3. Find the instantaneous rate of change of f(x) = e^(2x)e^(7x) at x = -1

The distance the actual weight is from the weight shown on the scale is

l x - 7.2 l

In the given statement is :

A store scale measures the weight of objects within 0.4 ounce of the actual weight. The store scale measured an object with an actual weight of x ounces, displaying 7.2 ounces on its screen.

And, Which expression, using absolute value, shows the distance the actual weight is from the weight shown on the scale

Now, Let's start the solution:

A store scale measuring an object with an actual weight = x ounces

and, displaying the weight on its screen is = 7.2 ounces

By using the absolute value

Hence, The distance the actual weight is from the weight shown on the scale is l x - 7.2 l

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Using proportions, it is found that she travels 60 miles from her house to the VAB on days her colleague drives.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The first step is finding the fraction corresponding to the 7 miles, hence considering that the total is of 100% = 1 and the fractions given above, we have that:

1 - 5/6 - 1/20 = 1 - 0.8333 - 0.05 = 0.1167.

The 7 miles represent 0.1167 of the trip, hence:

0.1167x = 7

x = 7/0.1167

x = 60.

She travels 60 miles from her house to the VAB on days her colleague drives.

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Answer:

8.9 cm

Step-by-step explanation:

We have
[tex]\overline {UV} = 16.8 cm\\\\\overline {WV} = 7.9 cm\\\\ Since all lines are scalars, \overline{WV} = \overline{VW}\\\textrm{We see that \overline{UW} + \overline{WV} = \overline{UV}\\\\\overline {UW} \\ = \overline {UV} - \overline {WV} = 16.9 - 7.9 = 8.9 cm}[/tex]

Answer:

47 , 52

Step-by-step explanation:

Answer:

first figure area is 47 square units

second figure area is 52

Step-by-step explanation:

I assume the grid units are single units (1, 2, 3, ...).

to be a function every value of x must have exactly one value of y.

but that is violated at x = 2. at that point y can be either +3 or -3 (indicated by the 2 points at x=2).

so, no, it is not a function.

the domain is the interval or set of all valid x (input) values.

since we have no continuous curve but single points, it is a set :

x € {-4, -3, -2, 1, 2, 3, 6}

the range is the interval or set of all valid y (function result) values. again, it is a set for the same reasons :

y € {-3, -2, 0, 1, 3, 4}

Items purchased:

x packs of pencils,

twice as many packs of erasers, total number of eraser packs = 2x

three times the number of tape rolls, number of tape rolls = 3x

total expenditure = x m + 2xn + 3xp = x(m + 2n + 3p)

We now have two possibilities:

1- All three goods are the same price:

cost of one pencil pack = cost of one eraser pack = cost of one roll of tape = m

x m + 2xm + 3xm = 6xm

total amount spent

2- The three goods are not the same price:

m = the cost of one pencil pack

n = the cost of one pack of erasers

One roll of tape costs p.

total expenditure = x m + 2xn + 3xp = x(m + 2n + 3p)

An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it. Let us understand how to write expressions. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression.

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Shift 2 units left:  y = [tex](x+2)^{2}[/tex]

shift up 9 units:  y =  [tex](x+2)^{2}[/tex]  + 9

reflect in the x-axis:  y = -  [tex](x+2)^{2}[/tex] - 9

y =[tex]x^{2}[/tex]

Shift 2 units left:  y = [tex](x+2)^{2}[/tex]

Then, shift up 9 units:  y =  [tex](x+2)^{2}[/tex]  + 9

Then, reflect in the x-axis:  y = -  [tex](x+2)^{2}[/tex] - 9

Each reference coordinate line is referred to as an axis of the system, or simply an axis (plural axes),  and its origin is at the ordered pair intersection (0, 0). The positions of the perpendicular projections of the point onto the two axes, represented as signed distances from the origin, can likewise be used to establish the coordinates.

The same idea may be used to determine the location of any point in three dimensions using three Cartesian coordinates.

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The two similar triangles in this problem are given by:

C. QRS and TUV

Similar triangles share these two features:

Hence, the similar triangles are QRS and TUV, as the side lengths proportions are given as follows:

3/6 = 2.4/4.8 = 1.8/3.6.

Hence option C is correct.

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The fluid force against the window is equal to 931.5 lb.

Given the following data:

Generally speaking, the fluid force that is exerted on the fish tank by the seawater is due to the liquid pressure acting over the given area. Also, the fluid force that is exerted on the fish tank is directly proportional to the depth of seawater.

The depth of seawater is given by:

Depth = 28.5 - 1.5

Depth = 27 inches.

Next, we would convert the unit of the depth of seawater and width of viewing portion in inches to feet:

1 inch = 12 feet

Depth = 27 inches to feet = 27/12 = 2.25 feet.

Width = 69/12 = 5.75 feet.

Now, we can calculate the fluid force against the window by using this formula:

Fluid force = (density × depth × width)/2

Fluid force = (64 × 2.25² × 5.75)/2

Fluid force = 1863/2

Fluid force = 931.5 lb.

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Complete Question:

The viewing portion of the rectangular glass window in a fish tank is 69 inches wide and runs from 1.5 inches below the water's surface to 28.5 inches below the surface. Find the fluid force against this portion of the window. The weight-density of seawater is 64 lb/ft. What is the fluid force against the window?

Answer:

5 hours

Step-by-step explanation:

28x = 60(440-x)

28x = 60*440 - 60x

88x = 60*440

x = 60*440/88

x = 300mi, distance Jon travels

300mi/60mph = 5hrs, the time it took them to meet

CHECKING OUR ANSWER

60MPH*5HR + 28MPH*5HR = 300MI + 140MI = 440MI

The probability that a four is obtained on at least one of the rolls 51.71 %.

We need to use this formula in order to find out the probability of getting 4

1 – 54/64

=1 -  625/1296

=  671/1296

= 51.71%

Hence , the probability that a four is obtained is  51.71 %.

A traditional die is a cube with each of its six faces marked with a different number of dots from 1 to 6. Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that proportion is true. The probability of an event is a number between 0 and 1 , where roughly speaking , 0 indicated impossibility of the event and 1 indicates certainty.

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The sign of the other integer is positive. Value of other integer is greater than 5.

When we add two numbers of the same sign, final number has the same sign of the initial numbers

For example, we add 3 and 8,

3+8= 11

Both the numbers 3 and 8 are positive so our result is also positive.

On the other hand when we add -3 and -8, then the result will be

-3 +(-8)= -11

Both the numbers are negative, so our result also negative.

When two numbers of different sign are being added then the sign of the larger number decide the sign of the final number

For example, we add -3 and 8.

-3+8= 5

8 is larger than 3, and has positive sign, so the result will also be positive.

Suppose other number is x.

-5+x>0 (As the sum is positive)

Add 5 on both the sides

-5+x+5>0+5

x>5

As we can see the number is greater than 5 and has a positive value.

Final answer: The sign of the other integer is positive. Value of other integer is greater than 5.

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Answer:

She made 118% profit.

Step-by-step explanation:

The distance of each of the paths are as follows;

25) Distance of Low Trail is; d = 17.1 km

26) Distance of willow walk is; d = 20.6 km

27) Distance of Pond Walk is; d = 8.5 km

28) Distance of Meadow Trail is; d = 22.8 km

The formula for distance between two coordinates is;

d = √[(x1 - x2)² + (y1 - y2)²]

25) Distance of Low Trail is;

d = √[(14 - 12)² + (-2 - 15)²]

d = 17.1 km

26) Distance of willow walk is;

d = √[(10 + 4)² + (12 - 1)²]

d = 20.6 km

27) Distance of Pond Walk is;

d = √[(-4 + 12)² + (12 - 15)²]

d = 8.5 km

28) Distance of Meadow Trail is;

d = √[(14 + 4)² + (12 + 2)²]

d = 22.8 km

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Answer:

1 2/15 inches

Step-by-step explanation:

First you need to make the denominator of the two fractions match.

4/5 and 1/3

the least common multiple of these is 15

4/5 becomes 12/15

1/3 becomes 5/15

add them together

17/15

subtract 15 from 17 because 15/15 is one

we get 2

put 2 as the numerator and 15 as the denominator

Yes , it is true that two pairs of adjacent sides of a kite are equal .

A quadrilateral with two pairs of adjacent sides equal in length is called a kite. Kites also have one pair of opposite angle equal as shown in the figure below.

Hence , the given statement is true .

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Answer: You're dividing, and the answer is 1/2, 1/4, 1/3, 1/8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using it's concept, there is a 0.462 probability that a randomly selected male student says that the school should adopt a dress code.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

From the table, we have that:

Hence the probability is given by:

p = 30/65 = 0.462.

0.462 probability that a randomly selected male student says that the school should adopt a dress code.

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Answer:

  648 m

Step-by-step explanation:

Given observations of two nests, one at 400 m, and the other at 300 m in a direction 135° from the first, you want to know the distance between the nests.

The law of cosines can be used to find the third side of a triangle, given two sides and the angle between them. It tells us ...

  c² = a² +b² -2ab·cos(C)

In this scenario, we have a=400, b=300, and C=135°. The distance c is then ...

  c² = 400² +300² -2·400·300·cos(135°) ≈ 419,705.63

  c ≈ √419,705.63 ≈ 647.8

The two nests are about 648 meters apart.

The intersection of the two planes is a Line.

According to the statement

We have to find that the Intersection of the planes.

So, For this purpose, we know that the

An intersection is a single point where two lines meet or cross each other.

From the given information:

A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors.

And then the intersection of the plane becomes:

Then

The intersection of two planes is a line. If the planes do not intersect, they are parallel.

They cannot intersect at only one point because planes are infinite.it means parallel planes have no intersection point.

So, The intersection of the two planes is a Line.

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By inductive reasoning we can say that the conclusion is based on observing the four numbers in the sequence.

We are given the arithmetic series as;

5, 10, 15, 20, .......

From the formula of the nth term of an arithmetic series, we know that;

a_n = a + (n - 1)d

where;

a is first term

n is position of term

d is common difference

Thus, for this series, it is clear that the common difference is 5. Thus the fifth term is;

a_5 = 5 + (5 - 1)5

a_5 = 5 + 20

a_5 = 25

Thus, by inductive reasoning we can say that the conclusion is based on observing the four numbers in the sequence.

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Answer:

Definition of perpendicular lines

Step-by-step explanation:

Answer:

Range is 21

I believe

Step-by-step explanation:

Answer:

D. x ≤ 5

Step-by-step explanation:

The closed circle means greater than or equal to (≤) or less than or equal to (≥). The open circle is greater than (<) or less than (>).

And since the circle is closed and the arrow is going to the right, than x is either greater than 5 or equal to 5

Answer:

4.88

Step-by-step explanation:

2+2+4+4+5+5+6+7+9=44

44÷9=4.88

Answer=4.88

The drawing shows a series of transformations and the sequence that moves Triangle I to Triangle II to Triangle III is translation followed by reflection.

A reflection in arithmetic is a form of geometrical transformation, wherein an item is flipped to create a reflect or congruent image. The bisector of the plane is referred to as the definition on the line of reflection, and it is perpendicular to the preimage and photograph.

In the coordinate plane we will draw the translation if we recognize the path and how far the figure have to be moved. To translate the factor P(x,y) , a units right and b units up, use P'(x+a,y+b) .

A translation is a form of transformation that takes every factor in a figure and slides it the equal distance in the equal path.

Here, the image is first translated and then rotated.

Therefore, the drawing shows a series of transformations and the sequence that moves Triangle I to Triangle II to Triangle III is translation followed by reflection.

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Answer:

see explanation

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = lw ( l is the length and w the width )

using the property [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a , then

A = 2[tex]\sqrt{7}[/tex] × 10[tex]\sqrt{7}[/tex]

  = 2 × 10 × [tex]\sqrt{7}[/tex] × [tex]\sqrt{7}[/tex]

  = 20 × 7

  = 140 ft²

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

the perimeter (P) is calculated as

P = 2(l + w)

  = 2(2[tex]\sqrt{7}[/tex] + 10[tex]\sqrt{7}[/tex] )

 = 2(12[tex]\sqrt{7}[/tex] )

 = 24[tex]\sqrt{7}[/tex] ft