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
Novosadov [1.4K]
3 years ago
15

What is the result of substituting for y in the bottom equation y=x+3 y=x^2+2x-4

Mathematics
1 answer:
8_murik_8 [283]3 years ago
6 0

The solutions are (2.1925, 5.1925) and (-3.1925, -0.1925)

<em><u>Solution:</u></em>

Given that,

y = x + 3 ------- eqn 1\\\\y = x^2 + 2x - 4  ----- eqn 2

<em><u>We have to substitute eqn 1 in eqn 2</u></em>

x + 3 = x^2 + 2x - 4

\mathrm{Switch\:sides}\\\\x^2+2x-4=x+3\\\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\\\x^2+2x-4-3=x+3-3\\\\\mathrm{Simplify}\\\\x^2+2x-7=x\\\\\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}\\\\x^2+2x-7-x=x-x\\\\\mathrm{Simplify}\\\\x^2+x-7=0

\mathrm{Solve\:with\:the\:quadratic\:formula}\\\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=1,\:c=-7\\\\x =\frac{-1\pm \sqrt{1^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}

x = \frac{-1 \pm \sqrt{ 1 + 28}}{2}\\\\x = \frac{ -1 \pm \sqrt{29}}{2}

x = \frac{ -1 \pm 5.385 }{2}\\\\We\ have\ two\ solutions\\\\x = \frac{ -1 + 5.385 }{2}\\\\x = 2.1925

Also\\\\x = \frac{ -1 - 5.385 }{2}\\\\x = -3.1925

Substitute x = 2.1925 in eqn 1

y = 2.1925 + 3

y = 5.1925

Substitute x = -3.1925 in eqn 1

y = -3.1925 + 3

y = -0.1925

Thus the solutions are (2.1925, 5.1925) and (-3.1925, -0.1925)

You might be interested in
Name two pairs of adjacent angles and two pairs of vertical angles in the figure
insens350 [35]
Adjacent angles :

IGJ and IGH

KGL and LGM

vertical angles :

JGK and HGM

IGJ and MGL


hope this helps

7 0
3 years ago
A naval engineer uses the function, P, to analyze the effects of water pressure on submarines. The function P(d) measures the pr
saw5 [17]

The function that the naval engineer uses related P (pressure) and d (depth of ocean).

<em>Is there any restriction on the domain ( d: depth of the ocean)? Yes!</em>

The domain would be from 0 (at sea level or 0 depth) until the depth of the ocean (which is not infinite). Hence, we can write:

0\leq d\leq DepthOfSeaFloor

Choice D is the correct one.


ANSWER: D

5 0
3 years ago
Read 2 more answers
Twenty more than four times a number is equal to the difference between 139 and three times the number. Find the number.
Lady_Fox [76]

Answer:

x = 17

Step-by-step explanation:

First, let's turn this into an equation:

twenty more ( +20 ) than four times a number ( 4x ) is equal ( = ) to the difference ( - ) between 139 and 3 times the number ( 3x ).

4x + 20 = 139 - 3x

Now let's solve:

Subtract 20 from each side:

4x = 119 - 3x

Add 3x to each side:

7x = 119

Divide each side by 7:

x = 17

5 0
2 years ago
The polygons in each pair are similar. Find the missing side length / first one has 4 &amp;x and second one has 12&amp;18
sergiy2304 [10]

Answer:

x = 6

Step-by-step explanation:

To find the missing side, write a proportion using side lengths from each similar shape. A proportion is an equation that sets equal two ratios.

\frac{4}{12}=\frac{x}{18}

Find x by cross multiplying numerator and denominator of each fraction.

4(18) = 12x

72 = 12x

6 = x

4 0
3 years ago
Which transformation would take Figure A to Figure B?
Charra [1.4K]
A reflection over the x-axis
5 0
3 years ago
Other questions:
  • Which player has best plus minus record -8,-3,-4,
    15·1 answer
  • Find the indicated derivative If f(x) = x^3 , find f’(-4)
    14·1 answer
  • Karen wants to buy a $22.50 jacket that is marked 20% off. Select from the drop-down menu to correctly complete the sentence. Th
    12·2 answers
  • What is a decmil for 9/10
    10·2 answers
  • Help on 10-13 please I will give brainliest and thanks
    12·2 answers
  • How do I solve -4|2-3|+2|-3+1|?
    9·1 answer
  • How do you write three hundred thousand five thousand sixty three in standard form
    5·1 answer
  • A rope is 225 centimeters long. You need the rope to be 112 meters long. How many centimeters should you cut off?
    9·2 answers
  • Find C.<br> Round to the nearest tenth
    15·1 answer
  • Sole The Equation<br><br> 0.75q²=108<br><br> 55 POINTS
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!