Which expression is equivalent to
14x-21
7
A. 2x - 21
B. 2x-3
c. 7x - 28
D. 7x - 14

The linear system could the graph represent is, x + y = 2 & 2x + 2y = 8

So, Option D is correct.

The equation of a straight line is a relationship between x and y coordinates, The equation of a straight line for given two points  is y-y₁ = y₂-y₁/x₂-x₁(x-x₁)

Given that,

The graph of  linear system

first line intersects the  x & y   axes at (2,0) & (0,2) respectively

Similarly, second line intersects the  x & y   axes at (4,0) & (0,4) respectively

By using two point form of the line we can write equation for both the lines,

x + y = 2  _____ (1)

x + y = 4  _____ (2)

by multiplying 2 in equation  (2)

2x + 2y  = 8

Hence, The linear system is  x + y = 2 & 2x + 2y = 8

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Answer: We can use the concept of conditional probability to find the probability that a student who passed the first test also passed the second. Conditional probability is the probability of an event occurring given that another event has already occurred.

The probability that a student who passed the first test also passed the second is the probability of both events occurring (passing both tests) divided by the probability of the first event occurring (passing the first test).

We can use the information provided to calculate this probability:

Probability of passing both tests = 0.45 (45%)

Probability of passing the first test = 0.60 (60%)

Probability of passing both tests given that the student passed the first test = (Probability of passing both tests) / (Probability of passing the first test) = 0.45 / 0.60 = 0.75

So the probability that a student who passed the first test also passed the second is 0.75 or 75%.

It means, if we know that a student passed the first test, there's a 75% chance that the student also passed the second test.

Step-by-step explanation:

The midpoint between (-7,-9) and (-0.5,-3) is (-3.75,-6)

The midpoint between two points in a Cartesian plane is the point that is equidistant from both points and is located exactly in the middle of the line segment connecting the two points. To find the midpoint, we need to average the x-coordinates and the y-coordinates of the two given points.

Given the points (-7,-9) and (-0.5,-3), the midpoint can be found by:

averaging the x-coordinates (-7 + -0.5) / 2 = -3.75

averaging the y-coordinates (-9 + -3) / 2 = -6

So, the midpoint between (-7,-9) and (-0.5,-3) is (-3.75,-6)

Alternatively, the midpoint formula is:

(x1+x2)/2 , (y1+y2)/2

So for the given points,

(x1,y1)= (-7,-9) and (x2,y2)= (-0.5,-3)

Midpoint (x,y) = (-7+(-0.5))/2 ,(-9+(-3))/2

= (-3.75,-6)

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The amount of vanilla in one container of pudding is given as follows:

One teaspoon.

The amount of vanilla in one container of pudding is found applying the proportions in the context of the problem, via a rule of three.

The rule of three is defined as follows:

1/6 teaspoon - 2/12 containers.

x teaspoon - 1 container.

The first line can be simplified as follows:

1/6 teaspoon - 1/6 containers.

(as 2/12 = 1/6).

Hence there is one teaspoon of vanilla in one container of pudding.

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Answer:

f(11) = 87

Step-by-step explanation:

substitute n = 11 into f(n) , that is

f(11) = 7 + 8(11 - 1) = 7 + 8(10) = 7 + 80 = 87

Barbara would choose the apples three times, so a visual model using Whole Numbers by Fractions would be created to determine the outcome. 2x

A whole can be represented by any number of equal parts, or fractions. The number of units of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. Numbers are expressed in mathematics as the ratio of the numerator to the denominator. In simple fractions, each of these is an integer. A complicated fraction contains a fraction in either the numerator or denominator. There is a difference between the numerators and denominators of true fractions. A sum that is a fraction of a whole is referred to as a fraction. You can evaluate it by dissecting the whole into smaller pieces. For example, 12 is used to represent one-half of a full number or item.

given

she is correct as  Barbara picked 36 apples

in one time she put 12 apples in the basket

Barbara would choose the apples three times, so a visual model using Whole Numbers by Fractions would be created to determine the outcome. 2x

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The values of the variables in the similar triangles are y = 2.25 units, x = 5 units and r = 3.75 units

Similar triangles are triangles that have the same shape, but possibly different size. Two triangles are similar if and only if their corresponding angles are congruent, that is, they have the same measure. When two triangles are similar, their corresponding side lengths are in proportion.

Since the triangles are similar. We write:

h/y = y/3

Since h = 3, we have:

3/4 = y/3

y = 9/4 = 2.25 units

x = √(4² + h²)        (Pythagoras theorem)

x = √(4² + 3²) = 5 units

r = √(y² + 3²)

r = √(2.25² +  3²)  = 3.75 units

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f(1) = -1

Quadratic equations form the shape of a parabola, which looks like a U-shape.

Graph

To find f(1) we need to find the y-value when x = 1. To do this, we can just look at the graph. Find where on the graph x = 1, then look for where the graph intersects this value. This graph has an x value of 1 when y = -1. We can see this at the coordinate point (1,-1). Thus, f(1) = -1.

Equation

We can also solve this using the equation of the function. This function is represented by f(x) = x² - 2. Now, to find f(1), plug 1 in for x.

This also shows that f(1) = -1.

Answer: 250

Step-by-step explanation:

249 is closer to 250 than 240

Answer:

Step-by-step explanation:

249 is rounded to closest to 250

If the equation be 3/2X+6 =2/5x+9 then the length of side AB is -15/11.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Two expressions joined by an equal sign form a mathematical statement known as an equation.

A condition on a variable (or variables) is a pair of expressions in the variable (or variables) that have the same value. The solution, also known as the root of the equation, is the quantity for which the equation holds true. Even if the LHS and RHS are switched, an equation still holds true.

Let the equation be 3/2X + 6 = 2/5x + 9

simplifying the equation, we get

15x + 27 = 4x + 12

15x = 4x - 15

11x = -15

Divide both sides by 11, we get

[tex]$\frac{11 x}{11}=\frac{-15}{11}$$[/tex]

[tex]$x=-\frac{15}{11}$$[/tex]

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The answer is 1.4

In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.

Given here:

2.6-1.2=1.4

Hence, The answer is 1.4

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}[/tex]

[tex]A = 2000\left(1+\frac{0.03}{12}\right)^{12\cdot 20}\implies A=2000(1.0025)^{240} \implies \boxed{A \approx 3641.51} \\\\\\ 3641.51~~ - ~~2000~~ \approx~~ \stackrel{earned~interest}{\boxed{1641.51}}[/tex]

The rocket reaches a maximum height of 1045.6 feet.

The height of the rocket under free fall is described by a parabola and parabolas are explained by second order polynomials, whose form are:

y = a · x² + b · x + c

Where:

The maximum height can be found by means of discriminant of the quadratic formula associated with following variant:

a · x² + b · x + (c - y) = 0

Discriminant

b² - 4 · a · (c - y) = 0

b² = 4 · a · (c - y)

b² / (4 · a) = c - y

y = c - b² / (4 · a)

If we know that a = - 16, b = 246 and c = 100, then the maximum height reached by the rocket is:

y = 100 - 246² / [4 · (- 16)]

y = 1045.563 ft

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The distance between the given 2 points (-2, 3) and (5, -3) is 9.21 units.

The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points.

This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.

So, we have the points:

(-2, 3) and (5, -3)

Distance formula: d=((x2 - x1)² + (y2 - y1)²)

Insert values and calculate as follows:

d=((5 - (-2))² + (-3 - 3)²)

d=((7)²+(-6)²)

d=√85
d=9.21

Therefore, the distance between the given 2 points (-2, 3) and (5, -3) is 9.21 units.

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1.20C + 3 >= 13.50

Where C is the number of chores Janie does.

On the left side of the inequality, 1.20C represents the amount of money Janie earns from doing chores, and 3 represents the amount of money she already has. The inequality states that the sum of the money she earns from doing chores and the money she already has must be greater than or equal to the cost of the CD (13.50).

This inequality can be simplified:

1.20C >= 10.50

C >= 8.75

Thus, Janie could do at least 8.75 chores to have enough money to buy the CD, since she can do fractions of chores.

Answer:

3 + 1.2 c > 13.50

Step-by-step explanation:

First of all, let's write an equation that gives us the income Janie gets for doing chores. As she earns 1.20 (I will omit the $ symbol for simplicity) for each chore c she makes we can write income depending on the amount of chores as:

income(c) = 1.2 c

If she  does 1 chore she gets 1.2, if she does 4 chores she gets 4.8 and so on for any c (obviously c is positive as she can do negative chores).

So, her total money will be the sum of what she earns for chores and the money she already has: 3.

money (c) = 3 + 1.2 c

If she does 2 chores she has 3+2.4=5.4 and so on for any c.

Now we need her money to be greater or equal to 13.50 in order to buy the CD. The inequality is:

money (c) > 13.50

3 + 1.2 c > 13.50

We can go further and solve it. First lets subtract 3 in both sides:

12 c > 10.50

Now, divide both sides by 1.2:

c > 10.50 / 1.2

c > 8.75

So, she needs at least 8.75 chores to earn enough money to buy the CD. As she can do fractions of chores the answer is 8.75 chores. Is she couldn't do fractions she would need at least 9 chores.

Answer:

6.8125

Step-by-step explanation:

The table of w = t + 11.2 is:

t     w

0    11.2

1     12.2

2    13.2

3    14.2

4    15.2

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,

w = t + 11.2

The table can be calculated as,

When t = 1, w = 1 + 11.2 = 12.2

When t = 2, w = 2 + 11.2 = 13.2

When t = 3, w = 3 + 11.2 = 14.2

When t = 4, w = 15.2

So on..

Thus,

t     w

0    11.2

1     12.2

2    13.2

3    14.2

4    15.2

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A speculator estimates that the price of the 0.29 carat diamond ring will be y = 1200 by y = 5000x - 250.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

given

y = 5000x - 250

y = 5000 * 0.29 - 250

y = 1200

A speculator estimates that the price of the 0.29 carat diamond ring will be y = 1200 by y = 5000x - 250.

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Answer:

To find out how many paddle balls will be in each hopper, you can divide the total number of paddle balls by the number of hoppers.

paddle balls ÷ hoppers = paddle balls per hopper

2798 ÷ 40 = 69.95

So there will be approximately 69.95 paddle balls in each hopper. Since it's not possible to put 0.95 of a paddleball in a hopper, you can round it to the nearest whole number. This means each hopper will have 70 paddleballs.

Step-by-step explanation:

Poopy man is my husband uwu

anyways ur answer is 3^x

Answer:

60

Step-by-step explanation:

360 degrees divided by 6 sides equal 60 degrees

The ratio of miles to hours is 24 to 2, which can be written as 24:2 or 12:1.

What is the ratio?

A ratio is a mathematical comparison of two or more quantities. It is used to show the relationship between the sizes of different quantities or amounts. It is typically expressed as a ratio of two numbers, such as 24:2, with a colon separating the numbers.

The ratio of miles to hours is 24 to 2. This can also be written as 24:2 or 12:1. It means that for every 24 miles, 2 hours are required to travel that distance.

Hence, The ratio of miles to hours is 24 to 2, which can be written as 24:2 or 12:1.

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The binomial probability that exactly 4 out of 8 customers will use the Self-Checkout is 0.008.

Binomial probability is the probability based on the binomial distribution.

The binomial distribution is used in statistics to summarize the likelihood that a value will take one of two independent values (for example, success or failure) under a given set of parameters or assumptions.

The binomial distribution formula is:

Pₓ = {ⁿ \ ₓ} pˣ qⁿ ⁻ ˣ

P = binomial probability

x = number of times for a specific outcome within n trials

{ⁿ \ ₓ} = number of combinations

p = probability of success on a single trial

q = probability of failure on a single trial

n = number of trials

Random sample, n = 8

Specific outcome within n trials = 4

pˣ = 0.5⁴

= 0.0625

qⁿ = (1 - 0.5)⁸ ⁻ ⁴

= 0.5⁴

= 0.0625

Pₓ = {ⁿ \ ₓ} pˣ qⁿ ⁻ ˣ

= 8/4 x 0.0625 x 0.0625

= 2 x 0.0625 x 0.0625

= 0.0078125

= 0.008

Thus, the probability of precisely 4 customers using the Self-Checkout is 0.008.

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60.759×10⁶ is the value of the expression (9.42×10⁴)(6.45×10²).

An expression is combination of variables, numbers and operators.

The given expression is (9.42×10⁴)(6.45×10²)

We have to find the value of the expression.

9.42×6.45×10²×10⁴

60.759×10²×10⁴

Bases are same then the powers will be added.

60.759×10⁶

Hence, 60.759×10⁶ is the value of the expression (9.42×10⁴)(6.45×10²).

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The general solution to the differential equation y'' + 2y = −18x^2e^(2x) by undetermined coefficients is y = (-9x^2)e^(2x).

The given differential equation is y'' + 2y = −18x^2e^(2x)

To solve this equation by undetermined coefficients, we first find the characteristic equation of the homogeneous equation, which is r^2 + 2 = 0.

The solutions to this equation are r = i and r = -i. Therefore the general solution to the homogeneous equation is yh(x) = c1 cos(x) + c2 sin(x)

Now, we use the method of undetermined coefficients to guess the form of the particular solution. Since the non-homogeneous term is −18x^2e^(2x), we guess that the particular solution is of the form

yp = (Ax^3 + Bx^2)e^(2x) + Cx^2e^(2x).

Substituting this into the differential equation, we get

y'' + 2y = (6Ax + 2B)e^(2x) + 2Cxe^(2x) = −18x^2e^(2x)

Equating the coefficients of the like terms, we get:

6A = 0, 2B = −18, and 2C = 0

Solving for A, B and C, we get A = 0, B = −9 and C = 0

Therefore, the general solution to the differential equation y'' + 2y = −18x^2e^(2x) by undetermined coefficients is y = (Ax^3 + Bx^2)e^(2x) + Cx^2e^(2x) = (-9x^2)e^(2x)

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Answer:

=4-347-12-8-7+27

=-343

*Mark me brainliest -_- *_*

Answer: (4-347-12)-(8+7-27)= -343

Answer:

Hint: everything in that big [] is to the power of zero. anything to the power of zero is one. so

1+(6-8)=?

The two factors of the first number 36 which their sum is equal to 13 are 4 and 9.

Factor is a number that divides another number without a remainder. That is if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product.

The first number 36 have the following factors:

1, 2, 3, 4, 6, 9, 12, 18, and 36.

the factors 4 and 9 will be the factors in question because;

4 × 9 = 36

4 + 9 = 13

Therefore, 4 and 9 are the two factors of 36 that their product is the first number 36 and their sum is the second number 13.

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Answer:

23

Step-by-step explanation:

1/2-2.5=9

1/2x=9+2.5

x=11.5/0.5

x=23