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mel-nik [20]
2 years ago
7

Given triangle ABC, A=105°, a=10cm, b=7cm, find B,C and c.

Mathematics
1 answer:
Whitepunk [10]2 years ago
4 0

The value of the side c will be 5.56 cm and angle C is 32.49° and angle B is 42.51°.

<h3>What is law of cosine?</h3>

Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

a² + b² – 2ab cos C = c²

Given triangle ABC, A = 105°, a = 10 cm, b = 7 cm.

Then we have

7² + c² – (2 · 7 · c) cos 105° = 10²

c² + 3.62c – 51 = 0

On solving, we have

c = 5.56

Then the angle C will be

10² + 7² – 2 · 7 · 10 · cos C = 5.56²

                149 – 140 cos C = 30.91

                                 cos C = 0.8435

                                        C = 32.49°

We know that

       ∠A + ∠B + ∠C = 180°

105° + ∠B + 32.49° = 180°

                         ∠B = 42.51°

Learn more about law of cosines here:

brainly.com/question/17289163

#SPJ1

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Which expression is equivalent to (x Superscript one-fourth Baseline y Superscript 16 Baseline) Superscript one-half?
Phantasy [73]

The expression that is equal to (x Superscript one-fourth Baseline y Superscript 16 Baseline) is x Superscript one-eighth Baseline y Superscript 8.

<h3>What is an Expression?</h3>

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that is equal to (x Superscript one-fourth Baseline y Superscript 16 Baseline) can be found by simplifying the given algebraic equation,

(x^{\frac14}y^{16})^{\frac12}\\\\=x^{(\frac14 \times \frac12)} \times y^{(16 \times \frac12)}\\\\= x^{\frac18}y^{8}

Hence, the expression that is equal to (x Superscript one-fourth Baseline y Superscript 16 Baseline) is x Superscript one-eighth Baseline y Superscript 8.

Learn more about Expression:

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5 0
2 years ago
Please help with the attached question. Thanks
Mademuasel [1]

Answer:

Choice A) F(x) = 3\sqrt{x + 1}.

Step-by-step explanation:

What are the changes that would bring G(x) to F(x)?

  • Translate G(x) to the left by 1 unit, and
  • Stretch G(x) vertically (by a factor greater than 1.)

G(x) = \sqrt{x}. The choices of F(x) listed here are related to G(x):

  • Choice A) F(x) = 3\;G(x+1);
  • Choice B) F(x) = 3\;G(x-1);
  • Choice C) F(x) = -3\;G(x+1);
  • Choice D) F(x) = -3\;G(x-1).

The expression in the braces (for example x as in G(x)) is the independent variable.

To shift a function on a cartesian plane to the left by a units, add a to its independent variable. Think about how (x-a), which is to the left of x, will yield the same function value.

Conversely, to shift a function on a cartesian plane to the right by a units, subtract a from its independent variable.

For example, G(x+1) is 1 unit to the left of G(x). Conversely, G(x-1) is 1 unit to the right of G(x). The new function is to the left of G(x). Meaning that F(x) should should add 1 to (rather than subtract 1 from) the independent variable of G(x). That rules out choice B) and D).

  • Multiplying a function by a number that is greater than one will stretch its graph vertically.
  • Multiplying a function by a number that is between zero and one will compress its graph vertically.
  • Multiplying a function by a number that is between -1 and zero will flip its graph about the x-axis. Doing so will also compress the graph vertically.
  • Multiplying a function by a number that is less than -1 will flip its graph about the x-axis. Doing so will also stretch the graph vertically.

The graph of G(x) is stretched vertically. However, similarly to the graph of this graph G(x), the graph of F(x) increases as x increases. In other words, the graph of G(x) isn't flipped about the x-axis. G(x) should have been multiplied by a number that is greater than one. That rules out choice C) and D).

Overall, only choice A) meets the requirements.

Since the plot in the question also came with a couple of gridlines, see if the points (x, y)'s that are on the graph of F(x) fit into the expression y = F(x) = 3\sqrt{x - 1}.

5 0
3 years ago
Read 2 more answers
What is the measure of an interior angle of a regular three-sided polygon?
noname [10]
The formula to find the measure of an interior angle is (n - 2) * 180/n, where n represents the number of sides in the polygon. In this problem, n would represent 3. 

Let's plug in the value for n
(3 - 2) * 180/3
Let's simplify that. 
=60

Now we know that the <span>measure of an interior angle of a regular three-sided polygon is 60</span>°. Your answer would be B!

Let me know if you have any questions regarding this problem!
Thanks!
-TetraFish
8 0
3 years ago
Read 2 more answers
What is 6(7-2p) =12p+42
mafiozo [28]

answer:

p = 0

step-by-step explanation:

6 (7-2p) = 12p + 42

42 - 12p = 12p + 42

     +12p   +12p

_______________

42 = 24p + 42

-42            -42

_____________

0 = 24p

_    ___

24    24

0 = p


<em>hope this helps! ❤ from peachimin (aka kayla)</em>


4 0
3 years ago
What is the measure of DG?
Masja [62]

Answer:

170

Step-by-step explanation:

7 0
3 years ago
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