2. (01.01 LC)
Which of the following is a defined term? (6 points)
Angle
Line
Point
Plane

Check the picture below.

Answer:

2/6

Step-by-step explanation:

Count up and over going from one point to the next and you get slope intercept. This one is up 2 over 6

Answer:

y = 1/3x - 3

Step-by-step explanation:

Slope-intercept form follows the format y = mx + b, where m is the slope of the line, and b is the y-intercept.

First let's find the slope. The slope is the amount the graph rises/runs. From point (0,-3), it rises by 1, and runs to the right by 3 where it meets the next point on the graph, meaning that the slope is 1/3.

Now, let's find the y-intercept. The y-intercept is the point on the graph where the line touches the y-axis. In this line, we can clearly see that the line touches (0,-3), therefore, the y-intercept is -3.

Using this information, we can construct the equation y = 1/3x - 3

Answer:

21

Step-by-step explanation:

In the diagram, the three tangents (segment touching a circle at one point) have equal length.

6y - 3 = 29 - 2y

8y = 32

y = 4

Since the lengths of segments AM and AN are equivalent, we can substitute the value of y into the expression, 6y - 3, to find AN.

6y - 3 = 6*4 - 3 = 24 - 3 = 21

[tex]-2(-1+2w)[/tex]

distribute

[tex]2-4w[/tex]

put in standard form

[tex]-4w+2[/tex]

Answer:

  (0, -2)

Step-by-step explanation:

The solution to a system of equations is the point on the graph where the lines intersect.

Here, both lines have a y-intercept of -2, so intersect there. The solution is ...

  (x, y) = (0, -2)

Answer:

6/10

Step-by-step explanation:

3/6 = 0.5

6/10 = 0.6

0.6>0.5

Then

6/10 is greater than 3/6

Based on the number of songs in each genre that Josiah listened to, the statements about his solution that are true are:

To find the average of the number of rock songs, he should have taken the average of rock songs he listened to which were 4 and 6:

= (4 + 6) / 2

= 5

Because he has a total of 1,500 songs on his player, he should have multiplied both the numerator and denominator by a number that would lead to 1,500 which is 75 and not 30.

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Step-by-step explanation:

There is 31 days in May so the probability is

[tex]p(bday \: in \: may) = \frac{2}{31} [/tex]

Answer:

$6455.

Step-by-step explanation:

The formula for this investment is:

A = P(1 + r/4)^4t      where P = amount deposited ,  A amount after t years,

                                r = rate (as a decimal fraction).

So we have:

7160.06 = P(1 + 0.026/4)^16

7160.06 = P * 1.109227

P = 7160.06 / 1.109227

  =  $6455.

The values of the three trigonometric ratios for angle L, in simplest form, are:

Given -

The triangle LMN is given in the question.

As the trigonometric properties of a triangle state that the value of sin, cos, and tan for the respective angle can be written as:

Using the above trigonometric properties, the value of sin(L):

Similarly, the value of cos(L):

And, the value of tan(L) is:

Therefore, the values of the three trigonometric ratios for angle L, in simplest form, are:

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The question you are looking for is given below:

What are the values of the three trigonometric ratios for angle L, in simplest form?

Answer:

a polygon with an interior angle of 108 is a pentagon

Hi there,

please see below for solution steps :

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

⨠ use the distributive property

[tex]\sf{7x-3(x-6)=30}[/tex]

[tex]\sf{7x-3x+18=30}[/tex]

⨠ combine like terms

[tex]\sf{4x+18=30}[/tex]

⨠ subtract both sides by 18

[tex]\sf{4x=30-18}[/tex]

[tex]\sf{4x=12}[/tex]

⨠ divide both sides by 4

[tex]\boxed{\sf x=3}[/tex]

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

The test That holds true for this inequality is given as 1/4 and 1

3/2 y - 2x > 1

The goal is to make y the subject

then

3/2 y > 2x + 1

We have to divide through the equation by 3/2

Such that  y  > 4/3 x + 2/3

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Answer:

c if lsrt lstr name two congruent segments

Answer:

[tex]\boxed{\sf 1\dfrac{1}{6}\ liters \ of \ water}[/tex]

Explanation:

Let the total water required water the entire ground be g

Equation:

[tex]\sf \dfrac{2}{7}\:g = \dfrac{1}{3} \ liters \ of \ water[/tex]

rearranging

[tex]\sf g = \dfrac{7(1)}{3(2)}[/tex]

simplify

[tex]\sf g = \dfrac{7}{6} \ liters \ of \ water[/tex]

rewrite in mixed fraction

[tex]\bf g = 1\dfrac{1}{6}\ liters \ of \ water[/tex]

The water required to water the entire ground is  1 1/6 liters.

0.8926 percent of the time, the shipment will be rejected.

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

A delivery of 50 cheap digital watches, 10 of which are flawed.

A digital watch's likelihood of malfunctioning

P = 10/50

= 0.2

Size of sample: n = 10

Additionally, if they find one or more samples to be defective, they reject the entire cargo.

Making use of the binomial probability formula:

[tex]P(x)={ }^{n} C_{x} p^{x}(1-p)^{n-x}[/tex]

The random variable x should stand in for the quantity of defective watches.

The chance that the delivery will be refused is:

[tex]\begin{aligned}&P(x \geq 1)=1-P(0) \\&=1-{ }^{10} C_{0}(0.2)^{0}(0.8)^{10}\end{aligned}[/tex]

= 1 - (0.8)

= 0.8926

As a result, 0.8926 percent of the time, the shipment will be rejected.

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I understand that the question you are looking for is:

A shipment of 50 inexpensive digital​ watches, including 10 that are​ defective, is sent to a department store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective. What is the probability that the shipment will be​ rejected

Answer:

6x^4-5x^3-8x^2+3x

Step-by-step explanation:

-factor it using FOIL (first outside inside last)

Therefore the hour hand travels 40.192in in 5 hours

A sector is said to be a part of a circle made of the arc of the circle along with its two radii.

The formula for calculating the area of a sector is expressed as;

A = r²β/2

where

r is the radius of the circle

β is the angle subtended

Since the the hour hand travel during 5 hours, the subtended angle by the sector will be;

β = 360/5

β = 72 degrees

Given the following parameters

r = 16/2

r = 8in

Substitute into the formula

A = 8²(72π)/360
A = 40.192in

Therefore the hour hand travels 40.192in in 5 hours

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Answer:

320 pages.

Step-by-step explanation:

We can simply multiply and add to find how many pages are in the book.

So we have (13 pg * 20 d) + (6 pg * 10 d) = 260 + 60 = 320.

Another way of solving is to set up a proportion for both the 20 and 10 days, find how many pages are read on these days, and add:

[tex]\frac{13pg}{1d}=\frac{xpg}{20d}\\ x=260pages\\\\\frac{6pg}{1d} =\frac{xpg}{10d}\\ x=60pg\\260+60=320[/tex]

The length is 25 feet and the width is 135 feet

What are consecutive odd integers?

Consecutive odd integers differ by 2. If x is an odd integer, then x + 2, x + 4 and x + 6 are consecutive odd integers.

How to find the perimeter of the rectangle?

⇒Perimeter of rectangle = 2(l+w)

The perimeter of a rectangle is 320 feet

let the length of a rectangle is x

The next consecutive odd integer is x+2

width = 5(x+2)

=5x+10

2(length + width) = 320

l+w=160

x+5x+10=160

6x=150

x=25

length = 25 feet

width = 5(25+2)=135 feet

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Answer:

1 boy to 15 girls.

Step-by-step explanation:

Since there is only two boys, I divided each number by two and got 1 to 15. Have an amazing day!

The ratio of boys to all children in the group is 1:16.

Given that in a group there are 2 boys and 30 girls.

We need to find the ratio of boys to all children.

To find the ratio of boys to all children in the group, we need to add the number of boys and girls together to get the total number of children.

Then, we can express the number of boys as a fraction of the total number of children.

Number of boys = 2

Number of girls = 30

Total number of children = Number of boys + Number of girls

Total number of children = 2 + 30 = 32

Now, we can express the number of boys as a fraction of the total number of children:

Ratio of boys to all children = Number of boys / Total number of children

Ratio of boys to all children = 2 / 32

To simplify the ratio, we can divide both the numerator and denominator by their greatest common divisor, which is 2:

Ratio of boys to all children = 1 / 16

So, the ratio of boys to all children in the group is 1:16.

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First symmetrically cut the octagon to get 8 pieces. (So that you will get the idea that this polygon is divided into 8 triangles)

Then find the area of one of the triangles:

Area of Triangle = [tex]\frac{1}{2} * b* h[/tex]

A = [tex]\frac{1}{2}[/tex] × 12 × 19

A = 114 cm²

To find the area of the whole octagon shape:

A = 114 × 8 = 912 cm²

Hope it helps!

Answer:

Step-by-step explanation:

You cannot do this unless you are certain that P is the center of the octagon. I don't know if that's solvable from the information given. So I will make the assumption that P is the center.

Determine the midpoint of BC. Call it E.  Draw a line from P to E. By symmetry EP = AP. BE = 1/2 * BC = 19/2 = 9.5 by construction

You have a trapezoid witch is 1/4 the area of the octagon. Three more trapezoids can fit into the octagon.

Formula

Area = (AP + BE)*PE / 2

Givens

AP = 12

BE = 9.5

PE = 12

Solution

Put the givens and constructions into the formula

Area = (12 + 9.5)*12/2

Area = 21.5 * 12/2

Area = 21.5 * 6

Area = 129

That's the area of one of the trapezoids. Multiply the area here by 4.

You get 516.

Answer:

$50

Step-by-step explanation:

x is distance and y is cost because the cost is dependent on the distance which makes the distance the independent variable. you can always use y=mx+b for these problems!!

Answer:

I x² +12x I = -32

Step-by-step explanation:

Absolute value equation:

  x = -4  ; x = -8

x + 4 = 0  and     x + 8 = 0

(x +4)(x + 8) = 0

x*x + x*8 + 4*x + 4*8 = 0

     x² + 4x + 8x  + 32 = 0

         x² + 12x   + 32   = 0

Absolute value equation:

  I x² + 12x I = -32

Answer:

Identity property of addition 8 + 0 = 8

Identity property of multiplication 8 x 1 = 8

Step-by-step explanation:

He mixed up his properties.  8 + 1  does not equal 8.  I want to know what I can add to 8 and that I would still get 8, the answer is zero.

The identity property of multiplication is showing that any number multiplied by 1 is itself.

The complete question is:

Create a matrix for this linear system:

what is the solution of the system?

[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]

The solution straight from the matrix as

[tex]$&x=\frac{1}{5}+\frac{7}{5} r \\[/tex]

[tex]$&y=-\frac{4}{5}-\frac{3}{5} r \\[/tex]

and z = r

A solution to a system of equations exists a set of values for the variable that satisfy all the equations simultaneously.

Given:

[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]

By applying two more row operations, we get

[tex]$&{\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\2 & 3 & -1 & -2\end{array}\right] R_{2}+(-2) R_{1} \rightarrow R_{2}} \\[/tex]

[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 5 & 3 & -4\end{array}\right] \frac{1}{5} R_{2} \rightarrow R_{2} \\[/tex]

simplifying the above matrix, we get

[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right] R_{1}+R_{2} \rightarrow R_{1} \\[/tex]

[tex]$&\equiv\left[\begin{array}{rrr|r}1 & 0 & -\frac{7}{5} & \frac{1}{5} \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right]$$[/tex]

The solution straight from the matrix as

[tex]$&x=\frac{1}{5}+\frac{7}{5} r \\[/tex]

[tex]$&y=-\frac{4}{5}-\frac{3}{5} r \\[/tex] and

z = r

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Here is the five-number summary:

Minimum: 9

Lower quartile:   11

Median: 24

Upper quartile:  34

Maximum: 45

Interquartile range: 23

The minimum number is the smallest number in the dataset. The  minimum number is 9. The maximum number is the largest number in the dataset. The maximum number is 45.

The first quartile, third quartile and the interquartile range are used to measure dispersion.

The first quartile : 1/4(n + 1)

1/4 x (12) = 3rd term = 11

The third quartile : 3/4 x (n + 1)

3/4 x (12) = 9th term = 34

Interquartile range = third quartile - first quartile

34 - 11 = 23

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

Median = 25

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies \begin{array}{llll} y+4=4(x-3)\implies y-(\stackrel{y_1}{-4})=\stackrel{m}{4}(x-\stackrel{x_1}{3})\\\\ ~\hfill (\stackrel{x_1}{3}~~,~~\stackrel{y_1}{-4}) \end{array}[/tex]

The depth of the 84 inches wide satellite dish that has the receiver located 15 inches above the vertex is 29.4 inches.

The location of the receiver = 15 inches above the vertex

Width of the dish = 84 inches

The receiver of a satellite dish is normally located at the focus (focal point).

Taking the shape of the satellite dish as a parabola, and writing the equation of the parabola as x² = 4•a•y, we have;

Coordinates of the focus = (0, a)

Where;

a = The distance of the focus above the vertex

Therefore;

a = 15 inches

The dish is horizontally spaced equally about the vertex.

The farthest point horizontally from the vertex, X, of the dish corresponds to the furthest vertically from the vertex, which is the maximum depth or height, Y.

At the maximum height, from the vertex, Y, (farthest point, vertically from the vertex), we have;

X = 84 ÷ 2 = 42

Which gives;

42² = 4 × 15 × Y

Y = 42² ÷ (4 × 15) = 29.4

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