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2 years ago

Four times a number decreased by seven

1 answer:

7 0

In order to answer this question, we must break this mathematical expression up into a series of mathematical operations (exponent, multiplication,division, addition, and/or subtraction):

"4 times a number" - The word "times" implies that we have to multiply 4 by an unknown number. We can simply label this unknown number as x.
"cubed" - In order to "cube" a number, we must raise it to the third power, or have an exponent of 3. Our unknown number of x now becomes x3 because we raised it to the third power.
"decreased by 7" - The word "decreased" implies that we must subtract 7 from the product of 4 multiplied by x3

With all of the information we now have, we can form an algebraic expression for this problem.
"4 times a number cubed decreased by 3" now becomes:
4x3 - 7

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Question 2: If I increase the price of a dress by 15%, what would<br> the multiplier be ?

sukhopar [10]

If the price was $1 and it increased by 15% it would now be $1.15 therefore the multiplier is 1.15 as that increases a number by 15%

6 0

2 years ago

(1 point) A fish tank initially contains 15 liters of pure water. Brine of constant, but unknown, concentration of salt is flowi

Drupady [299]

Answer:

a. $\dfrac{dx}{dt} = 6\frac{2}{3} \cdot c$

b. $x(t) = 6\frac{2}{3} \cdot c \cdot t$

c. $c = \dfrac{3}{8} \ g/L$

Step-by-step explanation:

a. The volume of water initially in the fish tank = 15 liters

The volume of brine added per minute = 5 liters per minute

The rate at which the mixture is drained = 5 liters per minute

The amount of salt in the fish tank after t minutes = x

Where the volume of water with x grams of salt = 15 liters

dx = (5·c - 5·c/3)×dt = 20/3·c = $6\frac{2}{3} \cdot c \cdot dt$

$\dfrac{dx}{dt} = 6\frac{2}{3} \cdot c$

b. The amount of salt, x after t minutes is given by the relation

$\dfrac{dx}{dt} = 6\frac{2}{3} \cdot c$

$dx = 6\frac{2}{3} \cdot c \cdot dt$

$x(t) = \int\limits \, dx = \int\limits \left ( 6\frac{2}{3} \cdot c \right) \cdot dt$

$x(t) = 6\frac{2}{3} \cdot c \cdot t$

c. Given that in 10 minutes, the amount of salt in the tank = 25 grams, and the volume is 15 liters, we have;

$x(10) = 25 \ grams(15 \ in \ liters) = 6\frac{2}{3} \times c \times 10$

$6\frac{2}{3} \times c =\dfrac{25 \ grams }{10}$

$c =\dfrac{25 \ g/L }{10 \times 6\frac{2}{3} } = \dfrac{25 \ g/L}{10 \times \dfrac{20}{3} } =\dfrac{3}{200} \times 25 \ g/L= \dfrac{75}{200} \ g/L = \dfrac{3}{8} \ g/L$

$c = \dfrac{3}{8} \ g/L$

4 0

2 years ago

What is the experimental probability that you will get exactly 2 out of the three correct

Dmitry [639]

Oh ok so the answer is .666666666666 etc infinite 6s

7 0

3 years ago

What is the answer to this equation? Algebra 1 . |10-6r| -3 = 13 ??

LUCKY_DIMON [66]

Answer:

r = -1 or r = 13/3

Step-by-step explanation:

Solve for r over the real numbers:

abs(10 - 6 r) = 16

Split the equation into two possible cases:

10 - 6 r = 16 or 10 - 6 r = -16

Subtract 10 from both sides:

-6 r = 6 or 10 - 6 r = -16

Divide both sides by -6:

r = -1 or 10 - 6 r = -16

Subtract 10 from both sides:

r = -1 or -6 r = -26

Divide both sides by -6:

Answer: r = -1 or r = 13/3

8 0

2 years ago

A piece of ribbon is cut into 3 different pieces A, B and C. The ratio of the length of A to the length of B is 3 : 4. The ratio

dusya [7]

Answer:

Step-by-step explanation:

$\frac{A}{B}:\frac{3}{4}$ and $\frac{B}{C}: \frac{8}{9}$ and we are told that C is 6cm longer than A. That means that C = A + 6.

We are going to cross multiply each one of those ratios. The first one gives us

4A = 3B and the second one gives us

9B = 8C. But since C = A + 6, then

9B = 8(A + 6) and

9B = 8A + 48 and

Now we will solve the first equation above for A:

If 4A = 3B, then

$A=\frac{3}{4}B$ and will use that as a sub for A in the second equation:

$9B=8(\frac{3}{4}B)+48$ and

9B = 6B + 48 and

3B = 48 so

B = 16.

Now that we know B, we can use it to solve for A:

4A = 3(16) and

4A = 48 so

A = 12.

Then we can use that all the way back in the expression we set up for C:

C = A + 6 so

C = 12 + 6 so

C = 18

12 + 16 + 18 is the length of the string: 46cm

3 0

3 years ago