Which system of equations has one solution? –5x – 10y = 24 5x + 10y = 16 3x + 4y = –7 –3x – 4y = 7 –12x + 8y = 16 12x – 8y = 16 –2x + 7y = –5 2x + 7y = –9

Answer:

14/15  

Step-by-step explanation:

find common denomerator 15

giving you -6/15 + 20/15

add

Answer:

Step-by-step explanation:

3^-6 × (3^4 ÷ 3^0)^2 = 3^-6 × (3^4 ÷ 1 )^2           {any number raise to zero = 1}

     = 3^-6 × (3^4 )^2

   =  3^-6 × (3^8)             [ (a^m)^n = a^ m*n ]

     = 3^ -6 + 8 = 3^2 = 3 * 3 = 9

Answer:

C

Step-by-step explanation:

(x+3)/3 =(y+2)/2

x/3 +3/3 = y/2 +2/2

x/3 +1 = y/2 +1

x/3 = y/2

Answer:

-11

Step-by-step explanation:

Given

[tex]\log_bA=3\\ \\\log_bC=2\\ \\\log_bD=5[/tex]

Use properties:

[tex]\log_b(A\cdot C)=\log_bA+\log_bC\\ \\\log_b\dfrac{A}{C}=\log_bA-\log_bC\\ \\\log_bA^k=k\log_bA[/tex]

Thus,

[tex]\log_b\dfrac{A^5\cdot C^2}{D^6}\\ \\=\log_b(A^5\cdot C^2)-\log_bD^6\\ \\=\log_bA^5+\log_bC^2-\log_bD^6\\ \\=5\log_bA+2\log_bC-6\log_bD\\ \\=5\cdot 3+2\cdot 2-6\cdot 5\\ \\=15+4-30\\ \\=-11[/tex]

First find m<HGC.

m<HGC=14 degrees (through vertical angles)

So...

m<HGE=14+78=92 degrees (through adjacent angles)

Now we have two parallel line cut by a transversal. And so... <HGE and <CEG are same side interior angles which means they are supplements (sum to 180 degrees)

m<HGE+m<CEG=180

92+m<CEG=180

m<CEG=88 degrees

<CEG and <CEB make a linear pair and are thus are supplements as well.

So...

m<CEG+m<CEB=180

88+m<CEB=180

m<CEB=92 degrees

m<CEB=4x=92

x=92/4=23 degrees

answer: 23 degrees

Answer:

The arc length, radius and the included angle are related as

r\theta=\widehat {XYZ}  where  \theta  is in radians.

The radius  r  is given by

r=\frac{\widehat {XYZ} }{\theta} \\ r=\frac{10.8}{1.8} \\ r=6\;units  

Correct choice is (B).

Step-by-step explanation:

Answer:

  7:00 pm

Step-by-step explanation:

You want to know Alexandra's arrival time if she started at the same time as Michael (8:00 am) and drove at 45 mph, while Michael drove at 55 mph and arrived at 5:00 pm.

Travel time is inversely proportional to speed, so the time it takes Alexandra to make the trip is 55/45 = 11/9 times what it take for Michael to make the trip.

Michael's travel time from 8 am to 5 pm is 9 hours, so Alexandra's travel time is ...

  (11/9)(9 h) = 11 h

She will arrive 2 hours after Michael does.

Alexandra arrives at 7:00 pm.

Answer:

x = 12

y = 5

Step-by-step explanation:

a triangle's side is divided by an angle bisector that bisects the opposite angle. Their relative lengths equals to the relative lengths of the other two sides of the triangle

x / 8 = 9 / 6

x = 9/6 * 8 = 12

(y-3) / 3 = 4 / 6

y - 3 = 4/6 * 3 = 2

y = 5

The equation of line T is 2x - y = 7 ⇒ (6x - 3y = 21)

Step-by-step explanation:

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size

Line L is mapped onto the line T by a dilation centered at the origin and  a scale factor of 3.

That means lint T is the image of line L after dilation

∵ The equation of line L is 2x - y = 7

∵ Line L is dilated by scale factor 3 and centered at origin

- That means multiply the equation of line L by 3 to find the

   equation of line t

∵ Line T is the image of line L after dilation

∴ The equation of line T is (3)(2x) - (3)(y) = (3)(7)

∴ The equation of line T is 6x - 3y = 21

Very important note:

The equation of line T is the same with equation of line L but multiplied by the scale factor 3 ⇒ L and T are coincide lines (same line)

That means the equation of lines T and L is 2x - y = 7

The equation of line T is 2x - y = 7 ⇒ (6x - 3y = 21)

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Answer:

  see attached

Step-by-step explanation:

The translation is 1 unit left and 5 units down. It is easy enough to count squares. It is just as easy to add (-1, -5) to each of the preimage coordinates.

Final answer:

To find how many times more water the bucket can hold than the jar, divide the bucket's capacity by the jar's capacity.

Explanation:

The bucket holds b liters of water, and the jar holds 8 fewer liters than the bucket. To find out how many times more water the bucket can hold than the jar, we need to compare their capacities. \

The bucket's capacity is b liters, and the jar's capacity is b - 8 liters.

To find the ratio of the bucket's capacity to the jar's capacity, we divide the bucket's capacity by the jar's capacity:

This ratio represents how many times more water the bucket can hold than the jar.

Answer:

Amount of screen time

Step-by-step explanation:

Explanatory variables are those variables that are not totally independent and are used to predict or explain differences in the response variable.

Having pointed what an explanatory variable is, we'll list the explanatory variable(s) in the question, using the definition above.

The Variable used to predict results here is the amount of screen time.

In that case, it is the explanatory variable.

And it's of numerical type.

In the described study, the explanatory or independent variable is the amount of computer screen time each day, as it is the variable that is being manipulated by the researcher in order to examine its effect on REM sleep.

In this particular research study, the explanatory variable, or the independent variable, is the amount of computer screen time each day. This is because the explanatory variable is the factor manipulated by the researcher to observe any potential effects on the outcome variable, which in this case, is the amount of REM sleep.

The participants were divided into four different groups, each exposed to a different amount of screen time: 2 hours, 4 hours, 6 hours, and 8 hours. These varying hours of exposure were purposely manipulated by the researcher to observe and measure any differences in the REM sleep duration. Therefore, the computer screen time is the explanatory variable or cause, and the observed alterations to the REM sleep will be the response, or the dependent variable.

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Answer:

127, 255  are the next 2 terms.

Step-by-step explanation:

The difference in terms  are 2,4,8,16,32 and so on.

Answer:

The 3rd one

Step-by-step explanation:

The steepest slope is basically the slope with the greatest absolute value. You can find slope by finding rise over run when given the graphs and finding change in y/change in x in the tables.

Function 1: -3

Function 2: (13-10)/(6-3) = 3/3 = 1

Function 3: 2

Function 4: (-4-(-12))/(2-4) = 8/-2 = -4

Function 4's slope has the greatest absolute value.

answer: the fourth one

Final answer:

To find how many text messages, x, Tim sent last month, use the equation: Total cost = fixed cost + variable cost. Given that Tim's phone bill was $30.58, the equation is $30.58 = $25.08 + $0.22x. Solving the equation gives x ≈ 25, so Tim sent approximately 25 text messages last month.

Explanation:

To find the number of text messages, x, Tim sent last month, we can use the equation:
Total cost = fixed cost + variable cost

Given that Tim's phone bill was $30.58, the fixed cost is $25.08. The variable cost is $0.22 per text message sent. Let's represent the number of text messages sent by x.

So, the equation becomes:
$30.58 = $25.08 + $0.22x

To solve for x, we need to isolate x. Subtract $25.08 from both sides of the equation:

$30.58 - $25.08 = $0.22x

Simplify:

$5.50 = $0.22x

Divide both sides of the equation by $0.22:

x = $5.50 / $0.22

x ≈ 25

Therefore, Tim sent approximately 25 text messages last month.

Sofia can spend at most $20.83 each week.

Step-by-step explanation:

Given,

Amount of given by Sofia's parent = $125

Number of weeks = 6

Let,

x represent the amount that Sofia can spend each week.

As Sofia has $125, therefore, she can spend maximum $125 or less than that.

[tex]6x\leq 125[/tex]

Dividing both sides by 6

[tex]\frac{6x}{6}\leq \frac{125}{6}\\x\leq 20.83[/tex]

Sofia can spend at most $20.83 each week.

Keywords: inequality, division

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Answer:

Scale : 1 mm = [tex]\frac{1}{3}\ m[/tex]

Or

Scale : 3 mm = 1 m

Step-by-step explanation:

Let the scale used be 1 mm = 'x' m

Given:

Actual width of kitchen is 12 m.

Length used by Kate in drawing is 36 mm.

So, 36 mm in drawing is equivalent to 12 m in actual.

Therefore, 1 mm in drawing is equivalent to 'x' m in actual.

Taking proportions and solving by cross multiplication, we get

[tex]\frac{36}{12}=\frac{1}{x}\\36x=12\\x=\frac{12}{36}\\x=\frac{1}{3}\ m[/tex]

Therefore, 1 mm in drawing is equal to [tex]\frac{1}{3}\ m[/tex] in actual.

Scale : 1 mm = [tex]\frac{1}{3}\ m[/tex]

Or

Scale : 3 mm = 1 m

Answer:

$48.72

Step-by-step explanation:

5.6 liters x $8.70 per liter= $48.72 total cost

Final answer:

To determine the total cost of the olive oil, multiply the quantity of 5.6 liters by the price per liter, which is $8.70. The total cost for the restaurant owner is $48.72.

Explanation:

The question asks us to calculate the total cost for a restaurant owner who buys 5.6 liters of olive oil at a price of $8.70 per liter. To find the total cost, we multiply the quantity of olive oil by the price per liter.

Calculation: Total cost = Quantity x Price per liter

Total cost = 5.6 liters x $8.70 per liter

Total cost = $48.72

Therefore, the restaurant owner will pay $48.72 for 5.6 liters of olive oil.

A relation is a function if there is exactly one output for each input ⇒ b

Step-by-step explanation:

Let us revise the meaning of relation and function

Examples:

{(1 , 2) , (-2 , 3) , (1 , 5) , (2 , 4)}

∵ x is the input

∵ y is the output

∵ The input 1 has two output 2 and 5

∴ The set above is a relation

{(1 , 2) , (-2 , 3) , (-1 , 5) , (2 , 4)}

∵ x is the input

∵ y is the output

∵ Each input has only one output

∴ The set above is a function

A relation is a function if there is exactly one output for each input

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Answer:

97

Step-by-step explanation:

9+7*9=72

9+18+10=37

10+10+7=27

7+9*10=97

Answer:I believe it's y=log(x-3)

Step-by-step explanation:

Answer:

see the explanation

Step-by-step explanation:

step 1

Identify the equation of the given line

we know that

The equation of the line in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

we have

[tex]m=5\\b=-1[/tex]

substitute

[tex]y=5x-1[/tex]

step 2

Identify the coordinates of four points on the line

First point

The given y-intercept

point (0,-1)

Second point

The x-intercept

For y=0

[tex]0=5x-1[/tex]

[tex]x=\frac{1}{5}=0.20[/tex]

point (0.20,0)

Third point

For x=1

[tex]y=5(1)-1=4[/tex]

point (1,4)

Fourth point

For x=2

[tex]y=5(2)-1=9[/tex]

point (2,9)

Answer:

[tex]f(x)+g(x)=5x^{3} +4x^{2}+x-8[/tex]

Step-by-step explanation:

Given:

Two functions are given:

[tex]f(x)=5x^{3} +3x^{2} -3[/tex]

[tex]g(x)=x^{2} +x-5[/tex]

Find [tex]f(x)+g(x)[/tex]

Solution:

[tex]f(x)+g(x)=(5x^{3} +3x^{2} -3)+(x^{2} +x-5)[/tex]

[tex]f(x)+g(x)=5x^{3} +3x^{2} -3+x^{2} +x-5[/tex]

[tex]f(x)+g(x)=5x^{3} +(3x^{2} +x^{2})+x-3-5[/tex]

[tex]f(x)+g(x)=5x^{3} +4x^{2}+x-8[/tex]

Therefore, the function of [tex]f(x)+g(x)=5x^{3} +4x^{2}+x-8[/tex]

Answer:

About the square root of 24 cubic centimeters

Answer: Its actually not. (maybe a typo)? The real bigger one is 5/8

Step-by-step explanation: So your question is "how much more is 1/8 than 5/8?" . The answer is its not. Lets do a example to help clarify. This is the butterfly method. this is by far the simplest way to compare fractions. Lets say your problem is " which is more, 5/8 or 3/4." the first thing you need to do is  line them up like so:

  5       3

  _       _

  8       4

The second thing to do is multiply the opposites.

  5       3

  _       _

  8       4

You would be multiplying 8*3 and 5*4 so like across or whatever.

put the answers on the equation like so,

20         24 <- Which ever in the top is bigger that would be 24. Which is 3/4

 5       3   ______________________________/

 _       _                                                                  

 8       4

3/4 is bigger in this problem.

Hope I helped!

:)

Answer:

f(x) - g(x) = (1/x) + 2 - 3x      or (f - g)(x)

Step-by-step explanation:

f(x)  = 1/x+2

-g(x) = 3x

can be summarized on line line as:

f(x) - g(x) = (1/x) + 2 - 3x      or (f - g)(x)

Answer:

For 1 is 1

For 4 is 1,2,4

Step-by-step explanation:

A fact family for 1, 4, and 4 can be created using addition and subtraction. The addition equations are 1 + 4 = 5 and 4 + 1 = 5. The subtraction equations are 4 - 1 = 3 and 4 - 3 = 1.

In mathematics, a fact family is a set of three numbers that can be used to create four different addition and subtraction equations. In this case, the numbers given are 1, 4, and 4. To create the fact family, we can use the numbers and their corresponding operations.

The addition equations would be: 1 + 4 = 5 and 4 + 1 = 5.

The subtraction equations would be: 4 - 1 = 3 and 4 - 3 = 1.

Therefore, the fact family for 1, 4, and 4 is: 1, 4, and 5 (addition) and 4, 1, and 3 (subtraction).

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Answer:

Step-by-step explanation:

2x=(360÷4)

2x = 90

Dividing by 2

x = 90/2

x = 45

By following the steps of simplifying, isolating, and solving for x, we find that x = 45 is the value that satisfies the given equation.

To solve the equation 2x = (360 ÷ 4) for x, we need to isolate x on one side of the equation. Follow these steps to find the value of x:

Step 1: Simplify the expression on the right side of the equation.

360 ÷ 4 = 90

Step 2: Replace the right side of the equation with its simplified value.

2x = 90

Step 3: To isolate x, divide both sides of the equation by 2.

(2x) ÷ 2 = 90 ÷ 2

This simplifies to:

x = 45

The solution to the equation is x = 45. To verify, you can substitute x = 45 back into the original equation:

2(45) = 90

90 = 90

Since both sides of the equation are equal, x = 45 is indeed the correct solution.

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Answer:

The total change in yardage of the team is by - 1 yards.

Step-by-step explanation:

Let us assume that the initial yardage of the team was x yards.

Now, the team gained 5 yards on their play of the game.

Hence, the team now has (x + 5) yards on their play of the game.

Next, the team lost 6 yards and finally, the team will have [(x + 5) - 6] = (x - 1) yards in total.

Therefore, the total change in yardage of the team is by - 1 yard. (Answer)

Answer:

The total change in yardage of the team is by - 1 yards.

Step-by-step explanation:

The total change in yardage of the team is by - 1 yards.

420 trees

210 minutes in 3 1/2 hours

x2 per minute

=420 trees in 3 1/2 hours

There are 420 trees will be sold in three and a half hours.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Every minute, there are two Christmas trees sold at the tree farm.

Now,

Since, Every minute, there are two Christmas trees sold at the tree farm.

Hence, Number of sold Christmas tree in 1 hour = 2 × 60

                                                                          = 120

So, Number of sold Christmas tree in 3 1/2 hour = 120 × 3 1/2

                                                                          = 120 × 7/2

                                                                          = 420

Thus, There are 420 sold Christmas tree in 3 1/2 hour.

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Answer:

20 = 3x+2y

Step-by-step explanation:

one box of crackers is $3 (3x)

one box of granola bars is $2 (2y)