Are the triangles congruent! (Help)

The amount invested in each stock, the stock interest rate and the

duration of the investment, determines the interest.

Reasons:

Let X represent the sum of the amount Brian invested, we have;

Amount invested in stock paying 5% dividend = [tex]\dfrac{X}{2}[/tex]

Amount invested in stock paying 9% dividend = [tex]\dfrac{X}{2}[/tex]

Total annual interest = $420

Required:

The amount invested in the stocks

Solution:

The amount invested is found as follows;

[tex]\dfrac{X}{2} \times 5\% + \dfrac{X}{2} \times 9\% = 420[/tex]

0.025·X + 0.045·X = 420

0.07·X = 420

[tex]\displaystyle \mathrm{The \ amount \ invested , \, X} = \frac{420}{0.07} = \mathbf{ 6,000}[/tex]

The amount he invested = $6,000 ($3,000 in each stock)

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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

[tex]\huge\mathfrak\pink{answer} [/tex]

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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:

haha.A. Write True if the statement is correct and False if it is not true. 1. In active voice, the subject of the sentence is doing the action, 2. In passive voice, the action is done on/upon the subject. 3. The doer of the action is followed by the verb in active voice. 4. The doer of the action is preceded by the verb in active voice, 5. The receiver of the action in active voice is preceded by the verb. 6. The receiver of the action in passive voice is followed by the verb. 7. In passive voice, meaning is clearer and more direct. 8. In active voice, meaning can be confusing and indirect, 9. The tone is authoritative and subjective in active voice, 10. The tone is neutral or objective in passive voice.

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.

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

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Answer:

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

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

if you add negative 4 to each of the x's, it would give you the number of y

Answer:

-4

Step-by-step explanation:

the explanation is up in my answer

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

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:

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).

Answer:

5.72

Step-by-step explanation:

(-16.75 + 16.75) = 0

0 + 5.72= 5.72

Therefore, the answer is 5.72

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:

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

Step-by-step explanation:

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:

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:

The equation of a straight line is always

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

The constant m always refers to the slope, and the constant b always refers to the y-intercept.

Simply substitute the numbers in:

[tex]y=-\frac{1}{2}x+3[/tex]

There's your equation!

Answer:its f

Step-by-step explanation:

the only answer left i hope this helps =)

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

Answer:

first 45-6=36 and 36×6=216 the answer is 216

Answer:

$63.75

Step-by-step explanation:

10% = 7.5

5% = 3.75

15% = 11.25

75.00

-11.25

63.75

Answer:

Option B

Step-by-step explanation:

[tex]PV = nRT\\\rule{150}{0.5}\\\rightarrow \frac{PV = nRT}{nR}\\\\\rightarrow \boxed{\frac{PV}{nR} = T}[/tex]

Hope this helps.

The equation for T will be;

⇒ T = PV/nR

Where, P, V, and T represent pressure, volume, and temperature, n represents the number of moles of gas, and R is a constant for the ideal gas.

Option B is true.

What is Linear equation?

When in an equation the highest power of variable is one then its called Linear equation.

Given that;

The equation for the ideal gas law is,

PV = nRT

Where, P, V, and T represent pressure, volume, and temperature,

n represents the number of moles of gas, and R is a constant for the ideal gas.

Now,

Solve the equation for T as;

PV = nRT

Divide both side by 'nR' we fet;

PV/nR = nRT/nR

PV/nR = T

T = PV/nR

Thus, The equation for T will be;

⇒ T = PV/nR

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#SPJ5

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:

Third one down

Step-by-step explanation:

Answer:

See below:

Step-by-step explanation:

Hello! My name is Galaxy and I will be helping you today!

We can solve this problem in two steps, one is Comprehending and another is Solving. I'll start off with Comprehending.

Comprehending

We can start off by looking at the problem, it wants us to find the percentage increase from 36 to 48. We can then find difference between 48 and 36; that would be 12.

Now that we know the increase from 36 to 48 is 12. We need to find how much percent 12 is of 36.

Now that we know what we have to do, we can start solving.

Solving

We can solve the problem by setting up and equation, but we can also just use our logic in finding it out.

Since we know that we need to find how much 12 is of 36, we can just solve for that and we will get our answer.

We can do that with one step.

[tex]\frac{12}{36}=0.33[/tex]

Since it is a percent, we can multiply 0.33 by 100 and we get our answer of 33%

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. :)

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.

Answer:

113.04 cm^2

Step-by-step explanation:

To find the area, you do radius squared, multiplied by [tex]\pi[/tex]

Radius is half of the diameter. 12/2 is 6

6^2×3.14=113.1