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3 years ago

Leticia charges $8 per hour to babysit. She babysat Friday night for 4 hours,

2 answers:

6 0

For this case we have that the variable "x" represents the number of hours that Leticia uses to take care of children on Saturday.

IF on Friday I use 4 hours ($ 8 each) and on Saturday "x" hours ($ 8 each) obtaining a profit of $ 72, we have the following equation:

$8 (4 + x) = 72$

We apply distributive property:

$32 + 8x = 72\\8x = 72-32\\8x = 40\\x = \frac {40} {8}\\x = 5$

So, on Saturday she spent 5 hours.

Answer:

$8 (4 + x) = 72\\x = 5$

FinnZ [79.3K]3 years ago

6 0

Answer:

Option A.

Option C.

Step-by-step explanation:

Let be "x" the amount of hours Leticia babysat on Saturday.

We know that she charges $8 per hour to babysit, she babysat Friday night for 4 hours and the total amount of money she earned on those two days was $72. Knowing this, we can set up the followin equation models this situation:

$8(4+x)=72$

Finally, we must solve for "x":

$8(4+x)=72\\\\32+8x=72\\\\8x=72-32\\\\8x=40\\\\x=\frac{40}{8}\\\\x=5$

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Which expression is equivalent to −76x+92?

KATRIN_1 [288]

Answer:

4(−19x+23) is equivalent to the expression

Step-by-step explanation:

5 0

3 years ago

Given: △ABC, m∠A=60°

kakasveta [241]

Answer:

perimeter = 28.68 cm

area = 15.48 cm^2

Step-by-step explanation:

1. complete the angles in the triangle. sum of all the angles in a triangle is 180 degrees.

therefore 180 - (60 +45) = 75

angle at B is 75 degrees

2. find the sides of the triangle using the sine formula for triangle

sin A/a = sin B/b = sin C/c

we have the angle at C and the side opposite C is also give, we can use that with any other

3. sin A/a = sin C/c

sin 60/a = sin 45/8

make a subject

a = 9.78 cm

4. sin A/a = sin B/b

sin 60/9.78 = sin 75/b

make b subject

b = 10.90 cm

with the three sides, we know that perimeter is the length around an object

adding all the lengths together will give the perimeter

perimeter = 10.90 + 8 + 9.78

= 28.68 cm

5. to find the area we need to find the high of the triangle since the expression for the area of a triangle is $area =\frac{1}{2} bh$

6. bisecting the side BC will give have as 4.89 cm

7. using Pythagoras theorem we can find the height of the traingle

c^2 = a^2 + b^2

8^2=(4.89)^2 + b^2

64 - 23.9121 = b^2

b= $\sqrt{40.0879}$

b =6.33 cm

insert this into the formula above will give the value for area

which is 15.48 cm^2

area = 1/2 (4.89)(6.33)

7 0

3 years ago

Find a power series for the function, centered at c. g(x) = 4x x2 2x − 3 , c = 0

BartSMP [9]

The power series for given function $g(x)=\frac{4x}{(x-1)(x+3)}$ is $g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)$

For given question,

We have been given a function g(x) = 4x / (x² + 2x - 3)

We need to find a power series for the function, centered at c, for c = 0.

First we factorize the denominator of function g(x), we have:

$\Rightarrow g(x)=\frac{4x}{(x-1)(x+3)}$

We can write g(x) as,

$\Rightarrow g(x)=\frac{1}{x-1}+\frac{3}{x+3}\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1+\frac{x}{3} }\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1-(-\frac{x}{3} )}\\$