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Alekssandra [29.7K]
4 years ago
10

A number is three times another number. The difference of these two numbers is 10. Find these number.​

Mathematics
2 answers:
Katyanochek1 [597]4 years ago
5 0

Answer:

\Large \boxed{\sf 15 \ and \ 5}

Step-by-step explanation:

Let the first number be x.

Let the second number be y.

x is 3 times y.

Difference of x and y is 10.

x=3y

x-y=10

Put x as 3y in the second equation.

3y-y=10

Combine like terms.

2y=10

Divide both sides by 2.

y=5

Plug y as 5 in the first equation.

x=3(5)

Multiply.

x=15

The two numbers are 15 and 5.

kow [346]4 years ago
3 0

Answer:

5,15

Step-by-step explanation:

let the numbers be x and y

but y = 3x

3x - x = 10

2x = 10

x = 5

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2. Let f(x) = 3x² -x+5, find f(x+1)​
Anna11 [10]

Answer:

f(x + 1) = 3x² + 5x + 7

Step-by-step explanation:

To find f(x + 1), substitute x = x + 1 into f(x), that is

f(x + 1) = 3(x + 1)² - (x + 1) + 5 ← expand (x + 1)² using FOIL

           = 3(x² + 2x + 1) - x - 1 + 5 ← distribute parenthesis by 3

           = 3x² + 6x + 3 - x - 1 + 5 ← collect like terms

           = 3x² + 5x + 7

8 0
3 years ago
Which fraction is equal to k in the equation below? <br>1\3 / 2= k
Nitella [24]

Answer:

0_10 =0_2

Step-by-step explanation:

Convert the following to base 2:

0_10

Hint: | Starting with zero, raise 2 to increasingly larger integer powers until the result exceeds 0.

Determine the powers of 2 that will be used as the places of the digits in the base-2 representation of 0:

Power | \!\(\*SuperscriptBox[\(Base\), \(Power\)]\) | Place value

0 | 2^0 | 1

Hint: | The powers of 2 (in ascending order) are associated with the places from right to left.

Label each place of the base-2 representation of 0 with the appropriate power of 2:

Place | | | 2^0 |  

| | | ↓ |  

0_10 | = | ( | __ | )_(_2)

Hint: | Divide 0 by 2 and find the remainder. The remainder is the first digit.

Determine the value of 0 in base 2:

0/2=0 with remainder 0

Place | | | 2^0 |  

| | | ↓ |  

0_10 | = | ( | 0 | )_(_2)

Hint: | Express 0_10 in base 2.

The number 0_10 is equivalent to 0_2 in base 2.

Answer: 0_10 =0_2

8 0
4 years ago
College students average 8.6 hours of sleep per night with a standard deviation of 35 minutes. If the amount of sleep is normall
Soloha48 [4]

Answer:

4.27%

Step-by-step explanation:

We have been given that college students average 8.6 hours of sleep per night with a standard deviation of 35 minutes. We are asked to find the probability of college students that sleep for more than 9.6 hours.

We will use z-score formula to solve our given problem.

z=\frac{x-\mu}{\sigma}

z = z-score,

x = Random sample score,

\mu = Mean,

\sigma = Standard deviation.

Before substituting our given values in z-score formula, we need to convert 35 minutes to hours.

35\text{ min}=0.58\text{ Hour}

z=\frac{9.6-8.6}{0.58}

z=\frac{1}{0.58}

z=1.72

Now, we need to find P(z>1.72).

Using formula P(z>a)=1-P(z, we will get:

P(z>1.72)=1-P(z

Using normal distribution table, we will get:

P(z>1.72)=1-0.95728

P(z>1.72)=0.04272

0.04272\times 100\%=4.272\%

Therefore, 4.27% of college students sleep for more than 9.6 hours.

7 0
3 years ago
= 2. Given the quadratic equation 3x2 – 8x + k = 0 has no real roots. Find the range of values of k.
VashaNatasha [74]

\text{If there  are no real roots, then}\\\\~~~~~\text{Discriminant} < 0\\\\\implies b^2 -4ac < 0\\\\\implies (-8)^2 -4 \cdot 3 k < 0\\\\\implies 64-12k < 0\\\\\ \implies 12k > 64\\\\\implies k > \dfrac{64}{12}\\\\\implies k > \dfrac{16}3\\\\\text{Interval,}~ \left( \dfrac{16}3, ~\infty\right)

6 0
2 years ago
The radius of this ball is 15 inches. Which equation gives the ball's surface area, in square inches?
victus00 [196]

Answer:

\large\boxed{S.A.=4500\pi\ in^2\approx14130\ in^2}

Step-by-step explanation:

The formula of a surface area of a ball (sphere):

S.A.=\dfrac{4}{3}\pi R^3

R - radius

We have R = 15in. Substitute:

S.A.=\dfrac{4}{3}\pi(15^3)=\dfrac{4}{3}\pi(3375)=4500\pi\ in^2

If you want to get an approximation, then:

\pi\approx3.14\\\\S.A.\approx(4500)(3.14)=14130\ in^2

5 0
3 years ago
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