Find the midpoint of the line segment with the given endpoints

We are given the following function:

We are asked to determine the value of p(8a). That means that we will substitute the value of "x = 8a" in the function, like this:

Now, we solve the exponents using the following property:

Applying the property we get:

Solving the products we get:

Since we can't simplify any further this is the final answer.

Answer:

13x + 16

Step-by-step explanation:

Add the like terms together, like terms are terms that have the same variable or power. Ex. x and 4x are like terms, 4x and 4 are not. x^2 and x^3 are not like terms, x^2 and 2x^2 are like terms.

3+9+5x+4+8x

5x+8x+3+9+4

13x + 16

The solution to the composite function expressions are;

1) (f + g)(x) =  2x(x + 3)

2) (f - g)(x) = 6(x + 3)

3) (f * g)(x) = x⁴ +  6x³ - 54x - 81

4) (f ÷ g)(x) = (x + 3)/(x - 3)

We are given the functions as;

f(x) = x² + 6x + 9 and g(x) = x² - 9

Thus;

1) The addition composite function is;

(f + g)(x) = f(x) + g(x)

= x² + 6x + 9 + x² - 9

= 2x² + 6x

= 2x(x + 3)

2) The subtraction composite function is;

(f - g)(x) = f(x) - g(x)

= x² + 6x + 9 - x² + 9

= 6x + 18

= 6(x + 3)

3) (f * g)(x) = f(x) * g(x)

(x² + 6x + 9) * (x² - 9)

x⁴ - 9x² + 6x³ - 54x + 9x² - 81

= x⁴ +  6x³ - 54x - 81

4) (f ÷ g)(x) = f(x) ÷ g(x)

(x² + 6x + 9) ÷ (x² - 9)

= ((x + 3)(x + 3))/((x + 3)(x - 3))

= (x + 3)/(x - 3)

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Answer:

−1  ≤  x  <  3

Step-by-step explanation:

Solve the system of inequalities.

X must be equal to or greater then -1 and smaller then 3.

You options are -1, 0, 1, & 2

Answer:

Proportional

Step-by-step explanation:

It follows the proportion of 1:10, 1 part bleach to 10 parts water.

The eight term of the geometric sequence 125/9, 25/3,5,3,.... is 243/625.

These steps to answer:

Question above is a geometric sequence consisting of 4 terms to find the 8th term, then we can use the geometric sequence formula below

Tn= a. r^n-1

is known

a= 125/9

r=T4/T2

r=3/5

then to find T4

Tn= a. r^n-1

T8=125/9. (3/5^8-1)

T8=125/9. (3/5)^7)

T8=125/9. (2187/78125)

T8=243/625

A geometric sequence is a sequence that satisfies the quotient of a term with the preceding terms which are of course consecutive. This thing has a constant value. Not only that, geometric sequences are also known as 'measurable sequences' which are still closely related to arithmetic sequences and series.

Examples of geometric sequences are a, b, and c. Then c/b = b/a = constant, this is where the quotient of adjacent terms will be obtained and then it is said to be the ratio of the geometric sequence which is given the symbol "r".

Another example, which is much easier to understand, is for example, if you have a sequence and a series: 2, 4, 8, 16, 32, ….. etc., then from the sequence and series it can be seen between the first and second terms and so on, have the same multiplier.

So, to find the nth term, you can easily find the ratio first. By knowing 'r', then you will easily find Tn.

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Answer:

7

Step-by-step explanation:

Write the ratio of the length of the tent in the drawing to the length of the actual tent. Write the ratio in fraction form.

32in.

14ft.

Simplify the fraction.

32in.÷2

14ft.÷2

=

16in.

7ft.

The scale of the drawing is 16 inches : 7 feet.

Answer:

7 hrs

Step-by-step explanation:

formula :- speed=distance/time

speed= 96kph

distance= 672 km

time=?

S=D/T

96=672/T

(cross multiply)

96T = 672

T = 672/96

T = 7 hrs

It takes 7 hours to travel a distance of 672 km at a speed of 96 kph.

Time = Distance/speed

Time = 672 / 96

Time = 7

It takes 7 hours to travel a distance of 672 km at a speed of 96 kph.

Answer:

an obtuse angle are angles that are greater than 90 degrees

Step-by-step explanation:

an obtuse angle are angles that are greater than 90 degrees

The equivalent linear equation in standard form is 4x + 3y = 5

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

Points = (-7, 11) and (8, –9)

Point-slope form is y - 11 = -4/3(x + 7).

Recall that the point-slope form is y - 11 = -4/3(x + 7).

So, we have

y - 11 = -4/3(x + 7).

Multiply through both sides by 3

This gives

3y - 33 = -4(x + 7).

Open the brackets

3y - 33 = -4x - 28

Evaluate the like terms

3y = -4x +  5

Add 4x to both sides

4x + 3y = 5

Hence, the equation is 4x + 3y = 5

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Answer:

1. 47
2. 4

Step-by-step explanation:

1. 4a + 5b

4(8) + 5 (3)

32+ 15
=47

2. 3a/2b
3(8)/2(3)
24/6
=4

The equation of the altitude from vertex A of the triangle is y = (3/2)x + 3/2.

To write an equation for the altitude from vertex A of the triangle where point A is (-1,0), point B is (8,-5), and point C is (2,-3), we need to use the slope-intercept form of an equation for the line that contains the side opposite vertex A. Here are the steps:

1. Find the slope of the line containing side BC using the slope formula: m = (yb - yc)/(xb - xc) = (-5 - (-3))/(8 - 2) = -2/3.

2. Find the equation of the line containing side BC using point-slope form: y - yb = m(x - xb). Using point B, we get: y + 5 = (-2/3)(x - 8). Simplifying, we get y = (-2/3)x + 19/3.

3. The altitude from vertex A of the triangle is perpendicular to side BC. Therefore, its slope is the negative reciprocal of the slope of side BC, which is 3/2.

4. We can find the equation of the altitude by using point-slope form again, this time using point A: y - ya = m(x - xa). Using point A and the slope 3/2, we get: y - 0 = (3/2)(x + 1). Simplifying, we get: y = (3/2)x + 3/2.

Summary: To find the equation of the altitude from vertex A of the given triangle, we first found the slope of the line containing the side opposite vertex A, which is BC. Then, we found the equation of this line using point-slope form. Next, we used the fact that the altitude is perpendicular to side BC and found its slope, which is the negative reciprocal of the slope of side BC. Finally, we used the point-slope form again to find the equation of the altitude using point A and its slope. The equation we obtained is y = (3/2)x + 3/2.

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Using the cosine rule, the distance the plane has flown during Jack's phone call can be calculated by taking the square root of the sum of the squares of the initial and final distances, minus twice their product, multiplied by the cosine of the angle difference.

To determine the distance the plane has flown during Jack's phone call, we can use the cosine rule in trigonometry.

The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

Let's denote the initial distance from Jack to the plane as d1 and the final distance as d2.

We know that the altitude of the plane remains constant at 2400 meters.

According to the cosine rule:

\(d^2 = a^2 + b^2 - 2ab \times cos(C)\)

Where d is the side opposite to the angle C, and a and b are the other two sides of the triangle.

For the initial angle of elevation (70°), we have the equation:

\(d1^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \timescos(70)\)

Similarly, for the final angle of elevation (50°), we have:

\(d2^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \times cos(50)\)

To find the distance the plane has flown, we subtract the two equations:

\(d2^2 - d1^2 = 2 \times 2400 \times a \times (cos(70) - cos(50))\)

Now we can solve this equation to find the value of a, which represents the distance the plane has flown.

Finally, we calculate the square root of \(a^2\) to find the distance in meters.

It's important to note that the angle of elevation assumes a straight-line path for the plane's movement and does not account for any changes in altitude or course adjustments that might occur during the phone call.

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Answer:

Step-by-step explanation:

(a) f(-4) = 7 - 8(-4) = 7 + 32 = 39

(b) f(0) = 7 - 8(0) = 7 - 0 = 7

(c) f(3) = 7 - 8(3) = 7 - 24 = 17

An item is regularly priced at $78. Martina bought it at a discount of 80% off the regular price. Martina paid $15.6

Sales price:  The price that is paid by the buyer at the time when something is sold: People who sold their homes through real estate agents typically did not get a higher sale price than people who sold their homes themselves

The formula for calculating sales price of an item is:

s=p-(p x d)

where,

s is the sales price (which we are going to calculate in this problem)

p is the regular price of the item which is $78

d is the discount rate which is 80%

which means out of 100 = 80/100

substitute the above values in the formula then we get

s=$78-($78 x 80/100)

s=$78-($6240/100)

s=$78-$62.4

s=$15.6

Martina paid $15.6

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To determine whether quality is associated with the source of the shipments, we need to test the competing hypotheses.

The competing hypotheses are as follows:

H0: Quality and source of shipment (vendor) are independent.
HA: Quality and source of shipment (vendor) are dependent.

To test these hypotheses, we can use a chi-square test for independence. The test statistic is calculated by comparing the observed frequencies with the expected frequencies under the assumption of independence.

b-1. To calculate the test statistic, we first need to create a contingency table with the observed frequencies of quality and source of shipment. Each cell in the table represents the count of shipments from a specific vendor with a specific quality.

For example, the table could look like this:

            | Vendor A | Vendor B | Vendor C
--------------------------------------------
Good Quality |   10     |   15     |   12
--------------------------------------------
Poor Quality |   20     |   25     |   18

Next, we calculate the expected frequencies assuming independence. The expected frequency for each cell is calculated by multiplying the row total by the column total and dividing by the total number of observations.

Finally, we calculate the chi-square test statistic by summing the squared differences between the observed and expected frequencies divided by the expected frequencies for each cell.

b-2. Once we have the test statistic, we can find the p-value associated with it. The p-value represents the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

To find the p-value, we need to consult the chi-square table or use a statistical software. The p-value will indicate the strength of evidence against the null hypothesis. The smaller the p-value, the stronger the evidence against the null hypothesis.

Based on the given options, the p-value falls within the range of 0.01 ≤ p-value < 0.025. Therefore, we reject the null hypothesis and conclude that there is evidence to suggest that quality and source of shipment are dependent.

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Answer:

X'= (-3,6)

Y'=(7,8)

Z'=(11,2)

Step-by-step explanation:

when a point is reflected over the y axis, (x,y) becomes (-x,y). so the x value is just multiplied by -1

Answer:

X′(−3, 6), Y′(7, 8), Z′(11, 2)

Step-by-step explanation:

Imagine you are a spy who needs to infiltrate a secret base located at the origin of the coordinate plane. You have three accomplices, X, Y, and Z, who are waiting for you at different points on the plane. X is at (3, 6), Y is at (-7, 8), and Z is at (-11, 2). You have a device that can reflect any point over the y-axis, which you plan to use to confuse the enemy guards. You decide to reflect X, Y, and Z over the y-axis to create X', Y', and Z', respectively. What are the coordinates of these new points?

To find the coordinates of X', you simply change the sign of the x-coordinate of X. So, X' is at (-3, 6). Similarly, to find the coordinates of Y' and Z', you change the sign of the x-coordinates of Y and Z. So Y' is at (7, 8) and Z' is at (11, 2). Now you have three new points that are symmetric to the original ones over the y-axis.

But wait! There's a problem. The enemy guards have noticed that something is wrong. They see four points on their radar: one at the origin (you) and three on the right side of the y-axis (X', Y', and Z'). They realize that these points are reflections of some other points on the left side of the y-axis. They quickly deduce that there must be a spy among them. They start searching for you.

You need to act fast. You use your device again to reflect yourself over the y-axis. This creates a new point at (-0, 0), which is exactly the same as (0, 0). You have effectively disappeared from their radar. You sneak into the base while they are busy looking for you on the wrong side of the plane.

You have successfully completed your mission. Congratulations! You are a master of reflections.

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

The description refers to the diagnosis of brief psychotic disorder, which consists of abnormal behaviors identical to those in schizophrenia lasting for at least 1 month but fewer than 6 months.

Brief psychotic disorder is a psychiatric diagnosis characterized by the presence of psychotic symptoms, such as hallucinations, delusions, disorganized thinking, or grossly disorganized or catatonic behavior. These symptoms are similar to those seen in schizophrenia, but the key distinction is that brief psychotic disorder lasts for a shorter duration, specifically between 1 month and 6 months.

During this period, individuals with brief psychotic disorder may experience a sudden onset of symptoms that significantly impact their thoughts, emotions, and behavior. However, unlike schizophrenia, the duration of symptoms in brief psychotic disorder is limited, typically resolving within a few weeks to a few months.

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The number of sections should be marked as "win" are 14

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

Students = 200

Wins = 70

Represent the number of sections with x

So, we have

Expected value of win = x/Size

This gives

70/200 = x/40

Evaluate

x = 40 * 70/200

So, we have

x = 14

Hence, the sections should be marked as "win" are 14

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Based on the above,  14 sections out of the 40 on the wheel need to be marked as "win".

To know the "win" sections on the prize wheel, one need to use the concept of expected value.

Let us assume the probability of winning is p, and each of the 40 sections has a probability of winning of p/40.

The expected number of winners is:

200*(p/40)=70

Note that:

Expected number of winners = Number of students × Probability of winning per spin

Hence:

70 = 200 × (p/40)

To get p, we have to rearrange the equation,. Hence it will be:

p/40 = 70/200

p/40 = 7/20

p = (7/20) × 40

p = 14

So, 14 of the whole 40 sections on the prize wheel need to be marked as "win"

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Answer: 1701

Step-by-step explanation:

It’s the simple math

243

    7=

1701

9514 1404 393

Answer:

  -5 ± 6i

Step-by-step explanation:

To use the quadratic formula, we need the equation in standard form. Adding 10x gives ...

  x^2 +10x +61 = 0

Then a=1, b=10, c=61, and the solutions are ...

  \(x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-10\pm\sqrt{10^2-4(1)(61)}}{2(1)}\\\\=\dfrac{-10\pm\sqrt{-144}}{2}=\dfrac{-10\pm12i}{2}\\\\ \boxed{x=\{-5-6i,-6+6i\}}\)

The type directions that lie in the (110) plane are Crystal planes are equivalent planes that represent a group of crystal planes with a common set of atomic indexes.

Crystallographers use Miller indices to identify crystallographic planes. A crystal is a three-dimensional structure with a repeating pattern of atoms or ions.In a crystal, planes of atoms, ions, or molecules are stacked in a consistent, repeating pattern. Miller indices are a mathematical way of representing these crystal planes.

Miller indices are the inverses of the fractional intercepts of a crystal plane on the three axes of a Cartesian coordinate system.Let us now determine which of the type directions lie in the (110) plane.[101] is not in the (110) plane because it has an x-intercept of 1, a y-intercept of 0, and a z-intercept of 1. So, this direction does not lie in the (110) plane.[110] is in the (110) plane since it has an x-intercept of 1, a y-intercept of 1, and a z-intercept of 0.

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The required reflection of the points N(-3, 1), G(0, 4), B(-1, 1) across the y-axis are N(3, 1),  G(0, 4), B(1, 1) .

Point (x, y) is reflected across the x-axis as (x, -y). The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse.

We have,

N(-3, 1), G(0, 4), B(-1, 1)

While, find reflected points we are considering y-axis as mirror,

Then,

Reflection of point N(-3, 1) across the y-axis

⇒ N(3, 1)

Reflection of point G(0, 4) across the y-axis

⇒ G(0, 4)

Reflection of point B(-1, 1) across the y-axis

⇒ B(1, 1)

Thus, required reflected points are  N(3, 1),  G(0, 4), B(1, 1) .

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It is  false that the value 5pi/4 is a solution for the given equation.

1. Collect the like terms

2. make the trigonometry ratio the subject of formula

3. Find the inverse of the trigonometry.

Given that a solution for the equation 3\(\sqrt{2}\) sinФ + 2 = -1.

Collect the like terms

3\(\sqrt{2}\)  Sin Ф = -1 - 2

3\(\sqrt{2}\)  SinФ = -3

Sin Ф = -3 / 3\(\sqrt{2}\)

SinФ = -1/\(\sqrt{2}\)

Rationalize the RHS

SinФ = -1/\(\sqrt{2}\)  x \(\sqrt{2}\) /\(\sqrt{2}\)

Sin Ф = -\(\sqrt{2}\) /2

Sin Ф = - 0.707

Ф = \(Sin^{-1}\)(-0.707)

Ф = 45°

Change the degree to radian

45 x \(\pi\)/180

\(\pi\)/4

Therefore, it is false that the value 5pi/4 is a solution for the given equation.

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Answer:

It's True

Step-by-step explanation:

I just took the quiz and the answer is true.

Answer:

y = 4

Step-by-step explanation:

2y=24-4y

Add 4y to both sides

2y+4y=24-4y+4y

6y=24

Divide both sides by 6

6y÷6=24÷6

y=4

I would say (I am abbreviating square root to sqrt)

1. 4 sqrt(8488) = 4 sqrt(2x2x2122) = 8 sqrt(2122)

2. 3 sqrt(6936) = 3 sqrt(6x34x34) = 102 sqrt (6)

3. 2 sqrt(8648) = 2 sqrt(2x2x2162) = 4 sqrt(2162)

Answer:

Please see attached picture for full solution.