What is the blank for 3.441 <>= 3.409

Answer:

-3x+8

Step-by-step explanation:

-x is the same as -1x

-2x plus -x is 3x

8 stays the same

Subtract the difference from the total, then divide by 2, that would be the age of the youngest, then add the difference to that for the age of the oldest.

37 - 5 = 32

32 / 2 = 16

The youngest is 16.

16 + 5 = 21

The oldest is 21.

The ages are 16 and 21.

the first answer is correct

Start with congruencies of 130°:

∠1 and 130° are vertical angles

∠2 and 130° are corresponding angles

∠5 and 130° are alternate exterior angles

m∠1 = m∠2 = m∠5 = 130°

∠7 and 130° are supplementary angles (which means their sum is 180°). So, ∠7 = 50°

Next, find congruencies of ∠7:

∠3 and ∠7 are vertical angles

∠4 and ∠7 are corresponding angles

∠6 and ∠7 are alternate exterior angles

m∠3 = m∠4 = m∠6 = m∠7 = 50°

Answer: B

Step 1. Divide both side by 16

100/16 = 6t - 13

Step 2. Dimplify 200/16 to 25/2

25/2 = 6t - 13

Step 3. Add 13 to both sides

25/2 + 13 = 6t

Step 4. Simplify 25/2 + 13 to 51/2

51/2 = 6t

Step 5. Divide both sides by 6

51/2/6 = t

Step 6. Simplify 51/2/6 to 51/2 * 6

51/2 * 6 = t

Step 7. Simplify 2 * 6 to 12

51/12 = t

Step 8. Simplify 51/12 to 17/4

17/4 = t

Step 9. Switch sides

t = 17/4

Final answer:

The equation 7.5x + 20y = 900 can be solved for y by substituting different values for x to find three combinations that satisfy the equation: (0 hours, 45 lawns), (40 hours, 30 lawns), and (80 hours, 15 lawns).

Explanation:

The equation 7.5x + 20y = 900 models the relationship between the hours worked (x) and lawns mowed (y) for Jon to save up $900. To find combinations that result in $900, we can select different values for x or y and solve for the other variable.

These three combinations represent different ways Jon can work hours and mow lawns to reach his goal of saving $900.

A. 405,000

B. 450,000

C. 540,000

Answer:

A. -1 1/5

Step-by-step explanation:

−4 4/5 ÷ 4 = -1.2

-1.2 as a fraction would be, -1 1/5

Hope this helps :-)

f(3) means you replace x with 3.

f(x) = 7-x

f(3) = 7-3

f(3) = 4

Hey there!!

Given :

f( x ) = 7 - x

What is f(x)?

f(x) is basically the y.

The question states :

y = 7 - x

Now, find ( 3 )

This states that, I have given the value for x and find y.

y = 7 - x

y = 7 - 3

y = 4

Hence, f(3) = 4

Hope helps!

Answer:

The Correct answer to this question for Penn Foster Students is: 214.4 J

Step-by-step explanation:

Hey there!!

First equation :

Given equation :

... 2 ( n + 1 ) + 1 = ( n - 5 ) + ( n - 2 )

Excluding the parenthesis and using the distributive property :

... 2n + 2 + 1 = n - 5 + n - 2

Combining all the like terms on each side :

... 2n + 3 = 2n - 7

Subtracting 2n and subtracting 3 on both sides :

... 0 = -10

Hence, the first equation has "zero" values.

Second equation :

Given equation :

... 3 ( n - 1 ) - 2 = 4 ( n - 4 ) - ( n - 1 )

Using the distributive property :

... 3n - 3 - 2 = 4n - 16 - n + 1

Combining all the like terms :

... 3n - 5 = 3n - 15

Adding 5 and subtracting 3n on both sides :

... 0 = -10

Hence, the second equation has "zero" values.

Hope my answer helps!!

Let

x-------> the length of the rectangle

y------> the width of the rectangle

we know that

the perimeter of the rectangle is equal to

[tex]P=2x+2y[/tex]

[tex]P=190\ in[/tex]

so

[tex]2x+2y=190[/tex]------> equation A

[tex]y=4\ in[/tex] ------> equation B

substitute equation B in equation A

[tex]2x+2*4=190[/tex]

[tex]2x+8=190[/tex]

therefore

the answer is

[tex]2x+8=190[/tex]

[tex]x^2(x+2)(x+6)=0\\\\x^2=0 \vee x+2=0 \vee x+6=0\\\\x=0 \vee x=-2 \vee x=-6[/tex]

Here we need to find the 3 solutions of the equation x^2*(x + 2)*(x + 6) = 0.

The solutions are:

x = 0, x = -2, and x = -6

Let's see how to get the solutions:

First, notice that for an equation like:

A*B*C = 0

We must have:

A = 0, or B = 0, or C = 0.

Notice that our equation x^2*(x + 2)*(x + 6) = 0 has 3 coefficients, we will get one solution by making each one of these equal to zero.

x^2 = 0

x = √0 = 0.

(x + 2) = 0

x = 0 - 2 = -2

(x + 6) = 0

x = 0 - 6 = -6

Then the 3 solutions are:

x = 0, x = -2, and x = -6

If you want to learn more, you can read:

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5 and 28 if wrong let me know

Answer:

13.5 kgs.

Step-by-step explanation:

Here we have to find conversion factor of lbs into kg.

For this we use the given information.

Given that the weight of a dog is 20 lbs and also 9 kg.

Hence we have conversion factor as

20 lbs = 9 kg

Or 1 lb =9/20 = 0.45 kg.

Using this, we find the 30 lb converted into kg.

For 1 lb, equivalent kg = 0.45

Hence for 30 lbs equivalent kg= 30(0.45) = 13.5 kg.

The answer is

T= 5j+s+2

t=5j+s+2. Your answer should be: t=5j+s+2.

Let's solve for t.

5j+s=t−2

Step 1: Flip the equation.

t−2=5j+s

Step 2: Add 2 to both sides.

t−2+2=5j+s+2

t=5j+s+2

z and 100 are on the same line so the total is 180

180-100=z

80=z

Please give Brianest

The answer is choice D) Two rays that share the same endpoint

======================================

Here's a full breakdown of the four choices

A. False. If the ray and line aren't touching, then an angle can't be formed.

B. False. Parallel lines never cross. The same issue as before (in part A) comes up.

C. False. Again the rays need to meet up somehow.

D. True. If you have two rays that share the same endpoint, then they form an angle. Think of it like a pair of scissors. Each blade is a ray. The blades are joined at a common node to allow the blades to swing open or closed. You could have an angle formed by line segments or lines, but they would have to intersect in some way.

Option D. two rays that share the same endpoint, is correct.

An angle is formed by:
A. any ray and any line
B. parallel lines
C. any two rays
D. two rays that share the same endpoint

The angle can be defined as the one line inclined over other line.

When the line as same end points and
one of the line is inclined over other by some measure called as angle.

Thus the option D two rays that share the same endpoint is correct

Learn more about Angles here:
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Remark

The best way to answer something like this is to actually graph both equations. I have done that for you below.

Red Line: f(x) = 1/4x - 1

Blue Line: g(x) = 1/2x - 2

Now look at the answers.

A: The first one is incorrect. You don't need the graph to tell you that. The larger the number in front of the x, the steeper the line. Put another way, the larger the slope, the steeper the line. The y intercept is lower however.

B is wrong. g(x) is steeper, but the y intercept is lower not higher than f(x) [Negatives do strange things].

C:The g(x) is steeper (we've said that a couple of times), and it has a lower y intercept.

D is correct.

E is just wrong. Both parts are incorrect.

Answer:

Max is currently 12 years old.

Step-by-step explanation:

Zeke's current age = 8 years

Lets take Max's current age as [tex]x[/tex] years.

Then Max's age 3 years ago = [tex]x-3[/tex]

Double Max's age 3 years ago = [tex]2*(x-3)[/tex]

Double Max's age 3 years ago + Zee's current age = 26

⇒ [tex]2*(x-3)[/tex] + [tex]8[/tex] = [tex]26[/tex]

=[tex]2*(x-3)+8=26[/tex]

=[tex]2x-6+8=26[/tex] (Simplifying the brackets)

=[tex]2x+2=26[/tex]

=[tex]2x+2-2=26-2[/tex][tex]2x=24

=[/tex][tex]x=12[/tex]

So Max's current age is 12 years.

Answer:

13

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

trust

23x-13=2(x+2)

First you would distribute the 2 into the parenthesis

It will look like this after: 23x-13=2x+4

Then you would subtract 2x on both sides because u have to get the x's on one side

It will look like this after:21x-13=4

Then you would add 13 to both sides

It will look like this after: 21x=17

Then you would divide 21 on both sides

Your final product is 21/17

The solution to the equation 23x - 13 = 2(x + 2) is found by distributing, subtracting 2x, adding 13, dividing by 21, and then checking the solution.

To solve the algebraic equation 23x - 13 = 2(x + 2), let's apply algebraic methods and justify each step:

Distribute the 2 into the parentheses on the right side of the equation: 23x - 13 = 2x + 4. This step applies the distributive property a(b + c) = ab + ac.

Subtract 2x from both sides to start isolating x: 21x - 13 = 4. This maintains the balance of the equation, following the subtraction property of equality.

Add 13 to both sides in order to get terms with x on one side and constants on the other: 21x = 17. This action uses the addition property of equality.

Divide both sides by 21 to solve for x: x = 17/21. This is done using the division property of equality to isolate the variable x.

Check the solution by substituting x back into the original equation to ensure that both sides are equal.

By following these steps, we arrive at the correct solution for x and justify the use of algebraic properties that ensure the balance and equivalence of the equation throughout the process.

Miguel rode his bike 20 miles in 2.5 hours

(1)Starting information is , In 2,5 hours Miguel traveled 20 miles

(2)Now we complete the table

In 2,5 hours distance traveled = 20 miles

So in 1 hour distance traveled = [tex]\frac{20}{2.5} =8 miles per hour[/tex]

Time             0   0.5       1         1.5       2        2.5

Distance       0    4         8         12       16         20

(3) The graph is attached below

(4) Equation y = kx

y is the distance

x is the time

Distance = k (time)

We know speed is 8 miles per hour

So k is 8

y = 8k is the final equation

(5) k is the constant of proportionality

the value of k= 8

so 8 is the constant of proportionality.

Answer:

Step-by-step explanation:

1). Miguel rode his bike 20 miles in 2.5 hours.

2). Since Miguel rode his bike with the speed = [tex]\frac{20}{2.5}=8[/tex] miles per hour

So the table will be

Time          0       0.5      1       1.5        2       2.5

Distance    0        4        8       12       16       20    

3). Graph for the given equation is attached.

4). Since y = kx represents the situation then for Distance y = 4 miles in time x = 0.5 hours

4 = k(0.5)

k = [tex]\frac{4}{0.5}=8[/tex]

Therefore, equation will be y = 8x.

5). Since y = kx

⇒ k = [tex]\frac{y}{x}[/tex]

Proportionality constant k represents the speed of Migual.

Final answer:

Frances will first have piano lessons, ballet lessons, and soccer on the 20th day as it is the least common multiple of the days she has each activity (4, 5, and 2 days respectively).

Explanation:

The student is asking about the day Frances will first have piano, ballet, and soccer activities all on the same day. This calls for finding the least common multiple (LCM) of the numbers representing the days on which she has each activity (every fourth, fifth, and second day).

Frances has piano lessons every fourth day, ballet every fifth day, and soccer every second day. To find the day when all three activities coincide, we need to calculate the LCM of 4, 5, and 2:

The first common multiple they all share is 20. Therefore, Frances will first have all three activities on the 20th day.

First isolate x by multiplying by x on both sides.  It will look like this:

(2/3)x=1.2

Then devise by (2/3) on both sides to get:

x= 1.2/(2/3)

The easiest way to get this is plug that into a calculator and get the answer:

x=1.8

Final answer:

To solve the proportion 2/3 = 1.2/x, we use cross multiplication resulting in the equation 2x = 3.6. Dividing both sides by 2 gives us x = 1.8.

Explanation:

To solve for x in the proportion 2/3 = 1.2/x, we can set up a cross multiplication. This will give us the equation 2x = 3.6 (since 2 multiplied by x equals 1.2 times 3). To find the value of x, we then divide both sides of the equation by 2, leading to x = 3.6 / 2.

Therefore, we get x = 1.8 after simplifying the division.

Answer:

For Ajay , [tex]y=200x+325[/tex]

For Tory, [tex]y=250x[/tex]

Step-by-step explanation:

Formula to find distance = rate × time

Rate of Ajay = 200

Rate of Tory = 250

In x minutes

Distance travelled by Ajay = 200 ×x = 200x

Distance travelled by Tory = 250 ×x = 250x

But Ajay was already ahead by 350 meters.

So for Ajay, the distance y traveled in x minutes

[tex]y=200x+375[/tex]

For Tory

[tex]y=250x[/tex]

Answer:

The rates are:

Ajay : 200

Tory : 250

I assume those are in meters per minute.

Now, we suppose that Ajay began the trail 325 meters ahead, so if we put the zero in Tory position, we got:

Ajay position = 325 meters + 200*x meters

Tory position = 250*x meters

Where x is the number of minutes after they started to bike.

From this, we can compare their positions, and see in which minute x Tory position and Ajay position are the same.

325 + 200x = 250x

325 = 250x - 200x = 50x

x = 325/50 = 6.5 minutes.

So before of x = 6.5 minutes, Ajay is ahead. After x =6,5 minutes, Tory is ahead.

Answer:

It's the first option

Step-by-step explanation:

I just answered the question on edge

The perimeter of the base of the larger pyramid is 12 cm, determined through the ratio of the volumes of the pyramids.

The volumes of similar figures are related by the cube of the ratio of their corresponding lengths. If the larger pyramid has a volume of 729 cm³ and the smaller pyramid has a volume of 64 cm³, then the ratio of their volumes is 729/64, which is the cube of the ratio of their corresponding lengths. Taking the cube root of this ratio gives 3/2, so the lengths in the larger pyramid are 3/2 times the lengths in the smaller pyramid. Thus, if the perimeter of the base of the smaller pyramid is 8 cm, the perimeter of the base of the larger pyramid is 3/2 times this, or 12 cm.

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Answer:

3d = 51 is the desired equation; its solution is d = 17.

Step-by-step explanation:

Let d represent Diego's score.  Then 3d = 51, or d = 17.

"51 is the product of Diego's score and 3" is written as 51=3x. We know this because "is" means "=", and "the product of" means multiplication. Since "Diego's score" is unknown, it would be a number x (multiplied by 3 would make it 3x). The answer to this is 17, because 51/3=17. :)