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4 years ago

Help, please! Solve 2a + 3b = 5 b = a - 5

Mathematics

2 answers:

Ahat [919]4 years ago

8 0

Answer: A = 4, B = -1

Step-by-step explanation: First, you write the equation out and substitute in a - 5 for b. Then you distribute the 3 to the a and the -5 to get "2a + 3a - 15". Then you add the 15 to both sides, and add the 2a and the 3a to get "5a = 20" Then you multiply by 5 to get a = 4. And if you're trying to find b you just do 4 - 5 to get -1.

damaskus [11]4 years ago

7 0

Answer:

a=2

Step-by-step explanation:

a=b+5

b=a−5

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Sally went to the clearance rack at a department store and found a shirt she wanted to buy. The shirt was $36.00 and is on sale

jeka57 [31]

Answer:

33.34%.

Step-by-step explanation:

Given that,

The actual price of the shirt = $36

Price on sale = $24

We need to find the percent of the decrease. The formula for the percentage is given by :

$\%=\dfrac{|\text{actual value-estimated value}|}{\text{actual value}}\times 100$

Putting all the values,

$\%=\dfrac{24-36}{36}\times 100\\\\=33.34\%$

So, the percentage decrease in the price of the shirt is 33.34%.

6 0

3 years ago

How is a coordinate grid a useful way to describe exactly where an object is?

Elenna [48]

Answer:

because you can show the exact points an object is at

Step-by-step explanation:

For example: A car goes x many miles in y minutes. You can easily see how many miles the car goes in y minutes.

Hope this helps!

6 0

3 years ago

Simplify this please

Ugo [173]

Answer:

$\frac{12q^{\frac{7}{3}}}{p^{3}}$

Step-by-step explanation:

Here are some rules you need to simplify this expression:

Distribute exponents: When you raise an exponent to another exponent, you multiply the exponents together. This includes exponents that are fractions. $(a^{x})^{n} = a^{xn}$

Negative exponent rule: When an exponent is negative, you can make it positive by making the base a fraction. When the number is apart of a bigger fraction, you can move it to the other side (top/bottom). $a^{-x} = \frac{1}{a^{x}}$ , and to help with this question: $\frac{a^{-x}b}{1} = \frac{b}{a^{x}}$ .

Multiplying exponents with same base: When exponential numbers have the same base, you can combine them by adding their exponents together. $(a^{x})(a^{y}) = a^{x+y}$

Dividing exponents with same base: When exponential numbers have the same base, you can combine them by subtracting the exponents. $\frac{a^{x}}{a^{y}} = a^{x-y}$

Fractional exponents as a radical: When a number has an exponent that is a fraction, the numerator can remain the exponent, and the denominator becomes the index (example, index here ∛ is 3). $a^{\frac{m}{n}} = \sqrt[n]{a^{m}} = (\sqrt[n]{a})^{m}$

$\frac{(8p^{-6} q^{3})^{2/3}}{(27p^{3}q)^{-1/3}}$ Distribute exponent

$=\frac{8^{(2/3)}p^{(-6*2/3)}q^{(3*2/3)}}{27^{(-1/3)}p^{(3*-1/3)}q^{(-1/3)}}$ Simplify each exponent by multiplying

$=\frac{8^{(2/3)}p^{(-4)}q^{(2)}}{27^{(-1/3)}p^{(-1)}q^{(-1/3)}}$ Negative exponent rule

$=\frac{8^{(2/3)}q^{(2)}27^{(1/3)}p^{(1)}q^{(1/3)}}{p^{(4)}}$ Combine the like terms in the numerator with the base "q"

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)}q^{(1/3)}}{p^{(4)}}$ Rearranged for you to see the like terms

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)+(1/3)}}{p^{(4)}}$ Multiplying exponents with same base

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(7/3)}}{p^{(4)}}$ 2 + 1/3 = 7/3

$=\frac{\sqrt[3]{8^{2}}\sqrt[3]{27}p\sqrt[3]{q^{7}}}{p^{4}}$ Fractional exponents as radical form

$=\frac{(\sqrt[3]{64})(3)(p)(q^{\frac{7}{3}})}{p^{4}}$ Simplified cubes. Wrote brackets to lessen confusion. Notice the radical of a variable can't be simplified.

$=\frac{(4)(3)(p)(q^{\frac{7}{3}})}{p^{4}}$ Multiply 4 and 3

$=\frac{12pq^{\frac{7}{3}}}{p^{4}}$ Dividing exponents with same base

$=12p^{(1-4)}q^{\frac{7}{3}}$ Subtract the exponent of 'p'

$=12p^{(-3)}q^{\frac{7}{3}}$ Negative exponent rule

$=\frac{12q^{\frac{7}{3}}}{p^{3}}$ Final answer

Here is a version in pen if the steps are hard to see.

5 0

3 years ago

7 whole number 2/3 -4 5/6 + 2 3/8

denis-greek [22]

Im not sure ask ur teacher

4 0

2 years ago

10. The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46

Zarrin [17]

Answer:

hope this helps

Step-by-step explanation:

The sum of the digits of a three-digit number is 11.

If the digits are reversed, the new number is 46 more than five times the old number.

If the hundreds digit plus twice the tens digit is equal to the units digit, then what is the number?

Write an equation for each statement:

"The sum of the digits of a three-digit number is 11."

x + y + z = 11

The three digit number = 100x + 10y + z

The reversed number = 100z + 10y + x

" If the digits are reversed, the new number is 46 more than five times the old number."

100z + 10y + x = 5(100x + 10y + z) + 46

100z + 10y + x = 500x + 50y + 5z + 46

combine on the right

0 = 500x - x + 50y - 10y + 5z - 100z + 46

499x + 40y - 95z = -46

"the hundreds digit plus twice the tens digit is equal to the units digit,"

x + 2y = z

x + 2y - z = 0

Three equations, 3 unknowns

x + y + z = 11

x +2y - z = 0

-----------------Addition eliminates z

2x + 3y = 11

From the 2nd equation statement, we know that the 1st original digit has to be 1

2(1) + 3y = 11

3y = 11 - 2

3y = 9

y = 3 is the 2nd digit

then

1 + 3 + z = 11

z = 11 - 4

z = 7

137 is the original number

Check solution in the 2nd statement

If the digits are reversed, the new number is 46 more than five times the old number."

731 = 5(137) + 46

731 = 685 + 46

7 0

3 years ago