Two of the angles in a triangle measure 88° and 84°. What is the measure of the third angle?

Answer:

  0 < m < 4-√12 ≈ 0.535898

Step-by-step explanation:

You want to know the range of values of m that will give |(x-1)(x-3)| = mx four distinct solutions.

The quadratic function f(x) = (x -1)(x -3) will be negative for values of x between the zeros: 1 < x < 3. Hence the absolute value function will invert the graph in that interval, as shown by the red curve in the attachment.

The line y = mx can only intersect that graph in 4 places in the first quadrant. The value of m must be greater than 0 and less than 1.

The upper limit of the slope will be defined by the value of m that makes the line intersect the inverted quadratic exactly once. That is, the discriminant of mx -(-f(x)) = 0 will be zero.

  mx +(x -1)(x -3) = x² +(m -4)x +3 = 0

  D = (m -4)² -4(1)(3) = (m -4)² -12 = 0

Solving for m gives ...

  (m -4)² = 12

  m -4 = ±√12

  m = 4 ±√12 ≈ 0.54 or 7.46

We can see from the attached graph that m ≈ 7.46 is an extraneous solution. This means the range of m will be ...

  0 < m < 4-√12

For the given linear equations, x = 63/4 i.e. None of the above options.

What is a linear equation, exactly?

Each term in a linear equation is either a constant or the product of a constant and a single variable raised to the first power. A linear equation in one variable has the general form: axe + b = 0, where a and b are constants and x is the variable. This equation's answer is a single value of x that solves the problem.

Now,

To use Cramer's Rule to solve this system of linear equations, we need to set up the following matrices:

A = 2/5 1/4

2/3 5/12

B = 9/20

3/4

The determinant of A is given by:

|A| = (2/5)(5/12) - (1/4)(2/3) = 1/30 - 1/18 = -1/90

The determinant of the matrix obtained by replacing the first column of A with B is given by:

|A1| = (9/20)(5/12) - (3/4)(2/3) = 9/80 - 1/4 = -7/40

The determinant of the matrix obtained by replacing the second column of A with B is given by:

|A2| = (2/5)(3/4) - (1/4)(9/20) = 3/10 - 9/80 = 3/40

Now, we can use Cramer's Rule to find the value of x:

x = |A1|/|A| = (-7/40)/(-1/90) = 63/4

Therefore, the value of x

x = 63/4

So the answer is not any of the given options.

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Scott does 35 sit-ups altogether every night.

A ratio is a comparison of two quantities, expressed as the quotient of one quantity divided by the other. Ratios can be written in different forms, such as using a colon (:) or a fraction (/).

For every 2 straight-leg sit-ups, Scott does 3 bent-leg sit-ups. Therefore, the ratio of straight-leg sit-ups to bent-leg sit-ups is 2:3.

If Scott does 10 straight-leg sit-ups every night, we can use this ratio to find out how many bent-leg sit-ups he does.

First, we can write the ratio as a fraction:

2/5 = 10/x

where x is the number of bent-leg sit-ups Scott does.

To solve for x, we can cross-multiply:

2x = 50

x = 25

Therefore, Scott does 25 bent-leg sit-ups every night.

To find the total number of sit-ups Scott does every night, we can add the number of straight-leg sit-ups to the number of bent-leg sit-ups:

10 + 25 = 35

Therefore, Scott does 35 sit-ups altogether every night.

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The following points are 5 or more units apart: A and B, G and D, G and F, G and E, F and E, E and B, (4, 3 and (4, -2), (6, -2) and (0, -2), (3, -7) and (3, -1)

When two points on a graph are 5 or more units apart, it means that there is a significant difference in the values of the function at those points.

For example, if we have two vertical or horizontal points (x1, y1) and (x2, y2) on a graph such that |x1 - x2| ≥ 5, it means that the x-values of the two points are at least 5 units apart.

Similarly, if |y1 - y2| ≥ 5, it means that the y-values of the two points are at least 5 units apart.

Using the above as a guide, the following points are 5 or more units apart

A and B, G and D, G and F, G and E, F and E, E and B, (4, 3 and (4, -2), (6, -2) and (0, -2), (3, -7) and (3, -1)

We have

N = (6, 8)

The point that is 8 or more units apart from N could be

Point = (6, 8 + at least 8)

So, we have

Point = (6, 8 + 9)

Point = (6, 17)

Hence, the point is (6, 17)

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Answer:

1 2 3 6 9 and 18

Step-by-step explanation:

the 111 factors of 18 is 1 2 3 6 9 ang 18

Yes, The function with a frequency of 2 has a greater period than a function with a frequency of 1/2.

What does the word" function" signify in calculation?

As a set of inputs with one for each, a function is defined as a relationship between them. A function, expressed simply, is an association between inputs where each input is connected to one and only one affair. A sphere, codomain, or range exists for every function. generally, f( x), where x is the input, is used to represent a function.

frequency of f(x) = 1/period of f(X)

              2 = 1/[tex]T_{f}[/tex]

             [tex]T_{g}[/tex] = 1/2

 frequency of g(X) = 1/period of g(X)

                   1/2 = 1/[tex]T_{g}[/tex]

                     [tex]T_{f}[/tex] = 2

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Note that the sum of all the regions equals the size of the universal set U, as it should be:

5 + 12 + 4 + 24 + 19 + 9 + 5 + 6 = 70.

To fill in the Venn diagram, we start with the given information:

n(A) = 33

n(B) = 36

n (B ∩ C) = 14

n (A ∩ C) = 9

n (A ∩ B ∩ C) = 5

n(U) = 70

n(C) = 24

n (A ∩ B) = 17

We can use the formula for the size of a set union to find n (B ∪ C):

n (B ∪ C) = n(B) + n(C) - n (B ∩ C)

n (B ∪ C) = 36 + 24 - 14

n (B ∪ C) = 46

We can also use the formula for the size of a set intersection to find n(A ∩ B):

n (A ∩ B) = n(A) + n(B) - n (A ∪ B)

n (A ∪ B) = n(A) + n(B) - n (A ∩ B)

n (A ∪ B) = 33 + 36 - 17

n (A ∪ B) = 52

n (A ∩ B) = 33 + 36 - 52

n (A ∩ B) = 17

Now we can start filling in the Venn diagram:

I = A ∩ B ∩ C = 5

II = A ∩ B - C = 12 (since n(A ∩ B) = 17 and n(A ∩ B ∩ C) = 5)

III = A ∩ C - B = 4 (since n(A ∩ C) = 9 and n(A ∩ B ∩ C) = 5)

IV = A - B - C = 24 (since n(A) = 33 and n(A ∩ B) = 17 and n(A ∩ C) = 9 and n (A ∩ B ∩ C) = 5)

V = B - A - C = 19 (since n(B) = 36 and n(A ∩ B) = 17 and n(B ∩ C) = 14 and n (A ∩ B ∩ C) = 5)

VI = B ∩ C - A = 9 (since n(B ∩ C) = 14 and n(A ∩ B ∩ C) = 5)

VII = C - A - B = 5 (since n(C) = 24 and n(A ∩ C) = 9 and n(B ∩ C) = 14 and n (A ∩ B ∩ C) = 5)

VIII = U - (A ∪ B ∪ C) = 6 (since n(U) = 70 and n(A) = 33 and n(B) = 36 and n(C) = 24)

Therefore, the completed Venn diagram would have:

I = 5

II = 12

III = 4

IV = 24

V = 19

VI = 9

VII = 5

VIII = 6

Note that the sum of all the regions equals the size of the universal set U, as it should be:

5 + 12 + 4 + 24 + 19 + 9 + 5 + 6 = 70

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The tiles to the correct boxes to complete the pairs-

A: [tex](-3^{-2} )^{0}[/tex] = 1; B: [tex]3^{3}.3^{1}. 3^{2} .3^{-12}[/tex] [tex]= 1/729[/tex]  C: [tex]-3^{5} / -3^{8}[/tex] = -1/27 ; D: [tex]-3^{-3}. 3^{-3}[/tex] = - 1/729.

We can determine how many times a phrase has been multiplied by itself using an index, which is a tiny number.

Indexes is the plural of index.

Remember that a power is the result of a particular number of identical factors? For instance, the number [tex]3^{7}[/tex] is a power, where the base is the number 3, and the index or exponent is the number 7.

Given number with exponents :

A: [tex](-3^{-2} )^{0}[/tex]

[tex]= (-3^{0} )\\= 1[/tex]

B: [tex]3^{3}.3^{1}. 3^{2} .3^{-12}[/tex]

[tex]= 3^{3 + 1 + 2 -12}[/tex]

[tex]= 3^{-6}\\= 1/729[/tex]

C: [tex]-3^{5} / -3^{8}[/tex]

[tex]= -3^{5-8}\\= - 3^{-3}\\\= -1/27[/tex]

D: [tex]-3^{-3}. 3^{-3}[/tex]

[tex]= -3^{-3 - 3}\\= -3^{-6}\\\\= -1/729[/tex]

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Answer:

Step-by-step explanation:

Answer:

155 Units

Step-by-step explanation:

Rate of Bug (given) = 11 units PER MINUTE

It never changed direction, so it was going in positive direction (assume).

In 7:15 pm (evening), it was at Point 100,

We want the point at which it was at 7:20 pm.

7:20pm - 7:15pm = 5 minutes

So, time passed 5 minutes. It's rate is 11 units PER MINUTE, so in 5 mins:

11 * 5 = 55 units

Assuming he is going in positive direction, the bug will be at:

100 + 55 = 155 Units

The best type of graph to display the results of this survey would be a histogram. A histogram is a graph that uses bars to represent the frequency distribution of a set of data. In this case, the shoe sizes would be grouped into intervals (e.g., 1-3, 4-6, 7-9, etc.) and the height of each bar would represent the number of students who have shoe sizes within that interval. A histogram is an effective way to show the overall pattern of the distribution of shoe sizes in the class.

A circle graph, also known as a pie chart, is useful for showing parts of a whole. It may not be the best choice for this survey since it does not show the distribution of shoe sizes as effectively as a histogram would.

A line plot, also known as a dot plot, is useful for showing the frequency of individual values in a small data set. It may not be the best choice for this survey since it may not be practical to list every individual shoe size.

A box plot, also known as a box-and-whisker plot, is useful for showing the distribution of a large data set. It may not be the best choice for this survey since the data set is likely to be small, and a histogram would be more appropriate for displaying the results.

For the given circle the circumference is 34.54.

What is circumference?

Circumference is the distance around the edge of a circle or any curved, circular object. It can be thought of as the perimeter of a circle.

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle.

Substituting the given value of the diameter, we get:

C = π(11)

Using π = 3.14, we can evaluate the expression:

C = 3.14(11)

C = 34.54

Therefore, the circumference of the circle is 34.54 (rounded to two decimal places).

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The product of the binomials (x-9) and (x+2) is x² - 7x - 18.

To find the product of the binomials (x-9) and (x+2), we can use the FOIL method, which stands for First, Outer, Inner, Last.

First: Multiply the first terms of each binomial: xx = x²

Outer: Multiply the outer terms of each binomial: x × 2 = 2x

Inner: Multiply the inner terms of each binomial: -9 × x = -9x

Last: Multiply the last terms of each binomial: -9 × 2 = -18

Now we can add up these four products to get the final answer:

x² + 2x - 9x - 18

Simplifying this expression, we get:

x² - 7x - 18

Therefore, the product of the binomials (x-9) and (x+2) is x² - 7x - 18.

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The grand canyon is 1600 meters deep at its deepest point. a rock is dropped from the rim above this point. express the height of the rock as a function of the time t in seconds. It will take approximately 18.05 seconds for the rock to hit the canyon floor.

The height of a rock dropped from the rim of the Grand Canyon can be expressed as a function of time, t, in seconds. To do this, we will use the free-fall equation, which states that the height of an object in free fall is given by:

a(t) = -1/2 * g * t^2 + h

where:
- a(t) is the height of the rock at time t,
- g is the acceleration due to gravity (approximately 9.81 meters per second squared),
- t is the time in seconds, and
- h is the initial height of the rock (1600 meters, in this case).

For the rock dropped from the rim of the Grand Canyon, the function becomes:

a(t) = -1/2 * 9.81 * t^2 + 1600

To find how long it will take the rock to hit the canyon floor, we need to find the value of t when the height, a(t), is equal to 0 (i.e., the rock reaches the floor).

0 = -1/2 * 9.81 * t^2 + 1600

Now, we'll solve for t:

1/2 * 9.81 * t^2 = 1600
t^2 = (1600 * 2) / 9.81
t^2 ≈ 325.99
t ≈ √325.99
t ≈ 18.05 seconds

Therefore, it will take approximately 18.05 seconds for the rock to hit the canyon floor.

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The angle of elevation of the ramp to the nearest degree is 34°.

we can use trigonometry to determine the angle of elevation of the ramp.To begin, we need to draw a diagram to visualize the problem.

Let's assume that the height of the end of the ramp is h, and the horizontal distance from the bottom of the ramp to the building is d.

From the diagram, we can see that we have a right-angled triangle where the height of the triangle is h, the base of the triangle is d, and the hypotenuse of the triangle is the length of the ramp.

Using the tangent ratio, we can write:

tanθ = opposite/adjacent

where opposite is the height of the triangle, and adjacent is the base of the triangle. Substituting the values we have, we get:

tanθ = h/d

Rearranging this formula, we can write:

θ = tan⁻¹(h/d)

Substituting the values we have, we get:θ = tan⁻¹(10/15)θ = 33.69°

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Answer:

A

Step-by-step explanation:

r=d/2

=6/2 =3

2πr

2×3.14×3

=18.84

Using the equation and cross-multiplication method, we know that the perimeter of the triangle IJK is 180.4 units.

A triangle is a polygon with three edges and three vertices.

It belongs to the basic geometric shapes.

A triangle having vertices A, B, and C is known as triangle ABC.

Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.

The closed, two-dimensional shape known as a triangle has three sides, three angles, and three vertices.

A triangle is part of a polygon.

So, we know that:

We must ascertain the value of x in order to determine the triangle's perimeter, IJK.

Using the ratio of comparable triangles and the triangles above, we have:

HF/KI = FG/IJ

Where,

HF = 35, KI = 77, FG = 27 and IJ = x

By changing the values, we obtain:

35/77 = 27/x

Take the cross product of the aforementioned equation, and we have:

35x = 27*77

x = 27*77/35 = 27 * 11/5 = 59.4

The triangle's perimeter is thus equal to the sum of its sides:

△IJK = 44 + 77 + 59.4 = 180.4

Therefore, using the equation and cross-multiplication method, we know that the perimeter of the triangle IJK is 180.4 units.

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Correct question:

Watch the help video on the perimeter of AIJK. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.

Answer:  24:1

Step-by-step explanation:

In the first step, you have to acknowledge how many of each tree there are in the question asked.

There is one cherry tree and 24 orange trees.

So the ratio of orange trees to cherry trees would be 24:1

Answer: 32

Step-by-step explanation:

Multiply by reciprocal. -> y >or= 32

32=32

24<32

16<32

8<32

Answer:

formula for area of a circle = πr²

πr² = 92cm² first circle

πr² = 62cm² second circle

now to find the radius of a circle having the sum of the other circle.

πr² = 92 + 62

3.142 × r² = 154

r² = 154/3.142

r² = 49.013

take square root of both sides

r = √49.013

r = 7.000cm ≈ 7cm

The final expression is 9c + 2.

What is an equation?

In mathematics, an equation asserts the equality of two expressions, usually separated by an equal sign (=). An equation is formed when two expressions are set equal to each other. The expressions can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

To simplify the expressions:

5c + 4c + 2 = 9c + 2

In this expression, we can add the coefficients of the like terms 5c and 4c to get 9c. Then we simply combine the constant term 2.

5c + 2[2c + 1] = 5c + 4c + 2

In this expression, we can distribute the 2 outside the brackets to get:

5c + 2(2c) + 2(1) = 5c + 4c + 2

Then, as in the previous expression, we can combine the like terms 5c and 4c to get 9c and simplify to get:

9c + 2

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An exponential function y = abx for a graph that passes through (2, 1) and (3, 4) is [tex]y = (1/16)(4)^x[/tex].

To write an exponential function in the form[tex]y = ab^x[/tex] that passes through the points (2, 1) and (3, 4), follow these steps:
Step 1: Write the general form of the exponential function:
[tex]y = ab^x[/tex]
Step 2: Plug in the coordinates of the first point (2, 1):
[tex]1 = ab^2[/tex]
Step 3: Plug in the coordinates of the second point (3, 4):
[tex]4 = ab^3[/tex]
Step 4: Solve for "a" and "b" using the equations from Steps 2 and 3.
We have two equations:
1)[tex]1 = ab^2[/tex]
2) [tex]4 = ab^3[/tex]
Divide equation 2 by equation 1 to eliminate "a":
[tex](4/1) = (ab^3)/(ab^2)[/tex]
4 = b.

Now that we have found "b," we can find "a" by plugging "b" back into either equation 1 or 2.

We'll use equation 1:
[tex]1 = a(4)^21 = a(16)[/tex]
a = 1/16
Step 5: Write the final exponential function using the values of "a" and "b":
[tex]y = (1/16)(4)^x[/tex].

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The patient is recieving nearly 35.5 miligrams of the drugs for  per kilogram per 24 hours.

First, we need to convert the child's weight from pounds to kilograms:

99 lbs / 2.205 = 44.9 kg

Next, we calculate the recommended dose for this weight:

40 mg/kg/24h x 44.9 kg = 1796 mg/24h

Since the recommended dose is divided into four equal doses, each dose should be:

1796 mg/24h ÷ 4 doses = 449 mg/dose

However, the physician ordered 400 mg every 6 hours, which is not the same as 449 mg every 6 hours. To calculate the actual dose per kilogram per 24 hours, we need to convert the ordered dose to the recommended dose:

400 mg/dose x 4 doses = 1600 mg/24h

Then, we divide the actual dose by the child's weight in kilograms:

1600 mg/24h ÷ 44.9 kg = 35.6 mg/kg/24h

Therefore, the patient is receiving 35.6 mg/kg/24h, which is slightly lower than the recommended dose of 40 mg/kg/24h.

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Answer:

There are 46 numbers in this sequence.

Answer:

AD = 9

Step-by-step explanation:

B is the midpoint of AC and BC = 2 so AC = 4.

BD is given as 7 so all we need to do is add up the given values:

AC + BD - BC = AD

4 + 7 - 2 = 9

The vector FC is (14, 0, 3/2, -7, -8, 6).

If you are given two vectors FC and F and C, with F represented as F(-2, 0, 0, 8, 2, 1) and C represented as C(12, 0, 3/2,

1, -6, 7), you can find the vector FC by subtracting the F vector from the C vector component-wise.

Step 1: Write down the F and C vectors.

F = (-2, 0, 0, 8, 2, 1)

C = (12, 0, 3/2, 1, -6, 7)

Step 2: Subtract the F vector from the C vector component-wise.

FC = C - F

FC = (12 - (-2), 0 - 0, 3/2 - 0, 1 - 8, -6 - 2, 7 - 1)

Step 3: Simplify the subtraction.

FC = (14, 0, 3/2, -7, -8, 6)

So, the vector FC is (14, 0, 3/2, -7, -8, 6).

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Shama needs to buy 10 plants for her garden.

From the graph, we have

Area = 8 * 5 = 40

To determine how many plants Shama needs to buy, we need to use the given rule that she buys 1 plant for every 4 square feet of the garden.

Therefore, we can divide the total area of the garden by 4 to find how many plants she needs to buy:

Number of plants = Area of garden ÷ 4

Substituting the given values, we get:

Number of plants = 40 ÷ 4

Number of plants = 10

Therefore, Shama needs to buy 10 plants for her garden.

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The cell that contributed most to the final result was Cell (1,2) with a contribution of 8.44.

we need to calculate the expected frequencies for each cell in the contingency table. We can use the formula:

Expected frequency = (row total x column total) / grand total

The grand total for the table is 80, so we can calculate the expected frequencies for each cell as follows:

Expected frequency of Cell (1,1) = (44 x 42) / 80 = 23.1

Expected frequency of Cell (1,2) = (44 x 38) / 80 = 20.9

Expected frequency of Cell (2,1) = (36 x 42) / 80 = 18.9

Expected frequency of Cell (2,2) = (36 x 38) / 80 = 17.1

Next, we need to calculate the contribution of each cell to the chi-square statistic. We can do this by subtracting the expected frequency from the observed frequency, squaring the result, and then dividing by the expected frequency.

The contributions of each cell to the chi-square statistic are as follows:

Contribution of Cell (1,1) = (37 - 23.1)2 / 23.1 = 8.30

Contribution of Cell (1,2) = (7 - 20.9)2 / 20.9 = 8.44

Contribution of Cell (2,1) = (9 - 18.9)2 / 18.9 = 4.52

Contribution of Cell (2,2) = (27 - 17.1)2 / 17.1 = 6.04

Finally, we can sum up the contributions of all the cells to get the chi-square statistic:

Chi-square statistic = 8.30 + 8.44 + 4.52 + 6.04 = 27.30

The cell that contributed most to the final result was Cell (1,2) with a contribution of 8.44. This cell had an observed frequency of 7, which was much lower than the expected frequency of 20.9. This indicates that there is a significant association between the two variables in this cell, and it is driving the overall result of the test.

In conclusion, by breaking down the chi-square statistic into its individual components, we can identify the cells that contribute most to the result and gain a deeper understanding of the relationship between the variables.

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The  probability that the person selects 2 coffees with artificial sweetener is 33/95.

Let A be the event that the first cup of coffee has artificial sweetener, and B be the event that the second cup of coffee also has artificial sweetener.

We want to find the probability of the intersection of A and B, i.e., the probability that both cups have artificial sweetener. We can use the formula for conditional probability:

P(A and B) = P(B|A) * P(A)

where P(B|A) is the probability of B given that A has occurred, and P(A) is the probability of A.

The probability of selecting a cup of coffee with artificial sweetener on the first draw is:

P(A) = 12/20

After the first cup has been drawn, there are now 11 cups with artificial sweetener left in the order, out of a total of 19 cups (since one cup has already been drawn). Therefore, the probability of selecting another cup with artificial sweetener on the second draw, given that the first cup had artificial sweetener, is:

P(B|A) = 11/19

So the probability of selecting two cups with artificial sweetener is:

P(A and B) = P(B|A) * P(A) = (11/19) * (12/20) = 33/95

Therefore, the probability that the person selects 2 coffees with artificial sweetener is 33/95.

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