Find the distance between the following pair of points.

A(-3,1), B(7,13)

The domain and range of trigonometric functions are as follows;

Function Domain Range

sin(x). All real numbers [-1, 1]

cos(x). All real numbers [-1, 1]

tan(x). {x| x ≠ -3•π/2, -π/2, π/2, } R

The domain and range of the inverse sine, cosine, and tangent are;

Function Domain Range

arcsin(x). (-1, 1) [-π/2, π/2]

arccos(x). (-1, 1) [0, π]

arctan(x) (-∞, ∞). [-π/2, π/2]

sin(x)

The domain of sin(x) is the set of possible values for x, for which sin(x) is defined, which is;

The range of sin(x) is the set of possible values output values of sin(x) is, which is; -1 ≤ sin(x) ≤ 1

cos(x)

Similarly;

tan(x)

tan(x) = sin(x)/cos(x), however, cos(x) = 0, when x = -3•π/2, -π/2, π/2, 3•π/2...

The domain of tan(x) is therefore;

sin(x) increases as cos(x) decreases, therefore;

The range of tan(x) = sin(x)/cos(x) is therefore;

arcsin(x)

The input of arcsin(x) is sin(x)

sin(x) = opposite/hypotenuse

Given that the magnitude of hypotenuse > opposite, the ratio, opposite/hypotenuse is < 1 in magnitude

The domain of arcsin(x) is therefore;

The range is the set of possible outputs, which is [-π/2, π/2], given that sin(x) is positive and negative from -π/2, π/2

arccos(x)

Similarly;

arctan(x)

The input of arctan(x) is tan(x)

tan(x) = sin(x)/cos(x)

The domain of arctan(x) is therefore;

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The rate of grapes said by Emika i.e., 0.4 pounds per dollar is the correct rate.

We know that the rate is nothing but the ratio of two different quantities which have different units.

In this question, we have been given two pounds of grapes cost $5

First we find the rate in pounds per dollar.

2 pounds of grapes = $5

As rate is the ratio of two different quantities, we find the ratio (pounds per dollar).

= 2 pounds /5 dollars

= (2/5) pounds per dollar

= 0.4 pounds per dollar              .......(1)

This means the rate of grapes is 0.4 pounds per dollar.

In this question, we have been given  Jordan says that's 2.5 pounds per dollar and Emika says it's 0.4 pounds per dollar.

From (1), we can clearly say that Emika is correct.

Therefore, the rate of grapes said by Emika i.e., 0.4 pounds per dollar is the correct rate.

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Answer:

D

Step-by-step explanation:

y < 3

10 combinations of two parts can be selected.

Combination is defined as the number of arrangements in a collection of items where the order of selection does not matter.

denoted by C(n,x)= ⁿcₓ=[tex]\frac{n!}{(x!)(n-x)!}[/tex]  ,

where n is the total number of elements in the set.

x is the number of selected objects.

According to the Question

Total number of elements = 5 = n

Number of objects to be selected = 2 = x

Substituting the values in the above formula

C(5,2)=[tex]\frac{5!}{2!*3!}[/tex]

[tex]=\frac{5*4*3!}{2*3!} \\ \\ =\frac{20}{2} \\ \\ =10[/tex]

Therefore , 10 combinations of two parts can be selected.

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If the school now has 1,378 students enrolled, last year, the number of students enrolled was B. 1,300.

Using the mathematical operations of addition, subtraction, division, and multiplication, we can determine the number of students.

Mathematical operations help us to determine unknown values, given a known domain.

Increase in school enrollment over last year's = 6%

Enrollment for the current year = 1,378

Let last year's enrollment = 100%

And the current year's = 1.06 (100 + 6)

Therefore, the enrollment last year = 1,300 (1,378/1.06)

Thus, the enrollment (number) last school year was B. 1,300.

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A large polymeric molecule that is nonpolar over most of its structure but very polar at one end DNA and Phospholipid.

DNA and phospholipid were two examples of huge polymeric molecules that would be polar solely on a single end although nonpolar on the majority of their structure, as opposed to the other alternatives, which would be all monomeric compounds. Nucleotides are used to help DNA create its polymeric structure. Phosphodiester linkage aids in the arrangement of the nucleotides.

The polar molecule would only be found in one area of the vast strand-like polymeric structure. At one extremity of the strand, there is a polar phosphate link; with its assistance, some other monomeric units were joined, generating the phosphodiester bonds. Two fatty acids and the first molecule of glycerol work together to generate the structure known as the phosphodiester.

The phosphate group is present in the polar head region of the phosphate group. This help in the polarity of the phospholipid structure making the head region of the polymeric molecule hydrophilic.  

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Answer:

-2

Step-by-step explanation:

2(2x + 3) + 5x + 1 = -11

x = -2

2(2× +3) + 5× +1 = -11

Multiply the 2 to what is in the bracket

4×+ 6 + 5× +1 = -11

Group liketerms

4× + 5× = -11 - 1 -6

simply it

9× = - 18

we will divide them by the co-efficient of ×

9× = - 18

________

9 9

x = - 2

Answer: 26

Step-by-step explanation:

Answer:

26 is the answer because we have to subtract when the signs of the number are diffrent and add when it is same . so +18 - (-8) = 26

Multiplying (-4) × (-5) we get 20. Here is the reason.

There are a few properties of integers which determine its operations. These principles or properties help us to solve many equations. To recall, integers are any positive or negative numbers, including zero. Properties of these integers will help to simplify and answer a series of operations on integers quickly.

All properties and identities for addition, subtraction, multiplication and division of numbers are also applicable to all the integers. Integers include the set of positive numbers, zero and negative numbers which are denoted with the letter Z.

Z= ( -5, -4,-3,-2,-1,0,1,2,3,4,5)

Integers have 5 main properties of operation which are:

Closure Property

Associative Property

Commutative Property

Distributive Property

Identity Property

While doing multiplication we use the following rules:

So using second rule we can write (-4×-5)= 20.

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Answer:

price of oranges is 6.63

Step-by-step explanation:

1)59.53-6.49=53.04

2) 53.04/8=6.63

The image after a dilation with a scale factor of 3 is A(-6, -3), B(0, 3), and C(3, -9) of triangle ABC.

Here, the coordinates are,

D = (-2, -1)

E = (0 , 1)

F = (1, -3)

After dilating triangle DEF using a scale factor of 3 and a center of dilation at the origin to form triangle ABC.

A = (-2 x 3, -1 x 3) = (-6, -3)

B = (0 x 3, 1 x 3) = (0, 3)

C = (1 x 3, -3 x 3) = (3, -9)

Line segments,

AB = 8.48

BC = 12.36

CD = 10.81

Therefore, after dilation by using a scale factor of 3 is  A(-6, -3), B(0, 3), and C(3, -9).

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If -3r + 1/2 = 4, then it is true that r=-7/6

The equation is given as:

-3r + 1/2 = 4

And the solution is given as

r=-7/6

The two-column proof is as follows:

Hence, if -3r + 1/2 = 4, then it is true that r=-7/6

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Answer:

-2.

Step-by-step explanation:

x = 0 where the line passes through the y axis.

So, from the diagram we see that at x = 0,  f(x) = -2.

a)The x co-ordinates of P and Q satisfy the equation x² + 4x - 5 = 0.

b)The co-ordinates of P and Q are (-5, -1) and Q = (1, 5).

The given equation of the circle is;

x² + y² = 26.

Th circle satisfies the line y = x + 4.

Thus, Put the value of y in the main equation.

x² + (x + 4)² = 26.

Simplify the equation;

x² + x² + 16 + 8x = 26

2x² + 8x - 10  = 0

Divide the equation by 2.

x² + 4x - 5  = 0  

Part a: This shows that x co-ordinates of P and Q satisfy the equation x² + 4x - 5 = 0.

Part b: Now, do the factorization of x² + 4x - 5  = 0.

(x + 5)(x - 1) = 0

x = -5 and 1.

For x = -5; y = -1

Point P = (-5, -1)

For x = 1; y = 5

Point Q = (1, 5)

Thus, the requires points P and Q are obtained.

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Answer:

989

Step-by-step explanation:

Answer:

986

The total area of the shaded regions in fraction of the total area of the block is 3/8 as the common fraction.

A common fraction, sometimes known as a common fraction, is a fraction with an integer numerator and denominator. A common fraction may be used to identify a portion of a larger whole or set.

Multiply each component of a fraction by both the denominator of another fraction to find the common denominator. To calculate the common denominator of 1/3 + 2/5, multiply the 1 through 3 by 5 and the 2 and 5 by 3. You should obtain a total of 5/15 + 6/15. The fractions can then be calculated.

Let's divide each square across four equal sections, for a total of 16 sections..

Using symmetry, one of the four portions in the top left square is shaded, and the same is true for the bottom right square.

Furthermore, two of the four squares inside this top right and bottom left corners are darkened.

Consequently,

the shaded area is:

{1 + 1 + 2 + 2}/ 16

6 /16 =  3 / 8

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Answer: your answer would be unimodal skewed. This graph only has one maxima, thus it can't be bimodal. However, it's not symmetric, meaning that it is skewed

Hope this helps you

Step-by-step explanation:

The histogram is solved and it is uni-modal skewed

A graph called a histogram is used to show the frequency distribution of a small number of data points for a single variable.

A histogram displays the frequency distribution of a set of continuous data. It is useful for visualizing the shape of the data distribution, such as whether it is symmetrical or skewed, and identifying any outliers or gaps in the data.

Given data ,

Let the histogram be represented as A

Now , the value of A is plotted on the graph

A. Unimodal skewed: This distribution has one peak (mode) and the tail of the distribution extends to one side. Depending on which side the tail is longer, it can be either positively skewed (tail extends to the right) or negatively skewed (tail extends to the left).

B. Bimodal symmetric: This distribution has two distinct peaks (modes) and is symmetric, meaning the left and right sides of the distribution are roughly mirror images of each other.

C. Unimodal symmetric: This distribution has one peak (mode) and is roughly symmetric, meaning the left and right sides of the distribution are roughly mirror images of each other.

D. Bimodal skewed: This distribution has two distinct peaks (modes) and the tail of the distribution extends to one side for each peak. Depending on which side each tail is longer, it can be either positively skewed (tail of one peak extends to the right and the other to the left) or negatively skewed (tail of one peak extends to the left and the other to the right).

E. Uniform: This distribution is flat and has roughly equal frequency for all values in the range of the dataset.

Hence , the histogram is unimodal skewed

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Answer:

Step-by-step explanation:

its 6 2 + 5 = 9-2 = 6

Answer:

16, 13, 5

Step-by-step explanation:

h(-3)=13-(-3)

h(-3)=13+3

h(-3)=16

h(0)=13-(0)

h(0)=13

h(8)=13-(8)

h(8)=5

Hope this helps.

Answer:

The product is rational.

Step-by-step explanation:

Answer:

let y=0

3x+6(0)=18

3x=18

x=6

(6;0)

Answer: 3

Step-by-step explanation: If you solve the equation, like I did in the attached image, you will see that the x-intercept is 3.

Answer:

D

Step-by-step explanation:

2x+6=-3x-14

2x+3x=-14-6

5x=-20

x=-4

Answer:

X = -4

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

The bacterial cell is about 7 × 10^(1) times smaller than the amoeba cell in scientific notations.

What are scientific notations?

Scientific notations are a way of representing either a very small or a very large number in the powers of 10. Scientific notations comprise digits from 1 to 9 with powers of 10.

Calculation of the amount by which a bacterial cell is smaller than the amoeba cell

Given the length of amoeba cell in scientific notations is 3.5 × 10^(- 4)

The length of a bacterial cell in scientific notations is 5 × 10^(- 6)

To obtain how small the bacterial cell is from the amoeba cell, we need to divide both the lengths i.e.

= 3.5 × 10^(- 4) / 5 × 10^(- 6)

= 0.7 × 10^(2)

= 7 × 10^(1)

Hence, the bacterial cell is about 7 × 10^(1) times smaller than the amoeba cell in scientific notations.

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A) Variance = 10.24

B) Standard Deviation = 3.2

One of the measurements of dispersion is the standard deviation, which is exclusively used for quantitative data. It aids in determining if the data's mean is a suitable measurement to reflect the core value.

TIME         FREQUENCY(f)  MIDPOINT(x)    d    d²     fd              fd²

0 - 0.9         43                          0.45             -3     9     -129            387

1.0 - 1.9         17                           1.45              -2    4     -34                68

2.0 - 2.9       19                            2.45             -1     1       -19               19

3.0 - 3.9        18                            3.45             0     0       0                  0

4.0 - 4.9        14                            4.45              1      1        14               14

5.0 -5.9         16                            5.45              2     4        32             64                            

∑f = 127                                                              

∑fd = -136  

∑fd² = 552

[tex]d = \frac{x - 3.45}{1}[/tex]

Standard Deviation = [tex]\sqrt \frac{fd^{2} }{N} - \sqrt \frac{(fd)^{2} }{N} * i[/tex]

[tex]\sqrt \frac{552}{127} -\sqrt (\frac{-136}{127})^{2} * 1[/tex]

√4.35 - √1.15

Standard Deviation = 3.2

(SD)² = (3.2)² = 10.24

Variance = 10.24

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Answer:

b=8

Step-by-step explanation:

-4b + 5 = -27

Move the 5 to the right side by subtraction, subtract five from the right side as well.

Now you should have:
-4b = -32

Now divide by -4 to get ‘b’ isolated, do this on both sides.

You should be left with:
b=8

The expression is simplified to 6√5 - 4√7

From the information given, we have that;

[tex]3\sqrt{5} - 2\sqrt{7} + \sqrt{45} - \sqrt{28}[/tex]

Let's find the surd forms with perfect squares and add into the formula

3√5 - 2√7 + √9 ×5 - √7× 4

Find the perfect squares of the expression

3√5 -  2√7 + 3√5 - 2√7

collect like terms

3√5 + 3√5 - 2√7 -  2√7

Add like terms

6√5 - 4√7

Thus, the expression is simplified to 6√5 - 4√7

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The height of the machine piston after 10 seconds is 2. 5m . Option B

Given the function;

y = 4.4 sin (0.4x -1.7) +2.3,

Where;

Given x as 10 seconds

y = 4. 4 sin ( 0.4(10) - 1. 7) + 2. 3

y = 4. 4 sin ( 4 - 1. 7) + 2. 3

y = 4. 4 sin (2. 3) + 2. 3

y = 4. 4(0. 04013) + 2. 3

y = 2. 47

y = 2. 5 meters in the nearest tenth

Thus, the height of the machine piston after 10 seconds is 2. 5m . Option B

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Answer:

D. 5.6 m

Step-by-step explanation:

Use your context clues.

All the other answers had O, like an X, so I put D, which was correct. *Wink*

Answer:

See explanation

Step-by-step explanation:

a. [tex]\sqrt{49}[/tex]=7

b. 0, [tex]\sqrt{49}[/tex]   ==> 0 is a whole number, not a natural number

c. -9, 0, [tex]\sqrt{49}[/tex]

d. -9, -3/7, 0, 0.25, 6.7, [tex]\sqrt{49}[/tex]

e. [tex]\sqrt{2}[/tex] since it has an infinite number of digits and can't be given as a ratio of two integers.

f. -9, -3/7, 0, 0.25, [tex]\sqrt{2}[/tex], 6.7, [tex]\sqrt{49}[/tex] ==> Real numbers consist of both rational and irrational numbers