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3 years ago

What is the value of x

Mathematics

1 answer:

Evgen [1.6K]3 years ago

6 0

Answer:

Step-by-step explanation:

Given

with reference angle 45°

hypotenuse (h) = x

perpendicular (p) = 6√2

Now

with reference angle 45°

sin 45° = p / h

1 / √2 = 6√2 / x

Cross multiply ✖

6√2 * √2 = x

x = 6 * 2

x = 12

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The graph of an exponential function passes through (1, 10) and (4, 80). Find the function that describes the graph.

svetlana [45]

Answer:

y = 5*2ˣ

Step-by-step explanation:

Exponential function:

y = abˣ

Ordered pairs given:

(1, 10) and (4, 80)

Substitute x and y values to get below system:

10 = ab
80 = ab⁴

Divide the second equation by the first one and solve for b:

80/10 = b³
b³ = 8
b = ∛8
b = 2

Use the first equation and find the value of a:

10 = a*2
a = 5

The function is:

y = 5*2ˣ

4 0

2 years ago

Read 2 more answers

Parker is laying pavers to build a patio in his backyard. Each square paver measures 2 feet on each side. He would like the pati

MatroZZZ [7]

Answer:

32 pavers

Step-by-step explanation:

step 1

Find out the area of one square paver

The area of a square is

$A=s^{2}$

where

s is the length side of the square

we have

$s=2\ ft$

substitute

$A=2^{2}\\A=4\ ft^{2}$

step 2

Find out the area of the rectangular patio

we know that

The area of a rectangle is

$A=LW$

we have

$L=16\ ft\\W=8\ ft$

substitute

$A=(16)(8)\\A=128\ ft^2$

step 3

Find out the number of pavers needed to build the patio

Divide the area of the rectangular patio by the area of one paver

$128\ ft^2/4\ ft^{2}=32\ pavers$

5 0

3 years ago

a shopper paid $52 for a handbag during a sale. The handbag was priced at 65% off its original price. Which equation can be used

aleksklad [387]

52 ×.65= X The answer would be $80. Hope i could be helpful :)

8 0

3 years ago

What is the area of the figure? The diagram is not drawn to scale.

Veronika [31]

The picture in the attached figure

we know that
the figure is a parallelogram
the area of parallelogram=base*height
in this problem
base=34 in
height=35 in
so
area=34*35----> area=1190 in²

the answer is
A. 1,190 in^2

4 0

3 years ago

How many 3 digit numbers are possible when a) the leading digit cannot be zero and the number must be a multiple of 4?

guajiro [1.7K]

Step-by-step explanation:

I assume the digits can be repeated.

so, e.g. 555 is a valid number for this problem, right ?

that means we start with permutations with repetition :

n^r

n = the total number of items to pick from.

r = the number of items being picked per result.

we have 10 digits (0,1,2,3,4,5,6,7,8,9), and we pick 3 of them.

that gives us (with very little surprise, I hope)

10³ = 1000 different possible numbers from 000 to 999.

from these numbers we eliminate all with leading 0.

as we handled all digits the same way and with the same priority, there is the same amount of numbers for every digit in the leading position.

that means 1/10 of the total amount of numbers has a leading 0, or a leading 1, or a leading 2, ...

so, we need to subtract 1/10 × 1000 from 1000 :

1000 - 1000×1/10 = 1000 - 100 = 900

that would be the numbers 100 to 999.

and we have one more condition : the number must be a multiple of 4.

how many are there ?

well, that's the funny thing about numbers : from all numbers 1/2 of them are multiples of 2 (or divisible by 2), 1/3 of them are multiples of 3 (or divisible by 3), and ... you guessed it, 1/4 of them are multiples of 4 (or divisible by 4). and so on.

and so, 1/4 of our 900 numbers are multiples of 4 :

1/4 × 900 = 225

so, there are 225 possible 3-digit numbers that are multiples of 4 and do not start with a 0.

6 0

2 years ago