1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mylen [45]
3 years ago
6

Which of the following are solutions to the equation below?

Mathematics
1 answer:
scoundrel [369]3 years ago
6 0

Answer:

The correct options for the solution values are:

  • x=2\sqrt{2}-5
  • x=-2\sqrt{2}-5

Step-by-step explanation:

Given the expression

x^2+10x+25=8

Subtract 25 from both sides

x^2+10x+25-25=8-25

Simplify

x^2+10x=-17

Add 25 or 5² to both sides

x^2+10x+5^2=8

as

x^2+10x+5^2=\left(x+5\right)^2

so the expression becomes

\left(x+5\right)^2=8

\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}

solve

x+5=\sqrt{8}

Subtract 5 from both sides

x+5-5=2\sqrt{2}-5

x=2\sqrt{2}-5

solve

x+5=-\sqrt{8}

Subtract 5 from both sides

x+5-5=-2\sqrt{2}-5

x=-2\sqrt{2}-5

Therefore, the solution to the equation

x=2\sqrt{2}-5,\:x=-2\sqrt{2}-5

Hence, the correct options for the solution values are:

  • x=2\sqrt{2}-5
  • x=-2\sqrt{2}-5

You might be interested in
What is the angle e in the triangle below? (Hint: Use an inverse trigonometric
yuradex [85]

Answer:

A

Step-by-step explanation:

sin θ=3/8

θ=sin ^{-1}(3/8)

≈22.02 °

5 0
2 years ago
Read 2 more answers
Please help me I don't understand
sashaice [31]
Answer is B because the red has 2 columns and 7 rows that is how you get 2/7 And the blue has 3 rows and 5 columns making 3/5
If you multiply these together you get the doubled colored (red/blue over the total of squares)
6/35
The other way which most likely I think you should choose this way is D why?? Because there are out of the red are 3 out of 7 rows that are combined with blue and 2 out of 5 of the blue column are combined with red This makes the 3/7×2/5 = with the 6/35 (combined colors/total)
3 0
2 years ago
What is the end behavior for f(x)=4x^4+2x^3-13x^2-14x+24?
Tpy6a [65]

Answer:

This means that f(x)→∞ as x→−∞ and f(x)→∞ as x→∞.

Step-by-step explanation:

Since the leading term of the polynomial (the term in a polynomial which contains the highest power of the variable) is x4, then the degree is 4, i.e. even, and the leading coefficient is 1, i.e. positive.

This means that f(x)→∞ as x→−∞ and f(x)→∞ as x→∞.

8 0
3 years ago
Solve x^3-7x^2+7x+15​
ruslelena [56]

Step-by-step explanation:

\underline{\textsf{Given:}}

Given:

\mathsf{Polynomial\;is\;x^3+7x^2+7x-15}Polynomialisx

3

+7x

2

+7x−15

\underline{\textsf{To find:}}

To find:

\mathsf{Factors\;of\;x^3+7x^2+7x-15}Factorsofx

3

+7x

2

+7x−15

\underline{\textsf{Solution:}}

Solution:

\textsf{Factor theorem:}Factor theorem:

\boxed{\mathsf{(x-a)\;is\;a\;factor\;P(x)\;\iff\;P(a)=0}}

(x−a)isafactorP(x)⟺P(a)=0

\mathsf{Let\;P(x)=x^3+7x^2+7x-15}LetP(x)=x

3

+7x

2

+7x−15

\mathsf{Sum\;of\;the\;coefficients=1+7+7-15=0}Sumofthecoefficients=1+7+7−15=0

\therefore\mathsf{(x-1)\;is\;a\;factor\;of\;P(x)}∴(x−1)isafactorofP(x)

\mathsf{When\;x=-3}Whenx=−3

\mathsf{P(-3)=(-3)^3+7(-3)^2+7(-3)-15}P(−3)=(−3)

3

+7(−3)

2

+7(−3)−15

\mathsf{P(-3)=-27+63-21-15}P(−3)=−27+63−21−15

\mathsf{P(-3)=63-63}P(−3)=63−63

\mathsf{P(-3)=0}P(−3)=0

\therefore\mathsf{(x+3)\;is\;a\;factor}∴(x+3)isafactor

\mathsf{When\;x=-5}Whenx=−5

\mathsf{P(-5)=(-5)^3+7(-5)^2+7(-5)-15}P(−5)=(−5)

3

+7(−5)

2

+7(−5)−15

\mathsf{P(-5)=-125+175-35-15}P(−5)=−125+175−35−15

\mathsf{P(-5)=175-175}P(−5)=175−175

\mathsf{P(-5)=0}P(−5)=0

\therefore\mathsf{(x+5)\;is\;a\;factor}∴(x+5)isafactor

\underline{\textsf{Answer:}}

Answer:

\mathsf{x^3+7x^2+7x-15=(x-1)(x+3)(x+5)}x

3

+7x

2

+7x−15=(x−1)(x+3)(x+5)

\underline{\textsf{Find more:}}

Find more:

6 0
3 years ago
Classify the following triangle. Check all that apply
Kamila [148]

Answer:

The triangle is obtuse, and isosceles.

Step-by-step explanation:

The triangle is obtuse because there is an angle above 90 degrees, which  is 104 degrees. The triangle is also isosceles due to the two lines in the triangle which indicate that the size of each side are equal to each other. For a triangle to be isosceles, there have to be at least two sides equal to each other, and in this case the triangle has those two equal sides.

5 0
3 years ago
Other questions:
  • What is the x-intercept of y=6x-7
    11·2 answers
  • what is the slope intercept form of the linear equation with a graph that passes through (-2,2) and is perpendicular to the grap
    11·1 answer
  • Damaris is replacing the carpet in her living room. How much carpet will she need?​
    14·1 answer
  • A truck rental company charges $25 per day plus $.32 per mile. If you paid $265, how many miles did you drive?
    14·1 answer
  • For 7 and 8, find the maximum or minimum point of the parabola​
    10·1 answer
  • We wish to give a 90% confidence interval for the mean value of a normally distributed random variable. We obtain a simple rando
    5·1 answer
  • Jonah’s restaurant bill comes to $50.65, and he leaves a 20% tip, then pay 7.25%tax of the original bill. What is Jonah’s total
    12·2 answers
  • Graph the line with the equation y= -2/5x -4<br><br><br>NEED ASAP PLS​
    11·1 answer
  • Simplify the expression:<br> 4(2 + 5q) = 1
    15·1 answer
  • What's the value of y ?<br><br><img src="https://tex.z-dn.net/?f=y%20%3D%20%20%28%20%7B%20-%202%20%7D%29%5E%7B2%7D%20" id="TexFo
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!