if the system of equations y=b/6x-3 and y=2/3x-3 has infinitely many solutions, what is the value of b?

Answer:

12

Step-by-step explanation:

ABC is a right triangle.

AC = 4

CB = 3

The legs have lengths of 4 and 3.

Now we use the Pythagorean theorem to find AB, the length of the hypotenuse.

a² + b² = c², for legs a and b, and hypotenuse c.

(AC)² + (CB)² = (AB)²

4² + 3² = (AB)²

16 + 9 = (AB)²

25 = (AB)²

AB = 5

perimeter = sum of lengths of sides

perimeter of triangle ABC = AC + CB + AB

perimeter = 4 + 3 + 5

perimeter = 12

Answer:

n = 10/3

Step-by-step explanation:

Let n be the number

[tex]n(-\frac{9}{44}) = -\frac{15}{22} \\ Cross multiply\\n = \frac{-44(-15)}{9(22)} \\n = \frac{660}{198} \\n = \frac{10}{3}[/tex]

1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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Answer:

$11820.466 ROUNDS TO $11820.47

Step-by-step explanation:

Using the compound interest formula:

X = P(1+r/n)^(nt)

where X = desired amount (15,000 in this case)

P = principle or initial amount

r = interest rate (0.03 or 3% in this case)

n = number of times the interest is compounded each year (2 in this case because interest is compounded semiannually)

t = time in years

you can begin to plug in your numbers

15,000 = P(1+0.03/2)^(2*8)  --> this will show you that they are looking to have 15,000 by the end of the 8 years, at a rate of 3% (0.03) with interest compounded semiannually

from here you can simplify (1+0.03/2)^(2*8)  to 1.27 (full decimal = 1.26898554765)

and then you have

15,000 = P * 1.26898554765

then divide 15,000 by 1.26898554765

and get P = 11820.466, which rounds to $11820.47

hope this helps!

Answer: P = 11820.47

Step-by-step explanation:

Formula for compound interest:

[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]

A = after amount =15000

P = Principal, initial/deposit amount = find this

r = rate in decimal form = .03

n = number of times it compounds in 1 year = 2   >semiannually

t = time in years > 8

[tex]15000 = P(1+\frac{.03}{2} )^{(2)(8)}[/tex]

[tex]15000 = P(1.015 )^{16}[/tex]

15000 = P(1.015 )^{16}

15000 = P(1.26899)

P = 11820.47

The number of years of employment is A. Nikhil has been with the company for 16 years, while Mae has been there for 4 years.

The system of equations given is:

x = 4y

x = 8 + 2y

You can solve the system by setting the two expressions for x equal to each other:

4y = 8 + 2y

2y = 8

2y / 2 = 8 / 2

y = 4

Substitute y = 4 into the first equation to solve for x:

x = 4 x 4

= 16

So, Mae (y) has been at the company for 4 years and Nikhil (x) has been at the company for 16 years.

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Answer:

A

Step-by-step explanation:

consider the coordinates of points C and A

C (4, - 1 ) and A (- 3, 2 )

4 → - 3 in the x- direction is - 7

- 1 → 2 in the y- direction is + 3

then the translation rule is

(x, y ) → (x - 7, y + 3 )

The 5th term in the expansion is 126 * (4x³y²)^5 * (-1/2y)^4, which simplifies to 126 * 4^5 * (x³)^5 * (y²)^5 * (-1/2)^4 * y^4.

To find the 5th term in the expansion of (4x³y² - 1/2y)^9, we can use the binomial theorem. The binomial theorem allows us to expand a binomial raised to a positive integer exponent.

The binomial theorem states that for any binomial (a + b)^n, the general term in the expansion can be written as C(n, k) * a^(n-k) * b^k, where C(n, k) represents the binomial coefficient, also known as "n choose k."

In our case, the binomial is (4x³y² - 1/2y)^9. The first term has an exponent of 9, so the last term will have an exponent of 0. Since we are looking for the 5th term, the exponent of y will be 9 - 5 = 4. The exponent of x will be 5, as 4x³ raised to the power of 5 gives x^15.

Using the binomial coefficient, we have C(9, 5) = 126.

Simplifying further, we get 126 * 1024 * x^15 * y^10 * (1/16) * y^4, which can be simplified as 126 * 64 * x^15 * y^14 * (1/16). The final result is 8064 * (x^15 * y^14) * (1/16), which can be further simplified if necessary.

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Answer:

Step-by-step explanation:

To determine which of the given ordered pairs represents the solution to the system of equations, we can substitute the values of x and y into the equations and check if they satisfy both equations.

The system of equations is:

Equation 1: x - 4y = 7

Equation 2: 5x + 9y = 6

Let's check each ordered pair:

(3, -1)

Substituting x = 3 and y = -1 into the equations:

Equation 1: 3 - 4(-1) = 7

3 + 4 = 7

7 = 7 (True)

Equation 2: 5(3) + 9(-1) = 6

15 - 9 = 6

6 = 6 (True)

Since both equations are satisfied, (3, -1) is a solution to the system.

(3, 1)

Substituting x = 3 and y = 1 into the equations:

Equation 1: 3 - 4(1) = 7

3 - 4 = 7

-1 = 7 (False)

Equation 2: 5(3) + 9(1) = 6

15 + 9 = 6

24 = 6 (False)

Since one or both equations are not satisfied, (3, 1) is not a solution to the system.

(1, -3)

Substituting x = 1 and y = -3 into the equations:

Equation 1: 1 - 4(-3) = 7

1 + 12 = 7

13 = 7 (False)

Equation 2: 5(1) + 9(-3) = 6

5 - 27 = 6

-22 = 6 (False)

Since one or both equations are not satisfied, (1, -3) is not a solution to the system.

(-1, -3)

Substituting x = -1 and y = -3 into the equations:

Equation 1: -1 - 4(-3) = 7

-1 + 12 = 7

11 = 7 (False)

Equation 2: 5(-1) + 9(-3) = 6

-5 - 27 = 6

-32 = 6 (False)

Since one or both equations are not satisfied, (-1, -3) is not a solution to the system.

Therefore, the ordered pair (3, -1) represents the solution to the system of equations.

Alex and Juana canoed 75% of the total distance on the first day of their trip.

To find the percentage of the total distance they canoed on the first day, we need to divide the distance they traveled on the first day by the total distance and then multiply by 100.

Total distance of the canoe trip = 32 miles

Distance traveled on the first day = 24 miles

Calculate the percentage.

Percentage = (Distance traveled on the first day / Total distance) [tex]\times[/tex] 100

Percentage = (24 miles / 32 miles) [tex]\times[/tex] 100

Percentage = (3/4) [tex]\times[/tex] 100

Percentage = 75%

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The correct rule for reflection across the y-axis is "Ty-axis (x, y) → (-x, y)."

The rule for reflection depends on the axis of reflection. In this case, we are given the options of Ty-axis (reflection across the y-axis) and Tx-axis (reflection across the x-axis). Let's analyze each option:

Ty-axis (x, y) → (-x, y):

This rule states that for a reflection across the y-axis, the x-coordinate of a point is negated while the y-coordinate remains the same. For example, if we have a point (2, 3) and reflect it across the y-axis, it becomes (-2, 3). The x-coordinate is negated, but the y-coordinate remains the same.

Ty-axis (x, y) → (x, y):

This rule states that for a reflection across the y-axis, both the x-coordinate and y-coordinate remain the same. This means that there is no change in the coordinates of the point after the reflection.

Tx-axis (x, y) → (-x, y):

This rule states that for a reflection across the x-axis, the y-coordinate of a point remains the same while the x-coordinate is negated. For example, if we have a point (2, 3) and reflect it across the x-axis, it becomes (2, -3). The y-coordinate remains the same, but the x-coordinate is negated.

Tx-axis (x, y) → (x, y):

This rule states that for a reflection across the x-axis, both the x-coordinate and y-coordinate remain the same. This means that there is no change in the coordinates of the point after the reflection.

Based on the given options, the correct rule for the reflection is Ty-axis (x, y) → (-x, y). This means that when reflecting a point across the y-axis, the x-coordinate is negated while the y-coordinate remains the same.

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Dennis bought some pears for his students. If every 3 students get pears, there will be 6 pears left. If each student gets 5 pears, 2 students will have no pears. So, there are 2 students in total.

Let's assume the total number of students is 'x'.

According to the first scenario, if each group of 3 students receives pears, there will be 6 pears left. This means that the number of pears must be a multiple of 3 plus 6. So, we can write the equation:

[tex]P = 3n + 6[/tex], where P represents the total number of pears and n is a positive integer.

In the second case, if two students are left out of the distribution of pears and each student receives five, the sum of the pear distributions should be a multiple of five plus two. This can be said as follows:

[tex]P = 5x + 2[/tex], where P represents the total number of pears and x is the total number of students.

Since both equations represent the same number of pears, we can equate them:

[tex]3n + 6 = 5x + 2[/tex]

Rearranging the equation, we get:

[tex]3n - 5x = -4[/tex]

Our next aim is to find a solution where n and x are positive integers. Starting by examining the values of n and x is a smart idea. Trial and error leads us to the conclusion that n = 4 and x = 2 satisfy the following equation:

[tex]3*4 - 5*2 = -4[/tex]

So, there are 2 students in total.

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The simplified values of each given expressions involving factorials are:

1) 3!6! = 4,320       2) 5!7! = 604,800

Factorials are the product of a given number and all positive integers smaller than it, denoted by an exclamation mark (!).

To evaluate and simplify the expressions involving factorials, calculate the factorials and then simplify the resulting values you get:

1. 3!6!

To calculate 3! (3 factorial), we multiply all the integers from 1 to 3:

3! = 3 × 2 × 1 = 6

Next, we calculate 6! (6 factorial) by multiplying all the integers from 1 to 6:

6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

Therefore, 3!6! = 6 × 720 = 4,320.

2. 5!7!

5! = 5 × 4 × 3 × 2 × 1 = 120

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040

Therefore, 5!7! = 120 × 5,040 = 604,800.

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i. The first two terms of the series are 50/3 and 100/9, and the fifth term is 800/243.

ii. The first two terms of the series are 0 and 3, and the fifth term is 48.

The first term of the series is can be obtained by substituting n=1 into the formula

Thus;

first term = 25(2/3[tex])^1[/tex]= 25(2/3) = 50/3

The second term of the series is obtained by substituting n=2 into the formula

second term = 25(2/3[tex])^2[/tex] = 25(4/9) = 100/9

The fifth term of the series is obtained by substituting n=5 into the formula

fifth term = 25(2/3[tex])^5[/tex] = 25(32/243) = 800/243

Therefore, the first two terms of the series are 50/3 and 100/9, and the fifth term is 800/243.

(ii) The first term of the series is obtained by substituting n=1 into the formula

first term = [tex]3(1-1)^2 = 3(0)^2 = 0[/tex]

The second term of the series is obtained by substituting n=2 into the formula

second term = [tex]3(2-1)^2 = 3(1)^2 = 3[/tex]

The fifth term of the series is obtained by substituting n=5 into the formula

fifth term = [tex]3(5-1)^2 = 3(16) = 48[/tex]

Therefore, the first two terms of the series are 0 and 3, and the fifth term is 48.

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Answer:

x>-3

Step-by-step explanation:

x-7<-10

x<-10+7

x<-3

x>-3

The number she'd have is:

Explanation:

First, let's see which number is in the tens place and which number is in the ones place (the units place).

In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).

So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :

550

That's not all, since we also add 1 to the tens:

560

Ayaan drank 11/4 bottles of water during the soccer game, which can be expressed as a mixed numeral 2 and 3/4.

To convert the fraction 11/4 to a mixed numeral, we need to determine the whole number part and the fractional part.

Divide the numerator (11) by the denominator (4).

11 ÷ 4 = 2 remainder 3

The quotient 2 represents the whole number part, and the remainder 3 represents the fractional part.

Write the mixed numeral using the whole number part and the fractional part.

The mixed numeral for 11/4 is:

2 and 3/4

Therefore, Ayaan drank 11/4 bottles of water during the soccer game, which can be expressed as a mixed numeral 2 and 3/4.

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The probability that exactly 20 out of 30 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.1031, or 10.31%.

To find the probability that exactly 20 out of 30 randomly selected adult smartphone users use their smartphones in meetings or classes, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = (n C k) * p^k * (1 - p)^(n - k),

where:

P(X = k) is the probability of exactly k successes,

n is the total number of trials (number of smartphone users selected),

k is the number of successes (number of smartphone users using their smartphones in meetings or classes),

p is the probability of success in a single trial (percentage of adults using smartphones in meetings or classes), and

(n C k) represents the binomial coefficient, which can be calculated as n! / (k! * (n - k)!)

Given that the percentage of adults using smartphones in meetings or classes is 42% or 0.42, we have p = 0.42. Also, n = 30 and k =

Substituting these values into the binomial probability formula:

P(X = 20) = (30 C 20) * 0.42^20 * (1 - 0.42)^(30 - 20).

To calculate the binomial coefficient (30 C 20), we can use the formula:

(30 C 20) = 30! / (20! * (30 - 20)!).

Calculating (30 C 20):

(30 C 20) = 30! / (20! * 10!) = (30 * 29 * 28 * 27 * 26 * 25 * 24 * 23 * 22 * 21) / (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) = 30,045,015.

Substituting the values into the formula:

P(X = 20) = 30,045,015 * 0.42^20 * (1 - 0.42)^(30 - 20).

Calculating the expression:

P(X = 20) ≈ 0.1031.

Therefore, the probability that exactly 20 out of 30 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.1031, or 10.31%.

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The probability for this case is P = 0.147

To solve this problem, we can use the binomial probability formula. In this case, we have a binomial distribution with the following parameters:

The formula for the probability of exactly x successes in n trials is:

[tex]P(X = x) = (N_x) * p^x * (1 - p)^(n - x)[/tex]

Where:

[tex](N_x) = n! / (x! * (n - x)!)[/tex]

Calculating the binomial coefficient:

[tex](30_{20}) = 30! / (20! * (30 - 20)!) = 30! / (20! * 10!)[/tex]

Using the given values, we can calculate the probability as follows:

[tex]P(X = 20) = (30_{20}) * (0.42^{20}) * (1 - 0.42)^{(30 - 20)} = 0.147[/tex]

that is the probability.

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Given

To find

We know that,

Let the third angle be ,'x'

then,

Hence,the third angle would measure 30°

Answer: 1.5mg of medicine is to be added to 500ml of water to gain a solution of 3mg per liter

Step-by-step explanation:

3mg per liter is needed. That is 3mg of medicine in 1000ml of water.

As we have only 1.5 mg of medicine that is half of 3mg. We have to add a half of one liter of water. that is 500 ml of water.

The solution to the system of equations, y = 3x + 15 and 3x + 3y = 9 is one unique solution, which is (-3, 6) [see image attached below].

To graph the system of equations and determine the solution, let's start with each equation individually:

y = 3x + 15

3x + 3y = 9

To graph the first equation, y = 3x + 15, we can plot a line with a slope of 3 and a y-intercept of 15. This line will have a positive slope, meaning it goes upward from left to right.

To graph the second equation, 3x + 3y = 9, we can rearrange it to the slope-intercept form y = (-1)x + 3, or simplified as y = -x + 3. This equation represents a line with a slope of -1 and a y-intercept of 3. This line will have a negative slope, meaning it goes downward from left to right.

Now, let's analyze the graphed lines and their intersection to determine the solution:

From the graphs as shown in the image attached below, we can see that the lines intersect at the point (-3, 6). This means that the solution to the system of equations is a single unique solution.

Therefore, the correct answer is option b. There is one unique solution (-3, 6).

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The slope of a line perpendicular to the line whose equation is x - 2y = -8 is -2.

In Mathematics and Geometry, perpendicular lines are two (2) lines that intersect or meet each other at an angle of 90° (right angles).

From the information provided above, the slope for the equation of line m is given  by:

x - 2y = -8

2y = x + 8

y = x/2 + 4

slope (m) of line m = 1/2

In Mathematics and Geometry, a condition that is true for two lines to be perpendicular is given by:

m₁ × m₂ = -1

1/2 × m₂ = -1

m₂ = -2

Slope, m₂ of perpendicular line = -2

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Answer:

Step-by-step explanation:

To eliminate the x term in the system of equations, you can multiply Equation P by a constant and then add or subtract it from Equation Q. Let's go through the given steps:

2(x + y = 8):

This step is incorrect because it only multiplies the entire Equation P by 2 without changing the other equation. It does not eliminate the x term.

-2(x + y = 8):

This step is incorrect because it multiplies Equation P by -2, but the equation should be subtracted from Equation Q, not multiplied by -2.

-1(2x + 5y = 24):

This step is incorrect because it only multiplies Equation Q by -1 without changing Equation P. It does not eliminate the x term.

-2(2x + 5y = 24):

This step is correct. By multiplying Equation Q by -2 and then adding it to Equation P, the x term will be eliminated. The resulting equation will involve only the y term, allowing you to solve for y.

Therefore, the correct step to eliminate the x term is -2(2x + 5y = 24).

To prove that the step -2(2x + 5y = 24) eliminates the x term in the system of equations, we need to show that when we perform the elimination, the resulting equation involves only the y term.

Given the system of equations:

Equation P: x + y = 8

Equation Q: 2x + 5y = 24

Multiplying Equation Q by -2:

-2(2x + 5y) = -2(24)

-4x - 10y = -48

Now, let's add Equation P and the modified Equation Q:

(x + y) + (-4x - 10y) = 8 + (-48)

Simplifying the left side of the equation:

x - 4x + y - 10y = 8 - 48

-3x - 9y = -40

As we can see, the resulting equation -3x - 9y = -40 involves only the y term. The x term has been eliminated.

Therefore, by performing the step -2(2x + 5y = 24), we have successfully eliminated the x term in the system of equations.

The Division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

To find the division of the sum of (7/8), (15/4), and (1/12) by their multiplication, we first need to calculate the sum and multiplication of the given fractions.

The sum of the fractions is:

(7/8) + (15/4) + (1/12)

To add these fractions, we need a common denominator. The least common multiple of 8, 4, and 12 is 24. Let's convert each fraction to have a denominator of 24:

(7/8) = (21/24)

(15/4) = (90/24)

(1/12) = (2/24)

Now we can add the fractions:

(21/24) + (90/24) + (2/24) = (113/24)

The multiplication of the fractions is:

(7/8) * (15/4) * (1/12)

To multiply fractions, we multiply the numerators and denominators:

(7*15*1) / (8*4*12) = (7/96)

Now we can divide the sum of the fractions by their multiplication:

(113/24) / (7/96)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(113/24) * (96/7) = (2712/168)

Therefore, the division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

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The equation which models the scenario is y = 2.625x

Using the given Parameters

cost per mile = 5.25/2 = $2.625

cost 'y ' for x miles can be modeled using the Multiplication operator thus :

Hence, we have

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Answer:

D

Step-by-step explanation:

A and D are both equidistant from the x- axis, that is

A is 3 units above the x- axis and D is 3 units below the x- axis

then the x- axis is the line of symmetry

Answer:

375/100

Reduce to lowest term

15/4 or 3 3/4

The value of x is approximately 80419.4861.

To find the value of x in the equation:

15 (2/3) × 3 (1/6) + 6 (1/3) = 11 (7/8) + x

Let's simplify each side of the equation separately:

On the left side:

15 (2/3) × 3 (1/6) can be calculated as follows:

15 (2/3) = 15 + (2/3) = 15 + 2/3 = 45/3 + 2/3 = 47/3

3 (1/6) = 3 + (1/6) = 3 + 1/6 = 18/6 + 1/6 = 19/6

So, on the left side, we have:

47/3 × 19/6 + 6 (1/3)

To multiply fractions, we multiply the numerators and denominators:

(47 × 19) / (3 × 6) + 6 (1/3)

47 × 19 = 893

3 × 6 = 18

So, we have:

893/18 + 6 (1/3)

Now, let's convert 6 (1/3) to a fraction:

6 (1/3) = 6 + (1/3) = 6 + 1/3 = 18/3 + 1/3 = 19/3

Now, we have:

893/18 + 19/3

To add fractions, we need a common denominator, which is the least common multiple (LCM) of 18 and 3, which is 18. Let's convert both fractions:

893/18 + 19/3 = (893 × 1) / (18 × 1) + (19 × 6) / (3 × 6)

= 893/18 + 114/18

Now, we can combine the fractions:

(893 + 114) / 18 = 1007/18

On the right side of the equation, we have 11 (7/8) + x. Let's convert 11 (7/8) to a fraction:

11 (7/8) = 11 + (7/8) = 11 + 7/8 = 88/8 + 7/8 = 95/8

Now, the equation becomes:

1007/18 = 95/8 + x

To solve for x, we need to get rid of the fraction on the right side. We can find a common denominator, which is 18 × 8 = 144:

(1007 × 8) / (18 × 8) = (95 × 18 + x × 144) / (8 × 18)

80456/144 = (1710 + 144x) / 144

Cross-multiplying gives us:

80456 × 144 = 1710 + 144x

11598864 = 1710 + 144x

Rearranging the equation:

144x = 11598864 - 1710

144x = 11597154

x = 11597154/144

Evaluating the expression:

x = 80419.4861

Consequently, x has a value of around 80419.4861.

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The correct statement from the graph is this: A. At point b, the level of investment spending is higher than at point a.

The diagram depicts an investment spending curve that is shifting to the left. This investment curve shifts to the right when factors like government and investment spending are increasing.

In the case of the above curve, the factors are decreasing. So in the case of the above curve, at point b, the IS is at a higher rate than at point A. So, option A is right.

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Complete Question:

Study the following diagram and answer the question. Which one of the following statements is correct? Select one: A. At point b, the level of investment spending is higher than at point a. B. At point a the demand for goods is higher than at point b. C. At point b, government spending will be higher since the level of output and income is higher. D. An increase in the interest rate causes a movement along the IS curve from point a to point b.

The value of x is 63

To determine the value of the variable, we have that;

From the information given, we have that;

x and x - 36 are complementary angles

Now, equate the angles to 90 degrees, we have;

x + x - 36= 90

collect the like terms, we get;

2x = 90 + 36

add the terms

2x =1 26

Divide by the coefficient

x = 63

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Complete question:

The angles X,(x-36)  are complementary. What is the value of x