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3 years ago

H(x)=4log2(x−6)+1 All real numbers greater than____

Mathematics

1 answer:

MariettaO [177]3 years ago

4 0

$\huge\underline\mathfrak\blue{Answer:-}$

The demoin is all real numbers greater than 6

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a positive number is 7 times another number if 3 is added to both the numbers then one of the new number becomes 5 by 2 times th

Neko [114]

Answer:

7 and 1

Step-by-step explanation:

Let the numbers be a and b.

A positive number is 7 times another number:

a = 7b

If 3 is added to both the numbers then one of the new number becomes 5 by 2 times the other new number:

a+3 = 5/2 × (b +3)

To solve this we substitute a with 7b in the second equation:

7b + 3 = 5/2 × (b +3) ⇒ multiplying both sides by 2
14b + 6 = 5b + 15 ⇒ collecting like terms
14b - 5b = 15 - 6
9b = 9
b = 1 ⇒ solved for b

Then, finding a:

a= 7b
a=7*1
a= 7 ⇒ solved for a

So the numbers are 7 and 1

3 0

3 years ago

What is 1 2/3 minus -5 2/3 as a fraction

Sati [7]

7 1/3 hope this helps!

7 0

3 years ago

One positive number is 14 less than another positive number. If the reciprocal of the smaller number is added to five times the

Kipish [7]

Let's call the two numbers $s$ and $l$ .

Given these variables, we can say: $s = l - 14$ , based on the first sentence in the problem.

Also, remember that the reciprocal of a number is simply 1 divided by the number. Thus, we can say that:

$\dfrac{1}{s} + 5\Big( \dfrac{1}{l} \Big) = \dfrac{1}{4}$

To solve, we can simply substitute $l -14$ in for $s$ in the second equation and solve.

$\dfrac{1}{l - 14} + \dfrac{5}{l} = \dfrac{1}{4}$

Set up

$\dfrac{l}{l(l - 14)} + \dfrac{5(l - 14)}{l(l - 14)} = \dfrac{1}{4}$

Get terms on the left side to a common denominator for easier addition

$\dfrac{l + 5l - 70}{l(l - 14)} = \dfrac{1}{4}$

Simplify

$4(6l - 70) = l(l - 14)$

Cross multiplication ( $\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc$ )

$24l - 280 = l^2 - 14l$

Simplify

$l^2 - 38l + 280 = 0$

Subtract $24l - 280$ from both sides of the equation

$(l - 10)(l - 28) = 0$

Factor left side of the equation

$l = 10, 28$

Zero Product Property

Now, notice that we have found two solutions, but the problem is only asking for one. This likely means that one of our solutions is extraneous. Let's take a look. Remember that the smaller positive number is equal to 14 less than the larger number. However,

$s = 10 - 14 = -4$ ,

Since $s$ is not positive in this case, $l = 10$ is not a solution.

Thus, $l = 28$ is our only solution. In this case,

$s = 28 - 14 = 14$ ,

which means that the smaller number is 14 and the larger number is 28.

5 0

3 years ago

PLEASE HELP ASAP

Igoryamba

Answer:

∠1 - 40°

Step-by-step explanation:

∠1 - 40°

b/c it's a right triangle and we have two angles given, 50° and 90°. Add them and subtract by 180° and get 40°.

∠2 - 140°

b/c an exterior (outside) angle is equal to the two most isolated / farthest angles added. The two most is angles are 105° and 35°, add them and get 140°.

∠3 - 40°

b/c ∠'s 1 and 3 are vertical angles meaning they're equal so since ∠1 is 40°, so is ∠3.

∠4 -

b/c ∠' s 2 and 4 are vertical angles meaning they're equal so since ∠2 is 140°, so is ∠4.

∠5 - 35°

b/c we have two angles, 105° and 40°. Add them and subtract by 180° and get 35°.

I hope that helps you out!!

5 0

3 years ago

A microwave is placed on top of two boxes. One box is 2 feet 9 inches tall, the other box is 4 feet 11 inches tall, and the micr

Liula [17]

The answer for this question would be
12ft and 2in

8 0

3 years ago

Read 2 more answers