How do you know that the triangle with side lengths 6, 8, and c is a right triangle?

Answer:

City's Area = 507.44 sq. mi.

Step-by-step explanation:

We will use population density formula to solve this problem easily.

We have:

Population Density = Total Population/ Land Area

Given,

Population Density = 24,403

Total Population = 12,383,007

We want land area, so we simply plug in the numbers into the formula and solve for City's Area. Shown below:

[tex]Population  \ Density = \frac{Total \ Population}{Land \ Area}\\24,403=\frac{12,383,007}{Land \ Area}\\Land \ Area = \frac{12,383,007}{24,403}\\Land \ Area = 507.44[/tex]

THe units is Square Miles, so we can say:

City's Area = 507.44 sq. mi.

1. 4(2+3c) = 56

c = 4

3. -29 = 5(2a-1)+2a

a = -2

5 . 7p-(3p+4) = -2(2p-1)+10

p=2

7. 1/2 (-4+6x) = 1/3x + 2/3*(x+9)

x=4

Step-by-step explanation:

1. 4(2+3c) = 56

[tex]4(2+3c) = 56\\8+12c = 56[/tex]

Subtracting 8 from both sides

[tex]8-8+12c = 56-8\\12c = 48[/tex]

Dividing both sides by 12

[tex]\frac{12c}{12} = \frac{48}{12}\\c = 4[/tex]

Checking:

[tex]4[2+3(4)] = 56\\4(2+12) = 56\\4(14) = 56\\56 = 56[/tex]

3. -29 = 5(2a-1)+2a

Simplifying

[tex]-29 = 10a-5+2a\\-29 = 12a-5[/tex]

Adding 5 on both sides

[tex]-29+5 = 12a - 5+5\\-24 = 12a[/tex]

Dividing both sides by 12

[tex]\frac{12a}{12} = \frac{-24}{12}\\a = -2[/tex]

Checking:

[tex]-29 = 5(2a-1)+2a\\-29 = 5[2(-2)-1]+2(-2)\\-29 = 5(-4-1) -4\\-29 = 5(-5) -4\\-29 = -25-4\\-29 = -29[/tex]

5 . 7p-(3p+4) = -2(2p-1)+10

Simplifying

[tex]7p-3p-4 = -4p+2+10\\4p-4 = -4p+12[/tex]

Adding 4 on both sides

[tex]4p-4+4 = -4p+12+4\\4p = -4p+16[/tex]

Adding 4p on both sides

[tex]4p+4p = -4p+4p+16\\8p = 16[/tex]

Dividing both sides by 8

[tex]\frac{8p}{8} = \frac{16}{8}\\p = 2[/tex]

Checking:

[tex]7p-(3p+4) = -2(2p-1)+10\\7(2)-[3(2)+4] = -2[2(2)-1] +10\\14 - (6+4) = -2 (4-1) +10\\14 - 10 = -2(3) +10\\4 = -6+10\\4=4[/tex]

7. 1/2 (-4+6x) = 1/3x + 2/3*(x+9)

Simplifying

[tex]\frac{1}{2} (-4+6x) = \frac{1}{3}x+\frac{2}{3}(x+9)\\\frac{-4}{2}+\frac{6x}{2} = \frac{x}{3} +\frac{2x}{3} + \frac{18}{3}\\-2+3x = \frac{x+2x+18}{3}\\-2+3x = \frac{3x+18}{3}\\3(-2+3x) = 3x+18\\-6+9x = 3x+18[/tex]

Adding 6 on both sides

[tex]-6+6+9x = 3x+18+6\\9x = 3x+24[/tex]

Subtracting 3x from both sides

[tex]9x-3x = 3x-3x+24\\6x = 24[/tex]

Dividing both sides by 6

[tex]\frac{6x}{6} = \frac{24}{6}\\x = 4[/tex]

Checking:

[tex]\frac{1}{2} [-4+6(4)] = \frac{1}{3}(4)+\frac{2}{3}(4+9)\\\frac{1}{2}(-4+24) = \frac{4}{3}+\frac{2}{3}(13)\\\frac{1}{2}(20) = \frac{4}{3} +\frac{26}{3}\\15 = \frac{4+26}{3}\\15 = \frac{30}{3}\\15=15[/tex]

Keywords: Linear equations

Learn more about linear equations at:

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Answer:

Step-by-step explanation:

c

Answer:

$18

Step-by-step explanation:

12*4=48

48-30=18

Answer:

k = 0.2980

Step-by-step explanation:

Given:

number of months t =3

number of hits y = 10000

The equation is modeled as

[tex]y= 4090e^{kt}[/tex]

We need to find value of k.

Now Substituting the values in above equation we get.

[tex]10000= 4090e^3k\\e^{3k}=\frac{10000}{4090}\\\\[/tex]

Now taking Anti log on both side to remove e we get,

[tex]3k = \ ln \frac{10000}{4090}\\\\3k = 0.8940\\k = \frac{0.8940}{3}= 0.2980[/tex]

Hence the value of k = 0.2980.

The value of k is 0.2981.

We are given that in the website's third month (t = 3), there were 10,000 hits. We need to find the value of k.

1. First, substitute y = 10000 and t = 3 into the given equation:

10000 = 4090e3k

2. Next, solve for the exponential term:

10000 / 4090 = e3k

This simplifies to:

10 / 4.09 = e3k

2.444 = e3k

3. Take the natural logarithm (ln) of both sides to solve for k:

ln(2.444) = 3k

Calculating ln(2.444) yields approximately 0.8944.

0.8944 = 3k

4. Finally, solve for k:

k = 0.8944 / 3

k ≈ 0.2981

Therefore, the value of k, rounded to four decimal places, is approximately 0.2981.

Answer:

2/3

Step-by-step explanation:

Cancel the common factor 2 = 2/3

Answer:

24

Step-by-step explanation:

in this, the blank is 'y'. I filled the x with -8

)(−8)−(−8−40)=(2)(−8)−(y−8)

Step 1: Simplify both sides of the equation.

(10)(−8)−(−8−40)=(2)(−8)−(y−8)

(10)(−8)+−1(−8−40)=(2)(−8)+−1(y−8)(Distribute the Negative Sign)

(10)(−8)+(−1)(−8)+(−1)(−40)=(2)(−8)+−1y+(−1)(−8)

(10)(−8)+8+40=(2)(−8)+−y+8

−80+8+40=−16+−y+8

(−80+8+40)=(−y)+(−16+8)(Combine Like Terms)

−32=−y+−8

−32=−y−8

Step 2: Flip the equation.

−y−8=−32

Step 3: Add 8 to both sides.

−y−8+8=−32+8

−y=−24

Step 4: Divide both sides by -1.

−y

−1

=

−24

−1

y=24

Answer:

y=24

Answer:

what' you should do to stay healthy is eat vegetables and fruits grains and anything else you know is good for you and you should also drink water everyday. what you shouldn't do to stay healthy is basically eat junk food and drink soda also eat lots of candy but eating healthy is much better

Answer:

Staying healthy physically can help you stay healthy emotionally too. If you're eating the right food and keeping fit, your body will be strong and help you to cope with stress and also fight illness. Eating well and exercising often when you're a teenager will also help you stay in good health later in life.

Step-by-step explanation:

The school net ball team drew 2 matches. The team won [tex]\frac{5}{8}[/tex] of total matches played

Given, A school netball team won ten matches, lost four and drew [tex]\frac{1}{8}[/tex] of the total played

Let the total number of matches played be "n"

Number of matches drawn = [tex]\frac{1}{8}[/tex] of n

Total matches played = number of won matches + number of lost matches + number of drawn matches

[tex]\begin{array}{l}{n=10+4+\frac{1}{8} n} \\\\ {n-\frac{1}{8} n=10+4}\end{array}[/tex]

Taking "n" as common from left hand side,

[tex]\begin{array}{l}{\mathrm{n}\left(1-\frac{1}{8}\right)=14} \\\\ {\mathrm{n} \times \frac{8-1}{8} \quad 14} \\\\ {\mathrm{n} \times \frac{7}{8}=14} \\\\ {\mathrm{n}=16}\end{array}[/tex]

So, they played 16 matches in total

Number of matches drawn = [tex]\frac{1}{8}[/tex] of n = [tex]\frac{1}{8} \times 16 = 2[/tex][tex]\text { Fraction of won matches }=\frac{\text { number of matches won }}{\text { number of matches played }}=\frac{10}{16}=\frac{5}{8}[/tex]

[tex]\text { Hence, the team drew } 2 \text { matches and won } \frac{5}{8} \text { of total played matches. }[/tex]

Answer:

[tex]y=4\sqrt{3}\ units[/tex]

Step-by-step explanation:

Triangle MRN is created by folding an equilateral triangle by half. Since triangle MRN is right triangle, the equilateral triangle must be folded along the height drawn to one side.

In equilateral triangle with side length of a units, the height is [tex]\dfrac{a\sqrt{3}}{2}\ units[/tex] and the height is greater than half the side because

[tex]\dfrac{a\sqrt{3}}{2}>\dfrac{a}{2}.[/tex]

The leg with length x units has the smaller projection (2 units long) than the leg with length y units has (6 units long).

This means the leg with length y units is the height of the equilateral triangle. If the leg with length y units is the height of the equilateral triangle, then the hypotenuse MN = 8 units is the side of the equilateral triangle and lex with length x units is half the side, so x = 4 units.

By the Pythagorean theorem,

[tex]y^2=8^2-4^2\\ \\y^2=64-16\\ \\y^2=48\\ \\y=4\sqrt{3}\ units[/tex]

The value of y is 4*sqrt(3) units.

The problem states that triangle MRN is created by folding an equilateral triangle in half. Since triangle MRN is a right triangle, the equilateral triangle must have been folded along its height. We are given that the side length of the equilateral triangle is 8 units. We are asked to find the value of y, which is the length of the leg of triangle MRN that is opposite the right angle.

Here's how we can solve the problem:

1. Identify the relevant information:

   - Triangle MRN is a right triangle.

   - The original equilateral triangle has side length 8 units.

   - We want to find the value of y, which is the length of the leg of triangle MRN opposite the right angle.

2. Use the properties of equilateral triangles:

   - In an equilateral triangle, all sides are equal and all angles measure 60 degrees.

   - The height of an equilateral triangle divides the triangle into two 30-60-90 triangles.

   - The height of an equilateral triangle with side length a is sqrt(3)*a / 2.

3. **Relate the information to find y:**

   - Since the equilateral triangle was folded along its height, the height of the equilateral triangle is also the hypotenuse of triangle MRN (side MN).

   - Therefore, MN = sqrt(3)*8 / 2 = 4*sqrt(3).

   - We are given that MN = 8, so 4*sqrt(3) = 8.

   - Solving for sqrt(3), we get sqrt(3) = 2.

   - Now we can use the Pythagorean theorem in triangle MRN: y^2 + (4)^2 = (8)^2.

   - Substituting sqrt(3) = 2, we get y^2 + 16 = 64.

   - Solving for y, we get y = sqrt(48) = 4*sqrt(3).

Therefore, the value of y is 4*sqrt(3) units.

Answer:

$7,500.00

Step-by-step explanation:

The Realtor commission will be 5% of $150,000.00

(5% * $150,000)/100% = $7,500.00

The realtor makes a 5% commission on a $150,000 house, which equates to a commission of $7,500 by multiplying the sale price by the commission rate (0.05).

To calculate the amount of commission a realtor earns on a house sale, you simply multiply the sale price of the house by the commission rate. In this case, the realtor makes a 5% commission on a $150,000 house sale. We calculate the commission as follows:

Therefore, the realtor will earn a commission of $7,500 for selling the $150,000 house.

Answer:

that's your answer...

Answer:

equation- 4÷x=-7

x= -4/7

Step-by-step explanation:

I think the answer is -4/7 i tried my best :)

so x=-4/7

Answer: x=-5

(^._.^)ﾉ

Step-by-step explanation:

4x-3=2x-13

Subtract

4x−3−2x=−13

Simplify

2x−3=−13

Add 3 to both sides

2x=−13+3

Simplify again

2x=-10

Divide both sides by 2

x=[tex]-\frac{10}{2}[/tex]

Simplify one last time

x=-5

You're finished! Not only that but you found the answer :3

Hope this helps, have a BLESSED and wonderful day! :-)

Answer: 10 free throws made, 9 two-point shots made

Step-by-step explanation:

x=number of free throws

y=number of two-point shots

x+y=19

x+2y=28

solve by elimination

x+2y=28

-(x+y=19)

--------------

y=9

x=10

Answer: 10 free throws made, 9 two-point shots made

Step-by-step explanation:

x=number of free throws

y=number of two-point shots

x+y=19

x+2y=28

solve by elimination

x+2y=28

-(x+y=19)

(Y=9

X=10)

Answer:

6x^3

Step-by-step explanation:

2160x^8/ 60x^2

2160/60=36

x^8-2 because your dividing

x^6

36x^6 (you're not done)

after you've got the square root

6x^3 because

36=6*6

and the square root of 6 is 2.45 which rounds to 3

(I'm pretty sure this is the answer).

The simplified form of [tex]\rm \sqrt{\dfrac{2160 x^8}{60x^2}[/tex] is 6x³ , Option C is the right answer.

Square root of a positive square number is the number itself.

[tex]\rm \sqrt{y^8} = y^4[/tex]

In the given question the expression given is

[tex]\rm \sqrt{\dfrac{2160 x^8}{60x^2}[/tex]

To simplify this

the numerator and the denominator has to be simplified first

[tex]\rm \dfrac{2160x^8}{60x^2}\\[/tex]

[tex]\rm \dfrac{2160}{60}\\ \\\\\ \dfrac{1080}{30}\\\\\\ \dfrac{540}{15} \\\\\\ \dfrac{108}{3}\\\\= 36[/tex]

[tex]\rm \dfrac{x^8}{x^2} \\\\= x^{8-2}\\\\= x^6[/tex]

Therefore

[tex]\rm \sqrt{36x^6}[/tex]

6x³

The simplified form of [tex]\rm \sqrt{\dfrac{2160 x^8}{60x^2}[/tex] is 6x³ , Option C is the right answer.

To know more about Square root

https://brainly.com/question/3120622

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Answer:

x=-3, y=5. (-3, 5).

Step-by-step explanation:

y=x+8

x+y=2

----------

x+x+8=2

2x+8=2

2x=2-8

2x=-6

x=-6/2

x=-3

y=-3+8=5

Answer:

(-3,5)

Step-by-step explanation:

Answer: f(x) = -3| x - 1 |  is really just  f(x) = -3| x - 1 | + 0.

now, what value of "x" makes the absolute value expression to 0?

well, let's just set it to 0 and check,

x - 1 = 0

x = 1

so if "x" ever becomes 1, the | x - 1| will turn to 0, therefore, the vertex is at   

f(x) = -3| (1) - 1 | + 0  -------------->  ( 1, 0 )

To calculate the change in water amount after 1/3 hour, the draining rate of -3.75 gallons per hour is multiplied by 1/3, resulting in a total change of -1.25 gallons of water.

The student has asked about the change in the amount of water in a bathtub after a certain period, given a constant rate of draining. The bathtub drains at a rate of -3.75 gallons per hour. To find the total change in the amount of water after 1/3 hour (20 minutes), we multiply the rate by the time.

First, we convert 1/3 of an hour to minutes:

1/3 hour = 60 minutes / 3 = 20 minutes.

Next, we calculate the change in water:

Change in water = Rate  imes Time

Change in water = -3.75 gallons/hour  imes 1/3 hour

Change in water = -3.75 gallons/hour  imes 0.3333... (repeating)

Change in water = -1.25 gallons.

Therefore, the bathtub will drain 1.25 gallons of water in 1/3 of an hour.

Answer:

1. C

2. A

The drawings will help

Remember: Keep, Change, Flip

Answer:

Henry uses 36 nails in large bookshelves and 52 nails in small bookshelves.

Step-by-step explanation:

Let in each large bookshelves Henry uses x nails and in each small bookshelves, Henry uses y nails.

Now, he built 10 small bookshelves and 1 large bookshelf, using a total of 412 nails.

So, 10x + y = 412 ......... (1)  

Again, he built 10 small bookshelves and 8 large bookshelves, using a total of 776 nails.

So, 10x + 8y = 776 ........... (2)

Now, subtracting equation (1) from equation (2) we get, 7y = 364

⇒ y = 52

Again, from equation (1) we get, 10x = 412 - 52 = 360

⇒ x = 36

Therefore, Henry uses 36 nails in large bookshelves and 52 nails in small bookshelves. (Answer)

Final answer:

Henry uses 36 nails for a small bookshelf and 52 nails for a large bookshelf, according to the system of equations derived from the information given.

Explanation:

Calculating the Number of Nails Used by Henry

To solve this problem, we will use a system of equations.
Let's define x as the number of nails used for a small bookshelf and y as the number of nails used for a large bookshelf. From the question, we have the following equations based on the information given:

10x + 1y = 412 nails (first scenario with 10 small and 1 large bookshelf)

10x + 8y = 776 nails (later scenario with 10 small and 8 large bookshelves)

We can use these two equations to find out the values of x and y. Let's subtract the first equation from the second to eliminate x from our calculations:

10x + 8y − (10x + 1y) = 776 − 412
7y = 364
y = 52

Now we know that Henry uses 52 nails for a large bookshelf. Next, we will find the number of nails for a small bookshelf by substituting the value of y into the first equation:

10x + 1(52) = 412
10x = 412 − 52
10x = 360
x = 36

Hence, Henry uses 36 nails for a small bookshelf.

Final answer:

The median of the data set 56, 21, 48, 17, 18 is 21, and the mean is 32 after arranging the data in ascending order and performing the necessary calculations.

Explanation:

To determine which statement about the data set 56, 21, 48, 17, 18 is correct, we need to calculate both the median and the mean.

To calculate the median:

To calculate the mean:

The correct statements about the data set are: The median is 21 and the mean is 32.

Answer:

The number of sides of the polygon with 135° interior angle is 8  

Step-by-step explanation:

Given as :

The measure of each interior angle of regular polygon = 135°

Let The total number of sides = n

So, each internal angle of a regular polygon with n sides = [tex]180^{\circ}- \frac{360^{\circ}}{n}[/tex]

or,   135°  = [tex]180^{\circ}- \frac{360^{\circ}}{n}[/tex]

or, [tex]\frac{360^{\circ}}{n}[/tex] = 180° - 135°

or,   [tex]\frac{360^{\circ}}{n}[/tex] = 45°

∴   n = [tex]\frac{360^{\circ}}{45^{\circ}}[/tex]

I.e  n = 8

Hence the number of sides of the polygon with 135° interior angle is 8  Answer

Answer:

3

Step-by-step explanation:

According to the Triangle Inequality Theorem, the sum of any 2 sides of any triangle must be greater than the length of the third side. That is:

AB + BC > AC and AB + AC > BC and AC + BC > AB

So in this case:

if AC + AB > BC

x + 12 > 15

After substracting 12 from each side of the equation, we get that:

x > 3

Hence, the value of x must be greater than 3.

Answer:

Here we have to use the Triangle Inequality Theorem, because the problem it's asking about the restriction of one side, with two sides given. This theorem, in words, states that the sum of the minor sides is more than the length of the major sides of all three. So, if we translate this to equation, we have:

[tex]AB + BC > AC[/tex]

Where [tex]AB=12[/tex]; [tex]BC=x[/tex] and [tex]AC=15[/tex]

Assuming that [tex]AC[/tex] is the longest side we applied the theorem to this problem. Now, replacing all values we have:

[tex]12+x>15\\x>15-12\\x>3[/tex]

Therefore, the unknown side must be greater than 3 to not violate the Triangle Inequality Theorem, which is always true about every triangle.

Answer: –1.8x – 4.5

Step-by-step explanation:

The guy above me obviously doesn’t know how to do this so here this is the correct answer

Answer:

–1.8x – 4.5

Step-by-step explanation:

Answer:

set the bottom equal to zero and exclude the x value you find when you solve the equation.

Step-by-step explanation:

Answer:

Remember that domain = x. You can discover the domain by looking at where the smallest and largest points of a graph are according to the x-axis. For example, look at the graph below. The domain would be - ∞ to  + ∞ because the parabola widens forever.

Answer: 26

Step-by-step explanation:

30-17=13

13+13=26

Answer:

26 boi

Step-by-step explanation:

Answer:

-7/48 in

Step-by-step explanation:

Assuming that the movement varies linearly with time,

3 years ------> -7/16 in

1 year -------> -7/16 ÷ 3 = -7/48 in

Answer:

The simplified expression is -4.4c+1.1−4.4c+1.1

Answer:

40 pounds

Step-by-step explanation:

Given: Cost of a candy [tex](c_1)[/tex]= [tex]\$ 12[/tex] per pound

           Cost of candy [tex](c_2) = \$ 19\ per\ pound[/tex]

           Total amount of mixture of be produced = [tex]70\ pound[/tex]

           Selling price of mixture = [tex]\$ 15 \ per\ pound[/tex]

Let´s x be the amount of [tex]c_1 [/tex] to be mixed in the mixture.

∴ Cost of [tex]c_1[/tex] in the mixture = 12x

Next, Cost of [tex]c_2[/tex] in the mixture = [tex](70 - x)\times 19[/tex]

And we know the cost of final mixture = [tex]70 \times 15 = 1050[/tex]

Now, putting all the value in the equation

⇒ [tex]12x + 19 \times (70 - x) = 1050[/tex]

⇒ [tex]1330 - 7x = 1050[/tex]

⇒ [tex]-7x = -280[/tex]

∴ [tex]x = 40\ pound[/tex]

∴ 40 pounds of candy worth $12 per pound to be mixed in the mixture.