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3 years ago

Use the diagram to answer the questions

Mathematics

1 answer:

IRISSAK [1]3 years ago

8 0

Answer:

1. B. BD

2. C. 15

3. A. 2

Step-by-step explanation:

1. From the figure,

∠DAB = ∠DAC

Therefore, BD is the bisector of ∠ABC.

2. From the figure, IG = GH

3x = 5x - 10

10 = 5x - 3x

2x = 10

x = 5

So, GH = 5x - 10

= 5(5) - 10

= 25 - 10

= 15

Therefore, GH = 15.

3. From the figure,

∠DAB = ∠DAC

10y = 8y + 4

10y - 8y = 4

2y = 4

y = 2

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Dave won a hot dog eating contest by eating 18 hot dogs in 10 minutes. He ate two more than twice the amount of the runner-up. W

geniusboy [140]

Answer:

The correct anser is option

B. 2x + 2 = 18

Step-by-step explanation:

Let the number of hot dogs eaten by the runner up be represented by x

If Dave ate 2 more than twice x, this means that the number eaten by him = 2x + 2

Since the total number of hot dogs eaten by Dave is 18

Therefore, the equation will be

2x + 2 = 18

So the number of hot dogs eaten by the runner-up is determined by solving for x

2x= 18-2

2× = 16

x = 16/2

x = 8

The runner up are 8

While Dave are

2×8 + 2 = 18.

7 0

3 years ago

Read 2 more answers

A quality control inspector has drawn a sample of 10 light bulbs from a recent production lot. Suppose 20% of the bulbs in the l

Neko [114]

Answer:

The probability is 0.0008.

Step-by-step explanation:

Let X represents the event of defective bulb,

Given, the probability of defective bulb, p = 20 % = 0.2,

So, the probability that bulb is not defective, q = 1 - p = 0.8,

The number of bulbs drawn, n = 10,

Since, binomial distribution formula,

$P(x=r) = ^nC_r p^r q^{n-r}$

Where, $^nC_r = \frac{n!}{r!(n-r)!}$

Hence, the probability that exactly 7 bulbs from the sample are defective is,

$P(X=7)=^{10}C_7 (0.2)^7 (0.8)^{10-7}$

$=120 (0.2)^7 (0.8)^3$

$=0.000786432$

$\approx 0.0008$

6 0

3 years ago

A circle with a centre 0, has an equation x2 + y2 = 25

GaryK [48]

The linear equation of the tangent at point A is given by:

$y = \frac{-4x + 25}{3}$

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

In this problem, to find the slope, we need to find the derivative at (4,3), using implicit differentiation. Hence:

$2x\frac{dx}{dx} + 2y\frac{dy}{dx} = 0$

$\frac{dy}{dx} = -\frac{x}{y}$

$\frac{dy}{dx} = -\frac{4}{3}$

Then:

$y = -\frac{4}{3}x + b$

We use point (4,3) to find b, hence:

$y = -\frac{4}{3}x + b$

$3 = -\frac{16}{3} + b$

$b = \frac{25}{3}$

Hence, the equation is:

$y = \frac{-4x + 25}{3}$

More can be learned about linear equations at brainly.com/question/24808124

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7 0

2 years ago

PLEASE HELP ASAP, I WILL GIVE 40 POINTS IF THE RIGHT ANSWER, AND BRAINLEST, ASAP

Julli [10]

Answer:

5/52

Step-by-step explanation:

There are 52 cards in a deck, with 26 red and 26 black cards. There are 2 red ones, 2 black threes, and 1 six of hearts. The # of favorable outcomes is 2 + 2 + 1 = 5, so the answer is 5/52.

7 0

1 year ago

-8/9 - (2 1/3)<br> show all your work

Sauron [17]

Answer:

1 8/9 - 1 2/3 = 2/

≅ 0.2222222

Step-by-step explanation:

How do you solve fractions step by step?

Conversion a mixed number 1 8/

to a improper fraction: 1 8/9 = 1 8/

= 1 · 9 + 8/

= 9 + 8/

= 17/

To find a new numerator:

a) Multiply the whole number 1 by the denominator 9. Whole number 1 equally 1 * 9/

= 9/

b) Add the answer from previous step 9 to the numerator 8. New numerator is 9 + 8 = 17

c) Write a previous answer (new numerator 17) over the denominator 9.

One and eight ninths is seventeen ninths

Conversion a mixed number 1 2/

to a improper fraction: 1 2/3 = 1 2/

= 1 · 3 + 2/

= 3 + 2/

= 5/

To find a new numerator:

a) Multiply the whole number 1 by the denominator 3. Whole number 1 equally 1 * 3/

= 3/

b) Add the answer from previous step 3 to the numerator 2. New numerator is 3 + 2 = 5

c) Write a previous answer (new numerator 5) over the denominator 3.

One and two thirds is five thirds

Subtract: 17/

- 5/

= 17/

- 5 · 3/

3 · 3

= 17/

- 15/

= 17 - 15/

= 2/

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(9, 3) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 3 = 27. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - seventeen ninths minus five thirds = two ninths

8 0

3 years ago