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3 years ago

5

Could 14 inches, 13 inches, and 16 inches be the dimension of a triangle? Explain your answer.

2 answers:

nika2105 [10]3 years ago

6 0

The angles would be different

Dafna11 [192]3 years ago

6 0

14+13>16 √
13+16>14 √
14+16>13 √
If each pair of possible sides is greater than the third side than the lengths can form a triangle.

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7. Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

morpeh [17]

Hey there!

<u>Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0</u>

Answer :

x = -4 or x = 2 ✅

Explanation :

<em><u>Quadratic</u></em><em><u> </u></em><em><u>formula </u></em><em><u>:</u></em><em><u> </u></em>ax² + bx + c = 0 where a ≠ 0

The number of real-number solutions <em>(roots)</em> is determined by the discriminant (b² - 4ac) :

If b² - 4ac > 0 , There are 2 real-number solutions

If b² - 4ac = 0 , There is 1 real-number solution.

If b² - 4ac < 0 , There is no real-number solution.

The <em><u>roots</u></em> of the equation are determined by the following calculation:

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

Here, we have :

a = 1
b = 2
c = -8

1) <u>Calculate </u><u>the </u><u>discrim</u><u>i</u><u>n</u><u>ant</u><u> </u><u>:</u>

b² - 4ac ⇔ 2² - 4(1)(-8) ⇔ 4 - (-32) ⇔ 36

b² - 4ac = 36 > 0 ; The equation admits two real-number solutions

2) <u>Calculate </u><u>the </u><u>roots </u><u>of </u><u>the </u><u>equation</u><u>:</u>

▪️ (1)

$x_1 = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x_1 = \frac{ - 2 - \sqrt{36} }{2(1) } \\ \\ x_1 = \frac{ - 2 - 6}{2} \\ \\ x_1 = \frac{ - 8}{2} \\ \\ \blue{\boxed{\red{x_1 = -4}}}$

▪️ (2)

$x_2 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_2 = \frac{ - 2 + \sqrt{36} }{2(1)} \\ \\ x_2 = \frac{ - 2 + 6}{2} \\ \\ x_2 = \frac{4}{2} \\ \\ \red{\boxed{\blue{x_2 = 2}}}$

>> Therefore, your answers are x = -4 or x = 2.

Learn more about <u>quadratic equations</u>:

brainly.com/question/27638369

6 0

2 years ago

Read 2 more answers

Find the mean, Find the median,<br> mode, and range <br> of each Data set 46, 35, 23, 37, 29, 53, 43

g100num [7]

Answer: mean- 38

median- 37

mode- no mode

range- 30

Step-by-step explanation:

5 0

3 years ago

The measure of the hypotenuse is? (side c)

Sliva [168]

Answer: 25
explanation:
7² + 24² = c²
49 + 576 = c²
625 = c²
c = √625
c= 25

or just know some pythagorean triples

4 0

3 years ago

Read 2 more answers

Angle e measures 126LaTeX: ^\circ∘. What is the measure of LaTeX: \angle∠h?

Oksana_A [137]

Option C: 126° is the correct answer

Step-by-step explanation:

When two lines intersect, the four angles are formed. The angles vertically opposite with same vertex are called vertical opposite angles.

The opposite vertical angles are equal.

In the given figure, the pairs of vertically opposite angles are e,h and f,g.

Given

∠e = 126°

The measurement of e and h will be equal as they are vertically opposite

So,

m∠e = m∠h

m∠h = 126°

Hence,

Option C: 126° is the correct answer

Keywords: Vertical angles, lines

Learn more about angles at:

#LearnwithBrainly

6 0

3 years ago

Construct 3 linear equation starting with qiven solution z = 1/3

Andreyy89

Answer:

(a) $9z+2=5$

(b) $21z-11=-4$

(c) $4z=2-2z$

Step-by-step explanation:

We are required to construct 3 linear equations starting with the given solution z = 1/3.

<u>Equation 1</u>

<u /> $z=\frac{1}{3}$ <u />

Multiply both sides by 9

$9z=\frac{1}{3}\times 9\\9z=3$

Rewrite 3 as 5-2

9z=5-2

Add 2 to both sides

Our first equation is: $9z+2=5$

<u>Equation 2</u>

<u /> $z=\frac{1}{3}$ <u />

Multiply both sides by 21

$21z=\frac{1}{3}\times 21\\21z=7$

Rewrite 7 as 11-4

21z=11-4

Subtract 11 from both sides

Our second equation is: $21z-11=-4$

<u>Equation 3</u>

<u /> $z=\frac{1}{3}$ <u />

Multiply both sides by 6

$6z=\frac{1}{3}\times 6\\6z=2$

Rewrite 6z as 4z+2z

4z+2z=2

Subtract 2z from both sides

Our third equation is: $4z=2-2z$

4 0

3 years ago