Multiply. Write the result in scientific notation.1.4 • 10^1)(8 • 10^4)

Answer:  [tex]24\sqrt{3}in^2[/tex] or  [tex]41.56in^2[/tex]

Step-by-step explanation:

You can find the area of a regular hexagon with the following formula:

[tex]A_{(hexagon)}=\frac{3\sqrt{3}s^2}{2}[/tex]

Where "s" is any side of the regular hexagon.

For this hexagon you know that the length of each side is 4 inches. Then, you must substitute [tex]s=4in[/tex] into the formula  [tex]A_{(hexagon)}=\frac{3\sqrt{3}s^2}{2}[/tex].

Therefore, the area of this regular hexagon is:

 [tex]A_{(hexagon)}=\frac{3\sqrt{3}(4in)^2}{2}[/tex]

 [tex]A_{(hexagon)}=24\sqrt{3}in^2[/tex] or [tex]A_{(hexagon)}=41.56in^2[/tex]

Answer:

the answer is 24 square root 3

Step-by-step explanation:

Answer:

is it a right triangle or no ?

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

x² = 5²+12²

x² = 25+144

x² = 169

x² = 13²

x = 13

Answer:

D. 12 units

Step-by-step explanation:

The distance between two points is found by

d = sqrt( (x2-x1)^2 + (y2-y1)^2)

   sqrt( (4 -4)^2 + (-5-7)^2)

 sqrt((0^2 + (-12)^2)

 sqrt(0+144)

sqrt(144)

12

The answer is:

It will take 7.5 hours to paint the room together.

Using the given information we need to write an equation considering both Colleen and Rebecca rates.

For Colleen we know that she can paint a room in 12 hours, so, her equation will be:

[tex]\frac{1Room}{12hours}*t=\frac{t}{12}[/tex]

Being "t" the time used to paint.

For Rebecca, we know that she can paint a room in 20 hours, so, her equation will be:

[tex]\frac{1Room}{20hours}*t=\frac{t}{20}[/tex]

Now, if we want to calculate the time needed to paint 1 room, we have:

[tex]\frac{t}{12}+\frac{t}{20}=1\\\\\frac{12*t+20*t}{12*20}=1\\\\\frac{12t+20t}{240}=1\\\\\frac{32t}{240}=1\\\\32t=240*1\\\\t=\frac{240}{32}=7.5[/tex]

Hence, we have that it will take 7.5 hours to paint the room together.

Have a nice day!

For this case, to find the roots of the function, we equate to zero.

[tex]x ^ 3 + 2x ^ 2-x-2 = 0[/tex]

We rewrite how:

[tex]x ^ 3 + 2x ^ 2- (x + 2) = 0[/tex]

We factor the maximum common denominator of each group:

[tex]x ^ 2 (x + 2) -1 (x + 2) = 0[/tex]

We factor the polynomial, factoring the maximum common denominator[tex](x + 2):[/tex]

[tex](x + 2) (x ^ 2-1) = 0[/tex]

By definition of perfect squares we have to:

[tex]a ^ 2-b ^ 2 = (a + b) (a-b)[/tex]

ON the expression[tex](x ^ 2-1):[/tex]

[tex]a = x\\b = 1[/tex]

So:

[tex](x ^ 2-1) = (x + 1) (x-1)[/tex]

Thus, the factorization of the polynomial is:

[tex](x + 2) (x + 1) (x-1) = 0[/tex]

[tex]x_ {1} = - 2\\x_ {2} = - 1\\x_ {3} = 1[/tex]

ANswer:[tex]x_ {1} = - 2\\x_ {2} = - 1\\x_ {3} = 1[/tex]

Answer:

The angle is 50.2°.

Step-by-step explanation:

The tree and its shadow from a right triangle with the tree being the perpendicular and the shadow being the base as shown in the figure attached.

Therefore the angle θ formed by the sun's rays and the ground is:

[tex]\theta = tan^-1(\frac{18}{15} )=\boxed{50.2^o}[/tex]

The angle formed by the sun's rays and the ground can be found using trigonometry and it is approximately 50.19°

Given: length of tree is 18 ft. and the shadow of tree is 15 ft.

To find: angle formed by suns rays and the ground

This question involves using trigonometry to find the angle formed by the sun's rays and the ground. We can use the tangent function which is:

[tex]\tan \theta = \frac{\text{perpendicular}}{\text{base}}[/tex]

Here the perpendicular is the length of the tree, base is the shadow of the tree and θ is the angle formed by suns rays and ground. So, plugging the values we get:

[tex]\tan \theta = \frac{18}{15}[/tex]

We see that 15 and 18 have 3 as a common factor so we can divide the numerator and denominator by 3 to simply the fraction and we get:

[tex]\tan \theta = \frac{6}{5} = 1.2[/tex]

To find the angle, we take the inverse tangent of the ratio:

[tex]\theta = tan^{-1} (1.2)[/tex]

θ ≈ 50.19°

Thus, the angle formed by the sun's rays and the ground is approximately 50.19°.

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Compare the ratio of the measure of corresponding sides, that is

AB = 6 and A'B' = 2

BC = 3 and B'C' = 1

Calculate the ratio of A'B'C' to ABC, then

scale factor = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

Answer:

9

Step-by-step explanation:

namely, how many times does 2/3 go in 6?

[tex]\bf 6\div\cfrac{2}{3}\implies \cfrac{6}{1}\div\cfrac{2}{3}\implies \cfrac{6}{1}\cdot \cfrac{3}{2}\implies \cfrac{3}{1}\cdot \cfrac{6}{2}\implies 3\cdot 3\implies 9[/tex]

For this case we have that by definition, the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

A: It is the radius of the cylinder

h: It's the height

We have according to the data that:

[tex]r = \frac {34} {2} = 17 \ m\\h = 27 \ m[/tex]

Substituting in the equation we have:

[tex]V = \pi * (17) ^ 2 * 27\\V = \pi * 289 * 27\\V = 24501.42\ m^3[/tex]

ANswer:

[tex]V = 24501.42\ m^3[/tex]

Answer:

Step-by-step explanation:

simplify both sides of the equation

-x^2+16=-7

subtract 16 form both sides

-x^2= -23

divide by -1

x^2=23

take square root

and your answer is x= plus or minus (square root) of 23 or -23

Answer:

Step by STEP explanation

Answer:

1536 in²

Step-by-step explanation:

S = 6s²

We are told that s = 16 inches, so plugging in:

S = 6 (16)²

S = 1536 in²

Answer:

Step-by-step explanation:

(LOOK AT THE PICTURE)

ΔADC and ΔCDB are similar (AAA). Therefore the corresponding sides are in proportion:

[tex]\dfrac{AD}{CD}=\dfrac{CD}{DB}[/tex]

We have

[tex]AD=16,\ CD=x,\ DB=9[/tex]

Substitute:

[tex]\dfrac{16}{x}=\dfrac{x}{9}[/tex]          cross multiply

[tex]x^2=(9)(16)\to x=\sqrt{(9)(16)}\\\\x=(\sqrt9)(\sqrt{16})\\\\x=(3)(4)\\\\x=12[/tex]

bear in mind that, a perpendicular line stemming from the right-angle like so, creates three similar triangles, a large one, containing the other two smaller ones, a medium and a small.

so.. .we can just use the medium and small proportions.

Check the picture below.

ANSWER

Yes,no two ordered pairs on this graph have the same first element

EXPLANATION

For a set of ordered pairs to be a function,there must not be any two points that have the same first elements.

This means that, the x-coordinates must not repeat for any two given points.

The graph given represents a function because,no two ordered pairs on this graph have the same first element.

Hence it would pass the vertical line test.

The third choice is correct.

The correct answer is: Yes, no two ordered pairs on this graph have the same second element.

To determine if a graph represents a function, one must apply the Vertical Line Test. This test states that a graph represents a function if no vertical line intersects the graph at more than one point. In other words, for every input (x-value), there is exactly one output (y-value). This is equivalent to saying that no two ordered pairs on the graph have the same first element (x-value) and different second elements (y-values).

The statement Yes, no two ordered pairs on this graph have the same second element correctly describes the condition for a graph to represent a function. It implies that for every y-value, there is only one x-value associated with it, which is the definition of a function.

The other options are incorrect for the following reasons:

- Yes, there is more than one ordered pair on this graph. While this statement may be true, it does not address the condition necessary for a graph to represent a function. A graph with multiple ordered pairs could still fail to be a function if any vertical line intersects the graph more than once.

- Yes, no two ordered pairs on this graph have the same first element. This statement is not relevant to the definition of a function. A function can have the same x-value associated with different y-values (which would be multiple ordered pairs with the same first element). The key is that for each x-value, there can only be one y-value.

- No, there is a limited number of ordered pairs on this graph. The number of ordered pairs being limited does not affect whether the graph represents a function. A function can have a finite or infinite number of ordered pairs. The defining characteristic is that there is exactly one output for each input, not the total number of ordered pairs.

Therefore, the correct justification for the graph representing a function is that no two ordered pairs on the graph have the same second element, ensuring that the graph passes the Vertical Line Test.

Answer:

34

Step-by-step explanation:

The volume is calculated as approximately 33.5 cubic inches when rounded to the nearest tenth.

The question asks us to calculate the volume of a sphere with a known radius using the value of 3.14 for pi. The formula for the volume of a sphere is V = (4/3)πr³. Given that the radius (r) is 2 inches, we substitute the given values into the formula to find the volume:

V = (4/3)πr³

V = (4/3) × 3.14 × (2 inches)³

V = (4/3) × 3.14 × 8

V ≈ 33.51 cubic inches

We then round the result to the nearest tenth to get the final answer:

The approximate volume of the ornament is 33.5 cubic inches.

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} r=4 \end{cases}\implies A=\pi 4^2\implies A=16\pi \implies \stackrel{\pi =3.14}{A=50.24}[/tex]

Answer:

50.24 sq units

Step-by-step explanation:

What is the question?

I would say there would be 5 blue pencils, 4 green pencils, and 2 red pencils. I say this because the chance of grabbing a green pencil is smaller than the blue, and the chance of grabbing a red one is smaller than the green one, as a result, we are left wit 5 blue pencils, 4 green pencils, and 2 red pencils.

Answer:

The first example: a · (b · c) = (a · b) · c

Step-by-step explanation:

The associative property regroups values by changing the location of parentheses. If you notice, the order of the values is not changed. Both sides have a x b x c, only the parentheses have been moved. Moving the parentheses changes the progression of what is multiplied (whatever is in the parentheses is multiplied together first) but doesn't change the final answer.

The statement a. (b . c)  =  ( a . b ) . c describes the correct property.

Associative property for multiplication states that rearranging the terms and brackets places in a multiplication of two or more than two terms does not change the result of the multiplication.

There are more properties multiplication is commutative also for example a×b = b×a

a . ( b . c ) = ( a . b) . c is the right answer here brackets have been changed according to the statement.

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Answer:

d

Step-by-step explanation: 0.2 x 100% = 102.1/ 20%= d

look below and can i have brainlyplus                                                             Start with the original price, $80.

If you take 20% off, then you will be paying 80% of the original price. Calculate 80% of $80.

80% of $80 = 80% * $80 = 0.8 * $80 = $64

After applying the 20% discount, the new price is $64.

Now you apply the 10% coupon.

Since you are taking 10% off the discounted price, you will be paying 90% of the discounted price.

90% of $64 = 0.9 * $64 = $57.6

The final discounted price is $57.60

Step-by-step explanation:

Answer:

a=4

Step-by-step explanation:

6.97a = 27.88

Divide 6.97a on both sides

6.97a/6.97a = 27.88/6.97a

a=4

6.97a = 27.88

Divide both sides by 6.97.

6.97a/6.97 = 27.88/6.97

a = 4

Answer:

the answer is 42.93

Step-by-step explanation:

just did it

Answer:

38: is A

39: is A

Step-by-step explanation:

To express rates in the lowest terms, divide both the numerator and denominator by their greatest common divisor. For unit rates, calculate the rate per single unit of item or time. Example: $7 for 2 kg simplifies to a rate of $3.50 per kg, six teachers for 108 students simplifies to one teacher for 18 students, $20 for 5 T-shirts becomes $4 per T-shirt, and 45 miles in half an hour translates to 90 miles per hour.

Question 38: Our goal is to express the rates in the lowest terms.

Question 39: Here, we will convert the given rates to unit rates.

Final answer:

The coordinates of the y-intercept of 5x − 5y = 4 are (0, -4/5).

Explanation:

The y-intercept of a linear equation represents the point where the line intersects the y-axis. To determine the coordinates of the y-intercept, we set the x-coordinate to 0 and solve for y. In the equation 5x - 5y = 4, To determine the coordinates of the y-intercept of the equation 5x − 5y = 4, we set the x-value to 0 since, by definition, the y-intercept occurs where the line crosses the y-axis (x=0). The equation simplifies to -5y = 4. we substitute x=0 and solve for y:

5(0) - 5y = 4
-5y = 4
y = -4/5

Therefore, the coordinate of the y-intercept is (0, -4/5).

Answer: option a

Step-by-step explanation:

You can calculate the volume of a prism with this formula:

[tex]V_{prism}=lwh[/tex]

Where l is the lenght, w is the width and h is the height.

You can identify from the figure that:

[tex]l=12cm\\w=5cm\\h=2.54cm[/tex]

Then, substituting these values into the formula, you get that the volume of this prism is:

[tex]V_{prism}=(12cm)(5cm)(2.54cm)=152.4cm^3[/tex]

Answer:

Final answer is choice a) [tex]Volume = 152.4 \, cm^3[/tex]

Step-by-step explanation:

Given that length of the prism = 12 cm

Given that width of the prism = 5 cm

Given that height of the prism = 2.54 cm

Then volume of the rectangular prism is given by formula:

[tex]Volume = (Length)(Width)(Height)[/tex]

[tex]Volume = (12 cm)(5 cm)(2.54 cm)[/tex]

[tex]Volume = 152.4 \, cm^3[/tex]

Hence final answer is choice a) [tex]Volume = 152.4 \, cm^3[/tex]

Answer:

44 and 46

Step-by-step explanation:

Let

x,x+2-----> the  two consecutive positive even integers

we know that

[tex](x+x+2)^{2}=x^{2}+(x+2)^{2} +4,048[/tex]

Solve for x

[tex](x+x+2)^{2}=x^{2}+(x+2)^{2} +4,048\\ \\4x^{2} +8x+4=x^{2}+x^{2} +4x+4+4,048\\ \\2x^{2} +4x-4,048=0[/tex]

Solve the quadratic equation by graphing

The solution is x=44

see the attached figure

therefore

the numbers are

x=44

x+2=46

Step-by-step Answer:

There is a total of 10 coins, 5 dimes, 2 quarters and three pennies.

By picking a coin, it could be any that shows up out of the 10, so the probability of picking any coin in particular is 1 / 10.

If there are 5 dimes, the probability of picking ANY one particular dime is 1/10, so with 5, the probability of picking ANY of the five dimes is 5/10 = 1/2.

Going along the same line of thought, the probability of picking any of quarters and pennies would be 2/10+3/10 = 5/10 = 1/2 as well.

Answer:

7

1

0.1666666667

The following exponents can be simplified as follows:

The exponent of a number says how many times to use the number in a multiplication.

For example: 8 to the Power 2( or 8^2)

In 8^2 the "2" says to use 8 twice in a multiplication,

so 8^2 = 8 × 8 = 64

In words: 8^2 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared".

So coming to the question:

a) 7^1 = 7 times 1 from definition that 7*1=7

b)To prove this one, I will go with the property of exponents:

  [tex]a^{(b-c)}=\dfrac{a^b}{a^c}[/tex]

implies:

[tex]4^0=4^{(2-2)}=\dfrac{4^2}{4^2} =1[/tex]

c)Applying the previous property:

[tex]6^{-1}=6^{0-1}=\dfrac{6^0}{6^1}=\dfrac{1}{6}[/tex]

Therefore, with the help of definitions and property of exponent, we can simplify it.

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Answer:

The number of students per year increasing

Answer: For Last Question 4.50

Step-by-step explanation:It depends on the price per pound. Let's say the price per pound is 50 cents (or 0.50). (This is an example, the answer I'm giving will most likely NOT be correct, due to the nature of your question - sorry!) To calculate the price of Derek's package, you would multiply 7 (the weight of the package) by 0.50 (the price per pound), which totals to 3.50 Next, to calculate the price for Keisha's package, you'd do the same thing, but instead of multiplying 7 by the price per pound, you would multiply 10 by the price per pound, or 0.50. This multiplies out to 5 dollars. Next you'd subtract Derek's price from Keisha's, which is 5 - 3.50 or 1.50. If it is asking for a percentage, it would be about 150%.