What is the x-coordinate of the image when M(4, −1) is reflected in y=3.

16 sample points (possible outcomes as to the classifications) exist.

What is the combination?

Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.

Here, we have

Given: An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices.

There are 4 possible classifications for the president (freshman, sophomore, junior, senior) and 4 for the vice president.

A total of (4)(4) = 16 sample points.

Hence, 16 sample points (possible outcomes as to the classifications) exist.

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Answer:

y = -1/3 x + 3

Step-by-step explanation:

To find the equation of the line that passes through the two points (-3,4) and (3,2) in slope-intercept form, we'll first find the slope of the line using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the two given points.

Plugging in the given points, we get:

m = (2 - 4) / (3 - (-3)) = -2 / 6 = -1/3

Next, we'll use the point-slope form of a line to find the equation of the line:

y - y1 = m(x - x1)

where (x1, y1) is one of the given points, and m is the slope of the line.

We'll use the first given point, (-3,4), so we have:

y - 4 = -1/3 (x - (-3))

Expanding the right side of the equation, we get:

y - 4 = -1/3 x + 1

Finally, we'll rearrange the equation to get it in slope-intercept form, which is:

y = -1/3 x + b

where b is the y-intercept. To find b, we'll plug in one of the given points and solve for b:

y = -1/3 x + b

4 = -1/3 * (-3) + b

4 = 1 + b

b = 4 - 1

b = 3

So the equation of the line in slope-intercept form is:

y = -1/3 x + 3

Answer: X^2+6.8^2=10.6^2

Step-by-step explanation:

The pythagorean theorem can be used to find the missing sides of triangles.

The formula is:

a^2+b^2=c^2, where c^2 is always the hypotenuse (the biggest and diagonal line) and a^2 and b^2 are the other side lengths

In this problem, plug in the values. So in this case, you have:

a^2+6.8^2=10.6^2

Hope this helps

Answer:

The small bamboo plant is 5.5 feet tall

Step-by-step explanation:

I  (1) = 16.5 ft, 3 times as tall as II

II (2) = ? ft

Let the first be x and the second be y, Than

x = 16.5 ft

x = 3y

y = x / 3

y = 16.5 / 3

y = 5.5 ft

The range is the set of all y-values used by the graph.

This graph's lowest y-value is 3 at the point (0,3).

The graph almost reaches as y-value of 12, but doesn't actually get there because of the closed circle at (-3,12).

The range is [3, 12) or { y | 3 ≤ y < 12}, depending on the notation needed.

A division problem that would lead to a division remainder of 400 is 2, 400 ÷ 500.

You need to find a division problem where the quotient would be such that there would be a remainder of 400.

In that case, the first thing to do is to ensure that the divisor is greater than 400. If it is less, then the remainder cannot be 400.

We can the pick the next hundred after 400 which would be 500. Then, we need to find a number that when divided by 500, would result in 400 as a remainder.

This can be 900, 1, 400, 1, 900, 2, 400 etcetera.

The trick is to ensure that the number is 400 more than a multiple of 500.

Picking 2, 400, the division is therefore:

= 2, 400 ÷ 500

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On solving the provided question, we can say that  x = central angle = 60 degrees, r = radius = 9 inches and L = 9.42

An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.

x = central angle = 60 degrees

r = radius = 9 inches

L = arc length

[tex]L = (x/360)*2*pi*r\\L = (60/360)*2*pi*9\\L = 3*pi\\L = 9.42477796076938\\L = 9.42[/tex]

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[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

The rate of the passenger's train is given as follows:

60 miles per hour.

Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:

v = d/t.

For the passenger train, the equation is given as follows:

v = 240/t.

vt = 240

t = 240/v.

For the freight train, the velocity is 20 miles slower than for the passenger train, hence:

v - 20 = 160/t

v = 160/t + 20.

Replacing the first equation into the second, the rate of the passenger train is obtained as follows:

v = 160v/240 + 20

v = 2v/3 + 20

v/3 = 20

v = 60 miles per hour.

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The tables with their equations are

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

Tables and equations

Table (a)

Here, we notice that:

The output is the reciprocal of the input

This is represented as

y = 1/x

Table (b)

Here, we notice that:

The output is the square root of the input

This is represented as

y = √x

Table (c)

Here, we notice that:

The output is the cube of the input

This is represented as

y = x³

Table (d)

Here, we notice that:

The output is the same as the input

This is represented as

y = x

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The sentence that uses the word "obstinancy" incorrectly is: if we eat out too often, its result in obstinancy and poor health. The Option C is correct.

Obstinancy is a noun that refers to the quality of being stubborn or resolutely unyielding. It describes a person's refusal to change their views, opinions, or actions, even in the face of compelling evidence or persuasive arguments. Example of its use: despite the pleas of his family, the man's obstinancy led him to continue his dangerous lifestyle.

We often use the word "obstinancy" for the followings:

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Answer:

Step-by-step explanation:

y=16. There are sixteen 1/2 in 8

PREMISES

y=8/.5

CALCULATIONS

y=8/.5

y=8(2)

y=

16

PROOF

If y=16, then the dependent value D(y) 8/.5 returns

y(.5)=8

Answer:

J.10

Step-by-step explanation:

You just have to add the numbers:

3 + 2 + (-4) + 3 + 7 + (-1) = 10

hope u like it, bye

The equation of the circle is (x-3)^2 + (y-4)^2 = 85.the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0 are     y = (-4/3)x + 11 and y = (-4/3)x + 9.

First, we find the center of the circle. Since the circle touches the line 3y-4x-24=0 at the point (0,8), the center must lie on the line perpendicular to this line and passing through (0,8), which has the equation 4y + 3x - 32 = 0. The intersection of this line with the line passing through (7,9) and perpendicular to the line 3y-4x-24=0 gives us the center of the circle:

Solving the equations 3y - 4x - 24 = 0 and 4y + 3x - 32 = 0 gives us the point (3,4), which is the center of the circle.

Now, we can find the radius of the circle by using the distance formula between the center (3,4) and the point (7,9):

r = √((7-3)^2 + (9-4)^2) = √(85)

So the equation of the circle is (x-3)^2 + (y-4)^2 = 85.

To prove that the circle also touches the x-axis, we need to show that the distance from the center (3,4) to the x-axis is equal to the radius. The equation of the x-axis is y=0, so the distance from (3,4) to the x-axis is simply 4. Since the radius is sqrt(85), which is also approximately equal to 9.22, we can see that 4 is indeed equal to the radius, so the circle touches the x-axis.

To find the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0, we first find the slope of this line, which is 3/4. The slope of a line perpendicular to this line is the negative reciprocal, which is -4/3.

To find the points of tangency, we need to find the intersection points of the line passing through (3,4) with slope -4/3 and the circle (x-3)^2 + (y-4)^2 = 85. This gives us two points of tangency: (0,7) and (6,1).

The tangent lines at these two points can be found using the point-slope form of the equation of a line, with the slope equal to the negative reciprocal of the slope of the line 3y-4x-24=0:

At (0,7), the tangent line has the equation y - 7 = (-4/3)(x-0), which simplifies to y = (-4/3)x + 7 + 4 = (-4/3)x + 11.

At (6,1), the tangent line has the equation y - 1 = (-4/3)(x-6), which simplifies to y = (-4/3)x + 9.

Therefore, the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0 are y = (-4/3)x + 11 and y = (-4/3)x + 9.

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The volume of a sphere is 1,436.03 cubic cm. Thus, the correct option is E.

Let r be the radius of the sphere. Then the volume of the sphere will be given as,

V = 4/3 πr³ cubic units

Sand is contained within a spherical with a 14 centimeters diameter. Roberto emptied the sphere's contents of sand.

The radius of the sphere is given as,

r = d/2

r = 14 / 2

r = 7 cm

Then the volume of the sphere is given as,

V = (4/3) x π x (7)³

V = 1.33 x 3.14 x 343

V = 1,436.03

The volume of a sphere is 1,436.03 cubic cm. Thus, the correct option is E.

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The correct options are given below.

A. 287.2 cm³

B. 861.6 cm³

C. 1,148.8 cm³

D. 9,190.6 cm³

E. 1,436.03 cm³

16.7, 6.7 and 22 degrees respectively are the measures of a, c and m<C

The given diagram is a triangle with the following sides

Hypotenuse = AC = 18

m<A = 68 Degrees

We need to determine the measure of a, b and m<C

Using the trigonometry identity

sin 68 = a/18

a = 18sin68

a = 16.7

Similarly;

cos68 = c/18

c = 18cos68

c = 6.7

Since the sum of angles in a triangle is 180 degrees, hence:

m<C = 90 - m<A

m<C = 90 - 68

m<C = 22 degrees

Hence the measure of a, c and m<C is 16.7, 6.7 and 22 degrees respectively.

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Answer:

  c. √2/30

  f. 13√3/14

  i. -11√10/24

Step-by-step explanation:

You want the sums of the fractions shown.

Two fractions can be added like this:

  [tex]\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}[/tex]

If the denominators have a common factor (k), then this can be reduced to ...

  [tex]\dfrac{a}{bk}+\dfrac{c}{dk}=\dfrac{ad+bc}{bdk}[/tex]

The product bdk is the least common denominator when k is the greatest common factor.

Here, the numerators have a common factor, so we can factor that out, perform the sum, then multiply the result by that numerator factor.

  [tex]\dfrac{\sqrt{2}}{5}-\dfrac{\sqrt{2}}{6}=\sqrt{2}\left(\dfrac{1}{5}-\dfrac{1}{6}\right)=\sqrt{2}\cdot\dfrac{6-5}{5\cdot6}=\boxed{\dfrac{\sqrt{2}}{30}}[/tex]

  [tex]\dfrac{3\sqrt{3}}{7}+\dfrac{\sqrt{3}}{2}=\sqrt{3}\left(\dfrac{3}{7}+\dfrac{1}{2}\right)=\sqrt{3}\cdot\dfrac{3\cdot2+7}{7\cdot2}=\boxed{\dfrac{13\sqrt{3}}{14}}[/tex]

The denominators have a common factor of 2: 6=3·2, 8=4·2.

  [tex]\dfrac{-5\sqrt{10}}{6}+\dfrac{3\sqrt{10}}{8}=\sqrt{10}\left(\dfrac{-5}{6}+\dfrac{3}{8}\right)=\sqrt{10}\cdot\dfrac{-5\cdot4+3\cdot3}{3\cdot4\cdot2}=\boxed{-\dfrac{11\sqrt{10}}{24}}[/tex]

Three possible rectangles of area 24 square inches are:

A rectangle with width 6 inches and length 4 inches

A rectangle with width 8 inches and length 3 inches

A rectangle with width 4 inches and length 6 inches

It should be noted that W and L are variables because their values can change, whereas A is a constant because it is fixed at 24 square inches. W and L can be any values as long as the product of their values is equal to 24.

In this case, W and L are variables and A is a constant.

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Answer:

The correct formula that expresses the statement "when x is equal to the square root of another number, s, plus the square root of two" is:

x = √s + √2

This formula says that x is equal to the square root of s plus the square root of 2.

Answer:

96 in²

Step-by-step explanation:

Length of Semiperimeter

[tex]\displaystyle s=\frac{1}{2}(a+b+c)=\frac{1}{2}(12+16+20)=\frac{1}{2}(48)=24[/tex]

Area of Triangle w/Heron's Formula

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{24(24-12)(24-16)(24-20)}=\sqrt{24(12)(8)(4)}=\sqrt{9216}=96[/tex]

Hence, the area of the triangle is 96 in².

Answer:

5x + 10y = 90

Step-by-step explanation:

x represents the mountain trail which she walked 5 miles

y represents the canal trail which she walked 10 miles

Answer: The x-axis is tangent to the curve when the value of y is equal to 0. So, to find the possible values of d when the x-axis is tangent to the curve, we need to solve the equation:

x^3/3 + 7x^2/2 + 10x + d = 0

To solve this equation, we need to use a method such as the cubic formula or a numerical method such as Newton-Raphson. However, it is not possible to determine a general solution for d without additional information, such as the value of x at which the tangency occurs. The possible values of d will depend on the specific value of x that satisfies the equation.

Step-by-step explanation:

Answer:

154.3° (to the nearest tenth)

Step-by-step explanation:

1 exterior angle=360/number of sides

360/14=25.714285

To get the one angle within the 14 sided polygon, take 1 exterior angle away from 180, as they are on a straight line

180-25.714285=154.285714

To the nearest tenth:

154.3°

The linear equation for the parallel line will be y=6x-3.

What exactly is a linear equation?

The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.

Now,

Line parallel to line y=6x-7 will have same slope which will be m=6

as general equation is y=mx+c where m=slope and c=constant.

For parallel line c will be as it is passing through (2,9)

9=6*2+c

c=9-12

c=-3

then the equation will be y=6x-3

Hence,

           The equation for the parallel line will be y=6x-3.

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The value of the variable is x = -6/9

A fraction is defined as the part of a whole number.

The different types of fractions are;

We are given the equation:

4/x = -18/3

To make 'x' the subject, cross multiply

-18x = 12

Now, divide both sides by the coefficient of x, we get;

x = 12/-18

x = -6/9

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Answer:

325 is a hundred times bigger than 32500

Step-by-step explanation:

if it is ten times bigger, add one 0 at the end

if it is one hundred times bigger, add two 0 at the end

The production possibility frontier based on the information is attached.

PPF0 is the curve before technological progress. PPF1 is the the curve after the advance in technology.

Before the advance in technology, the opportunity cost of treating HIV/AIDS increases as the world moves down along its PPF.

After the advance in technology, the opportunity cost of treating more HIV/ AIDS cases decreases as the world has to give up less other goods and services to treat additional HIV/AIDS patients. Or, by giving up the same amount of other goods and services, world can treat more HIV/AIDS patients now.

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Roman Rounds normally charges $18 for a large pizza.

What is the equation in one variable?

An equation in one variable is a mathematical statement that uses one variable and an equal sign to relate two expressions. The variable in the equation represents an unknown value, and the goal is often to find the value of the variable that makes the equation true.

Let's use p to represent the normal price of each large pizza charged by Roman Rounds.

Since the price of each pizza was reduced by $2 for the bulk order, the amount Mr. Mosley paid for 12 large pizzas is:

12(p - 2) = $192

We can simplify this equation by first distributing the 12 on the left side:

12p - 24 = $192

Then, we can isolate the variable p on one side of the equation by adding 24 to both sides:

12p = $216

Finally, we can solve for p by dividing both sides by 12:

p = $18

Therefore, Roman Rounds normally charges $18 for a large pizza.

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Answer:

Step-by-step explanation:

To determine the character of the solutions of the equation in the complex number system, we need to analyze the nature of the coefficients of the equation, specifically the discriminant, which is obtained by the equation: b^2 - 4ac, where a, b and c are the coefficients of the equation.

In this case, the equation is

3x^2 + 7x - 3 = 0

So, the coefficients are a = 3, b = 7, and c = -3.

We can now calculate the discriminant as follows:

b^2 - 4ac = 7^2 - 4 * 3 * -3 = 49 + 36 = 85

Since the discriminant is positive, we know that the equation has two distinct real solutions. The exact solutions can be obtained using the quadratic formula, but that's not required to determine the character of the solutions.

Therefore, the equation has two real solutions.