Solve for x in the following situation. Show your work.
11x-4/50=70/60

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:

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:

The correct answer is that AC = 4x - 2 or 2(2x - 1)

Step-by-step explanation:

1. Let's review the information given to us for solving the question:

AD = 6x + 10

CD = 2x + 12

2. Let's find the length of AC

AC = AD - CD

Replacing with the real values:

AC = (6x + 10) - (2x + 12)

AC = 6x + 10 - 2x - 12

AC = 6x - 2x + 10 - 12

AC = 4x -2 or 2(2x - 1)

Answer:

Step-by-step explanation:

c

Answer:

$18

Step-by-step explanation:

12*4=48

48-30=18

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:

false.

Step-by-step explanation:

$5 off is well $5 off so, we would be paying $45 for the item. If we took 25%, thats $12.50 therefore you would only pay $37.50. So the 25% saves you $7.50 so it si false. $5 is a worse deal.

Answer:

-6r + 5

Step-by-step explanation:

-4r - 2r + 5

= (-4 -2)r + 5

= -6r + 5

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:

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.

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.

Independent. Two events are dependent if knowing the result of the first one influences what you'd expect from the second.

Consider this example: if I have a sack with 3 black marble and 1 white marble, I have probability 75% of picking a blakc marble, and 25% of picking the white one.

If I pick the white one, and don't replace, the second pick will be dependent on the first one, because now I'm sure that I'll pick one of the black marbles, since they are the only ones left in the sack.

In your example, though, Wendy replaces the marble she picks first. This means that the second pick will take place in the exact same conditions of the first one, and knowing which marble she picked at first doesn't affect in any way the result of the second pick.

As another example, consider rolling two dice. Suppose that the first die lands showing 4. Does this affect in any way what you'd expect from the second die? Well, no: the numbers 1-6 are still equally probable to show up.

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:

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.

Answer:

10(x+9)

Step-by-step explanation:

Answer: 14

Step-by-step explanation:

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 and up

Step-by-step explanation:

35 / 5 = 7

Dan buys at least 7 bags

Answer:

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

Answer:

x=1+/-4i

Step-by-step explanation:

(x+1)/3-(2x-1)/x=-1

find the common denominator,

in this case, it's going to be 3x.

(x^2+x)/3x-(6x-3)/3x=-1

(x^2+x-6x+3)/3x=-1

x^2-5x+3=-3x

x^2-5x-(-3x)+3=0

x^2-5x+3x+3=0

x^2-2x+3=0

apply the quadratic formula in order to find the roots for x.

Since ax^2+bx+c=0, in this case,

a=1, b=-2, c=3

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

x=(-b+/-sqrt(b^2-4ac))/2a

x=(2+/-sqrt(4-12))/2

x=(2+/-8i)/2

x=1+/-4i

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:

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: 26

Step-by-step explanation:

30-17=13

13+13=26

Answer:

26 boi

Step-by-step explanation:

Answer:

41.2876137159

Step-by-step explanation:

100 divided by 7 is 14.2857142857 km per litres. Then 590 divded by 14.2857142857 is 41.2876137159 or 41.29 rounded

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:

1/6

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

1/2 of 12 is 6 so she has 6 yellow stickers

1/3 of 12 is 4 so she has 4 green stickers

that means she only has 2 stickers left because 6+4=10

2/12 of her stickers are blue but you can simplify it to 1/6 by dividing the numerator and denominator by 2

Answer:

Rhombi is the answer...

That is option C

Answer:

C

Step-by-step explanation:

Rhombi has quadrilateral with diagonal and are perpendicular.

Steps to solve:

10.2x + 9.4y when x = 2 and y = 3 ​

= 10.2(2) + 9.4(3)

= 20.4 + 28.2

= 48.6

______

Best Regards,

Wolfyy :)

Answer:

48.6 is the answer

Step-by-step explanation:

Okay, first you plug in the variables  x and y .

So now the new equation is 10.2x2 this is ,because everytime a number get put next to another number you multiply.  So .....

(10.2x2) + (9.4x3)=

20.4+28.2=

48.6

Answer:

c)1200

Step-by-step explanation:

Given: Students were packed shoulder to shoulder in a gym for a pep rally. The students were in a rectangular shaped area of [tex]7500[/tex] ft.

To Find: If each student on average took up a circular space with a diameter of [tex]2.5[/tex] ft what is the best estimate for the number of  students at the pep rally.

Solution:

Consider the figures attached

A student took up a circular space, if they were packed in rows each student acquired a circular space of [tex]2.5[/tex] ft and left some unused area as given in figures

Now,

Area acquired by a student is a square of side [tex]2.5[/tex] ft as given in figure

Area acquired by single student[tex]=(\text{length of square})^2[/tex]

                                                     [tex]=2.5\times2.5[/tex]

                                                     [tex]6.25\text{sq.ft}[/tex]

Total number of students            [tex]=\frac{\text{total area of rectangular gym}}{\text{area acquired by single student}}[/tex]

                                                     [tex]\frac{7500}{6.25}[/tex]

                                                     [tex]1200[/tex]

there are approximately [tex]1200[/tex] students in gym hence option b is correct.

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

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