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3 years ago

StartFraction (negative 7) squared Over (negative 7) Superscript negative 1 EndFraction

Mathematics

2 answers:

Elan Coil [88]3 years ago

8 0

Answer:

-343

Step-by-step explanation:

Given the expression: $\dfrac{(-7)^2}{(-7)^{-1}}$

You will notice that the terms in the numerator and denominator have the same base (-7).

This makes it very easy to simplify by applying the division law of indices.

$\dfrac{a^x}{a^y} =a^{x-y}$

Therefore:

$\dfrac{(-7)^2}{(-7)^{-1}}=(-7)^{2-(-1)}\\=(-7)^{2+1}\\=(-7)^3\\=-7 X -7 X -7\\=-343$

abruzzese [7]3 years ago

6 0

Answer:

-343

Step-by-step explanation:

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Solve each inequality. <br> 1. 5x + 2 <17

butalik [34]

Answer:

x<3

Step-by-step explanation:

5x+2<17

Subtract 2 from both sides.

5x<17−2

Subtract 2 from 17 to get 15.

5x<15

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

x=15/5

Divide 15 by 5 to get 3.

x<3

8 0

3 years ago

Find two consecutive odd integers such that the square of the first added to 3 times the second, is 24. Part a: Define the varia

fgiga [73]

Given:

There are two consecutive odd integers such that the square of the first added to 3 times the second, is 24.

To find:

Part a: Define the variables.

Part b: Set up an equations that can be solved to find the integers.

Part c: Find the integers.

Solution:

Part a:

Let x be the first odd integers. Then next consecutive odd integer is $x+2$ , because the difference between two consecutive odd integers is 2.

Part b:

Square of first odd integers = $x^2$

Three times of second odd integers = $3(x+2)$

It is given that the sum of square of first odd integers and three times of second odd integers is 24. So, the required equation is:

$x^2+3(x+2)=24$

Part c:

The equation is:

$x^2+3(x+2)=24$

It can be written as:

$x^2+3x+6=24$

$x^2+3x+6-24=0$

$x^2+3x-18=0$

Splitting the middle term, we get

$x^2+6x-3x-18=0$

$x(x+6)-3(x+6)=0$

$(x-3)(x+6)=0$

$x=3,-6$

-6 is not an odd integer, so $x=3$ and the first odd integer is 3.

Second odd integer = $x+2$

= $3+2$

= $5$

Therefore, the two consecutive odd integers are 3 and 5.

8 0

3 years ago

Large cheese pizzas cost $5 each and large one-topping pizzas cost $6 each.

dsp73

Answer:

$T=5c+6d$

Step-by-step explanation:

The correct question is

Large cheese pizzas cost $5 each and large one-topping pizzas cost $6 each.

Write an equation that represents the total cost, T, of c large cheese pizzas and d large one-topping pizzas.

Let

T -----> the total cost

c ----> the number of large cheese pizzas

d ---> the number of large one -topping pizzas

we know that

The total cost (T) is equal to the number of large cheese pizzas (c) multiplied by it cost ($5) plus the number of large one -topping pizzas (d) multiplied by it cost ($6)

$T=5c+6d$

8 0

3 years ago

Riders on a roller coaster must be at least 48 in tall my son is only 35 inches write an inequality to show how much can he grow

Deffense [45]

35+x>=48, x is amount he needs to grow

5 0

3 years ago

three quarts of latex enamel paint will cover about 270 square feet of wall surface. how many quarts will you need to cover 350

hichkok12 [17]

Answer:

Kitchen - 3.89 quarts or 3 $\frac{8}{9}$ quarts of latex enamel

Bathroom - 1.12 quarts or 1 $\frac{1}{9}$ quarts of latex enamel

Step-by-step explanation:

270 feet² for every 3 quartz.

We need how much ft² 1 quart can cover.

So,

270 ÷ 3 = 90 ft²

Every 1 quart covers about 90 ft² of wall.

For kitchen we need to cover 350 ft².

So,

350 ÷ 90 = 3.89 quarts or 3 $\frac{8}{9}$ quarts of latex enamel

For bathroom we need to cover 100 ft².

So,

100 ÷ 90 = 1.12 quarts or 1 $\frac{1}{9}$ quarts of latex enamel

8 0

3 years ago