Assuming no denominator equals zero, which expression is equivalent to the given expression?.

The solution the system of equations y = x – 15 and y = –2x + 3 is (6, -9)

An equation shows the relationship between numbers and variables in an expression.

Given the system of equations:

y = x – 15    (1) and

y = –2x + 3   (2)

From equation 1, substitute y = x - 15 into equation 2 using substitution method:

x - 15 = -2x + 3

x + 2x = 3 + 15

3x = 18

x = 6

substitute x = 6 in equation 1:

y = 6 - 15 = -9

y = -9

The solution is (6, -9)

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Answer:

D. (6, -9)

Step-by-step explanation:

Edge 2023

The second inequality in the system tells us about the budget of the cost of each package of notepad.

A mathematical comparison of two integers or algebraic expressions that uses the terms greater than, larger than or equal to, less than, or less than or equal represents inequalities.

Given that the budget for the notepads is $160.

Assume the cost of package of 24 is $16 for each package and the cost of package of 6 is $5.40 for each package.

The second inequality in the system of equations represents the equation of the budget that would be spent to buy the notepads.

Hence, 16x +5.40y ≤ 160 represents the budget.

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Answer:AC>BC>AB

Step-by-step explanation:We can compare the lengths of the sides with the angles given the side opposite to the largest angle is the largest and vice versa.

Angle ABC=75 greatest angle therefore the side opposite to it is the largest.

The way that the exponent illustrated as x ^7/3 can be written is 3✓x^7

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

Expressing large numbers in terms of powers is known as an exponent. Therefore, the exponent describes the number of times a number has been multiplied by itself.

Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is written as bn. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to base multiplication when n is a positive integer; therefore, bn is the result of multiplying n bases:

In this case, it should be noted that x ^7/3 will simply be the cube root of x raised to power 7. This is illustrated as x ^7/3.

Therefore, the correct option is C.

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Answer:

B

Step-by-step explanation:

Distance = rate x  time

The rate is 3/15

distance = (3/15) (50)

distance = 10 miles

The situations are classified as survey, observational study or experiment as follows:

3. Experiment.

4. Observational study.

5. Survey.

6. Survey.

7. Survey.

The definitions for each of these three cases are given as follows:

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The cylinder's volume is 2769.5 in³ with a base radius of 7 in and a height of 18 in.

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry.

The formula for calculating the volume of a cylinder is:

V = πr²h

where;

r is the radius = 7in

h is the height = 18in

Substitute the given parameters to have:

V = π(7)² * 18

V = 2769.5 in³

Hence the volume of the cylinder has a base radius of 7in and a height of 18in is 2769.5 in³

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The steps to  solve a line segment problem is

1. Draw a diagram of the line segment.

2. Label the endpoints and any given information.  

3. Use the given information to calculate the length of the line segment.

4. Use the Pythagorean Theorem to calculate the length of the line segment, if needed.  

5. Solve for the unknown variable.  

To solve a line segment problem, you must first draw a diagram of the line segment. Label the endpoints and any given information, such as the length of one of the sides of the line segment. Then you can use the given information to calculate the length of the line segment. If the length of the line segment is unknown, you can use the Pythagorean Theorem to calculate the length. After that, solve for the unknown variable, and then check your answer. With these steps, you can solve any line segment problem.

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The supplementary in the Diagram are Angles 1 and 2.

Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°.

From the diagram Angles 1 and 2 are angles on a straight line

Angles on a straight line are equals to 180 degree

hence, the supplementary angles are angles 1 and 2

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Solving the quadratic equation, we will see that the frisbee will hit the ground after 8.5 seconds.

We know that the height of the frisbee is modeled by the quadratic equation:

h(t) = -0.07*t^2 + 0.007*t + 5

The frisbee will hit the ground when h(t) = 0, so we just need to solve the quadratic equation:

0 = -0.07*t^2 + 0.007*t + 5

We can just use the quadratic formula to get the solutions:

[tex]t = \frac{-0.007 \pm \sqrt{0.007^2 - 4*(-0.07)*5} }{2*-0.07} \\\\t = \frac{-0.007 \pm 1.18 }{-0.14}[/tex]

We only care for the positive solution, which is:

t = (-0.007 - 1.18)/-0.14 = 8.5

So the frisbee will hit the ground after 8.5 seconds.

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Answer:

angle 1: 51

angle 2: 39

angle 3: 101

angle 4: 40

angle 5: 6

angle 6: 140

Step-by-step explanation:

I haven't done this in a while so hopefully this is right:) hope this helps

Answer:

Square

Step-by-step explanation:

each side of a square is equal and there are 4 line segments

One possible recursive function for this sequence is a n = a n-1 - 3, where a n is the nth term in the sequence and a n-1 is the previous term.

A function is a rule or mapping that relates a set of inputs to a set of outputs. It is a mathematical expression that takes one or more inputs and produces a corresponding output. Functions are essential for solving problems in mathematics, science, engineering, and computing. They can be used to describe relationships, simplify calculations, and to create models that enable us to understand the behavior of complex systems.

This recursive function states that each successive term in the sequence is three less than the previous term. Therefore, the sequence will continue to decrease by three each time. For example, the sixth term would be -11 (a 5 -3) and the tenth term would be -21 (a 9 -3).

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Answer:

see explanation

Step-by-step explanation:

calculate the slope m of the line using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, - 3 ) and (x₂, y₂ ) = (- 9, 6 )

m = [tex]\frac{6-(-3)}{-9-4}[/tex] = [tex]\frac{6+3}{-13}[/tex] = - [tex]\frac{9}{13}[/tex]

• Parallel lines have equal slopes.

Thus slope of a parallel line is m = - [tex]\frac{9}{13}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{9}{13} }[/tex] = [tex]\frac{13}{9}[/tex]

Answer:

See below

Step-by-step explanation:

The z-score corresponding to an observation of 284 is -1.02

To calculate the z-score, you need to know the mean (μ) and standard deviation (σ) of the normal distribution. Given that X~n(335, 50), the mean is 335 and the standard deviation is 50.

        (x - μ) / σ

       (284 - 335) / 50 = -1.02

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The equation that will be used to represent the number of purple and pink flowers would be =

For the pink flowers = r = 180 - 4(0)

For the purple flowers = r = 180 - 4(45)

A garden is defined as an area that is being prepared for the purpose of cultivation of various flower, shrubs and grass.

The total number of flowers in the garden = 180

The number of pink flower beds = 4

The number of purple flower beds = 4

The number of pink flowers in each bed = 45

Therefore, the number of total pink flowers = 4 × 45 = 180

Since the pink flowers is the total of 180 which is also the quantity of flowers in the garden, the quantity of flowers in the purple bed would be = 0

Thus, 180 = 4(45) + 4(0)

For the pink flowers = r = 180 - 4(0)

For the purple flowers = r = 180 - 4(45)

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In order to make Natasha's survey data more reliable, she could increase the sample size, conduct the survey on different day or time, or extend the days of the survey.

Conducting a survey with a sample size of only 30 workers, the survey results may not be representative of the entire population of 215 workers. Increasing the sample size would help to ensure that the survey results are more representative of the population. Moreover, she could also increase the data reliability by conducting the survey on different day or time can also gives different results since the transportation way can vary day by day. Another way Natasha could make the survey data more reliable would be to extend the survey over the course of several days rather than just one day.

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In order to make Natasha's survey data more reliable, she could increase the sample size, conduct the survey on different day or time, or extend the days of the survey.

Conducting a survey with a sample size of only 30 workers, the survey results may not be representative of the entire population of 215 workers. Increasing the sample size would help to ensure that the survey results are more representative of the population. Moreover, she could also increase the data reliability by conducting the survey on different day or time can also gives different results since the transportation way can vary day by day. Another way Natasha could make the survey data more reliable would be to extend the survey over the course of several days rather than just one day.

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Answer:

77.77

Step-by-step explanation:

The new value =

77 + The value of the percentage increase =

77 + (1% × 77) =

77 + 1% × 77 =

(1 + 1%) × 77 =

(100% + 1%) × 77 =

101% × 77 =

101 ÷ 100 × 77 =

101 × 77 ÷ 100 =

7,777 ÷ 100 =

77.77

Answer:

= 77.77

Step-by-step explanation:

1% = 1/100 = 0.01

Then:

77*0.01 = 0.77

77 increased 1% is:

77 + 0.77 = 77.77

Answer:

12

Step-by-step explanation:

The sum and difference between nine-tenths and seven-eighths is 71/40 and 1/40, calculated by addition and subtraction.

As per the fact, representing the words in numbers. So, nine tenths will be represented as: 9/10

Seven eighths: 7/8

Calculating the sum and difference as follows -

Sum = 9/10 + 7/8

Taking LCM we get 40

Sum = 9×4 + 7×5/40

Performing multiplication on Right Hand Side of the equation

Sum = 36 + 35/40

Sum = 71/40

Difference = 9/10 - 7/8

Difference = (9×4) - (7×5)/40

Performing multiplication on Right Hand Side of the equation

Difference = 36 - 35/40

Difference = 1/40

Hence, sum is 71/40 and difference is 1/40.

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Answer: sin(f) are correct trigonometric ratios for triangle DEF.

Step-by-step explanation: Sin(d) = cos(e) = tan(d) = sin(e) = tan(d) = sin(f)

The number of votes the Candidate B receive is (c) 60

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

Candidate A Candidate B

12 20

18 30

27 45

36 ?

The above parameters mean that

The rate increase proportionally

Using the above as a guide, we have the following ratio

Ratio = Candidate A : Candidate B

Using one of the values, we have

Candidate A : Candidate B = 12 : 20

substitute the known values in the above equation, so, we have the following representation

36 : Candidate B = 12 : 20

Express as fraction

Candidate B/36 = 20/12

So, we have

Candidate B = 36 * 20/12

Evaluate

Candidate B = 60

Hence, the number of votes is 60

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The expanded from of the expression y(3.05x−3.75)−2.25y as required to be determined I. the task content is; 3.05xy - 6y.

It follows from the task content that the expanded form of the given expression is to be determined.

Since the given expression is;

y ( 3.05x − 3.75 ) − 2.25y

Hence, by the distributive property; we have that;

3.05xy - 3.75y - 2.25y

= 3.05xy - 6y

Ultimately, the expanded form of the expression is; 3.05xy - 6y.

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Answer:

it's very simple D

if you throw -ve sign to g(x) sign will change

and do simple calculation

Answer:

To find the difference between the two functions, we can subtract g(x) from f(x):

f(x) - g(x) = (5x² - 2x + 7) - (2x² + 6x + 3)

= 5x² - 2x + 7 - 2x² - 6x - 3

= 3x² - 8x + 4

Therefore, the difference between the two functions is f(x) - g(x) = 3x² - 8x + 4, which is answer D.

Step-by-step explanation:

The number of miles you need to drive to pay less by taking rate 2 is less than 500 miles

Let

Number of miles = x

Rate 1:

30 + 0.12x

Rate 2:

60 + 0.06x

Rate 2 < Rate1

60 + 0.06x < 30 + 0.12x

60 - 30 < 0.12x - 0.06x

30 < 0.06x

divide both sides by 0.06

x < 30/0.06

x < 500 miles

Therefore, you need to drive less than 500 miles to pay less by taking rate 2.

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The equations that could be used to find the price of one tire patch is given as follows:

The price for each tire patch is constant, meaning that a linear function is used to model the situation.

He initially had $22.20, and then for each tire purchased, his amount decays by the slope, hence the function that models the situation is given as follows:

f(t) = 22.2 - tx.

In which t is the number of tires purchased.

He purchased 4 tires, hence:

f(4) = 22.2 - 4x.

After the purchase, he had $1.90 remaining, hence:

1.9 = 22.2 - 4x.

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The 4 basic types of lines are  Curved Lines, Straight Lines, Horizontal Lines, and  Vertical Lines.

How do lines work?

A straight group of points that stretch in opposing directions is what is known as a line.

the 4 basic types of lines are:

a) Curved Lines: A curved line is any line that is not straight. A curve results from a point that is not moving in a straight line.

b) Straight Lines: A straight line is the shortest path between any two points. We obtain a straight line if a point moves only in that direction.

c) Horizontal Lines: A horizontal line is any straight line that extends from left to right. Vertical lines are perpendicular to the y-axis and parallel to the x-axis.

d) Vertical Lines: From top to bottom or bottom to up, vertical lines are straight up and down. A vertical line is perpendicular to the x-axis and parallel to the y-axis.

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We will find the parallel line:

y = (2/3)*x - 11/3

And the perpendicular line:

y = (-3/2)*x + 5

Here we start with the linear equation, we will get:

2x - 3y = 9

We can rewrite it to get:

-3y = 9 - 2x

y = 9/-3  - 2x/-3

y = -3 + (2/3)x

Remember that two lines are parallel if the lines have the same slope, so the equation of the parallel line will be something like:

y = (2/3)*x + b

And this line must pass through (4, -1), replacing these values we will get:

-1 = (2/3)*4 + b

-1 = 8/3 + b

-1 - 8/3 = b

-3/3 - 8/3 = b

-11/3 = b

So the linear equation parallel is:

y = (2/3)*x - 11/3

Now let's find the perpendicular line. Remember that two lines are perpendicular if the product between the slopes is equal to -1, then if the slope of the perpendicular line is m, we need to solve:

m*(2/3) = -1

m = -3/2

Then the perpendicular line is something like:

y = (-3/2)*x + b

To find te value of b, we need to replace the values of the point (4, -1) there, we will get:

-1 = (-3/2)*4 + b

-1 = -6 + b

-1 + 6 = b

5 = b

So the perpendicular line is:

y = (-3/2)*x + 5

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