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
Anton [14]
1 year ago
8

Solve the system of equations below using the substitution method. x = y + 7 / 2 4x − 2y = 8

Mathematics
1 answer:
Verdich [7]1 year ago
3 0

Answer:

y = -3

x = \frac{1}{2}

Step-by-step explanation:

4(y + \frac{7}{2}) - 2y = 8  Distribute the 4.  Multiply everything in the parentheses by 4

4y + 14 - 2y = 8           4(\frac{7}{2}) = \frac{28}{2} = 14  Combine the like terms 4y and -2y

2y + 14 = 8         Subtract 14 from both sides

2y =  -6               Divide both sides by 2

y = -3  

Plug -3 in for y in either original equation.

4x - 2y = 8

4x -2(-3) = 8

4x + 6 = 8    Subtract 6 from both sides

4x = 2  Divide both sides by 4

x = \frac{2}{4} = \frac{1}{2}

Check:

x = y + \frac{7}{2}

\frac{1}{2} = -3+ \frac{7}{2}

\frac{1}{2} = \frac{-6}{2} + \frac{7}{2}

\frac{1}{2} = \frac{1}{2}

4x - 2y = 8

4(\frac{1}{2}) - 2(-3) = 8

2 + 6 = 8

8 = 8

You might be interested in
A circle is graphed with its center on the origin.The area of the circle is 49 square units.What are the coordinates of the x-in
neonofarm [45]

Answer:

3.95 and -3.95

Step-by-step explanation:

To graph a circle you can use the formula or (x – h)^2 + (y – k)^2 = r^2. So substituting in the given, we get x^2+y^2=49/pi. The x intercept is when y=0. So x^2=49/pi and so

x = sqrt(49/pi) and rounding to the nearest tenth, we get 3.95 and -3.95 because it isn’t a principal square root.

3 0
3 years ago
Mike's monthly pay after taxes is $2,300.
wlad13 [49]

Step-by-step explanation:

100%=>$2,300

45%=>x

x=$2,300×45÷100=$1035

The pay left for other purposes

$2300-$1035=$1265

Or:

100%=>$2,300

55%=>x

x=$2,300×55÷100=$1265.

5 0
3 years ago
Which is the slope-intercept form of an equation for the line containing
Thepotemich [5.8K]

Answer:

The answer is letter A.

Step-by-step explanation:

y=mx+b

-3=(-1)(0)+b

-3=0+b

0 0

-3=b

y= -1x-3

6 0
3 years ago
In slope-intercept form, what is the equation of a line perpendicular to y = 2x+ 7 that passes through the point (5,8)?
vfiekz [6]

Answer:

2

y = -0.5x + 10.5

Step-by-step explanation:

put a negative sign and 1 on top of the number next to the x to get the line thats perpendicular

2

y = -0.5x + 10.5

4 0
3 years ago
Three numbers in the interval $\left[0,1\right]$ are chosen independently and at random. What is the probability that the chosen
k0ka [10]

Let a,b,c be the randomly selected lengths. Without loss of generality, suppose a[tex]P(A + B \ge C) = P(A + B - C \ge 0)

where A,B,C are independent random variables with the same uniform distribution on [0, 1].

By their mutual independence, we have

P(A=a,B=b,C=c) = P(A=a) \times P(B=b) \times P(C=c)

so that the joint density function is

P(A=a,B=b,C=c) = \begin{cases}1 & \text{if }(a,b,c)\in[0,1]^3 \\ 0 & \text{otherwise}\end{cases}

where [0,1]^3=[0,1]\times[0,1]\times[0,1] is the cube with vertices at (0, 0, 0) and (1, 1, 1).

Consider the plane

a + b - c = 0

with (a,b,c)\in\Bbb R^3. This plane passes through (0, 0, 0), (1, 0, 1), and (0, 1, 1), and thus splits up the cube into one tetrahedral region above the plane and the rest of the cube under it. (see attached plot)

The point (0, 0, 1) (the vertex of the cube above the plane) does not belong the region a+b-c\ge0, since 0+0-1=-1. So the probability we want is the volume of the bottom "half" of the cube. We could integrate the joint density over this set, but integrating over the complement is simpler since it's a tetrahedron.

Then we have

\displaystyle P(A+B-C\ge0) = 1 - P(A+B-C < 0) \\\\ ~~~~~~~~ = 1 - \int_0^1\int_0^{1-a}\int_{a+b}^1 P(A=a,B=b,C=c) \, dc\,db\,da \\\\ ~~~~~~~~ = 1 - \int_0^1 \int_0^{1-a} (1 - a - b) \, db \, da \\\\ ~~~~~~~~ = 1 - \int_0^1 \frac{(1-a)^2}2\,da \\\\ ~~~~~~~~ = 1 - \frac16 = \boxed{\frac56}

5 0
2 years ago
Other questions:
  • Is the following graph a function?
    6·1 answer
  • Write out the sample space for the given experiment. Use the following letters to indicate each choice: M for mushrooms, A for a
    12·1 answer
  • What formula is used to find the circumference of a circle?<br><br> isn't it C = 2πr ?
    8·2 answers
  • A researcher took a random sample of 100 students from a large university. She computed a 95% confidence interval to estimate th
    5·1 answer
  • Find the value of 1÷3x when X=1​
    10·1 answer
  • A particular rocket taking off from the earth surface uses fuel at a constant rate of 12.5 gallons per minute the rocket initial
    11·1 answer
  • At basketball practice you made 21 out of 80 shots.
    10·2 answers
  • write each of the following word names as mixed if you purchase a hundred items that cost $0.25 each how much would the items co
    6·1 answer
  • Scrooge-
    14·1 answer
  • If c = 25 and B = 50 degrees, find a.
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!