Triangle ABC has coordinates A(4,-2), B(5,5), C(-1,3). Determine if triangle ABC is an equilateral triangle.

Triangle ABC is an ........ triangle because ..........

Answer:

1)  a = 1, b = -8, c = 17;  Vertex:   (4, 1)

2)  a = -1, b = -2. c = -2;  Vertex:   (-1, -1)

3)  a = -1, b = 6, c = -8;  Vertex:   (3, 1)

4)  a = -3, b = 6, c = 0;  Vertex:   (1, 3)

5)  a = -2, b = -16, c = -31;  Vertex:   (-4, 1)

6)  a = -1/2 or -0.5, b = -4, c = -6;  Vertex:   (-4, 2)

Step-by-step explanation:

The quadratic functions listed are all in standard form:

y = ax² + bx + c

where a, b, and c, are coefficients for each of the terms.

Vertex

To find the vertex of a parabolic equation in standard form. Calculate -b/2a. This will be your x-coordinate. Then substitute this back into f(x) to obtain the y-coordinate; The calculated point is your vertex.

1)   x = - b / 2a = - (-8) / 2 (1) = 8 / 2 = 4

    f(4) = 4² - 8 (4) + 17 = 16 - 32 + 17 = 1

   Vertex:   (4, 1)

2)  x = -b / 2a = - (-2) / 2 (-1) = 2 / (-2) = -1

    f(-1) = - (-1)² - 2 (-1) - 2 = -1 + 2 - 2 = -1

    Vertex:   (-1, -1)

3)  x = - b / 2a = - (6) / 2 (-1) = -6 / -2 = 3

    f(3) = - (3)² + 6 (3) -8 = -9 + 18 - 8 = 1

    Vertex:   (3, 1)

4)  x = - b / 2a = - (6) / 2 (-3) = -6 / -6 = 1

     f(1) = -3 (1)² + 6 (1) = -3 + 6 = 3

     Vertex:   (1, 3)

5)  x = - b / 2a = - (-16) / 2(-2) = 16 / -4 = -4

    f(-4) = -2 (-4)² - 16 (-4) - 31 = -32 + 64 - 31 = 1

    Vertex:   (-4, 1)

6)  x = - b / 2a = - (-4) / 2 (-0.5) = 4 / -1 = -4

    f (-4) = (-0.5) (-4)² - 4 (-4) - 6 = -8 + 16 - 6 = 2

    Vertex:   (-4, 2)

Caleb and Moesha bought a total of 50.4 kg of meat.

Caleb bought 26.4 kg of fish from the cold store.

Moesha bought 2.4 kg less than Caleb, which means she bought 26.4 kg - 2.4 kg = 24 kg of meat.

Therefore, the total amount of meat they bought together is:

26.4 kg + 24 kg = 50.4 kg

So Caleb and Moesha bought a total of 50.4 kg of meat.

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Answer:

You end at the coordinates (4, 2)

The first terms are a_1=  -4  a_2= -8/3  a_3= -16/9  a_4= -32/27

The series converges as a result  the series' sum, if it exists, is equal to -12.

What exactly are geometric series?

A geometric sequence is a set of numbers where each phrase following the first is obtained by multiplying the previous term by the common ratio , a constant. Consider the order 2, 4, 8, 16, 32, etc. as an example. Given that each term after the first is derived by multiplying the previous term by 2, this geometric series has a common ratio of 2.

The following is the formula for determining the nth term in a geometric sequence:

a n = arⁿ⁻¹

where "a" denotes the initial word and "r" denotes the common ratio 2.

A geometric sequence of infinite nature is the sum of an infinite geometric series. ¹. The following formula is used to calculate the sum of an infinite geometric series:

sum = a/ (1-r)

where "r" is the common ratio and "a" is the first term.

n=1, 2, 3, and 4 can be added to the formula for the nth term of a geometric sequence to find the first four terms of the series:

a n = arⁿ⁻¹

where r is the common ratio and an is the first term. As a result, we have:

n= 1

= -4(2/3)⁽¹⁻¹⁾   =  -4

n= 2

= -4(2/3)⁽²⁻¹⁾   = -8/3

n=3

= -4(2/3)⁽³⁻¹⁾  =   -16/9

n=4

= -4(2/3)⁽⁴⁻¹⁾  = -32/27

b) b) We must locate the common ratio "r" in order to establish whether the series converges or diverges. In this instance, r=2/3, satisfying |r|<1 ⁵ The series converges as a result.

c) The formula for the sum of an infinite geometric series can be used to determine whether the series has a sum.

sum = a/ (1-r) (1-r)

where "r" is the common ratio and "a" is the first term. In this formula, substituting a=-4 and r=2/3 results in:

sum = -4 / (1-2/3)

= -12

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The compositions of the given functions are as follows:

hf(x) = 3/(x² - 1)

fh(x) = (9 - x²)/x²

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.

The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

A mathematical phrase, rule, or law establishes the link between an independent variable and a dependent variable (the dependent variable).

So, we have:

h(x) =3/x, x and f(x) = x^2 - 1

Now, solve as follows:
h(x) = 3/x

f(x) = x² - 1

h(f(x)) = 3/f(x)

hf(x) = 3/(x² - 1)

f(h(x)) = (h(x))² - 1

= (3/x)² - 1

= 9/x² - 1

fh(x) = (9 - x²)/x²

Therefore, the compositions of the given functions are as follows:

hf(x) = 3/(x² - 1)

fh(x) = (9 - x²)/x²

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Correct question:

Suppose that the functions h and f are defined as follows. h(x) =3/x, x notequalto 0 f(x) = x^2 - 1 Find the compositions h composite function h and f composite function f Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.)

The first table in the question with the values(2,-3)(2,-2)(2,-1)(2,0)(2,1)represents the linear function.

A linear function is a type of mathematical function that has a constant rate of change or slope. This means that the function produces a straight line when graphed on a coordinate plane.

A linear function can be represented using the general form:

f(x) = mx + b

where m is the slope or rate of change, and b is the y-intercept or the point where the line intersects the y-axis.

In the given question, Option (1),

(2,-3)(2,-2)(2,-1)(2,0)(2,1).

If plotted on graph forms a straight line.

But all the other three options does not form a straight line.

Therefore, its a linear function.

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a) The distance traveled by the car is 240 km, b) the average speed of the car is 30 km/s, c) the speed of the car changes from increasing to constant to decreasing, d) and the total area under the curve 240 km/s.

a. To find the distance traveled by the car between 1 and 9 seconds, we need to find the area under the curve of the velocity-time graph between 1 and 9 seconds. By counting the number of squares, we can estimate the area to be approximately 24 square units. Since each square represents a velocity of 10 km/h and the time interval is 8 seconds, the distance traveled by the car is approximately 240 km.

b. The average speed of the car between 1 and 9 seconds is equal to the total distance traveled divided by the time taken, which is 240 km / 8 s = 30 km/s.

c. The speed of the car increases from 0 km/h to 60 km/h in the first 2 seconds, then remains constant at 60 km/h for the next 6 seconds, and finally decreases to 0 km/h in the last 2 seconds. Therefore, the speed of the car changes from increasing to constant to decreasing throughout its test run.

d. If we had a graph of velocity versus time for this test, the total area under the curve would represent the total displacement of the car, which is equal to the distance traveled in this case. Since the area under the curve is a trapezoid, we can calculate it as the average of the two parallel sides multiplied by the height, which is (0 + 60) / 2 x 8 = 240 km/s.

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The coordinates of the pre-image point A are (-4, 8).Hence, the correct answer is (-4, 8).

The given image point of A after a translation right 5 units and down 3 units is the point B(-3, -11).

To determine the coordinates of the pre-image point A, we need to move 5 units to the left and 3 units up.

Let the pre-image point A be (x, y).

Then, the image point B is obtained from A by translation of 5 units to the right and 3 units down.

So, we have the following equations:

y - (-11) = -3x - (-3)y + 11 = -3x + 9On

solving the above equations, we get

x = -4 and y = 8.

So, the coordinates of the pre-image point A are (-4, 8).

Hence, the correct answer is (-4, 8).

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After running the pump for 4 hours, the NTU measurement would be approximately 0.52.

To determine the NTU measurement after running the pump for 4 hours, we need to consider that the pump reduces the NTU by 10% each hour.

Here's the chart with the NTU values for each hour, rounded to the nearest hundredth:

Hours | NTU

0 | 0.80

1 | 0.72 (0.80 * (1 - 0.10) = 0.80 * 0.9)

2 | 0.65 (0.72 * (1 - 0.10) = 0.72 * 0.9)

3 | 0.58 (0.65 * (1 - 0.10) = 0.65 * 0.9)

4 | 0.52 (0.58 * (1 - 0.10) = 0.58 * 0.9)

After running the pump for 4 hours, the NTU measurement would be approximately 0.52.

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Answer:

Step-by-step explanation:

No of blue marbles=4

No of red marbles=3

Total number of marbles = 7

Probability of getting blue marbles = 4/7

Probability of getting red marbles= 3/7

The type of sampling used in each case of the students to pay tuition fee for the fall semester is simple random sampling.

Simple random sampling is the method that was applied in this instance. Each person in the population has an equal probability of being chosen for the sample when using simple random sampling. In this instance, the amount of tuition each participant in the sample paid for the autumn semester was questioned.

The type of sampling in the next case is stratified sampling. After classifying the students into freshmen, sophomores, juniors, or seniors, 25 students from each group are chosen. The sample will be representative of each group thanks to this technique.

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Complete question is:

A study wants to determine the average tuition that san jose state undergraduate students would pay per semester. each student in the following samples is asked how much tuition he or she paid for the fall semester. what is the type of sampling in each case?

A sample of 100 undergraduate San Jose State students is taken by organizing the students’ names by classification (freshman, sophomore, junior, or senior), and then selecting 25 students from each.

The solution set for that absolute value inequality is -19/2 < y < 13/2.

Answer:

3x=36

Step-by-step explanation:

The type of error depends on the level of significance and whether the test is one-tailed or two-tailed.

The type of error occurs if you fail to reject H0 when, in fact, it is not true.

The type of error that occurs when one fails to reject H0 when, in reality, it is false is type II error.

Type II error is an error in which one accepts a null hypothesis that should be rejected.

This type of error is the opposite of type I error, where one rejects a null hypothesis that is true.

A type II error is a serious issue because it suggests that a significant difference exists, but the statistical test fails to detect it.

There are two types of errors associated with hypothesis testing, type I and type II errors, depending on the significance level of the test.

A type I error occurs when the null hypothesis is rejected when it is true.

A type II error happens when the null hypothesis is not rejected when it is false.

A type I error, also known as an alpha error, is caused by rejecting the null hypothesis when it is true.

It occurs when the significance level is set too high or when a statistical test is not performed correctly.

A type I error occurs when the observed value lies in the rejection region of the null hypothesis, and we reject the null hypothesis even though it is true.

In conclusion, when one fails to reject H0 when it is false, a type II error occurs. On the other hand, when one rejects H0 when it is true, a type I error occurs.

The type of error depends on the level of significance and whether the test is one-tailed or two-tailed.

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Thus, the value of x in obtained in the simplest form for the unit circle is: x = -√5/3.

A circle with a radius of one unit and a centre at the origin is referred to as a unit circle just on Cartesian Plane (0, 0). When working with trigonometric functions including angle measurements, the unit circle is a useful tool that makes reference much simpler.

The equation of unit circle, radius r = 1 unit. :

x² + y² = 1.

For the given point P (x, 2/3), we can solve for x by substituting each quantity into the equation.

x² + (2/3)² = 1

x² + 4/9= 1.

Subtract 4/9 from both side.

x² = 5/9.  

Taking square root on both side.

x = √5/3

x = -√5/3

Thus, the value of x in obtained in the simplest form for the unit circle is: x = -√5/3.

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Complete question:

the point P=(x,2/3) lies on the unit circle shown below . what is the value of x in simplest form?

The diagram is attached.

Answer:

Draw a line perpendicular (90°) to the chord GH, half way along it's length

Now you know why it's easier to pick an easy length to start with. Make sure it goes past where the center of the circle should be. You can go straight across if that's easier.

Do the same for chord JK

The point of intersection of the 2 chord's perpendicular line is the centre of the circle

This should be enough to find the center of the circle, but you can add more chords to make sure

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The total cost of the water piping is $217.12 in the field.

Perimeter is the total length of the boundary or the outer edge of a two-dimensional geometric shape. It is the distance around the shape or the sum of the lengths of all its sides. The perimeter is usually measured in units such as centimeters, meters, feet, or inches, depending on the system of measurement used.

In the given question,

To calculate the total cost of the water piping, we need to first calculate the total length of the edges of the field.

For the rectangle, the length of its four edges can be calculated as:

2 x length + 2 x breadth = 2 x 68m + 2 x 64m = 136m + 128m = 264m

For the square extension, it has four edges each with length 26m, so the total length of its edges is:

4 x 26m = 104m

Therefore, the total length of the edges of the field is:

264m + 104m = 368m

To find the total cost of the water piping, we can multiply the total length of the edges by the cost per metre:

368m x $0.59/m = $217.12

So, the total cost of the water piping is $217.12.

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After multiplying the y-value of each point by 1/2, The new location of the blue point would be at x = 2, y = 1.

To apply the given transformation to the points in the graph using the cube root function, we would need to take the cube root of the y-value of each point and then multiply it by 1/2.

Then, we can drag the blue point to its new location based on the transformed coordinates.

For example, if we consider the point (2, 8) in the original graph, the transformed point would be:

(2, 8*(1/3) * 1/2) = (2, 1)

So, the new location of the blue point would be at x = 2, y = 1.

Similarly, we can apply this transformation to all the other points in the graph.

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Answer:

16

Step-by-step explanation:

4 + 12= 16

4 + 2 = 6

Add a 1 in front

Answer:

19

Step-by-step explanation:

20+5+13 / 2 = 19

Answer:

  145°

Step-by-step explanation:

You want the exterior angle of a triangle that has remote interior angles with measures 115° and 30°.

The measure of an exterior angle of a triangle is equal to the sum of the remote interior angles:

  ∠1 = 115° +30°

  ∠1 = 145°

__

Additional comment

You can see how this works if you consider the unmarked angle in the triangle to be "u", then its measure satisfies two sums: one is the sum of the interior angles; the other is the sum of angles of a linear pair.

  115° +30° +u = 180*

  ∠1 +u = 180°

Combining these equations, we have ...

  ∠1 +u = 115° +30° +u

If we subtract u from this equation, we have ...

  ∠1 = 115° +30°

Answer:

145°

Step-by-step explanation:

? + 30 + 115 = 180

? = 180 - 145

? = 35

180 - 35 = 145

m< 1 = 145°

2x + 8 should be right

If there is a significant difference in the average vitamin D levels between the control group and the experimental group receiving vitamin D supplements then t-test can be used to determine the significance of the difference.

To determine if the average vitamin D levels for sections 1 and 2 are significantly different, a t-test can be performed. The null hypothesis would be that there is no significant difference in the average vitamin D levels between the two groups, while the alternative hypothesis would be that there is a significant difference.

The t-test would provide a p-value, which can be used to determine the significance of the difference between the two groups. If the p-value is less than the chosen level of significance (usually 0.05), then it can be concluded that there is a significant difference in the average vitamin D levels between the two groups.

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The percentage of calories that comes from saturated fat in each serving of these crackers is 0.4%

To calculate the percentage of calories that come from saturated fat, we need to first determine how many calories come from saturated fat in one serving of crackers.

We know that each serving of crackers provides 120 calories, and 0.5 grams of saturated fat. We can convert the amount of saturated fat from grams to calories by multiplying it by 9 (since 1 gram of fat provides 9 calories).

0.5 grams of saturated fat x 9 calories per gram = 4.5 calories from saturated fat

Therefore, out of the 120 total calories in one serving of crackers, 4.5 calories come from saturated fat.

To find the percentage of calories that come from saturated fat, we can divide the number of calories from saturated fat by the total number of calories in one serving of crackers, and then multiply by 100.

(4.5 calories from saturated fat / 120 total calories) x 100 = 0.0375 x 100 = 0.4%

Therefore, each serving of crackers provides 0.4% of calories from saturated fat.

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The correct answer is:  [tex]x=\sqrt{28}, m \angle E=37^{\circ}[/tex]. Thus, option D is correct by using Pythagorean theorem.

In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be represented as:

[tex]c^2 = a^2 + b^2[/tex]

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Given that x is the hypotenuse of the right triangle and   [tex]$x = \sqrt{28}$[/tex], we can use the Pythagorean theorem to find the lengths of the other two sides. Since x is the hypotenuse, it will be equal to c in the Pythagorean theorem equation. Plugging in the values, we get:

[tex](\sqrt{28})^2 = a^2 + b^2[/tex]

[tex]28 = a^2 + b^2[/tex]

Now, we are given the measure of [tex]\angle E[/tex] which is  [tex]37^{\circ}[/tex]. In a right triangle, one angle is always  [tex]90^{\circ}[/tex], so the sum of the measures of the other two angles will be [tex]90^{\circ}[/tex] . Therefore, angle  must be one of the acute angles of the right triangle.

To find the value of a and b, we can use trigonometric ratios. In a right triangle, the sine, cosine, and tangent ratios are commonly used.

For [tex]$\angle E$[/tex], we can use the sine ratio, which is defined as:

[tex]$\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}$[/tex]

In our case, the opposite side of   [tex]$\angle E$ is $a$[/tex] and the hypotenuse is x. Plugging in the values, we get:

[tex]$\sin(37^{\circ}) = \frac{a}{\sqrt{28}}$[/tex]

Solving for a, we get:

[tex]$a = \sin(37^{\circ}) \cdot \sqrt{28}$[/tex]

Similarly, we can use the cosine ratio to find b. The cosine ratio is defined as:

[tex]\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]

In our case, the adjacent side of angle E is b and the hypotenuse is x. Plugging in the values, we get:

[tex]$\cos(37^{\circ}) = \frac{b}{\sqrt{28}}$[/tex]

Solving for b, we get:

[tex]b = \cos(37^{\circ}) \cdot \sqrt{28}[/tex]

Therefore, , the correct answer is The correct answer is:  [tex]x=\sqrt{28}, m \angle E=37^{\circ}[/tex], as given in option [tex]x=\sqrt{28},[/tex] m [tex]\angle E=37^{\circ}$.[/tex]

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The actual height of the statue is 0.0048 feet or 0.0576 inches.

The scale factor is a way to compare figures with similar appearances but distinct scales or measurements. Consider two circles that resemble one another but may have different diameters. The scale factor indicates how much a figure has increased or decreased from its initial value.

If the scale factor is 250:1, it means that every 250 units in the actual object correspond to 1 unit in the drawing. In this case, we know the height of the drawing is 1.2 feet, which is 1 unit in the drawing.

To find the actual height of the statue, we can use the scale factor to set up a proportion:

250 units (actual height) : 1 unit (drawing height) = x (actual height) : 1.2 feet (drawing height)

Cross-multiplying:

250x = 1.2

Dividing both sides by 250:

x = 0.0048

Therefore, the actual height of the statue is 0.0048 feet or 0.0576 inches.

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The best day to sell both stocks would be Day 2, as both stocks saw an increase in closing price. The total profit from selling both stocks on Day 2 would be $104.65.

The stock's trading price at the close of a trading day is known as the closing price. Up to the start of the following trading session, this is the stock's most recent price. The market hours for shares are 9:15 AM to 3:30 PM. In the case of equities, the closing price is determined as the weighted average price of the previous 30 minutes, or from 3:00 to 3:30 PM.

The price at which a stock first trades on an exchange on a trading day is known as the opening price. The market hours for shares are 9:15 AM to 3:30 PM. Nonetheless, the pre-market window, which runs from 9:00 AM to 9:08 AM, is when the exchange begins accepting orders.

According to the given information,

For Unix Co the change in closing price:

From Day 1 to Day 2:

8.78 - 8.15 = 0.63,

From Day 1 to Day 3:

8.06 - 8.15 = -0.09.

Now, for Cubix Inc we have:

Day 1 to Day 2:

16.92 - 15.65 = 1.27

Day 1 to Day 3:

14.35 - 15.65 = -1.30.

Thus, the best day to sell both stocks would be Day 2, as both stocks saw an increase in closing price.

Now, when we sell 65 shares of Unix Co at day 2 at 8.78 we have:

(8.78 - 8.15) x 65 = $41.15

For 50 shares of Cubix Inc:

(16.92 - 15.65) x 50 = $63.50.

Hence, the total profit from selling both stocks on Day 2 would be $41.15 + $63.50 = $104.65.

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Answer:

Step-by-step explanation:

The probability that a randomly selected car had automatic transmission or air conditioning or both is 0.92517.

Total number of cars sold, n = 147

Let A denotes the car is air conditioning.

And B denotes the car is automatic message transmission.

A = 81

B = 82

Number of cars that neither of these extras = 11

Only A = 54

Only B = 55

Now,

P(A ∩ B') = A/n

P(A ∩ B') = 81/147

P(A ∩ B') = 0.551

P(A' ∩ B') = 11/147

P(A' ∩ B') = 0.07483

The probability that a randomly selected car had automatic transmission or air conditioning or both is:

P(A ∪ B) = 1 - P(A' ∩ B')

P(A ∪ B) = 1 - 0.07483

P(A ∪ B) = 0.92517

The likelihood that an automobile chosen at random has either an automatic gearbox, air conditioning, or both is 0.92517.

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There are 4 red jellybeans in a jar of 20 total. The probability that you will choose a red jellybean from the jar is represented by the fraction 4/20.

The probability of picking a red jellybean out of the jar is the number of red jellybeans in the jar divided by the total number of jellybeans in the jar.

So, P(red jellybean) = number of red jellybeans / total number of jellybeans

= 4/20

= 1/5

Therefore, the fraction that represents the probability of picking a red jellybean out of the jar is 4/20.

The complete question is:-

You have a jar of 20 jellybeans, and 4 are red. Which fraction represents the probability that you will pick a red jellybean out of the jar?

A) 4/20

B) 16/20

C) 20/4

D) 20/16

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