Fundamental Trigonometric Identities are listed below:
[tex]sin^{2}[/tex]Θ + [tex]cos^{2}[/tex]Θ = 1[tex]sec^{2}[/tex]Θ - [tex]tan^{2}[/tex]Θ = 1[tex]cosec^{2}[/tex]Θ - [tex]cot^{2}[/tex]Θ = 1sinΘ = 1 / cosec Θ cos Θ = 1 / sec Θ tan Θ = 1 / cot Θ tan Θ = sinΘ / cosΘ cotΘ = cosΘ / sinΘMeaning of Fundamental Trigonometric IdentitiesFundamental Trigonometric Identities can be defined as the basic identities or variables that can be used to proffer solutions to any problem relating to angles and trigonometry.
In conclusion, A few Fundamental Trigonometric Identities are listed above.
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Which function is graphed below?
The graph of the function is y = arcsec(x).
You invested $7,000 into a money market account for 10 years at an annual interest rate of 3%. How much is the accrued interest?
The total interest accrued is $2,407.41 if you invested $7,000 into a money market account for 10 years at an annual interest rate of 3%.
What is invested amount?An investment is a payment made to acquire the securities of other firms with the intention of making a profit.
We are assuming the interest will be compounded annually
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
We have:
P = $7000
r = 3% = 0.03
t = 10 years
n = 1
[tex]\rm A = 7000(1+\dfrac{0.03}{1})^{1\times10}[/tex]
After calculating:
A = $9407.41
I = A - P = 9407.41 - 7000 = $2,407.41
Thus, the total interest accrued is $2,407.41 if you invested $7,000 into a money market account for 10 years at an annual interest rate of 3%.
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f(x)=7; find f(-3) and f(0.1)
Answer:
f(-3) = 7
f(0.1) = 7
Step-by-step explanation:
The function f(x)=7 gives an output of 7 for all inputs. In other words, no matter what we plug in for x, f(x) will equal 7.
When graphed, f(x)=7 produces a horizontal line at y=7. From there, you can also see that any value of x gives an output of 7.
a woman at a point a on the shore of a circular lake with radius 1.2 mi wants to arrive at the point B diametrically opposite A on the other side of the lake in the shortest possible time (see the figure). she can walk at the rate of 5 mi/h from C to B and row a boat at 3.5 mi/h from A to C . setting T (x) function to the time by interlaced AC, x is interlacted AC. how to move for shortest.
If she arrives by boat;
The distance she needs to row = Lake diameter
Distance = Lake diameter = 2 x Radius
Boat distance = 2 x 2 miles = 4 miles
So;
When moving on foot
The distance that needs to be moved D = Half of the circle circle
∴ D = π × Radius
The distance that needs to be moved D = π × 2 miles = 2π Miles
Arc length = Radius × θ
String length = radius x 2 x sin (θ / 2)
0 ≤ θ ≤ π, 0 ≤ sin (θ / 2) ≤ 1
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Question 9
Write the equation of the line passing through (3,-17) parallel to 8x - 7y=87
Rewriting the equation of the given line in slope-intercept form,
[tex]8x-7y=87\\\\-7y=-8x+87\\\\7y=8x-87\\\\y=\frac{8}{7}x-\frac{87}{7}[/tex]
The slope of the given line is thus 8/7, and since parallel lines have the same slope, the slope of the line we want to find is also 8/7.
Substituting into point-slope form,
[tex]y+17=\frac{8}{7}(x-3)\\\\y+17=\frac{8}{7}x-\frac{24}[7}\\\\\boxed{y=\frac{8}{7}x-\frac{143}{7}}[/tex]
How do you do this?
a) The ratio of the perimeters is the same as the scale factor, so the ratio is the perimeters is 2/3.
b) The perimeter of triangle ABC is [tex]36\left(\frac{3}{2} \right)=\boxed{54 \text{ ft}}[/tex]
c) The ratio of the areas is the scale of the scale factor. In this case, the ratio is [tex](2/3)^{2}=\boxed{4/9}[/tex]
d) The area of FDE is [tex]36(4/9)=\boxed{16 \text{ ft}^{2}}[/tex]
What graph best represents the data
A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. The correct option is A.
What is a graph?A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
A histogram is a statistical information presentation that employs rectangles to illustrate the frequency of data items in equal-sized numerical intervals. The independent variable is represented along the horizontal axis and the dependent variable is plotted along the vertical axis in the most frequent kind of histogram.
The best graph that can represent the given situation is Histogram. Hence, the correct option is A.
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Find BC.
plssss helpp!!!
Answer:
BC is 22.5 mi
Step-by-step explanation:
Using the pythagorean theorem formula. c² = a² + b²
BC² = AB² + AC²
BC² = 19² + 12²
BC² = 361 + 144
BC² = 505
√BC² = √505
BC = 22.5
Therefore BC is 22.5 mi
click on the attachment below and please help me with the question
The value of the length of the scaled up rectangle is 12.8 unit.
What is a Rectangle ?A rectangle is a polygon with four sides , the opposites are parallel and equal.
It is given in the figure that
A rectangle 4* 8 is scaled up and a new rectangle is formed α * 25.6
Scale factor = 25..6/8 =3.2
The value of the length therefore will be
4 * 3.2 = 12.8 unit
Therefore the value of the length of the scaled up rectangle is 12.8 unit.
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if a= (-3 -9 -3 -4 -3 9 7 9 -10) and b= (9 1 6 3 -10 5 -1 9 -9) find -7A -4B?
Answer: Choice A
[tex]\begin{pmatrix}-15 & 59 & -3\\16 & 61 & -83\\-45 & -99 & 106\end{pmatrix}[/tex]
===========================================================
Explanation:
In matrix A, the upper left corner is -3
Multiply this with -7 to get -7*(-3) = 21
So we'll have 21 in the upper left corner of matrix -7A. The other entries will be handled in a similar fashion.
Meanwhile, the upper left corner of matrix B is 9. Multiply this with -4 to get 9(-4) = -36 which is the upper left corner entry of matrix -4B
Combine those products: 21 + (-36) = -15
The number -15 is the upper left corner entry in matrix -7A-4B
This points us to choice A as the final answer.
25) Which graph represents the equation below? ) = w+ 2 A ܠܐ 5 4 (2, 4) 3 2 1 (-2,0) -5 -4 -3 -2 -1 0 -1 x 1 2 3 4 5 -2 -3 -4 -5 8 y
The given line equation is y=-1/2x+2
We have given the graph of the line
We have to determine the equation of the line,
We have to points(0,2) and (4,0)
What is the formula for the slope?
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
m=0-2/4-0
m=-2/4
m=-1/2
What is the slope point form?[tex](y-y_1)=m(x-x_1)[/tex]
[tex]y-0=-1/2(x-4)\\y=-1/2x+2[/tex]
Therefore the second option is correct
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In a study designed to examine the association of breakfast intake and body mass index (BMI), the National Heart, Lung, and Blood Institute Growth and Health Study recruited 2,379 adolescent girls. Frequency of breakfast consumption, dietary calcium and fiber, and BMI were recorded over a period of nine years. The study found that girls who ate breakfast more often tended to have a lower BMI [Source: J Am Diet Assoc. (2005) 105(6):938–45].
Which of the following conclusions can you make on the basis of this study?
From the given study, we can tell that the conclusion is; The frequency of eating breakfast is associated with lower BMI in adolescent girls.
How to arrive at statistics conclusions?From the study in the question, we see that a national institute is trying to examine the association of breakfast intake and body mass index (BMI).
Now, in the research we saw that the frequency is being counted about the type of foods being eaten by those surveyed to find out the impact on BMI.
From the study, we see that girls who ate breakfast more often tended to have a lower BMI. Thus, we can say that the conclusion is that The frequency of eating breakfast is associated with lower BMI in adolescent girls.
The missing options are;
A. The frequency of eating breakfast is associated with lower BMI in adolescent girls.
B. There is no relationship between eating breakfast and BMI in adolescent girls.
C. Eating breakfast makes adolescent girls thinner.
D. Skipping breakfast can contribute to obesity in adolescent girls.
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An investment company advertised that last year its clients, on average, made a profit of 10%. Assuming that average refers to
following claims must be true based on this information?
Note: More than one statement could be true. If none of the statements is true, mark the appropriate box.
Last year at least one of their clients made a profit of
exactly 10%.
Two years ago some of their clients made a profit of at least
10%.
Last year some of their clients made a profit of
0
10% or more.
O
O Last year all of their clients made a profit of more than 2%.
Last year, the number of their clients who made a profit of
10% or less was equal to the number of their clients who
made a profit of 10% or more.
The statements that are true based on the information are:
1. Last year at least one of their clients made a profit of exactly 10%.
3. Last year some of their clients made a profit of 10% or more.
Options 1 and 3 are the correct answer.
We have,
1. Last year at least one of their clients made a profit of exactly 10%.
- True.
The investment company advertised that, on average, their clients made a profit of 10%.
This means there must be some clients who made exactly 10% profit.
2. Two years ago some of their clients made a profit of at least 10%.
Not enough information is given to determine the accuracy of this statement.
The information provided only refers to last year's profits, not profits from two years ago.
3. Last year some of their clients made a profit of 10% or more.
- True.
The average profit of the clients was 10%, indicating that some clients made a profit of 10% or more.
4. Last year all of their clients made a profit of more than 2%.
- Not necessarily true.
The average profit was 10%, but this does not guarantee that all clients made a profit greater than 2%.
Some clients might have made less than 2% or even incurred losses.
5. Last year, the number of their clients who made a profit of 10% or less was equal to the number of their clients who made a profit of 10% or more.
- Not enough information is given to determine the accuracy of this statement.
The average profit of 10% does not tell us about the distribution of profits among clients to make this comparison.
Thus,
The statements that are true based on the information are:
1. Last year at least one of their clients made a profit of exactly 10%.
3. Last year some of their clients made a profit of 10% or more.
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Which statement is true about the end behavior of the
graphed function?
As the x-values go to positive infinity, the function's
values go to negative infinity.
As the x-values go to zero, the function's values go
to positive infinity.
As the x-values go to negative infinity, the function's
values are equal to zero.
As the x-values go to positive infinity, the function's
values go tO positive infinity.
Answer:
As the x-values go to positive infinity, the function's
values go to negative infinity.
Step-by-step explanation:
upon viewing the graph you will notice that the function in blue will appear to go down (negative) as you follow the x to the right, in the positive direction.
Making your answer to be as the x goes to positive inf (right) the values of the function go to negative inf (down).
Paulo is flying a kite as shown
in the right. Find the length of the kite string.
The length of the kite string is 50 ft
How to determine the length of the kite string?The string and the kite form a right triangle.
So, the length can be calculated using Pythagoras theorem as follows:
c^2 = 30^2 + 40^2
This gives
c^2 = 2500
Take the square roots
c = 50
Hence, the length of the kite string is 50 ft
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On a zip-line course, you are harnessed to a cable that travels through the treetops. You start at Platform A and zip to each of the other platforms. How far do you travel from Platform B to Platform C? Write your answer to the nearest tenth of a foot.
The distance between B and C is 26.926 units.
What is distance formula?The distance between coordinate P(x1 , y1) and coordinate Q(x2 , y2) is calculated using the distance formula: d = √[(x2 - x1)² + (y2 - y1)²]
The zip-line course distance from platform A to platform F are given
Coordinates of B = (-25, -20)
coordinates of C = (-15, 5)
Now, the distance between B and C is
= `√(5-(-20))² +((-15)-(-25))²
=√25² + 10²
= √725
= 26.926 units.
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How do I solve this problem? The green dots can be moved
Answer :
Points at (1, 3) and (3, 3) and (2, 1)
Explanation:
The original graph (dashed) is an absolute value function meaning f(x) = |x|
Given: y = 2f(x - 2) + 1
f(x - 2) means you plug in x - 2 for x in f(x) function
the new graph equation is: y = 2|x - 2| + 1
The graph will shift up 1 because +1The graph will shift right because -2The graph has a scale factor of 2The graph is V shaped because it is an absolute value graphLearn more about Absolute Value here: https://brainly.com/question/729268
Visual:
I will give brainliest to whoever answers!
Answer:
C 34 cm
Step-by-step explanation:
Area = L x W
72 = 8 x W then W = 9
Perimeter = 2 ( L+W) = 2 ( 8+ 9) = 34 cm
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{Area of rectangle: A = wl; whereas \boxed{\textsf a} is \underline{area}, \boxed{\textsf w} is \underline{width}, \& \boxed{\textsf{l}} is}\\\large\text{\underline{length}.}[/tex]
[tex]\large\text{a = wl}\\\\\large\text{wl = a}\\\\\large\text{w(8) = 72}\\\\\large\text{8w = 72}\\\\\large\textsf{DIVIDE 8 to BOTH SIDES}\\\\\rm{\dfrac{8w}{8} = \dfrac{72}{8}}\\\\\large\text{SIMPLIFY IT!}\\\\\rm{w = \dfrac{72}{8}}\\\\\rm{w = 9}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{width = \bf 9}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Graph the inequality.
y > |x-2| -5
Here is the graph! I hope this helps!
Answer:
^this means graph C.
Step-by-step explanation:
According to American Airlines, flight 71098 from New York to Los Angeles is on time 88.9% of the time. Assume that we randomly select 150 flights, use the normal approximation to the binomial to do the following:
a) approximately the probability that exactly 124 flights are on time.
b) approximate the probability that between 113 and 130 flights ,inclusive, are on time.
Using the normal approximation to the binomial, it is found that the probabilities are given as follows:
a) 0.0055 = 0.55%.
b) 0.2296 = 22.96%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters of the binomial distribution are given as follows:
n = 150, p = 0.889.
Hence the mean and the standard deviation of the approximation are:
[tex]\mu = E(X) = np = 150 x 0.889 = 133.35[/tex].[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{150(0.889)(0.111)} = 3.8473[/tex]Item a:
Using continuity correction, the probability is P(123.5 < X < 124.5), which is the p-value of Z when X = 124.5 subtracted by the p-value of Z when X = 123.5, hence:
X = 124.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{124.5 - 133.35}{3.8473}[/tex]
Z = -2.3
Z = -2.3 has a p-value of 0.0107.
X = 123.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{123.5 - 133.35}{3.8473}[/tex]
Z = -2.56
Z = -2.56 has a p-value of 0.0052.
Hence the probability is 0.0107 - 0.0052 = 0.0055 = 0.55%.
Item b:
The probability is P(112.5 < X < 130.5), which is the p-value of Z when X = 130.5 subtracted by the p-value of Z when X = 112.5, hence:
X = 130.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{130.5 - 133.35}{3.8473}[/tex]
Z = -0.74
Z = -0.74 has a p-value of 0.2296.
X = 112.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{112.5 - 133.35}{3.8473}[/tex]
Z = -5.42
Z = -5.42 has a p-value of 0.
Hence the probability is 0.2296 - 0 = 0.2296 = 22.96%.
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16x^2+?x+36 perfect square trinomial
Answer:
16x² +48x +36
Step-by-step explanation:
A perfect square trinomial is of the form ...
(a +b)² = a² +2ab +b²
We want to match this form.
__
comparing termsComparing the known terms, we see ...
16x² = a² ⇒ a = 4x
36 = b² ⇒ b = 6
filling in the missing termThe missing term is the linear term:
2ab = 2(4x)(6) = 48x
? = 48
Which x-value is in the domain of the function f (x) = 4cot(2x) + 3?
0
pi over 3
pi over 2
π
Answer: pi/3
Step-by-step explanation:
All of the other answers are asymptotes of the function, which by definition means they are not included in the domain, because they are undefined in the domain at that point. If you graph the function and graph all of those x values, you will see that (pi/3) is the only line that crosses the function.
Also, I took the test and got it right.
Only the value of x , [tex]\frac{\pi }{3}[/tex] is in the domain of the function.
What is domain of a function?The domain of a function is the set of values that we are allowed to plug into our function which makes the function defined.
What are the trigonometric functions?The trigonometric functions are also called the angle functions, which relates the angles and the ratios of the sides of a right angle triangle.
According to the given question.
We have a trigonomtery function.
[tex]f(x) = 4cot(2x)+3[/tex]
The above trigonometry function can be written as
[tex]f(x) = 4\frac{cos(2x)}{sin(2x)} + 3[/tex]
For the function to be defined the denominator can't be zero.
[tex]sin(2x) \neq 2n\pi ( n \in0, 1, 2, 3, ..)[/tex]
Therefore, from the given values for the x we can only put [tex]\frac{\pi }{3}[/tex] in the given function because [tex]\frac{\pi }{2}[/tex] makes the denominator o which makes the function undefined. Similarly for the π also.
Hence, only the value of x , [tex]\frac{\pi }{3}[/tex] is in the domain of the function.
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which of the following are characteristics of the graph of the square root parent function
Answer:
C
Step-by-step explanation:
Evaluate iint S sqrt 1+x^ 2 +y^ 2 dS where S is the helicoid: r(u, v) = u * cos (v) * i + u * sin (v) * j + vk with 0 <= u <= 1, 0 <= v <= 2pi
Given the parameterization
[tex]\vec r(u,v) = u\cos(v) \, \vec\imath + u\sin(v) \,\vec\jmath + v \,\vec k[/tex]
take the normal vector to be
[tex]\vec n = \dfrac{\partial\vec r}{\partial u} \times \dfrac{\partial \vec r}{\partial v} = \sin(v) \,\vec\imath - \cos(v) \,\vec\jmath - u \,\vec k[/tex]
(The order of partial derivatives in the cross product doesn't matter since this a scalar line integral.)
Compute the magnitude of the normal vector.
[tex]\|\vec n\| = \sqrt{\sin^2(v) + (-\cos(v))^2 + (-u)^2} = \sqrt{1+u^2}[/tex]
so that the area element reduces to
[tex]dS = \|\vec n\| \, du\,du = \sqrt{1+u^2}\,du\,du[/tex]
Evaluate the integrand at [tex]\vec r[/tex] to get
[tex]\sqrt{1 + (u\cos(v))^2 + (u\sin(v))^2} = \sqrt{1 + u^2}[/tex]
The surface integral reduces to
[tex]\displaystyle \iint_S \sqrt{1+x^2+y^2} \, dS = \int_0^{2\pi} \int_0^1 (1+u^2) \, du \, dv = 2\pi \int_0^1 (1+u^2) \, du = \boxed{\frac{8\pi}3}[/tex]
On a coordinate plane, an image has points (negative 2, 2), (0, 2), (2, 0), (0, negative 2), (negative 2, negative 2).
Use the image shown and a scale factor of 1/2 to find the pre-image. Which is the pre-image of A’?
If the scale factor is 1/2. Then the coordinate of the pre-image will be (-1, 1), (0, 1), (1, 0), (0, -1), and (-1, -1).
What is a transformation of geometry?A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.
Dilation does not change the shape, but changes the size of the geometry.
On a coordinate plane, an image has points (-2, 2), (0, 2), (2, 0), (0, -2), and (-2, -2).
The scale factor is 1/2. Then the coordinate of the pre-image will be
(-1, 1), (0, 1), (1, 0), (0, -1), and (-1, -1).
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Answer:D (-4) (-4)
Step-by-step explanation:
Which graph represents the function f(x)=2·4^x?
Answer:
A (top left)
Step-by-step explanation:
Assuming that the dot is multiplying the numbers, we get the function:
[tex]f(x) = 8^{x}[/tex]
First, lets knock off the obviously wrong answers.
Substitute 0 into the x spot, as anything to the power of zero is one.
[tex]f(0) = 8^{0}=1[/tex]
Automatically, the two answers on the right are incorrect, as y is not equal to 1 when x is 0.
Next, lets substitute 1 into the x spot, as anything to the power of one is itself.
[tex]f(1) = 8^{1} = 8[/tex]
As a result, the top left graph is correct, as y is equal to 8 when x is 1, unlike the bottom left graph.
THERE ARE 5 RED MARBLES, 8 BLUR MARBLES, AND 12 GREEN MARBLES IN A BAG. SEVERAL TRIALS ARE PERFORMED WITH THE RESULTS SHOWN IN THE TABLE. WHAT IS THE EDPERIMENTAL PROBABILITY OF RANDOMLY DRAWING A GREEN MARBLE?
The experimental probability is 56% i.e., 28.
What is probability?
The probability is the measure of the likelihood of an event to happen.
Given:
Total marbles= 8 + 12 + 5= 25 marbles
Total trials= 12+28+10 = 50 trials
So, the experimental probability is 56% for the green marble.
= 56% of 50
= 56 /100 *50
= 56/2
= 28
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A parallelogram has an area of 160 square meters and a height of 4 meters. What is the length of the base of the parallelogram?
The length of the base is 40 meters
How to determine the length of the base?We have:
Area= 160 square meters
Height = 4 meters
The area is calculated using:
Area = Base * Height
So, we have:
160 = Base * 4
Divide both sides by 4
Base = 40
Hence, the length of the base is 40 meters
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A line intersects the points (8, 2) and (12, -10). What is the slope of the line in simplest form? m = [?]
Work Shown:
[tex](x_1,y_1) = (8,2) \text{ and } (x_2,y_2) = (12,-10)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-10 - 2}{12 - 8}\\\\m = \frac{-12}{4}\\\\m = -3\\\\[/tex]
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = -3}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Goes through (8, 2) and (12, -10)}[/tex]
Find: [tex]\textsf{The slope of the line}[/tex]
Solution: In order to determine the slope of the line we need to use the slope formula where we just plug in the values and simplify.
Plug in the values
[tex]\textsf{y = }\frac{y_2 - y_1}{x_2 - x_1}[/tex][tex]\textsf{y = }\frac{-10 - 2}{12 - 8}[/tex]Simplify the expression
[tex]\textsf{y = }\frac{-12}{12 - 8}[/tex][tex]\textsf{y = }\frac{-12}{4}[/tex][tex]\textsf{y = -3}[/tex]Therefore, the slope of the line that fits the description that was provided in the problem statement is -3.
Write the inequality shown by the shaded region in the graph with the boundary line y=−4x+1.
Answer:
5 is the answer
Step-by-step explanation:
because it is
