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3 years ago

Which of the following exponential equations could be represented by the table below?

Mathematics

1 answer:

Nastasia [14]3 years ago

3 0

Answer:

Option 3: $y=(3)^{x-3}+2$

Step-by-step explanation:

See the attached figure.

We will make a table for each function of the options, then compare each one of them with the given table.

So, we can deduce that the function of option 3: $y=(3)^{x-3}+2$

is the exponential equations could be represented by the table.

Note both of the given table and $y=(3)^{x-3}+2$

has Horizontal Asymptote y =2

Which mean as x→-∞ ⇒ y→2

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A quilted block users eight parallelogram shaped pieces of clothe each with a base of 3/3/4 inches. How much fabric is needed to

borishaifa [10]

Answer:

The answer to the question is

37.5 ft² of fabric is needed to make the parallelogram pieces for 24 blocks.

Step-by-step explanation:

To answer the question, we note that a parallelogram is a four sided polygon having two opposite parallel sides.

Therefore in this question, we select our parallelogram to be a rectangle

Number of pieces of parallelogram in a quilted block = 8

Number of parallelogram in each quadrant of the quilted block = 2

Therefore the height of the rectangle = 2 × the base = 2× $3\frac{3}{4}$ = 7.5 inches

Therefore the area of each parallelogram = base × height

= $\frac{15}{4}*\frac{15}{2}$ = $\frac{225}{8}$ in²

since each quilted block uses 8 parallelogram, then the amount of fabric for each quilted block is

$\frac{225}{8} *8 = 225 in^2$

Hence 24 blocks wil require 24×225 in² = 5400 in²

However, since 144 in² = 1 ft² we have

5400 in² = 5400 in²× 1/144 ft²/in² = 37.5 ft².

7 0

3 years ago

435 L = ______ KL So what do i put in the blank spot ?? i dont know how to do this

docker41 [41]

$1000\ L-1KL\\ 435\ L-x\\ \\1000\cdot x=435\cdot1\cdot \ KL\ /:1000\\ \\x=0.435\ KL$

5 0

3 years ago

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The hypotenuse of a right angled triangle is 2√13 cm . If the smaller side is increased by 2 cm and the larger side is increased

White raven [17]

Statement:

The hypotenuse of a right angled triangle is 2√13 cm. If the smaller side is increased by 2 cm and the larger side is increased by 3 cm, the new hypotenuse will be √117 cm.

To find out:

The length of the larger side of the right angled triangle.

Solution:

Let us consider x as the smaller side and y as the larger side.

Then, in the right angled triangle,

x² + y² = (2√13)² ...(I) [By Pythagoras Theorem]

Now, if the smaller side is increased by 2 cm, then the smaller side will be (x + 2).

And if the larger side is increased by 3 cm, then the larger side will be (y + 3).

Then, in the new right angled triangle,

(x + 2)² + (y + 3)² = (√117)² [By Pythagoras Theorem]

or, x² + 2 × 2 × x + 2² + y² + 2 × 3 × y + 3² = (√117)²

or, x² + 4x + 4 + y² + 6y + 9 = (√117)²

or, x² + y² + 4x + 6y + 13 = (√117)²

Now, put the value of x² + y² from equation (I),

or, (2√13)² + 4x + 6y + 13 = (√117)²

or, (2 × 2 × √13 × √13) + 4x + 6y + 13 = (√117 × √117)

or, 52 + 4x + 6y + 13 = 117

or, 4x + 6y = 117 - 52 - 13

or, 4x + 6y = 52

or, 4x = 52 - 6y

or, x = $\frac {(52 - 6y)}{4}$ ...(II)

Now, put the value of x of equation (II) in (I),

x² + y² = (2√13)²

or, $\frac {(2704-624y +36y²)}{16}$ + y² = 52

or, $\frac {(2704-624y +36y² + 16y²)}{16}$ = 52

or, 52y²-624y + 2704 = 52 × 16

or, 52y² - 624y + 2704 - 832 = 0

or, 52y² - 624y + 1872 = 0

or, 52(y² - 12y + 36) = 0

or, y²-12y +36 = 0 ÷ 52

or, y²-12y +36 = 0

or, (y)² - 2 × 6 × y + (6)² = 0

or, (y - 6)² = 0

or, y - 6=0

or, y = 6

We have taken y as the length of the larger side of the right angled triangle.

So, the length of the larger side is 6 cm.

Answer:

6 cm

Hope you could understand.

If you have any query, feel free to ask.

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2 years ago

What is 270 divided by 6

morpeh [17]

Your answer would be 45,because 6 times 45 equals to 470,and thats how many times 6 can go into 470,exactly 45 times

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3 years ago

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A local weather station collected the 12 p.m. temperature at 5 different locations in its town: Temperatures, °F: {63, 59, 60, 6

AveGali [126]

Ok so add all of them together and you get 305 then divide it by how many numbers there are for the mean and you get 61 then add all of the diffrences from each number to the mean and we get 6 then 61 divided by 6 gets us 10.1 but round it to 10. hope this helped.

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3 years ago

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