply 12 by -2 and add that to the next coefficient:

[tex]\begin{bmatrix}{1} & {-5} & {-2} \\ {\square} & {-2} & {14} \\ {1} & {-7} & {12}\end{bmatrix}\begin{bmatrix}{24} & {} & {} \\ {-24} & {} & {} \\ {0} & {} & {}\end{bmatrix}\begin{cases}-2 \\ \square \\ \square\end{cases}[/tex]

The last number we got is the residue of the division, in this case, it is 0. Now we rewrite the polynomial but we subtract 1 to the order of the polynomial:

[tex]\frac{x^3-5x^2-2x+24}{x+2}=x^2-7x+12[/tex]

which situation can be represented by this inequality1.25x -6.50 > 50 A. Caleb has a balance of 6.50$ in his savings account and deposits 1.25$ each week. What is X the number of weeks must deposit 1.25$ in order to have a balance of more than 50$ in his savings account?B. Caleb earns 1.25% interest on the balance in his checking account and has to pay a monthly charge of 6.50$. What is X the balance that Caleb must have in his checking account in order to have an ending balance greater than 50$ after interest and fees.C. Caleb charges 1.25$ for gasoline plus 6.50$ per hour for mowing lawns. What is X the number of hours he has to mow lawns to earn more than 50$D. Caleb spends 6.50$ on supplies for a lemonade stand and sells each cup of lemonade for 1.25$. what is X the number of cups of lemonade Caleb must sell to earn profit of more than 50$

Answers

We need to find a situation that can be represented by the inequality below:

[tex]1.25\cdot x-6.5>50[/tex]

This means that there must be a variable for which each unit has a value of 1.25. There must be a fixed cost of 6.5, because we are subtracting that value and the end goal must be to have more than 50.

The only option for which this applies is the option D.

Caleb spent a fixed amount of 6.5, he earns 1.25 for each lemonade he sells and he wants to have a profit of more than 50.

Solve this inequality

Answers

[tex]\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{-8\leq 10-2x < 28 } \end{gathered}$} }[/tex]

Separate the inequality compound in the inequality system.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{{\left\{ \begin{array}{r}10-2x\geq -8 \\ 10-2x < 28 \ \end{array} \right.} } \end{gathered}$} }[/tex]

We solve to: 10 - 2x < 28

Order the unknown terms to the left side of the equation.[tex]\boxed{\bf{-2x < 28-10 }}[/tex]

Calculate the sum or difference.

[tex]\boxed{\bf{-2x < 18 }}[/tex]

Divide both sides of the equation by the coefficient of the invariable.[tex]\boxed{\bf{x > -\frac{18}{2} }}[/tex]

Clear the common factor

[tex]\boxed{\bf{x > -9} }}[/tex]

We solve to: 10 - 2x ≥ -8

Order the unknown terms to the left side of the equation.

  [tex]\boxed{\bf{-2x\geq -8-10 }}[/tex]      

Calculate the sum or difference.

[tex]\boxed{\bf{-2x\geq -18 }}[/tex]

Divide both sides of the equation by the coefficient of the invariable.

[tex]\boxed{\bf{x\leq \frac{-18}{-2} }}[/tex]

Determine the sign of multiplication and division.

[tex]\boxed{\bf{x\leq \frac{18}{2} }}[/tex]

Clear the common factor

[tex]\boxed{\bf{x\leq 9}}[/tex]

[tex]\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{x > -9 \ and \ x\leq 9 } \end{gathered}$} }[/tex]

We find the intersection.

Answer = [tex]\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{-9 < x\leq 9 } \end{gathered}$} }[/tex]

Alternative forms: x ∈ (-9, 9]
Other Questions
A student begins an inquiry for a two-page essay with the research question, "What aresome examples of mammals?" After doing some research, they discover they are moreinterested in focusing on marsupials. Which of the following would be their revised researchquestion? (1 point)O Are marsupials mammals?O Why do mammals exist?O What are the differences between mammals and marsupials?O What are some of the different types of mammals? Whats 12:28 reduced Exit Slip!Explain how Earth's tiltedaxis and its revolutionaround the Sun producesseasons. 2.) The amount of sleep that elementary school children get per night follows a Normal distribution with amean of 9.5 hours and a standard deviation of 0.55 hours.a.) Find the proportion of elementary school children who get between 9 and 10 hours of sleep pernight. Sketch the Normal curve and shade the area under the curve that is the answer to thequestion. problem 2 select all of the equations that represent a proportional relationship. (select all that apply.) the remaining length, , of a -inch rope after inches have been cut off: . the total cost, , after an sales tax is added to an item's price, : . the number of marbles each sister gets, , when marbles are shared equally among four sisters: . the volume, , of a rectangular prism whose height is cm and base is a square with side lengths cm: . HELP HELP HELP What is the x-intercept of the line with this equation 5x+15y=15 ? there is correspondence bias when young adults rely more on dispositional information in explaining behavior and ignore compelling situational information. Inside the nucleus, two protons are held together by a force which overcomes the repulsion. This force is called 20Which equation, when paired with the equation below, will create a system of equations with infinitelymany solutions?3x - 8y = -5A. 3x+ 8y = -5B.6x+ 16y = -10C.6x- 16y = -10D. -8x+ 3y = 5 Determine which integer will make the inequality 18 > 3x + 9 true. S:{3} S:{3} S:{9} S:{14} If a linear function has no restrictions, the domain of the function is How is Douglass motivated by his human needs While performing research for a school writing project, you discover a website that contains exactly the information you think will nicely round out your paper. Describe how you will incorporate the information into your project and the steps you will take to ensure you give proper credit to the author. A combined total of $41,000 is invested in two bonds that pay 6% and 7% simple interest. The annual interest is $2,700.00. How much is invested in each bond? Reread the introduction of the story . How does the imagery depicted in the beginning of the story contribute to, or set up , the story ? Consider what the house symbolizes . From the fall of the house if usher Evaluate express your answer in exact simplest form9P4= What is one way that cancer cells are physically different than normal cells? can you help me solve part A and B ASAP! THANKYOU Your lunch in the hospital cadet cost $6.50. Based on working 50weeks per year , how much will you spend on your lunch per year? Find the solution of each equation if the replacement set is 10 11 12 13