PLEASE HELP!!! give an explanation if you can

Let f(x) = (5)^x+1 .Evaluate f (-3) without using a calculator

rewona [7]

Answer:

$f\left(-3\right)=\frac{126}{125}$

Step-by-step explanation:

Given

$f\left(x\right)\:=\:\left(5\right)^x+1$

Putting x = -3 to find f(-3)

$f\left(-3\right)\:=\:\left(5\right)^{\left(-3\right)}+1$

as

$5^{-3}=\frac{1}{125}$ ∵ $\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}$

so

$f\left(-3\right)=\frac{1}{125}+1$

$\mathrm{Convert\:element\:to\:fraction}:\quad \:1=\frac{1\cdot \:125}{125}$

$f\left(-3\right)=\frac{1\cdot \:\:125}{125}+\frac{1}{125}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$f\left(-3\right)=\frac{1\cdot \:\:125+1}{125}$

$f\left(-3\right)=\frac{126}{125}$ ∵ $1\cdot \:125+1=126$

Thus,

$f\left(-3\right)=\frac{126}{125}$

6 0

3 years ago

Lesson 16

Goshia [24]

Answer:

546 ft³

Step-by-step explanation:

In the figure attached, the top view of the pool is shown. It can be decomposed into a trapezoid which height is 12 ft and which bases are 9 ft and 11 ft; and a rectangle which height is 1.5 ft and and it base is 11 ft.

Area of the trapezoid: (9 + 11)/2 * 12 = 120 ft²

Area of the rectangle: 1.5*11 = 16.5 ft²

Total area: 120 + 16.5 = 136.5 ft²

Volume of the pool: Total area * deep = 136.5 * 4 = 546 ft³

6 0

2 years ago

100 points PLEASE ANSWER ASAP thank you so much

uysha [10]

Answer:

X elevated to 21/25

Step-by-step explanation:

Exponent law say you have to multiplied the exponents:

(3/5)*(7/5) =

21/25

The mistake was using sumatory instead multiplication.

Regards

7 0

1 year ago

Read 2 more answers

A home-made baseball diamond is in the shape of a square. The distance from base to base is 80 feet because of space constraints

Lelu [443]

Call x the distance from home plate to second base.

There is a right triangle formed by homeplate, first base and second base. The sides of this triangle are 80 feet and 80 feet. The hypothenuse meets Pythagoras theorem:

x^2 = 80^2 + 80^2 = 2(80)^2
x = 80√2

Then the answer is the option D.

3 0

2 years ago

Read 2 more answers

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

amm1812

Answer:

The solution of this system of equations is (3 , -8)

Step-by-step explanation:

The given system is

x + 2y = -13

12x + 5y = -4

We make x the subject of the first equation and put it into the second:

$x = - 13 - 2y$

We put this expression for x into the second equation

12(-13-2y)+5y=-4

-156-24y+5y=-4

-24y+5y=-4+156

-19y=152

y=-8

We substitute y=-8 into x=-13-2y to get:

$x = - 13 - 2( - 8) = 3$

The solution of this system of equations is (3 , -8)

3 0

2 years ago