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nata0808 [166]
3 years ago
6

Triangle ABC is similar to Triangle QRS.

Mathematics
2 answers:
Yuki888 [10]3 years ago
7 0

For this case, we have that by definition, similar triangles are those that have the same shape but do not necessarily have the same size. When two triangles are similar, the corresponding angles are congruent and their corresponding sides are proportional.

That said, the angle S measures 102 degrees.

So, we know that the sum of the internal angles of a triangle is 180:

36 + 102 + R = 180\\R = 180-102-39\\R = 39

Thus, angle B is 39 degrees.

Answer:

Option A

lutik1710 [3]3 years ago
3 0

Answer:

102

Step-by-step explanation:

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1) -24, -4, 16, 36, ...<br> Find a23
viktelen [127]

We're given the Arithmetic Progression <em>-24, -4, 16, 36 ...</em> .

We know that a term in an AP is generally represented as:

\bf a_n\ =\ a\ +\ (n\ -\ 1)d

where,

  • a = the first term in the sequence
  • n = the number of the term/number of terms
  • d = difference between two terms

We need to find \sf a_2_3.

From the given progression, we have:

  • a = -24
  • n = 23
  • d = (-24 - (-4) = -20

Using these in the formula,

\sf a_2_3\ =\ a\ +\ (n\ -\ 1)d\\\\\\a_2_3\ =\ -24\ +\ (23\ -\ 1)\ \times\ (-20)\\\\\\a_2_3\ =\ -24\ +\ 22\ \times (-20)\\\\\\a_2_3\ =\ -24\ -\ 440\\\\\\\bf a_2_3\ =\ -464

Therefore, the 23rd term in the AP is -464.

Hope it helps. :)

7 0
2 years ago
What lump sum do parents need to deposit in an account earning 9%, compounded monthly, so that it will grow to $100,000 for thei
gogolik [260]

Answer:

They need to deposit $31,172.49

Step-by-step explanation:

The compound interest formula is given by:

A = P(1 + \frac{r}{n})^{nt}

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time the money is invested or borrowed for, in years.

In this problem

We want to find P for which A = 100000 when r = 0.09, n = 12, t = 13

So

A = P(1 + \frac{r}{n})^{nt}

100000 = P(1 + \frac{0.09}{12})^{12*13}

3.208P = 100000

P = \frac{100000}{3.208}

P = 31172.49

They need to deposit $31,172.49

6 0
3 years ago
What's the equation for twice the difference of a number and 6 is equal to three times the sum of the number and 3
alukav5142 [94]
2(x-6)=3(x+3)

Let's solve your equation step-by-step.

<span><span>2<span>(<span>x−6</span>)</span></span>=<span>3<span>(<span>x+3</span>)

</span></span></span>Step 1: Simplify both sides of the equation.

<span><span>2<span>(<span>x−6</span>)</span></span>=<span>3<span>(<span>x+3</span>)

</span></span></span><span>Simplify: (Show steps)

</span><span><span><span>2x</span>−12</span>=<span><span>3x</span>+9

</span></span>Step 2: Subtract 3x from both sides.

<span><span><span><span>2x</span>−12</span>−<span>3x</span></span>=<span><span><span>3x</span>+9</span>−<span>3x

</span></span></span><span><span><span>−x</span>−12</span>=9

</span>Step 3: Add 12 to both sides.

<span><span><span><span>−x</span>−12</span>+12</span>=<span>9+12

</span></span><span><span>−x</span>=21

</span>Step 4: Divide both sides by -1.

<span><span><span>−x/</span><span>−1</span></span>=<span>21/<span>−1

</span></span></span><span>x=<span>−21

</span></span>Answer:

<span>x=<span>−<span>21</span></span></span>
8 0
2 years ago
Complete the equation for the linear function whose graph contains the points
aniked [119]
Get the slope:
( 10-(-2) )/( 3 - (-1) ) = 3

Let's use letters to represent the ?'s.
y + k = m(x + 1)

Examine the equation:
Notice that if x were to equal -1, the equation would be equal to 0.
m(-1 + 1) = m(0) = 0

If x were to be -1, then y would have to be -2 since that is one of the points provided in the problem.

So now we have:
-2 + k = 0

Solve for k:
k = 2

So I know that 2 is the only number that will work for k.

Our new equation is y + 2 = m(x + 1)

Recall point slope form:
y - y1 = m(x - x1)

Our equation is in the same form as point slope form, so we know that m in our equation represents the slope.

We found the slope at the beginning, it was 3. So plug it in:
y + 2 = 3(x + 1)

Let's test our answer by plugging in a point. Let's try (3, 10):
10 + 2 = 3(3 + 1)
12 = 12

So our answer is correct:
y + 2 = 3(x + 1) is the answer.
4 0
2 years ago
Calculate the area of the shaded part of the figure.
Tju [1.3M]
The shaded area is 1/6 of the area of large circle without the small ones.
you can multiple what you already got for the large circle without small ones by 1/6 and that should give you the correct answer
4 0
3 years ago
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