Emir started out a card game with 500 points. for every hand he won, he gained 100 points

How to solve y=-x+4; y=2x-8 using substitution?

Novosadov [1.4K]

In this problem why is the easiest to substitute.
Just set the equations equal to each other because they both equal y

-x + 4 = 2x - 8
(You want to get all the x's to one side so add x to each side)
4 = 3x - 8
(next add 8 to both sides)
12 = 3x
(lastly divide 3 from both sides)
4 = x
You have got your x so now it is time to find that y just replace x to either of the two equations
y = 2(4) -8 or y = -(4) + 4
y = 8 - 8 y = 0
y = 0
Final Answer: y=0, x=4

4 0

4 years ago

Write an equation in slope intercept form, passes through (-1,-10), parallel to y=7

gregori [183]

The line y=7 is a horizontal line with a slope of 0.
Slope intercept form of
y=mx+b

would be
y-y1=m(x-x1)
m=0 and point of (-1,-10)
y-(-10)=0

y=-10

3 0

3 years ago

A cylinder has a radius of 2x + 3 and height of 3x + 2. Which polynomial in standard form best describes the total volume of the

Bogdan [553]

Answer:

$v = \pi {r}^{2} h \\ v = \pi {(2x + 3)}^{2} (3x + 2) \\ v = \pi(4 {x}^{2} + 12x + 9)(3x + 2) \\ v =( 12 {x}^{3} + 36 {x}^{2} + 27x + 8 {x}^{2} + 24x + 18)\pi \\ v =( 12 {x}^{3} + 44 {x}^{2} + 51x + 18)\pi$

6 0

3 years ago

Consider a multiple choice exam with 10 questions, and with 4 possible answers to each question (labeled A, B, C, and D). 1a. Wh

mrs_skeptik [129]

Answer:

(1a) 9.54e-07 (1b) 0.9437 (2) $10^8$

Step-by-step explanation:

We have n = 10 questions. For each question in the multiple choice exam, we can choose the correct answer with probability p = 0.25 or an incorrect answer with probability q = 0.75 (just by guessing). Besides is reasonable to believe that questions are independent. Let X be the random variable that represents the number of correct answers (just by guessing) observed during the n = 10 questions, so, X have a binomial distribution.

(a) The probability of getting a perfect score just by guessing is

$P(X = 10) = 10C10(0.25)^{10}(0.75)^{10-10} = 9.54e-07$

(b) The probability of getting at least one question correct, just by guessing

$P(X\geq1) = \sum_{x=1}^{x=10}10Cx(0.25)^{x}(0.75)^{(10-x)} = 0.9437$

2. Each RUID is 9-digits long, there are 10 digits, each of the nine positions for a digit of the RUID has 10 posibilities except the 4th and 5th positions which must be both 0. For the multiplication rule there can be $(10)^3(1)(1)(10)^5 = 10^8$ different RUIDS.

3 0

3 years ago

What is the value of x

Crank

Answer:

Step-by-step explanation:

Looking at the diagram,

Line DT is parallel to line line BM, therefore, triangle DHT is similar to triangle BHM. This means that

DH/DB = TH/MH

DH = 15 + 6 = 21

TH = 9 + x

Therefore

(9 + x)/21 = 9/6

Cross multiplying, it becomes

6(9 + x) = 21 × 9 = 189

54 + 6x = 189

Subtracting 54 from the left hand side and the right hand side of the equation, it becomes

6x + 54 - 54 = 189 - 54

6x = 135

Dividing the left hand side and the right hand side of the equation by 6, it becomes

6x/6 = 135/6

x = 22.5

5 0

4 years ago

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