solve the following systems of linear equations using substitution

4x - 2y = 20 and x - 4y = -16

Answer:

shown below

Explanation:

so first you can graph a dot at (2,-1), since it must go through that line. Then you can use the slope, 3, to figure out the next dot. The slope 3 can be put into a fraction, liking like 3/1. Then you use rise/run from your point (2,-1). You go up 3, and right 1. Using that, your next point is (3,2). Plot that dot, and then use a straight edge to draw your line. It looks like how it is in the picture.

The statements that are true are:

The x-coordinate of the solution is 1.

The y-coordinate of the solution is -1.

The solution to a system of equations that is graphed is the point at which the two lines intersect. The coordinates of the intersection point are the solution to the system of equations.

In other words, if we have two lines represented by two linear equations, the solution to the system of equations is the point where the two lines intersect. This point is unique and it satisfies both equations simultaneously.

Therefore, the graph shows that both lines intercept at (1, -1). Therefore, the statements that will be true are:

The x-coordinate of the solution is 1.

The y-coordinate of the solution is -1.

Learn more about the solution of a system on:

https://brainly.com/question/13729904

#SPJ1

Answer: look at the image for the answer, and give me brainliest

Step-by-step explanation:

Answer:

(a) 3/7

(b) 2/7

(c) 0 or Impossible

Step-by-step explanation:

(a) There are seven letters in total. Three of the letters are s. Therefore out of the seven cards, three are the letter s. - 3/7

(b) Again there are seven letters in total. Two of the letters are vowels. Therefore out of the seven cards, two are vowels. - 2/7

(c) Yet again there are seven letters in total. None of the letters are a. Therefore out of the seven cards, none are the letter a. It is impossible to get the letter a - 0/7

Hope this helps :)

Answer:

True

Step-by-step explanation:

2.5 times 2 = 5

So, the answer is true.

Answer:

X= 5

Step-by-step explanation:

If shape D is a reflection of shape C then the distance between the shape and the y-axis will be the same on both sides; so, if shape C has a 5cm distance between it and the y-axis, shape D will also have 5cm distance between it and the y-axis.

Answer:

18 and A i think

Step-by-step explanation:

i don t really know if this is right but since it only asks the area of E and not the whole cuboid

9 × 2 = 18

A also equals to 18 because it has the the same width and length as E.

hope this helps

The value of the measure of 5 is,

⇒ ∠5 = 105°

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

Two parallel lines are cut by a transversal.

And, the measure of 2 is 75°.

Here, Angle 2 and 3 are vertically opposite angle.

Hence, angle 2 and 3 are equal.

And, Angle 3 and 5 are adjacent angle.

Hence, We get;

⇒ ∠3 + ∠5 = 180°

⇒ 75 + ∠5 = 180°

⇒ ∠5 = 180 - 75

⇒ ∠5 = 105°

Thus, The value of the measure of 5 is,

⇒ ∠5 = 105°

Learn more about the angle visit:;

https://brainly.com/question/25716982

#SPJ5

Answer:

Step-by-step explanation:

The formula for the circumference of a circle is 2 * π * r, where r is the radius of the circle.

Given that the radius of the circle is 13 millimeters, the circumference of the circle is:

2 * π * 13 = 26 * π millimeters

Since the value of π is approximately 3.14, the approximate circumference of the circle is:

26 * 3.14 = 81.64 millimeters.

Check the picture below.

so from the provided information, we can say that the parabola has a vertex at (3 , 45) and it has a zero at (6 , 0) or we can say is just another point at (6 , 0)

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=3\\ k=45\\ \end{cases}\implies y=a(~~x-3~~)^2 + 45\hspace{4em}\textit{we also know that} \begin{cases} x=6\\ y=0 \end{cases} \\\\\\ 0=a(6-3)^2+45\implies -45=9a\implies \cfrac{-45}{9}=a\implies -5=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=-5(x-3)^2 + 45 \end{array}} ~\hfill[/tex]

Answer:

x/3 + 5 = 10

Move 5 to the side

x/3 = 5

Multiply both sides by 3

2x/3 = 15

Simplify

x = 15

The correct descriptions of the given numbers are as follows:

A rational number is one that can be written as P/Q, where P and Q are both integers and Q is greater than zero. An illustration of a rational number is 2/3.

However, an irrational number cannot be expressed using straightforward fractions. An example of an irrational number is √2.

Learn more about rational and irrational numbers at: https://brainly.com/question/20400557

#SPJ1

Answer: 67.5

Step-by-Step:

If Helen has 90 stamps, then 50% of what she has is 45 stamps.  Half of 45 is 22.5 which is 25% of what Helen has. To find out how many stamps Peggy has, we'll have to do 90 - 22.5 which is 67.5.

By evaluating an equation we will see that the value of the coins is $5.

Each nickel is whorth $0.10 and each quarter is whorth $0.25, so the value for n nickels and q quarters is given by the equation below:

v = q*0.25 + n*0.10

Here we know thathe has 10 nickels and 8 quarters, replacing that we will get:

v = 8*0.25 + 10*0.10

v = 4 + 1

v = 5

The value is 5 dollars.

Laern more about equations at:

https://brainly.com/question/13729904

#SPJ1

Answer:

y = -5/4x + 3

Step-by-step explanation:

slope-intercept form is:  y = mx + b

where 'm' represents slope and 'b' represents the y-intercept

basically we have to solve for 'y':

first step,  add -5x to each side to get:

-4y = 5x - 12

last step,  divide each side by -4 to get:

y = -5/4x + 3

slope equals -5/4

y-intercept equals 3

The area of the composite figure is equal to 216 square inches

The composite figure can be observed to be made up of six identical squares, so we shall calculate for the area of one square and then multiply the result by six to get the total area of the composite figure as follows:

area of a square = length²

area of the one square = 6 in × 6 in

area of the one square = 36 in²

total area of the composite figure = 36 in² × 6

total area of the composite figure = 216 in²

Therefore, the area of the composite figure is equal to 216 square inches.

Know more about area here:https://brainly.com/question/21135654

#SPJ1

Debbie should have included 8 as a possible choice. The correct inequality is p ≤ 8.

Debbie's error is that she did not include the possibility that exactly 8 passengers could fit in the van. Therefore, the correct inequality symbol to use would be less than or equal to, represented by "<=".

The correct inequality is p <= 8. This means that the number of passengers that can fit in the van is either less than or equal to 8. So, including 8 as a possible choice is also necessary to correctly represent the situation.

Hence the correct answer is C.

To know more about inequality, here

https://brainly.com/question/28823603

#SPJ4

--The given question is incorrect; the correct question is

"The Martins' van can hold up to 8 passengers. Debbie writes the inequality p <8, where p is the number of passengers that can fit in the van. Select the choice that provides the best explanation for Debbie's error and the correct answer in this case.

A. Debbie should have used 8p because 8 passengers can fit in the van. The correct inequality is 8p < 1

B. Debbie should have switched the inequality symbol to greater than. The correct inequality is p > 8.

C. Debbie should have included 8 as a possible choice. The correct inequality is p ≤ 8.

D. Debbie should have used the not equals sign to compare the two sides of the inequality. The correct answer is p = 8"--

Option B is the correct answer which is Paraphrasing plagiarism true for the Student Version.

It can be defined as the student's version displaying paraphrasing plagiarism.

This implies that the student was unable to make an appropriate in-text citation with the name of the author and date to display the reference to the original source.

The student's version also displays 'paraphrasing plagiarism' when the student was unable to make an appropriate in-text citation with the name of the author and date to display with reference to the original source.

An in-text citation is necessary despite the student paraphrasing the information and citing its bibliographical reference in order to avoid plagiarism.

To know more about Plagiarism:

https://brainly.com/question/17307455

#SPJ4

Full question:

In the case below, the original source material is given along with a sample of student work. Determine the type of plagiarism by clicking the appropriate radio button.

Original Source Material

Student Version

Learning is a complex set of processes that may vary according to the developmental level of the learner, the nature of the task, and the context in which the learning is to occur. As already indicated, no one theory can capture all the variables involved in learning.

References:

Gredler, M. E. (2001). Learning and instruction: Theory into practice (4th Ed.). Upper Saddle, NJ: Prentice-Hall.

A learning theory, there, comprises a set of constructs linking observed changes in performance with what is thought to bring about those changes.

References:

Driscoll, M. P. (2000). Psychology of learning for instruction (2nd Ed.). Needham Heights, MA: Allyn & Bacon.

A learning theory is made up of "a set of constructs linking observed changes in performance with whatever is thought to bring about those changes" (Driscoll, 2000). Therefore, since "learning is a complex set of processes that may vary according to the developmental level of the learner, the nature of the task, and the context in which the learning is to occur, it is apparent that no one theory can capture all the variables involved in learning" (Gredler, 2001).

Which of the following is true for the Student Version above?

Word-for-Word plagiarism

Paraphrasing plagiarism

This is not plagiarism

The function that represents the graph which is piecewise function is written as y = -5, x = 0 and y = - 6,  x ≠ 0.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The equation of the line that is parallel to x-axis is given as,

y = c

The equation passes through (1, -6), then we have

-6 = c

Then the equation is given as,

y = -6, x ≠ 0

And the other equation is given as,

y = - 5, x = 0

Then the piecewise function is given as,

y = -5, x = 0

y = - 6,  x ≠ 0

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ1

ok so to find the opposite of something like this you gotta simplify it first

a negative times a negative is a positive

-(-3) = 3

the opposite of 3 is... drumroll please...   -3

Hope this helps,

- Jeron :- )

Answer:

-3

Step-by-step explanation:

-(-3) is just positive 3

Answer: The interest for the loan for each day is 5000 x 6.9/100 = $345.

For the first installment, the interest will be for 60 - 1 = 59 days. So, the interest for this period will be 59 x $345/365 = $166.55.

The first installment will be $5000 + $166.55 = $5166.55.

For the second installment, the interest will be for 120 - 60 = 60 days. So, the interest for this period will be 60 x $345/365 = $168.76.

The second installment will be $5000 + $168.76 = $5168.76.

For the third installment, the interest will be for 180 - 120 = 60 days. So, the interest for this period will be 60 x $345/365 = $168.76.

The third installment will be $5000 + $168.76 = $5168.76.

Therefore, each installment will be $5166.55, $5168.76, and $5168.76.

Step-by-step explanation:

The prove of BC || AD is shown in below.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

⇒ ΔABE ≅ ΔCDE

Now, Prove of BC || AD is shown in below as;

⇒ ΔABE ≅ ΔCDE    ( Given )

Hence, We get;

⇒ AB ≈ DC

Now, In triangle ΔBEC and ΔDEA;

⇒ ∠BEC = ∠AED   (Vertically opposite angle)

⇒ BE = ED

⇒ AE = EC

Hence, By SAS congruency;

Triangle ΔBEC and ΔDEA are congruent.

Hence, We get;

⇒ BC = AD

Since, In a parallelogram ABCD;

⇒ AB = CD

⇒ AD = BC

Hence, We get;

⇒ BC || AD

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

The first graph represents [tex]f(x)=2(3) ^x[/tex].

Graph of a function:

All of the plane's points having the form (x, f(x)) that make up a function f's graph are gathered together. The graph of f is also referred as the graph of y = f. (x).

The given function is,

[tex]f(x)=2(3)^x[/tex]

Putting x = 1,

[tex]f(x)= 2(3)^1=6[/tex]

The point (1, 6) that is (x, f(x)) must therefore satisfy the condition or be on the curve of the function.

Only in case of the first graph, the point (1, 6) lies on the curve.

As a result, the first graph accurately depicts the function.

To learn more about a function's graph, go to:

https://brainly.com/question/12635801

#SPJ1

The probability of drawing a 1 or an even number from the set {1, 2, 3, 4} is 75%.

There are four cards in the set {1, 2, 3, 4}, of which two are even (2 and 4) and one is odd (1). To find the probability of drawing a 1 or an even number, we can add the probabilities of each event occurring:

P(1 or even) = P(1) + P(even)

Since each card is equally likely to be drawn, each of these probabilities is equal to the number of cards that satisfy the condition divided by the total number of cards:

P(1) = 1/4 (there is one card with a 1)

P(even) = 2/4 = 1/2 (there are two cards with even numbers out of four)

Therefore,

P(1 or even) = P(1) + P(even)

= 1/4 + 1/2

= 3/4

To express the answer as a percentage, we can multiply by 100:

P(1 or even) = 3/4 * 100%

=> 75%

To learn more about Probability :

https://brainly.com/question/24756209

#SPJ4

Richard can expect the population to be 4,100 people 4 years after he moved there.

To model the population growth, we can use an exponential equation in the form y = a * b^x, where a is the starting population (3,650), b is the growth factor, and x is the number of years after Richard moved there.

To find the value of b, we can use the population growth between the first year (x = 1) and the second year (x = 2). Let's call the population at x = 2 as P.

P = a * b^2

P = 3,869

Substituting the values, we get:

3,869 = 3,650 * b^2

Dividing both sides by 3,650, we get:

b^2 = 1.06

Taking the square root of both sides, we get:

b = 1.03

So, the exponential equation that models the Clover Hills population is:

y = 3,650 * 1.03^x

To find the population 4 years after Richard moved there (x = 4), we can substitute x = 4 into the equation:

y = 3,650 * 1.03^4

y = 3,650 * 1.129

y = 4,123.738

Rounding to the nearest hundred people, we get:

y = 4,100 people

Learn more about functions on:

https://brainly.com/question/10439235

#SPJ1

the probability of that there will be 2 defective items among them is 0.476 or 47.6%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Calculating the possibility of an event occurring is the focus of the math discipline of probability. Probability gauges the likelihood of an event occurring.

there are 4 defective items in a lot consisting of 10 items.

from this lot we select 5 items at random.

The number of ways in which 55 items can be selected 10 C 5 = 252.

Number of ways in which 2 defective systems and 3 non-defective systems can be selected

4C2 * 6C3 = 6*20=120

The probability = 120 / 252 = 0.476

Hence the probability of that there will be 2 defective items among them is 0.476 or 47.6%.

Learn more about probability, by the following link.

brainly.com/question/24756209

#SPJ4

The solution of the inequalities y > −3x + 3 and y > x + 2 will be (2, 5). Then the correct option is C.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The system of inequalities is given below.

y > −3x + 3

The region above the line is considered.

y > x + 2

The region above the line is considered.

The overlap portion of the region is the solution. Point (2, 5) lies in that region.

The solution of the inequalities y > −3x + 3 and y > x + 2 will be (2, 5). Then the correct option is C.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ1

Answer:

18 2-point shots.

Step-by-step explanation:

Two equations.

First modeling 2 point and 3 point shots as x and y.

2x + 3y = 60

Second, modeling the number of shots.

x + y = 26

Which you can alter to substitute.

x = 26 - y

Substitute.

2(26 - y) + 3y = 60

52 - 2y + 3y = 60

y = 8

The team made 8 3-point shots and 18 2-point shots.

The solution of the inequality is:

s ≥ -0.86

And the graph can be seen on the image at the end.

Here we want to find and graph the solution set of the inequality below:

(2/5)*s + 7 ≥ 3 - 4.2*s

To do so, first we need to isolate s in one of the sides, then let's do that:

(2/5)*s + 7 ≥ 3 - 4.2*s

(2/5)*s + 4.2*s ≥ 3 - 7

(2/5 + 4.2)*s  ≥ -4

And we know that 4.2 = 21/5

Then:

(2/5 + 21/5)*s  ≥ -4

(23/5)*s ≥ -4

s ≥ -4*5/23

s ≥ -20/23

s ≥ -0.86

The graph of this will something like the one below:

Learn more about inequalities at:

https://brainly.com/question/24372553

#SPJ1