7) Graph the systems of linear equations on your calculator ​

The value for the line segment FG represented by the algebraic expression 2x is equal to 4.

An algebraic equation is a mathematical statement that contains two equated algebraic expressions.

The sum of the line segments FG and GH is equal to FH so;

2x + x + 4 = 10

3x + 4 = 10

3x = 10 - 4 {subtract 4 from both sides}

3x = 6

x = 6/3

x = 2

line segment FG = 2(2) = 4

line segment GH = 2 + 4 = 6

Therefore, the value for the line segment FG represented by the algebraic expression 2x is equal to 4.

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He used five 40-cent stamps and eight 7-cent stamps.

Let x stand for how many 40-cent stamps he applied.

Let y stand in for the quantity of 7-cent stamps he applied.

41 cents = 40/100 = $0.40

7 cents = 7/100 = $0.07

To cover the $2.56 in postage, he uses 40-cent and 7-cent stamps. That implies

0.4x + 0.07y = 2.56

When you multiply something by 100, you get

40x + 7y = 256

7y = 256 -40x

The accompanying x and y values must both be whole numbers in order to satisfy the equation.

If x = 4,

7y = 256 - 40 × 4 = 96

y = 96/7 = 13.71

If x = 5,

7y = 256 - 40 × 5 = 56

y = 56/7 = 8

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Answer:

3:2

Step-by-step explanation:

A short-run economic event like a recession is more likely to have aggregate demand rather than aggregate supply as its main cause.

The theory used in this question is the Keynesian Theory of Income and Expenditure,

It asserts that total spending (C + I + G + X - M) equals total output (Y), where C represents consumption, I represents investment, G represents government spending, X represents exports, and M represents imports.

Step 1: In order to solve for G, we must first recall the equation for calculating Gross Domestic Product (GDP):

GDP = C + I + G + (X - M)

Step 2: We have five of the six variables given in the equation and can solve for G by rearranging the equation to solve for G.

GDP - C - I - (X - M) = G

Step 3: Substitute the given values for each of the variables in the rearranged equation, starting with GDP.

900 - 500 - 300 - (200 - 200) = G

Step 4: To simplify the problem, subtract 500 from each side.

400 - 300 = G

Step 5: 300 should be subtracted from each side of the equation.

100 = G

Therefore, Government spending G = 100.

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No, the equation 2x + 2 = x + 1 has solution which is equal to x = -1.

Mia gave statement for the equation:

Left hand side is double the right hand side implies it has no solution.

2x + 2 = x + 1

Verification for the solution:

Simplify the above equation by subtracting  'x' both the sides we get,

⇒ 2x - x + 2 = x - x + 1

⇒ x + 2 = 1

Now subtract '2' from both the sides of the equations we get,

⇒ x + 2 - 2 = 1 - 2

⇒ x = -1

The above equation has no solution is incorrect statement.

Therefore, the equation 2x + 2 = x + 1 has no solution is wrong statement as the solution is given by x = -1.

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If Desi has a coupon  that entitles him to 35% off the regular price of a sweater , then another expression that represents the price Desi will pay is 0.65x .

the original price of the sweater is = x ;

the percent discount that Desi gets by applying the coupon is = 35% ;

Desi gets 35% discount , it means that Desi only need to pay the remaining 65% of the price .

So , the remaining price of the sweater to be paid by Desi is = 65% of "x" ;

= 0.65x  ...(because 65% = 0.65 ) .

Therefore , the another expression representing the situation is 0.65x .

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Answer:

Step-by-step explanation:

-2y=2-3x-5y=10-5x

-2y=10-5x

2-3x-5y-5x

(SIMPLIFY)

5x-2y=10

2x-5y=8

(MULTIPLY BOTH SIDES)

-25x-10y=-50

4x-10y=16

(ELIMINATE ONE VARIABLE BY ADDING THE EQUATIONS)

-21x=-34

(DIVIDE BOTH SIDES)

X=34/21

(SUBSTITUTE THE VALUE OF X)

2x34/21-5y=8

(SOLVE EQUATION)

Y=-20/21

(A POSSIBLE SOLUTION IS)

(X,Y)=(34/21 , -20/21)

(CHECK THE SOLUTION)

-2x(-20/21)=2-3x 34/21 - 5x (-20/21)=10-5 X 34/21

(SIMPLIFY)

40/21=40/21=40/21

(X,Y)= (34/21 , -20/21)

(SOLUTION)

The correct answer is option B : False. Using a stratified sample guarantees that members of each group within a population will be sampled. and true statement is "Using a random sample guarantees that members of each group within a population have an equal chance of being sampled".

False. Using a systematic sample does not guarantee that members of each group within a population will be sampled. A systematic sample is a type of probability sampling in which a random starting point is chosen and then every nth item is selected from the population. This can lead to bias if the population contains patterns or cycles.

A true statement would be: "Using a random sample guarantees that members of each group within a population have an equal chance of being sampled."

The given statement is False

The correct form is given below-

Using a random sample guarantees that members of each group within a population have an equal chance of being sampled.

Thus, The correct answer is option B : False. Using a stratified sample guarantees that members of each group within a population will be sampled. and true statement is "Using a random sample guarantees that members of each group within a population have an equal chance of being sampled".

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The length of one string of lights in feet is closest to 23 feet.

The problem states that students plan to decorate the school's flagpole with strings of lights. One end of each string of lights will be attached to the top of the flagpole, and the other end will be attached to the ground.

The flagpole is 15 feet tall and the distance from the base of the flagpole to the ground is 8 feet. Since the string of lights is attached at the top of the flagpole and at the ground, the length of the string of lights is equal to the height of the flagpole plus the distance from the base of the flagpole to the ground.

Therefore, the length of one string of lights can be calculated by adding the height of the flagpole (15 feet) to the distance from the base of the flagpole to the ground (8 feet), which results in:

15 feet + 8 feet = 23 feet

So the length of one string of lights is 23 feet.

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The standard form of the equation of the line through the point (3,3) with slope -1/2 is y = -1/2x + 9/2.

The standard form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

We are given a point (3,3) and a slope of -1/2, we can use the point-slope form to write the equation of the line as follows -

y - 3 = -1/2(x - 3)

To convert this equation to standard form, we can simplify the equation as follows -

y - 3 = -1/2x + 3/2

y = -1/2x + 3 + 3/2

y = -1/2x + 9/2

Hence, the standard form of the equation of the line through the point (3,3) with slope -1/2 is y = -1/2x + 9/2.

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Answer:

Step-by-step explanation:

The selling price of a phone case with a 25% coupon is $56 and the original selling price of the phone case without any discount is $80.

What is the selling price?

The price at which an article is sold is known as the selling price of that article.

Given that you have a 25% off coupon and paid $42.00 for a phone case. The phone case was marked down 30%. So,

Let's consider that you use a 25% off coupon and then paid $42 for the phone case. The price of phone case including coupon is,

75 % of price  = $42.00

100% of price =

The time taken to cover the distance from the park to house with an average speed of 22km /h is 42 minutes.

Average speed is the directional speed of an object in motion as measured by a certain unit of time and seen from a particular point of reference. Average speed is a fundamental concept in kinematics, the branch of classical mechanics that investigates how bodies move.

Since average speed is a physical vector quantity, its magnitude and direction must be included in the definition. In the SI, speed is a coherent derived unit whose quantity is measured in metres per second (m/s), where speed is the scalar absolute value (distance) of average speed (metric system). The word "acceleration" describes a change in an object's speed, direction, or both.

we know that

distance = average speed × time

distance = 14×66/60 =15.4 km

now time = distance /average speed

time = 15.4×60/ 22 = 42 minutes

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The approximate measure of angle YZX is 39.4°. Option(B) is the correct answer.

we know that

In the right triangle XYZ

[tex]tan(Y Z X)= \frac{opposite side angle YZX}{adjacent side angle YZX}[/tex]

In this problem,

Opposite side angle YZX= XY = 12.4cm

Adjacent side angle YZX= YZ = 15.1cm

substitute the values,

[tex]tan ( Y Z X) = \frac{12.4}{15.1}[/tex]

[tex]Angle ( Y Z X) = arc tan( \frac{12.4}{15.1} )[/tex]

Angle ( Y Z X) = 39.4°

So,  the approximate measure of angle YZX is 39.4°.

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The complete question is:

In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm. Which is the approximate measure of angle YZX?

A .34.8°

B .39.4°

C .50.6°

D. 55.2°

The length of the ladder is 22 feet.

Let x = the height the ladder reaches on the wall.

Then 3x = the length of the ladder.

Substituting 15 for the foot of the ladder from the wall, we have:

15 + 3x = the length of the ladder

7 = 3x

x = 7/3

Substituting 7/3 for x in the equation 15 + 3x = the length of the ladder we have:

15 + 3(7/3) = the length of the ladder

15 + 7 = the length of the ladder

22 = the length of the ladder

The length of the ladder can be determined by first figuring out how high the ladder reaches on the wall. Let x equal the height the ladder reaches on the wall. Then, the length of the ladder, 3x, can be determined. Since the foot of the ladder is 15 feet from the wall, the equation 15 + 3x = the length of the ladder can be written. In this equation, 7 is the known value for 3x, since the ladder is 7 feet less than three times longer than the height it reaches on the wall. Therefore, x = 7/3. Substituting 7/3 for x in the equation 15 + 3x = the length of the ladder, the equation 15 + 3(7/3) = the length of the ladder can be written. Simplifying this equation, 15 + 7 = the length of the ladder can be written, which means the length of the ladder is 22 feet.

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The equations with the same y-intercept are y = 9x + 2, y = 8x + 2, y = 3x + 2 and y = (1/4)x + 2.

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The slope-intercept form of  the equation of a line is y = mx+b,

where m is the slope and b is the y-intercept

Let's compare the given equations with y = mx+b:

y = 5x - 2,     y-intercept (b) = -2

y = 9x + 2,    y-intercept (b) = 2

y = 8x + 2,    y-intercept (b) = 2

y = 3x - 7,     y-intercept (b) = -7

y = 3x + 2,     y-intercept (b) = 2

y = 3x + 4,     y-intercept (b) = 4

y = (1/4)x + 2, y-intercept (b) = 2

Therefore, y = 9x + 2, y = 8x + 2, y = 3x + 2 and y = (1/4)x + 2 have the same y-intercept

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The following are solutions to the inequalities;

7. c < 7

8. h < -4

9. r ≤ 55

Inequality is a relationship between two expressions or values that are not equal to each other. Lack of balance results in inequality.

In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs.

7. 8c - 21 < 35

8c < 35 +21

8c < 56

c < 7

8. -6h + 17 > 41

-6h > 41 - 17

-6h > 24

h < 24/-6

h < -4

9. r/5 - 2 ≤ 9

Multiplying through by 5

r - 10 ≤ 45

r ≤ 45 + 10

r ≤ 55

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Answer:

A dependent variable represents a quantity whose value depends on how the independent variable is manipulated. y is often the variable used to represent the dependent variable in an equation.

Step-by-step explanation:

The value of x would be 7 and perimeter of equilateral triangle would be 75.

What is Equilateral triangle and perimeter of equilateral triangle?

An equilateral triangle is one with the equal length on all three sides. To calculate the perimeter of an equilateral triangle given its area, we must first determine the length of its sides.

An equilateral triangle has three congruent sides, so if AABC is equilateral, we know that AB = BC = AC. We can use this information to write an equation for x, the length of one of the sides.

AB = BC = AC

given equations are,

4x-3 and 2x+11

as we know that, all sides of equilateral triangle are equal then,

4x-3 = 2x+11

2x = 14

x = 7

The perimeter of an equilateral triangle = 3 x side of equilateral triangle

Here, all sides of equilateral triangle are equal then sides = 25

Perimeter of an equilateral triangle = 3 x 25

Perimeter of an equilateral triangle = 75

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Answer:

Step-by-step explanation:

The function y = -2 is a constant function. It means that the output of the function is always equal to -2, regardless of the input value.

Here is a function table that shows the input and output values for y = -2:

x y

1 -2

2 -2

3 -2

4 -2

5 -2

As you can see, for any value of x, the output is always -2, since y = -2 is a constant function

Answer:

x²y²(x²-2xy)

Step-by-step explanation:

they each include an x²y² so you take out the x²y² from each, and then write what's remaining & then add a bracket.

Michael wants to place grass on the side of his lap pool, the area of the shaded region that he wants to cover with grass is 204 square yard.

We have to determine the area of the Shaded region that he wants to cover with grass.

By calculating the overall area and taking the area of the lap pool out, the area of the shaded area may be calculated.

We can see that the shape is the trapezium. So;

Area of trapezium = 1/2 × (Sum of parallel sides) × distance between them

Sum of parallel sides = 25 yd + (3 + 12) yd

Sum of parallel sides = 25 yd + 15 yd

Sum of parallel sides = 40 yd

Distance between them = 12 yd

Area of the trapezium = 1/2 × 40 × 12

Area of the trapezium = 40 × 6

Area of the trapezium = 240 square yd

Now finding the area of lap pool.

Area = length × width

Area = 12 × 3

Area = 36 square yd

Now finding the area of shaded region

Area = Area of the trapezium - Area of lap pool

Area = 240 - 36

Area = 204 square yard

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The distance between  G and H on this number line  is 10

What is number line?

A range of line is a pictorial representation of numbers on a immediately line. It’s a reference for evaluating and ordering numbers. it is able to be used to symbolize any real variety that consists of each whole quantity and herbal quantity. simply to don't forget, the whole wide variety is a set of numbers that encompass all counting numbers (1, 2, three,four,5,6 …….) and zero (0), whereas the herbal number is the set of all counting numbers i.e. 1, 2, three, 4, five, 6……..

Given in the number line,

The number line is from the -12 to 7

And

we have to find the distance between G and H on this number line

GH = -2+12

GH = 10

Hence, The distance between  G and H on this number line  is 10

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I get to pay a total cost of $89.16 for the meal.

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, multiplications and so on). Expressions are made up of terms. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is called a coefficient.

Pretax = 13% of meal cost

Tax = 7% of meal cost

Total = Meal cost + 13% of meal cost + 7% of meal cost

Total = $74.30 + (13/100 x $74.30) + (7/100 x $74.30)

Total = $74.30 + $9.659 + $5.201

Total = $89.16

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The coefficients of the terms on the right side of a binomial equation are the numbers in the triangle.

As the power increases, the expansion becomes more difficult to compute and takes longer. A binomial statement that has been raised to a very high power can be swiftly calculated using the binomial theorem. Find out everything there is to know about the binomial theorem, including its definition, characteristics, and uses.

The binomial theorem can be used to expand an expression that has been raised to any finite power. The binomial theorem is a helpful expansion method having applications in probability, probability theory, and algebra.

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[tex]\left[\begin{array}{ccc}16&22&16\\2&14&-1\\-5&17&-2\end{array}\right][/tex] is the result of the operation, Option A is correct.

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.

The given operations are

[tex]\left[\begin{array}{ccc}13&10&7\\6&8&1\\2&5&0\end{array}\right] -\left[\begin{array}{ccc}3&-2&6\\14&-6&11\\8&-12&9\end{array}\right] +\left[\begin{array}{ccc}6&10&15\\10&0&9\\1&0&7\end{array}\right][/tex]

In the given operation, the operators used are addition and subtraction

[tex]\left[\begin{array}{ccc}13-3+6&10+2+10&7-6+15\\6-14+10&8+6+0&1-11+9\\2-8+1&5+12+0&0-9+7\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}16&22&16\\2&14&-1\\-5&17&-2\end{array}\right][/tex]

Hence, [tex]\left[\begin{array}{ccc}16&22&16\\2&14&-1\\-5&17&-2\end{array}\right][/tex] is the result of the operation, Option A is correct.

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The decimal number and the fraction commonly used as approximations for pi are 3.142 and 22/7

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

pi

The pi variable is a mathematical constant that has the following fractional value

pi = 22/7

When converted to decimal in 3 decimal places, we have

pi = 3.142

Hence, the representations are 22/7 and 3.142

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There are 188 ways to pick one ace and next card as not a queen.

There are 4 aces in a normal 52 card deck, and once one is picked, there are 51 cards left.

If we want to pick two successive cards from a normal 52 card deck so that the first is an ace and the second is not a queen, we can use the following formula:

Number of ways = (number of aces) x (number of cards not a queen)

In this case, the number of aces is 4, and the number of cards not a queen is 47 (52 cards total - 4 queens - 1 ace that has been picked).

So the number of ways to pick two successive cards from a normal 52 card deck so that the first is an ace and the second is not a queen is 4 x 47 = 188.

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(i) 98³

(100-2)³

100³ + 2³ + 3(100*2)(100+2)

[by using the equation (a-b)3=a3+b3+3ab(a+b)]

1000000+8+(600*102)

The solution is 1000008+61200 1061208.

(ii) 188 × 212 = 39856

Given:

The ratio of 188 to 212

To locate

the importance of adopting a proper identity

Equation: (a + b) = (a2 - b2 ( a - b )

Solution:

Phase 1 of 2:

Note the supplied expression in writing.

The formula is 188 212. Step 2 of 2:

Find the expression's value.

188 × 212\s= ( 200 - 12 ) × ( 200 + 12 )

= ( 200 + 12 ) × ( 200 - 12 ) ( 200 - 12 )

= 200² - 12²

= 40000 - 144

= 39856

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The statistic is the average diameter of 100 bearings from the lot, which is 2.515 cm. This is outside the specified limits, resulting in the lot being mistakenly rejected.

The statistic in this case is the average diameter of the inspected bearings from the lot. The lot contains a boxcar of ball bearings, and the specified acceptance of the lot is that the average diameter must be 2.503 cm. The inspector happens to inspect 100 bearings from the lot and determines that the average diameter of these bearings is 2.515 cm, which is outside the specified limits. As a result, the lot is mistakenly rejected. The value of the statistic is the average diameter of the inspected bearings from the lot, which is 2.515 cm. This is the value that determined the lot's rejection, as it is outside the specified limits.

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