50 POINTS!
What is the reason for each step in the solution of the equation?

3(x+2)=4x+1
Drag and drop the reasons into the boxes to correctly complete the table.

slope = [tex]\frac{1}{4}[/tex]

to calculate the slope m use the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (8, 8 ) and (x₂, y₂ ) = (- 4, 5 ) ← 2 poinys on the line

m = [tex]\frac{5-8}{-4-8}[/tex] = [tex]\frac{-3}{-12}[/tex] = [tex]\frac{1}{4}[/tex]

To solve the given operation firat we take LCM for both terms.

As denominator of first term is 3 and second term is [tex] 12x-8 [/tex]

Therefore, the Lcm is [tex]3(12x-8) [/tex]

Now solving and making same denominator for each term

[tex]\frac{7}{3} [/tex] [tex]\times [/tex] [tex] \frac{12x-8}{12x-8} [/tex]

On multiplying we get

[tex]\frac{7(12x-8)}{3(12x-8)} [/tex] [tex]=\frac{84x-56}{3(12x-8)} [/tex]

Now solving other term

[tex]\frac{8}{12x-8} [/tex] [tex]\times [/tex] [tex]\frac{3}{3} [/tex]

On multiplying we get

[tex]\frac{24}{3(12x-8)} [/tex]

Now solving the expression by putting the values

[tex]\frac{84x-56-24}{3(12x-8)} [/tex]

[tex]\frac{84x-80}{12(3x-2)} [/tex]

[tex]\frac{4(21x-20)}{12(3x-2)} [/tex]

On solving we get

[tex]\frac{21x-20}{3(3x-2)} [/tex]

There denominator of the expression is

[tex]9x-6 [/tex]

Hope this will help

We are given

[tex]V=0.95h^2[/tex]

we can plug h=8

and then we can find volume

[tex]V=0.95(8)^2[/tex]

[tex]V=60.8ft^3[/tex]

so,

the amount of water in the container when h = 8 feet is 60.8 ft^3........Answer

Answer:

395.1

Step-by-step explanation:

Simplify  

0.95 ( 8 ) ^2.9= v

395.07956558

Paula's dog : Carolos' dog = 3 : 1

The total number of ratio units is 3+1 = 4, so each one stands for (48 lb)/4 = 12 lb.

Paula's dog weighs 3·12 lb = 36 lb.

Carlos' dog weighs 1·12 lb = 12 lb.

Answer:

The answer is the angels will be the equivalent.  

Explanation:

Lines on a plane that never meet. They are dependably a similar separation separated. Here the red and blue line sections are parallel.In different words, the slants of parallel lines are equivalent. Note that two lines are parallel if their slants are equivalent and they have distinctive y-blocks. As it were, opposite inclines are negative reciprocals of one another. Here is a fast survey of the slant/capture type of a line.

Answer:

Alternate Exterior Angles

Step-by-step explanation:

-20.04 because they are opposites

The opposite value of a number is a number that when added to the original number, results in zero. In this case, the opposite value of 20.04 is -20.04.

The question is asking for the opposite value of 20.04. In mathematics, the opposite value, also known as the additive inverse, is a number which when added to the original number, results in zero. In other words, it's the number you would have to add to a specific number to get a sum of zero. Therefore, the opposite value of 20.04 is simply -20.04.

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Answer:

c. Definition of altitude.

Step-by-step explanation:

We are given that segment QS is an altitude in ΔPQR and we are asked to find a justification used while proving the similarity of triangles ΔPSQ and ΔQSR.

Since we know that altitude meets opposite side at right angles. When QS will intersect line PR we will get two right triangles QSR and QSP right angled at S.

ΔPQR is similar to ΔPSQ as they both share angle P and right triangle. So their third angle should also be similar.

ΔPQR is similar to ΔQSR as they both share angle R and both have a right triangle at Q and S respectively. So they will have their third angle equal.

ΔPQR is similar to triangles ΔQSR and ΔPSQ. Therefore, ΔQSR is similar to ΔPSQ.

Therefore, by definition of altitude triangles ΔPSQ and ΔQSR are similar as ΔPSQ and ΔQSR are created from ΔPQR by altitude QS.

"Alternate" angles are on opposite sides off the transversal.

"Interior" angles are between the lines the transversal is crossing.

The appropriate choice for alternate interior angles is ...

... 5 and 3

Answer:

The pair of angles the are alternate interior angles are 5 and 3. Or C.

Step-by-step explanation:

Answer:

m - Meter - Length.

s - Second - Time.

K - Kelvin - Temperature.

kg - Kilogram - Mass.

Units you might use in these scenarios include meters or kilometers for distance, meters per second or kilometers per hour for speed, millimeters or inches for rainfall, gallons or liters for volume, gallons per minute or liters per second for flow rate, and calories for caloric intake.

In each of these scenarios, you would use different units to measure different things:

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Find the number needs to be added to both sides of the equation in order to complete the square

x ^2+16x=18

In completing the square , we take the coefficient of x and divide it by 2

Then square it and add it on both sides.

The coefficient of x  is 16

Half of 16 is 8

Then we square it . [tex](8)^2 = 64[/tex]

Add 64 on both sides

[tex]x ^2+16x + 64=18+64[/tex]

Now we factor x^2 + 16x+64

[tex](x+8)(x+8)=18+64[/tex]

[tex](x+8)^2=82[/tex]

so 64 is added to both sides of the equation in order to complete the square.

Answer:

A) -9/4

Step-by-step explanation:

The answer ends up becoming -2.25.

So if you do the math, that's -9/4. or add up 4 until you're at 9.

4, 8. Now we know we have 2 whole. What's left? 1/4.

So now we have, -2 1/4. or "-9/4".

Answer:

19:00 or 7:00 PM

Step-by-step explanation:

Baby armadillos need to be fed every four hours.

Baby bats need to be fed every three hours.

So we need to figure out when will they be fed again at the same time:

Basically, we need to find the LCM of two numbers i.e. 4 and 3. And the reason why are we finding the LCM is because that time difference will is the least common multiple of both the time differences, it is the smallest non-zero number that is the multiple of both 4 and 3.

The LCM of 4 and 3 is 12. So the time when they will be fed again at the same time will be 12 hours after 7:00 AM that is 19:00 hours or 7:00 PM.

Invested amount (P) = $300.

Time in years (t) = 2 years.

Balance after 2 years (A) = $329.49.

Let us assume rate of interest = r % compounds annually.

We know, formula for compound interest

[tex]A=P(1+r)^t[/tex]

Plugging values in formula, we get

[tex]329.49=300(1+r)^2[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}300[/tex]

[tex]\frac{300\left(1+r\right)^2}{300}=\frac{329.49}{300}[/tex]

[tex]\left(1+r\right)^2=1.0983[/tex]

Taking square root on both sides, we get

[tex]1+r=\sqrt{1.0983}[/tex]

[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}[/tex]

[tex]1+r-1=\sqrt{1.0983}-1[/tex]

[tex]r=\sqrt{1.0983}-1[/tex]

[tex]r=1.048-1[/tex]

r=0.048.

Converting it into percentage by multiplying by 100.

r=0.048 × 100

r  = 4.8 %

Therefore, the rate of interest on the account is 4.8% compounds annually.

If these are terms of a geometric sequence, they have a common ratio. That is, ...

... (k -1)/(2(1 -k)) = (k +8)/(k -1)

... (k -1)² = 2(1 -k)(k +8) . . . . . multiply by the product of the denominators.

... k² -2k +1 = -2k² -14k +16 . . . eliminate parentheses

... 3k² +12k -15 = 0 . . . . . . . . put in standard form (subtract the right side)

... 3(k +5)(k -1) = 0 . . . . . . . . . factor

Possible values of k are ... -5, +1. The solution k=1 is extraneous, as it makes the first two terms 0 and the third term 8. (It doesn't work.)

The value of k is -5.

_____

The three terms are 12, -6, 3. The common ratio is -1/2.

Answer: Option C) The midpoint of the segment.

Then, you draw a circle with radius the half of the distance between the center of the circle and the point outside the circle.

The tangency points are the points where this circle cuts the given circle.

Answer:

[12/(4c)] + [12/(6c)] = 2.5

Step-by-step explanation:

time = distance/speed

You know the speeds upstream (5-1)c and downstream (5+1)c, the distance, and the total time for both trips. This information can be combined to give the equation above.

_____

The first equation assumes the trips upstream and down took 2.5 hours each.

The second equation is an incorrect combination of the numbers, as the units on the left are miles²/hour and are equated to hours on the right.

The third equation makes appropriate use of the relation between speed, distance, and time.

Answer:

Last option as

[tex][12/(4c)] + [12/(6c)] = 2.5[/tex]

Step-by-step explanation:

Time = distance/speed

Speed of boat = 5c (given)

Hence upstream speed = 5c+c =6c and

downstream speed = 5c-c =4c

Distance remains the same 12 miles for up and down

Total time = 2.5 hours

The first equation assumes total time as 5 hours when it is actually 2.5 hours.

The second equation is an incorrect because time x distance will not yield any result instead distance /time should have been done.

The third equation calculates time taken for upstream and downstream and add to equate to 2.5 hours.

So this is correct.

Answer:

1. See below for the table

2a. Early Pay: y = 45

2b. Deposit Plus: y = 12 + 4x

2c. Daily Pay: y = 6x

3. See the second attachment for a graph.

Step-by-step explanation:

1. The deposit (Deposit Plus) and the flat rate (Early Pay) are paid whether or not any days are spent swimming. For Early Pay, there are no additional charges, so the total cost is the same regardless of the number of days spent swimming.

For Deposit Plus, the $4 per day cost will add $20 for each 5 swimming days.

For Daily Pay, the $6 per day cost will add $30 for each 5 swimming days.

2. As described above, the Early Pay and Deposit Plus have charges when the number of swimming days is zero. The Daily Pay does not. The Deposit is only paid once, not each day.

a. Early Pay: y = 45

b. Deposit Plus: y = 12 + 4x

c. Daily Pay: y = 6x

3. The above equations are graphed in the second attachment. You will note that the plan that results in a minimum charge depends on the number of swimming days.

Answer:

2a. Early Pay: y = 45

2b. Deposit Plus: y = 12 + 4x

2c. Daily Pay: y = 6x

Step-by-step explanation:

To work this problem, you must assume that Juan's pedaling speed adds to the wind speed when going downwind, and that the wind speed subtracts from Juan's pedaling speed going upwind. (In other words, Juan's pedaling speed is relative to the air, not the ground.)

Let w represent the wind speed in miles per hour.

... distance = speed × time

Juan's total distance is 40 miles, so we have ...

... 40 = (11.5 +w)×1.75 + (11.5 -w)×2.50

... 40 = 48.875 - 0.75w . . . . . simplify

... -8.875/-0.75 = w . . . . . . . . subtract 48.875, divide by -0.75

... w = 11.833... = 11 5/6

The wind was blowing 11 5/6 miles per hour.

_____

Compared with real-life experience, and working through the details, this problem makes no sense whatever. Pedaling a bicycle is not like rowing a boat, where the current of the medium directly affects speed.

If you work through the segments of the problem, you find that Juan traveled 40.833 miles with the wind in the first 1.75 hours, so actually finished the race and then some. He spent the next 2.5 hours being blown backward by the wind, even though he was pedaling forward at 11.5 mph. (How much sense does that make?)

The value of 2.704 is .004 because it is 3 spaces to the right of the decimal point.

Answer:

B

Step-by-step explanation:

The wording in the problem statement is ...

... "less than 3 years"

... "at least 3. but less than 6 years"

so we expect the inequality symbols to look like ...

... 0 ≤ x < 3

... 3 ≤ x < 6

These match the second piecewise function.

The only equation that has 3 as the coefficient of x (a slope of 3) is ...

... d.) y = 3x+4

_____

Happily, it also goes through the given point.

... 5/2 = 3(-1/2) +4

... 5/2 = -3/2 + 8/2 . . . . true

The equation of the line with a slope of 3 that passes through the point (-1/2, 5/2) is y = 3x + 4, which corresponds to answer option (d.) y = 3x + 4.

To find the equation of a line with a given slope and that passes through a specific point, we can use the point-slope form of a line, which is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the given point. So, for a line with a slope of 3 that goes through the point (-1/2, 5/2), we can plug in the values to get the equation.

Substituting into the point-slope form, we get y - 5/2 = 3(x + 1/2). Simplifying and solving for y will give us the equation of the line in the form of y = mx + b. After distributing and rearranging, the equation will be y = 3x + 4.

Therefore, the correct answer is (d.) y = 3x + 4.

In general, if you have a parent function, f(x), the graph of a daughter function f(x - h) + k is related with the graph of the parent function as per these rules:

Therefore, the graph of  f(x) = |x - h| + k is a translaion of h units to the right and k units upward fo the function f(x) = |x|.

Since, the graph of f(x) = |x| has vertex (0,0), the graph of f(x) =  |x - h| + k has vertex (h, k).

To visualize the images of the graph, assume some positive value for h and k. For instance, h = 3 and k = 5.

See the image attached showing the graphs for the functions f(x) = |x| (red line) and f(x - 3) + 5 = |x - 3| + 5 (blue line). As you can see, the blue line is the translation of the red line 3 units to the right and 5 units upward.

Answer:

its A

Step-by-step explanation:

i know things...

Answer:

One isosceles triangle

Step-by-step explanation:

Try this option (see the attachment, the answers are marked by red colour), note, the value of the left angle in not visible (task no. 3) >> solution not given.

The variation statement tells you that when the radius is multiplied by 5, the volume is multiplied by 5² = 25. When the height is multiplied by 1/2, the volume is multiplied by 1/2.

Both of these variations together will multiply the volume by 25·(1/2) = 25/2.

So, the revised volume is (2π in³)·25/2 = 25π in³.

option E) 30 is the answer for the square root of 75 times the square root of 12

We start by using the property of square roots that states the product of two square roots is the square root of the product of the numbers. This gives us:

[tex]\sqrt{75} \times \sqrt{12} = \sqrt {75 \times 12}[/tex]

Now we can simplify the expression by finding the product of 75 and 12. This gives us:

[tex]\sqrt {75 \times 12} = \sqrt{900} = 30[/tex]

Thus, the square root of 75 times the square root of 12 gives 30 as the answer. So, option E) 30 is the correct answer.

Correct question:

The square root of 75 times the square root of 12.

A. the square root of 63

B. 3 times the square root of 7

C. 3 times the square root of 3

D. 8 times the square root of 3

E. 30

Answer:

B. x = 5 and y = -13

Step-by-step explanation:

Subtract the constant on the left:

... (x +yi) = (9 -4i) -(4 +9i)

... = (9 -4 +i(-4-9))

... = 5 -13i

Matching real and imaginary parts, we see that ...

... x = 5, y = -13

Answer:

The first answer is that x = 3. The second is that x = 6.

Step-by-step explanation:

To find either of these, we need to follow the order of operations.

2 + x = 5 ----> Subtract 2 from both sides

x = 3

2(4x - 8) = 32 ----> Distribute

8x - 16 = 32 -----> Add 16 to both sides

8x = 48 -----> Divide both sides by 8

x = 6