Use this pattern when a binomial
can be written as the square of
one number minus the square of
another number.
4x² - 49 = (2x-7)(2x + 7)
2

The circumference of the circle shown above would be = 6πft. That is option A.

The formula which can be used to calculate tye circumference of a circle = 2πr

Where;

r = 3ft

π = to be calculated in terms of π

Circumference of the circle = 2×π × 3 = 6πft.

Learn more about circle here:

https://brainly.com/question/24375372

#SPJ1

Step-by-step explanation:

To find the total volume of the solution in liters, we need to add the volumes of the two ingredients:

500 mL + 1000 mL = 1500 mL

To convert mL to liters, divide by 1000:

1500 mL / 1000 = 1.5 L

So, the solution is 1.5 liters.

The ratios will be equal if the theorem that the product of the extremes equals the product means follows.

Let us understand the equality of ratios through example. The example ratio will be -

7:10 = 21:30

In this ratio, 7 and 30 are first and last numbers and hence they are extremes. The number 10 and 21 are in middle and hence considered mean. Now, we will perform multiplication to if the ratios are equal or not.

Product of extremes = 7 × 30

Extremes product = 210

Product of means = 21 × 10

Means product = 210

Since the products are equal, the ratios are also equal.

Learn more about ratio and proportion -

https://brainly.com/question/12024093

#SPJ4

The complete question is -

Are the following ratios equal? write yes or no. use the theroem that the product of the extremes equals the product means.

Ratio = 7:10 and 21:30.

Answer:

There will be 312 pennies and 162 nickels that will make up to $11.22 and there are 474 coins altogether.

Step-by-step explanation:

Here,

A penny is worth 1 cent.

A nickel is worth 5 cents.

A dime is worth 10 cents.

A quarter is worth 25 cents.

A dollar is worth 100 cents.

Let there be x pennies and y nickels.

x+y=474

0.01x+0.05y=11.22

Now,

0.01x+0.01y=4.74

0.01x+0.05y=11.22

subtracting both,

-0.04y=-6.48

y=6.48/0.04

y=162 nickels

x+162=474

x=312 pennies

There will be 312 pennies and 162 nickels totaling $11.22, for a total of 474 coins.

The uncorrected creatinine clearance value is 62.7mL/min

What is volume?

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface

Given:

U=76 mg/dL

P= 1.2 mg/dL

Let V= volume of urine in mm/min

V=1430mL/1440min

V=0.99mL/min

Use the formula:

UV/P

=(76 x .99)/1.2=62.7mL/min

The uncorrected creatinine clearance value is 62.7mL/min

To learn more about the volume from the given link

https://brainly.com/question/463363

#SPJ4

Using the data the frequency table is completed as follows

Age             Frequency

20-29               3

30-39                4

40-49                6

50-59               11

60-69               3

70-79                2

80-89                1

The number of times the data is repeated inside a given dataset is referred to as the frequency of the data sets.

A frequency distribution table is a tool for structuring the provided data in a way that makes sense and facilitates comprehension. Two or three columns make up a frequency distribution table. All of the results are presented in the first column as individual values or as class intervals.

Learn more about frequency distribution at

https://brainly.com/question/27820465

#SPJ1

Answer:

The function is growth with a growth rate of 7%

Step-by-step explanation:

The equation is in the form.

y = a * b^x

if b > 1 then it is growth.

If b < 1 it is decay.

Since b > 1 it is growth.  The growth rate is

b = 1+r

1.07 = 1+r

r= .07

7%

The function is growth with a growth rate of 7%

Due to length restrictions, we kindly invite to read the explanation below to know how the graph of the quartic function is made. Here is a summary:

Zeros: x = - 0.732, x = 0, x = 1, x = 2.732

Critical values: x = - 0.432 (minimum), x = 0.541 (maximum), x = 2.141 (minimum)

Increasing: - 0.432 < x < 0.541 and x > 2.141

Decreasing: x < - 0.432 and 0.541 < x < 2.141

Herein we find the definition of a quartic function, that is, a polynomial with grade 4, of which we must sketch its graph. This can be done from the understanding of the following information:

Zeros

Let be equal the polynomial to zero. All roots can be found by means of numerical methods:

x⁴ - 3 · x³ + 2 · x = 0

x = - 0.732 or x = 0 or x = 1 or x = 2.732

Critical values

Determine the first derivative, equal it to zero and find the roots of the expression:

4 · x³ - 9 · x² + 2 = 0

x = - 0.432 or x = 0.541 or x = 2.141

Determine the second derivative and evaluate it at each root found in previous step:

f''(x) = 12 · x² - 18 · x + 2

x = - 0.432

f''(- 0.432) = 12.015 (MINIMUM)

x = 0.541

f''(0.541) = - 4.226 (MAXIMUM)

x = 2.141

f''(2.141) = 18.469 (MINIMUM)

Finally, find the coordinates of the quartic function:

f(- 0.432) = - 0.587

f(0.541) = 0.693

f(2.141) = - 4.148

Interval behavior

Use the first derivative find the roots of the following inequalities:

Increasing

4 · x³ - 9 · x² + 2 > 0

- 0.432 < x < 0.541 and x > 2.141

Decreasing

4 · x³ - 9 · x² + 2 < 0

x < - 0.432 and 0.541 < x < 2.141

Finally, we build the sketch with the help of a graphing tool.

To learn more on polynomic functions: https://brainly.com/question/29780212

#SPJ1

The expression which is equivalent to (p - q)(x) is (x²-1) - 5(x-1) .

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

Since  p(x) = x² - 1 and g(x) = 5(x-1)

(p - q)(x) can be found by subtracting g(x) = 5(x-1) from p(x) = x² - 1. That is:

(p - q)(x) = (x²-1) - 5(x-1)

Thus,  (x²-1) - 5(x-1) is equivalent to (p - q)(x).

Learn more about function on:

brainly.com/question/1415456

#SPJ1

The required solution of the differential equation is given as y² = -4logx + 9.

The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.

here,
Given the differential equation,
Y’+2/x*y=0
Y' = -2/xy
y (dy/dx) = -2/x
ydy = -2/xdx
y²/2 = -2logx + C

From the initial condition y(1)=3
9/2 = -2log1 + c

c = 9/2

Now,
y²/2 = -2logx + 9/2
y² = -4logx + 9

Thus, the required solution of the differential equation is given as y² = -4logx + 9.

Learn more about implicit differentiation; https://brainly.com/question/11887805
#SPJ1

The five-number summary of the given data 18, 15, 1, 14, 18, 11, 12, 20, 13, 19, 14, 8, 24, 18, 17 is ,

Your data set's five-number summary offers you a general notion of how it is organised. You will, for instance, have your best value and lowest value (the maximum). The main reason you'll want to locate a five-number summary is to find other valuable statistics, like the interquartile range, also known as the middle fifty, even if it's important in and of itself.

The five number summary includes 5 items:

Step 1: Put your numbers in ascending order (from smallest to largest). For this particular data set, the order is:

1, 8, 11, 12, 13, 14, 14, 15, 17, 18, 18, 18, 19, 20, 24.

Step 2: For your data set, determine the lowest and maximum. This ought to be obvious now that your math is correct.

In the example in step 1, the minimum (the smallest number) is 1 and the maximum (the largest number) is 24.

Step 3: Find the median. The median is the middle number.

median = 17

Step 4: (This is not technically necessary, but it makes Q1 and Q3 easier to find).

(1, 8, 11, 12, 13, 14, 14, 15), 17, (18, 18, 18, 19, 20, 24).

Step 5: Find Q1 and Q3. Q1 can be thought of as a median in the lower half of the data, and Q3 can be thought of as a median for the upper half of data.

(1, 8, 11, 12, 13, 14, 14, 15), 17, (18, 18, 18, 19, 20, 24).

Step 6: Write down your summary found in the above steps.

minimum = 1, Q1 = 12, median = 17, Q3 = 19, and maximum = 24.

Learn more about Five number summary:

https://brainly.com/question/26671030

#SPJ4

Answer: -13

Step-by-step explanation: Here to help! So first, you do 8-12, then you get -4, right? So then, you multiply 2 times -4, then you get -8. After that, you add -5 to -8, so it's -5 + -8, and you get -13.

Answer:

-13

Step-by-step explanation:

-5+2(8-12)

distribute the 2

-5+16-24

add

11-24

subtract

-13

I) The angles are not equal then the two triangles are not Congruent.

ii) The point E is 1.5 from point B.

A line that divides the line into two distinct or equal segments is referred to as a "bisector." It is applied to angles and line segments.

A ray that divides an angle into two equal pieces is known as an angle bisector or the bisector of an angle.

Given:

As, <CAB = 19.4 and <DAB = 33.7

So,  CAD and DAB are not congruent.

ii) The point E should be located 1.5 away from point B.

Learn more about Bisector here:

https://brainly.com/question/28663444

#SPJ1

The discriminant is -2n - 24.

The equation has 2 real solutions.

The discriminant of a quadratic equation in the form ax^2 + bx + c = 0 is given by the formula b^2 - 4ac.

So, for the equation -3n^2 - 2n - 6 = 0, a = -3, b = -2, and c = -6.

Plugging these values into the formula, we get:

(-2)^2 - 4 * -3 * -6 = 4 + 72 = 76

So the discriminant is 76, which is greater than zero, so the equation has 2 real solutions.

learn more about discriminant of a quadratic equation: https://brainly.com/question/2507588

#SPJ1

The fraction to the garden that would probably remain for his other crops would be = 5/24

The portion of the garden in which potatoes are being planted = 2/3

The portion of the garden in which carrots are being planted = 1/8

Therefore,the fraction of the garden that is left without plants = X

But;

The whole garden is represented as 1.

That is;

1 = 2/3+1/8 +X

Make X the subject of formula;

X = 1 - (⅔+⅛)

X = 1-(19/24)

X = 1-19/24

X= 5/24.

Learn more about fraction here:

https://brainly.com/question/28699958

#SPJ1

Hamilton's method of allocating can be used to assign the 21 salespeople in the table in the following order:

2, 5, 6, 8.

Alexander Hamilton was the one who first suggested the strategy that now carries his name. In 1791, Congress approved of his strategy, but President Washington disapproved of it. It was commonly used from 1852 through 1911. He begins by figuring out exactly how many objects each group requires.

We'll use the terminology of shift and hours since the relevant question is about the allocated salesperson in order to calculate the appropriate number of salespeople for each shift.

Now total no. of customers given = 125 + 305 + 439 + 515 = 1375

Now total no of salesperson available = 21.

So, the divisor = 1375/21 = 65.47

Hamilton's approach is now used to determine the number of salespeople assigned by dividing the average number of customers per shift by the divisor.

So, the salesperson assigned are:

Morning = 125/65.47 = 2

Midday = 305/65.47 = 5

Afternoon = 430/65.47 = 6

Evening = 515/65.47 = 8 (Decimals rounded according to Hamilton's principle).

To know more about Hamilton's method of apportioning, visit:

brainly.com/question/24180735

#SPJ1

Answer:

4604 (when rounded to the nearest whole number)

Step by step explanations:

Using the exponential growth formula, we can determine Amuel's population at the time the factory shut down: N = N0 * e^(rt) (rt) Where r is the growth rate, t is the number of years the growth takes place, N is the ultimate population, N0 is the starting population, and r represents growth.

We may use the population data from 1995 and 1996 to get the growth rate: r = ln(1,381 / 1,256) / (1996 - 1995) (1996 - 1995) 

Putting the numbers in: r = 0.117 

Next, we determine how many years the growth took place: t = 13 years (2007 - 1994) Lastly, we enter the values into the formula as follows: N = 1,256 * e^(0.117 * 13) 

Calculating the answer, we discover: 4,604 persons (N = 1,256 * 3.63) Consequently, there were about 4,604 residents there when the facility shut down in 2007.

Answer:

6

Step-by-step explanation:

30 divided by 5 = 6

6 is the maximum possible number of groups possible.

Westside Carpet charges more per square foot for the carpet

Since the Carpet City charges $5 per square foot for a type of carpet. They charge an additional $95 for installation.

we can write the linear function for Carpet City charges as:

y = 5x + 95

where x is the number of square foot

From the table:

rate for Westside Carpet = 3250/642 = $5.06 per carpet

The the linear function for Westside Carpet is y = 5.06x

Thus, Westside Carpet charges more because 5.06 is greater than 5.

Learn more about linear function on:

brainly.com/question/29330381

#SPJ1

(a) To illustrate the information on a Venn diagram:

A Venn diagram is a graphical representation of the relationship between sets of items

This Venn diagram will visually represent the information given in the question and help to answer the questions about the number of students who passed each subject and the number of students who passed exactly one subject.

Read more about Venn diagram here:

https://brainly.com/question/24713052

#SPJ1

Answer:

392

Step-by-step explanation:

...................

Answer:

1.5322e+30

Step-by-step explanation:

calculator, there were too many numbers!

in essence, PEMDAS, but let's firstly convert the mixed fractions to improper fractions.

[tex]\stackrel{mixed}{7\frac{2}{3}}\implies \cfrac{7\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{23}{3}} ~\hfill \stackrel{mixed}{1\frac{2}{4}} \implies \cfrac{1\cdot 4+2}{4} \implies \stackrel{improper}{\cfrac{6}{4}} \\\\\\ \stackrel{mixed}{3\frac{6}{8}}\implies \cfrac{3\cdot 8+6}{8}\implies \stackrel{improper}{\cfrac{30}{8}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{23}{3}-\left(\cfrac{6}{4}+\cfrac{30}{8} \right)\implies \cfrac{23}{3}-\left( \cfrac{(2)6~~ + ~~(1)30}{\underset{\textit{using this LCD}}{8}} \right)\implies \cfrac{23}{3}-\left( \cfrac{12+30}{8} \right)[/tex]

[tex]\cfrac{23}{3}-\left( \cfrac{42}{8} \right)\implies \cfrac{23}{3}- \cfrac{42}{8}\implies \cfrac{(8)23~~ - ~~(1)42}{\underset{\textit{using this LCD}}{24}}\implies \cfrac{184-42}{24} \\\\\\ \cfrac{142}{24}\implies \cfrac{2\cdot 71}{2\cdot 12}\implies \cfrac{2}{2}\cdot \cfrac{71}{12}\implies \cfrac{71}{12}\implies 5\frac{11}{12}[/tex]

The average rate of change of a function f(x) on the interval [4, 9] is -67.

What is the average rate of change?

The average rate of change of a function between two points is the same that the slope of the line passes through these points (secant line).

The given table:

The average rate of change of a function f(x) over the interval [a, b] is

= f(b) - f(a)/b-a.

Interval : [4, 9]

f(9) = -419,

f(4) = -84

The average rate of change of a function f(x) on the interval [4, 9] is

=  f(9) - f(4)/9 - 4.

= -419 - (-84) / 5

= -297/ 5

= -67

Hence, The average rate of change of a function f(x) on the interval [4, 9] is -67.

To learn more about the average rate of change visit,

https://brainly.com/question/11627203

#SPJ1

Answer:

The top one is: 1/2x + 6

The bottom one is: -2x + 5

Step-by-step explanation:

The top function:

f(x) = mx + b

m is the slope and b in the y-intercept.  This is what you need to write the function.

The slope is 1/2.  The slope is the rise over the run. If you start at the point (-6,3) and go up one unit and 2 units to the right, you end up back on the line.  This is the slope.  If you follow that pattern, you will cross the y axis at (0,6).  6 is the y intercept.

The bottom function:

The slope is -2.  I you start at the point (1,3) and you go down 2 and one to the right, you will end up back on the line.  2/1 equals 2.

If you follow that pattern going backwards, 2 up and one to the left, you will be at the y-intercept (0,5) 5 is the y-intercept.

Step-by-step explanation:

To find the amount of money represented by C, we need to find the value of A and B first.

Since the ratio A:B is 2:5, we can assume that B is 5 times the amount of A.

Let's assume the amount of money represented by A is x.

Then B = 5x and C = 8x.

We know that the total amount of money split is £370, so we can write an equation:

x + 5x + 8x = £370

14x = £370

x = £26.43

So, the amount of money represented by C is 8x = 8 * £26.43 = £211.44

Answer:

[tex]y = \frac{3}{2}x + 6[/tex]

Step-by-step explanation:

Rearranging the equation:

[tex]4y = 6x + 24[/tex]

The coefficient of y has to be '+1' for the above equation to be considered as the slope-intercept form.

Dividing both sides of the equation by '4':

[tex]\frac{4}{4}y = \frac{1}{4}(6x + 24)[/tex]

Expand the brackets by applying the Distributive Law:

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

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

Divide the numerator and the denominator present in the coefficient of x by the Highest Common Factor '2':

[tex]y = \frac{3}{2}x + 6[/tex]

[tex]\huge{\color{grey}{\underline{\color{grey} {\underline{\color{grey} {\textbf{\textsf{\colorbox{black}{Answer:-}}}}}}}}}[/tex]