A cylindrical grain bin has a radius of 7 feet and a height of 25 feet. How many cubic feet can the unit hold?

⇛{5(√7+√5)}/2.

Step-by-step explanation:

Given,

5/(√7-√5)

The denominator is √7-√5.

We know that

The rationalising factor of √c-√a is √c+√a.

Therefore, the rationalising factor of √7-√5 is √7+√5. To rationalise the denominator of 5/(√7-√5), we multiply this by (√7+√5)/(√7+√5).

⇛{5/(√7-√5)}/{(√7+√5)/(√7+√5)}

⇛{5(√7+√5)}/{(√7-√5)(√7+√5)}

⇛{5(√7+√5)}/{(√7)²-(√5)} [∵ (a-b)(a+b)=a²-b²]

⇛{5(√7+√5)}/{(√7*7)-(√5*5)}

⇛{5(√7+√5)}/(7-5)

⇛{5(√7+√5)}/2

Hence, the denominator is rationalised.

Read more:

Similar Question;

rationalise the denominator 1/√20..

https://brainly.com/question/19473806?referrer

Its a bit late, but i wish someone would had answered so

Step 3:  

✔ B

Step 5:  

✔ D

Step 6:  

✔ A

Step 8:  

✔ C

:)

The first incorrect step in the given sequence is Step 3, where the equation is divided by 'a' on both sides instead of factoring it out and grouping the terms.

The quadratic formula is derived by completing the square on the general quadratic equation ax^2 + bx + c = 0. The first incorrect step in the given sequence is Step 3. In Step 3, the equation ax^2 + bx + c = 0 is divided by a on both sides, which results in the equation x^2 + (b/a)x + (c/a) = 0. However, the correct next step should be factoring out the leading coefficient a and grouping the terms.

Learn more about Quadratic Formula here:

https://brainly.com/question/32591097

#SPJ2

The more plot point the better but you must have at least three  points, a labeled X-axis and Y-axis, and a table for the data to be organized into.

Answer:

See the explanation below

Step-by-step explanation:

Scatter plot is a graph that employs Cartesian coordinates to show the values of typically two variables plotted on the horizontal and vertical axes for a given set of data. The name of the relationship between the two variables that is shown by the scatter plot is referred to as correlation.

The following are the features of a scatter plot:

1. An X axis also known as the horizontal axis), and a Y axis which is also known as the vertical axis.The reason for these two axes is to obtain the Cartesian coordinates of the two variables X and Y.

2. Dots: There are must be dots on a scatter graph. The purpose of each of the dots is to indicate one observation of the data set.

3. Unique position of each dot: The purpose of the position of each dot is to indicate the meeting point of X and Y values.

Answer: [tex]P=14units[/tex]

Step-by-step explanation:

The perimeter of a triangle is the sum of the lenghts of its sides.

Given the triangle ABC , its perimeter will be:

[tex]P=AB+BC+CA[/tex]

Then, you know that the lenghts of the sids of the triangle ABC are:

[tex]AB=3units\\BC=5units\\CA=\sqrt{(3)^2+(-5)^2}=\sqrt{9+25}=\sqrt{34}=5.83units[/tex]

Therefore, to find the perimeter of this triangle, you need to substitute these lengthts into the formula [tex]P=AB+BC+CA[/tex].

So, the perimeter of the triangle ABC is:

[tex]P=3units+5units+5.83units=13.83units[/tex]

To the nearest whole unit is:

[tex]P=14units[/tex]

Answer:

14 units

Step-by-step explanation:

.

Answer:

Jack took 6 minutes and 33 seconds longer to complete the race.

Step-by-step explanation:

54 minutes minus 47 minutes would equal 7 minutes longer, but Jack was not as far into the minute when he completed it as Ben was when he completed it, so the difference in time is actually going to be a bit less than 7 minutes. So the difference is going to be 6 minutes and the number of seconds between 39 and 12, with 39 going past the minute, that is. That equals out to 33 seconds, so the total difference in time is 6 minutes and 33 seconds.

Answer:

Lani's mom will need 80 ft of fencing

Step-by-step explanation:

We are looking for the perimeter of the garden. We know that the garden is 22 ft x 18 ft. This means that we can find the perimeter using this equation

[tex]22(2)+18(2)=80[/tex]

Set of transformations is a set conditioned by a function that transforms element from definition set to transformation set.

[tex]f: A\longrightarrow B[/tex], where A is definition set and B is transformation set.

Here is an example.

You are given definition set [tex]A=\{1, 2, 3\}[/tex] and a function [tex]f(x)=x^2[/tex]. To calculate which elements are in transformation set we write [tex]f(A)=\{1, 2, 3\}^2={1, 4, 9}\Longrightarrow\boxed{B=\{1, 4, 9\}}[/tex] and B is now the transformation set of definition set A that is conditioned by function f.

Hope this helps.

r3t40

Check the picture below.  So let's use those two points on the line.

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-0}{3-0}\implies \cfrac{3}{3}\implies 1 \\\\\\ \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-0=1(x-0)\implies y=x \\\\\\ -x+y=0\implies \stackrel{\textit{standard form}}{x-y=0}[/tex]

bearing in mind that the standard form is also a general form.

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

Answer:

B. x - y = 0

Step-by-step explanation:

Answer:

You did not give me any graphs but I've dealt with this question and the answer is: The Double Bar Graph if you have the graph that was put for my answer. Good luck, hope this helps. Double Bar Graph information:  Vertical double-bar graph with title Books Checked Out. Key shows grey equals boys and pink equals girls. Data graphed is Biography 8 boys and 10 girls, Mystery 18 boys and 15 girls, Science 14 boys and 11 girls, and Sports 12 boys and 14 girls.

Heres the graphs xd (I have the same test)

Principal P = $500,  Rate = 3 % = 3/100 = 0.03  would assume per year,

Time t = 6 months = (6/12) year = 0.5 year.

Simple Interest, I = P*r*t

                            = 500*0.03*0.5 = 7.5

Simple interest = $7.50

Answer: [tex]2x^4+2x+10[/tex]

Step-by-step explanation:

You need to remember the mulplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]

Knowing this, you can distributive the negative sign. Then you get:

[tex](-7x- 5x^4 + 5) - (-7x^4 - 5 - 9x)=-7x- 5x^4 + 5 +7x^4 + 5 + 9x[/tex]

Now you need to add the like terms. Then:

[tex]=2x+2x^4+10[/tex]

Finally, you can order the polynomial obtained in descending order. Therefore, the answer is:

[tex]=2x^4+2x+10[/tex]

ANSWER

[tex]( - \infty , - \frac{4}{3} ) \cup( \frac{1}{2} , \infty )[/tex]

EXPLANATION

The given function is

[tex]f(x) = \sqrt{ \frac{2x - 1}{3x + 4} } [/tex]

The domain refers to all values of x for which f(x) is defined.

This function is defined if

[tex] \frac{2x - 1}{3x + 4} > 0[/tex]

This implies that

[tex]x \: < \: - \frac{4}{3} \: or \: x \: > \: \frac{1}{2} [/tex]

Or

[tex]( - \infty , - \frac{4}{3} ) \cup( \frac{1}{2} , \infty )[/tex]

Answer:

- 896

Step-by-step explanation:

To find the 8 th term substitute n = 8 into the explicit formula

[tex]a_{8}[/tex] = 7 × [tex](-2)^{7}[/tex] = 7 × - 128 = - 896

The 8th term of the given geometric sequence is -896.

The explicit formula

an = 7 × (-2)(n - 1).

To find the 8th term, simply substitute 8 for n in the formula, giving us:

Answer:

Final answer is 10.5 gallons of water.

Step-by-step explanation:

Given that Joe is filling the washing machine to wash clothes. After one minute, there are 1.75 gallons of water in the washing machine. After two minutes, there are 3.5 gallons of water in the machine. After three minutes, there are 5.25 gallons in the machine. Now we need to determine If this pattern continues then about how many gallons of water will be in the washing machine after six minutes.

Look at the pattern of volume of the water at given minutes.

We see that 1.75 is added each minute.

then required equation of volume is

V=1.75t

So for t=6 minutes, volume is given by

V=1.75*6=10.5

Hence final answer is 10.5 gallons of water.

The amount of water in the washing machine after six minutes can be determined using an arithmetic sequence formula. The machine fills at a constant rate of 1.75 gallons per minute, so after six minutes, there will be 10.5 gallons of water in the machine.

The question provided concerns a pattern of water filling a washing machine, which falls under the subject of arithmetic sequences in mathematics. To determine how many gallons of water will be in the washing machine after six minutes, we need to recognize the sequence and apply the appropriate formula.

To solve this problem, we note that the washing machine fills at a constant rate of 1.75 gallons per minute because the amount of water increases by 1.75 gallons with each passing minute (1.75 gallons at minute one, 3.5 gallons at minute two, which is 1.75 x 2, and 5.25 gallons at minute three, which is 1.75 x 3).

Mathematically, this can be represented as an arithmetic sequence with the first term a1 = 1.75 gallons and the common difference d = 1.75 gallons. The nth term of an arithmetic sequence is given by the formula an = a1 + (n - 1)d. So, to find the amount of water after six minutes, substitute 6 for n, which yields:

a6 = 1.75 + (6 - 1) times 1.75

a6 = 1.75 + 5 times 1.75

a6 = 1.75 + 8.75

a6 = 10.5 gallons

Therefore, after six minutes, there will be 10.5 gallons of water in the washing machine if the pattern continues.

Answer:

True for B)y=-4x^2+9

Step-by-step explanation:

The a part of the equation is negative (-4x^2), and this quadratic function has a maximum, which means it opens down not up.

(I hope this helps)

Here all you need to know to solve this exercise:

1) When you write the equation of a line in the form

[tex]y=mx+q[/tex]

the slope is the coefficient m.

2) When you know that the line passes through a point [tex](x_0,y_0)[/tex] and has slope m, the equation of the line is given by

[tex]y-y_0=m(x-x_0)[/tex]

3) Let [tex]m_1,m_2[/tex] be the slopes of two lines. If the lines are parallel, then [tex]m_1=m_2[/tex]. If the lines are perpendicular, then [tex]m_1m_2=-1[/tex].

In the first exercise, using point 1, you can see that the slope of the given line is 2. We want a parallel line passing through the given point. So, our line has the same slope, and its equation is (see point 2)

[tex]y-2=2(x+1) \iff y = 2x+4[/tex]

Similarly, in the second exercise, the original slope is 1/3, so the perpendicular slope is -3. The equation will be, imposing the passage through the given point,

[tex]y-6 = -3(x-0) \iff y = -3x+6[/tex]

Answer:

see explanation

Step-by-step explanation:

19

The equation of a line in slope- intercept form is

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

y = 2x - 3 is in this form with slope m = 2

• Parallel lines have equal slopes, hence

y = 2x + c ← partial equation of parallel line

To find c substitute (- 1, 2) into the partial equation

2 = - 2 + c ⇒ c = 2 + 2 = 4

y = 2x + 4 ← equation of parallel line

20

Rearrange x - 3y = 5 into slope- intercept form

Subtract x from both sides

- 3y = - x + 5 ( divide all terms by - 3 )

y = [tex]\frac{1}{3}[/tex] x - [tex]\frac{5}{3}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{1}{3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3, so

y = - 3x + c

The line passes through (0, 6) ⇒ c = 6

y = - 3x + 6 ← equation of perpendicular line

Answer: The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.

Step-by-step explanation:

Answer:

a

Step-by-step explanation

-(575+266+75)+638

0.24/100 is the answer

.24 :) i hope this helped

Answer: The answer to your question is B.

Step-by-step explanation:

Final answer:

To calculate the value of Jack's investment after one year, we can use the formula for simple interest: Simple Interest = Principal x Rate x Time. Plugging in the values, we find that Jack's investment will be worth $5,340.72 after one year.

Explanation:

To calculate the value of Jack's investment after one year, we can use the formula for simple interest:

Simple Interest = Principal x Rate x Time

In this case, the principal is $5,280, the rate is 1.15% (which can be written as 0.0115), and the time is one year. Plugging in these values, we get:

Simple Interest = $5,280 x 0.0115 x 1 = $60.72

To find out the total value of the investment after one year, we need to add the simple interest to the principal amount:

Total Value = Principal + Simple Interest = $5,280 + $60.72 = $5,340.72

Therefore, Jack's investment will be worth $5,340.72 after one year.

Answer:

d

Step-by-step explanation:

a, b, and c are independent, because they don't necessarily affect the probability of each other.

In summary, the pair of events that are dependent is drawing a black sock from a drawer and then drawing another without replacement. This is because the first event changes the conditions for the second, affecting its probability.

Whether two events are dependent or independent affects the calculation of their probability. Independent events have no impact on the likelihood of each other occurring, while dependent events do.

Thus, Event d is the pair of dependent events.

Answer:

Option A) 4

Step-by-step explanation:

we know that

Applying the Intersecting Secant-Tangent Theorem

[tex]PA^{2}=(BE+PE)( PE)[/tex]

substitute the given values

[tex]6^{2}=(5+PE)( PE)\\ \\36=PE^{2}+5PE\\ \\PE^{2}+5PE-36=0[/tex]

Solve the quadratic equation by graphing

The solution is PE=4 units

see the attached figure

Answer:

The answer is 4

Step-by-step explanation:

Answer:

[tex]-\frac{3}{10}[/tex]

Step-by-step explanation:

Slope is the change in y coordinates by change in x coordinates.

Or  [tex]m=\frac{\delta y}{\delta x}[/tex]

Looking at the table, the change in each value of x is 10 (10 to 20 to 30 to 40).

Also, the change in each valueof y is -3 (20 to 17 to 14 to 11).

Note: change in y is negative since it is DECREASING.

Hence the slope would be -3/10

8x+7x=6x+28

15x=6x+28

15x-6x=28

9x=28

X=28/9

I hope this helps

ANSWER

36 cubic inches.

EXPLANATION

The volume of a square pyramid is calculated using the formula:

[tex]V = \frac{1}{3} {l}^{2} \times h[/tex]

where l² is the area of the base and h= 6 inches is the height of the square pyramid.

We substitute the values into the formula to get,

[tex]V = \frac{1}{3} \times 18 \times 6 \: {in}^{3} [/tex]

We simplify to get:

[tex]V = 6 \times 6 =3 6 {in}^{3} [/tex]

Therefore the volume of the square pyramid is 36 cubic inches.

Answer:

Area of square = 12.48 cm^2  

Step-by-step explanation:

Since the square has all sides equal, and when diagonal is made, square form two right angled triangles. Using Pythagoras theorem we can find the length of side of the square.

[tex]c^2 = a^2 + b^2[/tex]

where c = 5cm and a==b (square has all sides equal)

Putting value of b = a

[tex](5)^2 = a^2 + a^2\\25 = 2 a^2\\25/2 = a^2\\=> a^2 = 12.5\\ => \sqrt{a^2} = \sqrt{12.5}\\=> a = 3.53\, cm[/tex]

So, length of side of square = 3.53

Area of square = (3.53)^2

Area of square = 12.48 cm^2.  

The answer is:

The area of the given square is equal to [tex]12.5cm^{2}[/tex]

[tex]Area=12.5cm^{2}[/tex]

To solve the problem, we don't need to calculate the length of the sides of the square. We are given the diagonal length of the square, so using the following formula, we can calculate the are of the square without knowing the sides:

[tex]Area=\frac{diagonal^{2} }{2}[/tex]

So, substituting we have:

[tex]Area=\frac{(5cm)^{2} }{2}=\frac{25cm^{2} }{2}=12.5cm^{2}[/tex]

Hence, we have that the area of the given square is equal to [tex]12.5cm^{2}[/tex]

Have a nice day!

[tex]10 \div 20 = 0.5 \: and \: 9 \div 8 = 1.125[/tex]

Answer:

1800

Step-by-step explanation:

10√20 × 9√8

10 × 5√2 × 9 × 2√2

50√2 × 18√2

50 × 18 × 2 = 1800

Answer:

[tex]\large\boxed{y-1=-4(x+3)}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We have m = -4 and the point (-3, 1). Substitute:

[tex]y-1=-4(x-(-3))\\\\y-1=-4(x+3)[/tex]

Answer:

y-1=-4[x-(-3)]

Step-by-step explanation: