4x-3y=18 determine the missing coordinates in ordered pair

Answer:

(x-2)^2 + (y+3)^2 = 5.1^2

Step-by-step explanation:

The equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where h and k are the x and y values of the center of the circle respectively and r stands for the radius.

The center is given to us, at (2, -3) so we can plug that in:

(x-(2))^2 + (y- (-3))^2 = r^2

Simplify:

(x-2)^2 + (y+3)^2 = r^2

We can also solve for the radius by getting another point given to us: (3,2).

Using the pythagorean theorem, we can find how far the two points are away from each other:

a^2 + b^2 = c^2

1^2 + 5^2 = c^2
1 + 25 = c^2

26 = c^2

c ~ 5.1

Plug the radius we solved for in for r:
(x-2)^2 + (y+3)^2 = 5.1^2

Answer: x=2, y=4

Step-by-step explanation:

Since the lines are parallel, we can say that the larger triangle and the smaller triangle are similar. Thus. x+3/(2y-1) = (3/2x+2)/(3y-5). Also, note that there are hash lines, telling us that 2y-1 and 3y-5 are equal. Thus 2y-1=3y-5, and y=4. Plugging y=4 into the first equation yields: (x+3)/(7)=(3/2x+2)/(7), or x+3=3/2x+2. Then 1/2x=1, x=2.

Thus: x=2, and y=4

Answer:

x = 2

y = 4

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

As the line bisects the side of the triangle with the y-variables, then the line is the midsegment of the triangle. This means that the line also bisects the side of the triangle with the x-variables.

Therefore, the two expressions with the x-variable are equal.

Similarly, the two expressions with the y-variable are equal.

Solving for x:

[tex]\boxed{\begin{aligned}\dfrac{3}{2}x+2&=x+3\\\\\dfrac{3}{2}x+2-x&=x+3-x\\\\\dfrac{1}{2}x+2&=3\\\\\dfrac{1}{2}x+2-2&=3-2\\\\\dfrac{1}{2}x&=1\\\\2 \cdot \dfrac{1}{2}x&=2 \cdot 1\\\\x&=2\end{aligned}}[/tex]

Solving for y:

[tex]\boxed{\begin{aligned}3y-5&=2y-1\\\\3y-5-2y&=2y-1-2y\\\\y-5&=-1\\\\y-5+5&=-1+5\\\\y&=4\end{aligned}}[/tex]

Answer:

The length should be 11 feet and the width should be 6 feet. 11 feet is 5 feet more than 6 feet. 11 feet times 6 feet is 66 square feet.

Step-by-step explanation:

The two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. We denote the similarity of triangles here by ‘~’ symbol.

It is given that two triangles that are JKL and MNP are considered in which:

Now, from ΔJKL and ΔMNP, we have

∠K = ∠N (Given in the question)

∠L = ∠P(Given in the question)

Thus, by AA rule of similarity,

ΔJKL is similar to ΔMNP.

Therefore, the two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

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The number of $10 tickets sold is 1210 tickets.

The number of $20 tickets sold is 1344 tickets.

The number of $30 tickets sold is 827 tickets.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of each tickets sold, and then translate the word problem into an algebraic equation as follows:

Since the basketball team sold 3381 tickets overall, 134 more $20 tickets than $10 tickets and the total sales are $63,790, a system of three linear equations to model this situation is given by;

x + y + z = 3381

y - x = 134

10x + 20y + 30z = 63790  ⇒ x + 2y + 3z = 6379

Next, we would solve the system of three linear equations simultaneously as follows;

x + x + 134 + z = 3381

2x + 134 + z = 3381

z = 3247 - 2x

x + 2(x + 134) + 3(3247 - 2x) = 6379

x = 1210 tickets.

For the value of y, we have:

y = x + 134

y = 1210 + 134

y = 1344 tickets.

For the z-value, we have:

z = 3247 - 2x

z = 3247 - 2(1210)

z = 827 tickets.

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Complete Question:

A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3381 tickets overall. It has sold 134 more $20 tickets than $10 tickets. The total sales are $63,790. How many tickets of each kind have been sold?

How many $10 tickets were sold?

How many $20 tickets were sold?

how many $30 tickets sold?

Answer:

4,200

Step-by-step explanation:

70s = b

70(60) = b

4200 = b

Helping in the name of Jesus.

Answer:

A ∩ B = {7, 8}

Step-by-step explanation:

A = {1, 2, 5, 7, 8}

B = {6, 7, 8, 9}

A ∩ B = set of elements in both A and B

A ∩ B = {7, 8}

The amount of inches that the plant grows in 14 days is given as follows:

420 inches.

The proportional relationship that models the situation is given as follows:

i = 30d.

This means that the plant grows by 30 inches every day.

After 14 days, we have that d = 14, hence the size of the plant after 14 days is given as follows:

i = 30 x 14

i = 420 inches.

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Therefore, the slope-intercept equation of the line passing through the points (2,3) and (6,11) is y = 2x - 1.

To find the slope-intercept equation of the line passing through the points (2,3) and (6,11), we can use the formula for slope:

slope (m) = (change in y) / (change in x)

First, calculate the change in y and change in x using the given points:

change in y = 11 - 3 = 8

change in x = 6 - 2 = 4

Now, substitute the values into the slope formula:

slope (m) = 8 / 4 = 2

Next, we can use the point-slope form of the linear equation:

y - y1 = m(x - x1)

Choose one of the given points, let's use (2,3), and substitute the values into the equation:

y - 3 = 2(x - 2)

Simplifying the equation:

y - 3 = 2x - 4

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 2x - 1

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The equation of the linear relationship in slope-intercept form is y = 2x - 8. Option A is the correct answer.

To determine the equation of the linear relationship in slope-intercept form based on the table, we need to find the slope and y-intercept.

By observing the table, we can calculate the slope by selecting any two points. Let's choose the points (0, -8) and (4, 0).

Slope (m) = (change in y) / (change in x)

= (0 - (-8)) / (4 - 0)

= 8 / 4

= 2

Now that we have the slope, we can find the y-intercept by substituting the values of one point and the slope into the equation y = mx + b and solving for b.

Using the point (0, -8):

-8 = 2(0) + b

b = -8

Therefore, the equation of the linear relationship in slope-intercept form is: y = 2x - 8. Option A is the correct answer.

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The angle measure that belongs in the green box is given as follows:

70.67º.

We consider a triangle with side lengths and angles related as follows, as is the case for this problem:

Then the lengths and the sines of the angles are related as follows:

sin(A)/a = sin(B)/b = sin(C)/c.

The relation for this problem is given as follows:

sin(x)/12  = sin(76º)/12.34

Applying cross multiplication, the missing angle measure is given as follows:

sin(x) = 12 x sine of 76 degrees/12.34

sin(x) = 0.9436.

x = arcsin(0.9436)

x = 70.67º.

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The number the spinner is most likely to land on is 2

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

The spinner

From the spinner, we have the number that covers the largest area to be 2

i.e.

Largest area = 2

This means that the number it is most likely to land on is 2 and it has the highest probability

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Answer:

[tex]\frac{g^{125}}{2h^{8}}[/tex]

Step-by-step explanation:

[tex]2g^{5^{3}} =2g^{125}[/tex]

[tex]4h^{2^3} = 4h^{8}[/tex]

[tex]\frac{2g^{125}}{4h^8} = \frac{g^{125}}{2h^8}[/tex]

To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.

The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.

The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.

$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:

$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow

A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow

A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$

Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).

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The estimated mean salary in the neighborhood at a 90% confidence level based on the given sample is {1798.94, 1801.06}.

Given data:

Since we know the sample variance (s²), the standard deviation is:

s = √(s²)

s = √(10)

s = 3.16 pesos

Confidence Interval = Sample Mean ± (Critical Value * Standard Error)

The critical value is obtained from the t-distribution table based on the desired confidence level and degrees of freedom (n-1). For a 90% confidence level and 25 degrees of freedom, the critical value is 1.708.

SE = s / √n

SE = 3.16 / √26

SE = 0.618 pesos

Confidence Interval = 1800 ± (1.708 * 0.618)

= 1800 ± 1.055544

= {1798.94, 1801.06}.

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Para calcular la población de bacterias al cabo de 4 horas, primero necesitamos determinar cuántos intervalos de 20 minutos hay en 4 horas.

4 horas son equivalentes a 240 minutos. Dividiendo 240 minutos entre 20 minutos por intervalo, obtenemos 12 intervalos.

Dado que la población de bacterias aumenta un 25% cada 20 minutos, podemos aplicar este crecimiento a cada intervalo de 20 minutos.

Para cada intervalo de 20 minutos, la población de bacterias aumentará en un 25%.

Por lo tanto, podemos calcular la población de bacterias al final de los 12 intervalos de la siguiente manera:

Población final = Población inicial * (1 + tasa de crecimiento)^número de intervalos

Población inicial = 32,200 bacterias

Tasa de crecimiento = 25% = 0.25

Número de intervalos = 12

Población final = 32,200 * (1 + 0.25)^12

Realizando los cálculos, obtenemos la población final de bacterias al cabo de 4 horas.

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The radius of the semicircle protractor is approximately 4.693 cm.

Given,Perimeter of a semicircle protractor = 14.8 cm.

To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.

Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =[tex](1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693[/tex] cm.

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The set intersection X' ∩ Y' is expressed as; {e, 24}

We are given the sets as;

U = {a, b, c, d, e, f, 19, 20, 21, 22, 23, 24}

X = {a, b, c, 20, 21, 22}

Y = {b, d, f, 19, 21, 23}

Union of the sets A and B , denoted A ∪ B , is the defined as the set of all objects that are a member of A , or B , or both. The union of {1, 2, 3} and {2, 3, 4} is the set {1, 2, 3, 4} . Intersection of the sets A and B , denoted A ∩ B , is the set of all objects that are members of both A and B

Thus:

X' ∩ Y' is as follows;

X' = {d, e, 19, 23, 24}

Y' = {a, c, e, 20, 22, 24}

X' ∩ Y' = {e, 24}

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[tex]\underline{\underline{\purple{\huge\sf || ꪖꪀᦓ᭙ꫀ᥅}}}[/tex]

The given polynomial is:

p(t) = -t²(3 - 5t)(t² + t + 4)

To find the degree of the polynomial, we need to determine the highest power of t in the expression. This is given by:

degree = 2 + 1 + 2 = 5

So the degree of the polynomial is 5.

The leading term of the polynomial is the term with the highest power of t. This is given by:

leading term = -t² * 5t² = -5t^4

So the leading term of the polynomial is -5t^4.

The leading coefficient of the polynomial is the coefficient of the leading term. This is given by:

leading coefficient = -5

So the leading coefficient of the polynomial is -5.

The constant term of the polynomial is the term that does not contain any powers of t. This is given by:

constant term = -t²(3)(4) = -12t²

So the constant term of the polynomial is -12t^2.

To find the end behavior of the polynomial, we need to determine what happens to the value of the polynomial as t approaches positive or negative infinity. Since the degree of the polynomial is odd, we know that the end behavior will be opposite for t approaching positive or negative infinity. We can use the leading term to determine the end behavior:

- as t approaches positive infinity, the leading term approaches negative infinity, so the end behavior is p(t) → -∞ as t → ∞

- as t approaches negative infinity, the leading term approaches positive infinity, so the end behavior is p(t) → ∞ as t → -∞

So the end behavior of the polynomial is:

- p(t) → -∞ as t → ∞

- p(t) → ∞ as t → -∞

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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To construct a frequency histogram based on the given temperature data, we will use the temperature ranges as the x-axis and the number of days as the y-axis.

The temperature ranges and their corresponding frequencies are as follows:

30-39: 2 days

40-49: 26 days

50-59: 28 days

60-69: 8 days

70-79: 2 days

To create the histogram, we will represent each temperature range as a bar and the height of each bar will correspond to the frequency of days.

Using an appropriate scale, we can label the x-axis with the temperature ranges (30-39, 40-49, 50-59, 60-69, 70-79) and the y-axis with the frequency values.

Now, we can draw rectangles (bars) on the graph, with the base of each rectangle corresponding to the temperature range and the height representing the frequency of days. The height of each bar will be determined by the corresponding frequency value.

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Using the Venn diagram, each set and the number of elements in each set are:

a. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12}

b. A = {1, 3, 4, 5, 6, 8}

c. B = {4, 5, 6, 7, 9, 11}

d. C = {6, 8, 9, 12}

e. A ∪ B = {1, 3, 4, 5, 6, 7, 8, 9, 11}

f. A ∩ B = {4, 5, 6}

A Venn diagram is a pictorial representation used to visualize the relationships between different sets of objects or concepts.

a.) U is the universal set. This implies it contains all the elements in the set. Thus:

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12}

b.) A is all element (number) is set A (circle A). Thus:

A = {1, 3, 4, 5, 6, 8}

c.) B is all element is set B (circle B). Thus:

B = {4, 5, 6, 7, 9, 11}

d.) C is all element is set C (circle C). Thus:

C = {6, 8, 9, 12}

e.) A ∪ B is all element is sets A and B (circles A and B). Thus:

A ∪ B = {1, 3, 4, 5, 6, 7, 8, 9, 11}

f.) A ∩ B is all element is sets A and B (circles A and B) have in common. Thus:

A ∩ B = {4, 5, 6}

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Answer:

(x+3)^2 + (y+1)^2 = 16

Step-by-step explanation:

The equation of a circle is (x – h)^2 + (y – k)^2 = r^2, where h is the x value of the center, k is the y value of the center, and r is the radius.

We can see from the picture that the radius is at about (-3, -1) and the radius is about 4, so we can plug those in:
(x – (-3))^2 + (y – (-1))^2 = 4^2

Simplify:
(x+3)^2 + (y+1)^2 = 16

Answer:

Equation of circle:[tex](x + 3)^2 + (y + 1)^2 = 16[/tex]

Step-by-step explanation:

Given:

Center of the circle = (-3, -1)

Point on the circle = (1, -1)

In order to find the radius of the circle, we can use the distance formula.

distance =[tex] \boxed{\bold{\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}}[/tex]

where:

In this case, the distance formula becomes:

radius = [tex]\sqrt{(-3 - 1)^2 + ((-1) - (-1))^2}= \sqrt{16}=4[/tex]

Therefore, the radius of the circle is 4 units.

Now that we know the radius of the circle, we can find the equation of the circle using the following formula:

[tex]\boxed{\bold{(x - h)^2 + (y - k)^2 = r^2}}[/tex]

where:

In this case, the equation of the circle becomes:

=[tex](x + 3)^2 + (y + 1)^2 = 4^2[/tex]

=[tex](x + 3)^2 + (y + 1)^2 = 16[/tex]

This is the equation of the circle.

Answer: 2.8

Step-by-step explanation:

2x^2+6=10

2x^2=10-6

x^2=16 divided by 2

x= square root of 8

x=2.8

Answer: $227,226.51

Step-by-step explanation:

First, we need to convert the period to weeks.

9 1/2 years = 9.5 years

1 year = 52 weeks

9.5 years = 494 weeks

Next, we can use the formula for the future value of an annuity:

FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)

where:

PMT = payment amount per period

r = annual interest rate

n = number of compounding periods per year

t = number of years

Plugging in the given values:

PMT = $300

r = 0.055 (5.5% expressed as a decimal)

n = 52 (compounded weekly)

t = 9.5 years = 494 weeks

FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)

FV = $227,226.51

Therefore, the future value of the annuity is approximately $227,226.51.

Answer:

x < –18 or x > 10

Step-by-step explanation:

|x + 4| – 2 > 12

x + 4 - 2 > 12

x + 2 > 12

x > 10

-x - 4 - 2 > 12

-x - 6 > 12

-x > 18

x < 18

So, the answer is x < –18 or x > 10

Answer: D:  x < –18 or x > 10

Step-by-step explanation:

The implicit derivative is given as follows:

dx/dt(x = 4)  = 1/12.

The function in this problem is given as follows:

y = 3x² + 1.

The implicit derivative, relative to the variable t, is given as follows:

dy/dt = 6x dx/dt.

(the derivative of the constant 1 is of zero).

The parameters for this problem are given as follows:

x = 4, dy/dt = 2.

Hence the derivative is obtained as follows:

2 = 6(4) dx/dt

dx/dt = 2/24

dx/dt = 1/12.

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The manufacturing cycle efficiency (MCE) of Navems for its elevators is 38.6%

The correct answer choice is option A.

Manufacturing cycle efficiency (MCE) = Value-added production time / Total cycle time.

Value-added production time;

Inspection time = 12 days

Process time = 5 days

Total = 17 days

Total cycle time:

Wait time = 12 days

Inspection time = 12 days

Process time = 5 days

Move time = 6 days

Queue time = 9 days

= 44 days

Hence,

Manufacturing cycle efficiency (MCE) = Value-added production time / Total cycle time × 100

= 17 days / 44 days × 100

= 38.63636363636363

Approximately,

38.6%

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Each child will get 1 orange, and there will be one orange left over.

If you have five oranges and you need to distribute them among four children, then you need to find out how many oranges each child will get.

To do this, you can divide the total number of oranges by the number of children.

Let's see how to do this: Divide the number of oranges by the number of children.5 ÷ 4 = 1.25This means that each child will get 1.25 oranges.

However, since you can't give a child a fraction of an orange, you will need to round this number to the nearest whole number.

If the decimal is less than 0.5, you round down; if it's 0.5 or greater, you round up.

In this case, 1.25 is closer to 1 than to 2, so you round down to 1.

Therefore, Each child will receive one orange, with one orange remaining.

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Therefore, it would take approximately 36 minutes for 14 workers to complete the job.

To solve this inverse variation problem, we'll use the formula: t = k/w, where t represents the time needed, w represents the number of workers, and k is the constant of variation.

We can find the value of k by plugging in the given values of 9 workers and 56 minutes into the formula:

56 = k/9

To find the value of k, we multiply both sides of the equation by 9:

k = 504

Now that we know the constant of variation, we can determine the time it would take for 14 workers to complete the job. Plugging in the values into the formula:

t = 504/14

t ≈ 36

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