Solve the system of linear equations using the substitution method.

2d + 8y = 20 and y = 2

A. (1, 1)

B. 4, 4

C. (1, 2)

D. (2, 2)

The equation of the line will be expressed as x = 5.

Slope of a line may be defined as the steepness of a curve plotted on paper. The slope of a line between two points (x₁, y₁) and (x₂, y₂) can be calculated by formula m = (y₂ - y₁)/(x₂ - x₁).

If we have two points and we have to find equation of line through two points (x₁, y₁) then equation will be (y - y₁) = m(x - x₁) where m is the slope of line.

We have two points (5, 3) and slope is undefined.

Undefined slope can be expressed as 1/0. So, the equation of line through (5, 3) will be

(y - 3) = 1/0 (x - 5)

=> x - 5 =0

=> x = 5

This is the equation of line, and this line will be parallel to y-axis.

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If after one year, she received a total of $620 in interest.  The amount that she invest in each account is 2,000 amount invested at 7% , 8,000 amount invested at 6.

Let x represent the amount invested

Hence,

.07x + .06(10,000-x) =620

.07X+600-.06x = 620

Combine like terms

.01x =620-600

.01x=20

Divide both side by .01x

x=20/.01

x =2,000 amount invested at 7%

So,

10,000-2,000 = 8,000 amount invested at 6%

Check :

.07 × 2,000+.06× 8,000=620

150 + 480 = 620

620 =  620

Therefore we can conclude that $2,000 was invested at 7% and $8,000 was invested at 6%.

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Outward journey Speed = 20 km/hr , James stopped for  45  Mins  ,Average speed homewars 15 km/hr

What is speed, for instance?

From graph  Journey Started at 2PM

on 3PM  James covered 20 km

Hence Speed =  (20 - 0)/(3 -2) = 20 km/hr

outward journey Speed = 20 km/hr

Now outward Distance = 45 km

Time taken = 45/20 = 2 hr 15 min

Hence reached at 4 : 15 PM

Started home at 5 PM

James stopped for  45  Mins  (3/4 hrs)

Reached back at 8PM

time taken = 8 - 5 = 3 Hrs

Distance = 45 km

Average speed homeward = 45/3 = 15 km/hr

Average speed homeward =  15 km/hr

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"Subtract to eliminate x" is correct option that is option C for the given set of equations -3x+2y=-15 and -3x-6y=9. equation defines "A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis".

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

-3x+2y=-15

-3x-6y=9

subtract to eliminate x

8y=-24

For the given set of equations, -3x+2y=-15 and -3x-6y=9, option C, "Subtract to eliminate x," is the correct option. Equation explains "The general equation of a straight line is y = mx + c, where m stands for the gradient and y = c for the point where the line crosses the y-axis. This value c is referred to as the intercept on the y-axis. The equation of a straight line with gradient m and intercept c on the y-axis is represented by Y = mx + c ".

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The slope of the line is represented by the word m which is obtained as 0.5.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

To determine a line's inclination or steepness, use the slope formula. Calculating the ratio of the change in the y-axis to the change in the x-axis may be used to calculate the slope of any line.

From the graph, the data is observed as,

(x₁,y₁)=(0,1)

(x₂,y₂) = (-2,0)

The slope of the line is found as,

[tex]\rm m =\dfrac{0-1}{-2-0} \\\\ m = 0.5[/tex]

Thus, the slope of the line is represented by the word m which is obtained as 0.5.

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Answer:

[tex]1\frac{11}{20}[/tex]

Step-by-step explanation:

155% = 155 / 100 = 1.55

1.55 =155/1 × 100 / 100 = 155 / 100

155 / 100 = 31 / 20

31 / 20 = 1 11/20

Similarity Theorems

Triangles ABG and DCB are similar by the AA similarity postulate

"If two angles in one triangle are congruent to two angles in another triangle, then the two triangles are similar"

The steps previous to statement 7 prove angles C and B are congruent because they are formed by two parallel lines that intersect a common line.

On the other side, angles DBC and AGB are congruent also because they are both right angles.

With two corresponding congruent angles, the AA similarity postulate is satisfied and the triangles are similar.

A linear relationship between the distance that a car drives and the amount of gas left in the tank of the car is negative, and the value of r is -0.99

A linear relationship between the distance that a car drives and the amount of gas left in the tank of the car are negative because when a car travels a distance, it consumes fuel, and so fuel decrease with distance

Calculating the value of r

Given, r^2=98.01%

r^2=0.9801

r=±√0.9801

r=±0.99

Since r should be negative, so we pick the negative value and reject the positive value

r=-0.99

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The largest number of weights Jennifer could own is 798.

Repeated addition of the same number is made easier by multiplying the numbers. When we need to merge groups of similar sizes, we employ it. For instance, if there are 5 baskets, each containing 4 apples, we can use multiplication to get the total number of apples, which is 5 x 4 = 20 apples.

We can rapidly determine the total number of things by multiplying. When multiplying, we'll consider the number of groups with similar sizes and the number of items in each group.

Given: The collection of weights : 4 , 6 and 9 pounds

The total weight of the weights = 42 pounds

Thus the largest number of weights jennifer could own is 4+6+9 = 19 multiplied  by the total weight of the weights

= 19 × 42

= 798.

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Answer:

x = 29

y = -18

Step-by-step explanation:

5(29) + 6(-18) = 37

145 - 108 = 37

:)

We will have the following:

From the problem we will have the following expressions:

Now, from this we determine the value for the bill on september:

Now, since there are 3 people, the payment for each one is:

So, the payment for each one is $26.87 in September.

Answer:

Step-by-step explanation:

Statements and reasons.

1) ∠1 and ∠3 are supplementary

Reason: This is true because it is stated in the question.

2) ∠1 + ∠3 = 180º

Reason: By statement 1, ∠1 and ∠3 are supplementary, and by definition, supplementary angles sum up 180º.

3) ∠2 = ∠3

Reason: From the picture we see that ∠2 and ∠3 are opposite congruent angles, so they are equal.

4) ∠1 + ∠2 = 180º

Reason: from statement 2 we have ∠1 + ∠3 = 180º, and from statement 3 we have ∠2 = ∠3, so we have ∠1 + ∠2 = 180º.

5) ∠1 and ∠2 are supplementary

Reason: from statement 4 we have that ∠1 sum up ∠2, so by definition ∠1 and ∠2 are supplementary.

6) line m || line n

Reason: from the picture we see that ∠1 and ∠2 are internal collateral angles of the lines m and n, and from statement 5 we know that ∠1 and ∠2 are supplementary, so we have that the angle between line m and line n is 180°, and by definition, they are parallel lines.

Summary of the reasons

1) It is stated in the question

2) By statement 1 and by definition of supplementary angles.

3) Because they are opposite congruent angles, so they are equal.

4) By statement 2 and 3.

5) By statement 4, and by definition of supplementary angles.

6) By picture ∠1 and ∠2 are internal collateral angles of the lines m and n, and by statement 5 they are supplementary so they are parallel lines.

Answer:

First one is 92

Step-by-step explanation:

Answer:

1. 9/2

2. 7 3/13

3. 3 13/15

4. 3 25/27

5. 2 1/4

6. 3 30/91

7. 2 5/21

8. 6 3/5

Step-by-step explanation:

When I put it like 2 5/21 I mean it's a mixed number.

Now I'll tell you the steps.

1. Find the common denominator (The denominator is the bottom number of the fraction. To find it you have to write out the multiplies of each number and once a number is the same that's the common denominator.)

2. Multiply the numerator by the amount of times it took to find the common denominator. (The numerator is the top number of the fraction. And the amount of times you'll have to multiply the numerator depends. I'll put an example below)

Example:

4/20 ÷ 7/2

2 goes into 20, 10 times so you have to multiply 7 by 10.

Then you'll get

70/20.

Now you can solve it.

4/20÷70/20

(I put random numbers so the answer may turn out funky this is just an example.)

3. Divide the fractions

4. Simplify answer if possible

I hope this helped!

Answer:

discriminant =b^2 -4ac

= (12)^2 -4(-4)(-9)

=0

The slope-intercept form a of the equation of a line is:

Where m is the slope and b is the intercept.

For this exercise m = -1 and b = -1

To find the 'y' values of the table you just have to replace the x values into the equation:

And put these pairs into the graph and join them with a line:

All answers based on the Angles Properties.

Given,

From the figure,

Point P is on the bisector of ∠ABC

Fill the table in the given question.

Now, According to the question:

Statement                                                Reason

1. BP is the bisector                                     Given

2.  ∠ABP ≅ ∠CBP                            The definition of angular bisector

3. ∠BXP and ∠BYP are                                Given

     right angles.

4.  m ∠BXP ≅ m ∠BYP                         All right angles are congruent

5.   BP ≅ BP                                                 Reflexive Property

6. ΔBXP ≅ ΔBYP                                                 AAS

7.  PX ≅ PY                                                         CPCTC

8. Point p is equidistant                             Definition of equidistant.

   from the sides of ∠ABC

Hence, All answers in the table .

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Answer:

A: Common multiple of 4 and 6 is 24

B: They would both be common multiples but they are two different multiples of 4 and 6.

C: 3/4= 18/24    1/6= 4/24

Step-by-step explanation:

A common multiple is a number that two numbers can be multiplied to. Something that both 4 and 6 can be multiplied to is 24, but there are many other multiples of 4 and 6  as well.

Answer:

40

Step-by-step explanation:

why? because there are 5 pieces in each building set so 5×8=40 so the answer is 40

The inequality to find the number of tickets Isaac needs to sell to earn than $450 is 100 + 3x ≤ 450 and the number of times he will sell the tickets is 117.

So, the inequality can be:

Issac earns:-

Isaac wants to earn $450,

So, the inequality that can be formed here is:

Let, 'x' be the number of times Isaac sell the tickets.

By solving we will get:

Therefore, the inequality to find the number of tickets Isaac needs to sell to earn than $450 is 100 + 3x ≤ 450 and the number of times he will sell the tickets is 117.

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The points -5 2/3 and 5 1/3 in the number line attached

An equation shows the relationship between two or more numbers and variables.

Number line a line containing numbers marked at intervals.

The mixed fraction -5 2/3 is equivalent to -[(5 * 3 + 2)/3] = -17/3

The mixed fraction 5 1/3 is equivalent to [(5 * 3 + 1)/3] = 16/3

The points -5 2/3 and 5 1/3 are represented

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The probability that at least one of them will score a goal if they each play the ball once is 47/48.

Probability is a mathematical and scientific term that describes the possibility or occurrence of an event. Many events are difficult to predict with absolute accuracy. Only the likelihood of an event occurring, i.e. how likely it is, can be predicted using probability.

Given:

The probabilities of Wukong and Nice scoring in the match are 7/8 and 5/6 respectively.

The probability that at least one of them will score a goal is,

=  1 - P(both of them not scoring a goal)

So the probability of Wukong and Nice not scoring a goal in the match is,

(1 - 7/8) (1 - 5/6) =  (1/8)(1/6) = 1/48

Now the required probability is,

=  1 - P(both of them not scoring a goal)

= 1 - 1/48

= 47/48

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Answer: -10 or 9

Step-by-step explanation:

Let the number be x. Then,

[tex]x^2 +x=90\\\\x^2 +x-90=0\\\\(x+10)(x-9)=0\\\\x=-10, 9[/tex]

Answer:

y=12

Step-by-step explanation:

1.Took the ratio between x and y value.

18:6 is the same as 3:1 ratio this means that our y value will be 3 times greater than our x value.

Answer:

Step-by-step explanation: