Data is collected from a:

Solve the radical equation.

Scrat [10]

Answer:

there are no extraneous solutions to the equation

Step-by-step explanation:

Given

$\sqrt{8x+9}$ = x + 2 ( square both sides )

8x + 9 = (x + 2)² ← expand

8x + 9 = x² + 4x + 4 ( subtract 8x + 9 from both sides )

0 = x² - 4x - 5 ← in standard form

0 = (x - 5)(x + 1) ← in factored form

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 1 = 0 ⇒ x = - 1

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions.

x = 5 : $\sqrt{8(5)+9}$ = $\sqrt{49}$ = 7

right side = 5 + 2 = 7

left side = right side ⇒ x = 5 is a solution

x = - 1 : $\sqrt{8(-1)+9}$ = $\sqrt{1}$ = 1

right side = - 1 + 2 = 1

left side = right side ⇒ x = - 1 is a solution

There are no extraneous solutions

4 0

3 years ago

Read 2 more answers

A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 88 feetfeet less than th

Y_Kistochka [10]

Answer: The length of the ladder is 20 feet.

Step-by-step explanation:

Given : A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 8 feet less than the length of the ladder.

Mathematically,

Let x be the length of the ladder then

Distance from ground to the top of the ladder = x- 8

If distance from the bottom of the ladder to the building is 16 feet.

Since ground makes right angle with building , so the triangle made by ladder should be a right triangle.

By Pythagoras theorem of right triangle , we hae

$(Hypotenuse)=(Perpendicular)^2+(Base)^2$

$\Rightarrow\ x^2=(x-8)^2+16^2\\\\\Rightarrow\ x^2=x^2+64-16x+256\ [\text{Using identity :} (a-b)^2=a^+b^2-2ab]\\\\\Rightarrow 0=-16x+320\\\\\Rightarrow\ 16x=320\\\\\Rightarrow\ x=\dfrac{320}{16}=20$

Hence, the length of the ladder is 20 feet.

4 0

3 years ago

I need to know this soon idk what it is plz help

stepladder [879]

Answer:

16. 24.85

17. 0.9 seconds

Step-by-step explanation:

16. $10.95+$14.20=$25.15

$50-$25.15=$24.85

17. 5.75 seconds-4.85seconds=0.9 seconds

Your welcome, please mark me Brainliest!

8 0

4 years ago

If 11250 = m(600) + b and 7650 = m(400) + b, how do I find the values of b and m? I forgot how to compare when I have two differ

Lelu [443]

Answer:

$b=450$ and $m=18$

Step-by-step explanation:

This exercise is an example of linear system equations. A system of linear equations is a set of (linear) equations that have more than one unknown. The unknowns appear in several of the equations, but not necessarily in all of them. What these equations do is relate the unknowns to each other.

The easy way to solve this problem is by using the reduction method.The reduction method consists of operating between the equations, such as adding or subtracting both equations, so that one of the unknowns disappears. Thus, we obtain an equation with a single unknown.

Ordering the equations as a system equations.

$\left \{ {{600m+b=11250} \atop {400m+b=7650}} \right.$

Using the reduction method, let's substract the second equation with the first equation, in order to clear m.

600m + b = 11250

-400m - b = -7650

200m = 3600 --------> m = 3600/200 -----> m = 18

We can substitute the value of m in any of the two equations to obtain the unknow b.

Let's substitute the value of m in the second equation.

400(18) + b = 7650

7200 + b = 7650 -----> b = 7650 - 7200 -------> b = 450

We can check this values in both equations.

600m + b = 11250 -----> 600(18) + 450 = 11250

400m + b = 7650 -----> 400(18) + 450 = 7650

Satisfying the result of both equations.

6 0

4 years ago

Maria and her friend ride their bikes. They start at 12:47 and end at 2:29. How long did they ride their bikes for?

IRINA_888 [86]

Answer:

Their bide ride was 1 hour and 42 minutes

4 0

3 years ago