Determine the solution to the system of equations
x - 6y + 4z = -12
x + y = 0
2x + 2y = 0

Answer:

D. The longest side is twice as long as the shortest side.

Step-by-step explanation:

Given one angle is 30° and another is 60°, the third must be 90°, making a Special 30-60-90 triangle. In a 30-60-90 triangle, the hypotenuse (longest side) is twice (two times) as long as the shortest side.

Answer:

6.40

Step-by-step explanation:

For this we will divide,

look below for a explanation

Purchase Price:

$64

Discount:

(64 x 90)/100 = $57.60

Final Price:

64 - 57.60 = $6.40

The value of the test statistic is given as follows:

z = 2.17.

There is sufficient evidence to say that the mean wait time for customers is longer than 3.50 minutes.

The value of the test statistic is obtained using the z-distribution, as the population standard deviation is known in the context of this problem.

The equation that gives the test statistic is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which the parameters of the equation are listed as follows:

In the context of this problem, the values of these parameters are given as follows:

[tex]\overline{x} = 3.94, \mu = 3.50, \sigma = 1.30, n = 41[/tex]

(all values are taken from the text).

Then the numeric value of the test statistic is obtained as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{3.94 - 3.50}{\frac{1.30}{\sqrt{41}}}[/tex]

z = 2.17.

There is sufficient evidence to say that the mean wait time for customers is longer than 3.50 minutes, as the critical value for the right-tailed test with 95% confidence is of z = 1.645, and the test statistic is greater than this.

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The equation of the line passing through the given point that is

parallel to the given lines are;

16) y = ²/₃x + 6

17) y = ²/₇x - 1

18) y = ³/₄x - 11

19) y = -4x + 12

16) We are given the equation of a line as;

y = ²/₃x - 2

The general equation of a line in slope intercept form is ;

y = mx + c

where;

m is slope

c is y-intercept

Thus, equation passing through (-3, 4) is;

y - 4 = ²/₃(x - (-3))

y - 4 = ²/₃x + 2

y = ²/₃x + 6

17) We are given the equation of a line as;

-2x + 7y = 14

7y = 2x + 14

y = ²/₇x + 2

Thus, equation passing through (-7, -3) is;

y - (-3) = ²/₇(x - (-7))

y + 3 = ²/₇x + 2

y = ²/₇x - 1

18) We are given the equation of a line as;

3x - 4y = 16

4y = 3x - 16

y = ³/₄x - 4

Thus, equation passing through (8, -5) is;

y - (-5) = ³/₄(x - 8)

y + 5 = ³/₄x - 6

y = ³/₄x - 11

19) We are given the equation of a line as;

4x + y = 7

y = -4x + 7

Thus, equation passing through (2, 4) is;

y - 4 = -4(x - 2)

y - 4 = -4x  + 8

y = -4x + 12

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Based on the solution written by Jack to solve for x, the statement which is true is that: B. 6 is an extraneous solution because it creates a zero in the denominator.

In Mathematics, an extraneous solution can be defined as a type of solution (root) to a squared equation or transformed equation that is not a direct solution (root) of the original equation.

This ultimately implies that, extraneous solutions are numerical values that are obtained when we solve equations that are not solutions to the original equation as shown below:

1/(x - 5) = (x + 3)/(x - 6) - 9/(x² - 11x + 30)

1/(x - 5) = (x + 3)/(x - 6) - 9/(x - 6)(x - 5)

When x = 6, the denominator of the given equation becomes;

1/(x - 5) = (x + 3)/(x - 6) - 9/(6 - 6)(x - 5)

1/(x - 5) = (x + 3)/(x - 6) - 9/(0)(x - 5)

1/(x - 5) = (x + 3)/(x - 6) - 9/0

1/(x - 5) = (x + 3)/(x - 6) - undefined.

Therefore, six (6) is an extraneous solution solution to the original equation because it creates an undefined expression.

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In the transformation of a 2-dimensional shape on the coordinate plane. (x, y) → (-y, -x), the statement which is true is that: d. Transformation preserves distance and angle measure both.​

In Mathematics, a transformation can be defined as the movement of a point from its original (initial) position to a final (new) location. This ultimately implies that, when an object is transformed, all of its points would be transformed as well.

Based on the transformation rule (x, y) → (-y, -x), we can reasonably infer and logically deduce that it represents or models a rotation of the geometric shape, followed by a reflection, which both preserves distance and angle measure based on these transformation rules:

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Complete Question:

Look at the transformation of a 2-dimensional shape on the coordinate plane. (x, y) → (-y, -x). Which statement is true?

a. Transformation preserves only distance.

b. Transformation preserves only angle measures.

c. Transformation preserves neither distance nor angle.

d. Transformation preserves distance and angle measure both.​

The rules of proof is that every statement should be justified and never assume things when proofing in contradiction

The basic rules of proofs are as followings:

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The required range is [0,∞]

All values, or inputs, constitute a function's domain, while all values, or outputs, constitute its range.

When examining a graph, the range of the function is from up to down, and the domain refers to all of the values on the graph from right to left.

Therefore , the range of the function on the graph of  all real numbers extends from zero to positive infinity.

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P is equal to 8700% for population x time in hours.

P is equal to 8700% for population x time in hours. 2Ae%5E%28kx%29

K's model must be solved. ln%28p%29=ln%288700%29%

2Bkx%2Aln%28e%

29\skx%

2A1=ln%28p%29-ln%288700%

29\sk=%281%

2Fx%29%

28ln%28p%29-ln%288700%29%29

Replace the point (1,10000).

k=%281%

2F1%29%

28ln%2810000%

29-ln%288700%

29%

29\sk=ln%2810000%

29-ln%288700%

29 k=0.13926, which you might only desire to three or maybe even two significant figures.

You may just enter 10000% if you want p after two hours.

And it SHOULD be the same as 8700% (2810000%2F8700%).

Just give it a shot and see, 2Ae%5E%280.139%2A2%29. More particular, the model is highlighted by p=8700%. 2Ae%5E%280.139% 2Ax%29% 29.

Determine how long to double x.

Take the logs on both sides, then find x.

To put it more simply, start with this form: 2=1%2Ae%5E%280.13926%2Ax%29

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Multiple of 11 cant be prime number.

Prime numbers are those that are bigger than 1. Only the number itself and factor 1 are present. This indicates that no number other than 1 and the number itself may be used to divide these numbers without leaving a residue.

Now that multiples of 11 are being questioned, such as 22, 33, and 44, can they be prime numbers?

We know that prime numbers are those that can only be divided by themselves and by one , but since these multiples of 11 are all divisible by 11, they cannot be prime numbers.

The multiple of 11 cannot thus be a prime number.

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The equation that can be used to find x is

3x + 6 = 2x + 9

Option E is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Lydia started with 6 charms and bought 3 more packs.

Claudia started with 9 charms and bought 2 more packs.

If each pack had x charms.

This can be written as,

Lydia:

Number of charms = 6 + 3x

Claudia:

Number of charms = 9 + 2x

Now,

Lydia and Claudia have the same number of charms in their collections.

This can be written as,

6 + 3x = 9 + 2x

3x + 6 = 2x + 9

Thus,

The equation that can be used to find x is

3x + 6 = 2x + 9

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Answer:

Subtract 5

Step-by-step explanation:

72 , 67, 62, 57,..

    Each term is obtained by subtracting 5 from the previous term.

72 - 5 = 67

67 - 5 = 62

62 - 5 = 57

Answer:

Slope: positive

m = 3

Step-by-step explanation:

the slope is positive because the line goes up from left to right.

to find m:

m = (y2 - y1) divided by (x2 - x1)

x1 = -1, y1 = -4, x2 = 0, y2 = -1 <--taken from the points in the diagram

plug in the points:

m = (-1 - (-4)) divided by (0 - (-1))

m = (3) divided by (1)

m = 3

so, your m = 3

The probability for each event are

[A] -  36/1320

[B] -  36/1320

[C] -  36/1320

[D] -  The probability doesn’t change in any order.

        P(A) = n(A)/n(S)

        where -

        n(A) = Number of outcomes favorable to event A.

       n(S) = Total number of outcomes

We have Chelsey who puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.

[A] -

{3/12} x {3/11} x {4/10} =

36/1320

[B] -

{3/12} x {4/11} x {3/10}

36/1320

{C} -

{4/12} x {3/11} x {3/10}

36/1320

D) The probability doesn’t change in any order.

Therefore, the probability for each event are -

[A] -  36/1320

[B] -  36/1320

[C] -  36/1320

[D] -  The probability doesn’t change in any order.

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Answer: 18

D

Step-by-step explanation:

The constant of proportionality is y/x, not x/y, which is what your friend found.

X= 1

y=18

18/1=18

The 12 kinds of polygons are:

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

Hendecagon

Dodecagon

Tridecagon

Tetradecagon

Polygons:

A polygon is a closed shape figure that has a minimum of three sides and three vertices.

Poly → many

gon → angle

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1,384,190...............

The sixth chapter's Brother 0.66 pages were read.

According to the order of operations, you should perform multiplication and division first, going from left to right, before adding and subtracting.

Add and subtract from left to right while continuing to multiply and divide. the next step is to add and subtract from left to right.

Assumed the question is how many pages are in each chapter.

Let it be x:

6x + 8 = 12

6x = 4

x = 4 /6

x = 0.66.

The sixth chapter's Brother 0.66 pages were read.

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By using Unitary method, it can be calculated that

a) Quantity of butter Trevor uses = 200 [tex]\times[/tex] 2 = 400 g

   Quantity of oats Trevor uses = 200 [tex]\times[/tex] 3 = 600 g

b) 900 g of oats is required to make 16 flapjacks

What is Unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Here Unitary method will be required

a) Let Trevor use x g Syrup, 2x g butter and 3x g oats

Trevor uses 200 g syrup

So x = 200

i) Quantity of butter Trevor uses = 200 [tex]\times[/tex] 2 = 400 g

ii) Quantity of oats Trevor uses = 200 [tex]\times[/tex] 3 = 600 g

b) To make 8 flapjacks 150 g of syrup is used

   To make 1 flapjack [tex]\frac{150}{8}[/tex] g of syrup is used

   To make 16 flapjacks [tex]\frac{150}{8} \times 16[/tex] g of syrup is used

   To make 16 flapjacks 300g of syrup is used

   To make 16 flapjacks 300 [tex]\times[/tex] 3 g of oats is used

   To make 16 flapjacks 900 g of oats is used

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By solving a linear inequation, it can be concluded that

The sweater can be worn comfortably

What is a linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by > . < , ≤, ≥

A one degree inequation is known as linear inequation.

Here, the given linear inequation is

[tex]|t - 56| \leq 6\\t - 56 \geq -6 \ or \ t - 56 \leq 6\\t \geq 56 - 6 \ or \ t \leq 56+6\\t \geq 50 \ or \ t \leq 62\\50 \leq t \leq 62[/tex]

As 53° F lies between 50 and 62, the sweater can be worn comfortably

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Answer:

835786543225644323567

Answer:0.5

Step-by-step explanation:

here you go

Answer: 65 °

Step-by-step explanation:

Let x = measure of a base angle

Base angles of an isosceles triangle are equal

Sum of interior angles of a triangle is always 180:

x + x + (2x - 80) = 180

4x - 80 = 180

4x = 260

x = 65

Yes, two triangles can be proven congruent by SAS(Side angle side) congruence.

If any pair of comparable sides and their included angles are the same in both triangles, then the triangles are said to be congruent.

There are five ways to determine whether two triangles are congruent. It's one of them (SAS). Congruent Triangles provides a list. If any two comparable sides and their included angle in both triangles are same, then the triangles are congruent.

Why does this matter?

Due to the congruence of the triangles:

Third sides also have identical angles.

the other two complementary angles are equal

Two triangles, congruent since all three sides are the same length, but one flipped and rotatedCongruent triangles can be turned and/or mirror images of each other (reflected).

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The graph of the expression x² > -18 does not exist

From the question, we have the following inequality expression that can be used in our computation:

x2 > -18

This expression can be rewritten properly

So, we have the following representation

x² > -18

Next, we take the square roots of both sides of the expression

This gives

√x² > √-18

Evaluate the exponents

So, we have

x > 3√-2

The radical is a complex number

This means that the inequality expression cannot be graphed (because of the presence of the complex expression)

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Answer:

25 people

Step-by-step explanation:

10 people will be vaccinated for 2hrs

10 = 2

y people will be vaccinated for 5hrs

y = 5

(To find y we need to cross multiply)

10 = 2

y = 5

2y= 50

y=50/2

y=25

:- 25 people will be vaccinated in 5hrs.

Lets check if our answer is correct let us make 5 hrs our unknown x

10 = 2

25 = x

(cross multiply)

25×2=10x

50=10x

x=5hrs

so our answer is correct.

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Answer: 2 and 2/3

Step-by-step explanation: To divide these mixed numbers, I would first rewrite them as improper fractions.

You should be familiar with how do this and if you aren't, send me a comment below and I can give you a quick review.

So 5 and 2/3 becomes 17/3 and 2 and 1/8 becomes 17/8.

This gives us 17/3 ÷ 17/8.

When we divide fractions, we just change the division sign

to multiplication and take the reciprocal (flip) the second fraction.

So we have 17/3 · 8/17.

before multiplying, we can cross-cancel the 17's by dividing by their greatest common factor of 17 to get 1.

So we have 1/3 · 8/1 which is 8/3.

Now since 3 goes into 8 twice, our we have 2 as our whole fraction.

Since there is 2/3 left over, we have a fraction of 2/3.

So our final answer is 2 and 2/3.

The Linear equation that represents the above situation is given by

x + 3x + 15 = 63

A linear Equation is a Mathematical expression that is used to calculate an unknown number of values or any unknown quantity. Here we use variables to represent the unknown numbers.    

Here given that

Luke and Cade have started running

Luke runs 15 more miles than thrice of that of number of miles Cade runs

Since we don't know the number of miles run by Cade

Let us assume that Cade runs x miles

=> Number of miles run by Cade = x miles

From the given data,

The number of miles run by Luke will be = 3x + 15

=> Number of miles run by Luke and Cade = x + 3x + 15

Given that the total mile run by Luke and Cade =  63 miles  

=> x + 3x + 15 = 63

Therefore,

The Linear equation that represents the above situation is given by  

x + 3x + 15 = 63

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Answer:

x = 7

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

Given equation:

[tex]y=-2(x-7)^2+11[/tex]

The given equation is in vertex form.

The axis of symmetry of a parabola with a vertical axis of symmetry is:

where h is the x-value of the vertex.

As the vertex of the given equation is (7, 11), the axis of symmetry is:

Answer:

25 + 12.5v ≤ 170

Step-by-step explanation: