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2 years ago

Suppose a triangle has sides a, b, and c and the angle opposite the side of length a is acute what must be true?

Mathematics

1 answer:

ANTONII [103]2 years ago

4 0

The true statement about the triangle is (a) b^2 + c^2 > a^2

<h3>How to determine the true inequality?</h3>

The sides are given as:

a, b and c

The angle opposite of side length a is an acute angle

The above means that:

The side a is the longest side of the triangle.

The Pythagoras theorem states that:

a^2 = b^2 + c^2

Since the triangle is not a right triangle, and the angle opposite a is acute.

Then it means that the square of a is less than the sum of squares of other sides.

This gives

a^2 < b^2 + c^2

Rewrite as:

b^2 + c^2 > a^2

Hence, the true statement about the triangle is (a) b^2 + c^2 > a^2

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Just Need A Few Questions Answered To Finish My Quiz, Any Help Would Be Much Appreciated.

kvv77 [185]

Given the triangle

PQR

with points

P(8,0)

Q(6,2)

R(-2,-4)

And the triangle

P'Q'R'

with points

P'(4,0)

Q'(3,1)

R'(-1,-2)

Part A. Scale factor

Using the vertex

P( 8, 0)

P'(4,0)

the dilatation factor is given by

$\frac{4}{8}=\frac{1}{2}$

The triangle has a dilatation factor of 1/2

Part B:

P''Q''R'' after using P'Q'R' reflected about the y axis

to make a reflection over the y axis

coordinates (x,y) turn into coordinates (-x,y)

as follows

$P^{\prime}(4,0)\rightarrow P^{\prime\prime}(-4,0)$ $Q^{\prime}(3,1)\rightarrow Q^{\prime\prime}(-3,1)$ $R^{\prime}(-1,-2)\rightarrow R^{\prime\prime}(1,-2)$

Then triangle P''Q''R'' has coordinates

P''(-4,0)

Q''(-3,1)

R''(1,-2)

Part C:

PQR is congruent to P''Q''R''?

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.

Then the triangles are not congruent

8 0

1 year ago

Hi, can I get some help with this question? DON'T WORRY ITS JUST A ASSIGNMENT. NOT A TEST. Thank you

Alchen [17]

Answer:

Step-by-step explanation:

i looked at the graph!

3 0

3 years ago

Help me i need help asap

olganol [36]

Answer:

6.5

Step-by-step explanation:

when a negative is multiplied by a negative it in turns turns into a positive...hence 2+4.5

6 0

2 years ago

Kasey and Jordan are counting calories while eating lunch in the school cafeteria. In one week, Kasey had

malfutka [58]

Answer:

Jordan got 222 calories from pizza

Step-by-step explanation:

Given:

slices of pizza ate by Kasey =10

cups of fruit salad by Kasey= 5

slices of pizza ate by Jordan = 6

cups of fruit salad by Jordan= 7

Kasey's calorie count = 3070

Jordan calorie count = 2522

To Find:

calories Jordan got from pizza =?

Solution:

Let the calorie of one slice of pizza be x

and the calorie of one cup of fruit salad be y

According to the question, the equation that represents the Kasey's Scenario is

10x + 5y = 3070-------------------------------------(1)

Similarly the equation that represents the Jordan Scenario is

6x + 7y = 2522--------------------------------------(2)

multiply eq(1) by 6 we get

60x + 30y = 18420---------------------------------(3)

multiply eq(2) by 10 we get,

60x + 70y = 25220----------------------------------(4)

Subtracting eq (3) from (4) we get

60x + 70y = 25220

60x + 30y = 18420

(-) (-) (-)

-----------------------------------

0x + 40y = 6800

---------------------------------

=>40 y = 6800

=>y = $\frac{6800}{40}$

=> y = 170

So calorie of one cup fruit salad is = 170 calories

substituting the y values in eq 1 we get

10x + 5(170) = 3070

10x + 850 = 3070

10x = 3070 - 850

10x = 2220

x = $\frac{2220}{10}$

x= 222

So calorie of one pizza slice = 222 calories

Now we know that Jordan ate 6 slices of pizza

calories Jordan get from pizza = number of pizza he ate X calore per pizza slice

=> 6 x 222

=>1332 calories

6 0

3 years ago

If our school has about 300 seventh graders, about how many would be expect to watch 4 to

kykrilka [37]

Answer:

Step-by-step explanation:

7 0

3 years ago