The graphs below hace the same shape. What is the equation of the blue graph?

[tex]\bf 2y=-6x+8\implies y=\cfrac{-6x+8}{2}\implies y=\cfrac{-6x}{2}+\cfrac{8}{2} \\\\\\ y=-3x+4\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-3\implies -\cfrac{3}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{1}{3}}\qquad \stackrel{negative~reciprocal}{+\cfrac{1}{3}\implies \cfrac{1}{3}}}[/tex]

[tex]\bf \begin{cases} \boxed{y}=\log(2x+1)\\ y=3x-2 \end{cases}\qquad \stackrel{\textit{doing substitution on the 2nd equation}}{\boxed{\log(2x+1)}=3x-2}[/tex]

a quick note, I must say that writing y₁ and y₂ is a bit misleading, since it makes it appear as if they're two different variables, when they're the same one.

Answer:

B

Step-by-step explanation:

B) y1=log(2x+1), y2=3x-2

Answer:

P = (8, 0) and Q = (0, 6)

Step-by-step explanation:

To find where the line crosses the x- axis, substitute y = 0 into the equation and solve for x

3x + 4(0) = 24

3x = 24 ( divide both sides by 3 )

x = 8 ⇒ P = 8 ⇒ (8, 0 )

To find where the line crosses the y- axis substitute x = 0 into the equation and solve for y

3(0) + 4y = 24

4y = 24 ( divide both sides by 4 )

y = 6 ⇒ Q = 6 ⇒ (0, 6 )

Answer:

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

Step-by-step explanation:

[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=\dfrac{x}{2}-2=\dfrac{1}{2}x-2\\\\g(x)=2x^2+x-3\\\\(f+g)(x)=\left(\dfrac{1}{2}x-2\right)+(2x^2+x-3)\\\\=\dfrac{1}{2}x-2+2x^2+x-3\qquad\text{combine like terms}\\\\=2x^2+\left(\dfrac{1}{2}x+x\right)+(-2-3)\\\\=2x^2+1\dfrac{1}{2}x-5\\\\=2x^2+\dfrac{3}{2}x-5[/tex]

Answer:

Step-by-step explanation:

2.5, 3.8

To determine the time(s) when the ball is at a height of 150ft, we can substitute h = 150 and solve the quadratic equation -16t^2 + 100t = 150. By using the quadratic formula, we find two possible values for t: t = 3.75 seconds and t = 2.5 seconds.

The equation given in the question is h = -16t2 + v0t, where h is the height, t is the time, and v0 is the initial velocity. To determine the time(s) when the ball is at a height of 150ft, we can substitute h = 150 and solve for t.

150 = -16t2 + 100t

Rearranging the equation, we get 16t2 - 100t + 150 = 0. This is a quadratic equation which can be solved using the quadratic formula.

The quadratic formula is t = (-b ± √(b2 - 4ac)) / (2a). In this equation, a = 16, b = -100, and c = 150.

Plugging in these values, we get t = (100 ± √(1002 - 4 * 16 * 150)) / (2 * 16).

Simplifying further, we have t = (100 ± √(10000 - 9600)) / 32.

This simplifies to t = (100 ± √400) / 32.

Taking the square root, we get t = (100 ± 20) / 32.

This gives us two possible values for t: t = (100 + 20) / 32 = 120/32 = 3.75 and t = (100 - 20) / 32 = 80/32 = 2.5.

Therefore, the ball is at a height of 150ft at two times: t = 3.75 seconds and t = 2.5 seconds.

Answer:

1.) 2

Step-by-step explanation:

We have points (3,3) and (5,7) on the line.

Slope of a line = change in y ÷ change in x

i.e Slope = [tex]\frac{7 - 3}{5 - 3}[/tex] = 2

The slope of the line passing through the points (3, 3) and (5, 7) is 2. Therefore, the correct answer is option 1.

The given coordinate points are (3, 3) and (5, 7).

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

Here, slope = (7-3)/(5-3)

= 4/2

= 2

So, the slope is 2.

Therefore, the correct answer is option 1.

To learn more about the slope of a line visit:

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Hello There!

32% of 300 is 96

Work shown in image attached.

Answer:

96

Step-by-step explanation:

To get the solution, we are looking for, we need to point out what we know.

1. We assume, that the number 300 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 300 is 100%, so we can write it down as 300=100%.

4. We know, that x is 32% of the output value, so we can write it down as x=32%.

5. Now we have two simple equations:

1) 300=100%

2) x=32%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

300/x=100%/32%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 32% of 300

300/x=100/32

(300/x)*x=(100/32)*x       - we multiply both sides of the equation by x

300=3.125*x       - we divide both sides of the equation by (3.125) to get x

300/3.125=x

96=x

x=96

now we have:

32% of 300=96

[tex]|\Omega|=20+16+4=40\\|A|16+4=20\\\\P(A)=\dfrac{20}{40}=\dfrac{1}{2}[/tex]

Answer:

1/2

Step-by-step explanation:

16+4 =20 red and white marbles

40 marbles in all

20/40= 1/2

Answer:

minimum value of 7

Step-by-step explanation:

It is open up so it has a minimum

The minimum value is the lowest y

So we first must find the x that the point happens at which is -b/(2a)

So -(-8)/(2*1)=8/2=4

Now to find the y use y=x^2-8x+23

y=4^2-8(4)+23

y=16-32+23

y=-16+23

y=7  (lowest y-minimum value is 7)

Answer:

(1/6)^3 = 1/216, these events are independent.

Step-by-step explanation:

What happens in one roll has no effect on the other rolls, so these events are independent. The probility of any roll outcome is 1/6 since there are 6 sides. Since you want to roll a 6 AND a 5 AND a 4 you have to multiply the probabilities.

Answer:

[tex]\large\boxed{\dfrac{9}{12}\neq\dfrac{5}{20}\ \text{and}\ \dfrac{9}{12}\neq\dfrac{16}{24}}[/tex]

Step-by-step explanation:

[tex]\dfrac{9}{12}=\dfrac{9:3}{12:3}=\dfrac{3}{4}\\\\\dfrac{24}{32}=\dfrac{24:8}{32:8}=\dfrac{3}{4}\\\\\dfrac{6}{8}=\dfrac{6:2}{8:2}=\dfrac{3}{4}\\\\\dfrac{5}{20}=\dfrac{5:5}{20:5}=\dfrac{1}{4}\\\\\dfrac{16}{24}=\dfrac{16:8}{24:8}=\dfrac{2}{3}[/tex]

Answer:

6/8

Step-by-step explanation:

Units are written in bracelets.

[tex]F=ma \: \{kg\cdot\dfrac{m}{s^2}\}[/tex]

[tex]F=ma \: \{\boxed{\dfrac{kg\cdot m}{s^2}}=N\}[/tex]

Hope this helps.

r3t40

Answer:

Step-by-step explanation:

Force is defined as a function of mass (denoted by m) and acceleration (denoted by a) using this formula F=ma

units for mass m is kg

units for acceleration is metre/sec^2

Hence together we can write unit as

unit for force = [tex]Kg m/sec^2[/tex]

This can also be expressed as newtons

Unit for force = newtons also.

Answer:

z = 110°

Step-by-step explanation:

Since the figures are similar, then corresponding angles are congruent, thus

∠H = ∠D, that is

z = 110°

Since the figures are similar, then corresponding angles are congruent, thus

ABCD ~ EFGH

∠H = ∠D, that is

z = 110°.

Two angles in one triangle are equal to two angles in another triangle, then the triangles are similar

Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles. They are seen everywhere, for example, in equilateral triangles, isosceles triangles, or when a transversal intersects two parallel lines

There are many theorems based on congruent angles. Using the congruent angles theorem we can easily find out whether two angles are congruent or not. Those theorems are listed below:

To learn more about the Congruent angle, refer

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Answer:

The rate of simple interest is 9%

Step-by-step explanation:

* Lets talk about the simple interest

- The simple Interest Equation (Principal + Interest)  is:

  A = P(1 + rt)  , Where

# A = Total amount (principal + interest)

# P = Principal amount

# I = Interest amount

# r = Rate of Interest per year in decimal r = R/100

# R = Rate of Interest per year as a percent R = r * 100

# t = Time period involved in months or years

- The rule of the simple interest is I = Prt

* lets solve the problem

- Charles deposited $12,000

∴ P = $12,000

- He withdrew $5,000 from his account after one year

- He receives a total amount of $9,340 after 3 years

∴ A = $9340 and t = 3

- Lets find the inetrest after 1 year

∵ I = Prt

∵ P = 12000

∵ t = 1

∴ I = 12000(r)(1) = 12000r

- Lets subtract the money that he withdrew

∵ He withdrew $5000

∵ He deposit at first 12000

∴ He has after the withdrew 12000 - 5000 = 7000

- The new P for the next 2 years is 7000

- This amount will take the same rate r for another two years

- The total money is $9340

∵ I = A - P

∵ A = 9340

∵ P = 7000

∴ The amount of interest = 9340 - 7000 = 2340

- The amount of interest after 3 years is 2340

- Lets find the amount of interest in the two years

∴ I = 7000(r × 2) = 14000r

- The amount of interest after the 3 years is the sum of the interest in

  the 1st year and the other 2 years

∴ 2340 = 14000r + 12000r

∴ 2340 = 26000r ⇒ divide both sides bu 2340

∴ r = 2340 ÷ 26000 = 0.09

∵ The rate R in percentage = r × 100

∴ R = 0.09 × 100 = 9%

∴ The rate of simple interest is 9%

Answer:

We can easily simplify the expression by using a computational tool

The expression is

"6 x squared minus 54 x plus 84 over quantity 8 x squared minus 40 x plus 48 divided by quantity x squared plus x minus "

Please, see attached images below, for a full explanation

The prime factorizations of the numbers are

[tex]110 = 2\times 5 \times 11,\quad 40= 2^3\times 5,\quad 120=2^3\times 3\times 5[/tex]

The greatest common factor is composed by all common primes, taken with the lowest exponent possible. In this case, it will be

[tex]2\times 5 = 10[/tex]

Hello There!

It could not be C because there corresponding angles could not be congruent.

It also could not be B all the sides are proportional to each other.

I don’t think it could be D because that’s similar as well.

The only option that makes sense is “C”

Answer:

[tex]\large\boxed{V=Bh,\ 26x=B(6.5)\to B=4x}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of cylinder:}\\\\V=Bh\\\\\text{We have}\ V=26x\ m^3\ \text{and}\ h=6.5\ m.\\\\\text{Substitute:}\\\\26x=B(6.5)\qquad\text{divide both sides by 6.5}\\\\\dfrac{26x}{6.5}=B\to B=4x[/tex]

4x-22=62+2x

4x-2x=62+22

2x=84

x=84/2= 42

x= 42 is the answer

[tex]x=42[/tex]

Move the variables to one side and the constants to the other. [tex]4x-2x=62+22[/tex]

Combine the variables. [tex]2x=62+22[/tex]

Combine the constants. [tex]2x=84[/tex]

Divide both sides by 2. [tex]x=42[/tex]

Answer:

x = k/-4

Step-by-step explanation:

Answer:I got it wrong the answer is actually x=-4/k

Step-by-step explanation:

Apex approved

Answer: You can use it because the value of the integers tell you where a point might be located.

Hope this helps!

Answer:

SA = 1099 square inches.

Step-by-step explanation:

Just plug into the formula

SA = 2pir^2 + 2pi r h where pi = 3.14, r = 5 and h = 30

SA = 2 (3.14) (5^2) + 2 (3.14)(5)(30)

SA = 157 + 942

SA = 1099 square inches.

Answer:

1099.56 or 1099.6 dependong on what you wanna round to

Step-by-step explanation:

2×pi×5^2+2×pi×5×30

Final answer:

By using the principle of inclusion-exclusion, we can find that 50 people have both a DVD player and a CD player in a group of 100 people.

Explanation:

To find out how many people have both a DVD player and a CD player, we can use the principle of inclusion-exclusion.

According to the problem, there are 100 people in the group. Out of these, 70 have a DVD player, 60 have a CD player, and 20 have neither.

We can begin by subtracting those who have neither from the total to find out how many people have at least one of the devices:

100 - 20 = 80 people have at least one device.

Now, if we add the number of people who have a DVD player to the number of people who have a CD player, we would double count those who have both. So, we subtract the total number who have at least one device from this sum:

70 (DVD owners) + 60 (CD owners) - 80 (at least one device) = 50 people who have both a DVD and CD player.

Answer with explanation:

1.→→→ 3x-5y=15------(1)

6 x-10 y=30----(2)

Line 2 =2 * Line 1

These two lines are coincident.

Dependent

2.→→→ -2 x+4 y=-6-------(1)

Dividing both sides by , 2 we get

-x+2y= -3-----------------(1)

x+6 y=3------------(2)

These two are distinct lines ,it means they have a common point of intersection.

Consistent, and Independent

3.→→→

x-4y = -12-----------------(1)

3x-12 y= -9--------------(2)

Equation (2)=3 * Equation (1)

These two lines are coincident.

Dependent

4.→→→

3 x+y=3------(1)

6x+2y=-4------(2)

Dividing both sides by ,2 we get

3 x+y= -2

Both lines have distinct y intercepts that is ,3 and -2,but coefficient of x and y are equal. So, they are parallel lines.

Inconsistent

1.→→→ 3x-5y=15------(1)

6 x-10 y=30----(2)

Line 2 =2 * Line 1

These two lines are coincident.

Dependent

2.→→→ -2 x+4 y=-6-------(1)

Dividing both sides by , 2 we get

-x+2y= -3-----------------(1)

x+6 y=3------------(2)

These two are distinct lines ,it means they have a common point of intersection.

Consistent, and Independent

3.→→→

x-4y = -12-----------------(1)

3x-12 y= -9--------------(2)

Equation (2)=3 * Equation (1)

These two lines are coincident.

Dependent

4.→→→

3 x+y=3------(1)

6x+2y=-4------(2)

Dividing both sides by ,2 we get

3 x+y= -2

Both lines have distinct y intercepts that is ,3 and -2,but coefficient of x and y are equal. So, they are parallel lines.

Find the ordered pairs for y = 2ˣ by substituting various values of x into the equation, calculate y, and list the pairs. These can then be plotted on a graph to show the exponential relationship.

To determine the ordered pairs for the given function y = 2ˣ, you will perform substitutions for x with various values and calculate the corresponding y values. Once this is done, you can plot these points on a graph to visualize the function.

Choose a range of x-values (for example, -3, -2, -1, 0, 1, 2, 3).

Calculate the corresponding y-values using the equation y = 2ˣ.

List the ordered pairs (x,y).

Plot each pair on a coordinate graph.

Connect the points to represent the exponential graph.

Remember, shifting an exponential graph parallel to the x-axis can be done by adjusting the exponent's value.

Final answer:

The labor charge for a car repair job that takes 3.5 hours is $267.50. The difference in labor charges between a job that takes 2.4 hours and one that takes 6.3 hours is $214.50. Choosing between two similarly priced used cars requires additional information beyond the asking price.

Explanation:

The question asks for different computations related to the costs of car maintenance and repairs. Here is a solution to one of the calculations:

Labor Charge Calculation

The independent variable is the number of hours worked, and the dependent variable is the total labor charge. The equation to represent this situation is:

Labor Charge = $75 + ($55 × number of hours)

The slope is $55 as it represents the increase in charge per hour, and the y-intercept is $75 since it's the flat fee charged regardless of the hours worked.

For a job taking 3.5 hours:

Labor Charge = $75 + ($55 × 3.5) = $75 + $192.50 = $267.50

Difference in labor costs for two jobs (2.4 and 6.3 hours):

Labor Charge for 2.4 hours = $75 + ($55 × 2.4) = $75 + $132 = $207

Labor Charge for 6.3 hours = $75 + ($55 × 6.3) = $75 + $346.50 = $421.50

Difference = $421.50 - $207 = $214.50

In the context of Marvin shopping for a used car, it is not possible to provide a suggestion on which car to buy (the $4,000 or the $4,600 one) without additional information. Factors such as overall condition, future maintenance costs, and personal budget would need to be considered.

Answer:

3a/4b and 9a/12b are equivalent

Step-by-step explanation:

3a/4b is multiplied by 3/3 to get 9a/12b

Answer:

equivilent

Step-by-step explanation:

it is equivalent because if divide 9a and 12b both by 3, it equals 3a/4b.  Both fractions have the same lowest common denominator.

Hope this helps!

Hello There!

First we have to see how much does Gigi earns per hour.

For gardening, we are going to divide.

65 ÷ 5 ≈ 13

Gigi earns $13 for gardening for only 1 hour.

Second, we have to see how much Gigi earns per hour for office work.

We will divide

90 ÷ 9 ≈ 10

Now, we can see that Gigi earned $3 more per hour for gardening than for office work.

Answer:

d= 9.032 units

Step-by-step explanation:

Given

[tex]Circumference = 28.36[/tex]

We will use the formula for circumference of a circle to find it's radius and then diameter will be found using radius.

So,

[tex]C=2\pi r\\Putting\ the\ value\ of\ \pi and \C\\28.36 = 2 * 3.14 *r\\28.36=6.28* r\\r=\frac{28.36}{6.28}\\ r=4.516\ units[/tex]

Now to find the diameter:

d = r*2

d = 4.516*2

d= 9.032 units

Answer:

The diameter of the circle is 9.03 units

Step-by-step explanation:

The formula for calculating the circumference of a circle is [tex]C=\pi d[/tex].

From the question, the diameter of the circle is 28.36 units.

Since the circumference is rounded to the nearest hundredth, we substitute [tex]\pi=3.14[/tex]  and [tex]C=28.36[/tex] into the formula and solve for d.

[tex]\implies 28.36=3.14d[/tex]

Divide both sides by 3.14

[tex]\implies \frac{28.36}{3.14}=\frac{3.14d}{3.14}[/tex]

[tex]\implies 9.03=d[/tex].

Hence the diameter of the circle is 9.03 units to the nearest hundredths

Answer:

your line goes through both (0,6) and (12,0)

Step-by-step explanation:

Ok so you are describing some lines you see I think:

I see some of these as points you mentioned:

(0,6)  ,  (0,-6)  , (6,0)

So let's see which of these work:

(0,6)?

2(0)+4(6)=24

        24=24

(0,6) does work!

The other point you have listed with (0,6) is (12,0).

Let's try (12,0)

2(12)+4(0)=24

24+0=24

24=24

(12,0) works!

So your line goes through both (0,6) and (12,0)

Answer:

The correct option is A) Line through the point (0,6) and (12,0).

Step-by-step explanation:

Consider the provided equation 2x + 4y = 24.

Substitute x = 0 in the provided equation.

2x + 4y = 24

2(0) + 4y = 24

4y = 24

y = 6

Thus, the points which satisfy the equation is (0,6).

Now, substitute x = 12 in the provided equation.

2x + 4y = 24

2(12) + 4y = 24

24 + 4y = 24

4y = 0

y = 0

Thus, the points which satisfy the equation is (12,0).

Therefore, the correct option is A) Line through the point (0,6) and (12,0).