lay, November 08, 2021 8:53 AM Which sentence(s) below are true about the numbers 1,3, and 9? Circle the letter for all that apply. A Adding 1 to any of the numbers will make a composite number B Adding 2 to any of the numbers will make a prime number. C 3 and 9 are prime numbers. D All the numbers are factors of 9. E All the numbers are factors of any multiple of 3.

Answer:

It's D.

Step-by-step explanation:

31-4 = 27 , 63 + 27 = 90 :) so the answer's D. 31

Answer:

D) 31

Step-by-step explanation:.

It is a right angle. All right angles equal 90°. So the two angles add up to 90

90= 63 + x - 4

Add 4 to each side

94 = 63 + x

Subtract 63 to each side

31 = x

The pairs of triangles can be proven similar through SSS similarity is given by Third pair.

We know that the SSS similarity criteria will have the ratio of three corresponding sides of both triangles congruent.

1. KL / EG = HL / DG = HK / DE

3/6 = 6.5/13 ≠ 4/10

Thus, SSS similarity does not follow.

2. KL / EG = HL / DG = HK / DE

3/10 ≠ 6.5/13 ≠ 4/10

Thus, SSS similarity does not follow.

3. KL / EG = HL / DG = HK / DE

3/6 = 6.5/13 = 5/10

Thus, SSS similarity follow.

4. All three angles are congruent.

Thus, SSS similarity does not follow.

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The final answer is (f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.

(f o g)(x):

To find (f o g)(x), we substitute g(x) into f(x):

(f o g)(x) = f(g(x))

Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:

(f o g)(x) = f(g(x)) = f(x^2 - 8)

Now we replace x in f(x^2 - 8) with x^2 - 8:

(f o g)(x) = (x^2 - 8)^2 + 8

Simplifying further:

(f o g)(x) = x^4 - 16x^2 + 64 + 8

(f o g)(x) = x^4 - 16x^2 + 72

Therefore, (f o g)(x) = x^4 - 16x^2 + 72.

(g o f)(x):

To find (g o f)(x), we substitute f(x) into g(x):

(g o f)(x) = g(f(x))

Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:

(g o f)(x) = g(f(x)) = g(x^2 + 8)

Now we replace x in g(x^2 + 8) with x^2 + 8:

(g o f)(x) = (x^2 + 8)^2 - 8

Simplifying further:

(g o f)(x) = x^4 + 16x^2 + 64 - 8

(g o f)(x) = x^4 + 16x^2 + 56

Therefore, (g o f)(x) = x^4 + 16x^2 + 56.

(f o g)(2):

To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:

(f o g)(2) = 2^4 - 16(2)^2 + 72

(f o g)(2) = 16 - 64 + 72

(f o g)(2) = 24

Therefore, (f o g)(2) = 24.

In summary:

(f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

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Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of \(f(x)=(x-1)(x+7)\) has clear zeroes at \(x=1\) and \(x=-7\), showing that \(f(x) > 0\) when \(x < -7\) and \(x > 1\). To determine where the vertex is, we can complete the square:

\(f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16\)

So, we can see the vertex is (-3,-16), meaning that where \(x > -3\), the function will be increasing on that interval

The linear function for the total cost C is:

A function is an expression, rule, or law that defines a relationship between one variable.

Example:

\(f(\text{x}) = 2\text{x} + 1\)

\(f(1) = 2 + 1 = 3\)

\(f(2) = 2 \times 2 + 1 = 4 + 1 = 5\)

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The total cost for x cubic yards.

\(\bold{C = 28 + 48x}\)

Thus, the function is C = 28 + 48x.

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Answer:

Triangles in Geometry

Step-by-step explanation:

Step-by-step explanation:

The expression you provided involves taking the square root of a negative number, which results in an imaginary number. In standard real number arithmetic, the square root of a negative number is undefined. However, in the realm of complex numbers, we can define a square root of negative numbers using the imaginary unit "i," where i is defined as the square root of -1.

Let's break down the expression step by step:

√(-25) / √9

The square root of -25 can be written as √(-1 * 25), which can further be simplified as √(-1) * √25.

√(-1) is equal to "i," and the square root of 25 is 5.

So, the expression becomes:

i * 5 / √9

The square root of 9 is 3.

Now, we can simplify further:

i * 5 / 3

Thus, the simplified expression is (5i) / 3, where "i" represents the imaginary unit.

Answer:

The solution to the equation x + 9 = 18 + -2x is x = 3.

Step-by-step explanation:

To solve this equation for x, you can first simplify both sides of the equation by combining like terms.

x + 9 = 18 + -2x

Add 2x to both sides:

x + 2x + 9 = 18

Combine like terms:

3x + 9 = 18

Subtract 9 from both sides:

3x = 9

Finally, divide both sides by 3 to solve for x:

x = 3

Therefore, the solution to the equation x + 9 = 18 + -2x is x = 3.

HOPE THIS HELPED:)))

Answer:

3

Step-by-step explanation:

replace the + with - signs

x+9=18−2x

add the 2x to both equations and x becomes a 1 since we dont know its value.

3x+9=18

then you got to subtract 9 by 18 and that equals to 9 then

3x=9 3 divided by 9 is 3 and when simplified

and the answer is 3

The upper bound of a 99% confidence interval is found as 57.07.

For the stated question-

Thus, upper confidence bound (UCB) is estimated as;

UCB = x + z(α/2)×s/√n

UCB = 36.5 + 2.576×33.88/√18

UCB = 36.5 + 20.57

UCB = 57.07

Thus, the upper bound of a 99% confidence interval is found as 57.07.

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Answer:

90% confidence interval for the population proportion, p? 9.1 ... We will ignore the negative and just use 1.645. ... large a sample is needed in order to be 95% confident and within 3% if ... c) 90% confidence, n=21 ... We cannot use z because we do not have the population standard deviation. ... Find the Margin of Error.

Answer:

6

Step-by-step explanation:

12/2=6

Answer:

$45

Step-by-step explanation:

$3 times 15 days = $45

Answer:

its 10 times

Step-by-step explanation:

its because the value of 1 in the ten place and multiply by 10 to get the 1 in the hundred place or the 1 in the hundred place divide by 10 to get 1 in the tens place

Answer:

Only Figure 1 and Figure 3 Are Similar.

Step-by-step explanation:

Figure 1 and Figure 3 are proportional by 1:4 while the Figure 2 is not proportional to any of them.

Answer:

\(\frac{115\pi }{6} \\or\\19.16666667\pi\)

Step-by-step explanation:

Arc length is \(2\pi r*\frac{o}{360}\)

r is 46 theta is 75

\(2(46)\pi *\frac{75}{360} \\92\pi *\frac{75}{360} \\\frac{6900\pi }{360} \\\frac{115\pi }{6} or 19.166666667\pi\)

Answer: B

Step-by-step explanation:

Good Luck!

Answer:

11

Step-by-step explanation:

Substituting the values of x, y, and z into the expression, we get:

2x² - y + 2(z-1) = 2(2)² - 3 + 2(4-1)

= 2(4) - 3 + 2(3)

= 8 - 3 + 6

= 11

Therefore, if x = 2, y = 3, and z = 4, then the value of the expression 2x² - y + 2(z-1) is 11.

Answer:

11

Step-by-step explanation:

if x = 2, y = 3, and z = 4.

2x²-y + 2(z-1)

Substituting the given values of x, y, and z, we get:

2x² - y + 2(z-1) = 2(2)² - 3 + 2(4-1)

= 2(4) - 3 + 2(3)

= 8 - 3 + 6

= 11

Therefore, the value of the expression when x = 2, y = 3, and z = 4 is 11.

BODMAS (Brackets, Order, Division, Multiplication, Addition, Subtraction) is used to determine the sequence of operations in a mathematical expression. It is used to avoid confusion and ensure that everyone obtains the same answer from a mathematical expression. The rule states that the operations inside the brackets must be done first, followed by orders, then division and multiplication (from left to right), and finally addition and subtraction (from left to right).

Answer: the distance between the points (-2, 5) and (-4, -5) is approximately 10.198 units.

Step-by-step explanation:

(-2, 5) and (-4,-5) are two points in the coordinate plane.

The first point (-2, 5) has an x-coordinate of -2 and a y-coordinate of 5. This point is 2 units to the left of the y-axis and 5 units above the x-axis.

The second point (-4, -5) has an x-coordinate of -4 and a y-coordinate of -5. This point is 4 units to the left of the y-axis and 5 units below the x-axis.

To find the distance between these two points, we can use the distance formula:

distance = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

Plugging in the coordinates of the two points, we get:

distance = sqrt[(-4 - (-2))^2 + (-5 - 5)^2] = sqrt[(-2)^2 + (-10)^2] = sqrt[104]

So the distance between the points (-2, 5) and (-4, -5) is approximately 10.198 units.

Functions can be used to model real life scenarios

The function is given as:

\(\mathbf{V(t) = -t^3 + t^2 + 12t}\)

(a) Sketch V(t)

See attachment for the graph of \(\mathbf{V(t) = -t^3 + t^2 + 12t}\)

(b) The reasonable domain

t represents the number of weeks.

This means that: t cannot be negative.

So, the reasonable domain is: \(\mathbf{[0,\infty)}\)

(c) Average rate of change from t = 0 to 2

This is calculated as:

\(\mathbf{m = \frac{V(a) - V(b)}{a - b}}\)

So, we have:

\(\mathbf{m = \frac{V(2) - V(0)}{2 - 0}}\)

\(\mathbf{m = \frac{V(2) - V(0)}{2}}\)

Calculate V(2) and V(0)

\(\mathbf{V(2) = (-2)^3 + (2)^2 + 12 \times 2 = 20}\)

\(\mathbf{V(0) = (0)^3 + (0)^2 + 12 \times 0 = 0}\)

So, we have:

\(\mathbf{m = \frac{20 - 0}{2}}\)

\(\mathbf{m = \frac{20}{2}}\)

\(\mathbf{m = 10}\)

Hence, the average rate of change from t = 0 to 2 is 20

(d) The instantaneous rate of change using limits

\(\mathbf{V(t) = -t^3 + t^2 + 12t}\)

The instantaneous rate of change is calculated as:

\(\mathbf{V'(t) = \lim_{h \to \infty} \frac{V(t + h) - V(t)}{h}}\)

So, we have:

\(\mathbf{V(t + h) = (-(t + h))^3 + (t + h)^2 + 12(t + h)}\)

\(\mathbf{V(t + h) = (-t - h)^3 + (t + h)^2 + 12(t + h)}\)

Expand

\(\mathbf{V(t + h) = (-t)^3 +3(-t)^2(-h) +3(-t)(-h)^2 + (-h)^3 + t^2 + 2th+ h^2 + 12t + 12h}\)\(\mathbf{V(t + h) = -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h}\)

Subtract V(t) from both sides

\(\mathbf{V(t + h) - V(t)= -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h - V(t)}\)

Substitute \(\mathbf{V(t) = -t^3 + t^2 + 12t}\)

\(\mathbf{V(t + h) - V(t)= -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h +t^3 - t^2 - 12t}\)

Cancel out common terms

\(\mathbf{V(t + h) - V(t)= -3t^2h -3th^2 - h^3 + 2th+ h^2 + 12h}\)

\(\mathbf{V'(t) = \lim_{h \to \infty} \frac{V(t + h) - V(t)}{h}}\) becomes

\(\mathbf{V'(t) = \lim_{h \to \infty} \frac{ -3t^2h -3th^2 - h^3 + 2th+ h^2 + 12h}{h}}\)

\(\mathbf{V'(t) = \lim_{h \to \infty} -3t^2 -3th - h^2 + 2t+ h + 12}\)

Limit h to 0

\(\mathbf{V'(t) = -3t^2 -3t\times 0 - 0^2 + 2t+ 0 + 12}\)

\(\mathbf{V'(t) = -3t^2 + 2t + 12}\)

(e) V(2) and V'(2)

Substitute 2 for t in V(t) and V'(t)

So, we have:

\(\mathbf{V(2) = (-2)^3 + (2)^2 + 12 \times 2 = 20}\)

\(\mathbf{V'(2) = -3 \times 2^2 + 2 \times 2 + 12 = 4}\)

Interpretation

V(2) means that, 20 people were infected after 2 weeks of the virus spread

V'(2) means that, the rate of infection of the virus after 2 weeks is 4 people per week

(f) Sketch the tangent line at (2,V(2))

See attachment for the tangent line

The slope of this line is:

\(\mathbf{m = \frac{V(2)}{2}}\)

\(\mathbf{m = \frac{20}{2}}\)

\(\mathbf{m = 10}\)

The slope of the tangent line is 10

(g) Estimate V(2.1)

The value of 2.1 is

\(\mathbf{V(2.1) = (-2.1)^3 + (2.1)^2 + 12 \times 2.1}\)

\(\mathbf{V(2.1) = 20.35}\)

(h) The maximum number of people infected at the same time

Using the graph, the maximum point on the graph is:

\(\mathbf{(t,V(t) = (2.361,20.745)}\)

This means that:

The maximum number of people infected at the same time is approximately 21.

The rate of infection at this point is:

\(\mathbf{m = \frac{V(t)}{t}}\)

\(\mathbf{m = \frac{20.745}{2.361}}\)

\(\mathbf{m = 8.79}\)

The rate of infection is 8.79 people per week

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answer is here about stem and leaf

The angles <1, <2, and <3 will not add up to 180 degrees. The angles <1 and <2 are alternate interior angles, and the angles <2 and <3 are also alternate interior angles, AB is parallel to CD.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is always equal to 180 degrees. This means that if you measure the angles inside any triangle and add them up, the result will always be 180 degrees. This property holds true for all types of triangles, whether they are equilateral, isosceles, or scalene.

To understand this property, consider a triangle ABC with interior angles angle A, angle B, and angle C. If we draw a line segment from vertex A to a point D on side BC such that it is parallel to the side AB, then we can see that angle A and angle C are alternate interior angles of the parallel lines AB and CD. Similarly, angle B and angle C are alternate interior angles of the parallel lines BC and AD.

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The least among all 4 integers such that they sum up to 100 will be 22.

An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.

Integer; ....-2 , -1 , 0 , 1 , 2 , .....

Integers are non-decimal numbers and all integers are rational numbers.

Suppose the first integer is x.

The next three digits will be, x + 2, x + 4, and x + 6 correspondings.

Sum x + x + 2 + x + 4 + x + 6 = 100

(x + x + x + x) + (2 + 4 + 6) = 100

4x + 12 = 100

4x = 88

x = 22

Hence"The smallest of the four integers that add up to 100 is 22".

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Answer:

5x-60=x - solution,..........

Answer:

Answer:

5x +60/x -15x +15/x-20

60/x+15/x-15x+5x-20

75/x-10x-20

is your answer

combined liked terms by adding and subtracting.

Answer: F

Step-by-step explanation:

Answer:

Independent variable is what you are testing in a experiment.

Dependent variable is what you're measuring in a experiment.

Step-by-step explanation:

An example would be testing how fast plants can grow after two weeks of giving each plant a different amount of water.

The independent variable would be the plants. You are testing to see how fast the plants can grow depending on the amount of water you give each plant in a matter of two weeks.

The dependent variable would be the amount of water you give each plant. You are giving each plant different amounts of water each day in a span of two weeks to see which one will grow faster.

Hope this helps.

Answer:

4,000 pounds

Step-by-step explanation:

2,000 pounds = 1 ton

4,000 pounds = 2 tons

Chow,...!

Answer:  $4,000

Step-by-step explanation:

If the total earnings were $40,000 and the base pay was $10,000, then the commission earned would be $40,000 - $10,000 = $30,000.

Since the commission rate is 40%, we can set up the equation:

40% x Total Sales = Commission Earned

We know that the commission earned is $30,000, and we also know that 15 cars were sold. Therefore, we can solve for the average price of each car:

40% x Total Sales = Commission Earned

40% x (15 x Price per Car) = $30,000

6 x Price per Car = $30,000

Price per Car = $5,000

However, this is just the average price per car. Since the commission is based on the total sales, we need to calculate the actual commission earned on each car:

Commission per Car = 40% x Price per Car

Commission per Car = 40% x $5,000

Commission per Car = $2,000

Therefore, the total earnings of $40,000 divided by the number of cars sold (15) gives the amount earned per car:

Amount earned per Car = Total Earnings / Number of Cars Sold

Amount earned per Car = $40,000 / 15

Amount earned per Car = $4,000

Answer:

3 1/6

Step-by-step explanation:

Answer:

3 1/6

Step-by-step explanation: