Evaluate the integral by making the given substitution. (Use C for the constant of integration.)

∫ x^2√x^3+37 dx, u=x^3+37

Answer:

y = 3x - 11

Step-by-step explanation:

(3, -2) and (5, 4)

m = 4+2/5-3

m = 6/2

m = 3

y = 3x + b

4 = 3(5) + b

4 = 15 + b

b = -11

y = 3x - 11

The exponential function which passes through (0,-2),(1,0),(2,2) (5,3) is negative on the interval (-∞,1) and positive on  the interval (1,∞).

Given Function f is negative on the interval (-∞,1) and positive on the interval (1,∞)

We have to find the statement for which the exponential function' s values are given.

First option is having the statement which says that exponential

function passes through points (0,-6)(0.5,-2),(1,0),(2,2) (5,3). These points are showing the domain and value of the function which is codomain.

for x=0 it has -6,

for x=1 it has 0,

for x=2 it has 2,

for x=5 it has 3.

for x=0.5 it has -2

The description says that value of function is negative in interval (-∞,1) and positive in (1,∞) which is true for option A as it has negative values of -2 for x=0 and for x=2,5 it has value of 2 and 3.

Hence the function f is an exponential function passes through  (0, minus 6), (0.5, minus 2), (1, 0), (2, 2), (5, 3).

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There are 120 different combinations of 3 programmers that can be chosen to transfer to the new department

From the question, we have

Total number of programmers, n = 10

Numbers to programmers to select, r = 3

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 10 and r = 3

Substitute the known values in the above equation

Total = ¹⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 10!/(7! * 3!)

Evaluate

Total = 120

Hence, the number of ways is 120

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33 Caribbean dollars

Step-by-step explanation:

$6 US dollars = 16 Caribbean dollars,

6 into 16 =2.66 x 12 = 31.92 = 32 Caribbean dollars for $12 US dollars

The vertices of triangle image are L'(1, -4), M'(6, 4) and N'(7, -2).

Given that, triangle LMIN with vertices L(2, -8), M(12, 8) and N(14,-4).

Here, scale factor k=1/2

Now, by applying scale factor to the vertices, we get

L(2, -8)→1/2 (2, -8)→L'(1, -4)

M(12, 8)→1/2 (12, 8)→M'(6, 4)

N(14,-4)→1/2 (14, -4)→N'(7, -2)

Therefore, the vertices of triangle image are L'(1, -4), M'(6, 4) and N'(7, -2).

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"Your question is incomplete, probably the complete question/missing part is:"

Triangle LMIN with vertices L(2, -8), M(12, 8), and N(14,-4): k = ½.

Answer:

-3/4

Step-by-step explanation:

y=mx+b is in slope-intercept form, in which m=-3/4 and b=7, describing the slope and y-intercept of a linear equation respectively.

Answer:

1/2 is 1 example

Step-by-step explanation:

what

A fraction that is less than 5/8 is 4/8

The fraction is given as:

Fraction = 5/8

A fraction less than 5/8 will have the same denominator but a smaller numerator compared to 5/8

Take for instance, the numerator can be

1 to 4

So, we have;

Smaller fraction = 4/8

Hence, a fraction that is less than 5/8 is 4/8

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Answer: A quarter turn

Step-by-step explanation:

Answer:

x≈13.9

Step-by-step explanation:

a=c2﹣b2=752﹣73.72≈13.9036

Answer: m= -9

Step-by-step explanation: First use distributive property, -4(m) is -4m and -4(3) is -12. Then you have -4m -12 =24. Then use 12 and add it to the other side of the equation, cause of the subtraction sign, 12+24=36. Then you have -4m=36. Then divide the 4 to get the m by its self. 36 divided by -4 is -9. Your answer is m=-9

Hope this helps :)

The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

The surface area of the cylinder is 125.66

The surface area of a cylinder is the area occupied by its surface in a three-dimensional space. A cylinder is a three-dimensional structure having circular bases which are parallel to each other. It does not have any vertices. Generally, the area of the three-dimensional shapes refers to the surface area.

The surface area of a cylinder is calculated with the formula:

= 2π × r × h + 2πr2= 2πr (h + r) Square units

A=2πrh+2πr2

With the following parameters from the question:

r = 2

h = 8

Substituting the parameters into the formula

A = 2πrh+2πr2=

A = 2·π·2·8+2·π·22

A = 125.66371

Hence, the surface area of the cylinder is  125.66371

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Answer:

6.69 grams

Step-by-step explanation:

12 * .4425 = 5.31

12 - 5.31 = 6.69

Answer:

It is B.

Step-by-step explanation:

A C is anything between 73-76 %, while a B is anything between 83-86 %

The linear function that predicts the number of calculators sold per week (y) at a price of x dollars is, y = -400x + 46,000

To determine a linear function that predicts the number of calculators sold per week at a certain price, we can use the given information. Let's assign "x" as the price of the calculator and "y" as the number of calculators sold per week.
We have two data points:
At a price of $90, 10,000 calculators are sold per week.
At a price of $85, 12,000 calculators are sold per week.
Using these two points, we can find the slope of the linear function:
Slope (m) = (change in y) / (change in x)
= (12,000 - 10,000) / (85 - 90)
= 2,000 / -5
= -400
Now, let's use one of the data points to find the y-intercept (b):
Using the point (x, y) = (90, 10,000):
y = mx + b
10,000 = -400(90) + b
10,000 = -36,000 + b
b = 46,000
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The quantity of ribbon that Ali started with was 16/21 feet, based on the mathematical operation of addition.

The basic mathematical operations include addition, subtraction, division, and multiplication.

In the addition operation, two or more addends are added to obtain a result called the sum or total using the equation symbol (=) and the addition operand (+).

The quantity of ribbon attached to the rearview mirror = 2/7

The remaining quantity of ribbon after the attachment = 10/21

The quantity of ribbon Ali started with = 16/21 (2/7 + 10/21)

Thus, using the addition operation, we can conclude that Ali started with 16/21 feet of ribbon.

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First, calculate the surface area of the inside of the tank by multiplying the length, width, and height: 3 m * 2 m * 1.5 m = 9 m^2.

Then, calculate the surface area of the outside of the tank by adding the surface area of all 6 sides: 2 * (3 m * 1.5 m + 2 m * 1.5 m + 3 m * 2 m) = 24 m^2.

Finally, add the surface area of the inside and outside to get the total surface area: 9 m^2 + 24 m^2 = 33 m^2.

To find the amount of paint required, divide the total surface area by the coverage per kg of paint: 33 m^2 / 20 m^2/kg = 1.65 kg.

Answer:g(x) is flipped and 2 times as steep and shifted left 5

Step-by-step explanation:

Answer:

they are real numbers that are being used to answer this function

just had this problem

The weight of the person on earth will be 144 pounds if the weight of person on the moon is 24 pounds.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Suppose we have two ratio p : q and r : s.

If both these ratios are proportional, then we can write it as p: q : : r : s.

This is same as p : q = r : s or p/q = r/s

Given that, if you took a trip to the moon, your body weight would have a proportional change.

Body weight on earth if the person weighs 37 pounds on the moon = 222 pounds.

Body weight on earth if the person weighs 24 pounds on the moon = x pounds

Using proportion,

37 / 222 = 24 / x

37 x = 222 × 24

x = (222 × 24) / 37

x = 144 pounds

Hence the weight of the person on earth is 144 pounds.

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As per the system of linear equations concept, the solution of x is -1.282

Linear equations:

Linear equation is referred as the algebraic equation in which each term has an exponent of 1 and when graphed, the result is always a straight line.

Given,

Here we have the equations -4x - 1 = 5ˣ + 4

Now, we need to find the value of x by using the graph.

In order to plot the graph for the given linear equation,

First, we have to split the equation into two,

Like the following:

y = -4x - 1

y = 5ˣ + 4

Now, we plot the graph of both equations

Then we get the graph like the following.

Where the red line represents the equation y = -4x - 1 and the green line represents the equation y = 5ˣ + 4.

While we looking into the graph, we have identified the solution is,

x = -1.282

Therefore, the solution of x is -1.282

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Answer:

x^2 + 3x + 9 = (x + 3)(x + 3)

When x = 2, we have:

(2 + 3) * (2 + 3)

5 * 5

25

Answer:

100x + 13000y = 865000

Step-by-step explanation:

x = Series A price

y = Series B price

Answer:

1000 tiles

Step-by-step explanation:

Determine total floor space
800 x 10 = 8000 squared cm total floor space.
Divide floor space by size of tile
8000 / 8 = 1000 tiles now required to cover the floor.

The value of square root of x + y squared + z squared is 30

x = 2, y = 3 and z = -5

\(( \sqrt{x + y} )^{2} + z ^{2} \)

substitute the value of x, y and z

\( = ( \sqrt{2 + 3} )^{2} + - 5 ^{2} \)

simplify the square root and square

\( = (2 + 3) + 25\)

\( = 5 + 25\)

\( = 30\)

Ultimately, x + y squared + z squared is 30

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Answer:

\( x = 17.5 \)

Step-by-step explanation:

Since the two triangles are similar, their corresponding side lengths would be proportional. Therefore:

\( \frac{28}{16} = \frac{x}{10} \)

Cross multiply

\( x*16 = 10*28 \)

\( 16x = 280 \)

Divide both sides by 16

\( x = \frac{280}{16} \)

\( x = 17.5 \)

Answer:

{7, 9}

(Numbers from 1 to 10 equal to or greater than 7 are 7 and 9)

Step-by-step explanation:

We have to find the set of whole number greater than and equal to 7 from 1 to 10,

Now, From 1 to 10, the odd numbers are, 1,3,5,7,9,

And of these, 7 and 9 are equal to or greater than 7

So, we get the set,

{7, 9}

Answer:-39

Step-by-step explanation:

The first thing is to open the bracket.

By doing that, the question becomes -37-2.

note that plus×minus=minus.

Hence,-39 as the final answer

Answer:

Last option; 5/2+ i5/2