water in a vertical cylindrical tank of height 22 ft and radius 4 ft is to be pumped out. the density of water is 62.4 lb/ ft3. (a) the tank is full of water and all of the water is to be pumped over the top of the tank.

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{55}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{55}-\stackrel{y1}{(-11)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-3)}}} \implies \cfrac{55 +11}{8 +3} \implies \cfrac{ 66 }{ 11 } \implies 6[/tex]

[tex]\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-\stackrel{y_1}{(-11)}=\stackrel{m}{ 6}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 6 ( x +3) \\\\\\ y+11=6x+18\implies {\Large \begin{array}{llll} y=6x+7 \end{array}}[/tex]

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below

[tex](\stackrel{x_1}{15}~,~\stackrel{y_1}{545})\qquad (\stackrel{x_2}{44}~,~\stackrel{y_2}{864}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{864}-\stackrel{y1}{545}}}{\underset{run} {\underset{x_2}{44}-\underset{x_1}{15}}} \implies \cfrac{ 319 }{ 29 } \implies \text{\LARGE 11}[/tex]

Hence, the slope of the line is [tex]m=11[/tex].

What is the slope of line?

The slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says  [tex](x_1,y_1)[/tex]  and [tex](x_2,y_2)[/tex]can be easily determined by finding the difference between the coordinates of the points.

As we know that,

The slope has several names

(1) average rate of change

(2)rate of change

(3)delta[tex]Y[/tex] over delta[tex]X[/tex]

(4)Δ[tex]y[/tex]over Δ[tex]x[/tex]

(5)rise over run

(6)gradient

(7)constant of proportionality

So, the same cat wearing the different costumes to get the slope of the straight line, the two points are

[tex](x_1,y_1)=(15,545)\\(x_2,y_2)=(44,864)[/tex]

[tex]m=\frac{864-545}{44-15}\\\\m=\frac{319}{29}\\\\m=11[/tex]

Hence, the slope of the line is [tex]m=11[/tex].

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The vertex of y = |3x + 6| − 4 is (-2, -4) and the range of y = |3x + 6| − 4 is −4 ≤ y < ∞.

A parabola's vertex is the location at which it crosses its axis of symmetry. The vertex will be the lowest point on the graph, or the point at the base of the "U"-shape, if the coefficient of the x2 term is positive.

The point is called the vertex (h, k). As we are all aware, a parabola's conventional equation is y = ax2 + bx + c. The bottom of the U-shaped curve is where the vertex is located if the coefficient x2 is positive, and the top of the curve is where the vertex is located if it is negative.

Given,

y = |3x + 6| − 4

The vertex of y = |3x + 6| − 4 is,

We have to find the absolute values zeroes,

3x+6=0

x= -2

To find the value of y, substitute x value in the above,

y= -4

(x, y)=(-2, -4)

Therefore, the vertex of y = |3x + 6| − 4 is (-2, -4)

And now,

The range of y = |3x + 6| − 4 is,

It can be defined by f(x)≥k

k= -4

f(x)≥ -4

Therefore, the range of y = |3x + 6| − 4 is −4 ≤ y < ∞.

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Answer:

(−2, −4); −4 ≤ y < ∞

Step-by-step explanation:

Using the interest rate formula, we know that the simple interest rate on the loan is 5.75%.

Simple interest is calculated by multiplying the principal by the time, interest rate, and time period.

"Simple Interest = Principal x Interest Rate x Time" is the written formula.

The simplest method for computing interest.

So, the interest rate on the loan is:

Formula to be used: I = p*r*t

Where I am the interest, p is the principal amount, r stand for rates and t stands for time.

I = p*r*t

3450 = 3000*2*r

3450/6000 = r

r = 0.575%

That is a 5.75% interest rate

Therefore, using the interest rate formula, we know that the simple interest rate on the loan is of 5.75%.

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In the given situation, where polygons ABCD and KLMN are similar, the TRUE statement will be (A) "while the lengths of the matching sides of ABCD and KLMN are equal, ABCD's sides are only half as long as KLMN's."

A polygon is a closed polygonal chain made up of a finite number of straight-line segments and is a type of planar figure in geometry.

A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both.

A polygonal circuit's segments are referred to as its edges or sides.

So, provided that polygons ABCD and KLMN are identical, the correct condition can be "while the lengths of the corresponding sides of ABCD and KLMN are equal, ABCD's sides are only half as long as KLMN's."

Therefore, in the given situation, where polygons ABCD and KLMN are similar, the TRUE statement will be (A) "while the lengths of the matching sides of ABCD and KLMN are equal, ABCD's sides are only half as long as KLMN's."

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Complete question:
Which of these conditions might be true if polygons ABCD and KLMN are similar?

A. The measures of corresponding angles of ABCD and KLMN are equal, but the lengths of the corresponding sides of ABCD are half those of KLMN.

B. The measures of corresponding angles of ABCD and KLMN are in the ratio 1 : 2, but the lengths of corresponding sides of ABCD and KLMN are not proportional.

C. The lengths of the corresponding sides of ABCD and KLMN are equal, but the measures of corresponding angles of ABCD and KLMN are not equal.

D. The lengths of the corresponding sides of ABCD and KLMN are proportional, but the measures of corresponding angles of ABCD and KLMN are not equal.

E. The measures of corresponding angles of ABCD and KLMN are not proportional, but the lengths of corresponding sides of ABCD and KLMN are proportional.

Answer:

the length of the

rectangle when the width is 4 feet is 8

On solving the provided question, we get the following linear equation as the , that is  j = 6/20.

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

A mathematical equation is said to be linear if it has the formula y=mx+b, where m denotes the slope and b the y-intercept.

An algebraic equation is said to be linear if each term has an exponent of 1, and if the equation is graphed, it always produces a straight line. This is the basis for its designation as a "linear equation."

the linear equation:

[tex]17/20 = j + 11/20\\ 17/20 - 11/20 = j + 11/20 - 11/20\\ (17 - 11)/20 = j\\ 6/20 = j[/tex]

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We can add and subtract 4.5 in the left side to complete squares, then we can rewrite the quadratic equation as:

(x + 13)^2 = 4.5

Here we want to rewrite the quadratic equation:

x^2 + 26x + 164.5 = 0

To rewrite it in the desired way, we need to complete squares, remember that the perfect square trinomial is:

(a + b) = a^2 + 2ab + b^2

We can rewrite the given quadratic as:

x^2 + 26x + 164.5 = 0

x^2 + 2*13*x + 164.5 = 0

The missing term to complete squares is 13^2 = 169, so we can add and subtract 4.5 on the left side of that eqation to get:

x^2 + 2*13*x + 164.5 + 4.5 - 4.5 = 0

x^2 + 2*13*x + 169 - 4.5 = 0

(x + 13)^2 = 4.5

That is the equation we wanted to get.

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Answer:

Designate the remaining pair of coordinates as "set 2." Using the previous coordinates (3, 4) and (1, 2), the coordinate pair (1, 2) becomes "set 2" and will be your x2 and y2 values in the formula. Therefore, x1 is 3, y1 is 4, x2 is 1 and y2 is 2. Now that you have your values, you can plug them into the formula.

Number of glasses Victoria need to buy for restaurant are at least 31 from the inequality given by 10x + 368 ≥ 673.

As given in the question,

Number of glasses required in the restaurant at least 673.

Number of glasses currently available in the restaurant = 368

Number of glasses in each set used to sale = 10

Let 'x' represent the number of sets of the glasses Victoria need to buy.

Required inequality is given by :

10x + 368 ≥ 673

⇒ 10x + 368 - 368  ≥ 673 - 368

⇒ 10x ≥ 305

⇒ x ≥ 30.5

Number of sets bought by Victoria = At least 31

Therefore, from the inequality 10x + 368 ≥ 673 the number of sets of glasses bought by Victoria is equal to at least 31.

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The better option is to buy the Granola bar.

What is a unit value?

When the expenditures or value of production of an item is divided by the quantity, the result is known as a unit value. The unit value of a set of homogeneous products is the total value of the purchases/sales divided by the sum of the quantities.

To determine which is the better buy, you need to compare the price per granola bar for each option. To do this, you can divide the price of each pack by the number of granola bars it contains.

For the first pack of 100 granola bars, the price per granola bar is $8.67 / 100 granola bars = $0.09 per granola bar.

For the second pack of 50 granola bars, the price per granola bar is $5.48 / 50 granola bars = $0.11 per granola bar.

Since the price per granola bar is lower for the first pack, it is the better buy. You would save money by purchasing the first pack of 100 granola bars instead of the second pack of 50 granola bars.

Hence, the better option is to buy the Granola bar.

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Answer:

1. Yes

2. No

3. No

4. Yes

Step-by-step explanation:

To find out whether or not 3/5 will make each equation true, simply input 3/5 in the missing slots and solve to see if they equal to the value intended.

The number of negative and positive factors needed to guarantee a negative product with four factors with factors is 10 and there is a pastern

You should understand that the factors of a number is a number which can divide a number without a reminder

The factors must have a constant difference

Taking 1 as a factor for instance

1+5=5

Taking the number 20 for instance

The factors of 20 are

20=1,2,4,5,10,20

-1*20=-20

.1*-20=-20

-2*10=-20 and 2*-10=20

-4*5=-20 and 4*-5=20

The order is that the subsequent terms must be gotten by a difference of 1 and a divisor of 5

Therefore the number of factors is gotten by allocating by after the other a negative sign to the numbers

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$22500 is interest rate of common tock for each year.

What is an explanation of the interest rate?

An interest rate informs you of how much borrowing will cost you and how much saving will pay off.

                      Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the entire loan amount if you are a borrower.

Amount distributed as dividends = $15000

                 Total Preferred dividend to be paid  = $37500

       But Total Preferred dividend paid/avaiable = $15000

                              dividend per share(P.S)   = $0.60    **(15000 / 25000shares)

    Since the preferred stock cumulative dividend to be paid in Next year due to less payment in current year would be = $22500  or $0.90 per share        

                                      Remaining dividend  = 0

                       Equity dividend per share  = 0

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well, both telephones cost 48.67 * 2 = 97.34, now let's get the tax and add it to it

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7.11\% of 97.34}}{\left( \cfrac{7.11}{100} \right)97.34} ~~ \approx ~~ 6.92~\hfill \underset{total~price}{\stackrel{97.34~~ + ~~6.92}{\approx \text{\LARGE 104.26}}}[/tex]

The possible values of k are -0.56, -3.56, -2 and -1.

We have the equation of the parabola, y = 0.5 (x- 3 ) ( x+ k)

Substituting x=0, we get that i.e. y =0.5 * (-3) * k -1.5k

So, the y-intercept is (0,-1.5k).

Thus, the height of the triangle becomes |-1.5k| = 1.5k

Again, substituting y=0, 0 = 0.5 (x-3) (x+k) i.e. i.e. x0=(x-3) (x+k)=3 and x=-k

So, the x-intercepts are (3,0) and (-k,0).

Thus, the base of the triangle is 3+k if k>-3 or -3-k if k<-3.

As, area of a triangle = 1/2 * (base )* (height )

Substituting the values, we get,

1.5=1/2 *(3+k)*(1.5k)

i.e.3= 4.5 k + 1.5k ²

i.e. k = -0.56 and k = -3.56

or

1.5=1/2* (-3-k )*(1.5k)

i.e.

3 = -4.5 k - 1.5²

i.e. k = -2 and k = -1.

Thus, the possible values of k are -0.56, -3.56, -2 and -1.

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Answer:

The regualar hippo massed 4.45 times as much as the pygmy hippo. (Not sure what I should round to)

Step-by-step explanation:

First, convert each of the fractions to a whole number. To do this get the whole number to the left of the fraction multiply it by the denominator and add the numerator. Once you have found both masses. Get the mass of the regular hippo and divide by the pygmy hippos mass.

Reguar Hippo Mass Calcualtion:

24*2=48

48+1=49kg

Pygmy Hippo Mass Calcualtion:

5*2=10

10+1-11kg

Final Calcuation:

49/11=4.45kg

Answer: 4.45 times as much

Let me know if this helped!

A is the answer

Domain is all x-values and Range is y-values.

Hope this helps!!:)

the equation of the function is y=-2x+10

Answer:

D. 50

Step-by-step explanation:

number to 49.13

Answer:

A

Step-by-step explanation:

Answer:

%10

Step-by-step explanation:

If the gold steadily increased $400 over a four-month period, we need to figure out how much the gold increased each month.

400 ÷ 4 = 100

Now that we figured out that the gold steadily increased $100 every month, we now need to figure out what percent it grew.

1000 ÷ 100 = 10

The price grew %10 every month.

Answer:

n=-30

Step-by-step explanation:

-4.5n=135

n=135/-4.5

n=-30

Answer:

I think someone who walks 60 feet in 10 seconds. Let me know if I'm wrong.

Step-by-step explanation:

10/60=.16667

6/42=0.1428

Answer:  -130.

Step-by-step explanation: To round −74.41 to the nearest whole number, we look at the tens place, which is the digit 4 in the number −74.41. Since 4 is less than 5, we round down to the previous whole number, which is −74.

To round 55.816 to the nearest whole number, we look at the tens place, which is the digit 8 in the number 55.816. Since 8 is greater than or equal to 5, we round up to the next whole number, which is 56.

Now that we have rounded both numbers to the nearest whole number, we can easily subtract them to get an approximate answer:

-74 - 56 = -130

Therefore, an approximate solution to −74.41- 55.816 is -130.

i dont now when i can help but this is my answer

k = 4 will make the polynomial a perfect square of a binomial.

A trinomial that factors into a perfect square binomial yields the square of a binomial. For instance, because it factors to (x + y)2, the trinomial x2 + 2xy + y2 is a perfect square binomial.

The perfect square formula looks like:

[tex]ax^{2} +2abx+b^{2} =(ax+b)^{2} \\ax^{2} -2abx+b^{2} =(ax-b)^{2}[/tex]

Given polynomial is,

kx² +12x + 9

We have to find the value of 'k' for which the given polynomial is a square of a binomial.

To find this we will use the formula,

(a +b)² = a² +2ab + b²

kx² + 12x + 9 = kx² + 2(6x) + 3²

                     = kx² + 2(3)(2x) + 3²

By comparing this with the formula of (a + b)²,

b = 3

a = 2x

(2x)²+2(2x)(3) + 3² = (2x + 3)²

4x² + 12x + 9 = (2x + 3)²

Therefore, k = 4 will make the polynomial a perfect square of a binomial.

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k = 4 will make the polynomial a perfect square of a binomial.

What is perfect square binomial?

A trinomial that factors into a perfect square binomial yields the square of a binomial. For instance, because it factors to (x + y)2, the trinomial x2 + 2xy + y2 is a perfect square binomial.

How perfect square formula looks like?
The perfect square formula looks like:
Given polynomial is,
kx² +12x + 9
We have to find the value of 'k' for which the given polynomial is a square of a binomial.
To find this we will use the formula,
(a +b)² = a² +2ab + b²
kx² + 12x + 9 = kx² + 2(6x) + 3²
                    = kx² + 2(3)(2x) + 3²
By comparing this with the formula of (a + b)²,
b = 3
a = 2x
(2x)²+2(2x)(3) + 3² = (2x + 3)²
4x² + 12x + 9 = (2x + 3)²
Therefore, k = 4 will make the polynomial a perfect square of a binomial.

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The two column proof showing that AB ≅ CD and AD ≅ BC are congruent by CPCTC is as detailed below.

A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.

The two column proof that shows AB ≅ CD and AD ≅ BC is as follows;

Statement 1; Parallelogram ABCD with diagonal AC

Reason 1: Given

Statement 2; AB ║ CD and AD ║ BC

Reason 2; Definition of Parallelogram

Statement 3; ∠1 ≅ ∠2 and ∠3 ≅ ∠4

Reason 3; Definition of angle bisector

Statement 4; AC ≅ AC

Reason 4; Reflexive Property of congruence

Statement 5; ΔABC ≅ ΔCDA

Reason 5; ASA Congruency postulate

Statement 6; AB ≅ CD and AD ≅ BC

Reason 6; CPCTC

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Answer:

50

Step-by-step explanation:

ezpz

Answer: i think the next number should be 26

Step-by-step explanation: