What term can contain parallel lines

Answer:

Nine triangles

Step-by-step explanation:

Refer to image for diagram~

1. Draw a regular nonagon.

Since we are drawing a regular nonagon, all the sides of the nonagon must be equal and in proper place.

Refer to image 1 for diagram

2. Join all the vertices of a regular nonagon to its center.

Take any corner and draw a line from it to the center of the nonagon. This should also be done to the other vertices.

Refer to image 2 for diagram

3. Count the number of triangles formed by the lines.

When we look at the image, we can tell that nine triangles are formed when the vertices of a regular nonagon are joined to its center.

Refer to image 3 for diagram

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SOLUTION

We want to select the reason why the triangles in the image are similar.

We can see that both triangles have two congruent sides, that is 3 and 1, and 2.25 and 0.75. They also have a common angle as shown below.

So, we can see two sides that are congruent and a common angle.

Hence the answer is side-angle-side theorem SAS, option B

Answer:

n+30/5

Step-by-step explanation:

Simplify n/5

n/5+6

Rewrite the whole as an equivalent fraction

2.1 Add an integer to a fraction

Rewrite the whole as a fraction using 5 as the denominator: 6= 6/1=6×5/5

Equivalent fraction: the fraction thus generated looks different but has the same value as everything.

2.2 sum of the two equivalent fractions add two equivalent fractions that now have a common denominator

Combine the numerators, place the sum or difference over the common denominator, and then reduce to the lowest terms of possible:

n+6×5/5=n+30/5

Answer:

a) 7085g

b) 6346g

c) 5342g

Step-by-step explanation:

1kg = 1000g

If the confidence level is decreased, the width of the confidence interval will become narrower.

If the confidence level is decreased, the multiplier will decrease and the interval will become narrower.

If each of the following is decreased but everything else remains the same, the confidence interval will become narrower.

This is because a confidence interval is a range of values that is likely to contain the true population value with a specified level of confidence.

If the sample statistic is decreased, the width of the confidence interval will become narrower.

For confidence intervals for population means, the sample statistic is part of what determines the width of a confidence interval.

The standard error is another factor that determines the width of a confidence interval.

If the standard error is decreased, the width of the confidence interval will become narrower.

For confidence intervals for population means, the standard error is part of what determines the width of a confidence interval.

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Answer:

16.26°

Step-by-step explanation:

1. tanΘ= 7/24

2.\(tan^-1(\frac{7}{24} ) =\)Θ

3. Θ = 16.26°

To ensure the best test results, Anita should be provided with the following information before her spirometry:

1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.

2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.

3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.

4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.

The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.

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Substituting these values back into equation (i), we get D = 4(3) = 12. There are 3 nickels, 12 dimes, and 3 quarters in the collection.

Let's assume the number of nickels is N, the number of dimes is D, and the number of quarters is Q. From the given information, we can deduce three equations:

(i) D = 4N (since there are 4 times more dimes than nickels),

(ii) N + D + Q = 18 (since there are 18 coins in total), and

(iii) 5N + 10D + 25Q = 290 (since the total value of the coins is 290 cents or $2.90).

To solve these equations, we can substitute the value of D from equation (i) into equations (ii) and (iii).

Substituting D = 4N into equation (ii), we get N + 4N + Q = 18, which simplifies to 5N + Q = 18.

Substituting D = 4N into equation (iii), we get 5N + 10(4N) + 25Q = 290, which simplifies to 45N + 25Q = 290.

Now we have a system of two equations with two variables (N and Q). By solving these equations simultaneously, we find N = 3 and Q = 3.

Substituting these values back into equation (i), we get D = 4(3) = 12.

Therefore, there are 3 nickels, 12 dimes, and 3 quarters in the collection.

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Step-by-step explanation:

\(\dfrac{5}{8}+\dfrac{7}{8}=\dfrac{5+7}{8}=\dfrac{12}{8}=\dfrac{12:4}{8:4}=\dfrac{3}{2}=\dfrac{2+1}{2}=\dfrac{2}{2}+\dfrac{1}{2}=1\dfrac{1}{2}\)

Answer:

 \(1\frac{1}{2}\)

Step-by-step explanation:

5/8+7/8

--> 12/8

simplify :

--> 3/2

--> \(1\frac{1}{2}\) or 1.5

Answer:

df= 6g-10

Step-by-step explanation:

\(\frac{df+10}{6}\)= g

df+10= 6g

df= 6g-10

Answer:

D.11 in

Step-by-step explanation:

isosceles triangles have two congruent sides

The missing side length is congruent with the longer side ( this is pretty obvious )

If the longer side has a length of 11in and the missing side is congruent to the longer side then the missing side length equals 11 in

The volume of the triangular prism as described is; 20 cubic foot.

A triangular pyramid refers to pyramid which has a triangular base

It follows from the formula for calculating the volume of a triangular prism that;

Volume = (1/3) × base area × height.

Consequently,

volume of the prism = (1/3) ×5 × 12

Volume = 20 cubic foot

Therefore, volume of the triangular prism as described is; 20 cubic foot.

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Answer:

This is gebber gabber but yes

Step-by-step explanation:

9A:

The problem says 35% of the 3560 applications are from boys who lived in other states.

This can be expressed as:

3560*35% = 3560*0.35 = 1246 applications.

9B:

The problem says applications to the university (3560 applications) represented 40% of all applications.

This can be expressed as:

3560 = 40% * A, where A = number of applications received in all.

To find how many applications received in all, just solve for A.

A = 3560 / 0.4 = 8900 applications.

The key to these types of problems is that "of" signals multiplication. For example, 40% of all applications is 40% * all applications.

Answer:

392 miles

Step-by-step explanation:

318.5/6.5 = 49 miles per hour

49 miles per hour x 8 hours = 392 miles

1. Given matrices A and B, we can perform the specified operations to find the results: a. 2A + 3B:
2A = 2 * [
2
4
​

−3
7
​
] = [
4
8
​

−6
14
​
]

3B = 3 * [
3
5
​

−4
1
​
] = [
9
15
​

−12
3
​
]

Adding these two matrices element-wise, we get:
2A + 3B = [
4 + 9
8 + 15
​

−6 + (-12)
14 + 3
​
] = [
13
23
​

-18
17
​
]

b. 3A - 2B:
3A = 3 * [
2
4
​

−3
7
​
] = [
6
12
​

−9
21
​
]

2B = 2 * [
3
5
​

−4
1
​
] = [
6
10
​

−8
2
​
]

Subtracting the second matrix from the first matrix element-wise, we have:
3A - 2B = [
6 - 6
12 - 10
​

-9 + 8
21 - 2
​
] = [
0
2
​

-1
19
​
]

c. AB:
A = [
2
4
​

−3
7
​
]

B = [
3
5
​

−4
1
​
]

Multiplying these two matrices, we get:
AB = [
(2 * 3) + (4 * -4)
(2 * 5) + (4 * 1)
​

(-3 * 3) + (7 * -4)
(-3 * 5) + (7 * 1)
​
] = [
-10
14
​

-33
-8
​
]

d. BA:
B = [
3
5
​

−4
1
​
]

A = [
2
4
​

−3
7
​
]

Multiplying these two matrices, we obtain:
BA = [
(3 * 2) + (5 * -3)
(3 * 4) + (5 * 7)
​

(-4 * 2) + (1 * -3)
(-4 * 4) + (1 * 7)
​
] = [
-7
43
​

-11
-9
​
]

2. To verify the given properties:

a. A(BC) = (AB)C:
We have matrices A, B, and C given as:
A = [
2
4
​

−3
7
​
]

B = [
3
5
​

−4
1
​
]

C = [
0
3
​

2
−1
​
]

Calculating A(BC) on the left side:
BC = [
3
5
​

−4
1
​
] * [
0
3
​

2
−1
​
] = [
6
-4
​

-8
-7
​
]

A(BC) = [
2
4
​

−3
7
​
] * [
6
-4
​

-8
-7
​
] = [
12 - 32
24 - 28
​

-18 + 42
36 + 49
​
] = [
-20
-4
​

24
85
​
]

Calculating (AB)C on the right side:
AB = [
2
4
​

−3
7
​
] * [
3
5
​

−4
1
​
] = [
-10
14
​

-33
-8
​
]

(AB)C = [
-10
14
​

-33
-8
​
] * [
0
3
​

2
−1
​
] = [
0 - 6
0 + 14
​

0 + 66
0 - 8
​
] = [
-6
14
​

66
-8
​
]

Since A(BC) = (AB)C, the property is verified.

b. A(B + C) = AB + AC:
Using the given matrices A, B, and C:
A = [
2
4
​

−3
7
​
]

B = [
3
5
​

−4
1
​
]

C = [
0
3
​

2
−1
​
]

Calculating B + C on the left side:
B + C = [
3
5
​

−4
1
​
] + [
0
3
​

2
−1
​
] = [
3 + 0
5 + 3
​

-4 + 2
1 - 1
​
] = [
3
8
​

-2
0
​
]

A(B + C) = [
2
4
​

−3
7
​
] * [
3
8
​

-2
0
​
] = [
(2 * 3) + (4 * -2)
(2 * 8) + (4 * 0)
​

(-3 * 3) + (7 * -2)
(-3 * 8) + (7 * 0)
​
] = [
-2
16
​

-15
-24
​
]

Calculating AB + AC on the right side:
AB = [
2
4
​

−3
7
​
] * [
3
5
​

−4
1
​
] = [
-10
14
​

-33
-8
​
]

AC = [
2
4
​

−3
7
​
] * [
0
3
​

2
−1
​
] = [
6
-5
​

-6
17
​
]

AB + AC = [
-10
14
​

-33
-8
​
] + [
6
-5
​

-6
17
​
] = [
-4
9
​

-39
9
​
]

Since A(B + C) = AB + AC, the property is verified.

Therefore, both properties (a) and (b) have been verified.

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When the sum of their squares is as largest as possible the numbers are 0 and 20, when the sum of their squares is as small as possible, the numbers are 10 and 10

Sum of the two numbers = 20

First we have to find the sum of their squares is as large as possible

Consider the first number as x and second number as y

To get the largest values the value of x or the value of y should be zero

Then the two numbers are 0 and 20

To get the small as possible

x^2 + (20-x)^2 = x^2 + x^2 - 20x +400

= 2x^2 -20x + 400

= 2(x^2 - 10x + 100)

The one number will be 10 and the other number will be 10

Therefore, to get the largest value the numbers will be 0 and 20 and to get the smallest value the numbers will be 10 and 10

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Answer:

1.

\(C.\\sin(N)=\frac{\sqrt{3} }{2}\)

2.

\(x=82.1\)

3.

x = 18°

Step-by-step explanation:

1. The sine ratio is sin(θ) = opposite/hypotenuse, where θ is the reference angle.  When N is the reference angle, we see that side OP with a measure of 5√3 units is the opposite side and side NP with a measure of 10 units is the hypotenuse.

Thus, we can find plug everything into the sine ratio and simplify:

\(sin(N)=\frac{5\sqrt{3} }{10} \\\\sin(N)=\frac{\sqrt{3} }{2}\)

2. We can use the tangent ratio to solve for x, which is tan (θ) = opposite/adjacent.  If we allow the 75° to be our reference angle, we see that the side measuring x units is the opposite side and the side measuring 22 units is the adjacent side.  Thus, we can plug everything into the ratio and solve for x or the measure of the opposite side:

\(tan(75)=\frac{x}{22}\\ \\22*tan(75)=x\\\\82.10511777=x\\\\82.1=x\)

3. Since we're now solving for an angle, we must using inverse trigonometry.  We can use the inverse of the tangent ratio, whose equation is tan^-1 (opposite/adjacent) = θ.  We see that when the x° is the reference angle, the side measuring 11 units is the opposite and the side measuring 33 units is the adjacent side.  Now we can do the inverse trig to find the measure of x:

\(tan^-^1(\frac{11}{33})=x\\ 18.43494882=x\\18=x\)

Carter would make an annual salary of $96000 after 12 years working for the company

What is addition ?

Addition is a basic mathematical operation that combines two or more quantities to find a total or a sum. It is denoted by the symbol "+" and is usually taught in elementary school. In addition, the order of the numbers does not matter, meaning that you can add them in any order and still get the same result. For example, 3 + 5 is the same as 5 + 3, and the answer is 8 in both cases.

According to the question:
After 8 years, Carter would have received 8 salary raises of $3000 each:

8 x $3000 = $24000

Adding this to his starting salary of $60000 gives us:

$60000 + $24000 = $84000

Therefore, Carter would make an annual salary of $84000 after 8 years working for the company.

To find his salary after 12 years, we can simply calculate 12 salary raises of $3000 each and add it to his starting salary:

12 x $3000 = $36000

$60000 + $36000 = $96000

Therefore, Carter would make an annual salary of $96000 after 12 years working for the company.

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Answer:

4567899999

Step-by-step explanation:

rfghnmbgfdsrthnb  cxdfghn cxdfghjnm cdfrtgyhjmn  

Answer:

58.03 ft

Step-by-step explanation:

To solve for the total circumference of circle F, we can create a ratio of section angle measure to circumference. We know that these two attributes of a circle have a linear relationship because the formula for arc length (\(S = 2\pi r \cdot \frac{\theta}{360\°}\)) relies proportionately on the radius and angle measure of the section.

angle measure : circumference

               290°   :   46.75 ft

We can multiply this ratio by \(\frac{360}{290}\) to get the corresponding circumference for a 360° section (which is the entire circle).

\(\frac{360}{290}(290\° : 46.75 \text{ ft})\)

\(= 360\° : \boxed{58.03 \text{ ft}}\)

Therefore, the circumference of circle F is approximately 58.03 ft.

Answer:

The other number is -128/17

Step-by-step explanation:

Let the unknown number be x,

\( \tt \longmapsto \: x + \frac{ - 8}{17} = - 8\)

\( \tt \longmapsto \: x = \frac{ - 8}{1} + \frac{8}{17} \)

\( \tt \longmapsto \: x = \frac{ - 136 + 8}{17} \)

\( \tt \longmapsto \: x = \frac{ - 128}{17} \)

Answer: B  

(Use the distributive property on each side of the equation.)

Step-by-step explanation:

Answer:

Step-by-step explanation:

- 25x + 15y = 750

- (30, 0) are coordinates of x-intercept. If there is no pool-cleaning job student has to do 30 lawn-mowing.  

- (0, 50) are coordinates of y-intercept. If there is no lawn-mowing job student has to do 50 pool-cleanings.

- ( 15 , 25 ) mean 15 lawn-mowing and 25 pool-cleanings

$25(15) + $15(25) = $750

$375 + $375 = $750

The solution is, The graph in the attached figure.

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

Let,

x -----> total game tokens purchased

y ----> yearly cost in dollars

we have

Member

y = x/10 + 60 -----> equation A

Nonmember

y = x/5 -----> equation B

we know that

The equation A represent a linear equation in slope intercept form. The line A does have a y-intercept equal $60 (initial value or membership fee) and the slope is m=$(1/10) per game token purchased.

The equation B represent a proportional relationship between the variables x and y. The line B passes through the origin and the slope is m=$(1/5) per game token purchased

using a graphing tool

see the attached figure to better understand the problem:

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Bonsoir,

"Qui sont vos sportifs préférés ?

Je vais vous décrire mon athlète préférée et vous devrez prêter attention. À la fin, vous me direz de qui je parle, d'accord ?

Commençons

Question 1 : Quel sport pratique l'athlète ?

Football, basketball ou volleyball.

Elle joue au volley-ball

Ma sportive préférée, c'est une joueuse de volley-ball.

Elle est péruvienne et fait partie de l'équipe féminine du Pérou  de volley-ball.

Question 2 : Comment est-elle?

Moche, musclée ou petite?

Elle est musclée

Elle est brune et musclée.

Elle est grande et mince aussi.

Elle est très belle.

Question 3 : Comment sont ses cheveux

et ses yeux ?

Ses cheveux et ses yeux sont bruns.

Elle a les cheveux bruns ,  courts et frisés .

Ses yeux sont bruns( on dirait plutôt marron) comme ses cheveux.

Question 4 : Quel âge a-t-elle ?

Elle a vingt-quatre ans.

Question 5 : Est-elle de petite taille?

Non, elle est grande.

Elle fait 1, 85m!

Answer:

x=3 and y=−2

Step-by-step explanation:

Multiply the first equation by 4,and multiply the second equation by 3.

4(2x−3y=12)

3(3x+4y=1)

Becomes:

8x−12y=48

9x+12y=3

Add these equations to eliminate y:

17x=51

Then solve17x=51for x:

17x=51

17x

17

=

51

17

(Divide both sides by 17)

x=3

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

2x−3y=12

Substitute3forxin2x−3y=12:

(2)(3)−3y=12

−3y+6=12(Simplify both sides of the equation)

−3y+6+−6=12+−6(Add -6 to both sides)

−3y=6

−3y

−3

=

6

−3

(Divide both sides by -3)

y=−2

Answer:

\((3,-2)\)

Step-by-step explanation:

\(2x-3y=12\)

\(2(3)-3(-2)=12\)

\(6--6=12\)        Two negative signs together makes a addition

\(3x+4y=1\)

\(3(3)+4(-2)=1\)

\(9-8=1\)            

Answer:

∆QRS is an obtuse triangle

Step-by-step explanation:

\(x + 2x + 8x - 40 = 180 \\ 11x = 220 \\ x = 20\)

\( < q = 20 \\ < r = 8(20) - 40 = 120 \\ < s = 2(20) = 40\)

<R = 120° > 90° which makes this an obtuse triangle