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Rasek [7]
2 years ago
10

Galen wrote the statement "If the sum of the digits in a number is divisible by 3, the original number is divisible by 3." Which

statements are true regarding his work? Check all that apply.
A: The hypothesis of the statement is "If the sum of the digits in a number is divisible by 3."

B: An equivalent statement is "If the sum of the digits in a number is divisible by 3, then the original number is divisible by 3."

C: The statement is not a conditional statement because it does not include both an "if" and a "then" clause.

D:The statement can be proven true or false.

E:The conclusion of the statement is written before the hypothesis.
Mathematics
1 answer:
lord [1]2 years ago
6 0

the answer is B. good luck

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What is the answer please
Marina86 [1]
Hey there!

Use The Pythagorean theorem. It’s a^2+b^2=c^2. Plug in 11 and 60. The equation would be 11^2+60^2=c^2. Simplify to get 121+3600=c^2. Simplify again to get 3721=c^2. Sqaure root each side to get c=61. The answer is the last one, c=61.

I hope this helps!
8 0
2 years ago
Every day, Jorge buys a lottery ticket. Each ticket has a probability of of winning a prize. After six days, what is the probabi
Romashka [77]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Every day, Jorge buys a lottery ticket. Each ticket has a 0.16 probability of winning a prize. After six days, what is the probability that Jorge has won at least one prize? Round your answer to four decimal places.

Answer:

The probability that Jorge has won at least one prize after six days is

P(at least 1 win) = 0.6487

Step-by-step explanation:

Every day, Jorge buys a lottery ticket which has a 0.16 chance of winning a prize.

We want to find out the probability that Jorge has won at least one prize after six days.

P(at least 1 win) = 1 - P(not winning for 6 days)

We know that the probability of winning is 0.16 then the probability of not winning is

P(not winning) = 1 - 0.16 = 0.84

For 6 days,

P(not winning for 6 days) = 0.84×0.84×0.84×0.84×0.84×0.84

P(not winning for 6 days) = 0.84⁶

P(not winning for 6 days) = 0.3513

Finally,

P(at least 1 win) = 1 - P(not winning for 6 days)

P(at least 1 win) = 1 - 0.3513

P(at least 1 win) = 0.6487

6 0
2 years ago
For ΔABC, ∠A = 4x - 10, ∠B = 5x + 10, and ∠C = 7x + 20. If ΔABC undergoes a dilation by a scale factor of 1 3 to create ΔA'B'C'
VLD [36.1K]
We know that the angles of a triangle sum to 180°.  For ΔABC, this means we have:
(4x-10)+(5x+10)+(7x+20)=180

Combining like terms,
16x+20=180

Subtracting 20 from both sides:
16x=160

Dividing both sides by 16:
x=10
This means ∠A=4*10-10=40-10=30°; ∠B=5*10+10=50+10=60°; and ∠C=7*10+20=70+20=90.

For ΔA'B'C', we have
(2x+10)+(8x-20)+(10x-10)=180

Combining like terms, 
20x-20=180

Adding 20 to both sides:
20x=200

Dividing both sides by 20:
x=10

This gives us ∠A'=2*10+10=20+10=30°; ∠B'=8*10-20=80-20=60°; and ∠C'=10*10-10=100-10=90°.

Since the angle are all congruent, ΔABC~ΔA'B'C' by AAA.
5 0
2 years ago
Read 2 more answers
In the derivation of the quadratic formula by completing the square, the equation (x+b over 2a)^2=-4ac+b^2 over 4a^2 is created
vredina [299]

Answer:

The result of applying the square root property of equality to this equation is x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}.

Step-by-step explanation:

Consider the provided equation.

\left(x+\dfrac{b}{2a}\right)^2=\dfrac{-4ac+b^2}{4a^2}

As the above equation is formed by perfect square trinomial so simply applying the square root property as shown:

\sqrt{(x+\dfrac{b}{2a})^2}=\pm \dfrac{\sqrt{-4ac+b^2}}{\sqrt{4a^2}}\\x+\dfrac{b}{2a}=\pm \dfrac{\sqrt{b^2-4ac}}{2a}

Isolate the variable x.

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

Hence, the result of applying the square root property of equality to this equation is x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}.

4 0
1 year ago
Read 2 more answers
Determine the equation of the line that passes through the given points (if you have a graphing calculator, you can us the table
vladimir2022 [97]

Answer:

d. y = -2×

Step-by-step explanation:

First to solve find the slope using the formula, \frac{10+10}{-5-5}. The slope equals 20/-10 or -2. Then plug the slope and point, (-5,10), into slope-point form. y-10=-2(x+5), then solve for y. This gives you y=-2x+0 or y=-2x.

8 0
2 years ago
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