-3(2x-5)<5(2-x)
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Answer: [tex](x-10)^{2}+(y+3)^{2}=16[/tex]

Step-by-step explanation:

We know the center of the original circle is (-6, -3). After reflecting this over the line x=2, the new center is now (10, -3).

Thus, the equation of the circle is [tex](x-10)^{2}+(y+3)^{2}=16[/tex].

Answer:

[tex]98 \pi \:\: \sf units^2[/tex]

Step-by-step explanation:

[tex]\textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]

From inspection of the given diagram, circle C and circle D both have a radius of 7 cm.

Therefore:

[tex]\implies \textsf{Area of circle C}=\pi (7)^2=49 \pi \:\: \sf cm^2[/tex]

[tex]\implies \textsf{Area of circle D}=\pi (7)^2=49 \pi \:\: \sf cm^2[/tex]

Therefore, the sum of the areas of circle and circle D is:

[tex]\implies \textsf{Area of circle C}+\textsf{Area of circle D}=49 \pi + 49 \pi = 98 \pi \:\: \sf cm^2[/tex]

The sum of the areas of the circles is 98π units².

The correct option is D.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.

And the general formula of the circle,

(x – h)²+ (y - k)² = r²,

where (h, k) is the center and r is the radius of the circle.

The formula for the area of a circle is A=πr², where A is the area and r is the radius.

For circle C, the radius is 7, so its area is A_C = π(7)² = 49π units².

For circle D, the radius is also 7, so its area is A_D = π(7)² = 49π units².

The sum of the areas is therefore:

A_C + A_D = 49π + 49π = 98π units²

Therefore, the answer is (D) 98π units².

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An equation is formed of two equal expressions. Shaquana earns $10 less per hour than Vani.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The equation y=28.8x represents Vani's earnings in dollars and cents, y, for working x hours.

y = 28.8x

y/x = 28.8

Hence, Vani is paid $28.8 per hour.

The amount that Shaquana earned was $653.40 in 33 hours. Therefore, per hour she was paid

Amount per hour = $653.40/33 = $19.8 per hour

The difference between the two is,

Difference = $28.8 - $19.8 = $10

Hence, Shaquana earns $10 less per hour than Vani.

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Vani - 28.8

y=28.8x

Vani earns $28.80 per hour.

Shaquana -

653.40 / 33 = $19.80 per hour

Shaquana earns $19.80 per hour.

Vani − Shaquana = $28.80

$28.80−$19.80

=$9

Shaquana earns $9 less per hour than Vani.

Answer:

D.) x = − ½, x = 4

Explanation:

[tex]\rightarrow \sf (10x + 5)(11x - 44) = 0[/tex]

set the factors to zero

[tex]\rightarrow \sf 10x + 5 = 0, \ 11x - 44 = 0[/tex]

exchange the sides

[tex]\rightarrow \sf 10x = -5, \ 11x = 44[/tex]

exchange the sides

[tex]\rightarrow \sf x = -\dfrac{5}{10} , \ x = \dfrac{44}{11}[/tex]

simplify the following

[tex]\rightarrow \sf x = -\dfrac{1}{2} , \ x =4[/tex]

On solving

The value of y for the given equation at x=81 is 87.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Here, given equation;

       y = x + 6

     Put x = 81, we get

       y = 81 + 6

      y = 87

Thus, the value of y for the given equation at x=81 is 87.

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Let's take this problem step-by-step:

Let's convert the equation back into the standard form:

     ⇒ standard form: (x-h)² +(y-k)² = r²

       [tex]x^2+y^2-8x+10y + 37 = 0\\\rm \hookrightarrow x^2 - 8x + y^2+10y = -37\\\rm \hookrightarrow (x^2 - 8x) + (y^2 + 10y) = -37\\\rm \hookrightarrow (x^2-8x+16) + (y^2+10y+25) = -37 + 16 +25\\\rm \hookrightarrow (x-4)^2 + (y+5)^2 = 4\\\rm \hookrightarrow (x-4)^2 + (y+5)^2 = 2^2[/tex]

Based on the equation found

  ⇒ center: (4, -5)

   ⇒ radius: 2

Answer:

Hope that helps!

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The value of the number n as 1.5 * [tex]10^{-18}[/tex].

A power is the product of multiplying a number by itself.

(8.4*[tex]10^{9} \\[/tex])/n = (5.6* [tex]10^{27}[/tex])

n= (5.6* [tex]10^{27}[/tex]) / (8.4*[tex]10^{9} \\[/tex])

n= 1.5 * [tex]10^{-18}[/tex]

Hence, the value of n is n= 1.5 * [tex]10^{-18}[/tex]

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Answer:

8 in

Step-by-step explanation:

Volume of Cube = 512 in³

Formula : -

Volume of cube = side x side x side = side³

512 = 8 x 8 x 8 = 8³

So,

The length of one side of the jewelry box is 8 in.

The tension in both cables are calculated as; T₁ = 127.63 N and T₂ = 185.48 N

Resolving forces in the y direction gives us;

T₁ sin 29° + T₂ sin 53° = 210  ------(eq 1)

Resolving forces in the horizontal direction gives;

T₁ cos 29° = T₂ cos 53°   ----(eq 2)

T₁ = T₂ cos 53°/cos 29°

Thus;

(T₂ cos 53°/cos 29°)sin 29° + T₂ sin 53° = 210  

0.3336T₂ + 0.7986T₂ = 210

T₂ = 210/1.1322

T₂ = 185.48 N

Thus;

T₁ = 185.48 cos 53°/cos 29°

T₁ = 127.63 N

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Answer:

b - read explanation if you are confused for future problems

Step-by-step explanation:

Inverse variation is when x*y = k whereas direct variation (may come up in future problems) is when y = x*k

Remember that k is always a set value while x and y are values that can change

In this case y*x = k so k = 18 (since y is 9 when x is 2)

So when  x = 8

8y = 18

y = 18/8 = 9/4

Answer:

[tex] 19\% \: of \: 49[/tex]

[tex] \frac{19}{100} \times 49[/tex]

[tex]0.19 \times 49[/tex]

[tex]9.13[/tex]

Answer:

39.69

Step-by-step explanation:

A percentage is on a scale of 100 so we divide 19 by 100

that makes 0.19.

Then multiply 49 with 0.19 that makes 9.31 (this is 19% of 49)

49 - 9.31 = 39.69

Answer:

2 angles are 142 degrees

2 angles are 38 degrees

Step-by-step explanation:

In any parallelogram, the opposite angles are congruent.

So,

5x - 8 = 2x + 82

3x - 8 = 82

3x = 90

x = 30

Now lets plug in x into one of the angles:

5 ( 30 ) - 8

150-8

142

So, because that angle is 142, the other angle must also be 142. However, to make sure, we should still check.

2 ( 30 ) + 82

60 +82

142

As we can see, both angles are 142.

Now we have figured out 2 angles, and they are both 142. Now lets figure out the other 2 angles.

Any 4 sided shape has 360 degrees

142 + 142 = 284 degrees

Our 2 angles have 284  degrees in total.

if we subtract 284 from 360, we get 76.

Our remaining 2 angles have a total of 76 degrees. Because these angles are also opposite, we must divide by 2. 76/2 is 38.

So,

2 angles are 142 degrees

2 angles are 38 degrees

Answer:

y=⅓x+b

Step-by-step explanation:

So basically the formula of slope-intercept is:

y=mx+b

and m=⅓

so

y=⅓x+b and it includes the point (0, 6) so:

6=⅓(0)+b===> b=6===> y=⅓x+6

Answer:

Hello auggggh nice to meet you!

Step-by-step explanation:

An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is C.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Juanita’s salary once she completes 10 years, her salary will be increased to 3 times what she makes now plus $2,000. Now, if her salary is represented by s, then the expression that would represent her salary after 10 years is,

Salary after 10 years = 3s + 2000

Hence, the correct option is C.

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Answer:

C

Step-by-step explanation:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:\approx 9.2 \:\: units [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \textsf{Using distance formula : - } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{(2 - 0) {}^{2} + (0 - 9) {}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{(2) {}^{2} + (- 9) {}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{ 4 + 81} [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{85} \: \: units[/tex]

[tex]\qquad \tt \rightarrow \: \approx 9.2 \: \: units[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The distance between points A and B is 9.2 units.

We have,

To find the distance between two points (a, b) and (c, d) in a coordinate plane, you can use the distance formula:

Distance = √[(c - a)² + (d - b)²]

In this case, point A is (2, 0) and point B is (0, 9).

Now, plug the values into the distance formula:

Distance = √[(0 - 2)² + (9 - 0)²]

Distance = √[(-2)² + 9²]

Distance = √[4 + 81]

Distance = √85

Now, round the answer to the nearest tenth:

Distance ≈ √85 ≈ 9.2 (rounded to the nearest tenth)

Thus,

The distance between points A and B is 9.2 units.

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Answer:

Look down below and you will know the answer↓:

Step-by-step explanation:

He will have to work as between the range (of 20,0) and (0,20) points to earn more than $125.

So, What is inequality?

Inequality means is the relationship between two expressions that are not equal, so employing a sign such as ≠ “is not equal to,” > “greater than,” or < “less than.”.

Since then: Liam can work at most 20 hours a week, but he also needs to earn at least $125. His dog-walking job pays $7 per hour and his job as a car-wash attendant pays $11 dollars an hour. How can he earn $125.

He Let the Dog walking hours are represented by x and Car wash hours will be represented by y. The inequality will be formed as:

7x + 11y ≥ 125

x+y = 20

When we plot these two equations on the graph, we will get the range for the time from (20,0) and (0,20).

We Suppose that we will take a random point-like (5,15) when we put this value in the inequality, we get the total earning greater than $125.

7x + 11y ≥ 125

7 (5) + 11 ( 15 ) ≥ 125

35  + 165  ≥ 125

200 ≥ 125

Therefore, He has to work between the range (of 20,0) and (0,20) points to earn more than $125.

If 30 is half price, then what is full price?

You can set up this problem like this:

30 = x/2

OR

30 = (1/2)x

where x is the full price.

To solve, simply multiply each half by 2:

2(30) = 2((1/2)x)

x = $60

Answer:

Step-by-step explanation:

2.5

4 quarts per gallon

8 quarts per 2 gallons

2 quarts is half a gallon since 4 quarts is a full gallon

answer: 2.5

The substance's half-life is 5.5 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.125

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have an exponential function:

[tex]\rm N = N_oe^{-kt}[/tex]

Plug N = N⁰/2

[tex]\rm N_o/2 = N_oe^{-kt}[/tex]

[tex]\rm \dfrac{1}{2} = e^{-0.125t}[/tex]

Solving for t:

t = 5.54 ≈ 5.5 days

Thus, the substance's half-life is 5.5 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.125

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Answer:

3/4 is the slope

Step-by-step explanation:

Answer:

i don't know

Step-by-step explanation:

i

[tex] {3}^{18n} [/tex]

Answer:

9^10

Step-by-step explanation:

khan

Solution:

[tex]\dfrac{\left[\left(\sin ^{2} A+2 \times \sin A \times (1-\cos A)+(1-\cos A)^{2}\right]\right.}{\left[\left(1-\cos ^{2} A\right)-(1-\cos A)^{2}\right]}[/tex]

[tex]\dfrac{\left[\left(1-\cos ^{2} A\right)+2 \times \sin A \times (1-\cos A)+(1-\cos A)^{2}\right]}{\left[(1-\cos A)(1+\cos A)-(1-\cos A)^{2}\right]} [/tex]

[tex]\dfrac{(1-\cos A)[1+\cos A+2 \sin A+1-\cos A]}{[1-\cos A][1+\cos A-1+\cos A]} [/tex]

[tex]\dfrac{[2+2 \sin A]}{[2 \times \cos A]}[/tex]

[tex]\dfrac{2(1+\sin A)}{2 \times \cos A}[/tex]

[tex]\dfrac{1+\cos A}{\sin A} [/tex]

Hence Proved.

Answer:

42.3cm

Step-by-step explanation:

I think this is right :)

There were 144 students when the contest began

Equation is formed when an algebraic expression is equated by a constant or another algebraic expression.

On the basis of given data :

Let the total number of students are x

50% of the students are eliminated after the first round

the remaining students are 0.5x

After the second round = (1/3) * 0.5 x were remaining

and

(1/3) * 0.5 x = 24

then solving this equation will give the total number of students

0.5x = 24 * 3

x = 24*3 /0.5 = 144

Therefore there were 144 students when the contest began

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Answer:

3y⁷ + 2y⁵ - 4y³ + y + 12

Step-by-step explanation:

2y⁵ + y + 3y⁷ - 4y³ + 12

(greatest - least powers)

I hope this helps!

Answer: I love the picture example

Step-by-step explanation:

We will first find the heigh of the kite from his hand to a point in the air.

Then, we will add 3 feet to the result.

So, how to find the vertical line of the right triangle?

Well, we have the vertical line = x

We also got the hypothenuse, equal to 100 feet

And also theta, equal to 25 degrees.

We can calculate sine because the sine of 25 degrees = opposite side (the height line) over (divided by) the hypothenuse

sin(25) = x/100 feet

multiply 100 feet on both sides, to cancel to 100 feet on the right side.

100sin(25) = x

100(0.442) = x

x = 42.2  feet

Height = 42.2 + 3 feet (the yoda's hand =) =  45.2 feet (total)

Rounded to the nearest tenth.

I also did the verification, so it is the correct answer.

Easy as that =]]

Height of the kite from 3ft above the ground

[tex]\\ \rm\Rrightarrow sin\Theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\\ \rm\Rrightarrow sin25=\dfrac{P}{100}[/tex]

[tex]\\ \rm\Rrightarrow P=100sin25[/tex]

[tex]\\ \rm\Rrightarrow P=42.26\approx 42ft[/tex]

Height from the ground