What is the value of sec theta given the diagram below?

Answer:

x >4                         or            x < -12/5

Step-by-step explanation:

An absolute value has 2 solutions, a positive and a negative.  Remember to flip the inequality for the negative solution

|5x-4|>16

5x-4 > 16        5x-4 < -16

Add 4 to each side

5x-4 +4> 16+4   or     5x-4+4 < -16+4

5x > 20                or        5x < -12

Divide each side by 5

5x/5 > 20/5          or         5x/5 < -12/5

x >4                         or            x < -12/5

Answer:

AE=3

Step-by-step explanation:

1. Consider right triangle BOh. In this triangle, OB=10 (hypotenuse), OH=6 (leg), then by the Pythagorean theorem,

[tex]BH^2=BO^2-OH^2\\ \\BH^2=10^2-6^2\\ \\BH^2=100-36\\ \\BH^2=64\\ \\BH=8.[/tex]

2. Since OH⊥BC, then BC=2BH=16.

3. Use the secants property: If two secant segments are drawn to a circle from the same external point, the product of the length of one secant segment and its external part is equal to the product of the length of the other secant segment and its external part.

Thus,

[tex]AE\cdot FA=AB\cdot AC.[/tex]

So,

[tex]AE\cdot (AE+9)=2\cdot (2+16)\\ \\AE(AE+9)=36\\ \\AE^2+9AE-36=0\\ \\D=9^2-4\cdot (-36)=81+144=225\\ \\AE_{1,2}=\dfrac{-9\pm\sqrt{225}}{2}=-12,\ 3.[/tex]

The segment cannot be of negative length, therefore, AE=3.

Intersecting Secant Theorem helps to establish the relation between two secants of a circle. The length of the side AE will be equal to 3 units.

When two line secants of a circle intersect each other outside the circle, the circle divides the secants into two segments such that the product of the outside segment and the length of the secant are equal to the product of the outside segment and the other secant's length.

a(a+b)=c(c+d)

If we look into the triangle BOH, then the length of the side BH using the Pythagoras theorem can be written as,

[tex]OB^2=OH^2+BH^2\\\\10^2 = 6^2 + BH^2\\\\BH= 8\rm\ units[/tex]

Now, the length of BC will be twice the length of BH, therefore, the length of the line BC can be written as,

[tex]\text{Length of BC} = 2 \times (\text{Length of BH})\\\\\text{Length of BC} = 2 \times 8 = 16\rm\ units[/tex]

Now, using the Intersecting secant theorem the length of AE can be written as,

[tex](AB \times AC) = (AE \times FA)\\\\2(2+16) = AE(AE+9)\\\\36=AE^2+9AE\\\\AE^2+9AE-36 = 0\\\\AE^2+12 AE - 3AE -36=0\\\\AE(AE+12)-3(AE+12)=0\\\\(AE-3)(AE+12)=0\\\\AE = 3, -12[/tex]

Since the length can not be negative, therefore, the length of the side AE will be equal to 3 units.

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Answer:

Step-by-step explanation:

Determine the fraction of total interest owed.

After the seventh month of a 12-month loan,

the numerator is: {(n + 11) + (n + 10) + (n + 9) + (n + 8) + (n + 7) + (n + 6) + (n + 5)} =  

(63)

, and

the denominator is: {(n) + (n + 1) + ... + (n + 11)} =  

(78)

.

Therefore, the fraction is numerator/denominator (to the nearest tenth) =  

(80.8) %.

To determine the fraction of total interest paid after the seventh month of a 12-month loan, find the numerator and denominator, calculate the sums, and divide them.

To determine the fraction of total interest paid after the seventh month of a 12-month loan, we need to find the numerator and denominator of the fraction. The numerator is given by the sum of all the amounts owed in the previous months, while the denominator is the sum of all the amounts owed for the entire loan term.

In this case, the numerator is {(n + 11) + (n + 10) + (n + 9) + (n + 8) + (n + 7) + (n + 6) + (n + 5)}, and the denominator is {(n) + (n + 1) + ... + (n + 11)}. Simply calculate these sums and then divide the numerator by the denominator to obtain the fraction of total interest paid.

For example, if n = 100, the numerator would be {(100 + 11) + (100 + 10) + (100 + 9) + (100 + 8) + (100 + 7) + (100 + 6) + (100 + 5)} and the denominator would be {(100) + (100 + 1) + ... + (100 + 11)}. Once you have the numerator and denominator, divide them to get the fraction, which can be represented as a decimal to the nearest tenth.

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Answer:

A

Step-by-step explanation:

A is correct.  This absolute value is the distance (unsigned) between -2/3 and +5/3, which is 7/3.  Note that This distance is | 5/3 - (-2/3) |, or 7/3.

Answer:

137.1

Step-by-step explanation:

Add the area of the semicircle to the area of the rectangle. The area of the semicircle is going to be [tex]\pi r^{2}[/tex] / 2. r standing for radius. the radius is 4 (half of the diameter). When you plug in 4 for r you get approximately 25.1. Then you have to add that to the area of the rectangle which is just 14x8 which equals 112.

25.1 + 112 = 137.1

Answer:

137.1

Step-by-step explanation:

So what you wana do is multiply 8 x 14 which equal 112 so u can rule out 212.5 (too big) and 86.9 (too little) now u have 137.1 and 162.2 now what u wana do is look at the nearest one cause the space we have left is very small so know we can rule out 162.2 so your answer is 137.1!

                                 Foot note: plz tell me if this helps!

Answer:

The mean absolute deviation (MAD) of this data set is 2.4

Step-by-step explanation:

step 1

Find the mean

To find out the mean sum all values and divide by the number of values in the data set

we have the set of data

[tex][2, 4, 7, 2, 3, 7, 9, 3, 1, 7][/tex]

The number of values is 10

so

The mean is equal to

[tex][2+4+7+2+3+7+9+3+1+7]/10=45/10=4.5[/tex]

step 2

Find out the absolute value of the difference of each value from that mean

[tex]\left|2-4.5\right|=2.5[/tex]

[tex]\left|4-4.5\right|=0.5[/tex]

[tex]\left|7-4.5\right|=2.5[/tex]

[tex]\left|2-4.5\right|=2.5[/tex]

[tex]\left|3-4.5\right|=1.5[/tex]

[tex]\left|7-4.5\right|=2.5[/tex]

[tex]\left|9-4.5\right|=4.5[/tex]

[tex]\left|3-4.5\right|=1.5[/tex]

[tex]\left|1-4.5\right|=3.5[/tex]

[tex]\left|7-4.5\right|=2.5[/tex]

so

we have

[tex][2.5, 0.5, 2.5, 2.5, 1.5, 2.5, 4.5, 1.5, 3.5, 2.5][/tex]

step 3

we know that

The Mean Absolute Deviation (MAD) is the mean of those distances

[tex][2.5+0.5+2.5+2.5+1.5+2.5+4.5+1.5+3.5+2.5]/10=24/10=2.4[/tex]

therefore

The mean absolute deviation (MAD) of this data set is 2.4

Answer:

4

Step-by-step explanation:

How many selfies did Tania take? (my first answer would be too many, but that's probably not the answer you're looking for :-) )

We know that each cousin appear 2 or 3 times overall.

If she would have taken each cousin exactly 2 times, that would be 16 cousins/photos

If she would have taken each cousin exactly 3 times, that would be 24 cousins/photos

We know there's exactly 5 cousins per photo...

so we have to find a multiple of 5 cousins/photos that is between 16 and 24.

The only possibility is 20 cousins/photos.  20 / 5 = 4 photos.

Answer:

Step-by-step explanation:

You need to notice that when altitude goes up, temperature goes down. That means the correlation is negative.

The table shows the temperature decrease to be monotonic (nowhere does it go up when altitude increases), so the correlation is strong.

The strong negative correlation number available to you is -0.986.

___

If you want confirmation, you can put the numbers into your favorite graphing calculator and tell it to compute the correlation for you.

Answer:

∠MLN = 21°

Step-by-step explanation:

∠MLN = ∠MLO - ∠OLN = 52° - 31° = 21°

Answer:

The right answer is the first answer

Step-by-step explanation:

Look to the attached file

Answer:

The correct answer option is A. [tex]|A|=\begin{vmatrix}-3 &2 \\ 4&-15 \end{vmatrix}\\\\\\|A_{x}|=\begin{vmatrix}-9 &2 \\ -25 &-15 \end{vmatrix}\\\\\\|A_{y}|=\begin{vmatrix}-3 &-9 \\ 4 &-25\end{vmatrix}[/tex].

Step-by-step explanation:

We are given the following system of linear equations:

[tex]-3x+2y=-9[/tex]

[tex]4x-15y=-25[/tex]

We can create a matrix  AX = b where A is a 2×2 matrix created by the coefficients of x and y and b is a 2×1 matrix formed by the term after equality.

So the correct answer option is:

[tex]|A|=\begin{vmatrix}-3 &2 \\ 4&-15 \end{vmatrix}\\\\\\|A_{x}|=\begin{vmatrix}-9 &2 \\ -25 &-15 \end{vmatrix}\\\\\\|A_{y}|=\begin{vmatrix}-3 &-9 \\ 4 &-25\end{vmatrix}[/tex]

Answer:

d 60 ft 2

Step-by-step explanation:

The area of a rectangle is length*width so the area of this rectangle is 7.5 * 8 or 60ft²

Answer:

2x+13y+4

Step-by-step explanation:

So what you want to do is, take 8y multiple that by 2 which is 16y. Then you take 16y and 5y add those together which is 21y.your gonna do the same thing with 4x and -2x which is 2x.and then bring down the 6. Answer(2x+21y+6)

[tex]\bf y=\cfrac{1}{x+1}+x\qquad \qquad \begin{cases} u=x+1\\ \frac{du}{dx}=1\\[-0.5em] \hrulefill\\ u-1=x \end{cases}\qquad \qquad y=\cfrac{1}{u}+(u-1) \\\\\\ y=u^{-1}+u-1\implies \cfrac{dy}{du}=\stackrel{\textit{chain-rule}}{-u^{-2}\cdot \cfrac{du}{dx}}+\stackrel{\textit{chain-rule}}{1\cdot \cfrac{du}{dx}}+0 \\\\\\ \cfrac{dy}{dx}=-\cfrac{1}{u^2}\cdot 1+1\cdot 1\implies \cfrac{dy}{dx}=-\cfrac{1}{u^2}+1\implies \cfrac{dy}{dx}=-\cfrac{1}{(x+1)^2}+1[/tex]

Answer:

A: addition property of equality

Step-by-step explanation:

The answer would be 4/10.

3/10 + 4/10 = 7/10

Answer:

[tex]\frac{4}{10}[/tex] or when it's simplified [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

[tex]\frac{7}{10} - \frac{3}{10}=\frac{4}{10}=\frac{2}{5}[/tex]

To find the length of the rectangular field, set up an equation using the given information and solve for the width. Then, add 10 to the width to find the length of the field.

To find the length of the rectangular field, we can set up an equation using the given information. Let's let x represent the width of the field. Since the length is 10 feet more than the width, we can represent the length as x+10. The perimeter of a rectangle is given by the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width. In this case, we know that the perimeter is 600 feet, so we can set up the equation: 600 = 2(x+10) + 2x. Solving this equation will give us the value of x, which represents the width. Once we have the width, we can find the length by adding 10 to the width.

Let's solve the equation:

The width of the field is 145 feet. To find the length, we add 10 to the width: 145 + 10 = 155 feet. Therefore, the length of the field is 155 feet.

Final answer:

The enrollment in the French class compared to the Spanish class is 18/25 as a fraction and 72% as a percent.

Explanation:

To find the enrollment in the French class compared to the Spanish class as a fraction, we need to use the information given that enrollment in French class is 0.72 of enrollment in Spanish class. This means that for every 1 student in the Spanish class, there are 0.72 students in the French class.

To represent this as a fraction, we can write it as 0.72/1 or simply 72/100. Simplifying this fraction gives us 18/25.

To find the enrollment in the French class compared to the Spanish class as a percent, we can convert the fraction 18/25 to a percent. To do this, we divide 18 by 25 and multiply by 100. This gives us 72%.

Answer:

Yes, because 2nd picture

Step-by-step explanation:

we know that

If the side lengths of a triangle satisfy the Pythagoras Theorem, then is a right  triangle  

The Pythagoras Theorem states that

[tex]c^{2}=a^{2}+b^{2}[/tex]

where

c is the greater side

a and b are the legs of triangle

we have

[tex]c=70\ ft[/tex]

[tex]a=42\ ft[/tex]

[tex]b=56\ ft[/tex]

substitute

[tex]70^{2}=42^{2}+56^{2}[/tex]

[tex]4,900=4,900[/tex]

therefore

Is a right triangle

Final answer:

Kelsey's porch does form a right triangle because the sum of the squares of the side lengths (42 feet and 56 feet) equals the square of the hypotenuse (70 feet) when applying the Pythagorean Theorem.

Explanation:

To determine if Kelsey's porch forms a right triangle, we need to apply the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the lengths of the two perpendicular sides (a and b) is equal to the square of the length of the hypotenuse (c).

The formula is a² + b² = c².

For Kelsey's porch, the side lengths are:

Side a = 42 feet

Side b = 56 feet

Side c (potential hypotenuse) = 70 feet

Let's calculate:

42² + 56² = 70²

1764 + 3136 = 4900

4900 = 4900

Since the sum of the squares of the two shorter sides is equal to the square of the longest side, the porch does form a right triangle. The answer is Yes.

Answer:

radius = 16 inches

C = 32pi or approximately 100.48 inches

Step-by-step explanation:

We know the diameter is twice the radius

d = 2r

32 = 2r

Divide each side by 2

32/2 =2r/2

16 =r

The radius is 16 inches

The circumference is equal to

C = pi * diameter

C = pi *32

C = 32 pi inches

Letting pi  be approximated by 3.14

The circumference is approximately 100.48 in

The radius is 16 inches.

This is because the radius is half the diameter and since we know that the diameter is 32 inches you just have to divide it by 2.

The circumference is 32 pi

This is because the circumference is 2 times pi times radius. This means that is is diameter times pi. This is because we know that that 2 times the radius is equal to the diameter.

Answer:

Option D [tex]y=-3x[/tex]

Step-by-step explanation:

we have the points

(-3,9) and (0,0)

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem the line passes through the origin, then the line represent a direct variation

Find the constant of proportionality k

[tex]k=y/x[/tex]

For the point (-3,9)

[tex]k=9/-3=-3[/tex]

so

the equation is

[tex]y=-3x[/tex]

Answer:

y = -3x

Step-by-step explanation:

it's what the test said

Answer:

sqrt(678)=

26.0384331

Step-by-step explanation:

For this case we must find the value of the following expression:

[tex]\sqrt {678}[/tex]

This expression can not be simplified. Its excata form is the same. On the other hand, if we introduce this expression in a calculator, we find that the decimal form of the expression is: 26.0384

Answer:

26.0384

Answer:

The domain is

x ≥ -11/4

Step-by-step explanation:

Please, see attached images below

The equation is

f(x) = √(4x+9+2)

f(x) = √(4x+11)

Since the argument of the root must be positive or equal to zero

4x +11 ≥ 0

x ≥ -11/4

The domain is

x ≥ -11/4

52/107= .486 so there’s a 48.6% that they are in 10th grade

Answer: more then 190

Step-by-step explanation:

if you multiply $19 by 12 (12 months in a year) you get $228

Miss Lacey will have to pay more than $190 for the gym membership.

A product is the result of the multiplication, an expression that identifies factors to be multiplied.

Miss Lacey is paying $19 p.m for the gym membership fees. So she will have to pay for one year =19*12 because there are 12 months in a year.

=218

which is greater than $218.

Hence Miss Lacey will have to pay more than $190 for the gym membership fees.

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Answer:

100.

Step-by-step explanation:

These are all of the steps to completely and correctly solve this question.

Hope this helps!!!

Kyle.

Answer:

3x + y = 12

Step-by-step explanation:

x = 6 - t

y = 3t - 4

We have to convert these equations in rectangular form which means that we have to express them in terms of x and y only. For this we have to eliminate "t".

From first equation we get the value of t as:

x + t = 6

t = 6 - x

Using this value in second equation, we get:

y = 3(6 - x) - 4

y = 18 - 3x - 12

3x + y = 6

This is the equation in rectangular form.

I got you, you'll get a super grade!

D.) Company III has the best discount price of $132.

Option A is incorrect because $49.50 is 25% of $198, not 25% off. Option B is not the best choice because Patricia will end up spending about $30 more. Option C is also not the best option because Patricia can save $16 if she does not chose Company I. So, we are left with our only answer choice, Option D.

Hope this helps ya, please slide me Brainliest :D

To get the system of equations in terms of x and y, solve for any other parameters and substitute back into the other equations.

y=2/x+8

Eliminate the parameter:

Angle Y equals Angle S

Answer:

line graph

Step-by-step explanation:

Line graphs easily help the visual learner to interpret data and understand peaks and decreases in certain levels. It connects data points and allows people to see what is actually going on.

Answer:

line graph

Step-by-step explanation:

The explanations of each plot are:

Scatter plot

It is used to see the correlation between two variables. The correlation can be positive (increases), negative (decreases) or zero (no correlation at all). This plot can be used to draw a trend line to study the correlation between variables using an equation, generally a line and which prosses is call line regression.

Line graph

Is like the scatter plot but instead of leaving the data or points without connection the line graph connects the points, representing the data, with a line, so to easily show a tendency between variables, which generally tends to increase.

This plot is an easy way to show a tendency, but the scatter plot can give more statistical information about a correlation between variables.

box-and-whisker plot

Shows the median and the quartiles of the data, i.e. shows a interval in which the recollected data can be found and its frequency of repetition.

stem-and-leaf plot

Allows to simultaneously see the frequency distribution of the variable and its graphic representation and its constructed by separating, in each data, the last digit of the right (the leaf) to the remaining digits (the Stem).  

So, to easily show numerical data in ascending order it can be used the line graph, but it can be used de scatter plot to give deeper statistical information too.