3a + 3b is equivalent to 3(a + 2b).
A true
B false

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

Answer:

-60

Step-by-step explanation:

1/4w + 5 = w/3 + 10

Collect like terms

1/4 w - 1/3 w = 10 - 5

Find lcm of 4 &3 = 12 and subtract

-1/12 w = 5

Multiply both sides by 12

-w = 5 x 12

-.w = 60

Divide both sides by -1

w = -60

I hope this was helpful, Please mark as brainliest

Answer:

D.

the addition property of equality

Step-by-step explanation:

Given the expression in

Step 2: 9d - 5 = -15

The addition property of equality was used to get step 3.

That is

9d - 5 = -15

Move -5 over the equality sign and it becomes +5

9d = -15 + 5

9d = -10

OR add 5 to both sides of the equation as shown below

9d - 5 +5 = -15 + 5

9d = -10 which we have in step 3

The justification for step 3 is the subtraction property of equality, which allows us to subtract the same number from both sides of an equation to maintain its balance.

The correct answer is A: the subtraction property of equality.

Here is why: In the step before (step 2), we have 9d - 5 = -15. When we move to step 3, we're solving 9d = -10 which means we added 5 to both sides of the equation. By doing so, we subtract 5 from the left side to get 9d and add 5 to -15 on the right side to get -10. This action is consistent with the subtraction property of equality, which states that you can subtract the same number from both sides of an equation and the equation will still hold true.

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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]

Answer:

It certainly doesn't make sense. Her equation means

5 times some number is 25.

hope it helps!

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).

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:

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

Answer:

  linear inequality (not a function)

Step-by-step explanation:

The given inequality is linear in the variables x and y. It maps x to an infinite number of possible values for y, so the relation is not a function.

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

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

Answer:

1

Step-by-step explanation:

(12 - 4) - (6 / 2) - (2 * 2)

(8) - (3) - (4)

1

Answer:

1

Step-by-step explanation:

go to google calculator

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

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:

Option D. y=4x+35

Step-by-step explanation:

From the graph take the points (5,50) and (50,250)

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{250-50}{50-5}[/tex]

[tex]m=\frac{200}{45}=4.4[/tex]

Find the equation of the line in slope intercept form

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

we have

[tex]m=4.4\\point\ (5,50)[/tex]

substitute

[tex]50=4.4(5)+b[/tex]

solve for b

[tex]b=50-22\\b=28[/tex]

substitute

[tex]y=4.4x+28[/tex]

therefore

The equation that BEST models the data is

[tex]y=4x+35[/tex]

Answer:

47,754,000

Step-by-step explanation:

4 is located at thousand (place)

Answer:

b

Step-by-step explanation:

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

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]

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.

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:

Step-by-step explanation:

6x ≤ -18.....divide both sides by 6

x ≤ -18 / 6

x ≤ -3

ok...so ur gonna have a closed circle because the inequality contains an equal sign......ur gonna put that closed circle on -3 and shading will go to the left because it is less then

closed circle on -3, shaded to the left <==

Answer:

closed circle on -3 and shaded to the left

Hope it Helped <3

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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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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Keywords : slope, line, passes

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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].

For more details, refer to the link:

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Answer:

Y=X

Step-by-step explanation:

Answer:

8x + 5

Step-by-step explanation:

By adding

2x + 6 + 6x -1

8x + 5

Answer:

The answer is D

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

False

True

False

False

Step-by-step explanation:

1. We have to get the sum as follows :

[tex]3\frac{4}{9} + 4\frac{6}{9}[/tex]

= [tex]\frac{31}{9} + \frac{42}{9}[/tex]

= [tex]\frac{31 + 42}{9}[/tex]

= [tex]\frac{73}{9}[/tex]

= [tex]8\frac{1}{9} \neq 7\frac{1}{9}[/tex]

So, this is false.

2. We have to get the sum as follows :

[tex]4\frac{5}{6} + 1\frac{3}{6}[/tex]

= [tex]\frac{29}{6} + \frac{9}{6}[/tex]

= [tex]\frac{29 + 9}{6}[/tex]

= [tex]\frac{38}{6}[/tex]

= [tex]6\frac{2}{6}[/tex]

So, this is true.

3. We have to get the difference as follows :

[tex]4\frac{5}{8} - 2\frac{4}{8}[/tex]

= [tex]\frac{37}{8} - \frac{20}{8}[/tex]

= [tex]\frac{37 - 20}{8}[/tex]

= [tex]\frac{17}{8}[/tex]

= [tex]2\frac{1}{8} \neq 2\frac{3}{8}[/tex]

So, this is false.

4. We have to get the difference as follows :

[tex]7\frac{5}{8} - 4\frac{2}{8}[/tex]

= [tex]\frac{61}{8} - \frac{34}{8}[/tex]

= [tex]\frac{61 - 34}{8}[/tex]

= [tex]\frac{27}{8}[/tex]

= [tex]3\frac{3}{8} \neq 3[/tex]

So, this is also false. (Answer)

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:

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.