use a number line to find the difference-6.5 - 2

Answer:

x = 6\(\sqrt{2}\) = 8.485

Step-by-step explanation:

In a 45-45-90 triangle, the hypotenuse is \(\sqrt{2}\) times the length of a leg.

So, if you are given the hypotenuse, then divide its length by \(\sqrt{2}\)

x = 12/\(\sqrt{2}\) = 12\(\sqrt{2}\)/2 = 6\(\sqrt{2}\) = 8.485

Answer:

D

Step-by-step explanation:

Ecology definition of niche

From SOHCAHTOA.

Cos37 = x/25

x= 25cos37

x=21.5 = 22.

When rounded to the nearest integer... 20

Option A is legit

Answer:

The correct answer is B. 15

Step-by-step explanation:

Ap3x Approved

Answer:

B) A=135, B=77

Step-by-step explanation:

A + 45 = 180

135(A) + 45 = 180

103 + B = 180

104 + 77(B) = 180

The power series representation of f(x) centered at x = 0 is: f(x) = ∑(n=0 to ∞) \([(-1)^n * (5 * x^(n+1))/(n+1)]\). To find the power series representation of the function f(x) = 5ln(1+x), we can use the Taylor series expansion of ln(1+x).

The Taylor series expansion of ln(1+x) is given by:

ln(1+x) = x - \((x^2)/2 + (x^3)/3 - (x^4)/4\)+ ...

Substituting this into the function f(x), we have:

f(x) = 5(x -\((x^2)/2 + (x^3)/3 - (x^4)/4\) + ...)

Expanding this further, we have:

f(x) = 5x - \((5x^2)/2 + (5x^3)/3 - (5x^4)/4\)+ ...

The power series representation of f(x) centered at x = 0 is:

f(x) = ∑(n=0 to ∞) [\((-1)^n * (5 * x^(n+1))/(n+1)\)] where ∑ represents the summation notation.

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Using the alternative form of the dot product and the given magnitudes and angle, we find that u - v is equal to -75√3.

To find the value of u - v using the alternative form of the dot product, we need to have the magnitudes (lengths) of vectors u and v and the angle between them. Let's denote the magnitude of vector u as ||u|| = 15, the magnitude of vector v as ||v|| = 10, and the angle between u and v as θ = 5π/6.

The alternative form of the dot product states that:

u · v = ||u|| ||v|| cos(θ),

where u · v is the dot product of u and v, ||u|| and ||v|| are the magnitudes of u and v respectively, and θ is the angle between u and v.

Substituting the given values, we have:

u · v = (15)(10) cos(5π/6).

To simplify further, we need to evaluate the cosine of 5π/6. The cosine of 5π/6 is -√3/2, because the angle 5π/6 corresponds to the reference angle π/6 in the second quadrant.

Substituting this value, we have:

u · v = (15)(10) (-√3/2).

Simplifying the expression, we get:

u · v = -75√3.

Therefore, u - v = -75√3.

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Given expression is  \(x⁵/⁹\).

Recall to write the nth root of a number, we have to type root(n).

For example, to get\(³√4x\), type "\(root(3)(4x)\)".

We can write the expression x⁵/⁹ as follows:

\($$\frac{x^5}{9}$$\)

Let's rewrite the expression as:

\($$\frac{x}{\sqrt[9]{9}}^5$$\)

Let's write the nth root of a number by typing root(n).

Therefore, the final answer becomes:

\($$\frac{x}{root(9)(9)}^5$$\)

Therefore, the given expression in radical form is   \(\frac{x}{root(9)(9)}^5\)

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The type of transformation that is shown in the graph below is reflection.

option C.

A rotation is a form of transformation that turns a figure about a point. We call this point the center of rotation.

A figure and its rotation maintain the same shape and size but will be facing a different direction.

A reflection can be thought of as folding or "flipping" an object over the line of reflection.

So we can conclude that rotation involves rotating a figure around a fixed point, while reflection involves creating a mirror image of a figure across a line.

Rotation changes the orientation of the figure, while reflection changes its position relative to the line of reflection.

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(a) The 7th row of Pascal's Triangle is 1 7 21 35 35 21 7 1.

(b) The expansion of (x + y)⁷ = x⁷ + 7x⁶y + 21x⁵y² + 35x⁴y³ + 35x³y⁴ + 21x²y⁵ + 7xy⁶ + y⁷.

(a) In The 7th row of Pascal's Triangle, we simply need to add the numbers in the 6th row that are adjacent and above to get the corresponding numbers in the 7th row. Using the formula for the nth row of Pascal's Triangle, we can write:

1 6 15 20 15 6 1 ⇒ add adjacent numbers to get:

1 7 21 35 35 21 7 1

(b) Pascal's Triangle:- Pascal's Triangle is an arithmetical arrangement of numbers, starting with 1 at the top and a left and right number that increases by 1 with each row. The total numbers are formed by adding the two numbers above it.

Arranging the triangle in this way exhibits the symmetry of the coefficients of the polynomials generated by binomial expansion. Rows of Pascal's triangle have been proved to include the coefficients of the binomial expansion; the row number indicates the exponent of the binomial (when it is raised to a power).

Therefore, for (x + y)^7, we will use the seventh row of Pascal's Triangle. Each of the coefficients is multiplied by the appropriate powers of x and y and then summed together in order to expand the equation.

(x + y)⁷ = x⁷ + 7x⁶y + 21x⁵y² + 35x⁴y³ + 35x³y⁴ + 21x²y⁵ + 7xy⁶ + y⁷

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A graphical device used for enumerating sample points in a multiple-step experiment is a tree diagram.

A tree diagram is a way of determining probabilities of different outcomes based on numerous different events.

It helps in identifying all the probable outcomes of an experiment and helps in understanding the likelihood of each of these events.

A tree diagram starts with a single root node that is then divided into different branches based on the potential outcomes of an experiment that are mutually exclusive.

These branches then split again into sub-branches until the final potential outcomes of an experiment are reached.

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It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. Hence:

Rate of the machine = 3 pounds / 20 seconds = 0.15 pound per second

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second

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The total weight of 16 packages of 3-inch molding junction boxes and each weighs 6 1/4 pounds is 100 pounds.

In order to find the total weight of 16 packages of 3-inch molding junction boxes, we need to first determine the weight of one package, and then multiply that by 16.

The problem states that one package weighs 6 1/4 pounds. To convert this mixed number into an improper fraction, we multiply the whole number (6) by the denominator of the fraction (4), and add the numerator (1) to get 25. This gives us:

6 1/4 pounds = 25/4 pounds

Now that we know the weight of one package is 25/4 pounds, we can multiply by 16 to find the total weight of 16 packages:

25/4 pounds x 16 = 400/4 pounds

Simplifying the fraction, we get:

400/4 pounds = 100 pounds

Therefore, the total weight of 16 packages of 3-inch molding junction boxes is 100 pounds.

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What is true about ΔXWZ is that the ratio of its altitude to the corresponding altitude in ΔYWZ is equal to the ratio of the length of XW to the length of YZ.

If ΔYWZ is similar to ΔYXW, it means that these two triangles have corresponding angles that are equal and corresponding sides that are proportional. In this case, we are specifically interested in the altitude of ΔWXZ, which we will denote as h.

Since ΔYWZ is similar to ΔYXW, we can establish the following proportion based on their corresponding sides:

YZ/YX = YW/YW

Let's denote the length of YZ as a and the length of YW as b. We can rewrite the proportion as:

a/YX = b/YW

Now, let's consider ΔXWZ. Since XW is common to both triangles, we can conclude that the altitude of ΔXWZ, which we will denote as k, is also proportional to the altitude of ΔYWZ (h). Therefore, we can express this proportion as:

k/h = XZ/YZ

To establish a relationship between k and h, we need to find a way to relate XZ to YZ. Using the proportion established earlier, we can substitute a for YZ:

k/h = XZ/a

To relate XZ to YZ, we need to find a relationship between XZ and YX. Again, using the similarity of the triangles, we have:

XZ/YZ = XW/YW

Substituting the value of YZ (a) from the earlier proportion, we have:

XZ/a = XW/YW

Now, we can combine the two proportions to find the relationship between k and h:

k/h = (XW/YW) * (YW/a)

Simplifying further, we get:

k/h = (XW/a)

From this equation, we can conclude that the ratio of the altitudes k/h in ΔXWZ and h in ΔYWZ is equal to the ratio of XW to YZ. In other words, the ratio of the altitudes is equal to the ratio of the corresponding sides in the similar triangles.

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The owner of a landscaping company can determine how much time, on average, his employees spend mowing one lawn by taking hours per lawn.

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The total cost of pizza and drinks, is an illustration of a linear function.

The model that represents the situation is: \(\mathbf{10 + 3d = 19}\)

The given parameters are:

\(\mathbf{Total =19}\)

\(\mathbf{1\ pizza =10}\)

\(\mathbf{1\ drink =d}\)

The cost of 3 drinks will be 3d

The total cost would then be:

\(\mathbf{Total = 10 + 3d}\)

Substitute 19 for Total

\(\mathbf{10 + 3d = 19}\)

Rewrite the above equation as:

\(\mathbf{3d + 10 = 19}\)

Hence, the model that represents the situation is: \(\mathbf{10 + 3d = 19}\)

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Answer:

QV = 36 UNITS

Step-by-step explanation:

Centroid of a triangle divides the median in the ratio 2 : 1.

QU is the median and V is Centroid. Therefore,

QV : VU = 2 : 1

Let QV = 2x & VU = x

QV + VU = QU

2x + x = 54

3x = 54

x = 54/3

x = 18

QV = 2x = 2*18 = 36

Answer:

Probability = 0.500

Step-by-step explanation:

If it is given that the reader is a teen, we have a total of 80 readers, where 40 of those readers have Rowling as their favorite.

So the probability that the reader's favorite is Rowling given that the reader is a teen is the number of teen readers that have Rowling as favorite (40) over the total number of teen readers (80)

Probability = 40 / 80 = 0.500

The surface area of a cylinder is found using the following formula:

Replace for the given values of radius and height:

It means that the surface area of the cylinder is 622.

The correct answer is D. 622 sq units.

The ounces of onions is 5 ounces.

Let the onions be represented by x.

The recipe uses 4 times more carrots than onions. The carrots will be 4 × x = 4x.

Therefore, the equation will be:

4x + x = 25

5x = 25

Divide by 5

x = 25/5

x = 5

Therefore, the ounces of onions is 5 ounces.

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Answer:

Step-by-step explanation:

The ounces of onions is 5 ounces.

The recipe uses 4 times more carrots than onions. The carrots will be 4 × x = 4x.

Therefore, the equation will be:

4x + x = 25

5x = 25

Divide by 5

x = 25/5

x = 5

Therefore, the ounces of onions are 5 ounces.

Using Basic proportionality theorem, the value of x is 6.

The other two sides of a triangle are divided in the same ratio if a line drawn parallel to one side of a triangle intersects the other two sides at distinct spots.

The fundamental proportionality theorem aids in determining the lengths at which a line parallel to the third side divides the two sides of a triangle. It can also be used to determine how two equiangular triangles relate to one another.

By basic proportionality theorem,

⇒ 5 / 17 = 2x + 3 / 10x - 9

Now, Cross multiplying,

⇒ 5(10x - 9) = 17(2x + 3)

⇒ 50 x - 45 = 34x + 51

⇒ 16 x = 96

⇒ x = 6

So, the sides of triangle are -

2x + 3 = 2(6) + 3 = 15

10x - 9 = 10(6) - 9 = 51

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Answer:

Step-by-step explanation:

0.017 m/min is the height of increasing water.

What is the volume of a cylinder?

A cylinder's volume refers to the amount of interior room it has to hold a given quantity of material.

Formula to calculate the volume of a cylinder

volume = π r² h

where r is the radius of the cylinder and h is the height.

Here, we have

radius = 6m

dV/dt = 3

We have to find:  dh/dt

volume = π r² h

Differentiating both sides with respect to t, we get

dV/dt = π[2r(dr/dt)h + r²(dh/dt)]

r remains constant (r = 6), dr/dt = 0

So, dV/dt = πr²(dh/dt)

Substituting the values, we get

2 = π(6)²(dh/dt)

dh/dt = 2/(36π)

= 0.017m/min

Hence, 0.017 m/min is the height of increasing water.

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Answer: A. \(-\frac{2}{3} x^3+5x\)

Step-by-step explanation:

The answer is A, \(-\frac{2}{3} x^3+5x\) because a binomial has two terms

In other words if there is a single sign like '+'

Answer:

15.09

Step-by-step explanation:

with reference angle 28°

perpendicular (p) = 8

base (b) = x

Now

tan 28° = p / b

0.53 = 8 / x

x = 8 / 0.53

x = 15.09

Answer:

Step-by-step explanation:

1 tablespoon = 3 teaspoons

You need to fill the tablespoon a third full. Not accurate, but that's what you have to do.

:::::

1¼ + ½ = 1¾

you need to fill the 2 cup measuring cup ⅞ full to get 1¾ cups.