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4 years ago

Which postulate or theorem proves that △ RNM and △ QNP are congruent?

Mathematics

2 answers:

Zigmanuir [339]4 years ago

7 0

SAS since ∠RNM is congruent ∠PNQ by vertical angles which will give you the angle you need for SAS.

Aliun [14]4 years ago

3 0

Answer:

B) SAS congruence postulate

Step-by-step explanation:

We have marked that RN and NQ are congruent. We also have marked that MN and NP are congruent.

∠MNR≅∠QNP because they are vertical angles. Vertical angles are opposite angles that share only a vertex; these are vertical angles so they are congruent.

This gives us two sides and an included angle; this is SAS.

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Find the face value of the 20-year zero-coupon bond at 4.4%, compounded semiannually, with a price of $8,375.

umka21 [38]

Given:

Time,

t = 20 years

Rate,

r = 4.4%

Price

= $8,375

Now,

The yield will be:

= $\frac{4.4}{2}$

= $1.1$ (%)

Time will be:

= $20\times 2$

= $40 \ periods$

As we know the formula,

⇒ $Price \ of \ bond = \frac{Face \ value}{(1+\frac{r}{2} )^{n\times 2}}$

By substituting the values, we get

$8375=\frac{Face \ value}{(1+\frac{0.044}{2} )^{20\times 2}}$

$8375=\frac{Face \ value}{(1.022)^{40}}$

$8375=\frac{Face \ value}{2.3880083}$

The face value will be:

$Face \ value = 2.3880083\times 8375$

$=20,000$ ($)

Learn more about face value here:

brainly.com/question/14862802

5 0

3 years ago

Simplify. -15-(-3)+6

miv72 [106K]

-15 - (-3) + 6

-15 - (-3) = -15 + 3 = 3 - 15 = - 12

-12 + 6 = 6 - 12 = -6

Your answer is -6

3 0

3 years ago

Read 2 more answers

What is √49 times 7?

krek1111 [17]

Well,
First solve the square root which is 7
Funny enough, this makes 7 * 7 = 49
So the answer is 49!
Hope I helped!

8 0

3 years ago

Read 2 more answers

∠2= ∠5 , because they are

Contact [7]

$\sf \red {alternate \: angles}$

$\huge \purple{ \underbrace{ \overbrace{Hope \: it \: helps}}}$

3 0

3 years ago

Transforming quadratic graphs

rewona [7]

Answer:

f(x) = 3(x - 2)² + 4

f(x) = 3x² - 12x + 16

Step-by-step explanation:

Vertex form of a parabola:

y = a(x - h)² + k

Standard form of a parabola:

y = ax² + bx + c

Let's find the vertex of this parabola.

(h, k) → (2, 4)

In order to find the a-value (vertex form), let's use another point besides the vertex on the parabola.

Using (3, 7) for (x, y), let's substitute this point and the vertex (2, 4) for (h, k) into the vertex form equation and solve for a.

7 = a[(3) - (2)]² + 4

Simplify using PEMDAS.

7 = a(1)² + 4
7 = a + 4

Subtract 4 from both sides.

a = 3

Now we have (h, k) and a of the vertex form.

y = a(x - h)² + k → y = 3(x - 2)² + 4

In order to convert from vertex to standard form, simplify the equation by FOILing.

y = 3(x - 2)² + 4

y = 3(x² - 4x + 4) + 4

Distribute 3 inside the parentheses.

y = 3x² - 12x + 12 + 4

Combine like terms.

y = 3x² - 12x + 16

Therefore, we have the answer:

Vertex form:

f(x) = 3(x - 2)² + 4

Standard form:

f(x) = 3x² - 12x + 16

8 0

3 years ago