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The sοlutiοn οf the system οf equatiοn is x = 0 and y = 7/3.

If there is nο sοlutiοn tο a system οf equatiοns, it is incοnsistent system; οtherwise, there must be at least οne sοlutiοn. If a set οf equatiοns has infinitely many sοlutiοns, it is dependent.

Every οne οf the equatiοns in a system οf equatiοns must have a sοlutiοn in οrder fοr the system tο be cοnsistent. This demοnstrates that a set οf values fοr the variables may simultaneοusly satisfy all οf the system's equatiοns and shοw that they are nοt mutually exclusive.

There is nο sοlutiοn tο an equatiοn system that satisfies all οf the equatiοns in the system. This indicates that nο cοmbinatiοn οf values fοr the variables can cοncurrently satisfy all οf the system's equatiοns since they are incοmpatible.

The given equatiοns are:

y = 2/3x + 7/3

-4x+6y=14

Substituting the value of y in the second equation:

-4x + 6y = 14

-4x + 6(2/3x + 7/3) = 14

-2x + 4x + 14 = 14

2x = 0

x = 0

Substitute the value of x = 0 we have:

y = 2/3(0) + 7/3

y = 7/3

Hence, the solution of the system of equation is x = 0 and y = 7/3.

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Complete question:

Given system of equations y = 2/3x + 7/3 and -4x + 6y = 14

Find the value of x and y.

Answer:

80°

Step-by-step explanation:

sides of angle =180°

y= 180-(45+55) = 80°

x=y because x is vertically opposite to y

therefore x =80°

The equivalent exponential equations are given as follows:

\(2^{4x} = 2^{3(x - 3)}\)

The exponential expression for this problem is defined as follows:

\(2^{4x} = 8^{x - 3}\)

The number eight is the third power of 3, that is:

8 = 2³.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:

\(8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}\)

Meaning that the correct option is given by the fourth option.

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A transformation would accomplish this include the following: C. a rotation 180° counterclockwise about the origin.

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure 180° counterclockwise about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point X (0, 4)  →  Coordinates of point Y = (0, -4)

Coordinates of point X (1, 3)  →  Coordinates of point Y = (-1, -3)

In conclusion, we can logically deduce that this transformation rule (x, y) → (-x, -y) would map Figure X onto Figure Y.

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Answer:

$28

20 plus 40 percent

that's the answer

Answer:

54 in³

Step-by-step explanation:

9×3×2 = 54 in³

_______

The linear function that describes the distance (in miles) is therefore y = 65x + 80

We have to find the slope and the intercept in other to get the linear function

The data points are:

(1, 145) and (3, 275).

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

fixing the data points we have

m = (275 - 145) / (3 - 1)

= 130 / 2

= 65

y = mx + b

(1, 145):

145 = 65(1) + b

b = 145 - 65

= 80

y intercept is 80

The linear function is therefore y = 65x + 80

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Answer:

$ 4,688.00

Step-by-step explanation:

I = 4000 × 0.043 × 4 = 688

I = $ 688.00

$ 688.00 + $ 4,000.00 = $ 4,688.00

Answer:

y = (x - 2)(x + 1)(x + 3)

Step-by-step explanation:

horizontal intercepts at x = 2, -1, -3

->  y = 0 when x = 2, x = -1, and x = -3

Think x minus what equals y?

1. y is 0 and x is 2 -> 0 = (2 - 2) -> y = (x - 2)

2. y is 0 and x is -1 -> 0 = (-1 - (-1)) -> y = (x + 1)

3. y is 0 and x is -3 -> 0 = (-3 - (-3)) -> y = (x - 3)

so the equation is y = (x - 2)(x + 1)(x + 3)

since y = 0 when x = 2, x = -1, and x = -3

We want to find a polynomial given that we know its roots.

We will get:

p(x) = x^3 + 2*x^2 - 5*x - 6

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

A polynomial with the roots {x₁, x₂, ..., xₙ} and a leading coefficient A, we can write it as:

p(x) = A*(x - x₁)*(x - x₂)*...*(x - xₙ)

Here we know that the roots (horizontal intercepts) are {2, -1 , -3} but we do not know the leading coefficient, so we will use A = 1.

Then the polynomial is:

p(x) = (x - 2)*(x + 1)*(x + 3)

Expanding that we get:

p(x) = (x^2 - x - 2)*(x + 3)

p(x) = x^3 + 2*x^2 - 5*x - 6

This is a possible equation for the polynomial with the given horizontal intercepts.

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The equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

We have to given that,

A number line is shown in image.

Since,

A number lines are the horizontal straight lines in which the integers are placed in equal intervals.

And, All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

Now, By given number line,

Point C is two point left from point 8.

Hence, The point C is denoted as,

⇒ C = 8.2

⇒ C = 82/10

⇒ C = 8 2/10

Therefore, the equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

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Answer:ratio is 14:54 = 42:B. Beavers = 162

Step-by-step explanation:

The ratio demonstrates how often one number is multiplied by another.

The approximate number of beavers exists 162.

The ratio demonstrates how often one number is multiplied by another. When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage.

The relationship or comparison between two numbers in the same unit to determine how much larger one number is than the other is known as a ratio.

The 42 beavers were tagged and released by the New Jersey Division of Fish and Wildlife, which monitors the beaver population in the Raritan River. After a week, they had captured 54 beavers, 14 of which were marked. There are 54 Beavers in all, and 14 Beavers have tags.

Let the ratio be 14 : 54.

As 42 tagged beavers were released.

simplifying the above equation, we get

14 × 3 : 54 × 3

= 42 : 162

Therefore, the approximate number of beavers exists 162.

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Answer:

15 m

Step-by-step explanation:

perimeter of rectangle = 2 ( l + b )

l = 4.5

b = 3

p = 2 ×( 4.5 + 3)

p = 2 × ( 7.5)

p = 15 m

We cannot make any definitive inferences about the entire school population, however, so the answer is E. None of the above.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The total number of students are 10+11+23+6=50

Based on the survey of 50 students about their preference for an additional sports team, we can observe that lacrosse is the most popular sport among the surveyed students, with 23 supporters.

It is likely that there would be enough interest to form an ice hockey team, as there were 11 supporters.

We cannot make any definitive inferences about the entire school population, however, so the answer is E. None of the above.

Hence, We cannot make any definitive inferences about the entire school population, so the answer is E. None of the above.

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The table shown below represents the results from a sample group of 50 students

surveyed about a preference for an additional sports team.

Sports Team    Number

Gymnastics       10

Ice hockey         11

Lacrosse             23

Swimming           6

If the school has 500 students, what can be inferred from the survey?

A. There would not be enough students to form a 20-person ice hockey

team.

B. About half of the students prefer lacrosse to the other sports.

C. Fewer than ten students in the school prefer swimming to the other

sports.

D. About 10% of the students prefer gymnastics.

E. None of these

Answer will be 27.

Given,

3√81

Now, to solve the expression the squares of whole numbers and square roots for some numbers must be known.

For example, squares of

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81
10² = 100

Square roots,

√100 = 10

√81 = 9

√64 = 8

√49 = 7

√36 = 6

√25 = 5

√16 = 4

√9 = 3

√4 = 2

√1 = 1

Now ,

3√81 = 3× 9

= 27.

Thus the value is 27.

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Answer: The quotient is 3y² + 2y - 1.

Step-by-step explanation:

You can use long division to solve this expression by setting the dividend under the roof and the divisor outside as you would normally do when dividing numbers.

1) Look at the first term of the dividend, 15y³, and the first term of the divisor, 5y. Determine what value multiplied by 5y would give you 15y³. The answer is 3y², and given the number, you multiply it by the WHOLE divisor.

3y²(5y + 6) = 15y³ + 18y² <-- subtract this from the dividend.

2) Continue this process and make sure to drag down the next term for each new value you form after subtracting. Keep in mind of any negative values! When you reach up to -5y, determine what value multiplied by 5y would give you the value of -5y, which would be -1.

3) You should be left with a remainder of 0, leaving you with a quotient of 3y² + 2y - 1.

Answer:

c=m+s

Step-by-step explanation:

Answer:

$312.2

Step-by-step explanation:

Given that:

Amount earned per hour = $11.15

Number of hours worked = 28 hours

Straight time pay is the total amount earned in a given pay period. Hence,

Starlight time pay earned during the period he worked will be :

Amount per Hour * number of hours

$11.15 * 28 = $312.2

Answer:

-46

Step-by-step explanation:

4(-8x + 5) = -32x - 26

-32x + 20 = -32x - 26

-32x + 32x = -26 - 20

x = -46

Answer:

-32x+20=-32x-26

20=-26

so unequal or undefined

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

Let's denote:

- The number of orders Diane served as `D`

- The number of orders Sam served as `S`

- The number of orders Boris served as `B`

From the problem, we know:

1. `D + S + B = 54` (the total number of orders they served)

2. `D = S - 6` (Diane served 6 fewer orders than Sam)

3. `B = 2S` (Boris served 2 times as many orders as Sam)

We can substitute equations 2 and 3 into equation 1 to solve for the variables:

Substitute `D` and `B` in equation 1:

`(S - 6) + S + 2S = 54`

Combine like terms:

`4S - 6 = 54`

Add 6 to both sides:

`4S = 60`

Divide by 4:

`S = 15`

Now that we know `S = 15`, we can find `D` and `B` by substituting `S` into equations 2 and 3:

`D = S - 6 = 15 - 6 = 9`

`B = 2S = 2 * 15 = 30`

So, Diane served 9 orders, Sam served 15 orders, and Boris served 30 orders.

The absolute value function that matches the graph is given as follows:

y = -|x + 1| + 1.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex in this problem are given as follows:

(-1, 1).

Hence:

y = a|x + 1| + 1.

The function is reflected over the x-axis with a slope of -1, hence the leading coefficient a is given as follows:

a = -1.

Thus the function is:

y = -|x + 1| + 1.

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Answer:

B

Step-by-step explanation

We have

using a graph tool

see the attached figure

The solution of the system is the shaded area

we know that

The line is solid

The line passes through points and and is shaded above the line.

The line is solid

The line passes through points and and is shaded below the line

The two lines intersect at one point

therefore

the answer is the option

B) Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded above the line.

Answer:

\(26 > c > 58\)

Step-by-step explanation:

Given

\(a,b =42; 16\) --- 2 sides

Required

The inequality for the third side

To do this, we make use of:

\(a + b < c\)

\(a + c < b\)

\(b + c < a\)

So, we have:

\(42 + 16 < c\)

\(16 + c < 42\)

\(42 + c < 16\)

This gives:

\(58 < c\)

\(c < 26\)

\(c<-26\)

The usable inequalities are:

\(c < 26\) and \(58 < c\)

Rewrite:

\(c < 26\) and \(c > 58\)

So, the inequality is:

\(26 > c > 58\)

Answer:

C.

y=−1/2x+2

Step-by-step explanation:

Find the negative reciprocal of the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )  to find the line perpendicular to  4 x − 2 y = 9 .

y = − 1 /2 x + 2

Step-by-step explanation:

Answer is 247 so there up I have send photos

The proportion of Arts majors who have not found a job is 8%, rounded off to two decimal places.

To find the proportion of Arts majors who have not found a job, we first need to calculate the total number of students who have not found a job.

The total number of students who have not found a job would be 1500 - 1380 = 120.

To calculate the proportion of students who have not found a job, we can divide the number of students who have not found a job by the total sample size:

The proportion of students who have not found a job = 120 / 1500 = 0.08 or 8%.

Therefore, the proportion of Arts majors who have not found a job is 8%, rounded off to two decimal places. This suggests that a majority of the graduating Arts majors from the University of Western Cape have found employment before their graduation.

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Answer:

225

Step-by-step explanation:

if you convirt them all to fractions and make it 5/1*10/1*36/1=225

The equation of the line that passes through the point (-3, 7) and has a slope of -5/3 is y - 7 = (-5/3)(x + 3).

We are given the point (-3, 7) and the slope of the line as -5/3.The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept.

To obtain the equation of the line, we need to substitute the values of slope and point in the slope-intercept form and solve for b.(7) = (-5/3)(-3) + b 21/3 = b.

Now we have the value of b, and we can substitute the values of m and b in the slope-intercept form.y = (-5/3)x + 21/3 is the equation of the line in slope-intercept form.

To obtain the equation in the standard form Ax + By = C, we multiply each term by 3.3y = -5x + 7Add 5x to both sides5x + 3y = 7.

This is the equation of the line in standard form.

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what does it mean?

?????????????????????????

Answer:

A) measures the space inside in cubic units

Step-by-step explanation: