Max rewrote the function f(x) = 4x² + 16x + 8 in vertex form by completing the square.

He concluded that the vertex is (-2, 4), which was incorrect. Consider Max's work, listed below.

In which step did Max make a mistake?

Step 1: f(x) = 4x² + 16x + 8

Step 2: f(x) = 4(x² + 4x) +8

Step 3: f(x) = 4(x² + 4x + 4) +8-4

Step 4: f(x) = 4(x + 2)² +4

Answer:

4(20+b)≤-17

Step-by-step explanation:

I hope this helps!

Answer:

$45

Step-by-step explanation:

The watch was sold on sale of 40%. This means that the price of the watch on sale is 60% of the original price. (100%-40%=60%)

So, you find the 60% of the original price, $75.

75*0.6=45

Hope that helps!!!

Answer:

Your answer is that X=1

Answer:

The answer is 1.

Step-by-step explanation:

12x-15-4x+1 = -6

8x = 8

Therefore x = 1

Answer:

PQ

Step-by-step explanation:

Parallel lines are a pair of lines in a plane that do not meet/intersect

Answer:

The cost of each kg of almonds is $1.75

The cost of each kg of jelly beans is $2.5

Step-by-step explanation:

We will use the system of linear equations to solve the question

Assume that the cost of 1 kg of almonds is $x, and the cost of 1 kg of jelly beans is $y

∵ For 2 kilograms of almonds and 3 kilograms of jelly beans,

   the total cost is $11

→ Multiply 2 by x and 3 by y, then equate their sum by 11

∴ 2x + 3y = 11 ⇒ (1)

∵ For 6 kilograms of almonds and 5 kilograms of jelly beans, the

   total cost is $23

→ Multiply 6 by x and 5 by y, then equate their sum by 23

∴ 6x + 5y = 23 ⇒ (2)

Now we need to solve this system of equations to find the values of x and y

→ Multiply equation (1) by -3 to make the coefficient of x in it equals

  the coefficient of x in equation (2) in values and differences in signs

∵ -3(2x) + -3(3y) = -3(11)

∴ -6x + -9y = -33 ⇒ (3)

→ Add equations (2) and (3) to eliminate x

∵ (6x + - 6x) + (5y - 9y) = (23 + -33)

∴ -4y = -10

→ Divide both side by -4 to find the value of y

∵  [tex]\frac{-4y}{-4}=\frac{-10}{-4}[/tex]

∴ y = 2.5

→ Substitute the value of y in equation (1) to find x

∵ 2x + 3(2.5) = 11

∴ 2x + 7.5 = 11

→ Subtract 7.5 from both sides

∵ 2x + 7.5 - 7.5 = 11 - 7.5

∴ 2x = 3.5

→ Divide both sides by 2 to find the value of x

∵ [tex]\frac{2x}{2}=\frac{3.5}{2}[/tex]

∴ x = 1.75

∵ x represents the cost of 1 kg of almonds

∴ The cost of each kg of almonds is $1.75

∵ y represents the cost of 1 kg of jelly beans

∴ The cost of each kg of jelly beans is $2.5

Answer:

C

Step-by-step explanation:

Answer:

x= 12h +15

Step-by-step explanation:

Answer:

x = -25

Step-by-step explanation:

solve for x by simplifying both sides of the equation, then isolating the variable.

Answer:

Lol, here is the answer again. Good luck

9514 1404 393

Answer:

  34°

Step-by-step explanation:

∠FZE and ∠BZC are vertical angles, so are congruent. The angle sum theorem tells us ...

  ∠BZC +∠CZD = ∠BZD

  (2x+5) +x = 107

  3x = 102

  x = 34

The measure of ∠CZD is 34°.

Answer:

900,000

Step-by-step explanation:

Answer:

The answer is that the measure of ∠α is ≈ 20° when rounded to the nearest °

Step-by-step explanation:

To find the measure of ∠α you need to use the reciprocal of the formula for the law of sine which says that a/Sinα = b/Sinβ = c/Sin C. The reciprocal of this gives the new equation that states Sinα/a = Sinβ/b = Sin C/c, and this will help you to find the measure of the missing angle in °'s.

In the triangle line segment BC = 5units is opposite to point A & ∠α. Line segment AC = 7units  is opposite of point and ∠β which is = 28°. And finally, the hypotenuse length and the values of point C & ∠C are unknown, so they aren't important to solving the problem. Knowing all this you can plug in all the known values into the new formula, and start working on figuring things out.

To find the measure ∠α, you first write down everything, putting things into their proper places, so since you're solving for sinα you want the equation to look like this:

sinα/5 = sin28°/7

Then for the second step, you want to isolate the sinα. (To get it by itself × both left and righthand sides by 5 to begin simplifying).

This leaves you with :

sinα = sin28°÷7 · (5)    [And allows you to now solve for the right side of the equation, bringing us to our third step which is to once again simplify. So what you want to do is whip out your calculator and set it to degree mode, so you can find the of sin28° which is = 0.46947156278. Then ÷ that by 7, which will get you a number = 0.06706736611. Finally, take 0.06706736611 × 5,  and you will get the value = 0.33533683056, as your final answer in the third step]

Your equation should now look something like this :

sinα = 0.06706736611 × 5 or 0.33533683056

Moving onto the fourth step, you need to use the inverse of the trig function of sin to get your absolute value. (remember the inverse of sine or acrsin = sin^-1) Here you will need to multiply sin^-1 by 0.33533683056.

And also by now, you'll want to stop writing the equation as sinα = sin^-1 ×

0.33533683056, otherwise you won't get an answer, instead, you'll need to write:

α = sin^-1 × 0.33533683056

So once you do that for the fifth and final step, you'll need to simplify the equation on the righthand side one last time, and you should get the answer of α = 19.5930217327°. Which when rounded to the nearest ° is ≈ 20°.

Answer:

I think it is 6.24

Step-by-step explanation:

not really sure

Answer:

150

Step-by-step explanation:

Answer:

1/15

Step-by-step explanation: Just equate the values like my last ans

Answer:

Step-by-step explanation:

Step 1:

Put value of b = 5/6

1/(12(5/6)+5

1/60/6 +5

1/10+5

Answer:

1/15 or 0.06666

Answer:

A, c(x)=5+21x

Step-by-step explanation:

`

Answer:

Step-by-step explanation: C. 2x+3=1/2(4x+2)+2 hopes this helps:)

The equations that are identities are option B x – 4(x + 1) = –3(x + 1) + 1 and option C 2x + 3 = 1/2(4x + 2) + 2.

To check which equation is an identity, we need to simplify each equation and see if it is true for all values of x.

A. 3(x – 1) = x + 2(x + 1) + 1

Expanding the right side:
3(x – 1) = x + 2x + 2 + 1
3x – 3 = 3x + 3-3 = 3

This is a contradiction and cannot be true for any value of x. Therefore, option A is not an identity.

B. x – 4(x + 1) = –3(x + 1) + 1
Expanding both sides:
x – 4x – 4 = –3x – 3 + 1
-3x – 3 = -3x – 3

This equation simplifies to -3x - 3 = -3x - 3, which is true for all values of x. Therefore, option B is an identity.

Similarly,

Option C is an identity.

Option D is not an identity.

Learn more about equations here:

brainly.com/question/10413253

#SPJ7

Answer:

D. NM=12; mK=70°

Step-by-step explanation:

KN≈KM so they have the same 55° and then

180°-55°-55°=70° and

6*2=12

Answer:

Positive Slope

Step-by-step explanation:

The slope is going up Right

Answer:

0,4

Step-by-step explanation:

Answer: c: $65

Step-by-step explanation:

Answer:

1. 10 nickels and 34 dimes

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

bexause u are a kid so dont ask this question again

3/4 of 12 is  9

I hope it helps!

Answer:

9 is 3/4 0f 12

Step-by-step explanation:

Multiply by the numerator of the fraction and divide by the denominator.

You can do this in either order.

12 × 3 = 36  then 36 ÷ 4 = 9  OR

12 ÷ 4 = 3    then  3 × 4 = 9

Answer:

  translated (x, y) → (x - 2, y + 2) and rotated 90° counterclockwise about the origin

Step-by-step explanation:

The image point is in the 3rd quadrant, and the pre-image point is in the first quadrant. This means there has been any of ...

The only answer choice involving the appropriate rotation is ...

  translated (x, y) → (x - 2, y + 2) and rotated 90° counterclockwise about the origin

__

Checking this, we have

  (x, y) ⇒ (x -2, y +2) . . . . translation left 2, up 2

  (x -2, y +2) ⇒ (-y -2, x -2) . . . . followed by 90° CCW rotation

  J(9, 1) ⇒ J'(-3, 7) . . . . . consistent with the given image point

Answer: c is the answer

Answer:

true

Step-by-step explanation:

Complete Question

The complete is shown on the first uploaded image

Answer:

The correct option are option 2 and option 4

Step-by-step explanation:

From the question we are told that

   The sample size is  n = 12  

    The test statistics is  [tex]t \approx 1.434[/tex]

    The level of significance is  [tex]\alpha = 0.05[/tex]

    The  rejection region is    t>1.796

   The null hypothesis [tex]H_o: \mu_d=0[/tex]

    The alternative hypothesis is  [tex]H_a : \mu_d >0[/tex]

 From the given values we see that t <  1.796(i.e   1.434 < 1.796 ) which implies that t is not within the rejection region

  Hence we fail to reject the null hypothesis

The conclusion is that there is insufficient evidence to suggest that that the husbands are significantly older than the wife.

Answer:

1

Step-by-step explanation:

The bars around the j mean absolute value, meaning any number inside those brackets, you make it positive. So, 6-5=1