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Butoxors [25]
3 years ago
8

the system of equations is graphed on the coordinate plane y=-1/2x-1 and y=1/4x-4 enter the coordinates of the solution to the s

ystem of equations in the boxes​
Mathematics
2 answers:
pochemuha3 years ago
7 0

Answer:

The coordinates are ( 4, -3).

Step-by-step explanation:

We can find the coordinates by solving the 2 equations

y =  1/4x-4

y = -1/2x-1

As both left sides of the equation are y we can say:

-1/2x-1 = 1/4x-4

-1/2x - 1/4x = -4 + 1

-3/4 x = -3

x = -3 * -4/3

x = 4.

- and y = 1/4(4) - 4 = -3.

dusya [7]3 years ago
3 0

Answer:

  • (4, -3)

Step-by-step explanation:

<em>See the attached graph.</em>

<u>The intersection of the lines gives us the solution:</u>

  • (4, -3)

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The graph of the parabola is now vertically translating by 3 units up
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The area of a gymnasium is (27x + 18) square units. Factor 27x + 18 to find possible dimensions of the gymnasium.
Veronika [31]

Answer:

Dimension of gymnasium= 9 units and (3x+2) units.

Step-by-step explanation:

We have been given the area of a gymnasium is 27x+18 square units. We are asked to find possible dimensions of gymnasium by factoring our given expression for area of gymnasium.

Let us factor our greatest common factor of our given expression. We can see that 9 is the GCF of our given expression.

(9\times 3x+9\times 2)

Upon factoring out 9 from our given expression we will get,

9(3x+2)

Therefore, the possible dimensions of the gymnasium will be 9 units and (3x+2) units as we will get the same area for gymnasium by multiplying these both dimensions.  

8 0
3 years ago
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15X^2+20x factor greatest common monomial
velikii [3]
Both 15 and 20 can be divided evenly by 5, so 5 is the greatest common monomial:  5(3x^2 + 4x)  or  5x(3x + 4) 
4 0
3 years ago
Consider the question of whether the home team wins more than half of its games in the National Basketball Association. Suppose
spayn [35]

Answer:

0.0037 = 0.37% probability that the home team would win 65% or more of its games in a simple random sample of 80 games

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

The home team therefore wins 50% of its games

This means that p = 0.5

Determine the probability that the home team would win 65% or more of its games in a simple random sample of 80 games

Sample of 80 means that n = 80 and, by the Central Limit Theorem:

\mu = p = 0.65

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.5*0.5}{80}} = 0.0559

This probability is 1 subtracted by the pvalue of Z when X = 0.65. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.65 - 0.5}{0.0559}

Z = 2.68

Z = 2.68 has a pvalue of 0.9963

1 - 0.9963 = 0.0037

0.0037 = 0.37% probability that the home team would win 65% or more of its games in a simple random sample of 80 games

7 0
2 years ago
I WILL GIVE BRAINLEST!!! (6 points!)
vlada-n [284]

Answer:

OPTION A: 2x + 3y = 5

Step-by-step explanation:

The product of slopes of two perpendicular lines is -1.

We rewrite the given equation as follows:

2y = 3x + 2

⇒ y = $ \frac{3}{2}x + 1 $

The general equation of the line is: y = mx + c, where 'm' is the slope of the line.

Here, m = $ \frac{3}{2} $.

Therefore, the slope of the line perpendicular to the line given = $ \frac{-2}{3} $ because $ \frac{3}{2} \times \frac{-2}{3} = -1 $.

To determine the equation of the line passing through the given point and a slope we use the Slope - One - point formula which is:

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The point is: (x₁, y₁) = (-2, 3)

Therefore, the equation is:

y - 3 = $ \frac{-2}{3} $(x + 2) $

⇒ 3y - 9 = -2(x + 2)

⇒ 3y - 9 = -2x - 4

⇒ 2x + 3y = 5 is the required equation.

6 0
3 years ago
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