One hundred less than a twice a number is five

The values of[tex]a^3 + 8b^3[/tex]are 280 when b = 3 and 125 when b = 5/2.

To find the value of [tex]a^3 + 8b^3[/tex], we can use the given information about a and b. Let's proceed step by step:

1. We are given that a + 2b = 10. We can rearrange this equation to express a in terms of b: a = 10 - 2b.

2. We are also given that ab = 15. Substituting the expression for a from the previous step into this equation, we get (10 - 2b)b = 15.

3. Expanding the equation, we have [tex]10b - 2b^2 = 15.[/tex]

4. Rearranging the equation, we get[tex]2b^2 - 10b + 15 = 0.[/tex]

5. This is a quadratic equation in terms of b. We can solve it using factoring, completing the square, or the quadratic formula. In this case, we can factor the equation as (b - 3)(2b - 5) = 0.

6. From the factored equation, we find two possible values for b: b = 3 or b = 5/2.

7. To find the corresponding values of a, we substitute these values of b into the expression a = 10 - 2b. We find a = 4 when b = 3, and a = 0 when b = 5/2.

8. Now, we can calculate the value of [tex]a^3 + 8b^3[/tex] using the values of a and b we found. For the case when b = 3, we have [tex]a^3 + 8b^3 = 4^3 + 8(3)^3[/tex] = 64 + 216 = 280. For the case when b = 5/2, we have[tex]a^3 + 8b^3 = 0^3 + 8(5/2)^3 = 0 + 8(125/8) = 125.[/tex]

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Answer:

20

Step-by-step explanation:

1.2x = 24

x = 20

Answer:

20

Step-by-step explanation:

1.2x = 24

x = 20

Step-by-step explanation:

Answer: where is the figure tot he right???

Step-by-step explanation:

Answer:

Hi guys! Its 6, I took the quiz and I was sure to check after!!

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Answer: A. 4(8m-2) and 32m -8

Step-by-step explanation: First distribute the 4 to 8m and -2 to get 32m - 8 which is equal to 32m - 8.

32m - 8 = 32m - 8

Hope this helps! :)

Answer:

The first one

Step-by-step explanation:

4(8m-2)=32m-8

Answer:

x

Step-by-step explanation:

Answer:

$0.11

Step-by-step explanation:

price ($28.16) divided by amount (265) = unit rate

the factors of P(x) are:(x + 4)(x - 6)(x + 3)

If P(-4) for the polynomial function P(x) = x³ + 11x² + 34x + 24 equals zero, then it means that x + 4 is a factor of the polynomial function.

Let's substitute -4 for x in the polynomial function, then we'll have:

P(-4) = (-4)³ + 11(-4)² + 34(-4) + 24P(-4) = -64 + 176 - 136 + 24P(-4) = 0If P(-4) is zero, then the polynomial has a factor of x + 4.

We can find out the other factor by dividing the polynomial by x + 4:x³ + 11x² + 34x + 24 ÷ (x + 4) = x² + 7x + 6(x + 4) + (-10x - 24)x² + 7x + 6 + (-10x - 24) = x² - 3x - 18

We can now factor this quadratic polynomial: x² - 3x - 18 = (x - 6)(x + 3)

Therefore, the factors of P(x) are:(x + 4)(x - 6)(x + 3)

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Answer:

x=5

Step-by-step explanation:

9x=4x+25

-4x  -4x

5x=25

x=5

Answer:

the answer is 76 mph

Step-by-step explanation:

Answer:

76 Mph

Step-by-step explanation:

Divide 608 by 8 to get 76.

After you get 76 from dividing you can then check your answer by multiplying 76 by 8 to get 608.

Thus 76 is the answer.

Hope this helps and have a great day.

Answer:

79 degrees

Step-by-step explanation:

x and the angle that measures 79 degrees are alternate interior angles, which makes them the same measure.

Alternate interior angles are both on the inner sides of the parallel lines but on opposite sides of the transversal, which is the diagonal line crossing m and n. Another way you can identify these angles is by noticing the "Z" shape that they make.

I hope this helps! Please comment if you have any questions.

Answer:

844,000

Step-by-step explanation

Last three numbers are the hundreds, that's what you round when doing thousands. If it is higher than 500, then raise it to the next thousand, if not then keep it the same. In this case, 590>500, so I will round up to 844,000.

Answer:

5/9

Step-by-step explanation:

Answer:

[tex]\frac{16}{21}[/tex]

Step-by-step explanation:

I hope this helps!

Answer:

13.7

Step-by-step explanation:

A{2} + B{2} =C{2} \\

6{2} +B{2} =15{2} \\

6x6+B(2) =15x15\\

36+B(2)=225\\

            -36\\

            \sqrt{189} =13.7

The dimensions of the framed picture would be "x + 2" centimeters for the width and "x + 8" centimeters for the length, where "x" represents the width of the original rectangular picture.

To determine the dimensions of the framed picture, we can use the information. Let's assume the width of the picture is "x" centimeters.

Since the rectangular picture is 6 centimeters longer than it is wide, the length of the picture would be "x + 6" centimeters.

When a frame 1 centimeter wide is placed around the picture, it adds 1 centimeter to each side of the picture.

Therefore, the width of the framed picture would be "x + 2" centimeters (2 additional centimeters for the frame on both sides) and the length would be "x + 6 + 2" centimeters (2 additional centimeters for the frame on both sides).

In simplified form, the dimensions of the framed picture would be width: "x + 2" centimeters and length: "x + 8" centimeters.

The complete question is "'A rectangular picture is 6 cm longer than it is wide. A frame 1 cm wide is placed around the picture. Write a polynomial that represents the area of the frame?"

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Answer:

The ball will not get up to 125 ft

Step-by-step explanation:

The initial velocity of the golf ball = 85 ft/s

The function for the height, h, in feet, of the golf ball is h = -16·t² + 85·t + 1/12

Where;

t = The time in seconds of flight of the golf ball

We have at maximum height, dh/dt = 0, which gives;

dh/dt = d(-16·t² + 85·t + 1/12)/dt = 0

-32·t + 85 = 0

t = 85/32

Given that d²h/dt² = d(-32·t + 85)/dt = -32 which is negative, the obtained point, t = 85/32, above is a maximum point

Substituting the value of t at the maximum into the function for the height h, to obtain the value for the maximum height, we have;

h[tex]_{(max)}[/tex] = h(85/32) = -16 × (85/32)² + 85× (85/32) + 1/12  ≈ 112.974

The maximum height reached = h[tex]_{(max)}[/tex] = 112.974 ft.

The maximum height reached ≈ 112.974 ft

Therefore, the ball will not get up to 125 ft.

Answer:

false

Step-by-step explanation:

0 is a whole number not natural

Natural Number can be classified as "Positive Integer" or "Counting Numbers". So think about it, In real life, we count from 1 right? We do not start from 0 for counting numbers.

So it's false.

The system of equations is:x + y = 70......(1)where x is the number of limited edition soccer balls and y is the number of Pro NSL soccer balls.

65x + 15y = 2400......(2)where 65 is the price of one limited edition soccer ball and 15 is the price of one Pro NSL soccer ball.By solving the system of equations above, we get:x + y = 70......(1)65x + 15y = 2400......(2)Solving equation (1) for x, we get:x = 70 - y.Substitute the value of x in equation (2) and solve for y:

65(70 - y) + 15y = 24004550 - 65y + 15y = 2400-50y = -3150y = 63

Substitute the value of y in equation (1) and solve for x:x + y = 70x + 63 = 70x = 7.Therefore, 7 limited edition soccer balls were sold and 63 Pro NSL soccer balls were sold. The given problem requires us to find the number of limited edition soccer balls and Pro NSL soccer balls sold in a sports store that sold a total of 70 soccer balls in one month and collected $2400. We are given that a limited edition soccer ball costs $65 and a Pro NSL soccer ball costs $15. We need to solve a system of equations to find the solution.Therefore, let x be the number of limited edition soccer balls and y be the number of Pro NSL soccer balls. The first equation is:x + y = 70We know that the total number of soccer balls sold is 70. Hence, the sum of limited edition and Pro NSL soccer balls will be 70. The second equation is:65x + 15y = 2400We know that the total revenue collected is $2400. Hence, the total revenue earned from limited edition soccer balls will be $65x and the total revenue earned from Pro NSL soccer balls will be 15y. Therefore, the sum of revenue earned from limited edition soccer balls and Pro NSL soccer balls will be 65x + 15y. By solving these equations, we can get the solution.Therefore, by solving the equations, we get 7 limited edition soccer balls and 63 Pro NSL soccer balls were sold in the store.

Hence, the store sold 7 limited edition soccer balls and 63 Pro NSL soccer balls.

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Answer:

Joseph pays £133.20

Step-by-step explanation:

740 - 296 = 444

30% of 444 = 133.20

Therefore he pays £133.20

Answer:

The median and IQR

Step-by-step explanation:

Hope it helps

Answer:

By solving the question y =11

Answer:

y=11

Step-by-step explanation:

The sequence is arithmetic. The common difference is 6. Answer: b

If a sequence is arithmetic, there exists a common difference d that is added to each term to get the next term. For instance, given the sequence 2, 5, 8, 11, 14, ...  to get each of the subsequent terms, we add 3. 2 + 3 = 5; 5 + 3 = 8, and so on.

The given sequence is 2,7,13,20, ...To determine whether it is an arithmetic sequence, we need to find the common difference d.

Subtract each subsequent term from its preceding term;7 - 2 = 513 - 7 = 620 - 13 = 7

Therefore, the common difference d is 6.

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Answer:

-4

Step-by-step explanation:

3x-8x+4=24

-5x=24-4

-5x=20

x=-4

Answer:

Step-by-step explanation:

[tex]3x + 4 - 8x = 24 \\ [/tex]

Simplify the expression on the left side of the equation

That's

[tex]4 - 5x = 24[/tex]

Subtract 4 from both sides of the equation

[tex]4 - 4 - 5x = 24 - 4\\ - 5x = 20[/tex]

Divide both sides by - 5

[tex] \frac{ - 5x}{ - 5} = \frac{20}{ - 5} \\ [/tex]

We have the final answer as

[tex]x = - 4 \\ [/tex]

Hope this helps you

Answer:0.06

Step-by-step explanation:

Answer:

0.006

Step-by-step explanation:

3/20 = 0.15 + 1/25 = 0.19 - 11/60

= 0.00666666

Answer:

Step-by-step explanation:

given data

mints $0.96 per pound

chocolates $4.70 per pound

lollipops $0.07 each

cost of each items based on the amount item

mints $0.96*0.75= 0.72

chocolates $4.70*1.5=7.05

lollipops $0.07*15=1.05

total cost= 0.72+7.05+1.05

total cost=$8.82

Answer:

The answer is 8.82

Step-by-step explanation:

Answer:

They represent the rise and run of the graph.

Step-by-step explanation:

The difference between the x-axis of the points represents the "run" of the graph (or how much you should run along x-axis to get to the next point.)

The difference between the y-axis of of the points represents the "rise" of the graph (or how much you should rise up the y-xis to get to the next point).

The ratio of rise to run is the slope of the graph, which tells us  how many steps should we take on the y-axis for every step we move forward on the x-axis.

Answer:

x<6

Step-by-step explanation:

5x < 30 divide by 5

x=6

Answer:

Step-by-step explanation:

21