The sum of 2 of the exterior angles of a triangle is 222 degrees. What is the measure of the third exterior angle?

C) graph of a quadratic function with a minimum at 2.5, negative 2.25 and x intercepts at 1 and 4

Standard Form of a Quadratic Function: ax² + bx + c = 0, where a ≠ 0

Given function: x² - 5x + 4

⇒ a = 1, b = -5, c = 4

The minimum of a function is the lowest point of its parabola. We can use the following formula to find the vertex or the minimum of the function: [tex]x=\dfrac{-b}{2a}[/tex] . This will give us the x-value of the vertex, and we will need to solve for the y-value.

The vertex or minimum.

Step 1: Find the x-value of the vertex.

[tex]\\\implies x=\dfrac{-(-5)}{2(1)}\\\\\implies x=\dfrac{5}{2}=2.5[/tex]

Step 2: Find the y-value of the vertex by substituting 2.5 as the value of x in the given function.

[tex]\\\implies x^2 - 5x + 4\\\\\implies 2.5^2-5(2.5)+4\\\\\implies 6.25-12.5+4\\\\\implies -2.25[/tex]

Vertex: (2.5, -2.25)

The x-intercepts (roots).

We can use the Quadratic Formula to find the roots of this function.

Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] when [tex]ax^2+bx+c=0[/tex]

Equation: x² - 5x + 4 = 0

⇒ a = 1, b = -5, c = 4

Step 1: Substitute the values of a, b, and c into the formula. 

[tex]\\\implies x=\dfrac{\bold{-(-5)}\pm\sqrt{\bold{(-5)^2}\bold{-4(1)(4)}}}{\bold{2(1)}}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{25-16}}}{2}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{9}}}{2}\\\\\implies x=\dfrac{5\pm3}{2}[/tex]

Step 2: Separate into two possible cases.

[tex]x_1=\dfrac{5-3}{2}\implies \dfrac{2}{2}\implies \boxed{1}\\\\x_2=\dfrac{5+3}{2}\implies \dfrac{8}{2}\implies \boxed{4}[/tex]

The x-intercepts of the given function are 1 and 4.

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Answer:

n = 100

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

given A = 40π , then

πr² × [tex]\frac{n}{360}[/tex] = 40π

π × 12² × [tex]\frac{n}{360}[/tex] = 40π

144π × [tex]\frac{n}{360}[/tex] = 40π ( divide both sides by π )

144 × [tex]\frac{n}{360}[/tex] = 40 ( multiply both sides by 360 to clear the fraction )

144n = 14400 ( divide both sides by 144 )

n = 100

Answer:

396 gold bars

Step-by-step explanation:

first of all we will find numbers of gold bar 7*99

which is 693 and

we will find number of silver bars 11*99

which is 1089

then 1089-693=

396

By assuming that 1 + 1 = 3, we will reach an absurd.

To do this, we need to reach an absurd.

Let's assume that we are working with integer numbers, and let's assume that 1 + 1 is equal to 3.

Then we can write:

1 + 1 = 3

Now, if we subtract 1 in both sides, we get:

(1 + 1) - 1 = 3 - 1

1  = 2

Now we can subtract 1 again so we get:

1 - 1 = 2 - 1

0 = 1

This is an absurd, then the statement:

1 + 1 = 3

is false.

So we conclude that:

1 + 1 isn't 3.

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The amplitude, Period, Horizontal Shift and Vertical Shift of both graphs are as detailed below.

3)a. Amplitude is the distance between the center line and the positive or negative peak of the graph. Thus, the amplitude is 0.5.

b. The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 3.

c. Looking at the graph, ideally the coordinate (3, -1.5) should have been on the y-axis which is at (0, -1.5). This means it was shifted by 3 units to the right side.

d. The positive peak should be equal to the negative peak but in this case, it is not so and as such the center should be on the x-axis which means that the graph was shifted down vertically by 2 units.

4) a. Amplitude is the distance between the center line and the positive or negative peak of the graph. Thus, the amplitude is 3 - 1 = 2

b. The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 6.

c. Looking at the graph, ideally the coordinate (4, -1) should have been on the y-axis which is at (0, -1). This means it was shifted by 4 units to the right side.

d. The positive peak should be equal to the negative peak but in this case, it is not so and as such the center should be on the x-axis which means that the graph was shifted up vertically by 1 unit.

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Triangle ABC is dilated by a scale factor of 5 to get A'(-15, -5), B'(10, -10) and C'(-5, -20)

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

Triangle ABC has vertices at A(-3, -1), B(2, -2) and C(-1, -4). It is then dilated by a scale factor of 5 to get A'(-15, -5), B'(10, -10) and C'(-5, -20)

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Answer:

C) -9

Step-by-step explanation:

x + 19 must be half x + 29 because triangles RBC and RST are similar by SAS and RB is half of RS and RC is half of RT.

2(x + 19) = x + 29

2x + 38 = x + 29

x + 38 = 29

x = -9

Answer:

Step-by-step explanation:

Solution

The length of all the rectangles is 7

You need the width to be               4

Area rectangle = L*w

Area rectangle = 7*4

Area rectangle = 28

Answer: B

The equation of the line parallel to the line KL passing through the points (-6, 8) and (6, 0), and going through the point M (-4, -2) is 2x + 3y = -6. The point satisfying this equation is (-6, 2). Thus, the 2nd option is the right choice.

Slope of the line KL = (8 - 0)/(-6 - 6) = 8/(-12) = -2/3.

Using the formula of the slope of the line passing through the points (x₂, y₂) and (x₁, y₁), as m = (y₂ - y₁)/(x₂ - x₁).

The slope of the line parallel to the line KL will be equal to the slope of KL.

Thus, the slope of the required line is m = -2/3.

The required line also passes through point M (-4, -2).

Thus, the equation of the required line will be,

y - (-2) = (-2/3)(x - (-4)) {Using the equation of the line passing through the point (x₁, y₁) and a slope m, as y - y₁ = m(x - x₁)},

or, y + 2 = (-2/3)(x + 4),

or, 3(y + 2) = -2x - 8,

or, 2x + 3y = -6.

From the given points, only the point (-6, 2) satisfies the equation.

Thus, the equation of the line parallel to the line KL passing through the points (-6, 8) and (6, 0), and going through the point M (-4, -2) is 2x + 3y = -6. The point satisfying this equation is (-6, 2). Thus, the 2nd option is the right choice.

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The provided question is incomplete. The complete question is:

"On a coordinate plane, line K L goes through (negative 6, 8) and (6, 0). Point M is at (negative 4, negative 2). Which point could be on the line that is parallel to line KL and passes through point M?

(–10, 0)

(–6, 2)

(0, –6)

(8, –10)"

Answer:

[tex]x=-3[/tex]

Step-by-step explanation:

Given equation:

[tex]\dfrac{2x}{x+1}+\dfrac{3(x+1)}{x}=5[/tex]

Make the denominators the same:

[tex]\implies \dfrac{2x}{x+1} \cdot\dfrac{x}{x}+\dfrac{3(x+1)}{x} \cdot \dfrac{x+1}{x+1}=5[/tex]

[tex]\implies \dfrac{2x^2}{x(x+1)}+\dfrac{3(x+1)^2}{x(x+1)} =5[/tex]

Combine the fractions:

[tex]\implies \dfrac{2x^2+3(x+1)^2}{x(x+1)} =5[/tex]

Multiply both sides by x(x+1):

[tex]\implies 2x^2+3(x+1)^2 =5x(x+1)[/tex]

Expand the brackets:

[tex]\implies 2x^2+3(x^2+2x+1) =5x^2+5x[/tex]

[tex]\implies 2x^2+3x^2+6x+3 =5x^2+5x[/tex]

Combine like terms:

[tex]\implies 5x^2+6x+3=5x^2+5x[/tex]

Subtract 5x² from both sides:

[tex]\implies 6x+3=5x[/tex]

Subtract 5x from both sides:

[tex]\implies x+3=0[/tex]

Subtract 3 from both sides:

[tex]\implies x=-3[/tex]

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a. The equation we get is 10(1.5 + x) = 80, where x is the number of hours Sheila can afford to hire the babysitter.

b. Sheila can afford the babysitter for 6 hours and 30 minutes.

c. The equation we get is 15(1 + x) = 80, where x is the number of hours Sheila can afford to hire the new babysitter.

d. Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.

Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.

a. We assume the hours affordable to Sheila be x hours.

Per hour charge of the babysitter = $10.

Time taken by the babysitter traveling = 1.5 hours.

Therefore, total chargeable time = 1.5 + x.

Therefore, the total charge by the babysitter = $10(1.5 + x).

This needs to be equal to the amount Sheila is willing to spend, that is, $80.

Thus, the equation we get is: 10(1.5 + x) = 80.

b. We are asked to determine the hours Sheila can afford to hire the babysitter.

We have got the equation 10(1.5 + x) = 80, where x is the hours Sheila can afford to hire the babysitter.

Thus, by solving this equation, we can determine the hours Sheila can afford to hire the babysitter.

10(1.5 + x) = 80,

or, 1.5 + x = 8,

or, x = 8 - 1.5 = 6.5 = 6 hours and 30 minutes.

Thus, Sheila can afford the babysitter for 6 hours and 30 minutes.

c. Per hour charge of the new babysitter = $15.

Time taken by the new babysitter traveling = 1 hour.

Therefore, total chargeable time = 1 + x.

Therefore, the total charge by the new babysitter = $15(1 + x).

This needs to be equal to the amount Sheila is willing to spend, that is, $80.

Thus, the equation we get is: 15(1 + x) = 80.

d. We are asked whether Sheila affords the same amount of babysitting from the second sitter as she could from the first sitter.

To determine this, we need to find the hours she affords from the second babysitter, for which, we solve the equation 15(1 + x) = 80 as  follows:

15(1 + x) = 80,

or, 1 + x = 80/15,

or, x = 80/15 - 1 = 65/15 = 13/3 = 4 hours and 20 minutes.

Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.

Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.

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The set {h| 0 ≤ h ≤ 60} describe the domain of p(h).

According to the statement

We have given that the brenton gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour.

and we have to find that the those set which describes the domain of p(h).

So,for this purpose

In this case, the domain represents the set of hours he is permitted to work

From the question, we understand that he cannot work more than 60 hours

This means that, the least number of hours to work is 0, and the highest is 60

So, the domain is 0 to 60

When represented properly, the domain of P(h) is (b)  {h| 0 ≤ h ≤ 60}.

So, The set {h| 0 ≤ h ≤ 60} describe the domain of p(h).

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Brenton’s weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week. Which set describes the domain of P(h)? {h| 0 ≤ h ≤ 40} {h| 0 ≤ h ≤ 60} {P(h)| 0 ≤ P(h) ≤ 1,400} {P(h)| 0 ≤ P(h) ≤ 1,800

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Answer:

B.{h|0<h<60}

Step-by-step explanation:

Rule 1:

1, 3, 7, 15, 31, 63, 127, 255, 511, 1023 etc

Rule 2:

40, 24, 16, 12, 10, 9, 8.5, 8.25, 8.125, 8.0625 etc

Hope this helps!

Using the binomial distribution, the probabilities are given as follows:

a) 0.4159 = 41.59%.

b) 0.5610 = 56.10%.

c) 0.8549 = 85.49%.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the values of the parameters are:

n = 3, p = 0.76.

Item a:

The probability is P(X = 2), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{3,2}.(0.76)^{2}.(0.24)^{1} = 0.4159[/tex]

Item b:

The probability is P(X < 3), hence:

P(X < 3) = 1 - P(X = 3)

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{3,3}.(0.76)^{3}.(0.24)^{0} = 0.4390[/tex]

Then:

P(X < 3) = 1 - P(X = 3) = 1 - 0.4390 = 0.5610 = 56.10%.

Item c:

The probability is:

[tex]P(X \geq 2) = P(X = 2) + P(X = 3) = 0.4159 + 0.4390 = 0.8549[/tex]

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Answer:

Step-by-step explanation:

To check this, we need to know whether

2

1

​

=

3

2

​

We have,  

2

1

​

=

2×3

1×3

​

=

6

3

​

and  

3

2

​

=

3×2

2×2

​

=

6

4

​

We find that

6

3

​

<

6

4

​

, which means that  

2

1

​

<

3

2

​

.

Therefore, The ratio 1:2 is not equivalent to the ratio 2:3

Answer:

No, they aren't equal.

Step-by-step explanation:

Answer: [tex]42x^3 y^2[/tex]

Step-by-step explanation:

[tex]A=(3xy)(14x^2 y)=42x^3 y^2[/tex]

More likely -You are more likely to commit a Type I error

According to statement

we have to find the type 1 error by using the significant levels.

we are commit a MORE LIKELY to find the error by rejecting a true null hypothesis using the 0.05 level of significance than using the 0.01 level of significance.

So, More likely -You are more likely to commit a Type I error

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the answer of this question is 38 and i hope it s  correct

The radius of the cone's base in the unit is 9*7x².

Given:

To find:

Solution:

As we know, the volume of the cone formula is

V = πr²h/3

So, lets us compare the above formula with the given expression;

πr²h/3 = 3*7x³

Here, h is represented as x, we get;

πr²x/3 = 3*7x³

πr²/3 = 3*7x²

r²= 9*7x²

Hence, the radius of the cone's base, in units, is 9*7x².

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Answer:

Yes.

Step-by-step explanation:

Yes, the given line can be used to make reasonable predictions of the number of cheese pizzas that will be sold, since the scatter points clearly show a trend.

As time goes on, the number of pizzas sold is getting bigger, and the trend is what created the line.

The data was taken over 8 consecutive weeks, so we can assume that it can be used in our prediction.

Since the trend has been pretty consistent over periods of time, we can expect it to continue in the upcoming weeks.

Answer: 3/7

Step-by-step explanation:

The value of x from the given expression is 23

Given the following equation

√3x+12 = 9

Square both sides

√3x+12)² = 9²

3x + 12. = 81

Subtract 12 from both sides

3x + 12 - 12 = 81- 12

3x = 69

x = 23

Hence the value of x from the given expression is 23

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Answer:

This would be true for a rectangle and a square.

Step-by-step explanation:

Rectangles and square have 90 angles.  The exterior angles would also equal 90 because 90 + 90 is 180.  An interior angle and the exterior angle are supplements (add together to 180).

Answer:

1/7

Step-by-step explanation:

When 2 lines are perpendicular the gradient of one is the reciprocal of the other :

If the gradient of A was 2 the gradient of B would be 1/2.

If the gradient of a is 7 the gradient of b would be 1/7 .

Hope this helped and have a good day

The location of the points on Cartesian plane are listed below:

Figure 1: A(x, y) = (0, 4), B(x, y) = (5, 0)

Figure 2: A(x, y) = (8.5, 4), B(x, y) = (2.5, 1.5)

A point on a Cartesian plane can be represented by rectangular system of coordinates with the form:

(x, y)

Where:

Now we proceed to represent each point:

Figure 1: A(x, y) = (0, 4), B(x, y) = (5, 0)

Figure 2: A(x, y) = (8.5, 4), B(x, y) = (2.5, 1.5)

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Answer:

[tex]\displaystyle \\\sum_{k=0}^4 45-2.5k=200[/tex]

Step-by-step explanation:

We start off with the term 45 and decrease by 2.5 each term, ending with four 2.5's subtracted from 45.

Therefore, our index starts at k=0 and ends at 4. The general term can be defined then as [tex]\displaystyle \\\sum_{k=0}^4 45-2.5k[/tex] and evaluating yields 200.

Answer:

These lines are perpendicular.

Step-by-step explanation:

Put both equations in the slope intercept form of a line.

y = -6x - 8  This is already in the slope intercept form for a line

-x + 6y = 12  Add x to both sides of the equation

6y = x + 12  Divide through the whole equation by 6

y = 1/6x +2  

Now we compare the two slopes of -6 and 1/6.  They are negative reciprocals of each other.  That means that the line are perpendicular.

Yes

See

3 contractors took 8hours

4 contractors took 6hours

We observe

So it's inverse variation

Answer:

[tex]\fbox {Yes}[/tex]

Step-by-step explanation:

An inverse variation can be seen when two factors are compared, if one factor is seen to be increasing, then naturally the factor should be decreasing.

Here, as the number of contractors increase, the time taken to complete the work decreases.

∴ Hence, this represents an inverse variation.