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3 years ago

Geometry help!! How did they get this answer?

Mathematics

1 answer:

Illusion [34]3 years ago

4 0

The sum of all the angles in a triangle is 180 degrees. The triangle in the picture is also an equilateral triangle because of the markings on it (the three arches and ticks show that the sides with the markings are congruent.)

So since an equilateral triangle has 3 angles and the angles are congruent, we can divide 180 by 3 to find out how many degrees each angle is; 60 degrees.

Since all angles are equal, angle A = angle B = angle C = 60 degrees.

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Courtney needs blue and brown ribbon to use to make a bow for a dress. According to her pattern she needs 11.2 inches of brown r

Stells [14]

Answer: Expression used to find the total ribbon she used = x+11.2

Explanation:

Let the length of blue ribbon to use to make a bow for a dress be x

And

The length of brown ribbon is used to make a bow for a dress = 11.2 inches

Expression need to find the total ribbon she used will be sum of blue and brown ribbon altogether

i.e. x+11.2 inches

So, the required expression will be x+11.2 inches

5 0

3 years ago

Pat picked a card from a standard deck, looked at it, and then put it back. He then picked a second card. What is the probabilit

AlekseyPX

Answer: 17/52

Step-by-step explanation:

There are 52 total cards in a standard deck.

The number of diamonds in a deck of cards is 13 and there are 4 jacks in a deck of cards.

So the propabibilty of Pat picking a diamond is 13/52 and the probability of Pat picking a jack is 4/52. Now you have to add the two probabilities together.

You do not remove any digits because Pat put the card back into the deck, he didn't take it away. So we do not take away from the total

13 + 4 = 17

You do not need to change the denominator cause 52 is the same.

So 17/52 is the probability of Pat picking a diamond or a jack

I hope this helped!

3 0

3 years ago

Write the equation of the line that has a slope of 3 and passes through (5, 11)

Marina CMI [18]

Answer:

3x-4

Step-by-step explanation:

y=ax+b general type of the line

a is the slope

y=3x+b

put 5 instead of the x and put 11 instead of the y

11=15+b

b=(-4)

Equation is 3x-4

4 0

3 years ago

Factor f(x) = 15x^3 - 15x^2 - 90x completely and determine the exact value(s) of the zero(s) and enter them as a comma separated

Illusion [34]

Answer:

$x=-2,0,3$

Step-by-step explanation:

We have been given a function $f(x)=15x^3-15x^2-90x$ . We are asked to find the zeros of our given function.

To find the zeros of our given function, we will equate our given function by 0 as shown below:

$15x^3-15x^2-90x=0$

Now, we will factor our equation. We can see that all terms of our equation a common factor that is $15x$ .

Upon factoring out $15x$ , we will get:

$15x(x^2-x-6)=0$

Now, we will split the middle term of our equation into parts, whose sum is $-1$ and whose product is $-6$ . We know such two numbers are $-3\text{ and }2$ .

$15x(x^2-3x+2x-6)=0$

$15x((x^2-3x)+(2x-6))=0$

$15x(x(x-3)+2(x-3))=0$

$15x(x-3)(x+2)=0$

Now, we will use zero product property to find the zeros of our given function.

$15x=0\text{ (or) }(x-3)=0\text{ (or) }(x+2)=0$

$15x=0\text{ (or) }x-3=0\text{ (or) }x+2=0$

$\frac{15x}{15}=\frac{0}{15}\text{ (or) }x-3=0\text{ (or) }x+2=0$

$x=0\text{ (or) }x=3\text{ (or) }x=-2$

Therefore, the zeros of our given function are $x=-2,0,3$ .

7 0

4 years ago

In his first year, a math teacher earned $32,000. Each successive year, he

Ivan

Answer:

Step-by-step explanation:

Each successive year, he

earned a 5% raise. It means that the salary is increasing in geometric progression. The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence(amount earned in the first year).

r represents the common ratio.

n represents the number of terms(years).

From the information given,

a = $32,000

r = 1 + 5/100 = 1.05

n = 20 years

The amount earned in his 20th year, T20 is

T20 = 32000 × 1.05^(20 - 1)

T20 = 32000 × 1.05^(19)

T20 = $80862.4

To determine the his total

earnings over the 20-year period, we would apply the formula for determining the sum of n terms, Sn of a geometric sequence which is expressed as

Sn = (ar^n - 1)/(r - 1)

Therefore, the sum of the first 20 terms, S20 is

S20 = (32000 × 1.05^(20) - 1)/1.05 - 1

S20 = (32000 × 1.653)/0.05

S20 = $1057920

3 0

3 years ago