What is an equivalent expression for 1.5(3x + 4) +0.25(6x + 8)?
(25 points)

The equation of the line of reflection should be [tex]y=x[/tex].

Given information:

Triangle ABC has points (6, 3.7), (5.4, 2), (1, 3). Triangle A' B'C' has points (3.7, 6), (2, 5.4), (3, 1).

A'B'C' is the reflection of the triangle ABC.

It is required to find the equation of the line of reflection.

Now, from the given coordinates of triangle ABC and its reflection, it is clear that the x and y-coordinates have interchanged their values. For example, coordinate (6,3.7) has become (3.7,6).

Therefore, the equation of the line of reflection should be [tex]y=x[/tex].

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Answer:

Y=X

Step-by-step explanation:

See the graphs

First Case:

Here we have the following function:

[tex]h(x)=2sin(2x)-3[/tex]

In order to graph this function, first let's take:

[tex]f(x)=sin(x)[/tex]

Step 1. Compress horizontally this function by 1/2, so it becomes:

[tex]f_{1}(x)=sin(2x)[/tex]

Step 2. Stretch vertically this function, so it becomes:

[tex]f_{2}(x)=2sin(2x)[/tex]

Step 3. Shift the graph of the function three units down.

[tex]f_{2}(x)=2sin(2x)-3[/tex]

Second Case:

Applying a similar method, we get:

Step 1. Compress horizontally this function by 1/2, so it becomes:

Step 2. Stretch vertically this function, so it becomes:

Step 3. Shift the graph of the function tow units down.

Finally, the graphs are shown below.

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Answer:

[tex]x<5[/tex]

Step-by-step explanation:

we have

[tex]-7x+14>-3x-6[/tex]

Solve for x

Group terms that contain the same variable

[tex]-7x+3x>-6-14[/tex]

[tex]-4x>-20[/tex]

Divide by -4 both sides

Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol  

so

[tex]x<5[/tex]

The solution is the interval (-∞,5)

All real numbers less than 5

In a number line the solution is the shaded area at left of x=5 (open circle)

The value of x=5 is not included in the solution

The unknown resistance is approximately 0.44 Ω.

Solution:

Total (equivalent) resistance = 0.28 Ω

Resistance 1 = ?

Resistance 2 = 0.81 Ω

To find the unknown resistance.

Formula for determining equivalent resistance in a parallel circuit:

[tex]$\frac{1}{R_{e q}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}[/tex]

Substitute the given values in the formula.

[tex]$\frac{1}{0.28}=\frac{1}{R_{1}}+\frac{1}{0.81}[/tex]

[tex]$3.571=\frac{1}{R_{1}}+1.235[/tex]

Subtract 1.235 on both sides of the equation, we get

[tex]$2.282=\frac{1}{R_{1}}[/tex]

Take reciprocal to find [tex]R_1[/tex].

[tex]$R_{1}=\frac{1}{2.282}[/tex]

[tex]$R_{1}=0.44[/tex]

[tex]R_1[/tex] = 0.44 Ω

The unknown resistance is approximately 0.44 Ω.

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

Define the three sides to be a,b,c such that a < b < c

So c is the longest side, and 'a' is the shortest with b in the middle.

"longest side is 4 ft shorter than twice the shortest side" means that c = 2a-4

"third side is 3 ft longer than the shortest side" so b = a+3

Both b and c are in terms of 'a', allowing us to do substitutions like so

a+b+c = perimeter

a+b+c = 59

a+(a+3)+c = 59 .... first substitution, plug in b = a+3

a+(a+3)+(2a-4) = 59 ... second substitution, plug in c = 2a-4

4a-1 = 59 .... combine like terms

4a = 59+1 ... add 1 to both sides

4a = 60

a = 60/4 ... divide both sides by 4

a = 15

The shortest side is 15 ft

b = a+3 = 15+3 = 18

The middle side is 18 ft

c = 2a-4 = 2*15-4 = 26

The longest side is 26 ft

---------------------

Check:

The three sides should add up to a perimeter of 59 ft

a+b+c = 15+18+26 = 59

so the answer is confirmed

Answer:

[tex]Leg_1 = 15\\Leg_2 = 26\\Leg_3 = 18[/tex]

Step-by-step explanation:

Form an equation.

[tex](x)+(2x-4)+(x+3)=59[/tex]

Combine like terms.

[tex]4x-1=59[/tex]

Add 1 to both sides, then divide both sides by 4.

[tex]4x=60\\\\\frac{4x}{4}=\frac{60}{4}\\\\x = 15[/tex]

Plugin in 15 for x

[tex]Leg_1 = 15\\Leg_2 = 2(15)-4=26\\Leg_3 = 15 + 3=18[/tex]

Answer:

The answer is D

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

180cm

Step-by-step explanation:

Vol of sphere = (4/3) pi r^3 and vol of cylinder = pi r^2 h

so

(4/3) pi 15^3 = pi (5)^2 h

(4/3) * 15^3 = 25h

h =  [(4/3) * 15^3 ] / 25  =  180 cm

Step-by-step explanation:

according to the question,

vol.of sphere = vol of cylinder

4/3πR³=πr²h

refer to the attached file.

thanks for the question!!

Step-by-step explanation:

Total Distance run by Katrina

[tex]=6 \times circumference \: of \: circular \: track \\ \\ = 6 \times 2 \pi \: r \\ = 6 \times 2 \times 3.14 \times 20 \\ = 240 \times 3.14 \\ = 753.6 \: m \\ [/tex]

Midpoint of AC = (–1, –1)

Solution:

In the given graph we can find the coordinates of A and C.

Coordinates of A = (–4, 2)

Coordinates of C = (2, –4)

Here, [tex]x_1=-4,x_2=2,y_1=2,y_2=-4[/tex]

Let us find the midpoint of the segment AC.

Midpoint formula:

[tex]$\text{Midpoint} =\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)[/tex]

               [tex]$=\left(\frac{-4+2}{2}, \frac{2-4}{2}\right)[/tex]

               [tex]$=\left(\frac{-2}{2}, \frac{-2}{2}\right)[/tex]

               [tex]$=(-1, -1)[/tex]

Midpoint of AC = (–1, –1)

Option D is the correct answer.

Hence the coordinates of the midpoint of the line segment AC is (–1, –1).

Answer:

8x + 5

Step-by-step explanation:

By adding

2x + 6 + 6x -1

8x + 5

Answer:change in y) / (change in x)

More formally, if a line passes through two points (x1,y1) and (x2,y2), then the slope m of the line is given by the formula:

m=y2−y1x2−x1

In the case of the points (4,9) and (1,6), we get:

m=6−91−4=−3−3=1

Step-by-step explanation:

Answer:

slope = 3

Step-by-step explanation:

Graph

To find the proportion of trick-or-treaters not dressed as knights, subtract the proportion dressed as knights from 1. Therefore, the proportion of trick-or-treaters not dressed as knights is 7/13.

To find the proportion of trick-or-treaters that were not dressed as knights, we need to subtract the proportion of trick-or-treaters who were dressed as knights from 1. If 6 out of every 13 trick-or-treaters were dressed as knights, then the proportion of trick-or-treaters not dressed as knights is 1 - (6/13) = 7/13.

In the realm of probability and proportions, calculating the proportion of trick-or-treaters not adorned in knightly attire involves a straightforward yet insightful approach. We initiate this quest by recognizing that the sum of all probabilities within a given context equals 1, which encapsulates all possible outcomes. Since we know that 6 out of every 13 trick-or-treaters don the guise of knights, we can deduce that the proportion of those not dressed as knights is the remainder of this whole, represented as 1 - (6/13). Simplifying this expression reveals that 7 out of every 13 trick-or-treaters fall into the category of not being attired as knights.

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Answer:

B = (x + 7)^2 + (y +3)^2 = 4

Step-by-step explanation:

The equation of a circle with center (-7, -3) and radius 2 is (x + 7)² + (y + 3)² = 4.

The equation of a circle with a center at point (-7, -3) and a radius of 2 can be written based on the standard form of the circle equation (x - h)² + (y - k)² = r², where (h,k) is the center of the circle and r is the radius.

Plugging in the values given in the question, the equation simplifies to: (x + 7)² + (y + 3)² = 4.

Answer:

1. a) $ 25

b) $65

2) a) 246,000 followers

b) In 20 years

3a) $65

b) $85.25

Step-by-step explanation:

1. A linear equation is modeled by [tex]y=mx+b[/tex]

where b is the one time fee you pay and m=$8 is how much you pay per hour.

y is the total cost and x is the number of hours.

Hence the equation becomes: [tex]y=8x+b[/tex]

Since Jill rented for 3 hours and paid $49, x=3 and y=49.

We substitute and solve for the one-time fee, b.

This implies that:

[tex]49=8(3)+b[/tex]

49=24+b

b=49-24=25.

a) The fee is $25

b) We now write the equation in full to get: [tex]y=8x+25[/tex]

To find the cost for 5 hours we put x=5 into this equation and solve for y.

[tex]y=8(5)+25[/tex]

y=40+25=$65

2a) We still use the equation y=mx+b.

b is the number of followers he started with.

This time m=-12,000 because he is losing followers at the rate of 12,000

The equation becomes: y=-12,000x+b

After 4 years he was down to 198,000.

This implies that, when x=4,y=198,000

We substitute to get:

[tex]198,000=-12,000(4)+b[/tex]

[tex]198,000=-48,000+b[/tex]

[tex]b=198,000+48,000=246,000[/tex]

Hence he started with 246,000 customers

b) The equation now becomes [tex]y=-12,000x+246,000[/tex]

To find how many years he will have 6000 followers, we substitute y=6000 and solve for x.

[tex]6000=-12,000x+246,000[/tex]

[tex]6000-246,000=-12,000x[/tex]

[tex]-240,000=-12,000x[/tex]

[tex]x=\frac{240,000}{12,000}[/tex]

x=20.

3. We still use the equation: y=mx+b.

This time m=0.25 is the rate per mile.

This implies y=0.25x+b

Since Kyle drove 32 miles and spent $73, we have y=73 when x=32

We substitute these values and solve for x.

[tex]73=0.25(32)+b[/tex]

[tex]73=8+b[/tex]

[tex]b=73-8[/tex]

[tex]b=65[/tex]

Hence the one-time fee is $65

b) The equation now becomes:

[tex]y=0.25x+65[/tex]

To find how much it will cost to drive 81 miles, we substitute x=81 and solve for y.

[tex]y=0.25*81+65[/tex]

[tex]y=20.25+65[/tex]

[tex]y=85.25[/tex]

The cost for 81 miles is $85.25

The planes are 618.75 miles from starting point

Solution:

Let t is the travel time of the jet

Then  (t + 3) is the travel time of the propellar

When the jet overtakes the propellar, they will traveled the same distance

Distance is given as:

[tex]Distance = speed \times time[/tex]

A jet plane traveling at 550 mph

[tex]Distance\ by\ jet = 550 \times t\\\\Distance\ by\ jet = 550t[/tex]

propeller plane traveling at 150 mph

[tex]Distance\ by\ propellar = 150 \times (t+3)[/tex]

Equate both distance

[tex]550t = 150(t+3)\\\\550t = 150t + 450\\\\550t - 150t = 450\\\\400t = 450\\\\t = \frac{450}{400}\\\\t = 1.125[/tex]

[tex]Distance = 550 \times t = 550 \times 1.125\\\\Distance = 618.75[/tex]

Thus they are 618.75 miles from starting point

The distance both planes are from the starting point when the jet overtakes the propeller is 451.125 miles.

This question is a math problem involving relative speed and distance traveled. In this case, we are solving for the distance each plane has flown from their respective starting points once the jet plane overtakes the propeller plane.

To start, let's think of the problem in terms of a timeframe. We know the propeller plane had a 3-hour head start. Now, we need to determine how long it took for the jet plane to catch up to the propeller plane. To calculate this, we must find the difference in speed between the two planes (550 mph - 150 mph = 400 mph), and then divide the time difference (3 hours) by the relative speed (400 mph) which equals 0.0075 hours.

Next, we compute the distance covered by the propeller plane in 3.0075 hours (150 mpg * 3.0075 hours = 451.125 miles). Both planes are at this same distance from the starting point when the jet plane overtakes the propeller plane.

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Answer:

1. 8s-6

2. 13t-6

3. 32r

4. 5-4q+42r

5.no like terms

6. 107-106x

7. 16a2−15a

8. 28t

9. 4s+r+2rs

10. 7pt-3p+4t

11. 26x2−x

12. 107c

13. 16q+9

14. -23k

15. 151x

Step-by-step explanation:

Answer:3

Step-by-step explanation:

5,7,12

Answer: a=-5

Step-by-step explanation:

2(a + 3) = −4

2a+6=-4

2a=-10

a=-5

Answer:

Your answer is a= -5. So A would be your answer.

3 67/100

3 will stay a whole number so you put that as the whole number. 67 is 67 percent of a whole. so you put it over 100.

The solution is x = 2 and y = 4

Solution:

Given system of equations are:

y = 2x -------- eqn 1

x = -y + 6 ----------- eqn 2

We can solve the system of equations by substitution method

Substitute eqn 1 in eqn 2

x = -2x + 6

Move the variables to one side and constants to other side

x + 2x = 6

3x = 6

Divide both sides of equation by 3

x = 2

Substitute x = 2 in eqn 1

y = 2(2)

y = 4

Thus the solution is x = 2 and y = 4

Answer:

y = (2/3)x -3

Step-by-step explanation:

find the slope using ( y1 - y2 ) / ( x1 - x2)

slope: 2/3

y-intercept: -3

use y = mx + b

Answer:

d ≥ 13.46

Step-by-step explanation:

Chris has to pay low balance fee if her bank balance falls below $10.

Her balance was -$3.46 before the statement date.

Now, Chris has to deposit a minimum amount of $(3.46 + 10) = $13.46 to her bank account and then only she does not need to pay a fee.

If the deposit amount is d, then the inequality to represent the situation is

d ≥ 13.46 (Answer)

Final answer:

Chris needs to deposit at least $13.46 to prevent a bank fee because her balance was -$3.46. By adding $3.46 to the minimum required balance of $10, we determine the least deposit amount through the inequality d ≥ 13.46.

Explanation:

To solve the situation where Chris avoids a fee by making a deposit, d, we must write an inequality that reflects her balance being above $10 after the deposit. Originally, her balance was -$3.46. Therefore, after deposit d, her new balance must be equal to or greater than $10 to prevent the fee. The inequality representing this situation is:

d - 3.46 ≥ 10

When you add $3.46 to both sides to isolate d, the inequality becomes:

d ≥ 13.46

This inequality indicates that Chris's deposit must be at least $13.46 to avoid the bank fee.

2/9

Step-by-step explanation:

Slope in calculated as the ratio of change in y values divided by the change in x values

slope, m=Δy/Δx

Δy=8-6=2

Δx=6--3=9

m=2/9

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Step-by-step explanation: Begin by studying the pattern.

Notice that the 1 + 1 is 2, 2 + 3 is 5, 5 + 5 is 10, and 10 + 7 is 17.

So thus far, we're adding 1, 3, 5, and 7. Notice that each of these numbers have a difference of 2 so we would add 9 to get to next number and so on.

Answer:

Step-by-step explanation:

x = small barrettes

y = large barrettes

13x + 11y = 142.......multiply by -1

13x + 12y = 149

-----------------------

-13x - 11y = -142 (result of multiplying by -1)

13x + 12y = 149

------------------------add

y = 7..........large barrettes used 7 yards

13x + 11y = 142

13x + 11(7) = 142

13x + 77 = 142

13x = 142 - 77

13x = 65

x = 65/13

x = 5........small barrettes used 5 yards

Final answer:

Kimberly uses 5 yards of ribbon for each small barrette and 7 yards of ribbon for each large barrette. The problem was solved using a system of equations and the elimination method.

Explanation:

To solve the problem using a system of equations and the elimination method, we first need to define variables for the unknown quantities we are trying to find. Let's let x represent the number of yards of ribbon used for each small barrette and y represent the number of yards of ribbon used for each large barrette.

From the information given, we can set up the following system of equations representing the two craft fairs:

For Rockport: 13x + 11y = 142

For Westminster: 13x + 12y = 149

Now, we will solve these equations using the elimination method. To eliminate one of the variables, we can subtract the first equation from the second equation.

13x + 12y - (13x + 11y) = 149 - 142This simplifies to:

y = 7

Using the value of y, we can substitute it back into either equation to find x. Plugging it into the first equation:

13x + 11(7) = 142

13x + 77 = 142

13x = 142 - 77

13x = 65

x = 65 / 13

x = 5

Therefore, Kimberly uses 5 yards of ribbon for each small barrette and 7 yards of ribbon for each large barrette.

Answer:

47,754,000

Step-by-step explanation:

4 is located at thousand (place)

Answer:

b

Step-by-step explanation:

Answer:

x=-2, y=-3. (-2, -3).

Step-by-step explanation:

y=8x+13

-4x-5y=23

----------------

-4x-5(8x+13)=23

-4x-40x-65=23

-44x-65=23

-44x=23+65

-44x=88

x=88/-44

x=-2

y=8(-2)+13=-16+13=-3

Final answer:

The constant of proportionality is $0.833 per package, and the equation representing the cost C of sending p packages is C = 0.833p.

Explanation:

To find the constant of proportionality for the given shipping situation, we divide the total cost by the number of packages shipped. In this case, it costs $5 to send 6 packages, which gives us a constant of proportionality of $5 / 6 packages. This can be simplified to approximately $0.833 per package.

The equation to represent this relationship would be C = 0.833p, where C represents the total cost in dollars and p represents the number of packages. This shows that for each package sent, the cost will increase by approximately $0.833.

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

Work Shown:

x - 3.4 > 17/68

x - 3.4 > 0.25

x - 3.4 + 3.4 > 0.25 + 3.4 .... add 3.4 to both sides

x > 3.65

Any number larger than 3.65 will work in place of x

Choice A does not work since 3.4 is not larger than 3.65

Choice B and choice C is the same story as well since 21/68 = 0.3088 approximately

Only choice D is larger than 3.65