The line segments are translated 2 units to the left to form J′K′ and M′N′. Which statement describes J′K′ and M′N′?

Answer:

D. [tex]\angle AOB[/tex]

Step-by-step explanation:

Since we know that complementary angles add up-to 90 degrees.

We can see from our given diagram that angle EOA and angle EOC is a linear pair of angles. The measure of angle EOA is 90 degrees, so EOC will be 90 degrees as well (Linear pair of angles must add up to 180 degrees).

We can also see that [tex]\angle EOC=\angle EOD+\angle COD[/tex].

Upon substituting value of angle EOC we will get,

[tex]90^o=\angle EOD+\angle COD[/tex]

We can see from our given diagram that angle COD and angle AOB are vertical angles.

[tex]\angle COD=\angle AOB[/tex]

Since vertical angles are equal, so by substitution property of equality we will get,

[tex]90^o=\angle EOD+\angle AOB[/tex]

Therefore, [tex]\angle AOB[/tex] is complementary to  [tex]\angle EOD[/tex] and option D is the correct choice.

Final answer:

To find the constant of proportionality k when y varies directly as x^2, given that x=2 and y=8, set up the equation y = k × x^2 and solve for k, resulting in k = 2.

Explanation:

If y varies directly as x2, it means that y is equal to k times x2, where k is the constant of proportionality. To find k when x is 2 and y is 8, we set up the following equation based on the definition of direct variation:

y = k × x^2

Substitute the given values into the equation:

8 = k × (2^2)

Solve for k:

8 = k × 4

k = 8 / 4

k = 2

Thus, the constant of proportionality, k, is equal to 2 when x is 2 and y is 8.

Answer:

B. Multiply by 2; 64, 128.

A) 265,000* 1.023 = $271,095

B) 42,000,000*0.06 = 2,520,000*0.20 = $504,000

C) 504000 - 468000 = 36000/504000 = 0.0714 = 7.1%

Answer:  The correct option is

(C) [tex]4x^2+2x+6.[/tex]

Step-by-step explanation:  We are given the functions f(x) and g(x) as follows :

[tex]f(x)=2x+6,\\\\g(x)=4x^2.[/tex]

We are to find the value of (f+g)(x).

We know that

for any two functions p(x) and q(x), we have

[tex](p+q)(x)=p(x)+q(x).[/tex]

So, we get

[tex](f+g)(x)\\\\=f(x)+g(x)\\\\=2x+6+4x^2\\\\=4x^2+2x+6.[/tex]

Thus, the required value is [tex](4x^2+2x+6).[/tex]

Option (C) is CORRECT.

To avoid getting a flat tire, one should maintain correct tire pressure, avoid sharp objects on the road, inspect the tires frequently, and consider using tire liners or puncture-resistant tires.

To avoid getting a flat tire on a bicycle, regular maintenance is important. This includes checking the tire pressure routinely, which should be ideally conducted every few weeks. Correct tire pressure prevents the tires from getting punctured easily. It's also essential to avoid sharp objects on the road, as these can cause punctures. Regularly inspecting the tires for small cuts and objects stuck into them can also help prevent a flat tire. Lastly, using tire liners or puncture-resistant tires can further protect your tires from getting flat.

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Final answer:

The two solutions of the quadratic equation 2x squared + 1 = 5x are j = 1 and k = 1/2. The value of (j-1)(1-k) with these solutions is 0.

Explanation:

To solve the equation 2x squared + 1 = 5x, we first bring all terms to one side to get a quadratic equation:

2x2 - 5x + 1 = 0
Using the quadratic formula, x = [-b ± √(b2 - 4ac)]/(2a), where a = 2, b = -5, and c = 1, we find that the two solutions (j and k) of the equation are j = 1 and k = 1/2.

The value of (j-1)(1-k) with these values is:
(j - 1)(1 - k) = (1 - 1)(1 - 1/2) = (0)(1/2) = 0
Therefore, the value of (j-1)(1-k) is 0.

Answer:

The value of the equation for n is [tex]n=\frac{d +2}{4}[/tex].

Step-by-step explanation:

Consider the provided equation.

[tex]d = 4n - 2[/tex]

We need to solve the equation for n.

Add 2 from both the sides.

[tex]d +2= 4n - 2+2[/tex]

[tex]d +2= 4n [/tex]

Divide both side of the equation with 4.

[tex]\frac{d +2}{4}= \frac{4n}{4} [/tex]

[tex]\frac{d +2}{4}= n [/tex]

Hence, the value of the equation for n is [tex]n=\frac{d +2}{4}[/tex].

"Cary is 8 years older than Dan. In 5 years the sum of their ages wil equal 96. Find both their ages now. Solve using equations." 

x = Dan's age now
x + 8 = Cary's age now {Cary is 8 yrs older than Dan} 

x + 5 = Dan's age in 5 years
x + 13 = Cary's age in 5 years 

x + 5 + x + 13 = 96 {in five years the sum of their ages will be 96}
2x + 18 = 96 {combined like terms}
2x = 78 {subtracted 18 from both sides}
x = 39 {divided both sides by 39}
x + 8 = 47 {substituted 39, in for x, into x + 8} 

Dan is 39 years old
Cary is 47 years old

Solution 1:

If |a| = |b|, then either a = b or a = -b. Hence, if |2x - 1| = |3x + 5|, then either 2x - 1 = 3x + 5 or 2x - 1 = -(3x + 5).

If 2x - 1 = 3x + 5, then x = -6. If 2x - 1 = -(3x + 5), then x = -4/5. Therefore, the solutions are x = \boxed{-6, -4/5}.

Solution 2:

Another approach is to square both sides. Squaring both sides, we get 4x^2 - 4x + 1 = 9x^2 + 30x + 25 (because |a|^2 = a^2 for all a). This simplifies to 5x^2 + 34x + 24 = 0, which factors as (x + 6)(5x + 4) = 0, so the solutions are x = -6 and x = -4/5, as before. You must be careful when using this approach because squaring both sides of an equation can introduce false solutions. Thus, we need to check that both of these "solutions" work in the original expression before declaring them correct.

let x = angle

x = 1/2(90-x)

2x = 90-x

3x=90

x = 90/3 = 30

x = 30 degrees

The pulse corresponding to one pixel is approximately 1.27 microseconds.

In this case, we can calculate the duration of the pulse corresponding to one pixel by dividing the time required to redraw the display by the total number of pixels.

Given that the display is redrawn 75 times a second, and the display has a resolution of 1024x768 pixels, the total number of pixels is 1024 * 768 = 786,432 pixels.

To find the duration of the pulse corresponding to one pixel, we can divide the time required to redraw the display (1/75 seconds) by the total number of pixels (786,432 pixels).

Therefore, the pulse corresponding to one pixel is approximately 1.27 microseconds.

The recursive formula that could be used for measuring the total amount of money is f(n+1)=f(n)+20.

Given that,

Based on the above information, we can see that there are 20 increments in every next number.

So, the equation should be f(n+1)=f(n)+20

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1. 10 cm

2. 15 mm

3. 2 cm

Hope this helps even though it's pretty late!

Answer:

$166.50

Step-by-step explanation: