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3 years ago

5

Find a counterexample: Two sides of a

1 answer:

Shkiper50 [21]3 years ago

6 0

Answer: Any isosceles triangle is a counter example. More specifically, a triangle with sides 7, 7 and 3

When forming your triangle, make sure you apply the triangle inequality theorem. This is the idea where adding any two sides leads to a result larger than the third side. So we have

7+7 = 14 which is larger than 3

7+3 = 10 which is larger than 7

By definition, an isosceles triangle has two congruent sides. Some books say "at least 2 congruent sides", but I'll go with the first definition. If you want all three sides to be congruent, then you'd go for the term "equilateral".

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I have a question that says " jada has read 3/5 of a book. She has read 75 pages so far. How many pages are in the whole book?"

jok3333 [9.3K]

Answer and Step-by-step explanation:

To solve, we would multiply by the reciprocal of the portion Jada has read, and multiply that number to 75.

The reciprocal means the the value, but flipped, so $\frac{3}{5}$ will become $\frac{5}{3}$ .

Now we do 75 times $\frac{5}{3}$ /

$\frac{75 * 5}{3} \\\\\\\\\frac{375}{3} \\\\\\\\125$

So, there are 125 total pages in the book.

<em><u>#teamtrees #PAW (Plant And Water)</u></em>

3 0

2 years ago

The base of a triangle is nine centimeters longer than the perpendicular height. If the area of the triangle is 180 square centi

Rom4ik [11]

Answer:

<em>The base is 24 cm long.</em>

Step-by-step explanation:

<u>Equations</u>

Let's call

b= base of the triangle

h=height of the triangle

The base is 9 cm longer than the height, thus:

b = h + 9

The area of the triangle is:

$\displaystyle A=\frac{bh}{2}$

$\displaystyle A=\frac{(h+9)h}{2}$

And its value is 180:

$\displaystyle \frac{(h+9)h}{2}=180$

Multiplying by 2:

$(h+9)h=360$

Operating:

$h^2+9h-360=0$

Factoring:

$(h-15)(h+24)=0$

The only valid positive solution is:

h = 15 cm

And b = h + 9 = 24

b = 24 cm

The base is 24 cm long.

7 0

3 years ago

A bag contains 8 red balls and 4 white balls. Two balls are drawn without replacement. (Enter your probabilities as fractions.)

RoseWind [281]

Answer:

total marbles;12

after drawing red total counts are 7 red and 4 white 11 in total

probabilities are 4/11

6 0

2 years ago

An arch is in the shape of a parabola. It has a span of 100 feet and a maximum height of 25 ft.

faltersainse [42]

Answer:

$y=-\frac{1}{100}(x-50)^2+25$

the height of the arch 10 feet from the center is 24 feet

Step-by-step explanation:

An arch is in the shape of a parabola. It has a span of 100 feet, the vertex lies at the center 50 and the maximum height of 25 ft.

Vertex at (50,25)

vertex form of the equation is

$y=a(x-h)^2+k$ , (h,k) is the center

$y=a(x-50)^2+25$

the parabola starts at (0,0) that is (x,y)

$0=a(0-50)^2+25$

subtract 25 from both sides

$-25=a(-50)^2$

$-25=a(2500)$

divide both sides by 2500

$a=-\frac{1}{100}$

$y=-\frac{1}{100}(x-50)^2+25$

the height of the arch 10 feet from the center.

center is at 50, 10 feet from the center so x=40 and x=60

$y=-\frac{1}{100}(40-50)^2+25$

y=24

the height of the arch 10 feet from the center is 24 feet

4 0

3 years ago

Alan, Bianca, and Charles are counting in turn. Alan says "one," Bianca says "two," and Charles says "three." Then it's Alan's t

timama [110]

Bianca would say fifty nine

8 0

2 years ago