Triangles LMN and FGH are shown. True or False questions
1.MN/NL=GH/HF
2.LM+MN+NL=FG+GH+HF
3.Triangle LMN is similar to triangle FGH.

Answer:

The integer representing the change is -43,200 gallons

Step-by-step explanation:

Here, we want to get the integer that represents the change in the number of gallons drained from the reservoir each week

Total number of hours per week would be 2 * 3 = 6 hours ;

6 hours is same as 6 * 60 = 3600 minutes

in a minute 12 gallons are drained

In 3600 minutes, the number of gallons drained would be;

3600 * 12 = 43,200 gallons are drained

Given :

An equation 2cot x = -3sec x .

To Find :

the values of x in [0, 360°) which satisfy the given equation.

Solution :

Converting cot x and sec x in the form of sin x and cos x.

[tex]\dfrac{2cos \ x}{sin\ x}= \dfrac{-3}{cosx}\\\\2cos^2 x +3 sin\ x =0\\\\2( 1 - sin^2 x ) + 3sin \ x = 0 \\\\2sin^2 x -3sin\ x -2 = 0\\\\2sin^2\x -4sin\ x + sin\ x -2 = 0\\\\2sin\ x( sin\ x - 2 )+ 1( sin \ x - 2 ) = 0\\\\sin \ x = \dfrac{-1}{2} \ or\ sin \ x = 2[/tex]

Neglecting sin x = 2 because sin x cannot be greater than 1.

x = π - π/6, π + π/6

x = 5π/6 and x = 7π /6

Therefore, the values of x in [0,360°) is  5π/6 and x = 7π /6 .

Step-by-step explanation:

Quesion 1

The cost of one chair can be found by dividing the cost of the total chairs by the number of chairs

hence, cost per chair= 150/50= $3 per chair

Question 2

let us find the number of walnuts per bag

= 330/6

=55 walnuts per bag

hence in two bags there will be 55*2= 110 walnuts

Question 3

Option D is an example of a unit rate.

The unit rate is defined as the cost of one unit of an item, or the value that represents a unit of a quantity... D 18 miles driven in a week

Answer:

-7

Step-by-step explanation:

The y intercept of a line is the y value of the line when the x value = 0

In this case we are given the coordinates (0, -7)

so when x =0   y= -7

Therefore, the y- intercept is -7

Answer:

-7

Step-by-step explanation:

The y intercept of a line is the y value of the line when the x value = 0

In this case we are given the coordinates (0, -7)

so when x =0   y= -7

Therefore, the y- intercept is -7

Let, age of Carmen, Antoine and Katy is C, A and K.

And it is given that :

[tex]A - C = 5\dfrac{1}{4}[/tex]                …1)

[tex]K-C = 11 \dfrac{1}{2}[/tex]              ...2)

We need to find the difference in Antoine's age and Katy's age.

Subtracting equation 2) from 1), we get :

[tex]( A - C ) - ( K-C) =5\dfrac{1}{4} - 11\dfrac{1}{2}\\\\A - K = -6\dfrac{1}{4}\\\\K-A = 6\dfrac{1}{4}[/tex]

Therefore, Katy is [tex]6\dfrac{1}{4}[/tex] years older than Antoine.

Answer:

[tex]x = \frac{ - 3b}{4} \: or \: b[/tex]

Step-by-step explanation:

[tex] \frac{1}{b + x} = \frac{3b}{2 {x}^{2} } - \frac{1}{x} [/tex]

[tex] = > \frac{1}{b + x} = \frac{3b - 2x}{2 {x}^{2} } [/tex]

[tex] = > 2 {x}^{2} = (b + x)(3b - 2x)[/tex]

[tex] = > 2 {x}^{2} = 3 {b}^{2} - 2bx + 3bx - 2 {x}^{2} [/tex]

[tex] = > 2 {b}^{2} = 3 {b}^{2} + bx - 2 {x}^{2} [/tex]

[tex] = > 3 {b}^{2} + bx - 4 {x}^{2} = 0[/tex]

[tex] = > 3 {b}^{2} + 4bx - 3bx - 4 {x}^{2} = 0[/tex]

[tex] = > b(3b + 4x) - x(3b + 4x) = 0[/tex]

[tex] = > (3b + 4x)(b - x) = 0[/tex]

Hence,

[tex]x = \frac{ - 3b}{4} \: or \: b[/tex]

Answer:

$7.198 * 10^6

Step-by-step explanation:

Given that :

Total Area of Alaska = 5.9 * 10^5 mi²

Cost of Alaska per square mile = $12.20

Total amount paid to purchase Alaska:

(Total area in square miles * Cost per square mile)

(5.9 × 10^5) * $12.20

(5.9*12.20) * 10^5

71.98 * 10^5 dollars

= $7.198 * 10^6

Hence, amount the United States paid Russia for the purchase of Alaska is approximately $7.198 * 10^6

Answer:

1. Write the expression:       (5.9 × 105)(12.2)

2. Multiply the decimal values:      

✔ 71.98

× 105

3. Write in scientific notation:      

✔ 7.198

×  

✔ 10 to the sixth power

The United States paid Russia approximately  

✔ $7,200,000

for Alaska.

Step-by-step explanation:

Answer:

X= 24

Step-by-step explanation:

Answer:

Step-by-step explanation:

The two shapes are similar

As per similarity, the corresponding sides have same ratio. Knowing the ratio we can find the value of the side x:

Answer:

if you mean that it look like this < or this > then its “less than or equal to“ or “greater than or equal to”

I hope this helped!!

OH and have a merry Christma!!!!!

Answer:

anybody agree that its c

Step-by-step explanation:

Answer:

hope this helps

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

refer attachment for detailed answer

Answer: -120

Hope this helps!!

Answer:

-120

Step-by-step explanation:

Step-by-step explanation:

Amount of green clay at the start = 57g + 31g = 88g.

Amouny of green clay used = 88g - 18g = 70g.

Hence 70g of green clay was used during the week.

Answer:

1. B

2. A

3.C

Step-by-step explanation:

50 !

hope this helps :)

Answer:

5x-19+[tex]\frac{69}{x+3}[/tex]

Step-by-step explanation:

Answer:

0.05n + 0.10 d =24.40

Step-by-step explanation:

Nickel is worth 0.05 of a dollar(1)

The system of equations below would be the best to use to find the number of nickels and dimes Anthony had at the end of the first week is:

n + d = 368

0.05n + 0.10d = 24.40

The number of nickels and dimes Anthony saved at the end of the first week can be determined using two equations. This is known as simultaneous equations.

The total number of nickels and dimes in the jar is 368. This can be represented with the equation:

nickels + dimes = 368

n + d = 368. This would be the first equation.

A nickel is equal to 0.05 of a dollar and a dime is equal to 0.1 of a dollar. The total sum of money in the jar is $24.40. This means that the value of dimes and nickels in the jar is $24.40. This can be represented with the equation: 0.05n + 0.10d = 24.40. This is the second equation.

To learn more about simultaneous equations, please check: brainly.com/question/23589883?referrer=searchResults

Answer:

I think it is A (38.47)

Step-by-step explanation:

I believe this because I had a math qouiston like this and when I found this A was the only comen answer and when I clicked on my 38.47 I was right

Answer:

The answer is X > 1 hope that helps!

Step-by-step explanation:

hope it helps!!!!

please mark brainliest

Answer:

The price of adult ticket is £38.

Step-by-step explanation:

First, you have to form equations in terms of a (adult) and c (child) :

[tex]2a + 4c = 152 - - - (1)[/tex]

[tex]a = 2c - - - (2)[/tex]

Next, you have to solve these equations by substitution :

[tex](2)→(1)[/tex]

[tex]2(2c) + 4c = 152[/tex]

[tex]8c = 152[/tex]

[tex]c = 152 \div 8[/tex]

[tex]c = 19[/tex]

[tex]substitute \: c = 19 \: into \: (2)[/tex]

[tex]a = 2 \times 19[/tex]

[tex]a = 38[/tex]

Answer:500 miles

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

Distance= 308 miles

Step-by-step explanation:

Giving the following information:

The distance between Dallas and San Antonio is on a map is 13.7 inches.

2 inches = 40 miles

To calculate the distance between Dallas and San Antonio, we will use the following formula:

Distance= (12/2)*40 + 1.7*40

Distance= 308 miles

12/2= first 12 inches

Answer: 275$

I'm not entirely sure I did this right! But at least try!!!

Step-by-step explanation:

20/100 = 55/x (cross multiply)

20x = 5,500 (divide)

X = 275

The original price of the pair of jeans is $ 68.75

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

The sale price of the jeans = $ 55.00

The discounted percentage of the pair of jeans = 20 %

Let the original price of the jeans be = A

To calculate the original price of the jeans ,

Original price of the jeans A will be discounted percentage less than and is equal to the sale price of the jeans

So ,

Original price of the jeans A - discounted percentage of the pair of jeans = Sale price of the jeans

And ,

A - ( 20/100 ) A = 55

( ( 100A - 20A ) / 100 )A = 55

(80/100 ) A = 55

( 4/5 ) A = 55

Multiply by 5/4 on both sides , we get

A = ( 55 x 5 ) / 4

A = 275/4

A = $ 68.75

Therefore , Original price of the jeans A = $ 68.75

Hence , the original price of the jeans is $ 68.75

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Answer:

C

Step-by-step explanation:

Answer:

2 is the value that provides the same result with f(x) and g(x).

Step-by-step explanation:

You can solve this by saying:

f(x) = g(x)

and then solving for x.

So let's do it:

[tex]f(x) = g(x)\\-0.5x + 2 = 2x - 3\\2x + 0.5x = 2 + 3\\2.5x = 5\\x = 2[/tex]

This tells us that when x = 2, the two functions will have identical values.  Let's try them out to confirm it!

f(x) = -0.5x + 2

f(2) = -0.5 * 2 + 2

f(2) = -1 + 2

f(2) = 1

g(x) = 2x - 3

g(2) = 2 * 2 - 3

g(2) = 4 - 3

g(2) = 1

So we can see that 2 is the value that produces the same result in both charts.

The input value that produces the same output value in both charts is 2. so the correct answer is option D.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

here, we have,

You are given two functions  f (x) = -0.5X +2 and g(x) = 2x - 3

x      f(x)

-3     3.5

-2     3

-1     2.5

0     2

1      1.5

2     1

3     0.5

The second table is given below:-

x      g(x)

-3      

-2      

-1      

0    

1      

2      

3      

We will put the points and will find the value of functions:-

g(-3) = 2(-3) - 3 = -6 -3 = -9

g(-2) = 2 -(-2) -3 = -7

g(-1) = 2( -1) -3 = -3

g(0) = 2 - 0  - 3 = -3

g(1) = 2.1 - 3 = -1

g(2) = 2.2 -3 = 1

g(3) = 2.3 -3 = 3

Hence the second table will be

x      g(x)

-3      -9

-2      -7

-1       -5

0       -3

1        -1

2       1

3       3

The input value that produces the same output value in both charts is 2.

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Answer:

Area of each piece = 104 [tex]cm^{2}[/tex]

Possible dimensions are 26 cm by 4 cm, 13 cm by 8 cm.

Step-by-step explanation:

Given that:

Dimensions of the rectangular board as:

Length of the board is 10 cm longer than its width.

Width of the board = 26 cm

Length of the board = 26 + 10 = 36 cm

The rectangular board is divided into 9 equal pieces.

To find:

Area of each piece and

the possible dimensions of each piece = ?

Solution:

First of all, let us calculate the area of bigger rectangular board.

Area of a rectangle is given by the following formula:

[tex]Area = Length \times Width[/tex]

Area = 26 [tex]\times[/tex] 36 [tex]cm^2[/tex]

Area of each smaller rectangle = [tex]\frac{26\times 36}{9} = 104\ cm^2[/tex]

To find the possible dimensions, we need to find the factors of 104.

104 = 26 [tex]\times[/tex] 4

104 = 13 [tex]\times[/tex]  8

Therefore, the Possible dimensions are 26 cm by 4 cm

and

13 cm by 8 cm.