2(a+b)+ 4m(a+b) factor out the greatest common factor​

The best ending for the sale you are chasing depends on the context of the sale and the nature of your relationship with the customer.

However, if we assume that the sale is going well and you want to close it, then "C. is awesome" is not the best ending because it does not provide a clear call to action or address any potential concerns the customer may have.

Instead, a more effective ending could be something like: "Thank you for considering our product/service. I believe it will be a great fit for your needs and I'd love to help you get started.

Shall we go ahead and finalize the purchase?" This ending is friendly, confident, and provides a clear call to action that encourages the customer to make a decision.

It also acknowledges the customer's potential concerns and offers help to address them if needed.

In summary, the best ending for a sale depends on the specific context and customer, but a clear call to action and addressing any potential concerns are key elements to consider.

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The variable represents time. The time in which a person runs a mile will depend on the speed of that person, and that can take almost any value, thus, here the variable is continuous.

First, when a variable is discrete and when it is continuous?

A variable is discrete if it only can take some selected values on a given interval, while a variable is continuous if it can take any value (or at least a dense set) of values in that interval.

For example, the numbers that one can roll on a dice form a discrete set, because the values can only be {1, 2, 3, 4, 5, 6}, just to given an example.

Now, in this case, the variable represents time. Time almost always is a continuous variable, in this case, the time is the time in which a person runs a mile. So that variable can take almost any value (depends on the speed of the person).

So we conclude that this is a continuous variable.

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To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

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Answer:

22° + m<C = 90°

Step-by-step explanation:

We are given that <A (which is equal to 22°) and <B are vertical angles, and that <B is complementary to <C.

We want to write an equation that will help us solve <C.

Recall that vertical angles are congruent by vertical angles theorem.

This means that <A ≅ <B; it also means that the measure of <B is also 22°.

Also recall that complementary angles add up to 90°.

This means that m<B + m<C = 90°.

Since we deduced that m<B is 22°, we can substitute that value into the equation.

Hence, an equation that can be used to solve for <C is:

22° + m<C = 90°

The correct statement is;

False,  because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be  x = 2π/3 + 2nx and x = 4π/3 + 2nx.

Option D

From the information given, we have that;

All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx

There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx

Such that n is an integer.

This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.

The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.

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let's reword it, since the wording is crummy

"How many grams of active ingredient is contained in 500mL of a solution which is 30% of the active ingredient?"

namely, what is 30% of 500?

\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 500}}{\left( \cfrac{30}{100} \right)500}\implies 150~mL\)

Hence, the ingredient is contained in  \(500\)ml of a \(30\)% solution is \(150ml\).

What is the percentage?

A percentage is a number or ratio expressed as a fraction of \(100\). It is often denoted using the percent sign, "%"

Here given that,

Number of ingredient is contained in \(500\)ml of a \(30\)% solution.

As

\(\frac{30}{100}*500=150ml\)

Hence, the ingredient is contained in  \(500\)ml of a \(30\)% solution is \(150ml\).

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Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

Answer:

D. -3 + 2i and E. 3+2i are the zeroes for the equation.

Step-by-step explanation:

Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

Answer:

ljknmi

Step-by-step explanation:

i did this last year

Answer:

k-j is diameter

L-i is radius

N-M is chord

Step-by-step explanation:

jk is 8 units

so length of IL will be 4 units

because radius is half of a diameter.

It would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

To calculate the time it would take to drive from Statesville, NC to Washington, DC, we can divide the distance of 389 miles by the average speed of 65 mph.

Time = Distance / Speed

Time = 389 miles / 65 mph

Time ≈ 5.98 hours

Therefore, it would take approximately 5.98 hours to drive from Statesville, NC to Washington, DC on interstates with an average speed of 65 mph.

To calculate the cost of driving to Washington, DC, we need to know the number of gallons of gas required for the trip. We can find this by dividing the distance by the car's mileage, which is 29 miles per gallon.

Number of gallons = Distance / Mileage

Number of gallons = 389 miles / 29 miles per gallon

Number of gallons ≈ 13.41 gallons

The cost of gas can be calculated by multiplying the number of gallons by the cost per gallon, which is $3.89.

Cost = Number of gallons * Cost per gallon

Cost ≈ 13.41 gallons * $3.89/gallon

Cost ≈ $52.18

Therefore, it would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

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Answer:

90 cm3

Step-by-step explanation:

You multiply 2 by 5 which is 10, then by 9 and get 90 cm3

The required value of trigonometric ratios is,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

We know that,

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Therefore,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

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The complete factorization of the polynomial is:

h(x) = (x - 3)*(x - 1)*(x + 2)

Here we have the polynomial:

g(x)= x³ - 2x² - 5x + 6

And we know that x = 3 is a zero, then (x - 3) is a factor.

So if f(x) = a*x² + b*x + c

We can write:

h(x) = (x - 3)*f(x)

Let's find f(x).

Expanding that:

x³ - 2x² - 5x + 6 = (x - 3)*(a*x² + b*x + c)

x³ - 2x² - 5x + 6 = ax³ + bx² + cx - 3ax² - 3bx - 3c

x³ - 2x² - 5x + 6 = ax³ + (b - 3a)x² + (c - 3b)x - 3c

Comparing like terms, we can see that:

a = 1

b - 3 a = -2

c - 3b = -5

-3c = 6

With the first and last equation we can get:

a = 1

c = 6/-3 = -2

Now with one of these values and the second or third equation we can find the value of b.

b - 3 a = -2

b - 3*1 = -2

b - 3 = -2

b = -2 + 3 = 1

Then:

f(x)  = x² + x - 2

The zeros of this quadratic function are given by:

x = -1±3 / 2

so, we get,

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

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

Then we can factorize this as:

f(x) = (x - 1)*(x + 2)

And then we can write h(x) as:

h(x) = (x - 3)*(x - 1)*(x + 2)

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complete question:

For the polynomial below, 3 is a zero.

g(x)= x³ - 2x² - 5x + 6

Express g (x) as a product of linear factors.

Answer:

Expression : $462.30 * m

The radius of the semicircle protractor is approximately 4.693 cm.

Given,Perimeter of a semicircle protractor = 14.8 cm.

To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.

Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =\((1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693\) cm.

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Answer:

1/2

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

The y coordinate of the vertex is -5.

Answer:

vertex  =  (1/4 , -81/8)

Step-by-step explanation:

f(x) = y

f(x) = 2x²-x-10

a= 2

b= -1

c = -10

-b/2a

-(-1)/(2(2))

1/4

x = 1/4

f(x) = 2x²-x-10

y = 2x²-x-10

y = 2(1/4)²-(1/4)-10

y = 2/16-1/4-10

y = 2/16-4/16-160/16

y = -2/16-160/16

y = -162/16

y = -81/8

Answer:

6:2

Step-by-step explanation:

Answer:

6:2

Step-by-step explanation:

This simply means for every 6 triangles there are going to be 2 circles, so if you had 12 triangles there would be 4 circles.

So think of it kinda like:

6 triangles = 2 circles and so on.

Answer:

d. 6b

Step-by-step explanation:

Simplify the following:

\( \longrightarrow \) 3(a + 2b) - 3a

3(a + 2b) = 3a + 6b:

\( \longrightarrow \) 3a + 6b - 3a

Grouping like terms,

3a + 6b - 3a = 6b + (3a - 3a):

\( \longrightarrow \) 6b + (3a - 3a)

3 a - 3 a = 0:

\( \longrightarrow \) 6b

Answer:

  4 and 5

Step-by-step explanation:

For answering questions like this, it can be useful to remember a few of the powers of small integers:

  2^4 = 16

  2^5 = 32

A logarithm can be considered to be an exponent of the base.

  \(\log_b(x) = a \ \Longleftrightarrow\ b^a=x\)

The ordering of powers of 2 relative to the number of interest (17) is ...

  16 < 17 < 32

  2⁴ < 17 < 2⁵ . . . . . . . . . . . . . . . . . . . expressed as powers of 2

  log₂(2⁴) < log₂(17) < log₂(2⁵) . . . . . log₂ of the above inequality

  4 < log₂(17) < 5 . . . . . . . . . . . . . . . . showing the values of the logs

Log₂(17) lies between 4 and 5.

__

Additional comment

Using the "change of base" formula, you can use a calculator to find the value of log₂(17). It shows you the value is between 4 and 5.

  log₂(17) = log(17)/log(2) . . . . . . using logs to the same base

Answer:

don't listen to the other person

Step-by-step explanation:

We can conclude from the graph that -

A function is a relation between a dependent and independent variable.

Mathematically, we can write → y = f(x) = ax + b.

Given is a graph as shown in the image.

{ 1 } -

At $60 the maximum profit is reached.

{ 2 } -

The breakeven point occurs at price $40.

{ 3 } -

For $60 and $70, the revenue is greater than the expenses.

{ 4 } -

For $100 and $120, the revenue is less than the expenses.

Therefore, we can conclude from the graph that -

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The process of solving a proportion is given below.

We are given that;

To show the process of solving a proportion

Now,

A proportion is an equation that states that two ratios are equal. For example, if we have 2 4 = 3 6\({\\displaystyle {\\frac {2} {4}}= {\\frac {3} {6}}}\) , then we have a proportion.

To solve a proportion, we need to find the value of a missing term that makes the equation true. There are different methods to solve a proportion, but one common method is cross-multiplication. Here are the steps to solve a proportion by cross-multiplication:

Multiply the numerator of one ratio by the denominator of the other ratio.

For example, if we have 2 4 = x 6

\({\\displaystyle {\\frac {2} {4}}= {\\frac {x} {6}}}\) , then we multiply 2 by 6 and get 12.

Multiply the denominator of the first ratio by the numerator of the second ratio.

For example, if we have 2 4 = x 6

\({\\displaystyle {\\frac {2} {4}}= {\\frac {x} {6}}}\) , then we multiply 4 by x and get 4x.

Set the two products equal to each other. For example,

if we have \(2 4 = x 6 {\\displaystyle {\\frac {2} {4}}= {\\frac {x} {6}}}\), then we set 12 = 4x.

Solve for the missing term. For example, if we have 12 = 4x, then we divide both sides by 4 and get x = 3.

Check your answer by plugging it back into the original proportion.

For example, if we have x = 3, then we plug it back into 2 4 = x 6 \({\\displaystyle {\\frac {2} {4}}= {\\frac {x} {6}}}\) and get 2 4 = 3 6

\({\\displaystyle {\\frac {2} {4}}= {\\frac {3} {6}}}\) , which is true.

Therefore, by proportion answer will be given below.

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Answer:

about $2546.88

Step-by-step explanation:

You would multiply 15x20 to find the area, which is 300 sq ft. Then, you would find the cost per square foot by dividing 2275/300 which is 7.58 rounded to the nearest hundredth. Now that you have the cost per square foot, you find the area of 12x28 which is 336. Then, you just multiply 336(7.58) which is equal to $2546.88

Pythagorean theorem is represented by triangle B.

In this question we find four cases of triangle, of which we must determine what triangle can be explained by Pythagorean theorem. This theorem offers a relationship between the three sides of the triangle:

r² = x² + y²

Where:

Please notice that hypotenuse is the longest side of the triangle. Graphically speaking, there is a right triangle, that is, a triangle with one right angle. Then, triangle B express the relationship according to Pythagorean theorem.

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Answer:

Based on the given data, there is no evidence to support the claim that the standard deviation of the heights of women aged 25 to 34 have a different standard deviation from men aged 25 to 34

Step-by-step explanation:

The standard deviation for the heights of men aged 25 to 34, σ₀ = 2.9

The population variance, σ₀ = 2.9² = 8.41

The significance level of the test = 0.05

The number of randomly selected women in the sample, n = 16

The given heights of the 16 randomly selected women are listed as follows;

62.13, 65.09, 64.18, 66.72, 61.15, 67.50, 64.65, 63.09, 63.80, 64.21, 60.17, 68.28, 66.49, 62.10, 65.73, 64.72

By using the Mean (Average) and standard deviation of a sample formula from Microsoft Excel, we have;

The mean height of the women, \(\overline x\) = 63.37563

The standard deviation of the variance, s₂ = 2.2 78511

The null hypothesis, H₀; σ = 2.9

The alternative hypothesis, H₀; σ ≠ 2.9

The chi-square test is given as follows;

T = (N - 1)(s/σ₀)²

Therefore, we have;

T = (16 - 1)(2.278511/2.9)² ≈ 9.2597

The critical value for the lower tail = 6.908

The critical value for the upper tail = 28.845

For the critical region, we have;

Reject H₀ if T <6.908 or T > 28.845

Therefore, given that the critical T is larger than 6.908 and less than 28.845, we fail to reject the null hypothesis, and there is not enough statistical evidence to prove that there is a difference in the standard deviation of the heights of men and women aged 25 to 34