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Dvinal [7]
3 years ago
14

Ralph runs at a constant rate of 3 miles per hour how long will it take Ralph to run 15 miles

Mathematics
2 answers:
LenaWriter [7]3 years ago
5 0
15/3=5 hours is your answer
Artist 52 [7]3 years ago
3 0

Answer:

5 hr.

Step-by-step explanation:

Just took the quiz and got it right.

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Dana is 25 years old. She has $12,000 in a savings account, $800 in government bonds, $11,000 in a retirement account, and owns
Anastaziya [24]

Answer: APEX --- $12,800

Step-by-step explanation:

8 0
3 years ago
A prism and two nets are shown below:
nikdorinn [45]
Part a : Net A because when you fold it up it will look like the wanted prism

Part b : AB = 3 in
BC = 5 in
CD = 7.2 in

Part c : area of one triangle = 4*3 = 12 / 2 = 6
6 * 2 = 12 (because there are 2 triangles)
7.2 * 3 = 21.6
7.2 * 4 = 28.8
7.2 * 5 = 36
Add them all up : 12+21.6+28.8+36 = 98.4
So surface area is 98.4 in
4 0
3 years ago
Find the roots of:
Elena-2011 [213]

\large\displaystyle\text{$\begin{gathered}\sf \pmb{1) \  2x^3-7x^2+8x-3=0 } \end{gathered}$}

Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:

  | 2  -7    8  -3

<u>1 |      2   -5   3</u>

  | 2   -5    3  0

<u> 1 |      2     -3   </u>

    2   -3     0

So the factorization is (x-1)² (2x-3)=0. So:

                     \bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2}  }

\large\displaystyle\text{$\begin{gathered}\sf \pmb{2) \  x^3-x^2-4=0 } \end{gathered}$}

Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:

      |  1  -1  0  -4

  <u>2  |     2  2     </u>

         1  2  2  0

So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.

                   \bf{ 1^2-4(2)(2)=1-16=-15 < 0 \quad \Longrightarrow \quad x=2 }

\large\displaystyle\text{$\begin{gathered}\sf \pmb{3) \  6x^3+7x^2-9x+2=0 } \end{gathered}$}

Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:

   | 6    7       9      2

<u>-2 |      -12    10     -2</u>

     6    -5     1       0

So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula:

         \bf{ x_{2, 3}&=\dfrac{5\pm \sqrt{(5)^2-4(6)(1)}}{2(6)}=\dfrac{5\pm \sqrt{25-24}}{12}=\dfrac{5\pm 1}{12} }}

                     \large\displaystyle\text{$\begin{gathered}\sf  \begin{matrix} x_1=-2&\ \ \ \ \ \ x_{2}=\dfrac{6}{12} \qquad &\ \ \ x_3=\dfrac{4}{12}\\ &\ \ \ x_2=\dfrac{1}{2} \qquad &x_3=\dfrac{1}{3} \end{matrix} \end{gathered}$}

6 0
2 years ago
What is 6.2% times 0.62
miv72 [106K]

Answer:

0.03844

Step-by-step explanation:

0.62*6.2%

=0.62*0.062

=0.03844

3 0
2 years ago
A 24 inch board is to be cut into three pieces so that the second piece is twice as long as the first piece and the third piece
Anastaziya [24]

F=length of first piece=x; S=length of second piece=2x

T=length of third piece=3x

.

F+S+T=24 inches

x+2x+3x=24 inches

6x=24in

F=x=4in

ANSWER 1: The length of the first piece is 4 inches.

.

S=2x=2(4in)=8in

ANSWER 2: The length of the second piece is 8 inches.

.

T=3x=3(4in)=12 inches.

ANSWER 3: The length of the third piece is 12 inches.

.

CHECK:

F+S+T=24in

4in+8in+12in=24in

24in=24in

7 0
2 years ago
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