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3 years ago

Geometry

1 answer:

8 0

Hi,
Answer should be letter B, since it is the one conclusion you get using both the law of detachment and the law of syllogism.

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What two numbers multiply to 30 and add to -17

victus00 [196]

Answer:

-15 and -2

Step-by-step explanation:

Since a negative times a negative equals a positive, but when added, still stays a negative, the factors must both be negative.

Negative Factors of 30:

-30 + -1 = -31

-15 + -2 = -17

-10 + -3 = -13

-6 + -5 = -11

The two factors of 30 that add up to -17 are -15 and -2.

Hope this helps. Have a nice day.

4 0

3 years ago

brenda and her bestfriend went on a vacation together. They both paid for a flight, and brenda had a fancy room for $150 per nig

AURORKA [14]

Answer:

What is the question?

Step-by-step explanation:

1. Write all of the question to receive a correct answer.

7 0

3 years ago

A rubber ball is dropped onto a hard surface from a height of 9 feet, and it bounces up and down. At each bounce it rises to 80%

8_murik_8 [283]

There are 12 inches in a foot, so 9ft = 108in. Also, 80% = 0.8. Therefore the formula is: h(n) = 108 * 0.8^n. To find the bounce height after 10 bounces, substitute n=10 into the equation: h(n) = 108 * 0.8^10 = 11.60in (2.d.p.). Finally to find how many bounces happen before the height is less than one inch, substitute h(n) = 1, then rearrage with logarithms to solve for the power, x: 108 * 0.8^x = 1; 0.8^x = 1/108; Ln(0.8^x) = ln(1/108); xln(0.8) = ln(1\108); x = ln(1/108) / ln(0.8) = -4.682 / -0.223 = 21 bounces

4 0

3 years ago

Exercise 3.5. For each of the following functions determine the inverse image of T = {x ∈ R : 0 ≤ [x^2 − 25}.

masya89 [10]

a. The inverse image of f(x) is f⁻¹(x) = ∛(x/3)

b. The inverse image of g(x) is $g^{-1}(x) = e^{x}$

c. The inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

<h3 /><h3>The domain of T</h3>

Since T = {x ∈ R : 0 ≤ [x^2 − 25} ⇒ x² - 25 ≥ 0

⇒ x² ≥ 25

⇒ x ≥ ±5

⇒ -5 ≤ x ≤ 5.

<h3>Inverse image of f(x)</h3>

The inverse image of f(x) is f⁻¹(x) = ∛(x/3)

f : R → R defined by f(x) = 3x³

Let f(x) = y.

So, y = 3x³

Dividing through by 3, we have

y/3 = x³

Taking cube root of both sides, we have

x = ∛(y/3)

Replacing y with x we have

y = ∛(x/3)

Replacing y with f⁻¹(x), we have

So, the inverse image of f(x) is f⁻¹(x) = ∛(x/3)

<h3>Inverse image of g(x)</h3>

The inverse image of g(x) is $g^{-1}(x) = e^{x}$

g : R+ → R defined by g(x) = ln(x).

Let g(x) = y

y = ln(x)

Taking exponents of both sides, we have

$e^{y} = e^{lnx} \\e^{y} = x$

Replacing x with y, we have

$y = e^{x}$

Replacing y with g⁻¹(x), we have

So, the inverse image of g(x) is $g^{-1}(x) = e^{x}$

<h3>Inverse image of h(x)</h3>

The inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

h : R → R defined by h(x) = x − 9

Let y = h(x)

y = x - 9

Adding 9 to both sides, we have

y + 9 = x

Replacing x with y, we have

x + 9 = y

Replacing y with h⁻¹(x), we have

So, the inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

Learn more about inverse image of a function here:

brainly.com/question/9028678

5 0

2 years ago

A school wants to put on a dance recital Middle School dancers have short programs that run 4 minutes long High School performer

sp2606 [1]

Answer: The answer is $\textup{M}+\textup{H}\leq 10~~\textup{and}4\textup{M}+7\textup{H}\leq 90.$

Step-by-step explanation: Given that a school wants to put on a dance recital. The programs of Middle school dancer will be short of 4 minutes each and programmes of High school performers will be long of 7 minutes each.

Number of middle school dances is "M" and number od high school dances is "H".

Since there cannot be more than 10 dances all together, so fisrt inequality can be written as

$\textup{M}+\textup{H}\leq 10.$

Also, the entire recital must take maximum 90 minutes, so the second inequality can be written as

$4\textup{M}+7\textup{H}\leq 90.$

Thus, the pair of inequalities is

$\textup{M}+\textup{H}\leq 10,\\\\4\textup{M}+7\textup{H}\leq 90.$

6 0

3 years ago