Use elimination to solve the system of equations.
4y + 3x = -6
y-x=-5
How can you eliminate the z-terms in this system?
4y + 3x = -6
Y-=-5 +
KO
Multiply by ? on both sides.
2
3
4
5
O

The equivalent expression of 225/625m⁴n⁶ is 3/5m²n³.

What is the square root?

A number y such that y = x², or a number y whose square is x, is referred to as the square root of a number x in mathematics. For instance, since 4² = 2 = 16, 4 and -4 are the square roots of 16.

We have,

225/625m⁴n⁶

So, simplifying the given equation,

= 225/625m⁴n⁶

dividing the numerator and denominator by 25 we get,

= 9/25m⁴n⁶

again by taking the square root of the numerator and denominator we get,

= 3/5m²n³.

Hence, the equivalent expression of 225/625m⁴n⁶ is 3/5m²n³.

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well, we know it was 480, then we reduce it by 50.

if we take 480 to be the 100%, what's 50 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 480 & 100\\ 50& x \end{array} \implies \cfrac{480}{50}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 48 }{ 5 } ~~=~~ \cfrac{ 100 }{ x }\implies 48x=500\implies x=\cfrac{500}{48}\implies x=\cfrac{125}{12}\implies \boxed{x\approx 10.4}[/tex]

now, the TV is only 480 - 50 = 430, then it gets reduced another 50.

if we take 430 to be the 100%, what's 50 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 430 & 100\\ 50& y \end{array} \implies \cfrac{430}{50}~~=~~\cfrac{100}{y} \\\\\\ \cfrac{ 43 }{ 5 } ~~=~~ \cfrac{ 100 }{ y }\implies 43y=500\implies y=\cfrac{500}{43}\implies \boxed{y\approx 11.6}[/tex]

hmmm the absolute change of the reductions?   that sounds like 480 - 50 - 50 = 380.

well, the overall percentage hmmm well, that's the $100 reduction total.

if we take $480 as the 100%, what's $100 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 480 & 100\\ 100& z \end{array} \implies \cfrac{480}{100}~~=~~\cfrac{100}{z} \\\\\\ \cfrac{ 24 }{ 5 } ~~=~~ \cfrac{ 100 }{ z }\implies 24z=500\implies z=\cfrac{500}{24}\implies z=\cfrac{125}{6}\implies \boxed{z\approx 20.8}[/tex]

A master's degree earner's typical weekly salary is $3,092.94.

What is the meaning of percentage?

A percentage in mathematics is a number or ratio that may be stated as a fraction of 100.In determining a percentage of a number, we should first divide it by 100 before multiply the outcome by 100. As a result, the proportion refers to a part per 100. The word "percent" refers to a fraction of one hundred. The letter "%" stands for it.

Considering that the median gross weekly wage for a bachelor's degree holder was $2,117.00.

If any one had mater degree, then an increase in the median weekly income of about 46.1%.

To find the increment multiply $2,117.00 with increase rate:

The increment is $2,117.00 × 46.1% = 2,117.00 × 46.1/100= $975.937

The total the median weekly income is

$975.937 + $2,117.00

= $3,092.937

≈ $3,092.94

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Using simplification by factorisation and division

(x² + 6x + 9)/(x² - 9) = (x + 3)/(x - 3) and (3x² - 9)/(x² - x - 6) = 3x/(x + 2)

To simplify the equations, we shall factorize both the numerator and the denominator, and divide through by a common factor.

for the equation (x² + 6x + 9)/(x² - 9);

the numerator:

x² + 6x + 9 = x² + 3x + 3x + 9

x² + 6x + 9 = x(x + 3) +3(x + 3)

x² + 6x + 9 = (x + 3)(x + 3)

the denominator:

x² - 9 = x² - 3²

x² - 9 = (x + 3)(x - 3) {difference of two squares}

(x² + 6x + 9)/(x² - 9) = (x + 3)(x + 3)/(x + 3)(x - 3)

divide through by the common factor (x + 3)

(x² + 6x + 9)/(x² - 9) = (x + 3)/(x - 3)

For the equation; (3x² - 9)/(x² - x - 6)

the numerator:

3x² - 9 = 3x(x -3)

the denominator:

x² - x - 6 = x² -3x + 2x - 6

x² - x - 6 = x(x - 3) + 2(x - 3)

x² - x - 6 = (x + 2)(x - 3)

divide through by the common factor (x - 3)

(3x² - 9)/(x² - x - 6) = 3x/(x + 2)

Thus, (x + 3)/(x - 3) and 3x/(x + 2) are the results for simplifying (x² + 6x + 9)/(x² - 9) and (3x² - 9)/(x² - x - 6) respectively using factorization.

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Answer: 180

Step-by-step explanation:

all 3 angles equal 180 degrees if you divide by 3 each angle will be 60 degrees

The reported confidence interval will contain the population proportion of consumers 95% of the time.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.

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Answer: x : x e R and R >

Step-by-step explanation:

Answer: x = 4

Step-by-step explanation:

5x - 3 ≥ 13

Substitute x with 4

5(4) - 3 ≥ 13

20 - 3 ≥ 13

17 ≥ 13

17 is greater than or equal to 13

Answer:

  A – see below

Step-by-step explanation:

You want to identify the graph of f(x) = (x -1)/(x² -x -6).

The function can be factored as ...

  [tex]f(x) = \dfrac{x-1}{(x-3)(x+2)}[/tex]

The numerator is zero when x=1, so that is where the x-intercept lies.

The denominator is zero for x=-2 and x=3, so those are the locations of the vertical asymptotes.

The graph that has vertical asymptotes at x=-2 and x=3, and an x-intercept of x=1 is Graph A.

<95141404393>

JK is a midsegment of triangle FGH. Hence, the values of x and y are 18 and 14 respectively.

A triangle's midsegment is a line segment that connects the midpoints or centers of two of its opposite or adjacent sides.

Given that, JK is a midsegment of triangle FGH.

Also the values of:

FG = 28

FJ = x

JH = 10

JK = y

As, JK is midsegment of FG, we have:

JK = FG / 2

y = 28 / 2

y = 14

So, the value of y could be 14.

Also, FG = 28

FJ + JH = FG

10+x = 28

x = 28 - 10

x = 18

So, the value of x could be 18.

Hence, the values of x and y are 18 and 14 respectively.

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Answer:

x=10

Y=14

Step-by-step explanation:

big ideas

Answer:

1. 2

2. 7

3. 15

4. 80

5. 70

Step-by-step explanation:

Answer:

1st question's answer is 2 x 90 = 180

2nd question's answer is 70 x 7 =490

3rd question's answer is 240 = 4 x 60

4th question's answer is 9 x 80 = 720

5th question's answer is 70 x 8 =560

The trigonometric expression (sec x - csc x) / (1 - tan x) is equivalent by trigonometric formulas and algebra properties to - sin x.

Herein we find a trigonometric expression that must be rewritten in terms of sin x by means of trigonometric formulas and algebra properties. The original expression is shown below:

(sec x - csc x) / (1 - tan x)

First, the original expression is written:

(sec x - csc x) / (1 - tan x)

Second, use the definitions of secant, cosecant and tangent:

[(1 / cos x) - (1 / sin x)] / [1 - (sin x / cos x)]

Third, use algebraic properties to simplify the expression:

[(sin x - cos x) / (sin x · cos x)] / [(cos x - sin x) / cos x]

[(sin x - cos x) · cos x] / [sin x · cos x · (cos x - sin x)]

- sin x

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Answer:

k = 44

Step-by-step explanation:

[tex]\frac{3}{4}[/tex]k = 12  Multiple both sides by [tex]\frac{4}{3}[/tex]

k = 44

Answer:

k = 44

Explanation:

You can write this into an equation, where k x 3/11 = 12. If you multiply both sides of the equation by 11 and divide by 3, you get k by itself.

k x 3/11 = 12

3k/11 = 12

3k = 132

k = 44

We know that,

By definition, no function is symmetrical about the x-axis (or any other horizontal line). Because the one flipped with respect to the horizontal violates the vertical line test.

On the other hand, functions can be symmetric about a vertical line or a point. In particular, functions symmetric about the y-axis are also "even" functions, and functions symmetric about the origin are also "odd" functions. Because of this correspondence between graph symmetry and function equality or oddness, "symmetry" in algebra is usually applied to the y-axis and the origin.

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Answer:

  yes: f(x) = 0

Step-by-step explanation:

You want to know if a function exists that is symmetrical about the y-axis and the origin.

A graph is symmetrical about the y-axis if and only if ...

  f(-x) = f(x)

A graph is symmetrical about the origin if and only if ...

  f(-x) = -f(x)

For both conditions to be met, we must have ...

  f(x) = -f(x)

  2f(x) = 0 . . . . . add f(x)

  f(x) = 0 . . . . . . . divide by 2

The graph of f(x) = 0 will be symmetrical about the y-axis and the origin. (It is the x-axis.)

Answer:

------------------

Multiply both sides by ax - 2 to clear fractions:

Comparing both sides we can guess that -8a = 24 ⇒ a = - 3, then:

We see both coefficients match, hence a = - 3 is a right choice.

The equation of each quadratic in the picture of formula and graphs attached is y=-1(x+8)^2 +9 and y=1/4*(x-6)^2 +3

What is Graph Transformation?

When a graph is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects." For instance, by simply pushing the graph of the function g(x) = x2 up by 3 units, the graph of the function f(x) = x2 + 3 is generated. graph transformations are highly useful for graphing functions without having to start from scratch since they allow you to move, extend, compress, or reflect the curve. The graph of the parent function is either "moved," "resized," or "reflected" by a graph transformation. The three primary categories of graph transformations are as follows:

A)

first of all we need to find which type of parabolic graph is it

from the picture give we can clearly see it is a x^2=-4ay type of graph

and using graph transformation formula

i.e. y= a(x-h)^2 + k

where h = -8

k=9

we get y=a(x+8)^2+9

as we know (-5,0) lie on this graph

so,

0=a(-5+8)^2+9

a=-1

so the equation is y=-1(x+8)^2 +9

B)

first of all we need to find which type of parabolic graph is it

from the picture give we can clearly see it is a x^2=-4ay type of graph

and using graph transformation formula

i.e. y= a(x-h)^2 + k

where h = 6

k=3

we get y=a(x-6)^2+3

as we know (0,12) lie on this graph

so,

12=a(0-6)^2+3

a=1/4

so the equation is y=1/4*(x-6)^2 +3

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Equations representing the total costs for plan A and B are A = 19 + 0.50x and B = 13 + 1.5x, respectively, where x is the number of movies watches.

Cost of both the plans will be equal for 6 movies.

What is a linear equation?

Given that, Wyatt is deciding between two different film streaming sites to subscribe to, plan A costs $19 per month plus $0.50 per film watched, plan B costs $13 per month plus $1.50 per film watched.

According to question,

A = 19 + 0.50x and

B = 13 + 1.5x

For costs being equal, we have,

A = B

19 + 0.50x = 13 + 1.5x

x = 6

Hence, for 6 films the costs of both the plans will be equal and equation for both the plans are A = 19 + 0.50x and B = 13 + 1.5x

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The solution for the given logarithmic expression would be x = 8.

What are the logarithms?

In mathematics, the logarithm is the inverse function of exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

Given:

  [tex]log_2(256)[/tex]

Let

            [tex]x=log_2(256)[/tex]

By using the property of logarithms we can write

          [tex]2^x=256\\\\2^x=2^8\\[/tex]

Since the bases are the same, the two expressions are only equal if the exponents are also equal.

      x = 8.

Hence, the solution for the given logarithmic expression would be x = 8.

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Answer:

Step-by-step explanation:

Reason 2: The box in the corner of the angle indicates that the angle is a right angle, which is 90 degrees.

Statement 3:

m<abd +m<dbc=m<abc

Answer:

12 km

Step-by-step explanation:

4.4 * 2.727 km = 11.9988   ( using a calculator)

              since the smallest factor (4.4)  has only 2 significant digits , your answer should be rounded to only 2 S.D.      so   = 12 km

By ratios ,orange = 15 , apple = 10 , coconut = 20 are needed to make 45 liters of this cocktail.

What does the math ratio mean?

When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. A proportion is an equation that sets two ratios at the same value.

                   As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls)

orange = 3

apple = 2

coconut = 4

total = 9

orange =  3/9  * 45  = 15

 apple = 2/9  *  45  = 10

coconut = 4/9  * 45  = 20

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The complete question is -

In a fruit cocktail, the ratio of orange juice to apple juice to coconut milk is 3:2:4, respectively. How much of each type is needed to make 45 liters of this cocktail?

- The null hypothesis Is: [tex]$H_0: \mu=4.5$[/tex]

- The alternative hypothesis Is: [tex]$H_1: \mu \neq 4.50$[/tex]

- The test statistic is: t=-0.43

- The p-value of the test is of 0.6684.

What is p-value?

The p-value Is of 0.6684>0.05, which means that we can conclude that the population of student course evaluations has a mean equal to [tex]\mathbf{4 . 5 0}$.[/tex]

We are going to test If the mean Is equals to 4.50, thus, the null hypothesis Is:

[tex]H_0: \mu=4.5[/tex]

At the alternative hypothesis, we test If the mean Is different to 4.50, that is:

[tex]H_1: \mu \neq 4.50[/tex]

Since we have the standard devlation for the sample, the t-distribution is used. The value of the test statistic Is:

[tex]t=\frac{\pi-\mu}{\frac{\sqrt{n}}{\sqrt{n}}}$$[/tex]

For this problem:

[tex]$$\begin{aligned}& t=\frac{4.30-1.5}{\frac{2.21}{\sqrt[3]{80}}} \\& t=-0.43\end{aligned}$$[/tex]

We are testing If the mean is dlfferent from a value, thus, the p-value of test is found using a two-talled test, wlth t=-0.43 and [tex]$80-1=79 \mathrm{df}$[/tex].

Using a t-distribution calculator, the [tex]$\mathrm{p}$[/tex]-value is of [tex]$\mathbf{0 . 6 6 8 4}$[/tex].

The p-value is of 0.6684 > 0.05, which means that we can conclude that the population of student course evaluations has a mean equal to 4.50.

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The area of the rectangular yellow region is of:

30 cm².

The area of a rectangle of base b and height h is obtained as the multiplication of these dimensions, as follows:

Area = base x height.

From the image given at the end of the answer, these dimensions are given as follows:

Then the area of the yellow region is calculated as follows:

Area = 10 x 3 = 30 cm².

The problem asks to obtain the area of the rectangular region, considering that:

The region is given by the image shown at the end of the answer.

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let's convert the mixed fractions to improper fractions and then let's proceed.

[tex]\stackrel{mixed}{12\frac{3}{35}}\implies \cfrac{12\cdot 35+3}{35}\implies \stackrel{improper}{\cfrac{423}{35}} ~\hfill \stackrel{mixed}{5\frac{31}{35}}\implies \cfrac{5\cdot 35+31}{35}\implies \stackrel{improper}{\cfrac{206}{35}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]12\frac{3}{35}~~ + ~~x~~ = ~~5\frac{31}{35}\implies \cfrac{423}{35}+x=\cfrac{206}{35}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{35}}{35\left( \cfrac{423}{35}+x \right)=35\left( \cfrac{206}{35} \right)} \\\\\\ 423+35x=206\implies 35x=-217 \\\\\\ x=\cfrac{-217}{35}\implies x=\cfrac{-31}{5}\implies {\Large \begin{array}{llll} x=- 6\frac{1}{5} \end{array}}[/tex]

to convert an improper fraction like -31/5 to a mixed fraction, well, first off, we nevermind the sign, so we only use 31/5 and then we divide 31 ÷ 5.

hmm 31 ÷ 5 gives us a quotient of 6, and a remainder of 1, we put the quotient upfront and the remainder as the numerator, with the old denominator and sign back in.

Answer:

x= -4 y= -1

6x - y = - 23

-y=-23-6x

y=6x+23, use this to plug in for y in the second equation.

2x + 5y = -13

2x + 5(6x+23) = -13

2x+30x+115=-13

x= -4, use this to plug in for x in the first equation.

6x - y = - 23

6(-4)-y=-23

-24-y=-23

-y=-23+24

-y=1

y= -1

Step-by-step explanation: not doing this to steal points

Answer:

here is your solution.

Step-by-step explanation:

x=4 & y=1

Answer:

k is greater or equal to -5

Step-by-step explanation:

[tex] - 5 \leqslant k[/tex]

here, -5 is on the left side of the inequality sign which means it is less than or equal to k.

each pound of shimp costs $13.99

The statement is true , that the given sample follows binomial distribution.

If a random variable has two alternative outcomes (success or failure), it has a binomial distribution.

Each draw must be separate from the ones that came before it.

There is a set number of drawn components.

We randomly select 15 students, and since the sample size of 15 is less than 10% of the total population, we can assume that each draw is independent.

Because X has a binomial distribution, success is determined by whether the student is left-handed (failure is determined by whether the student is not left-handed).

The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for success or failure as the possible outcomes of an experiment.

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Based on the SAS, SSS, and the transitive property of congruence, the reason why ΔABC ≅ ΔGHJ is because of option B.

The SAS is a triangle theorem that states that two triangles are congruent if they both have two pairs of congruent sides and a pair of included congruent angles.

On the other hand, the SSS states that two triangles that have three pairs of congruent sides are equal.

The transitive property of congruence states that if two triangles are congruent to a third triangle, then all three triangles are congruent to each other.

Based on the SSS, triangle ABC is congruent to triangle DEF.

Based on the SAS, triangle DEF is congruent to GHJ.

Therefore, based on the transitive property of congruence, triangle ABC is congruent to triangle GHJ.

Therefore, the reason why ΔABC ≅ ΔGHJ is because of the reason given in option B.

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The required simplified solution of the given expression is given as √3(√7 - 2).

Given that,
To determine the simplified solution of the √(√21-2√3)²

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
= √(√21-2√3)²
=√21-2√3       (√a² = a)
= √3(√7 - 2)

Thus, the required simplified solution of the given expression is given as √3(√7 - 2).

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