10.(02.06 LC)
The number line below represents which combined inequality? (5 points)

Answer:

6w - 24 cm = perimeter

Step-by-step explanation:

width = w cm

length = 2w - 12 cm

perimeter = all sides added together

[w] + [w] + [2w - 12] + [2w - 12]

(combine like terms)

6w - 24 cm = perimeter

Answer:

It's C

Step-by-step explanation:

because 1.04 is closest to 1

Unit Rate

It measures how much one quantity varies with respect to another.

We are interested in calculating the unit rate that measures the number of kilometers that Bandile's large truck uses by liter of fuel. It's called the efficiency.

We calculate the unit rate as the division of both quantities. The truck uses 20 liters per 100 kilometers. The efficiency is:

The efficiency of Bandile's large truck is 5 km per liter

Answer:

(1)Hoops shadow would be 6 ft (2) model would be 3 cms

Step-by-step explanation:

9 / 3 = 3   3 x 2 = 6 ft

15 / 5 =3    3 x 1 = 3 cm

y=3x

Step-by-step explanation:

y=3x-5

but

m=x+5/3

replace m in 3m to 3(x +5/3)

i.e

y=3(x+5/3)-5

y=3x +5-5

y=3x

Answer:

The answer to this question should be D. 0.67

Hope this helped.

ANSWER

Number of selection possible = 729

Number of dog =3

Number of colors he wants to buy for each dog = 9

If repetition of colors are allowed, the number of selection for the three dogs

= 9³ = 729

To calculate the mean, median, and mode, we first need to know what each of these terms represents. The mean, also known as the average, is the sum of all the values divided by the total number of values. To find the mean, add up all of the values and divide by the number of values. The median is the middle value in a set of data when it is arranged in order from least to greatest. The mode is the value that occurs most frequently in a set of data. Here's an example to illustrate these concepts:

Let's say we have a set of data consisting of the following values: 2, 5, 5, 7, 8, 10, 12. To find the mean, we add up all of the values and divide by the number of values. In this case, the sum of the values is 49 (2+5+5+7+8+10+12) and there are 7 values, so we divide 49 by 7 to get the mean, which is approximately 7. To find the median, we first need to arrange the data in order from least to greatest: 2, 5, 5, 7, 8, 10, 12. The middle value is 7, so that is the median. To find the mode, we look for the value that occurs most frequently. In this case, 5 occurs twice, which is more than any other value, so the mode is 5.
In conclusion, the mean, median, and mode are all measures of central tendency that can be used to describe a set of data. The mean is the average value, the median is the middle value, and the mode is the value that occurs most frequently. When calculating these measures, it is important to carefully consider the data and choose the appropriate method for finding each value.

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Answer:

I'm sorry but I couldn't see the hole question

The amount of water that must be pumped into the tank to eliminate 50% of the salt is x = V/â (50% of initial s).

The amount of water that must be pumped into the tank to eliminate 50% of the salt can be calculated using the differential equation dsdx=âsV, where s is the amount of salt, x is the amount of water pumped in, and V is the volume of the solution which is 10,000 gallons in this case. This equation can be rearranged to give x=V/âs. To eliminate 50% of the salt, we can set s equal to 50% of its initial value and calculate the corresponding x value. Therefore, the amount of water that must be pumped into the tank to eliminate 50% of the salt is x = V/â (50% of initial s).

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Answer:

\(\sin\beta=\dfrac{8}{17}\)

\(\cos\beta=\dfrac{15}{17}\)

\(tan\beta=\dfrac{8}{15}\)

\(\csc\beta=\dfrac{17}{8}\)

\(\cot\beta=\dfrac{15}{8}\)

Step-by-step explanation:

The secant ratio is the reciprocal of the cosine ratio.

\(\sec \beta= \dfrac{1}{\cos \beta}\)

Therefore, if sec β = 17/15 then:

\(\dfrac{1}{\cos \beta}=\dfrac{17}{15}\)

\(\cos \beta=\dfrac{15}{17}\)

The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse of a right triangle:

\(\cos\beta= \sf \dfrac{adjacent}{hypotenuse}\)

Therefore, the length of the side adjacent angle θ is 15 and the length of the hypotenuse is 17.

\(\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}\)

We can use Pythagoras Theorem to calculate the length of the side opposite angle β:

\(15^2+O^2=17^2\)

\(O^2=17^2-15^2\)

\(O=\sqrt{17^2-15^2}\)

\(O=\sqrt{64}\)

\(O=8\)

Therefore, the length of the side opposite angle β is 8.

Now we have the lengths of the three sides of the right triangle, we can find the other trigonometric function of angle β.

\(\boxed{\begin{minipage}{8cm}\underline{Trigonometric functions}\\\\$\sf \sin\beta=\dfrac{O}{H}\quad\cos\beta=\dfrac{A}{H}\quad\tan\beta=\dfrac{O}{A}$\\\\\\$\sf\csc\beta=\dfrac{H}{O}\quad\sec\beta=\dfrac{H}{A}\quad\cot\beta=\dfrac{A}{O}$\\\\\\where:\\\phantom{ww}$\bullet$ $\beta$ is the angle.\\\phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle.\\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse.\\\end{minipage}}\)

Given values:

Substitute these values into the six trigonometric functions:

\(\sin\beta=\dfrac{O}{H}=\dfrac{8}{17}\)

\(\cos\beta=\dfrac{A}{H}=\dfrac{15}{17}\)

\(tan\beta=\dfrac{O}{A}=\dfrac{8}{15}\)

\(\csc\beta=\dfrac{H}{O}=\dfrac{17}{8}\)

\(\sec\beta=\dfrac{H}{A}=\dfrac{17}{15}\)

\(\cot\beta=\dfrac{A}{O}=\dfrac{15}{8}\)

Answer:

-6

Step-by-step explanation:

because -6+-4= 10 but idek how its wrong

Answer:

Simplified: \(\frac{77}{20}\)        Mixed: 3\(\frac{17}{20}\)

Step-by-step explanation:

Answer:

he has 5 minutes left

Step-by-step explanation:

18÷1/2=9-4=5

The volume of the volleyball is  6,367.4 cm³

For a sphere of radius R, the circumference is:

C = 2*3.14*R

and the volume is:

V = (4/3)*3.14*R³

Here the circumfernce is 72.2cm, then we can write:

72.2cm = 2*3.14*R

(72.2cm/2*3.14) = R

11.5cm = R

Then the volume is approx:

V = (4/3)*3.14*(11.5cm)³ = 6,367.4 cm³

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Answer:

The Area of the trapezium is \(60cm^2\)

Step-by-step explanation:

Given,

Height (h)= 8cm

Sum of the parallel sides (a+b)= 15cm

Area of trapezium = \(1/2*h*(a+b)\)

                              =\(1/2*8*15\)

                              =\(4*15\)

Area of trapezium=60cm^2

Answer: Area = 60 cm²

Step-by-step explanation:

To find the area of a trapezium we use the formula

Area of trapezium = 1/2 (sum of parallel sides) × height

∴ Area = 1/2 ×15 cm × 8 cm

           = 60 cm²

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The solution to the equation is x = 10 or x = -2.

An equation refers to a mathematical expression showing that two expressions are equal.

It must have variables (e.g. a, c, x, y), constants (like 1, 13, 50, etc), and mathematical operations (like +, -, *, /).

To solve for x, we shall start with the given equation:

x + 6 = √(2x + 29) + 9

Subtract 9 from both sides:

x - 3 = √(2x + 29)

Square both sides:

\((x - 3)^2\) = 2x + 29

Expand the left side:

\(x^2\) - 6x + 9 = 2x + 29

We then subtract 2x and 9 from both sides:

\(x^2\) - 8x - 20 = 0

Next, actor the quadratic equation:

(x - 10)(x + 2) = 0

Therefore, the equation x = 10 or x = -2

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Answer:

√38

Step-by-step explanation:

√38

step 1: Check which squared numbers can be multiplied by another number to get 38.

Start with these numbers: 4, 9, 16, and 25

Step 2: Testing out the numbers

√25 × __ = 25 can't be divided by 38

√16 × ___ = 16 can't be divided by 38

√9 × ____ = 9 can't be divided by 38

√4 × ____= 4 can't be divided by 38

Step 3: Answer

After trying the square root numbers that could possibly work with √38 none work; which means √38 can't be simplified. So the answer is √38

I hope this helps!

The area of the Region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

To find the area of the region bounded by y = √x, y = 2-x², and y = -√2x, we need to graph the equations and determine the points of intersection. Then we can integrate to find the area.

Firstly, we'll graph the equations and find the points of intersection:

y = √xy = 2-x²y = -√2xGraph of y = √x, y = 2-x², and y = -√2xWe need to solve for the points of intersection, so we'll set the equations equal to each other and solve for x:√x = 2-x²√x + x² - 2 = 0Let's substitute u = x² + 1:√x + u - 3 = 0√x = 3 - u

(Note: Since we squared both sides, we have to check if the solution is valid.)u = -2x²u + x² + 1 = 0 (substituting back in for u

)Factoring gives us:u = (1, -2)We can then solve for x and y:x = ±1, y = 1y = 2 - 1 = 1, x = 0y = -√2x = -√2, x = 2y = 0, x = 0Graph of y = √x, y = 2-x², and y = -√2x with points of intersection to find the area, we need to integrate.

The area is bounded by the x-values -1 to 2, so we'll integrate with respect to x:$$\int_{-1}^0 (2 - x^2) - \sqrt{x} \ dx + \int_0^1 \sqrt{x} - \sqrt{2x} \ dx$$

We can then simplify and integrate:$$\left[\frac{2x^3}{3} - \frac{2x^{5/2}}{5/2} + \frac{4}{3}x^{3/2}\right]_{-1}^0 + \left[\frac{2x^{3/2}}{3} - \frac{4x^{3/2}}{3}\right]_0^1$$$$= \frac{4}{3} + \frac{4}{3} - \frac{4}{15} + \frac{4}{3} - \frac{4}{3}$$$$= \frac{32}{15}$$

Therefore, the area of the region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

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Answer:

3x

Step-by-step explanation:

Simplified expression: 3x-3r+67

Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

Let's assume the number of miles driven is represented by 'm'. The cost of renting a moving truck for one day at Rentals Plus can be calculated using the equation:

Cost at Rentals Plus = $5.24 + $4.46 * m

Similarly, the cost of renting a moving truck for one day at Speedy Move can be calculated using the equation:

Cost at Speedy Move = $85.24 + $0.46 * m

To find the number of miles that makes the costs equal, we can set up the equation:

$5.24 + $4.46 * m = $85.24 + $0.46 * m

By rearranging the equation, we can solve for 'm':

$4.46 * m - $0.46 * m = $85.24 - $5.24

$4 * m = $80

m = $80 / $4

m = 20

Therefore, Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

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Answer:

C

Step-by-step explanation:

\(f'(x)=g(x) * (x^2-4)\\0=g(x)*(x^2-4)\\x={-2,2}\\f(-4) = -\\f(-2) = 0 \\f(0) = +\\f(2) = 0 \\f(4)= -\\\\\)

It decreases from negative infinity to -2, then increases, so x=-2 is a rel. min.

It increases from x=-2 to x=2, then decreases to infinity, so x=2 is a rel. max.

1/4π radians is approximately equal to 45 degrees.

To convert a value from radians to degrees, multiply the value by 180/π. For example, to convert π/4 radians to degrees, multiply π/4 by 180/π to get 45 degrees. This conversion is useful for converting angles between the two units of measurement.

Degrees = Radians × 180/π.

Therefore, to convert 1/4π radians to degrees, we have:

Degrees = (1/4π) × (180/π) ≈ 45°

Hence, 1/4π radians is approximately equal to 45 degrees.

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Answer:

x = 135

Step-by-step explanation:

m = length of perpendicular line to hypotenuse

81/m = m/144

m² = 81 x 144 = 11664

m =√11664 = 108

Using the Pythagorean theorem:

x² = 81² + 108² = 6561 + 11664 = 18225

x = √18225 = 135

9514 1404 393

Answer:

  x = 135

Step-by-step explanation:

Side x is the geometric mean of the hypotenuse segments it touches.

  x = √(81×(81+144)) = √81×√225 = 9×15

  x = 135

Answer:

Step-by-step explanation:

Answer:

D) Several planets will be very small and difficult to represent.

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.

Here,

the two numbers' primary factors are as follows:

-25\(b^{2}\) + 15b

Common prime factors can be multiplied to determine the GCF:

=> -25\(b^{2}\)  = -(5)(5) * \(b^{2}\)

=> 15b = (5)(3)b

The expression can be factored in the following fashion because the GCF is 5b:

=> -(5)(5) * \(b^{2}\) +  (5)(3)b

=> (5b)(-5b+3)

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

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Answer:

-4 + 8 = 4

5 - 8 = -3

8 + (-5) = 3

-7 + 5 = -2

-5 + 4 = -1

Answer:

Step-by-step explanation:

4(3x - 5) = 6x - 2                     Remove the brackets

12x - 20 = 6x - 2                     Subtract 6x from both sides

12x - 6x - 20 = -2                   Add 20 to both sides

6x = -2 + 20

6x = 18                                    Divide both sides by 6

x = 18/6

x = 3

Answer:

you answer is 0

Step-by-step explanation:

If you do the math it goes to this

4(3x-5)=6x-2

x=?

so you would do the distributive property for the perenthasese

so..

4(4x3X-4x5) = 4x3= 12x. 4x5=20. 12x-20= -8x

then you would do 6x-2 = 4x

then 8x+4x=0

Answer:

Ratio 3 : 1

First person 5 biscuits 

Second person 15 biscuits 

Step-by-step explanation:

“one person gets three times as many as the other”  means  “the ratio is 3 to 1 or just 3 : 1”

………………………

Let x be the number of biscuits that the first person got then the second person should get 3x biscuits.

It’s clear that we have to solve this equation:

x + 3x = 20

Solving:

x + 3x = 20

⇔ 4x = 20

⇔ x = 20/4 = 5

Final answer:

First person: 5 biscuits

Second person: 3×5 = 15 biscuits