The base of a rectangular prism is 7 cm long,and 5 cm wide. If the surface area of the prism
is 310 cm², what is the volume of the
prism?

Answer:

1886.5

Step-by-step explanation:

2πr=154

2*22/7*r=154

44/7r=154

44r=1078

r=24.5

now,

area=πr²

     =22/7*(24.5)²

    =1886.5

As we know that the area of an equilateral triangle with side a is given by ;

So , now using formula in our question, putting the value of the side, we can thus obtain

[tex]{:\implies \quad \sf Area=\dfrac{\sqrt{3}}{4}(16)^{2}}[/tex]

Putting value of √3 ≈ 1.73 and cancelling 4 we have ;

[tex]{:\implies \quad \sf Area\approx 1.73\times 64}[/tex]

[tex]{:\implies \quad \sf Area\approx 110.72\:\: cm^{2}}[/tex]

[tex]{:\implies \quad \sf Area\approx 110.7\:\: cm^{2}}[/tex]

This is the required answer

I'm not sure but I think the answer is - 1/2

Answer:

Last graph: [tex]\langle-7,-9\rangle[/tex]

Step-by-step explanation:

Here, [tex]u=\langle-2,-7\rangle[/tex] and [tex]v=\langle5,2\rangle[/tex]. Thus, [tex]u-v=\langle(-2)-5,(-7)-2\rangle=\langle-7,-9\rangle[/tex], making the last graph the correct answer.

Answer:

4

Step-by-step explanation:

Slope = 4

(0,-1) and (1,3)

Answer:

600 billion toys

Step-by-step explanation:

40,000 × 15,000,000 = 600,000,000,000

Answer:

two balls are of the same color

Step-by-step explanation:

5 blue and 3 red. so its not the same number of each. and there is no white balls.

Answer:

36

Step-by-step explanation:

you simplify 26 simplify it again and the simplify answer is 36

Answer:

1 / 100. is the answer. got it correct.

Step-by-step explanation:

Answer:

=> 28 - x = 24

=> x = 24 - 28

=> x = -4

therefore, 28 - 4 = 24

Answer:

2

Step-by-step explanation:

Answer:

(1 / 2 US cups) / (1 / 4 US cups) = 2

Step-by-step explanation:

PLZ MARK Brainliest

Answer:

1,035 divide by 5 = 207

1,766 divide by 8 = 220.75

Answer:

[tex](4, -1, 3)[/tex]

Step-by-step explanation:

We have the system of equations:

[tex]\left\{ \begin{array}{ll} x+2y+z =5 \\ 2x-y+2z=15\\3x+y-z=8 \end{array} \right.[/tex]

We can convert this to a matrix. In order to convert a triple system of equations to matrix, we can use the following format:

[tex]\begin{bmatrix}x_1& y_1& z_1&c_1\\x_2 & y_2 & z_2&c_2\\x_3&y_2&z_3&c_3 \end{bmatrix}[/tex]

Importantly, make sure the coefficients of each variable align vertically, and that each equation aligns horizontally.

In order to solve this matrix and the system, we will have to convert this to the reduced row-echelon form, namely:

[tex]\begin{bmatrix}1 & 0& 0&x\\0 & 1 & 0&y\\0&0&1&z \end{bmatrix}[/tex]

Where the (x, y, z) is our solution set.

Reducing:

With our system, we will have the following matrix:

[tex]\begin{bmatrix}1 & 2& 1&5\\2 & -1 & 2&15\\3&1&-1&8 \end{bmatrix}[/tex]

What we should begin by doing is too see how we can change each row to the reduced-form.

Notice that R₁ and R₂ are rather similar. In fact, we can cancel out the 1s in R₂. To do so, we can add R₂ to -2(R₁). This gives us:

[tex]\begin{bmatrix}1 & 2& 1&5\\2+(-2) & -1+(-4) & 2+(-2)&15+(-10) \\3&1&-1&8 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\0 & -5 & 0&5 \\3&1&-1&8 \end{bmatrix}[/tex]

Now, we can multiply R₂ by -1/5. This yields:

[tex]\begin{bmatrix}1 & 2& 1&5\\ -\frac{1}{5}(0) & -\frac{1}{5}(-5) & -\frac{1}{5}(0)& -\frac{1}{5}(5) \\3&1&-1&8 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\3&1&-1&8 \end{bmatrix}[/tex]

From here, we can eliminate the 3 in R₃ by adding it to -3(R₁). This yields:

[tex]\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\3+(-3)&1+(-6)&-1+(-3)&8+(-15) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&-5&-4&-7 \end{bmatrix}[/tex]

We can eliminate the -5 in R₃ by adding 5(R₂). This yields:

[tex]\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0+(0)&-5+(5)&-4+(0)&-7+(-5) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&0&-4&-12 \end{bmatrix}[/tex]

We can now reduce R₃ by multiply it by -1/4:

[tex]\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\ -\frac{1}{4}(0)&-\frac{1}{4}(0)&-\frac{1}{4}(-4)&-\frac{1}{4}(-12) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}[/tex]

Finally, we just have to reduce R₁. Let's eliminate the 2 first. We can do that by adding -2(R₂). So:

[tex]\begin{bmatrix}1+(0) & 2+(-2)& 1+(0)&5+(-(-2))\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 0& 1&7\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}[/tex]

And finally, we can eliminate the second 1 by adding -(R₃):

[tex]\begin{bmatrix}1 +(0)& 0+(0)& 1+(-1)&7+(-3)\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 0& 0&4\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}[/tex]

Therefore, our solution set is [tex](4, -1, 3)[/tex]

And we're done!

Answer:

The correct option is ⇒ Point W means that that unit rate is $2.5 per pound.

Step-by-step explanation:

The question missing the graph and the options

The options for the questions are:

1) Point R means that that unit rate is $10 per pound.

2) Point R means that that unit rate is 4 pounds per dollar

3) Point W means that that unit rate is $2.5 per pound.

4) Point W means that that unit rate is 2.5 pounds per dollar.

And see the attached figure.

As shown in the figure attached

The unit rate will be the total cost per weight

By calculating the unit rate for the graph = (y2-y1)/(x2-x1)

using the given points (4,10) , (1,2.5)

the unit rate = (10-2.5)/(4-1) = 7.5/3 = 2.5

The unit rate means that it will cost $2.5 per pound and this is a gree with the point W which have the same meaning.

So, The correct answer is option 3.

Step-by-step explanation:

Solution:

perimeter of rectangle = 2 ( Length + Width )

Find length/width:

2 (length + length) = 48

2(length) = 24

length = 12 cm

width = 12 cm

⇒ The dimensions of square: 12 x 12

If the square cut into half, the dimensions of either length or width will half.

Therefore, the perimeter of rectangle:

→ 2 (length + width)

→ 2 ( 12 + 6 )

→ 2 ( 18 )

→ 36 cm

Answer:

  £40.

Step-by-step explanation:

In terms of ratio units, Stephen and Bridget together get 3+2 = 5, while Paul receives 4. That is, Paul gets 4/5 of their combined total, or ...

  4/5 · £50 = £40

Paul gets £40.

Given parameters:

Ratio of their money = 3 : 4 : 2

Total amount received by Stephen and Bridget = 50

Unknown :

How much did Paul get = ?

Solution:

The amount Paul got is a fraction of the total.

  We need to find the total amount first;

  Amount Stephen and Bridget got  = [tex]\frac{ratio of stephen and bridget}{total ratio} x total amount[/tex]

let the total amount = y;

                   50  = [tex]\frac{3+2}{9}[/tex] x y

                    [tex]\frac{5y}{9}[/tex]  = 50

                      5y = 450  

                      y = 90

Now, the amount Paul got;

                         = [tex]\frac{4}{9} x 90[/tex]

                          = 40

The amount Paul got is £40

Answer:

30454

Step-by-step explanation:

subtraction on a calculator

42812-12358=30454

Answer:

its A

Step-by-step explanation:

Answer:

It is c

Step-by-step explanation:

Letters are

No repetitions

Distinct permutation:-

Answer:

1/3 - (-5/3) = 2

Step-by-step explanation:

1/3 - (-5/3)

Subtracting a negative is the same as adding a positive.

1/3 + 5/3 = 6/3, or 2

Answer:

3. What figures are formed when a diagonal is drawn in a quadrilateral

a. triangles

4. which is TRUE about the sides of a parallelogram?

b. 2 pairs of sides are parallel and equal

5. if two diagonal are drawn in a rhombus or in a square, which of the following will be formed

a. 2 triangles of the same size

6. which of the following describes the sides of a square or of a rhombus

c. all sides are equal​

Answer:

Put an open circle on 5 and have the arrow point in the positive direction.

Step-by-step explanation:

Answer:

a > 5 or a ∈ ( 5 , ∞ )

Step-by-step explanation:

Answer/Step-by-step explanation:

Given:

Emiliano thinks x = 40 is the solution to the equation 1/2x = 80

Note:

An equation is the statement that equalizes two mathematical expressions.

An expression is the combination of variables and constants connected with mathematical operations.

Solve:

Substituting the value of x, in the equation

1/2(4) = 80

    20 ≠ 80

Thus,   it isn't satisfied. Hence, Emiliano's answer is wrong.    

Correct Way to Solve;                

Multiply both sides by 2

2 · [tex]\frac{1}{2}x[/tex] = 80 · 2

Simplify

x = 160

~Learn with Lenvy~

Answer:

yes, (I think)

because 27 more students left this year with a pass and last year the percentage would of been lower I don't know

The college is incorrect, it is 28.125%

Percentage is defined as ratio expressed as a fraction of 100.

No. of students in college in last year = 123 -27 = 96

The number of students leaving college ratio = (27/96)×100%

⇒0.28125×100%

⇒28.125%

The college says,

'The number of students leaving college with a pass in English has increased by 24% from last year

Hence, The college is incorrect, it is 28.125%

Learn more about percentage

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