Select the correct answer.
Which statement about this system of equations is true?


A. The system has no solution.
B. The system has a unique solution at (0,6).
C. The system has a unique solution at (0,-4).
D. The system has infinitely many solutions.

The equation of the linear function is A(t) = -975t + 15000

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

The table of values

From the table of values, we have:

A(t)         t

11,100   4

7200   8

3300   12

From the above table of values, we can see that

As t increase by 4, the value of A(t) decreases by 3900

This means that the table of values is a linear relation, and the slope is

slope = -3900/4

slope = -975

A linear equation is represented as

y = mx + c

Where

slope = m

So, we have

A(t) = -975t + c

Using the points on the table, we have

11000 = -975 * 4 + c

Evaluate

c = 15000

So, we have

A(t) = -975t + 15000

Hence, the equation is A(t) = -975t + 15000

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Option D) f(x) = |x|, is Correct.

What is parent function?

A parent function is a basic or fundamental function that serves as the starting point for a family or group of related functions. These functions can be obtained by applying a transformation to the parent function, such as shifting, stretching, or reflecting it.

The absolute value parent function is represented by the following function:

D. f(x) = |x|

The absolute value function is defined as |x| = x for x >= 0 and |x| = -x for x < 0. Graph of this function is a V-shape, and it's also known as "the absolute value of x" function. It is a reflection of the linear function f(x) = x across the x-axis and will always have a slope of 1 and a y-intercept of 0.

A. f(x) = x is a linear function, slope is 1 and y-intercept is 0, This is not absolute value function

B. f(x) = 2ˣ is the exponential function, and it is not an absolute value function

C. f(x) = x² is the quadratic function, it's a parabola opening upwards and not an absolute value function

D. f(x) = |x| is the absolute value function, V-shape and it's an example of the absolute value parent function.

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Answer:

The slope is 0.75.

The equation is y=0.75x-2

Step-by-step explanation:

Approx 16 revolutions the wheel go through to travel the distance 25 meters by a diameter of 50 cm.

In the given question, a wheel having a diameter of 50 cm.

If the elf travels a distance of 25 meters then we have to find how many revolutions did the wheel go through.

Since we have the wheel's diameter, we can determine the radius of the wheel. As we already know, the length of a wheel's revolution is equal to its circumference, which is a circle with a diameter of 2πr.

We will now enter the radius value into the algorithm to determine how many revolutions the wheel must make. To reach the desired result, divide the total distance by the distance covered in one revolution to determine the number of revolutions needed to travel 25 m.

r = [tex]\frac{50}{2}[/tex] = 25 cm

The radius of the wheel is 25 cm.

Now we put the value of r in the formula of circumference.

2πr = 2π×25

2πr = 50π cm

Total distance is 25 m. So we convert m in cm by multiplying the 100.

Now the total distance is 2500 cm.

2500 = n × 50π

Now putting the value of π = 3.14

2500 = n×50 × 3.14

2500 = n×157

Divide by 157 on both side, we get

n = 15.924

n = 16(approx)

Hence, approx 16 revolutions the wheel go through to travel the distance 25 meters by a diameter of 50 cm.

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In the given case, Matthew would have a negative z score and John would have a positive z score.

A z-score is a measurement of how far an observation or data point is from the distribution's mean. An observation is said to be above the mean if the z-score is positive, while it is said to be below the mean if the z-score is negative. Therefore, it is possible that John's z-score would be positive, showing that he is taller than the average for his age group if he is one of the tallest children in his class at the age of 7.

In contrast, if 12-year-old Matthew is among the smallest students in his class, it is likely that his z-score will be negative, suggesting that he is shorter than the norm for his age group. Therefore, John would have a positive z-score but Matthew would have a negative one if he is shorter than average for his age group.

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The sales tax rate on the item = 8%

We know that the sales tax is nothing but the purchase price times the percentage of tax.

An item costs $430 before tax.

This means, the purchase price is 430 dollars.

The sales tax is $34. 40

To find: the sales tax rate as a percentage

First we find a ratio of the sales tax to the cost of the items before tax.

Sales tax / Pre-tax value of item = (34.40) / 430

Now we write a proportion where the pre-tax value is proportional to 100% and solve for the percentage of sales tax.

i.e., (34.40) / 430 = sales tax percent / 100

So, the sales tax percent  = 8%

Therefore, the sales tax is of 8%

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1) 1000 AA Batteries in one Case.

2) 10,000 AA Batteries in One carton.

3) 100,000 AA Batteries in 10 cartons.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

The Store sells AA batteries in the order below:

⇒ 10 batteries in 1 packages

⇒ 10 packages in 1 box

⇒ 10 boxes in 1 case

⇒ 10 cases in 1 Carton

1) We want to determine how many AA batteries are in 1 Case;

Using Multiplication

Number of AA Batteries in 1 Case = 10 Batteries × 10 package × 10 box

                                                    = 1000 AA Batteries

2) We want to determine how many AA batteries are in 1 Carton;

From Part (a),

There are 1000 AA Batteries in 1 Case.

Since, There are 10 Cases in 1 carton.

Number of Batteries in 1 carton = 10 × 1000

                                                 = 10,000 AA Batteries

3) 10 Cartons

⇒ 1 carton = 10000 AA Batteries

Therefore, We get;

⇒ 10 Cartons = 10 × 10000

                    = 100,000 AA Batteries

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Answer:     [tex]\frac{3}{8}[/tex]➗[tex]\frac{3}{4}[/tex]

Step-by-step explanation:  Are you looking to work out and calculate how to multiply 3/8 by 3/4? In this really simple guide, we'll teach you exactly what 3/8 times 3/4 is and walk you through the step-by-process of how to multiply two fractions together.

In a reaction the amount f a substance which react with another substance is known as it's equivalent.

The definition of equivalent is "weight in grams of a substance that displaces or combines with one gram of hydrogen."

It is an important part of chemistry and comes under stoichiometry. In every reaction there is a reactant which forms the suitable product and the amount of that is calculated using stoichiometry.

The mole ratio is a typical sort of stoichiometric relationship that compares the amounts in moles of any two components in a chemical process.

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

or in this case, hourly wage :)

to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{200}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{200}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{10}-\underset{x_1}{0}}} \implies \cfrac{ 200 }{ 10 } \implies \cfrac{20}{1}\cfrac{dollars}{hour}\qquad \textit{\$20 per hour}[/tex]

The estimated solution of the system 3x + y = 10 and y = 6x + 1 is (1, 7)

An equation is used to show the relationship between numbers and variables.

The standard form of a linear equation graph is:

y = mx + b

Where m is the slope of the line and b is the y intercept.

Given the linear equation:

3x + y = 10

y = -3x + 10   (1)

y = 6x + 1     (2)

Subtracting equation 2 from 1 to solve using elimination method gives:

0 = -9x + 9

9x = 9

x = 1

put  x = 1 in eqn 2:

y = 6(1) + 1

y = 7  

The solution is (1, 7)

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Point O is where the diagonals in a rhombus MNLP intersect. If the side is 8 inches long and the measure of the angle MNL is 120 degrees, then NP is 8 inches.

A rhombus is a quadrilateral with all of its sides being the same length and both pairs of opposite sides being parallel. The following formula can be used to determine the length of diagonals when applying the law of cosines to triangles made out of the rhombus's diagonal (x) and sides(a): diagonal [tex]x=a\sqrt{2+2\cos \theta}[/tex].

Given the sides of the rhombus, MNLP is 8 inches each and the ∠MNL is 120°. Then, let's take the diagonal NP as x and calculate this using the above formula as follows,

[tex]\begin{aligned}x&=8\sqrt{2+2\cos120^{\circ}}\\&=8\sqrt{2+2(-0.5)}\\&=8\sqrt{2-1}\\&=\mathrm{8\;inches}\end{aligned}[/tex]

The required answer is 8 inches.

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Uma is correct, because getting an even number is an event.

The term probability refers to the likelihood of an event occurring.

Given that;

Bridget says that when a standard number cube is rolled getting an even number is an outcome.

And, Uma says that getting an even number is an event.

Now,

We know that;

When a standard number cube is rolled then getting an even number is an event.

Hence, Uma statement is correct.

Thus, Uma is correct, because getting an even number is an event.

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Answer:

ANGLE 5 IS CONGURENT TO ANGLE 4

PLEASE MARK BRAINLIEST

Answer:

alright, lets say danetta's dinner bill is 20 dollars, and she ordered 4 things, so the equation would be x times 5=20, and edwards would be 25 dollars, so that equation would be x times 5=25

Step-by-step explanation:

Using the regression concept to find the equation and applying derivative, The rate of change is 10.

Regression analysis is a group of statistical procedures used in statistical modeling to determine the associations between a dependent variable and one or more independent variables. The dependant variable's predicted value in basic linear regression is given by the equation = b0 + b1x. In order to minimize the total sum of squared errors, the values of b0 and b1 are derived from the data using the equation line = b0 + b1X. 

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.

from the given data,

y= a + bx is our regression line.

a=8 and b =10

y=8+10x is the line.

derivate the line , we get,

[tex]\frac {dy}{dx} = 10[/tex]

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The length c of the right angle triangle is 9 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a right angle triangle is 180 degrees.

The sides of a right angle triangle can be found using trigonometric ratios as follows:

Therefore,

sin 60° = opposite / hypotenuse

where

opposite side = c

hypotenuse side = 6√3 ft

Hence,

sin 60° = c / 6 √3

cross multiply

c = 6√3 × sin 60

c  = 6√3 × √3 / 2

c = 6 × 3 / 2

c = 18 / 2

Therefore,

c = 9 units

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Answer:

  2m⁴ +0m³ -3m² +0m +7

Step-by-step explanation:

You want the index form of 2m⁴-3m²+7.

The index form of a polynomial has terms with all indices present in decreasing order, using 0 coefficients where necessary.

The given polynomial is missing indices 3 and 1, so we add those with coefficients of 0:

  2m⁴ +0m³ -3m² +0m +7

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤. To ‘solve’ an inequality means to find a range, or ranges, of values that an unknown x can take and still satisfy the inequality.

Suppose we want to solve the inequality x + 3 > 2.

We can solve this by subtracting 3 from both sides:

x + 3 > 2

x > −1

So the solution is x > −1. This means that any value of x greater than −1 satisfies x + 3 > 2.

Inequalities can be represented on a number line such as that shown in the image attached below. The solid line shows the range of values that x can take. We put an open circle at −1 to show that although the solid line goes from −1, x cannot actually equal −1.

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The measure that would be most useful to determine if the people can safely use the elevator is B. Mean

The most useful measure to determine if the people can safely use the elevator would be the mean weight of the people, as it would give an idea of the average weight of the group and if it is below 4,500 pounds.

The mode is the most common value in a set of data and does not give information about the weight of the entire group. The interquartile range is a measure of the spread of the middle 50% of the data and does not give information about the average.

In conclusion, the correct option is B.

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No, horizontal asymptote is not represented by y- axis it is represented by the x -axis.

Therefore, the horizontal asymptote is not represented by the y-axis, it is represented by the x-axis.

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The correct option is option (E) 15

To calculate the number of cookies they will need, they first determine the number of students who will be attending the meeting. Since attendance is down by 25%, the number of students attending is 108*(1-0.25) students.

=108 students * 0.75 = 81 students.

To figure out the number of cookies they will need, they multiply the number of students by the number of cookies per student, which is 81 students * 2 cookies= 162 cookies.

Since each recipe makes 15 cookies, they need to make 162 cookies / 15 cookies/recipe = 10.8 recipes.

Since they cannot make partial recipes, they round up and make 11 recipes of cookies for their smaller party.

As 11 is not a given  option, we consider the option which is greater than 11, which is 15.

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The formula to calculate the distance:

d = √(x₂ - x₁)² + (y₂ - y₁)²

The points are:

We substitute and solve:

d = √(-5(-2))² + (-4-1)²

d = √7² + (-5)² = √49 + 25

d = √74 ====> Alternative "A"

Therefore , the solution of the given problem of equation comes out to be  9x^3 - 8x^2.

A mathematical equation is a formula that uses the equal sign (=) to connect two statements and express equality. A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The equal sign is a crucial part of mathematical formulas, especially equations. Algebra is frequently utilized in equations. Algebra is used in mathematics when it is difficult to determine a precise quantity.

Here,

Polynomial function total

Polynomial functions are those that have a leading degree of three or higher. given the total;

(7x^3-4x^2)+(2x^3-4x^2)

Expand => (7x 3-4 times) + (2x 3-4 times)

= > 7x^3-4x^2 + 2x^3-4x^2

assemble similar terms

=> 7x^3 + 2x^3 - 4x^2 -4x^2

=> 9x^3 - 8x^2

Therefore , the solution of the given problem of equation comes out to be 9x^3 - 8x^2.

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An indirect proof is an argument that begins with the assumption that a conclusion is false, then uses logical reasoning to show that the assumption leads to a contradiction.

a fact or assertion that contradicts what someone else said or that differs from another fact or assertion to the point where one of them must be incorrect.

A situation or set of ideas that contradict one another is called a contradiction. A contradiction would be saying out loud that you support the environment while never remembering to empty the recycling. A statement that contains opposing ideas is frequently referred to as a "contradiction in terms."

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Answer:

-4 + 6x.

Step-by-step explanation:

8 - 3(4 - 2x)

= 8 - 12 + 6x

= -4 + 6x.

The correct answer is 6x - 4

Simplify :

8 - 3(4 - 2x)

8 - (12 - 6x)               (using BODMAS rule)

8 - 12 - (-6x)            

( 8 -12) + 6x        

-4 + 6x

= 6x - 4

Answer:

80

Step-by-step explanation:

[tex]6\frac{2}{3} *12[/tex]

First, write the fractions as improper fractions.

[tex]\sf\frac{20}{3} *\frac{12}{1}[/tex]

Multiply.

[tex]\sf\frac{240}{3}[/tex]

Divide.

80

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{6\dfrac{2}{3}\times 12}[/tex]

[tex]\mathsf{= \dfrac{6\times3+2}{3}\times\dfrac{12}{1}}[/tex]

[tex]\mathsf{= \dfrac{18 + 2}{3} \times\dfrac{12}{1}}[/tex]

[tex]\mathsf{= \dfrac{20}{3} \times\dfrac{12}{1}}[/tex]

[tex]\mathsf{= \dfrac{20\times12}{3\times1}}[/tex]

[tex]\mathsf{= \dfrac{240}{3}}[/tex]

[tex]\mathsf{= 240\div 3}[/tex]

[tex]\mathsf{= 80}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{80}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Audrey and Billy are as far as 367 meters apart.

The displacement of an object is its distance covered or moved in a specific direction. Displacement is an example of vector quantity.

A vector quantity is generally any type of quantity which can be expressed in magnitude and direction. Some examples include: weight, displacement, acceleration, force, etc.

Since Audrey walked 285 meters west and Billy walked 213 meters south from the same starting location, then we can determined the distance far apart by applying the Pythagorean theorem.

So that,

/hyp/^2 = /opp/^2 + /adj/^2

Let their distance apart be represented by s,

s^2 = 231^2 + 285^2

      = 53561 + 81225

s  = (134586)^1/2

s = 366.86

Audrey and Billy are as far as 367 meters apart.

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