A rectangle container that has a length of 25cm,a width of 37cm, and a height of 21cm a is filled with water to a depth of 18 cm. When an additional 7 liters of water are poured into the container, some water overflows.How many liters water overflows the container?use words,pictures,and numbers to explain your answer.(Remember:_1cm3=1 mL.)

well, let's grab a couple of points off the line hmmmm let's see, the lines runs through (0, 4) and also (3,5), so let's use those to get its slope and thus its function.

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{5}) ~\hfill slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-4}{3-0}\implies \cfrac{1}{3}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=\cfrac{1}{3}(x-0)\implies y-4=\cfrac{1}{3}x \\\\\\ y=\cfrac{1}{3}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

for z the fraction value is 1/26 and for other letters then Z is 25/26

Answer: 15/4

Step-by-step explanation:

1. 12/1 - 33/4

2.  48/4 -33/4

3. 15/4

If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a parallelogram.

A triangle is a three-sided polygon that consists of three edges and three vertices.

If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a quadrilateral, specifically a parallelogram.

The two identical triangles, when combined in this way, will have their bases aligned and their vertices opposite each other, forming two pairs of parallel sides.

A parallelogram, which is a quadrilateral with opposite sides that are parallel and congruent.

Hence, If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a parallelogram.

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Rel. Max:

-1 , x=0

Rel. Min:

-6 ,x=5

Increasing in the interval(s)

(-infinty ,0) U (5, infinity)

[ i doubt the above answer]

Decreasing in the interval(s)

(0,5)

Domain

it could be R

Range

R

Step-by-step explanation:

Look at the picture.

The function has a realtive maximum of -1 at x = 0.

The function has a realtive minimum of -6 at x = 5.

The function is increasing on the intervals: (-∞, 0> and <5, ∞).

The function is decreasing on the interval: <0, 5>.

The domain of the function is: (-∞, ∞) = R

The range of the function is: (-∞, ∞) = R

Answer:

y = 100x + 400

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 400) and (x₂, y₂ ) = (1, 500) ← 2 points from the table

m = [tex]\frac{500-400}{1-0}[/tex] = 100

note the line crosses the y- axis at (0, 400) ⇒ c = 400

y = 100x + 400 ← equation of line

The equation of the line represented by the following table in slope-intercept form is y = 100x + 400.

The equation of a straight line in the form y = mx + c where m is the slope of the line and c is its y-intercept is known as the slope-intercept form. Here both the slope (m) and y-intercept (c) have real values. It is known as slope-intercept form as it gives the definition of both the slope and y-intercept.

Slope of a straight line can be found using two given points say (x1,y1) and (x2,y2).

Slope (m) = (y2 - y1) / (x2 - x1) .

Taking any two arbitrary points, from the table given aside we have x1 = 0, x2 = 1, y1 = 400 and y2 = 500

⇒ Slope (m) = (y2 - y1) / (x2 - x1) .

=  (500 - 400)/(1 - 0)

∴  Slope (m) = 100 .

The y-intercept of the line is the value of y coordinate when the value of x = 0. In other words, y-intercept is the point where the curve touches the y-axis.

∴ From the table, y-intercept (c) = 400 .

Thus, we have slope (m) = 100 and y-intercept (c) = 400 .

The equation of straight line is y = 100x + 400 .

Therefore, the equation of the line represented by the following table in slope-intercept form is y = 100x + 400.

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Answer:

(3a-1)(3a+1)

Step-by-step explanation:

This is the difference of two squares so we can factorise using the rules

x^2-y^2 = (x-y)(x+y)

In this case x = 3a and y = 1 since (3a)^2 = 9a^2 and 1^2 = 1

Answer: (x - 3) (2x-1)

Answer:

(x+3)(2x+1)

Step-by-step explanation:

I got it right on khan academy.

[tex]\bf y=\cfrac{2}{3}x\stackrel{\stackrel{b}{\downarrow }}{-3}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf 6x-7y=21\implies -7y=-6x+21\implies y=\cfrac{-6x+21}{-7}\implies y=\cfrac{6x-21}{7} \\\\\\ \stackrel{\textit{distributing the denominator}}{y=\cfrac{6x}{7}-\cfrac{21}{7}}\implies y=\cfrac{6}{7}x\stackrel{\stackrel{b}{\downarrow }}{-3}[/tex]

y=mx+b

b=y intercept

get into this form with no coefficient to y

Original: yint: -3

1)x+4y=12

4y=-x+12

y=-.25+3

b=3

2)2/3x+3y=-3

3y=2/3x-3

y={doesn't matter}x-1

b=-1

3)-2/3x+3y=6

3y=-2/3x+6

y={doesn't matter} +2

b=2

4) 6x-7y=21

-7y=-6x+21

y=6/7-3

b=-3

4 is the answer

Answer: 1.25

Step-by-step explanation:

Because...

All you have to do is divide the length value by 3

and your answer will be 1.25.

* Hopefully this helps:) Mark me the brainliest:)!!!

Answer:

1.25yd

Step-by-step explanation:

couted through table

Answer:

About 57.5 inches

Step-by-step explanation:

From the points which relates height and age a linear model was made. This allow us to estimate joanna’s height in those years the points are missing. For example, when she was 11 years old, her height was about 57.5 inches.

Answer:

57.5

Step-by-step explanation:

Answer:

3x+24 more widgets

Step-by-step explanation:

A company owns two manufacturing plants:

To find how many more items the first plant produces daily than the second plant, we have to subtract from the number of widgets the first plant produces the second plant produces. So,

[tex](8x+17)-(5x-7)\\ \\=8x+17-5x+7\ [\text{Eliminate brackets}]\\ \\=(8x-5x)+(17+7)\ [\text{Combine the like terms}]\\ \\=3x+24[/tex]

Answer:

3x + 24

Step-by-step explanation:

The question simply requires us to find the difference between the daily production levels of the two plants;

The first plant produces 8x + 17

The second plant produces 5x - 7

The difference between these two expressions will be our required solution;

(8x + 17) - ( 5x - 7) = 8x + 17 - 5x + 7

= 8x - 5x +17 + 7 = 3x + 24

Answer:

[tex]31\frac{1}{2}ft^2[/tex]

Step-by-step explanation:

From the information given each of the three rectangular countertops has dimension [tex]4\frac{3}{8}[/tex] by  [tex]2\frac{2}{5}[/tex] feet.

The area of a rectangular shapes is the product of the dimensions.

Each rectangular countertop has area;

[tex]4\frac{3}{8}\times 2\frac{2}{5}=\frac{35}{8}\times \frac{12}{5} =10\frac{1}{2}ft^2[/tex]

Therefore the number of square feet tiles needed to cover all the countertops is [tex]=3\times 10\frac{1}{2}=31\frac{1}{2}ft^2[/tex]

The answer is:

The total surface area of the pyramid is:

[tex]TotalSurfaceArea=192ft^{2}[/tex]

To calculate the surface area of a square pyramid, we need to use the following formula:

[tex]TotalSurfaceArea=\frac{1}{2}pl+BaseArea[/tex]

Where,

p, is the perimeter of the base.

l, is the slant of the pyramid.

Base area, is the area of the square base.

Now, from the statement we know that the base has a length of 6 feet, and the height of a face (slant) is 13 feet.

So, calculating, we have:

[tex]BaseArea=BaseLength^{2}=(6ft)^{2} =36ft^{2}[/tex]

[tex]Perimeter=4*side=4*6feet=24feet[/tex]

The total surface area will be:

[tex]TotalSurfaceArea=\frac{1}{2}l+BaseArea[/tex]

[tex]TotalSurfaceArea=\frac{1}{2}*24ft*13ft+36ft^{2}[/tex]

[tex]TotalSurfaceArea=156ft^{2}+36ft^{2}=192ft^{2}[/tex]

Hence, we have the total surface area of the pyramid is:

[tex]TotalSurfaceArea=192ft^{2}[/tex]

Have a nice day!

Answer:

1.27, -6.27 to the nearest hundredth,

or if you require it in exact form,

-2.5 + √14.25,   -2.5 - √14.25.

Step-by-step explanation:

x^2 = -5x + 8

x^2 + 5x  = 8

Competing the square:

(x + 2.5)^2 - 6.25 = 8

(x + 2.5) = 14.25

x + 2.5 = +/-√14.25

x = -2.5 + √14.25,   -2.5 - √14.25

x = -2.5 + 3.77,  -2.5 - 3.77

= 1.27, -6.27.

half an hour past 7, will be 7 plus 30 minutes then 7:30.

we could also come from the other way, and say is 30 minutes before 8 o'clock.

Check the picture below.

so let's notice, the base is a 6x6 square, and triangular faces have a base of 6 and an altitude/height of 5.  So we can just get the area of the square and the triangles and sum them up and that's the area of the pyramid.

[tex]\bf \stackrel{\textit{triangles' area}}{4\left[ \cfrac{1}{2}(6)(5) \right]}+\stackrel{\textit{square's area}}{(6\cdot 6)}\implies 60+36\implies 96[/tex]

For this case we have that by definition, the surface area of a regular pyramid, is given by:

[tex]SA = \frac {1} {2} p * l + B[/tex]

Where:

p: Represents the perimeter of the base

l: The inclination height

B: The area of the base

Now, since the base is square we have:

[tex]B = 6 ^ 2 = 36 \ cm ^ 2\\p = 6 + 6 + 6 + 6 = 24 \ cm\\l = 5 \ cm[/tex]

Then, replacing the values:

[tex]SA = \frac {1} {2} 24 * 5 + 36\\SA = 60 + 36\\SA = 96 \ cm ^ 2[/tex]

ANswer

[tex]96 \ cm ^ 2[/tex]

First, find the area of lot A.

To find the area, multiply the length by the width.

33*42=1,386

Now, subtract the area of lot a from the total area. This will give us the area of lot b.

1,848-1,386=462

The area of lot b is 462 square feet.

Finally, divide the area of lot b (462) by its length to find the width. Since they both share a side, we know that it’s length is 42 feet.

462/42=11

Lot b is 11 feet wide.

Hope this helps!

Answer:

y = 3x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (1, 0) ← 2 points on the line

m = [tex]\frac{0+3}{1-0}[/tex] = 3

The line crosses the y- axis at (0, - 3) ⇒ c = - 3

y = 3x - 3 ← equation of line

The equation of line l will be;

⇒ y = 3x - 3

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (1, 0) and (0, -3).

Now,

Since, The equation of line passes through the points (1, 0) and (0, -3).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 3 - 0) / (0 - 1)

m = - 3 / - 1

m = 3

Thus, The equation of line with slope 3 is,

⇒ y - 0 = 3 (x - 1)

⇒ y  = 3x - 3

Therefore, The equation of line passes through the points (1, 0) and

(0, -3)  will be;

⇒ y = 3x - 3

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Answer :

1. -3x + 6 = -9

-3x = -9 - 6

-3x = -15

x = -15 / -3

x = 5

2. 5m + 4m = 72

9m = 72

m = 72 / 9

m = 8

3. 6d - 10d = 40

-4d = 40

d = 40 / -4

d = -10

4. 2(x + 4) = 30

2x + 8 = 30

2x = 30 - 8

2x = 22

x = 22 / 2

x = 11

5. 78 = -2(m + 3) + m

78 = -2m - 6 + m

78 = -m - 6

78 + 6 = -m

84 = -m

m = -84

Answer:

Solutions: (2,10), (4,5)

Not solutions: (1,12), (6,10), (12,8), (18,6)

Step-by-step explanation:

Let x be the number of packages of pasta and y be the number of jars of pasta sauce. If pasta costs $1 for a 1-pound package, then x packages of pasta cost $x and weigh x pounds. If pasta sauce costs $3 for a 1.5 pound jar, then y jars cost $3y and weigh 1.5y pounds.

1. Tyler has $36, then

[tex]x+3y\le 36.[/tex]

2. Tyler can carry up to 20 pounds of food in his backpack, then

[tex]x+1.5y\le 20.[/tex]

You get the following system of inequalities:

[tex]\left\{\begin{array}{l}x+3y\le 36\\ x+1.5y\le 20\end{array}\right.[/tex]

Now substitute the coordinates of each point:

(1,12):

[tex]\left\{\begin{array}{l}1+3\cdot 12=37> 36\\ 1+1.5\cdot 12=19\le 20\end{array}\right.[/tex]

False, because first inequality doesn't hold.

(2,10):

[tex]\left\{\begin{array}{l}2+3\cdot 10=32\le 36\\ 2+1.5\cdot 10=17\le 20\end{array}\right.[/tex]

True, both inequalities hold.

(4,5):

[tex]\left\{\begin{array}{l}4+3\cdot 5=19\le 36\\ 4+1.5\cdot 5=11.5\le 20\end{array}\right.[/tex]

True, both inequalities hold.

(6,10):

[tex]\left\{\begin{array}{l}6+3\cdot 10=36\le 36\\ 6+1.5\cdot 10=21> 20\end{array}\right.[/tex]

False, because secondt inequality doesn't hold.

(12,8):

[tex]\left\{\begin{array}{l}12+3\cdot 8=36\le 36\\ 12+1.5\cdot 8=24> 20\end{array}\right.[/tex]

False, because second inequality doesn't hold.

(18,6):

[tex]\left\{\begin{array}{l}18+3\cdot 6=36\le 36\\ 18+1.5\cdot 6=27> 20\end{array}\right.[/tex]

False, because second inequality doesn't hold.

Answer:

39.9

Step-by-step explanation:

A good trick to remember is SOH CAH TOA.

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

Here, we're given an angle and the opposite side, and we want to find the adjacent side.  So we need to use tangent.

tan 31° = 24 / x

x = 24 / tan 31°

x ≈ 39.9

To calculate for this data set, the mean is 73, the median is 74 after sorting the numbers, and the mode is 72 as it appears more than once.

To find the mean, you add up all the numbers in the set and divide by the total count of numbers. For the provided data set:

To find the median, you first sort the data from lowest to highest, then find the middle number. If there is an even number of data points, the median is the average of the two middle numbers.

The mode is the number that occurs most frequently in the data set. For this set, the mode would be the number that appears more than once.

Answer:

(a) What is the probability that you roll a 6?

1/6

(b) What is the probability that you either roll a 6 or do not roll a 6?

1

(c) What is the probability that you don't roll a 6?

5/6

Step-by-step explanation:

(a) What is the probability that you roll a 6?

In a 6- sided cube, a 6 occurs only once. That is only one face is labelled 6. Therefore, the probability that you roll a 6 is;

(number of faces labelled 6)/(totals number of sides) = 1/6

(b) What is the probability that you either roll a 6 or do not roll a 6?

The probability of rolling a 6 was found to be, 1/6.

On the other hand, the probability of not rolling a 6 is;

(number of faces not labelled 6)/(totals number of sides) = 5/6

Therefore, the probability that you either roll a 6 or do not roll a 6 is;

1/6 + 5/6 = 1

These two events are mutually exclusive and exhaustive.

(c) What is the probability that you don't roll a 6?

The probability of not rolling a 6 is;

(number of faces not labelled 6)/(totals number of sides) = 5/6

We have 5 faces not labelled 6 out of 6 possible faces or outcomes

For this case we must solve each of the equations proposed:

A) [tex]m ^ 2 + 9 = 58[/tex]

Subtracting 9 from both sides of the equation we have:

[tex]m ^ 2 = 49[/tex]

Applying root to both sides of the equation:

[tex]m = \sqrt {49}\\m = \pm7[/tex]

B) [tex]7e ^ 2 = 28[/tex]

We divide between 7 on both sides of the equation:

[tex]e ^ 2 = \frac {28} {7}\\e ^ 2 = 4[/tex]

We apply root to both sides of the equation:

[tex]e = \pm \sqrt {4}\\e = \pm2[/tex]

C) [tex]d ^ 2 + 6 = 70[/tex]

Subtracting 6 on both sides of the equation:

[tex]d ^ 2 = 64[/tex]

We apply root to both sides of the equation:

[tex]d =\pm \sqrt {64}\\d = \pm8[/tex]

D) [tex]\frac {1} {2} n ^ 2-10 = 62[/tex]

We add 10 to both sides of the equation:

[tex]\frac {1} {2} n ^ 2 = 72[/tex]

We multiply by 2 both sides of the equation:

[tex]n ^ 2 = 144[/tex]

We apply root to both sides of the equation:

[tex]n = \pm \sqrt {144}\\n =\pm12[/tex]

Answer:

[tex]m = \pm7\\e = \pm2\\d = \pm8\\n = \pm12[/tex]

Answer: First Option

Step-by-step explanation:

The formula to calculate the volume of a cylinder is:

[tex]V = \pi(\frac{d}{2})^2*h[/tex]

Where d is the diameter of the cylinder and h is the height.

Notice that the term d is squared. This means that to increase the volume of a cylinder it is more efficient to increase its diameter as well. Therefore, look for the cylinder with the largest diameter among the options.

The first cylinder is 90 ft in diameter and 40 ft in height and its volume is

[tex]V = \pi(\frac{90}{2})^2*40[/tex]

[tex]V=254469\ ft^3[/tex]

You can verify that it is the tank that has the highest volume

ANSWER

"If x=7, then x - 2 = 5"

EXPLANATION

Let

[tex]p \to \: q[/tex]

be a propositional statement.

The converse of this statement is

[tex]q \to \: p[/tex]

In other words, the converse of the statement,

"If p then q" is "If q, then p"

The given given conditional statement is

"If x - 2 = 5, then x = 7"

Therefore the converse is

"If x=7, then x - 2 = 5"

Answer:

Step-by-step explanation:

[tex]x^2+5x+6=0\\\\x^2+2x+3x+6=0\\\\x(x+2)+3(x+2)=0\\\\(x+2)(x+3)=0\iff x+2=0\ \vee\ x+3=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\x=-2\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x=-3[/tex]

Answer:

$16.50/hr

Step-by-step explanation:

Current pay is 1.00($15/hr).

Current pay plus a 10% raise is 1.10($15/hr) = $16.50/hr

After receiving a 10% raise on a $15 per hour wage, you would be earning $16.50 per hour.

If you are currently making $15 per hour and you receive a 10% raise, you can calculate your new hourly wage by first determining the amount of the raise and then adding it to your current wage. To find the raise amount, you multiply your current wage by the raise percentage expressed as a decimal. In this case:

Amount of raise = Current hourly wage  imes Raise percentage

Amount of raise = $15 per hour  imes 0.10 (since 10% = 0.10)

Amount of raise = $1.50 per hour

Now, you add this raise to your current hourly wage to find your new hourly wage:

New hourly wage = Current hourly wage + Amount of raise

New hourly wage = $15 per hour + $1.50 per hour

New hourly wage = $16.50 per hour

To give an example for comparison, if your job pays $10 per hour and your boss gives you a $2 per hour raise, that is a 20% increase because the percentage change is calculated as $2/$10 = 0.20 or 20%. In your case, the 10% raise increases your wage by $1.50, making it $16.50 per hour after the raise.

Answer:

First option: [tex]y=(x + 8)(x + 3)[/tex]

Step-by-step explanation:

Given the quadratic equation [tex]y = x^2 + 11x + 24[/tex], you need to factor it.

To do this, you need to find two number that when you add them you get 11 and when you multply them you get 24. These numbers are: 8 and 3.

Therefore, knowing this, you can factor the quadratic equation:

[tex]y = x^2 + 11x + 24\\\\y=(x + 8)(x + 3)[/tex]

Then, [tex]y = x^2 + 11x + 24[/tex] is equivalent to the graph of the equation [tex]y=(x + 8)(x + 3)[/tex], which matches with the first option.