Solve the inequality and express your answer in interval notation.
x2 - 12x + 5 <0

Since you have the answers, I'll just show the steps on how to get there.

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Problem 19

[tex](1+4i)^2\\\\(1+4i)(1+4i)\\\\1*1 + 1*4i + 4i*1 + 4i*4i\\\\1 + 4i + 4i + 16i^2\\\\1 + 4i + 4i + 16(-1)\\\\1 + 4i + 4i-16\\\\(1-16) + (4i+4i)\\\\(1-16) + (4+4)i\\\\-15 + 8i\\\\[/tex]

Keep in mind that [tex]i = \sqrt{-1}[/tex] by definition. Squaring both sides leads to [tex]i^2 = -1[/tex]

In the second step, I used the idea that x^2 = x*x. Right after that, I used the FOIL rule to expand everything out.

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Problem 21

We could follow the same idea as problem 19, but I'll use a different approach.

[tex](A+B)^2 = A^2+2AB+B^2\\\\(3+i)^2 = 3^2 + 2*3*i + i^2\\\\(3+i)^2 = 9 + 6i - 1\\\\(3+i)^2 = 8 + 6i\\\\[/tex]

The formula on the first line is the perfect square binomial formula.

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Problem 23

The FOIL rule can be used if you want, but I'll use the difference of squares rule instead.

[tex](m+n)(m-n) = m^2 - n^2\\\\(3+5i)(3-5i) = (3)^2 - (5i)^2\\\\(3+5i)(3-5i) = 9 - 25i^2\\\\(3+5i)(3-5i) = 9 - 25(-1)\\\\(3+5i)(3-5i) = 9 + 25\\\\(3+5i)(3-5i) = 34\\\\[/tex]

It turns out that multiplying any complex number of the form a+bi with its conjugate a-bi will result in a purely real number (that has no imaginary part). More specifically: [tex](a+bi)(a-bi) = a^2+b^2[/tex]

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Problem 25

We could use the difference of squares rule again, but I'll show a different approach. This time using the distribution rule. The FOIL rule could also be used if you wanted.

[tex](6+7i)(6-7i)\\\\x(6-7i)\\\\6x-7xi\\\\6(x)-7i(x)\\\\6(6+7i)-7i(6+7i)\\\\6(6)+6(7i)-7i(6)-7i(7i)\\\\36+42i-42i-49i^2\\\\36-49(-1)\\\\36+49\\\\85\\\\[/tex]

I used x = 6+7i and the substitution property to help distribute. Lines 3 and 6 are where distribution is applied.

Answer:

$63.75

Step-by-step explanation:

10% = 7.5

5% = 3.75

15% = 11.25

75.00

-11.25

63.75

Rewrite the system of equations in matrix form.

[tex]\begin{bmatrix}1&2&-2\\3&7&-1\\2&4&m\end{bmatrix} \mathbf x = \mathbf b[/tex]

This system has a unique solution [tex]\mathbf x = \mathbf A^{-1}\mathbf b[/tex] so long as the inverse of the coefficient matrix [tex]\mathbf A[/tex] exists. This is the case if the determinant is not zero.

We have

[tex]\det(\mathbf A) = m+4[/tex]

so the inverse, and hence a unique solution to the system of equations, exists as long as m ≠ -4.

Answer:

y + 2 = (11/17)(x - 8)

Step-by-step explanation:

Working with the x- and y-components of the given points, we see that the x component increases by 17 and the y-component decreases by 11.  Thus, the slope of this line is m = rise / run, or 11/17.

Start with the general point-slope form:  y - k = m(x - h) and use the coordinates of the 2nd point for h and k in this equation:

                                                                    y + 2 = (11/17)(x - 8)

                                                                     This is based on the point (-2, 8)

                                                                     and the slope 11/17.                                                                  

This result is the desired equation in point-slope form.  If we wish to reduce this, proceed as follows:

17(y + 2) = 11x - 88, or 17y + 34 = 11x - 88

This last result simplifies to 17y = 11x - 54, or y = (11/17)x -54/17 (which is in slope-intercept form).

9514 1404 393

Answer:

Step-by-step explanation:

All of these exponential function problems use the same equation, but with different plug-in values. These can be easily accommodated by a spreadsheet or graphing calculator.

The general form of the value after t years is ...

  (initial value)×(1 +annual growth rate)^(years)

The growth rate is positive for an increase, negative for a decrease.

a) Initial value: 22385; growth rate: -0.14; years: 10

  value after 10 years: $22385×(1-0.14)^10 = $4953.84

__

b) initial value: 290; growth rate: 0.09; years: 5

  population after 5 years: 290(1+.09)^5 = 446

__

c) initial value: $4000; growth rate: -0.10; years: 8

  value after 8 years: $4000(1 -0.10)^8 = $1721.86

Selling the car for $1500 is selling it for less than its estimated value. That may not be a good decision.

_____

Additional comment

The property value of the car is not the only consideration when evaluating the sale. Other costs related to the car may come into play, and there may be tax implications.

Answer:

[tex]\frac{5a^2b^2}{4}[/tex]

Step-by-step explanation:

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Explanation:

Your teacher wants you to use the angle-angle-side congruence theorem, which abbreviates to AAS. Note in the diagram that we have two pairs of angles marked.

So we have the info about the angles being congruent, and that takes care of the two "A"s in AAS.

We just need a pair of sides to be congruent. Specifically, we need the pair of sides that are not between the angles mentioned for either triangle. If we went for this option, then we'd go for ASA instead of AAS. The order is important.

So we have two possible answers

If either of those were given to us, then we can use the AAS theorem.  Unfortunately PR = UT isn't listed, but QR = ST is listed. So this is why choice B is the answer.

Side note: Both QR and ST are opposite the double arc angle.

Answer:

QR≅ST

Step-by-step explanation:

With AAS congruence, you need 2 angles and a non-included side. On ΔPQR, that could be either PR or QR. PQ is the included side as it is between the angles, and therefore cant be used for this congruence theorem.

As said above, it can be either PR or QR, but it has to be QR in this case as there is no answer option for PR.

On the other triangle, the corresponding side is ST. ∠S and ∠Q are corresponding, and US is the included side, so that leaves only ST.

Finally, the information you need to prove that the triangles are congruent is QR≅ST.

Answer:

I think it is b I’m not quite sure though. Sorry if wrong…

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

i have no clue

Step-by-step explanation:

but you can look it up on brainly

Answer: 49 : 32

Step-by-step explanation:

12 1/4 = 49/4

12 1/4 : 8 = 49/4 : 8

12 1/4 : 8 = 49/4 : 8/1

12 1/4 : 8 = 49/4 : 32/4

12 1/4 : 8 = 49 : 32

12 1/4 : 8 = 49 : 32

Answer:

6

Step-by-step explanation:

8-2

=8+-2

=6

the sum just means when u add them both together hope this helps! u just do 8 take away 2 because its a negative

Answer:

x^2/b^2 + y^2/a^a = 1

Step-by-step explanation:

I believe that is the answer, also theanswerme answered this question. :)

Functions can be represented on graphs and graphs can also be represented as functions.

The given parameters are:

Points = (-8,0), (5,-2) and (8,3)

Absolute Maximum  = (-4,5)

Absolute Minimum  = (2,-6)

Start by plotting the points (including the absolute maximum and the absolute minimum) without connecting the dots (see attachment 1)

The decreasing interval [tex]\mathbf{-4 \le x \le 2}[/tex]  implies that the graph decreases from x =-4, to x =-2

See attachment (2) for the rough sketch of the graph that represents the given points and the decreasing interval

Read more about graphs at:

https://brainly.com/question/19277419

Answer:

1. 1

2. 14

3.9

4. 15

5.17

step-by-step explanation:

take X and times it by 4 then add 9

Answer:

a+y≤1000 and 25a+12.50y>15000

Step-by-step explanation:

Answer:its f

Step-by-step explanation:

the only answer left i hope this helps =)

Answer:

yes its correct

Step-by-step explanation:

but for the check where did you get the 12? you might want to redo that part but otherwise its right

Answer:

P = 6.28

Step-by-step explanation:

To find the perimeter of a circle, you would use the formula 2πr.

The diameter = x and x = 2

The radius of a circle is half the diameter so r = 1.

Now we just substitute to get our answer:

2 · [tex]\pi[/tex] · r = P

2 · 3.14 · 1 = P

6.28 · 1 = P

6.28 = P

P = 6.28

Answer:

5 because its 1 aed so if he buys 5 toys it will be 5 aeds and bye!

Step-by-step explanation:

because its 1 aed so if he buys 5 toys it will be 5 aeds and bye!

Answer:

4 pounds

Step-by-step explanation:

Add 16 64 divided

The snowy owl weighs is 4 pounds.

A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We have been given that A snowy owl weighs 64 ounces.

16 ounces (oz) = 1 pound (lb)

We have to determine the number of pounds the owl weighs.

Let x pounds would be the owl weighs

We can write this as a ratio as

16 ounces (oz) : 1 pound (lb) = 64 ounces : x pounds

⇒ 16/1 = 64/x    

⇒ (16)(x) = 64

Divide each side by 16

⇒ x =64/16

⇒ x = 4

Therefore, the snowy owl weighs is 4 pounds.

Learn more about the Ratio here:

brainly.com/question/1504221

#SPJ2

Answer:

Kevin Drove For 6 Hours and 40 Minutes

Step-by-step explanation:

56 times 6.4 Equals 358.4

Convert it into miles 56MI X 6.4(HR) = 358.4MI

Answer:

x=7°

Step-by-step explanation:

From the picture it tells us that all side are equal

so that means every side is 60°

Let's make an equation

9x-3°=60°

add 3 on both sides

9x=63°

divide both sides by 9

x=7°

Answer:

Because integers don't have decimals. An irrational number has a forever repeating decimal (that is random).

Step-by-step explanation:

Jeremy is incorrect because a negative plus a negative will always be a negative.

9514 1404 393

Answer:

Step-by-step explanation:

Let d represent the number of daffodil bulbs you buy. Then 60-d is the number of crocus bulbs. The total cost will be ...

  0.45(60 -d) +0.65(d) = 35.00

  27 +0.20d = 35

  0.20d = 8 . . . . . . . . . subtract 27

  d = 40 . . . . . . . . . . multiply by 5

  60 -40 = 20 . . . . . crocus bulbs

You can buy 20 crocus bulbs and 40 daffodil bulbs for $35.

1. -40 - 180 = -220

2. -40 - 175 = -135

3. -40 - 185 = -225

4. 2:15 = -40

2:18 = 185

distance b/w them is = -40 - 185 = - 225

hope this answer helps you dear! btw I'm not sure but hope so this helps...!!

I agree with the first person that answered.