Complete the identity: sec(t) - cos(t) = ?
1) sec(t)csc(t)
2) -2tan²(t)
3) 1 + cot(t)
4) sin(t)tan(t)​

Answer:

10x² + 8x + 22

Step-by-step explanation:

The perimeter of a rectangle is the measurements of all four side lengths added together

(you can simply multiply both side lengths by 2, because they are the same on both sides--but I'll write them all out for clarity)

side A (top): 5x² + 3x + 7

side B (right): x + 4

side C (bottom): 5x² + 3x + 7

side D (left): x + 4

perimeter = side A + side B + side C + side D

5x² + 3x + 7 + x + 4 + 5x² + 3x + 7 + x + 4

now, as you might have noticed, this is a long equation

so, we must combine like terms:

(this is the problem reordered so like terms are next to each other:)

(5x² + 5x²) + (3x + x + 3x + x) + (7 + 4 + 7 + 4)

10x² + 8x + 22

So, the perimeter of this rectangle is 10x² + 8x + 22

hope this helps! have a lovely day :)

By applying the radioactive simple decay model, we find that the initial quantity of the radioactive isotope is equal to approximately 5.63 grams.

Mass of radioactive isotopes (m (t)), in grams, decay exponentially in time according to the following model:

[tex]m(t) = m_{o}\cdot e^{-t/\tau}[/tex]     (1)

Where:

The time constant can be found in terms of half-life:

τ = t'/㏑ 2

If we know that t' = 24100 yr, t = 1000 yr and m(t) = 5.4 g, then the initial mass of the radioactive isotope is:

τ = 24100 yr/㏑ 2

τ ≈ 34768.95 yr

[tex]5.4 = m_{o}\cdot e^{-1000/24100}[/tex]

[tex]m_{o} = 5.629\,g[/tex]

By applying the radioactive simple decay model, we find that the initial quantity of the radioactive isotope is equal to approximately 5.63 grams.

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Answer:

The answer is

[tex]a \sin(theta) [/tex]

Step-by-step explanation:

The solution is in the image

Answer:

x=80

Step-by-step explanation:

x=0.7x+24

We move all terms to the left:

x-(0.7x+24)=0

We get rid of parentheses

x-0.7x-24=0

We add all the numbers together, and all the variables

0.3x-24=0

We move all terms containing x to the left, all other terms to the right

0.3x=24

x=24/0.3

x=80

Answer:

x = 80

Step-by-step explanation:

We are given the following equation.

x = 0.7x + 24

And we want to solve it for x.

For these kinds of equations, the way to solve for x is to isolate x on one side.

Because we have terms with x on both sides of the equation, we need to remove it from one side.

It's a good idea to remove x from the right side, as we also have our numbers on that side. If we move it to the left side, there aren't any numbers there, so we can more easily solve this equation.

Here is our equation again:

x = 0.7x + 24

Subtract 0.7x from both sides.

x = 0.7x + 24

-0.7x -0.7x

______________________

0.3x = 24

Now, we have variables on one side, and numbers on the other, but we aren't done yet.

Remember that we are solving for x, not 0.3x. (When x is written by itself, it is the same as 1x).

So, in order to find the value of 1x, we need to divide both sides by 0.3, as when a number is divided by itself, the value is 1. If there is a variable, the value will be 1*that variable (e.g. 1n, or n)

**Note that we don't divide by 0.3x, as if we did that, the left side would equal just 1, not 1x.

So, let's divide both sides by 0.3.

0.3x = 24

÷0.3   ÷0.3

__________

x = 80

Topic: solving linear equations

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[tex]\Large\maltese\underline{\textsf{A. \space What is Asked}}[/tex]

Find the slope of the line that contains the points (-8,-2) and (-17,4)

[tex]\Large\maltese\underline{\textsf{B.\space This problem has been solved!}}[/tex]

If we are given two points, we can easily find the slope of the line that passes through the points. With points (y₂, y₁) and (x₂, x₁), the slope is [tex]\bf{\dfrac{y2-y1}{x2-x1}[/tex].

Similarly, with points (-8,-2) and (-17,4) the slope is.

[tex]\bf{\dfrac{4-(-2)}{-17-(-8)}}[/tex] | as we can see, it is possible to simplify this further

[tex]\bf{\dfrac{4+2}{-17+8}}[/tex] | simplify

[tex]\bf{\dfrac{6}{-9}[/tex] | reduce

[tex]\bf{-\dfrac{2}{3}}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

                    [tex]\bf{=-\dfrac{2}{3}}[/tex]

[tex]\boxed{\bf{aesthetic\not101}}[/tex]

Using the equation of slope of a line, the slope of the line that have the given coordinates is -2/3

The slope of a line represents the measure of how steep the line is, or the rate at which the line rises or falls as you move along it. It is calculated as the ratio of the vertical change (change in y-coordinates) to the horizontal change (change in x-coordinates) between any two points on the line.

If you have two points on a line, (x₁, y₁) and (x₂, y₂), the slope (m) can be calculated using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Substituting the values into the formula above;

m = 4 - (-2) / -17 - (-8)

m = 4 +  2 / -17 + 8

m = 6 / -9

m = -2/3

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Answer: 110

Step-by-step explanation:

<ABC = <DEF

180 - <DEF = 180 - 70

<BED = 110

Using the binomial distribution, it is found that there is a 0.3222 = 32.22% probability that at least 3 Canadian are on CERB in the sample.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters are:

n = 10, p = 0.2.

The probability that at least 3 Canadian are on CERB in the sample is:

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]

[tex]P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684[/tex]

[tex]P(X = 2) = C_{10,2}.(0.2)^{2}.(0.8)^{8} = 0.3020[/tex]

Then:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1074 + 0.2684 + 0.3020 = 0.6778.

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.6778 = 0.3222[/tex]

0.3222 = 32.22% probability that at least 3 Canadian are on CERB in the sample.

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The equation of the line that passes through (-10,-7) and (-5,-9) is y=-2.5x-31.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

The slope of the line is,

Slope, m = (-10+5)/(-7+9) = -5/2 = -2.5

Substitute any one of the points in the equation of the line,

-7 = -2.5(-10) + C

-7 = 25 + C

C = -31

Hence, the equation of the line that passes through (-10,-7) and (-5,-9) is y=-2.5x-31.

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Answer: the answer is y = - 2/5x - 11

Step-by-step explanation:

it’s correct on khan academy

Answer:

568.3 into the nearest hundred

5.683

Answer:

568

Explanation:

A whole number is a number without any fractional part; in other words, it does not have any non-zero digits after the decimal point.

When you round a number to the nearest whole number, first look at the digit right after the decimal point;

• if the digit is less than 5, then the nearest whole number is the original number, but without any digit after the decimal point. [rounding down]

• if the digit is 5 or greater than 5, then the nearest whole number is the next whole number (i.e., add 1 to the original number and remove the digits after the decimal point). [rounding up]

Answer:

Option B

Step-by-step explanation:

Slope

And

These are acceleration

Y intercept is (0,2) as x coordinate is 0

This is initial velocity 2m/s

The runner stopped at 8s

Answer:

33, 165, 133

Step-by-step explanation:

Check this file for the solution!

Answer:

33, 165, 133

Step-by-step explanation:

let the first number be n then

second number is 5n

third number is n + 100

sum the 3 numbers and equate to 331

n + 5n + n + 100 = 331 , that is

7n + 100 = 331 ( subtract 100 from both sides )

7n = 231 ( divide both sides by 7 )

n = 33

5n = 5 × 33 = 165

n + 100 = 33 + 100 = 133

the numbers are 33, 165, 133

(3,6) (4,6) (5,6) (6,6) (4,5) (5,5)

Each of these pairs is equiprobable and which i will be using throughout the exercise:

[tex]p(pair) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} [/tex]

[tex]p(a) = (\frac{1}{36} \times 2) \times 4 + \frac{1}{36} \times 2 = \frac{5}{18} [/tex]

The 2 (2!) is to account for permutations like ( 3 , 6 ) and ( 6 , 3 ) and the 4 are the different combinations that are composed of different numbers.

The 2 (2!) is to account for permutations like ( 3 , 6 ) and ( 6 , 3 ) and the 4 are the different combinations that are composed of different numbers.Whereas combinations like ( 5 , 5 ) cannot be switched in order, so we do not multiply by 2!

(1,3) (2,2) (2,6) (4,4) (5,3) (6,6) (1,4) (2,3) (5,5) (4,6)

[tex]p(not \: b) = ( \frac{1}{36} \times 2) \times 6 + \frac{1}{36} \times 4 = \frac{4}{9} [/tex]

[tex]p(b) = 1 - p(not \: b) = 1 - \frac{4}{9} = \frac{5}{9} [/tex]

Hence the value of the expression above are as listed below

f(6+4) = 25

f(6)+f(4) = 20

f(6-4) = 1

f(6)-f(4) = 6

f(6*4) = 67

f(6)*f(4) = 91

Given the expression below f(x) = 3x - 5

f(6+4) = f(10) =3(10) - 5

f(6+4) = 25

f(6) = 3(6) - 5

f(6) = 18 - 5 = 13

f(4) = 3(4) - 5

f(4) = 7

f(6)+f(4) = 13+7

f(6)+f(4) = 20

f(6-4) = f(2) =3(2) - 5

f(6-4) = 1

f(6) = 3(6) - 5

f(6) = 18 - 5 = 13

f(4) = 3(4) - 5

f(4) = 7

f(6)-f(4) = 13-7

f(6)-f(4) = 6

f(6*4) = f(24) =3(24) - 5

f(6*4) = 67

f(6) = 3(6) - 5

f(6) = 18 - 5 = 13

f(4) = 3(4) - 5

f(4) = 7

f(6)*f(4) = 13*7

f(6)*f(4) = 91

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An ordinal number is a number that specifies how something ranks in respect to other numbers. The correct option is B.

An ordinal number is a number that specifies how something ranks in respect to other numbers, such as first, second, third, and so on. This order or sequence might be determined by size, importance, or chronology.

The example that illustrates the ordinal number is "Gracie told Bradly she would be the first one to go down the slide".

Hence, the correct option is B.

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Answer:

m = 10/3

(as a decimal: m = 3.333...)

Step-by-step explanation:

5m - 8 = 2m + 2

 5m - 8 = 2m + 2

- 2m       - 2m              (make all "m" on one side to isolate variable)

 3m - 8 = 2    

      + 8 + 8              (get m entirely on 1 side)

3m = 10

÷3      ÷3                         (divide by 3 to get 1m)

m = 10/3

(as a decimal: m = 3.333...)

hope this helps!! have a lovely day :)

Answer:

I'm not too sure but:

L = (-2,-3)

M = (-9,-3)

K = (-2,-8)

J = (-9,-8)

Step-by-step explanation:

What we know:

We know that we go through the x axis then the y axis hence the saying "Along the corridor, Up the stairs".

Due to us knowing this we use where the letters (L, M, K & J) are placed on the diagram and use the "Along the corridor, Up the stairs" technique to figure out the answer.

This means that L is (-2,-3), M is (-9,-3), K is (-2,-8) & J is (-9,-8).

Yet again as I said at the top i'm not too sure but this is what I think is correct.

I hope it helps! :)

Answer: A, C, C.

100%

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

what 3 logy z^9 means you need to break it into two pieces, one log y z^9 means to find the exponent of y, and you can think z^9 as a number, and then if we multiple it with 3, which means three logs are summed,(the property of multiplication:3*2 means 2+2+2), thus log + log

has the property that the y is same z^9*z^9*z^9=z^(9+9+9)=z^27

Answer:

p = 2.7x - 20

p(90) = $223

Step-by-step explanation:

revenue → f(x) = 3x  ,where x is the number of downloads.

the statement “Your profit p is $20 less than 90% of the revenue for x downloads”

means

[tex]p=90\% f\left( x\right) -20[/tex]

means

[tex]p=\frac{90}{100} \times f\left( x\right) -20[/tex]

means

[tex]p=\frac{9}{10} \times (3x) -20[/tex]

means

[tex]p=\frac{9}{10} \times (3x) -20[/tex]

means

[tex]p=2.7x -20[/tex]

………………………………

the profit for 90 downloads :

= p(90)

= 2.7×(90) - 20

= $223

Answer:

The histogram

The histogram is a popular graphing tool. It is used to summarize discrete or continuous data that are measured on an interval scale. It is often used to illustrate the major features of the distribution of the data in a convenient form.

Hope it helps :)

Answer:

D. Histograph can be used to display an interval of values from a data set

Answer:

1.39b + 2.49m = 50.73

1.29b + 2.69m = 51.63

Step-by-step explanation:

Systems of linear equations are used when we have 2 equations that both contain 2 unknown variables. Since we are trying to find the price of bread and milk, we can let b = num of bread and m = num of milk.

Betty spends $50.73 buying b loaves of bread and m gallons of milk, so the first equation would be 1.39b + 2.49m = 50.73. Betty spends $51.63 buying b loaves of bread and m gallons of milk at Store B, so the second equation is 1.29b + 2.69m = 51.63.

The coordinates of the mid-point between points B and C is given by:

(-5, -10).

The mid-point between two points is the halfway point between them, and is found using the mean of the coordinates.

The points in this problem are given as follows:

B(-40, -30), C(30, 10)

Hence the coordinates of the mid-point are:

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m=1/4

(or m=0.25)

M= rise/run

= 1/4

Hope this helps!

Using the continuity concept, it is found that the function is continuous for all real values.

A function f(x) is continuous at x = a if it is defined at x = a, and:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

In this problem, we are given a piece-wise function, hence we have to look at the points where the definition of the function changes. In this problem, it can only be discontinuous at x = 0, which we have to verify.

Then:

The 3 values are equal, hence the function is continuous at x = 0 and for all real values.

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Considering the slopes of the given lines, they are parallel lines.

The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:

The first line, in standard form, is given by:

5y = x + 5

y = 0.2x + 1.

The slope is of m = 0.2.

For the second line, we have that:

25y = 5x - 75

y = 0.2x - 3

The slope is of m = 0.2.

Same slope, hence the lines are parallel.

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Answer:

Point A

Step-by-step explanation:

Point A is closest to 9

every line counts as 0.1

Answer:

i am not sure

Step-by-step explanation: