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3 years ago

-4x+9y=9 x-3y=-6 Solve using Elimination

Mathematics

1 answer:

taurus [48]3 years ago

8 0

Answer:

Step-by-step explanation:

Multiply the first equation by 4,and multiply the second equation by 1.

4(x−3y=−6)

1(−4x+9y=9)

Becomes:

4x−12y=−24

−4x+9y=9

Add these equations to eliminate x:

−3y=−15

Then solve−3y=−15for y:

−3y=−15 (Divide both sides by -3)

y=5

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

x−3y=−6

Substitute5foryinx−3y=−6:

x−(3)(5)=−6

x−15=−6(Simplify both sides of the equation)

x−15+15=−6+15(Add 15 to both sides)

x=9

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Classify the following triangle. Check all that apply.

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Answer:

A and B

Step-by-step explanation:

It's definitely not equilateral or isosceles because none of the side lengths are equal. Therefore, it is scalene. Since all of the angles are acute, it's not obtuse or right, therefore it is acute.

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4 years ago

& Consider the national income model Y=C+I C = ayx + 50 1= 24 Y=Y-I T= 20

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3 years ago

Solve rational Equation Please Show Full Steps Please!

pochemuha

Answer:

x=1

Step-by-step

Step 1:

Simplify x/x2

Dividing exponential expressions :

1.1 x1 divided by x2 = x(1 - 2) = x(-1) = 1/x1 = 1/

Equation at the end of step 1:

2 1 1

(((—+1)-—)-1)-((2•—)-1) = 0

x x x

STEP 2:Rewriting the whole as an Equivalent Fraction:

2.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using x as the denominator :

1 1 • x

1 = — = —————

1 x

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2 - (x) 2 - x

——— = ———

x x

Equation at the end of step 2:

2 1 (2-x)

(((—+1)-—)-1)-————— = 0

x x x

STEP 3:

Simplify 1/x

Equation at the end of step 3:

2 1 (2 - x)

(((— + 1) - —) - 1) - ——————— = 0

x x x

STEP4:

Simplify: 2/x

Equation at the end of step 4:

2 1 (2 - x)

(((— + 1) - —) - 1) - ——————— = 0

x x x

STEP 5:

Rewriting the whole as an Equivalent Fraction :

5.1 Adding a whole to a fraction

Rewrite the whole as a fraction using x as the denominator :

1 1 • x

1 = — = —————

1 x

Adding fractions that have a common denominator :

5.2 Adding up the two equivalent fractions

2 + x x + 2

————— = —————

x x

Equation at the end of step 5:

(x + 2) 1 (2 - x)

((——————— - —) - 1) - ——————— = 0

x x x

STEP 6:Adding fractions which have a common denominator :

Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(x+2) - (1) x + 1

——————————— = —————

x x

Equation at the end of step 6:

(x + 1) (2 - x)

(——————— - 1) - ——————— = 0

x x

STEP 7:

Rewriting the whole as an Equivalent Fraction :

7.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using x as the denominator :

1 1 • x

1 = — = —————

1 x

Adding fractions that have a common denominator :

7.2 Adding up the two equivalent fractions

(x+1) - (x) 1

——————————— = —

x x

Equation at the end of step 7:

1 (2 - x)

— - ——————— = 0

x x

STEP 8:

Adding fractions which have a common denominator :

8.1 Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

1 - ((2-x)) x - 1

——————————— = —————

x x

Equation at the end of step 8:

x - 1

————— = 0

STEP 9:

When a fraction equals zero :

9.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

x-1

——— • x = 0 • x

Now, on the left hand side, the x cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

x-1 = 0

.2 Solve : x-1 = 0

Add 1 to both sides of the equation :

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One solution was found :

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3 years ago

We are promoting a new book. The price was originally set at $26 and an average of 825 books were sold monthly. After research,

NARA [144]

Answer:

Step-by-step explanation:

The price that will maximize sales and the number of projected sales can be found in the vertex of a quadratic equation. We need to use the puzzle of the info given to somehow create a set of biomials that can be multiplied together to get this quadratic. We will separate the number of books sold from the price of the books in a table of sorts:

# of books $ per book

We know that a number of 825 books was sold when the price per book was $26.

# of books $ per book

825 $26

If we have a $1 decrease in price per book, let's use as our unknown the number of $1 decreases in price per book. In other words, x = # of $1 decreases.

If we decrease the price per book by $1, we are decreasing the price by 1x which is 1 dollar.

If, when we decrease the price per book by $1, we are selling the original 825 books plus another 75 books at the $1 decrease per book. Now we have in our table

# of books $ per book

825 + 75x 26 - x

Under # of books, the expression in words says, "we are still selling 825 books, but now we are adding an additional 75 books per month when we lower the cost $1 per book".

Under $ per book, the expression in words says, "the cost per book is the starting cost minus $1".

To get the quadratic that results from this, multiply the 2 expressions together to get

$P(x)=-75x^2+1125x+21450$ or, if we want to keep things positive:

$P(x)=75x^2-1125x-21450$

We can factor a 75 out of each term to make the numbers a bit smaller:

$P(x)=75(x^2-15x-286)$

Use the quick formulas for h and k to solve for the vertex. You could complete the square to get there, but once you know these formulas, there's no need to go through the very long long process of completing the square.

$h=-\frac{b}{2a}$ and $k=c-\frac{b^2}{4a}$

These formulas come from the quadratic equation. h here will give us the number of $1 decreases we need to maximize k, the profit from this amount decreases.

Our a = 1, b = -15 and c = -286. Filling in for h:

$h=-\frac{-15}{2}$ and

$h=\frac{15}{2}$ so

h = 7.5 That is the number of decreases

Filling in for k:

$k=-286-\frac{(-15)^2}{4}$ and

$k=-286-\frac{225}{4}$ so

k = 342.25 That is the maximum projected sales from this amount of decreases in price.

But we are not done. We need to use the 7.5 to find out what the best price would be to maximize the sales and therefore, the profit. Going back to our cost expression, 26 - x, using 7.5 for x:

26 - 7.5 = $18.50

This means that if we sell books at $18.50 rather than $26, we can expect to earn $342.25 per month in book sales.

4 0

3 years ago

A TV show, Lindsay and Tobias, recently had a share of 10, meaning that among the TV sets in use, 10% were tuned to that sh

liberstina [14]

Answer:

0.43 = 43% probability that none of the households are tuned to Lindsay and Tobias.

0.57 = 57% probability that at least one household is tuned to Lindsay and Tobias.

0.813 = 81.3% probability that at most one household is tuned to Lindsay and Tobias.

Step-by-step explanation:

For each household, there are only two possible outcomes. Either they are tuned to Lindsay and Tobias, or they are not. The probability of a household being tuned to Lindsay and Tobias is independent of other households. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$n = 8, p = 0.1$

Find the probability that none of the households are tuned to Lindsay and Tobias.

This is $P(X = 0)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{8,0}.(0.1)^{0}.(0.9)^{8} = 0.43$

0.43 = 43% probability that none of the households are tuned to Lindsay and Tobias.

Find the probability that at least one household is tuned to Lindsay and Tobias.

Either none is tuned, or at least one is. The sum of the probabilities of these events is 100%. From the first question

p + 43 = 100

p = 57%

0.57 = 57% probability that at least one household is tuned to Lindsay and Tobias.

Find the probability that at most one household is tuned to Lindsay and Tobias.

$P(X \leq 1) = P(X = 0) + P(X = 1)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{8,0}.(0.1)^{0}.(0.9)^{8} = 0.43$

$P(X = 0) = C_{8,1}.(0.1)^{1}.(0.9)^{7} = 0.383$

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.43 + 0.383 = 0.813$

0.813 = 81.3% probability that at most one household is tuned to Lindsay and Tobias.

5 0

4 years ago