Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 7 sin(x) 4 sec(x) tan(x) dx
Answers
The solution of the given integral \(\int\{7sin(x)4sec(x)tan(x)} \, dx\) is 14sec(x) + C
To evaluate the integral of \(\int\{7sin(x)4sec(x)tan(x)} \, dx\) , follow these steps:
Step 1: Simplify the integrand
Using the property sec(x) = 1/cos(x) and tan(x) = sin(x)/cos(x), we can rewrite the integrand as: 7sin(x) * (4/cos(x)) * (sin(x)/cos(x))
Step 2: Simplify further
Combine terms and simplify to get: (28sin^2(x))/cos^2(x)
Step 3: Perform substitution
Let u = cos(x), then du = -sin(x) dx. Therefore, -1/2 du = sin(x) dx.
Substitute u in the integrand and replace sin(x) dx with -1/2 du: \(\int (-1/2)(28/u^2) \, du\)
Step 4: Simplify the new integrand
Simplify to get: \(\int{(-14/u^2)} \, du\)
Step 5: Integrate with respect to u
Now, integrate the simplified integrand: \(\int{(-14/u^2)} \, du\) = -14\(\int {(1/u^2) } \, du\)= -14\(\int {(u^{-2})} \, du\)
Using the power rule for integration (integrating \(u^n\) gives \(u^{n+1}/(n+1)\), we get: \(-14(u^{-1}/(-1))\)+ C
Step 7: Substitute back x
Replace u with cos(x): \(-14 (cos^{-1}(x))/(-1)\) + C = 14/cos(x) + C
Step 8: Rewrite the final answer
Using the property sec(x) = 1/cos(x), the final answer is: 14sec(x) + C
Therefore, the value of the given integral is ∫7 sin(x) 4 sec(x) tan(x) dx = 14sec(x) + C, where C is the constant of integration.
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Related Questions
a:b = 1:5
a:c = 2:1
how many times is b bigger than c
Answers
b is 10 times bigger than c. the ratio A:b is equivalent to the ratio a:c multiplied by 5: A:b = (a:c) * 5
To determine how many times b is bigger than c, we need to compare their respective ratios.
Given:
A:b = 1:5
a:c = 2:1
To make a comparison, we can find the relative sizes of b and c by considering the ratios they have with other variables.
From the ratio A:b = 1:5, we can rewrite it as A:b = 2:10 (multiplying both sides by 2).
Comparing the ratios A:b and a:c, we can see that the ratio A:b is equivalent to the ratio a:c multiplied by 5:
A:b = (a:c) * 5
Substituting the given ratios, we have:
2:10 = (2:1) * 5
Now, we can compare the values of b and c directly:
b = 10
c = 1
Therefore, b is 10 times bigger than c.
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Your friend Frans tells you that the system of linear equations you are solving cannot have a unique solution because the reduced matrix has a row of zeros. Comment on his claim. The claim is right. The claim is wrong. Need Help?
Answers
Answer: Incorrect
Step-by-step explanation:
Your friend Frans' claim is incorrect. A row of zeros in the reduced matrix means that the corresponding equation in the system is redundant and does not provide any additional information. This does not necessarily mean that the system does not have a unique solution. In fact, a row of zeros in the reduced matrix is common when solving systems of linear equations using Gaussian elimination, and it can still lead to a unique solution or even an infinite number of solutions. Therefore, Frans' claim is wrong.
Let A be a diagonalizable matrix whose eigen values satisfy that A2 = A + 1. Then A satisfies A) A² = A +1 B) A² = A + 2 C) A² = A D) A² = A + 1
Answers
D) A^2 = A + 1 this equation represents diagonal matrices with the same eigenvalues on the diagonal.
Let λ be an eigenvalue of the matrix A, and let v be the corresponding eigenvector. Since A is diagonalizable, we can write A = PDP^(-1), where D is the diagonal matrix containing the eigenvalues on the diagonal, and P is the matrix whose columns are the eigenvectors.
We know that A^2 = A + 1, so we can substitute A with its diagonalizable form:
(PDP^(-1))^2 = PDP^(-1) + 1.
Expanding the square and applying the matrix multiplication rules, we get:
PD^2P^(-1) = PDP^(-1) + 1.
Since D is a diagonal matrix, D^2 will have the eigenvalues squared on the diagonal. Therefore, we have:
P(D^2)P^(-1) = PDP^(-1) + 1.
Multiplying both sides by P^(-1) on the right, and by P on the left, we obtain:
D^2 = D + 1.
This equation holds because P^(-1)P = I (the identity matrix), and D and D^2 are diagonal matrices with the same eigenvalues on the diagonal.
Therefore, the correct answer is D) A^2 = A + 1.
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to maximize its profit, a monopolist would choose which of the following outcomes? a. q = 45 and p = 45 b. q = 60 and p = 30 c. q = 30 and p = 30 d. q = 30 and p = 60
Answers
To maximize its profit, a monopolist would choose option d: q = 30 and p = 60.
To maximize profit, a monopolist would choose the outcome that corresponds to the highest profit level.
Profit is calculated as total revenue minus total cost.
Let's analyze each option:
a. q = 45 and p = 45:
In this case, the monopolist produces a quantity of 45 units and sets the price at $45.
To determine if this is the optimal choice, we need to compare the revenue and cost associated with this outcome with the other options.
b. q = 60 and p = 30:
Here, the monopolist produces a higher quantity of 60 units but sets a lower price of $30.
c. q = 30 and p = 30:
This option represents a lower quantity of 30 units and a price of $30.
d. q = 30 and p = 60:
In this scenario, the monopolist produces a lower quantity of 30 units but sets a higher price of $60.
To determine the optimal outcome, we need to consider the monopolist's cost structure.
Without information about costs, we cannot definitively identify the optimal choice.
The monopolist would consider both revenue and cost implications to maximize profit.
However, we can make some general observations:
Option a (q = 45 and p = 45) and option c (q = 30 and p = 30) result in the same price and may have similar revenue implications.
The choice between these options would depend on the cost structure and profit margins.
Option b (q = 60 and p = 30) could result in higher revenue due to the higher quantity sold, but the lower price may affect profit margins.
Option d (q = 30 and p = 60) may result in higher prices and potentially higher profit margins, but the lower quantity sold may affect revenue.
Ultimately, the monopolist would need to assess the revenue, cost, and profit implications of each option to determine the optimal outcome for maximizing profit.
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Tanya who's worked out a budget that allows her to pay her mortgage and save for her three young children's college funds
Answers
Answer: fixed rate mortgage
Step-by-step explanation:
Its correct
Fixed rate mortgage will be for Tanya who's worked out a budget that allows her to pay her mortgage and save for her three young children's college funds.
What is Fixed rate mortgage?A fixed rate mortgage is one in which the interest rate remains constant for the duration of the loan.
This means that the monthly payment amount remains constant, making budgeting and planning easier for borrowers.
Tanya should look for a mortgage with a low interest rate and a manageable monthly payment that fits into her budget.
A shorter loan term means a higher monthly payment but less overall interest paid over the life of the loan.
Tanya has worked out a budget that allows her to pay her mortgage while also saving for her three young children's college funds.
Thus, the answer is Fixed rate mortgage.
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Your question seems incomplete, the probable complete question is:
Tanya who's worked out a budget that allows her to pay her mortgage and save for her three young children's college funds Which Mortgage is Right?
The expression 2(x2 - 4) – (x2 - 8x + 12) is equivalent to
-
A.
x2 - 8x + 4
B.
x2 + 8x - 4
С.
x2
- 8x + 20
D.
x2 + 8x - 20
Answers
Answer:
D
Step-by-step explanation:
A rectangle is inscribed in a circle. Find the area of the shaded region. Use 3.14 for .
Answers
Answer:
Find the area of both the square and circle and subtract the circle’s area from the square’s
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
f(x)=-1/2 x² - xfind the axis of symmetry, vertex, domain, and range.
Answers
The axis of symmetry = -1
The vertex = (-1, 1/2)
The domain = all real numbers
The range = all real numbers less than or equal to 1/2
Explanations:The given function is:
\(f(x)\text{ = -}\frac{1}{2}x^2-x\)Note that for a function, f(x) = ax² + bx + c, the axis of symmetry is given by:
x = -b/2a
From the given function f(x):
a = -1/2, b = -1, c = 0
The axis of symmetry is therefore calculated as:
\(\begin{gathered} x\text{ = }\frac{-(-1)}{2(\frac{-1}{2})} \\ x\text{ = -1} \end{gathered}\)Axis of symmetry: x = -1
The vertex of a quadratic equation is given as (h, k)
The axis of symmetry is the x-coordinate of the vertex, therefore, h = -1
To find k, let x = h and f(x) = k in the given equation
\(\begin{gathered} k\text{ = -}\frac{1}{2}h^2-h \\ k\text{ =}-\frac{1}{2}(-1)^2-(-1) \\ k\text{ = -}\frac{1}{2}+1 \\ k\text{ = }\frac{1}{2} \\ \end{gathered}\)The vertex of the equation = (-1, 1/2)
Since f(x) is a quadratic function, the domain of the function f(x) is a set of all real numbers
To find the range:
Since a = -1/2 < 0, the graph is opening downwards.
Therefore, the range is given as y ≤ k
Since k = 1/2, the range is y ≤ 1/2
Roland runs, bikes, and swims 124 hours every month.
How many hours a month does Roland spend swimming?
62 hours per month
24.8 hours per month
37.2 hours per month
Answers
Answer: 62 hours per month
Step-by-step explanation:
How do I find the measure of multiple angles in a triangle
Answers
To find the missing angles we are going to use two properties.
The complementary angle: that wen a line cross another line the sum of bout angles will be equal to 180 for example:
The sum of the internal angles: The sum of the internal angle of a triangle must be equal to 180 for eample:
So in the example you send me, first we calculate the complementary angle of 110 so:
\(\begin{gathered} 110+x=180 \\ x=70º \end{gathered}\)Now we find the missing angle of the big triangle so:
\(\begin{gathered} 70+70+x=180 \\ x=180-140 \\ x=40 \end{gathered}\)Now for opposite angles and alternate angles we know that the first internal angle of the small triangle is also 40º
For the same statement the oposit angle of 98º will be another internal angle of the small triangle, and we can calculate the last internal angle so:
\(\begin{gathered} 40+98+x=180 \\ x=42 \end{gathered}\)and finaly the missing angle will be the complementary angle of 42 so:
\(\begin{gathered} \text{?}+42=180 \\ \text{?}=180-42 \\ \text{?}=138º \end{gathered}\)
find the domain of f(x)=3/2x^2-4x
Answers
Answer:
(-∞,∞) {x/x ∈ R}
Step-by-step explanation:
(Solve): 6x^3 -x^2 - 19x - 6 = 0
Answers
Answer:
Step-by-step explanation:
After some trial and error, we can find that x = 2 is one solution to this problem. We know that then (x-2) is a solution. We can then do polynomial division to get a quadratic equation. We can then solve the quadratic equation to get the other two factors which are -1/3 and -3/2. You can also graph it and find the roots as well. There isn't a really good method to do this and it is more like trial and error.
Still consider using anomaly detection for intrusion detection. Let's analyze a case. Suppose Alice's computer has 4 files (not realistic but for easy calculation...), and here are some data: Fo F1 F2 F3 Filename Over time Access Rate (On) 0.2 0.1 0.4 0.3 Recent Access Rate (Rn) 0.15 x 0.45 Y Suppose ER=0(On – Rm) < 0.1 means normal 1. (1.5 pts) Give an example X & Y so the recent access rate will be considered abnormal. Show the equation you used to get your X & Y. 2. (1.5 pts) How much to differ on average for each file at the maximum so that it won't trigger an alarm while "working" towards Trudy's desired frequency? Show your equation used. Edit View Insert Format Tools Table 12pt Paragraph | B BI U Av av TP w :
Answers
I'm sorry, but the question seems incomplete or there may be some typos. It is not clear what is meant by "ER=0(On – Rm) < 0.1 means normal". Additionally, there are some missing values in the table. Can you please provide more information or clarify the question?
i count in equal steps my first number is -2 my fifth number is 26 whats my third number
Answers
The required third number will be 12 when numbers are in the A.P.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The given data as
first number = - 2
fifth number = 26
Assume that the given numbers are in the A.P.
The formula to find the general term of an arithmetic sequence is,
Tₙ = a₁ + (n-1)d ...(i)
Substitute the value of n = 5 and a₁ = -2 in the above formula
T₅ = a₁ + (5-1)d
26 = -2 + 4d
4d = 28
d = 7
For finding the third term (number):
T₃ = -2 + (3-1)7
T₃ = -2 + (2)7
T₃ = -2 + 14
T₃ = 12
Therefore, the required third number will be 12 when numbers are in the A.P.
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A landscaping company mixes its own proprietary blend of topsoil that costs
$29.15 per ton to make. The blend contains soil that costs $27.65 per ton and
organic compost that costs $42.65 per ton. If the company already has 18
tons of soil on hand, how many tons of compost do they need to mix in?
Write your answer as a whole number or as a decimal rounded to the nearest
tenth.
Answers
The number of tons of compost that you need to mix in is 1.80 tons.
How many tons of compost is needed?The first step is to form a system of linear equations using the information provided in the question.
$27.65a + $42.65b = (29.15 x 18)
$27.65a + $42.65b = 524.70 equation 1
a + b = 18 equation 2
Where:
a = tons of soil
b = tons of organic compost
In order to determine the value of b, multiply equation 2 by 27.65
27.65a + 27.65b = 497.70 equation 3
Subtract equation 3 from equation 1
15b = 27
b = 27 / 15
b = 1.80
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 Sales a video games in consoles fell from $1,150 million to $1,030 million in one year. Find the percent decrease
Answers
On solving the provided question we can say that Therefore, the percent decrease in video games sales in consoles is approximately 10.43%.
What is percentage?Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the percent symbol (%). For example, if a student scores 80 out of 100 in a test, the percentage score is calculated as (80/100) x 100, which is equal to 80%. This means the student scored 80% of the total marks available in the test. Percentages are commonly used to express rates of change, proportions, and percentages of a whole, and they are used in many fields, such as finance, science, and statistics.
$1,150 million - $1,030 million = $120 million
$120 million ÷ $1,150 million = 0.1043
0.1043 x 100% = 10.43%
Therefore, the percent decrease in video games sales in consoles is approximately 10.43%.
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can smbody help me out?
Answers
Answer:
C. 30(-2)= -60 is the correct answer
Step-by-step explanation:
What is 1,000 x 0.051?
Answers
1000x0.051=51
Answer:
51
Step-by-step explanation:
1000×0.051=51 so your answer is 51
Write the equation of a line perpendicular to 5x−9y=−8 that passes through the point (−5,8).
Answers
Answer: y = -(9/5)x - 1
Step-by-step explanation:
Rewrite the equation in standard form: y = (5/9)x+(8/9). [y=mx+b]
A line perpendicular to this would have a slope that is the negative inverse of the original slope (5/9), which would make it -(9/5). The y-intercept would also change, but we don't know the value, yet. For now, we'll use "b" for the y-intercept. This results in a perpendicular line:
y = -(9/5)x + b
We can calculate b, the y-intercept, by using the point (-5,8) and solving for b.
8 = -(9/5)*(-5) + b
8 = (9) + b
b = -1
The line perpendicular to 5x−9y=−8 that passes through the point (−5,8) is
y = -(9/5)x - 1
A special safe lets you choose from 9 symbols for a 3-symbol-long pass code. You may enter a symbol any number of times. How many potential pass codes are there?
19,683
729
84
504
Answers
Multiplication is the process of multiplying. The number of potential pass codes are 729. The correct option is B.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Given that a special safe lets you choose from 9 symbols for a 3-symbol-long pass code. Therefore, the number of options available for each of the three place is 9.
Now, the total number of ways in which the potential pass codes can be made are,
Number of potential pass codes = 9 × 9 × 9 = 729
Hence, the number of potential pass codes are 729.
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Determine the rectangular form of each of the following vectors: (a) Z=6∠+37.5 ∘
= (b) Z=2×10 −3
∠100 ∘
= (c) Z=52∠−120 ∘
= (d) Z=1.8∠−30 ∘
=
Answers
the rectangular forms of the given vectors are obtained by using the respective trigonometric functions with the given magnitudes and angles.
(a) Z = 6∠37.5° can be written in rectangular form as Z = 6 cos(37.5°) + 6i sin(37.5°).
(b) Z = 2×10^-3∠100° can be written in rectangular form as Z = 2×10^-3 cos(100°) + 2×10^-3i sin(100°).
(c) Z = 52∠-120° can be written in rectangular form as Z = 52 cos(-120°) + 52i sin(-120°).
(d) Z = 1.8∠-30° can be written in rectangular form as Z = 1.8 cos(-30°) + 1.8i sin(-30°).
In each case, the rectangular form of the vector is obtained by using Euler's formula, where the real part is given by the cosine function and the imaginary part is given by the sine function, multiplied by the magnitude of the vector.
the rectangular forms of the given vectors are obtained by using the respective trigonometric functions with the given magnitudes and angles. These rectangular forms allow us to represent the vectors as complex numbers in the form a + bi, where a is the real part and b is the imaginary part.
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A particle accelerates uniformly from 7 ms-1 to 21 ms-1 in 8 s.
How far does it travel in this time?
(b) Lewis is travelling in a car along a straight road. He wonders whether the car is accelerating uniformly.
Lewis estimates that the car takes
5 s to travel a distance of 75 m from A to B, 15 s to travel a distance of 315 m from A to C.
Lewis models the acceleration as a constant a ms-2. He also takes the
speed of the car at A to be u ms-1, as shown in the diagram above.
(i) By considering the motion from A to B, show that
75 = 5u + 12.5a
(ii) Find a second equation involving u and a.
(iii) Hence find the value of u and show that a = 1.2
Thank you very much in advance if you take the time to help me out!
Answers
9514 1404 393
Answer:
A) 112 m
Bi) 75 = 5u +12.5a
Bii) 21 = u +12.5a
Biii) a = 0.6; u = 13.5
Step-by-step explanation:
A) The average speed is ...
(7 m/s +21 m/s)/2 = 14 m/s
At that speed, in 8 seconds the car travels ...
(14 m/s)(8 s) = 112 m
__
B) Using similar reasoning, we note Lewis's average speed from A to B is ...
(75 m)/(5 s) = 15 m/s
(i) If acceleration is uniform, this is the speed at the middle of the interval. It will be the sum of the initial speed (u) and the increase due to acceleration over half the interval (2.5a). So, the relation we've described is ...
15 = u +2.5a
Multiplying by 5 gives the relation we're to show:
75 = 5u +12.5a
__
(ii) The average speed in the second interval is ...
(315 m)/(15 s) = 21 m/s
The midpoint of that interval is 5+(15/2) = 12.5 s after the start of timing. Then the second equation can be ...
21 = u + 12.5a
__
(iii) The solution to these two equations is ...
(21) -(15) = (u +12.5a) -(u +2.5a) . . . . . subtract the 1st equation from the 2nd
6 = 10a
a = 0.6 . . . . not 1.2
Then the value of u is ...
u = 15 -2.5(0.6)
u = 13.5
_____
The attached graph shows the velocity vs time curve and a table of velocity and distance values. The table values match those in the problem statement, even if the equation value for acceleration does not match the problem statement.
f(t) is the velocity as a function of time
d(x) is the distance as a function of time
You will note that d(5) = 75, and d(5+15) = d(20) = 75 +315 = 390.
What is the radius of the circle with equation (x+1/5)^2+(y-2/5)^2=1/25
Answers
Answer:
r = \(\frac{1}{5}\)
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x + \(\frac{1}{5}\) )² + (y - \(\frac{2}{5}\) )² = \(\frac{1}{25}\) ← is in standard form
with r² = \(\frac{1}{25}\) , then
r = \(\sqrt{\frac{1}{25} }\) = \(\frac{1}{5}\)
The radius of the circle is, r = 1/5 units.
What is equation of circle?An equation of circle with center (h, k) and radius 'r' is,
(x - h)²+(y - k)² = r²
For given example,
the equation of the circle is, (x+1/5)^2+(y-2/5)^2=1/25
By comparing with standard equation of circle (x - h)²+(y - k)² = r²,
we have h = -1/5, k = 2/5 and r² = 1/25
We need to find the radius of the circle,
r² = 1/25
By taking square-root,
we have r = 1/5 units
Therefore, the radius of the circle is r = 1/5 units.
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Which is true about the relationship between 1 inch and 1 foot?
A. 1 inch is 12 times as long as 1 foot. B. 1 foot is 12 times as long as 1 inch. C. 1 foot is 6 times as long as 1 inch. D. 1 inch is 6 times as long as 1 foot
Answers
Option B is true about the relationship between 1 inch and 1 foot.
What is conversation?
A unit's use depends on the context; for example, a room's area is expressed in meters, yet a pencil's length and thickness are expressed in centimeters and millimeters, respectively. Therefore, converting one unit to another is necessary. We must first understand the link between units in order to comprehend the concept of unit conversion. When addressing many problems in mathematics, unit conversion is necessary. Mathematical conversions are necessary to perform the necessary calculations.
There are 12 inches in 1 foot. This means that 1 foot is 12 times longer than 1 inch. Therefore, option B is correct. Option A is incorrect because it states that 1 inch is 12 times as long as 1 foot, which is the opposite of the correct relationship. Option C is incorrect because it states that 1 foot is 6 times as long as 1 inch, which is half of the correct relationship. Option D is incorrect because it states that 1 inch is 6 times as long as 1 foot, which is the opposite of the correct relationship.
Hence, Option B is true about the relationship between 1 inch and 1 foot.
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Write the equation of the line that has a slope of -3 and a y-intercept of 2 in slope-intercept form.
Answers
Answer:
Step-by-step explanation:
Well, the linear equation of a line is:
y=mx+b
Where
m
is the slope and
b
is your y-intercept
So, you can just plug the numbers into the equation
m = − 3
and
b = − 2
y = − 3x-2
What is the degree of 5x cubed plus 3X squared minus 4X plus one
Answers
Answer: 3
Step-by-step explanation:
The degree of a polynomial is the biggest exponent in the expression
\(5x^{3} +3x^{2} -4x + 1\)
yep, basically 3
the width of a rectangle is 2 inches less than its length, and the area is 35 sq inches. what are the length and width of the rectangle?
Answers
Answer:
5 and 7
Step-by-step explanation:
What is the area of a regular octagon inscribed in a circle of radius 5 meters?
Answers
1) We can visualize that regular octagon inscribed this way:
2) We can decompose that regular octagon as isosceles triangles since this the radius is known
But note that we only have the length of the radius:
3) So let's find the base of the triangle, note that the interior angle is:
Finding the height:
Now, let's find the area of one triangle and then multiply by 8 to get the area of the whole Octagon:
\(\begin{gathered} AJ=5\cdot\sin(67.5)\Rightarrow AJ\approx4.6194 \\ BJ=5\cdot cos(67.5)\approx1.9134 \\ A_{\Delta}=\frac{1}{2}\cdot2\cdot(1.9134)\cdot(4.6194)\approx8.83875996 \\ 8\cdot8.8375996\approx70.7007968\approx70.711m² \end{gathered}\)
PLEASE HELP ASAP ON THESE TWO QUESTIONS BLESS YOUR HEART IF YOU HELP ME 9) Look for two points and find the sloope.
10) Plot the given points and find the slope.
Answers
Answer:
the two points are (-3,-3
Step-by-step explanation:
You must first check if the line is a straight line two the you check the intersection of the two points and the write it
A. [-2,3]
B. [-4,5]
C. [1,3]
D. [-5,0]
PLEASE ANSWER ASAP !!!
![A. [-2,3] B. [-4,5]C. [1,3] D. [-5,0] PLEASE ANSWER ASAP !!!](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/kKzGtzFAhqOzGyNKNkv7sFCC3YSZJS8t.png)