Annette bought 3 notebooks for $0.80 each and a pack of pens for $1.20. She gave the clerk some money and got back
$1.40 in change. How much money did Annette give the clerk

The complete question is

find the slope of the tangent line and the equation of the tangent line at the given point, \(x^2y-5xy^2\)\(+6=0\) at the point (3,1).

Answer:

Tangent  = 1/23 , equation of tangent  = 23y - x = 20

Step-by-step explanation:

We are given the equation

\(x^2y-5xy^2\)\(+6=0\)

upon differentiation the given function we get

d (\(x^2y-5xy^2\)\(+6=0\)) /dt

= \(2xy +x^2dy/dx - 5y^2 -10xy dy/dx =0\)

upon substituting x=3 ,y=1 we will get

dy/dx = 1/23

now the equation of the tangent will be

y-1 = 1/23 (x-3)

23 (y-1) = x- 3

23y - 23 = x -3

23y - x = 20

Option D. The mountainous geography of Athens influence the economy as The people of Athens relied on sea trade.

Greece's rugged terrain caused some areas, particularly Athens, to become dependent on trade. Many Greeks went on to become seafaring tradesmen and merchants. Greeks engaged in trade with other Mediterranean people for pottery, wine, and olive oil. They communicated with the outside world by sailing to neighboring islands.

The geography of the area influenced the ancient Greeks' political system and way of life. Mountains, seas, and islands formed natural barriers between the Greek city-states, forcing the Greeks to relocate to coastal areas.

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Allison pays 1.9% of the $6,500 on taxes, so:

Allison pays for her taxes $123.5

Answer:

Step-by-step explanation:

x=100 (vertically opposite angle)

Answer: integer and rational

Step-by-step explanation:

Answer:

51.5

Step-by-step explanation:

Answer:

---------------------------

To find the median of the given data set, we need to first arrange the data in numerical order:

There are a total of 8 numbers in this set, which is an even number, so to find the median we need to take the average of the two middle numbers:

Therefore, the median of the data set is 51.5.

The truck driver would deliver 105 packages in a 7 hours day

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let y represent the number of packages delivered by the truck driver in x hours. Using the point (1, 15) and (4, 60). Hence, the equation is:

y - 15 = [(60-15)/(4-1)](x - 1)

y = 15x

For a 7 hour day (x = 7):

y = 15(7) = 105

The driver would deliver 105 packages in 7 hours

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Answer:

f = 86

Step-by-step explanation:

f = 9/5c + 32

~Substitute

f = 9/5(30) + 32

~Simplify

f = 54 + 32

f = 86

Best of Luck!

Answer:

Isoceles

Step-by-step explanation:

Isoceles triangles have 2 sides that are the same length.

Answer:

A.

Step-by-step explanation:

Let's think of this as a clock.  We can see that the 2 lines start in the same place, around 3 o'clock.  Next, one of the line segments shifts down to around 6 o'clock.  Next, it shifts to about 9 o'clock.  Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.

We can also just use a regular circle, with one of the line segments moving 90 degrees each time.

Hope this helps! :)

The linear model for the cost, \(C\), of waste collection as a function of the number of kilograms, \(w\) is  \(C = 4w +70\) .

Given,

The monthly charge for a waste collection service for 100 kg of waste = $470

so, \((x_{1} , y_{1} ) = (100, 470)\)

The monthly charge for a waste collection service for 175 kg of waste = $770

so, \((x_{2} , y_{2} ) = (175, 770)\)

In this question, We are supposed to find a linear model for the cost, C, of waste collection as a function of the number of kilograms, w.

So, we will use two point slope form :

\(y - y_{1} = \frac{y_{2} - y_{1} }{x_{2}- x_{1} } (x-x_{1} )\)

Substitute the values:

\(y - 470 = \frac{770- 470 }{175- 100 } (x-100)\)

\(y - 470 = \frac{300 }{75} (x-100)\)

\(y - 470 = 4 (x-100)\)

\(y - 470 = 4x-400\)

\(y = 4x +70\)

Now, replace \(y\) with C and \(x\) with w

\(C\) \(= 4w +70\)

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Answer:

9

Step-by-step explanation:

The \(n\)term is \(2n+1\).

\(S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)\)

The number of terms that needed to make the sum to 99 is 9

The first term of the arithmetic progression = 3

The common difference = 2

The sum of n term is = (n/2) [2a+(n-1)d]

Where a is the initial term

d is the common difference

Substitute the values in the equation

(n/2) [2(3)+(n-1)2] = 99

(n/2) [6 + 2n - 2] = 99

(n/2)[4+2n] = 99

n(2 + n) = 99

2n + \(n^2\) = 99

\(n^2\) + 2n - 99 = 0

Split the terms

\(n^2\) - 9n +11n - 99 =0

n(n -9) + 11(n - 9) = 0

(n + 11)(n - 9) = 0

n = -11 or 9

Since n cannot be a negative number, therefore n = 9

Hence, the number of terms that needed to make the sum to 99 is 9

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The measure of angle D is 45°

Similar triangles have the same corresponding angle measures and proportional side lengths. When two triangles are similar, the corresponding angles are equal.

And also the ratio of corresponding sides of similar triangles are equal.

To know the corresponding angles

side AC is corresponding to side EF, therefore angle D is congruent to angle A

angle D = 45°

OR , we can use the sum of angles In a triangle , which is 180°

angle D = 180 -( 72+63)

= 180 - 135

= 45°

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The probability that the next person will purchase one or more costumes can be found by dividing the number of visitors who purchased one or more costumes by the total number of visitors.

The total number of visitors is 105 + 41 + 8 = 154.

The number of visitors who purchased one or more costumes is 41 + 8 = 49.

So the probability that the next person will purchase one or more costumes is 49/154, which is approximately 0.32 to the nearest hundredth.

Answer:

56

Step-by-step explanation:

24x2+4x2

Simplify

48+8

Solve

56

The domain of the function f(x) is all real numbers except x = -7. In interval notation, we can express the domain as (-∞, -7) ∪ (-7, +∞).

To find the domain of the function f(x) = (x - 3)/(x + 7), we need to determine the values of x for which the function is defined.

The function is defined for all values of x except those that make the denominator, x + 7, equal to zero.

Division by zero is undefined in mathematics.

So, we set the denominator equal to zero and solve for x:

x + 7 = 0

x = -7

Hence, the only value that makes the denominator zero is x = -7. Therefore, the domain of the function f(x) is all real numbers except x = -7.

In interval notation, we can express the domain as (-∞, -7) ∪ (-7, +∞).

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Answer:

"If the time taken by the person to get to work is T minutes, the equality that models this situation is   | t - 50 | = 10 the minimum time taken by the person to get to work is 40 min, the maximum time taken is 60 min.

Step-by-step explanation:

The difference between the time and 50 minutes is 10 minutes.

This can be expressed as:

The minimum and maximum time can be found by solving the equation above:

The blanks to be filled in as:

Answer:

∠ABC = 63.26°

Step-by-step explanation:

cos ∠ABC = (9/2)/10

cos ∠ABC = 0.45

∠ABC = 63.26°

Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.

The most common symbols used in inequalities are:

">" (greater than): indicates that the value on the left side is larger than the value on the right side.

"<" (less than): indicates that the value on the left side is smaller than the value on the right side.

"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.

"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.

"≠" (not equal to): indicates that the values on both sides are not equal.

Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.

Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

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In a sample size of 75 people in the Boomer Generation, proportionately, the estimated number of people who prefer to shop in-store is 63.

Proportion shows the relative number of objects or people in the whole.

Proportions are ratios equated to each other.

They are expressed as fractional values, in decimals, percentages, and fractions.

The percentage of Boomers who want to shop in-store = 84%

The sample size of the Boomer Generation = 75

The estimated number of Boomers in the sample size who want to shop in-store = 63 (75 x 84%)

Thus, 63 Boomers representing 84 percent of 75 want to shop in-store.

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Answer:

students=315 adults=135

Step-by-step explanation:

3s=7a

s+a=450

s=450-a

3(450-a)=7a

1350-3a=7a

1350=7a+3a

1350=10a

a is 135

a is adult

s=450-a

s=450-135

s=315

branlist please

There were 8 slices in the whole pizza.

An equation means the formula that expresses the equality of two expressions by connecting them with the equals sign =.  Let us assume the number of slices in the whole pizza is "x".

Since Jim ate two slices which is 25% of the pizza, we will set up the equation:

2 = 0.25x

To solve for "x":

2 / 0.25 = x

x = 8.

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Answer: 12.3 seconds.

Step-by-step explanation: Hope It Helps :)

Answer:

To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.

So, 7/10 divided by 1/3 can be written as:

(7/10) ÷ (1/3) = (7/10) x (3/1)

Multiplying the numerators and denominators, we get:

(7 x 3) / (10 x 1) = 21/10

Therefore, the answer is 21/10, which is an improper fraction. We can simplify it to a mixed number by dividing the denominator into the numerator.

21 ÷ 10 = 2 with a remainder of 1, so the mixed number is:

= 1 1/10

Hence, the answer is 1 1/10 or 11/10.

Step-by-step explanation:

7/10  /  (1/3)   is equal to   7/10  *  3/1   =  (7*3) / (10*1) = 21/10 = 2  1/10

1. The Fill ups are as follow:

AB² +  BC² = AC. AD + AC. CD

2. Segment addition postulate

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

BC/ AC = CD/ BC and AB/ AC = AD/ AB

Now, BC² = AC. CD  and AB² = AC. AD

Using, Addition Property of Equality

AB² +  BC² = AC. AD + AC. CD

and, AB² +  BC² = AC (AD + CD)  [factor]

AD + CD = AD (segment addition postulate)

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PLATO

i got it correct :)

Answer:

the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.

Answer:

12h greater than or equal to 1200

Step-by-step explanation:

Let h = the number of hours worked. Since they make $12 per hour, then 12h represents how much they make. They need $1200 for the event, so they need to make AT LEAST that amount. That means 12h must be greater than or equal to $1200.

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:

a) 6/9

b) 66.66%

Step-by-step explanation:

a) Total number of the small triangles inside the big triangle=9

and the shades = 6

friction of shaded = 6÷9

b) percentage of shaded = 6÷9 ×100

=66.6666%