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Marrrta [24]
2 years ago
14

Select All of the possible solutions for the following inequality.

Mathematics
1 answer:
MariettaO [177]2 years ago
6 0

Answer:

-12,-9,-3

MARK ME BRAINLIEST PLEASE

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Brainliest pls help
Airida [17]
<h3>Volume:</h3>

With this prism, first separate it into a rectangular prism and a right triangle prism.

First, with the rectangular prism, it would have the units 5 * 5 * 6.3. Then with the right triangle prism, it would take the rest of the remaining space of it, being 3 * 5 * 6.3

The equation for the volume of a rectangular prism is L*W*H and the equation for the volume of a right triangle prism is (L*W*H) / 2.

With this, plug the numbers in for both prisms to get the volume of each of them:

<u>Rectangular prism Volume</u>

5*5*6.3

<em>157.5</em>

<u>Right triangle prism Volume</u>

(3*5*6.3) / 2

94.5 / 2

<em>47.25</em>

Lastly, combine these two values to get the total volume:

157.5 + 47.25 = 204.75 (Round Up) -->

<em><u>204.8 cm^3 = Total Volume </u></em>

<h3>Surface Area:</h3>

Next, with the surface area of the prism. For this, lets combine all of the faces of the prism then add them all up.

First, lets do the bottom of the prism, or the base. It uses the lengths 8 cm and 6.3 cm. Lets do L * W to get the area of this face:

8 * 6.3 = 50.4

Next, lets do the slant side of it, which has the lengths 5.8 and 6.3.

5.8 * 6.3 = 36.54

Then, the top side with the lengths 5cm and 6.3 cm.

5.3 * 6.3 = 33.39

After that, the left side face that opposite to the slantly one:

5 * 6.3 = 31.5

Saving the most tedious part of it for last, the right trapezoids. Luckily, there is an equation for this:

<em>1/2 x (Sum of parallel sides) x (perpendicular distance between the parallel sides).</em>

<em>So, within each of these right </em>trapezoids, there's the parallel sides of 5 and 8. There's also a perpendicular side of 5cm. With this, we can plug this into the equation to solve for this part:

1/2 x (5+8) * (5)

1/2 x (13) * (5)

1/2 x (65)

32.5

Since there's two of them, times this by 2:

32.5 * 2 ---> 65.

Now, with the area of all of the faces, these can be added up for the total surface area:

50.4 + 36.54 + 33.39 + 31.5 + 65 ---> 216.83 (Round Down)-->

<u><em>216.8 cm^2 = Total Surface Area</em></u>

<em />

8 0
2 years ago
The difference between two positive integers is 7 and the sum of their squares is 949. What are the numbers?
Darina [25.2K]

Answer:

25 and 18

Step-by-step explanation:

Let's say that the first number is x and the second one is y.

First, the difference between them is 7, so x-y=7

Next, the sum of their squares is 949, so x²+y² = 949

We have

x-y=7

x²+y²=949

One thing we can do to solve this problem is to solve for x in the first equation, plug that into the second equation, and go from there

Adding y to both sides in the first equation, we have

x = 7 + y

Plugging that into the second equation for x, we have

(7+y)²+ y² = 949

expand

(7+y)(7+y) + y² = 949

49 + y² + 7y + 7y + y² = 949

combine like terms

2y² +14y + 49 = 949

subtract 949 from both sides to put this in the form of a quadratic equation

2y² + 14y - 900 = 0

divide both sides by 2

y² + 7y - 450 = 0

To factor this, we want to find 2 numbers that add up to 7 and multiply to -450.

The factors of 450 are as follows:

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.

Note that we want to find two numbers with a difference of 7, as one will have to be negative for the multiplication to end up at -450. Two numbers that stand out are 18 and 25. To make them add up to 7, 18 can be negative. We therefore have

y² + 25y - 18y - 450 = 0

y(y+25) - 18(y+25) = 0

(y-18)(y+25) = 0

Solving for 0,

y-18 = 0

add 18 to both sides

y=18

y+25 = 0

subtract 25 from both sides

y= -25

As the question states "two positive integers", this means that y must be positive, so y = 18. We know x-y=7, so

x-18 = 7

add 18 to both sides to isolate x

x = 25

7 0
2 years ago
Number is a factor of 51?
soldi70 [24.7K]
Only 1 and 51 are factors of 51. 
7 0
3 years ago
Isaac and victoria share money in the ratio 2:5<br> victoria recieves £6.60
iren2701 [21]
2.64
6.60/5=1.32 (that’s your rate)
2 x 1.32=2.64
This means that Isaac gets £2.64
6 0
3 years ago
What is the square root of 64 multiplied by 2
Tamiku [17]

Answer:

its 16

as we know the square root of 64 is 6 and when it is multiplied by 2 its answer is 16.

Step-by-step explanation:

6 0
3 years ago
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