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mart [117]
3 years ago
8

Complete the equation. Round to the nearest hundredth where necessary.

Mathematics
1 answer:
Alexandra [31]3 years ago
7 0

Answer:

D

Step-by-step explanation:

There are 1.61 km in 1 mi.

10 mi × (1.61 km/mi) = 16.1 km

You might be interested in
Solve for x if sqrt (3x-8) + 1 = sqrt (x+5)
In-s [12.5K]

The solution of x in the given expression \mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}} is 4. However, if it is \mathbf{\sqrt{(3x-8)+1} = \sqrt{(x+5)}}, it is 6.

<h3>What is the solution to algebraic expression?</h3>

The solution to the given algebra expression involving surds can be seen in the steps below.

Given that:

\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}

Remove the square roots, we have:

12x - 32 = 4x² - 48x + 144

Solving the quadratic equation at the RHS and equating it to LHS, we have:

x = 11, x = 4

Verifying the solutions by replacing the value of x with the given equation:

  • x = 11 False
  • x = 4 True

Therefore, we can conclude that the value of x = 4

NOTE:

Given that:

\mathbf{\sqrt{(3x-8+1)} = \sqrt{(x+5)}}

Square both sides

3x - 7 = x +5

Solve for x

3x - x = 5 + 7

2x = 12

x = 6

Learn more about solving to algebraic expressions here:

brainly.com/question/4344214

#SPJ1

5 0
2 years ago
24 : 8 = 3 : ?<br>7 : 35 = ? : 5<br>in detail please
Simora [160]
24 : 8 = 3 : 1 because 24 divided by 8 = 3 so
3 = 1

7 : 35 = 1 : 5 because 35 divided by 7 is 5 so
5 = 1
8 0
3 years ago
A radioactive substance decreases in the amount of grams by one-third each year. If the starting amount of the
katovenus [111]

Answer:

The sequence is geometric. The recursive formula is a_{n}=2/3a_{n-1}

Step-by-step explanation:

In order to solve this problem, you have to calculate the amount of the substance left after the end of each year to obtain a sequence and then you have to determine if the sequence is arithmetic or geometric.

The substance decreases by one-third each year, therefore:

After 1 year:

1452-\frac{1}{3}(1452)

Using 1452 as a common factor and solving the fraction:

1452(1-\frac{1}{3})=1452(\frac{2}{3})=968

You can notice that in general, after each year the amount of grams is the initial amount of the year multiplied by 2/3

After 2 years:

968(\frac{2}{3})=\frac{1936}{3}

After 3 years:

\frac{1936}{3}(\frac{2}{3})=\frac{3872}{9}

The sequence is:

1452,968,1936/3,3872/9....

In order to determine if the sequence is geometric, you have to calculate the ratio of two consecutive terms and see if the ratio is the same for all two consecutive terms. The ratio is obtained by dividing a term by the previous term.

The sequence is arithmetic if the difference of two consecutive terms is the same for all two consecutive terms.

-Calculating the ratio:

For the first and second terms:

968/1452=2/3

For the second and third terms:

1936/3 ÷ 968 = 2/3

In conclussion, the sequence is geometric because the ratio is common.

The recursive formula of a geometric sequence is given by:

a_{n}=ra_{n-1}

where an is the nth term, r is the common ratio and an-1 is the previous term.

In this case, r=2/3

7 0
3 years ago
The formula for centripetal acceleration, a, is given below, where v is the velocity of the object and r is the object's distanc
julsineya [31]

Answer:

Step-by-step explanation:

For this case we have the following equation:

a = v ^ 2 / r

From here, we must clear the value of speed.

We have then:

v ^ 2 = a * r

v = root (a * r)

Answer:

the formula for the velocity is:

v = root (a * r)

3 0
2 years ago
Read 2 more answers
Which of the following represents the zeros of f(x) = x3 − 11x2 + 38x − 40?
Delvig [45]
The answer is <span>5, 4, 2
</span>
Among all choices we have 5, so
x = 5
x - 5 = 0
Let's divide the expression by (x - 5) using the long division:
                          x³ - 11x² + 38x - 40
(x - 5)  * x² =      x³ - 5x²                   Subtract
____________________________
                              -6x² + 38x - 40
   (x - 5) * (-6x) =    -6x² + 30x          Subtract
____________________________
                                           8x - 40
                    (x - 5) * 8 =     8x - 40   Sutract
____________________________
                                              0

Thus: x³ - 11x² + 38x - 40 = (x - 5)(x² - 6x + 8)

Now, let's simplify x² - 6x + 8.

x² - 6x + 8 = x² - 2x - 4x + 8 =
                  = x² - 2*x - (4*x - 4*2) = 
                  = x(x - 2) - 4(x - 2) =
                  = (x - 4)(x - 2)

Hence:
x³ - 11x² + 38x - 40 = (x - 5)(x - 4)(x - 2)
To calculate zero:
x³ - 11x² + 38x - 40 = 0
(x - 5)(x - 4)(x - 2) = 0
x - 5 = 0            or             x - 4 = 0              or      x - 2 = 0
x = 5                 or              x = 4                   or      x = 2
3 0
3 years ago
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