Help with my study guide only answer topic 7 problem A

Step-by-step explanation:

Use the product rule for finding the derivative of a product of functions. Use the quotient rule for finding the derivative of a quotient of functions.

Answer:

length: 9 units width: 2 units

Step-by-step explanation:

The formula to find the area of a rectangle is length*width (LW)

x+3 is the length and x-4 is the width; together they multiply up to 18

(x+3)(x-4) = 18

x^2 - 4x + 3x - 12 = 18 (multiply it out using FOIL)

x^2 - x - 12 = 18 (combine like terms on the left side)

x^2 - x -30 = 0 (subtract 18 from both sides so that the right side is 0)

Think what two numbers multiply up -30 and add up to -1 (5 and -6)

(x+5)(x-6) = 0 (factor it)

x+5 = 0 and x-6 = 0 (solve using zero-product property)

x = -5 and x = 6 (solve)

x = 6 (only this one works since you cannot have a negative side length)

(6+3)(6-4) = 18 ? (plug in to find side lengths and check)

9 * 2 = 18 (Correct!)

Answer:

  length: 9 ft

  width: 2 ft

Step-by-step explanation:

This can be worked using a quadratic equation, or it can be worked by considering factors of the area value.

__

The difference in length between the long side (x+3) and the short side (x-4) is ...

  (x +3) -(x -4) = 3+4 = 7 . . . . feet

The area formula is ...

  A = LW

The given area is 18 square feet, so we want to find numbers that multiply to give 18 and that differ by 7 in their values. Here are the integer factors of 18:

  18 = 1×18 = 2×9 = 3×6

Of these factor pairs, the values 2 and 9 differ by 7.

The garden is 9 feet long and 2 feet wide.

_____

Additional comment

We can check to see if these numbers are consistent with the given expressions:

  x+3 = 9  ⇒  x = 6

  x -4 = 6 -4 = 2 . . . . the other dimension we found

__

If you solve this using a quadratic equation, you will find that dimensions -2 ft and -9 ft also pop out. That is x +3 = -2, or x = -5 is also a solution to the quadratic. Of course, that is an extraneous solution, which we avoid by considering only positive factors of 18.

The quadratic equation we're referring to is A=18 ⇒ (x+3)(x-4) = 18.

Answer:

[tex]4*6^\frac{5}{2}[/tex]

Step-by-step explanation:

Use [tex]\sqrt[n]{a^x}=a^{\frac{x}{n} }[/tex] to rewrite [tex]\sqrt{6^5}[/tex] as [tex]6^\frac{5}{2}[/tex].

[tex]4*6^\frac{5}{2}[/tex]

[tex]~~~~~~~4x^2-12x+9=0\\\\\implies (2x)^2-2 \cdot 2x \cdot 3+3^2 = 0\\\\\implies (2x-3)^2 = 0\\\\\implies 2x -3 = 0\\\\\implies x =\dfrac 32[/tex]

Step-by-step explanation:

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We conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.

In an arithmetic sequence, the difference between any two consecutive terms is a constant.

Here we know that:

[tex]a_1 = 3/5\\a_8 = 1/4[/tex]

There are 7 times the common difference between these two values, so if d is the common difference:

[tex]a_1 + 7*d = a_8\\\\3/5 + 7*d = 1/4\\\\7*d = 1/4 - 3/5 = (5 - 12)/20 = -7/20\\\\d = -1/20[/tex]

Then the sum of the first 8 terms is given by:

[tex]3/5 + (3/5 - 1/20) + (3/5 - 2/20) + ... + (3/5 - 7/20)\\\\8*(3/5) - (1/20)*(1 + 2 + 3+ 4 + 5 + 6 + 7) = 3.4 = 34/10 = 17/5[/tex]

So we conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.

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The formula for calculating the volume of a cube is expressed as V = L³. The volume of the cube is 1/27 cubic meters

The formula for calculating the volume of a cube is expressed as:

V = L³

where:

L = 1/3cm

Substitute

V = (1/3)³
V = 1/3³

V = 1/27 cubic meters

Hence the volume of the cube is 1/27 cubic meters

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The figure is the combination of the rectangle and square. Then the area of the figure will be 13 square units.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

Then the area of the geometry will be

The figure is the combination of the rectangle and square.

Then we have

Area = 3 x 3 + 4 x 1

Area = 9 + 4

Area = 13 square units

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Answer:

17

Step-by-step explanation:

The median of a data set can simply be thought of as the middle value/number.

You could list all values out:

16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19

and then find what the middle of 24 would be (There are an even number of values, so both numbers in places 12 and 13 are considered the median, meaning that we find the average of these two values to be our median)

the 12th value is 17, and the 13th value is 17, meaning that the median is 17.

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

You could also calculate what would be 12 "in" from the data set. The first 4 values are 16 (12 - 4 = 8 ; 8 values left to go until middle) And then take the remaining 8 places to find the 12th value (9 - 8 = 1), so you know that the 12th value is the 8th repetition of 17.

There is still one more value of 17, so that is also the 13th placed value.

In this method of finding the middle number, the median is still 17.  

The median of these ages is 17.

The median exists as the middle number in a sorted checklist of numbers and can be better descriptive of that data set than the average. The median exists sometimes utilized as objected to the mean when there exist outliers in the sequence that might skew the average of the values.

The median of a data set can only be considered as the middle value.

Let the values be 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19

To find the middle of 24 would be (There exist an even number of values, so both numbers in places 12 and 13 exist considered the median) the 12th value stands at 17, and the 13th value stands at 17, indicating that the median exists at 17.

You have to calculate an estimate of 12 "in" from the data set. The first 4 values exist 16 (12 - 4 = 8; 8 values left to go until middle)

Consider the remaining 8 places to estimate the 12th value (9 - 8 = 1)

The 12th value exists in the 8th repetition of 17.

Therefore, the median of these ages is 17.

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Answer:
10

Step-by-step explanation:

-3x+7x-8=34+9x-2

(Combine like terms)

4x-8=32

(Add 8 to each side)

4x=40

(Divide by 4)

X=10

Answer:

12 is 50% of 24

7 is 20% of 35

9 is 10% of 90

20/60 is 33.33%

Nani wait what I don't know

Option third "words per minute, because the independent quantity is the minutes" is the correct choice.

It is defined as the change in values of a dependent variable with respect to the independent variables.

We have a statement:

Which of the following is the most appropriate unit to describe the rate at which a person reads?

As we know the rate of change is the ratio of change in y to change in x.

y is the dependent quantity and x is the independent quantity.

Rate of change = change in y/change in x

Rate at which a person reads = words/minute

Word is the dependent quantity and minute is the independent quantity.

Thus, option third "words per minute, because the independent quantity is the minutes" is the correct choice.

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If you spin the spinner 52 times, we expect the spinner to land on purple approximately 13 times in 52 spins.

Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.

Since there are 4 equal-sized sectors on the spinner, the probability of landing on purple on any given spin is 1/4.

To find the expected number of times the spinner will land on purple in 52 spins, we can multiply the probability of landing on purple by the total number of spins:

Expected number of times landing on purple = (Probability of landing on purple) x (Total number of spins)

Expected number of times landing on purple = (1/4) x (52)

Expected number of times landing on purple = 13

Therefore, we expect the spinner to land on purple approximately 13 times in 52 spins.

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Answer:

False

Step-by-step explanation:

9(k-2)=-6 and k=1

9(1-2)=-6

9(-1)=-6

-9=-6

No, -9 doesn't equal -6.

So this system of equations is false.

Hope this helped! :)

2x - 3y = 7 can be rewritten as y = 2/3x - 7/3, therefore, the equation that is a linear equation is: C. 2x - 3y = 7.

A linear equation is expressed in the slope-intercept form as y = mx + b.

2x - 3y = 7, rewritten in slope-intercept form would be:

-3y = -2x + 7

y = -2x/-3 + 7/-3

y = 2/3x - 7/3

m = 2/3 and b = -7/3

Therefore, the equation that is a linear equation is: C. 2x - 3y = 7.

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The domain is  All real numbers except odd integer multiples of 2π/3 , Option B is the correct answer.

A function is defined as a mathematical statement that identifies the relation between a dependent and an independent variable.

A function has a defined range and domain.

In the given function

y = (5/3)tan(3x/4)

Domain is the all the value at which the function is defined .

Tan x is defined for every value except at

x = (2n+1)π/2

The domain of the function y = (5/3)tan(3x/4) is

3x/4 = (2n+1)π/2

x = (2n+1)2π/3

Therefore the domain is  All real numbers except odd integer multiples of 2π/3 , Option B is the correct answer.

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The equation for the sinusoidal function described is given as follows:

[tex]y = 4\cos{\left(\frac{1}{2}x\right)} + 2[/tex]

We want a function with a y-intercept at it's maximum value, hence we use the cosine equation, given by:

[tex]y = A\cos{\left(\frac{2\pi}{B}x\right)} + C[/tex]

In which:

The amplitude is of 8, hence 2A = 8 -> A = 4. This would represent a function between -4 and 4, but we want between -2 and 6, hence the vertical shift is of C = 2.

As for the period, we have that:

[tex]B = 4\pi[/tex]

Then, the equation is given by:

[tex]y = 4\cos{\left(\frac{1}{2}x\right)} + 2[/tex]

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Answer:

18

Step-by-step explanation:

my answer is correct,try to read the question,

if the length of larger triangle is 6 times so it means 6 ×5= 30 and you will times 3 to 6=18

so that's why it has lenght of 30

because the. larger triangle is 6 times bigger than smaller rectangle

100%✓sure answer

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The area of the park is 1640 square meters.

A quadrilateral is a plane shape with four sides and four angles.

The above figure is made up of two quadrilateral; a square and a trapezium.

Analysis:

Area of park = area of square + area of trapezium

Area of park = 1/2(a + b)h + s x s

where a = length of smaller parallel side of the trapezium = 40m

           b = length of the larger parallel side = 48m

           h = height of trapezium = 35m

           s = length of side of square = 10m

Area of park = 1/2(40 + 48)x35 + 10 x 10 = 1640 square meters

In conclusion, the area of the park is 1640 square meters

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Answer:

Step-by-step explanation:

Let the number of people were surveyed is x.

We have 60% of x is 48 people.

Set this as equation and solve:

Correct choice is C.

Answer:

C.  80

Step-by-step explanation:

Given:

Let x be the total number of people surveyed.

Set up a ratio of people to percentage and solve for x:

[tex]\implies \sf 48 : 60 = x : 100[/tex]

[tex]\implies \sf \dfrac{48}{60}=\dfrac{x}{100}[/tex]

[tex]\implies \sf x=100 \cdot \dfrac{48}{60}[/tex]

[tex]\implies \sf x=\dfrac{4800}{60}[/tex]

[tex]\implies \sf x=\dfrac{480}{6}[/tex]

[tex]\implies \sf x=80[/tex]

Therefore, the total number of people who were surveyed was 80.

Answer:

(-21, 54.5)

Step-by-step explanation:

Hello there!

We have two methods to solve this problem.

We will limit ourself to Substitution method.

3x – 2y = -4.................... 1.

4x + 2y = 25................... 2.

First lets manipulate eq.2 in terms of y.

4x + 2y = 25

2y = 25 - 4x

y = 25/2 - 2x .............. eq.3

Substitute eq.3 into eq.1

3x – 2(25/2 -2x) = -4

Solve for x.

Opening the brackets

3x - 25 - 4x = -4

-x = 21

x = -21

Substitute x into equation 3

y = 25/2 - 2x

=> y = 25/2 - 2(-21)

= 54.5

In terms of x and y; (x,y)

= (-21, 54.5)

I hope this helps.

Have a nice studies.

The equation represented by the graph will be y = eˣ. Then the correct option is A.

The missing graph is given below.

Functions are found all across mathematics and are required for the creation of complex relationships.

The graph is given below.

The exponential graph is always positive and the graph is also positive of the Real value of x.

The equation represented by the graph will be y = eˣ.

Then the correct option is A.

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The measure of the remote exterior angle is 128°.

From the information given, x = y + z. Therefore, .(198 - 5n) = (5n + 37( + (n + 7)

198 - 5n = 6n + 44

Collect like terms

154 = 6n + 5n

154 = 11n

n = 154/11

n = 14

The value of angle x will be:

= 198 - 5n

= 198 - 5(14)

= 198 - 70

= 128

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Step-by-step explanation:

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The attached number line represents points of the lowest recorded temperatures

The table is given as:

City                 Lowest Recorded Temperature

Morgantown       7°F below 0

Charlotte            6°F above 0

Huntsville           4°F above 0

Bluefield            8°F below 0

To rewrite the table, we use the following representations:

So, we have:

City                 Lowest Recorded Temperature

Morgantown       -7

Charlotte            6

Huntsville           4

Bluefield            -8

See attachment for the number line that represents the above points

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