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3 years ago

What is the measure of ABC?

Mathematics

1 answer:

Viefleur [7K]3 years ago

5 0

Answer:

Step-by-step explanation:

Hi there!

In order to find the answer to this question we must know about:

The angles of intersecting chords theorem

The theorem states that if two chords intersect the angles formed at the intersection is equal to half the sum of its intercepted arc and it's vertical angle's intercepted arc.

Angle ABC is formed by intersecting chords meaning that the measure of angle ABC is equal to half the sum of its intercepted arc + it's vertical angle's intercepted arc ( angle ABC vertical angle is angle EBD. Angle EBD's intercepting arc is arc ED. )

Angle ABC intercepted arc is AC

Hence Angle ABC = 1/2 ( arc AC + arc ED)

Arc ED = 44 and arc AC = 82

Thus, angle ABC = 1/2(82 + 44)

82 + 44 = 126

126/2=63

Hence Angle ABC = 63

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Please help me I will give thanks and points!

makkiz [27]

1.31, 1.4, and 1.44.

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6 0

3 years ago

Answer these questions

Gnom [1K]

1. Ratio between onions and tomatoes:

There are 3 onions and 4 carrots.

Therefore, required ratio is 3:4

2. Ratio between tomatoes to cups of chicken stock:

There are 6 tomatoes and 5 cups of chicken stock.

Hence, the required ratio is 6:5.

3. Sticks of butter to bananas:

There are 1 stick of butter and 2 bananas.

So, the required ratio is 1 to 2.

4. Teaspoons of salt to teaspoons of black pepper:

There are 2 teaspoons of salt and 1 teaspoon of black pepper.

Please refer attached figure.

5. Let's calculate the ratio of cups of chocolate chips to tomatoes.

There are 3 cups of chocolate chips and 6 tomatoes.

Hence, the required ratio is 3:6 and on simplifying, 1:2.

5 0

3 years ago

A rectangular parking lot has an area of 15,000 feet squared, the length is 20 feet more than the width. Find the dimensions

faust18 [17]

Dimension of rectangular parking lot is width = 112.882 feet and length = 132.882 feet

<h3>Solution:</h3>

Given that

Area of rectangular parking lot = 15000 square feet

Length is 20 feet more than the width.

Need to find the dimensions of rectangular parking lot.

Let assume width of the rectangular parking lot in feet be represented by variable "x"

As Length is 20 feet more than the width,

so length of rectangular parking plot = 20 + width of the rectangular parking plot

=> length of rectangular parking plot = 20 + x = x + 20

The area of rectangle is given as:

$\text {Area of rectangle }=length \times width$

Area of rectangular parking lot = length of rectangular parking plot $\times$ width of the rectangular parking

$\begin{array}{l}{=(x+20) \times (x)} \\\\ {\Rightarrow \text { Area of rectangular parking lot }=x^{2}+20 x}\end{array}$

But it is given that Area of rectangular parking lot = 15000 square feet

$\begin{array}{l}{=>x^{2}+20 x=15000} \\\\ {=>x^{2}+20 x-15000=0}\end{array}$

Solving the above quadratic equation using quadratic formula

General form of quadratic equation is

${ax^{2}+\mathrm{b} x+\mathrm{c}=0$

And quadratic formula for getting roots of quadratic equation is

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

In our case b = 20, a = 1 and c = -15000

Calculating roots of the equation we get

$\begin{array}{l}{x=\frac{-(20) \pm \sqrt{(20)^{2}-4(1)(-15000)}}{2 \times 1}} \\\\ {x=\frac{-(20) \pm \sqrt{400+60000}}{2 \times 1}} \\\\ {x=\frac{-(20) \pm \sqrt{60400}}{2}} \\\\ {x=\frac{-(20) \pm 245.764}{2 \times 1}}\end{array}$

$\begin{array}{l}{=>x=\frac{-(20)+245.764}{2 \times 1} \text { or } x=\frac{-(20)-245.764}{2 \times 1}} \\\\ {=>x=\frac{225.764}{2} \text { or } x=\frac{-265.764}{2}} \\\\ {=>x=112.882 \text { or } x=-132.882}\end{array}$

As variable x represents width of the rectangular parking lot, it cannot be negative.

=> Width of the rectangular parking lot "x" = 112.882 feet

=> Length of the rectangular parking lot = x + 20 = 112.882 + 20 = 132.882

Hence can conclude that dimension of rectangular parking lot is width = 112.882 feet and length = 132.882 feet.

3 0

3 years ago

What is the gcf of 23 and 50

valkas [14]

Answer:

The greatest common factor of 23 and 50 is 1

Step-by-step explanation:

7 0

3 years ago

Ms. B drives a maximum of 10 miles per week. If she drives 5 days per week, how much per day?

DanielleElmas [232]

Answer:

2 miles about

Step-by-step explanation:

10 miles max divided by 5 days is two miles per day

7 0

3 years ago