Given the following augmented matrix which represents a linear system, solve the linear system for z, y, and z. If there is an infinite number of solutions then express the solutions in terms of z as the parameter. If there isn't a solution, then be sure to put "no solution in each answer. 20 75-7 -6-7 1 -36 -3 4-4 18 I 0

Answer: -5

Step-by-step explanation:

Answer:

-5 is the correct answer

Transitive property of segment congruence states that if two segments are congruent to the same segment, then they are congruent to each other. Mathematically, it can be written as, if AB ≅ JK and JK ≅ ST, then AB ≅ ST.

In the given problem, it is given that AB is congruent to JK and JK is congruent to ST. Therefore, it can be concluded that AB is congruent to ST because of the transitive property of segment congruence, i.e., AB ≅ JK ≅ ST ⇒ AB ≅ ST.Let’s have a brief discussion on how transitive property of segment congruence holds true.

It is based on the fact that segments that are equal to the same segment are equal to each other. Therefore, if AB ≅ JK, then AB and JK have the same length. Similarly, if JK ≅ ST, then JK and ST have the same length. Now, since AB and JK have the same length, and JK and ST also have the same length, it can be concluded that AB and ST are also equal. Hence, AB ≅ ST is proved using the transitive property of segment congruence.

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Answer:

Step-by-step explanation:

B is congruent to JK

Defintion of transitive property of segment

Answer:

check: 50+160+130+20 = 360

50:160 = 5 : 16

Step-by-step explanation:et the smaller of the unknown angles be 5x and the larger of the two be 16x

so 130+20+5x+16x = 360

21x = 210

x = 10

so the two missing angles are 50° and 160°

check: 50+160+130+20 = 360

50:160 = 5 : 16

The expression is -10 > 2x+ 14.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

Negative ten is no less than two times a number plus 14

let the number x

so, two times a number plus 14

= 2x+ 14

and, Negative ten is no less than two times a number plus 14

-10 > 2x+ 14

hence, the expression is -10 > 2x+ 14.

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Answer:

she cant

Step-by-step explanation:

Sarkis cannot draw a triangle with these side lengths. Therefore, option A is correct.

Given that, a triangle with sides measuring 4 ft, 10 ft, and 16 ft.

What are the conditions to construct a triangle?

In the triangle, the sum of any two sides is always greater than the third side. The difference between any two sides of the triangle is always less than the third side.

Sarkis cannot draw a triangle with these side lengths. Therefore, option A is correct.

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The correct answer about the savings account that Zoe opened, represented by the equation b(x)=675(1.045)ˣ is B. Daniella says the balance in the account increases at a rate of 4.5% each year.

An equation is a mathematical statement that two or more algebraic expressions (the combination of variables with constants and mathematical operands) are equal or equivalent.

This equation is known as the future value equation, formula, or function.

Initial investment = $675

Compound interest rate = 4.5% (0.045 x 100)

Future value factor = 1.045 (100% + 4.5%)

Based on the future value function above, we can conclude that the compound interest rate is 4.5%, which is equivalent to 0.045 as given in the equation.

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\(\huge \bf༆ Answer ༄\)

Let's solve ~

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:x + y = 15 \: \: \: \: \: (1)\)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:x - y = 3 \: \: \: \: \: (2)\)

From adding both equations, we get ~

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:x + y + x - y = 15 + 3\)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:2x = 18\)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:x = 18 \div 2\)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:x = 9\)

Now, plug the value of x in equation 1 to find the value of y ;

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:x + y = 15\)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:9 + y = 15\)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:y = 15 - 9\)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:y = 6\)

The value of y and x in the equation is 6 and 9 respectively

Given:

x + y = 15

x - y = 3

x + x = 15 + 3

2x = 18

x = 18/2

x = 9

x - y = 3

9 - y = 3

- y = 3 - 9

-y = -6

y = 6

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Answer:

480y  

Step-by-step explanation:

multiply 6 x 8 x 60= 480

Answer:

-80%

Step-by-step explanation:

there is a drastic decrease from sales

Answer:

80%

Step-by-step explanation:

use the percent change formula.

Percent change = [ (difference between initial and final value) ÷ initial value) x 100

= [(80 - 16) ÷80] x 100

= (64 ÷ 80) x 100

= 0.8 x 100

= 80%

Answer: scalene, right

Step-by-step explanation:

None of the side lengths of the triangle are equal, so the triangle is scalene.

This triangle also has a right angle, so it is a right triangle.

Answer:

D. And E.

Step-by-step explanation:

It is a right triangle because it has a corner that is 90 degrees. It is also scalene because all of the sides and angles have different values.

Answer:

i think its 3

Step-by-step explanation:

because have of 12 is 6 and half of 6 is 3

Answer:

Step-by-step explanation:

It will have a perimeter of:

Answer:

A i think

Step-by-step explanation:

when theres function i like to think of vending machines

if you pick 5 you get soda

but in b if you pick 5 you get soda,candy,orange juice, etc.

so b is wrong

c is the same

if you pick 1 you get chips

but in c if you pick 1 you can also get chips, gummies, etc

i feel like D is wrong but im still thinking of how to explain it, ill edit my comment when i figure it out!

Edit:

D may look right, but pay very attention! theres some where 1 is equal to another number and where 2 also equals another number

(1, 2) and (1, 0)

(2, 3) and (2,1)

It is important to know that the transformation rule for a reflection across y = -x is

The transformation rule for a reflection across the x-axis is

So, if we combine both rules, we get the following

This rule belongs to a counter-clockwise 90° rotation about the origin.

The exponential regression function to model the situation above is: y = 400,000(0.841)^x

The exponential regression function to model the situation is:

y = ab^x

where,

y = flour in grams

x = number of weeks since the bakery opened

a = initial amount of flour (Y-intercept) = 400,000 grams

b = growth factor

To find the value of b, we can use any two points from the table. Let's use the first and second points.

When x = 0, y = 400,000

When x = 1, y = 336,400

Substituting these values in the equation, we get:

400,000 = ab^0

336,400 = ab^1

Simplifying these equations, we get:

a = 400,000

b = 0.841

Therefore, the exponential regression function is:

y = 400,000(0.841)^x

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Answer:

Step-by-step explanation:

Given the expression 4x-1 = 4x+7, we are to simplify the expression and find the value of x. To do that the following steps must be carried out.

Step 1: collect the like terms by regrouping the expression

4x-1 = 4x+7

4x - 4x = 7+1

0x = 8

Step 2: Dividing both sides by the number next to x

0x/0 = 8/0

x = ∞

Any constant dividing zero will always return infinity as a value.

Answer: 13.1

Step-by-step explanation:

(2.5)+(7*9)/(5) = 2.5+63/5 = 65.5/5 = 13.1

Answer:

13.1

Step-by-step explanation:

Given rational expression:

\(\dfrac{m+(7 \cdot 9)}{n}\)

To determine the value of the given expression when m = 2.5 and n = 5, substitute the given values into the expression and solve.

\(\begin{aligned}m=2.5, n=5 &\implies \dfrac{2.5+(7 \cdot 9)}{5}\\\\&\implies \dfrac{2.5+63}{5}\\\\&\implies \dfrac{65.5}{5}\\\\&\implies \dfrac{65.5 \cdot 2}{5 \cdot 2}\\\\&\implies \dfrac{131}{10}\\\\&\implies 13.1\end{aligned}\)

The z-value for the test statistic is equal to 9.64.

In Mathematics and Statistics, the z-value for the test statistic of a population can be calculated by using the following mathematical equation;

\(t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }\)

Where:

By substituting the given parameters into the formula for z-test statistic, we have the following;

z-test statistic, t = (6.1 - 3.7)/(2.4/√93)

z-test statistic, t = (6.1 - 3.7)/(2.4/9.6436507609929549957600310474327)

z-test statistic, t = 2.4/0.24886840673530206440671047864342

z-test statistic, t = 9.64

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if the population standard deviation is increased while the sample size is 28, the confidence interval will become wider. This is because there is more variability in the sample mean, and therefore more uncertainty in the estimate of the population parameter.

If the sample size is 28 and the population standard deviation is increased, there will be a direct impact on the confidence interval. This is because the confidence interval is calculated based on the sample mean and the standard deviation. If the population standard deviation is increased, it means that there is more variability in the population. This increase in variability will lead to wider confidence intervals.
A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. The width of the confidence interval is determined by the sample size, the standard deviation, and the level of confidence.
In this case, if the population standard deviation is increased, it means that the sample standard deviation will also increase. The sample mean will be relatively more variable than it would be if the population standard deviation was lower. This increase in variability will cause the confidence interval to become wider, as there is more uncertainty in the estimate of the population parameter.
In summary, if the population standard deviation is increased while the sample size is 28, the confidence interval will become wider. This is because there is more variability in the sample mean, and therefore more uncertainty in the estimate of the population parameter. It is important to note that increasing the sample size can help to reduce the impact of increased population standard deviation on the confidence interval, as a larger sample size provides more accurate estimates of the population parameter.

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The only possible rational zero of the polynomial is 0

The possible zeros of the polynomial P(v) = 14v^5 + 6v^4 + 5v^3 - 4v^2 + 2v can be found by using the Rational Root Theorem. This theorem states that if a polynomial has rational zeros, they will be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

In this case, the constant term is 0 and the leading coefficient is 14. The factors of 0 are just 0, and the factors of 14 are 1, 2, 7, and 14. Therefore, the possible rational zeros of the polynomial are 0/1, 0/2, 0/7, and 0/14, which all simplify to just 0.

This means that the only possible rational zero of the polynomial is 0. However, there may also be irrational or complex zeros. To find these, we would need to use other methods, such as synthetic division or the quadratic formula.

In conclusion, the possible zeros of the polynomial P(v) = 14v^5 + 6v^4 + 5v^3 - 4v^2 + 2v are 0 and any irrational or complex numbers that satisfy the equation.

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Amanda needs to pay 1440 cedis for purchasing 8 cakes on discounted price.

Cost price is the amount we pay to buy an item at which it is available.

Here,

Selling price of a cake = 200 cedis

Discount because of sale = 10% on each unit.

                                              (Only if 4 cakes purchased at a time)

Amanda purchased 8 cakes

So, Amanda need to pay only 90 percent of the total amount.

Total cost price of 8 cakes for Amanda = (200 X 90%) X 8

                                                                  = 180 X 8

                                                                  = 1440

Thus, Amanda needs to pay 1440 cedis for purchasing 8 cakes on discounted price.

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By applying standard deviation concept, it can be concluded that all the students had the same score.

The mean is the average of all the scores. It is calculated by adding up all the scores and dividing them by the number of scores.

The standard deviation is a measure of how spread out the scores are. It is calculated by finding the difference between each score and the mean, squaring those differences, finding the average of those squared differences, and then taking the square root of that average.

If all the scores are the same, then the difference between each score and the mean will be 0. This means that the standard deviation will also be 0. Therefore, the correct answer is "all the students had the same score."

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The existing system with one service crew is cheaper.

Given: The crew of mechanics at the Highway Department garage repair vehicles that break down at an average of 12 vehicles per hour (approximately Poisson in nature). The mechanic crew can service an average of 3 vehicles every 10 minutes with a repair time distribution that approximates an exponential distribution.

The crew cost is approximately $50 per hour. The cost associated with lost productivity from the breakdown is estimated at $80 per vehicle per hour (or any fraction thereof).

We need to find which system is cheaper, the existing system with one service crew, or a revised system with two service crews.

Calculation of existing system cost:

Let's calculate the existing cost by servicing with one crew.

λ = 12/hourμ = 3/20 = 0.15/minute

ρ = λ/μ = 12/0.15 = 80 (since 0 < ρ < 1,

we can use Little's Law)Cost of 1 crew = $50/hour

Cost of lost productivity = $80/hour

We know that if λ is the rate at which the jobs arrive at the system, and μ is the rate at which jobs are serviced, the average number of jobs in the system is given by L, which is:

L = λ/μ L = 80

So, the average number of vehicles in the system is 80.

Therefore, the total cost per hour = cost of 1 crew + cost of lost productivity= $50 + 80 × 80 = $50 + $6400 = $6450

Calculation of revised system cost: Now, let's calculate the cost of servicing with two crews.

Each crew now serves at a rate of μ/2 = 0.15/2 = 0.075/minute.ρ = λ/μ = 12/0.075 = 160 (since 0 < ρ < 1, we can use Little's Law)

The average number of vehicles in the system is:L = λ/μ L = 160

So, the average number of vehicles in the system is 160.

Therefore, the total cost per hour = cost of 2 crews + cost of lost productivity= 2 × $50 + 160 × 80 = $100 + $12800 = $12900

Since the cost of the revised system is higher than the existing system, it's cheaper to continue with the existing system.

Therefore, the existing system with one service crew is cheaper.

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Answer:

18

Step-by-step explanation:

\(\frac{TS}{QS}=\frac{TU}{QR}\\ \frac{33}{44} =\frac{x}{24} \\44x=792\\x=18\)

The range of the function g(x) is given as follows:

[0, ∞).

From the graph of the function given in this problem, y assumes all real non-negative values, hence the interval notation representing the range of the function is given as follows:

[0, ∞).

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The type of graph that represents a system of linear equations that has multiple common coordinate pairs as a solution is called a line of best fit.

A line of best fit is a line drawn through data points that are scattered on a graph in order to illustrate a relationship between the data.

This line helps identify patterns in the data, and when plotted, multiple points can exist on the same line, which in this case represents the multiple common coordinate pairs.

To create a line of best fit, you will need to calculate the slope and the intercept for the equation that models the data. Then, you can plot the points onto the graph and draw a line through them.

The resulting line will be the line of best fit, which represents the multiple common coordinate pairs that are solutions for the system of linear equations.

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Answer

Area of the real dining hall = 72 m²

Explanation

The area of any rectangular shape is given as

Area = L × W

where

L = Length of the rectangle

W = Width of the rectangle

For this question, we have been given the dimensions of the dining hall in the drawing and told that

5 cm in the drawing = 6 m in reality

So, if the real length of the dining is L

5 cm = 6 m

10 cm = L

We can write a mathematical relationship by cross multiplying

(5) (L) = (10) (6)

5L = 60

Divide both sides by 5

(5L/5) = (60/5)

L = 12 m

If the real width of the dining hall is W

5 cm = 6 m

5 cm = W

We can write a mathematical relationship by cross multiplying

(5) (W) = (5) (6)

5W = 30

Divide both sides by 5

(5W/5) = (30/5)

W = 6 m

So, for the real dining hall,

Length = 12 m

Width = 6 m

Area = Length × Width

Area = 12 × 6

Area = 72 m²

Hope this Helps!!!

Answer:

D) 0

Step-by-step explanation:

Recall that slope is rise over run...

Specifically: m= (y2 - y1)/(x2 - x1)

Since all the y values are constant (3) in the table, this signifies that the slope is 0.

For example:

(3 - 3)/(-7 - 0) = 0

Therefore, the answer is D) 0.