Determine the measures of the arcs and angles:
*It may help to find all central angle measures before answering the hotspots.
If you do any calculating, you can type that into the hotspot with your final answer.
m HE
m HD
m DG
m EG
m < DEG
m < HGE
Answers
The values of the arc length and angles are:
HE = 62
HD = 118
DG = 62
EG = 118
∠DEG + ∠HGE = 62
We have,
The central angle is equal to the intercepted arc length.
So,
62° = HE
And,
∠A = HD
∠A + 62 = 180
∠A = 180 - 62
∠A = 118
HD = 118
And,
DG = ∠M (say)
∠A + 118 = 180
∠M = 180 - 118
∠M = 62
DG = 62
And,
∠A is opposite to ∠N (say)
So,
∠A = ∠N = 118
∠A = EG
EG = 118
And,
From the definition of the exterior angle.
∠DEG + ∠HGE = 62 ______(1)
Also,
The sum of the three angles in AEG = 180
∠EAG + ∠DEG + ∠HGE = 180
∠EAG = 180 - 62 = 118
So,
∠DEG + ∠HGE = 180 - 118
∠DEG + ∠HGE = 62 _______(2)
Thus,
HE = 62
HD = 118
DG = 62
EG = 118
∠DEG + ∠HGE = 62
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Related Questions
A quantity shrinks at a continuous rate of
per year. Its effective growth rate is
per year.
Answers
Answer:
Based on the information provided, there seems to be a discrepancy between the given information about the quantity shrinking at a continuous rate and the requested information about its effective growth rate. If a quantity is shrinking continuously, it is not experiencing growth, and therefore there is no effective growth rate. Nonetheless, assuming that the requested information was about the effective shrinkage rate of the quantity per year, this information can be extracted from the given information that "A quantity shrinks at a continuous rate of 33% per year." The effective shrinkage rate of the quantity can be calculated as follows:
Let r be the continuous shrinkage rate of the quantity
The effective shrinkage rate of the quantity is given by the expression (1 - r).
From the given information , r = 33% = 0.33.
Therefore, the effective shrinkage rate of the quantity is (1 - r) = (1 - 0.33) = 0.67 or 67% per year.
Note that if the phrase "effective growth rate" was a mistake, and the original intent was to ask for the shrinkage rate, then the above calculation gives the answer. Otherwise, further clarification is needed.
You may be interested in visiting A quantity's size after t years is given by A(t) =...
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Step-by-step explanation:
The question refers to the concept of continuous growth or shrinkage, and the effective growth rate in a financial context. Despite missing figures, assuming a quantity shrinks at a continuous rate of 3% and its effective growth rate is 2%, it implies a net shrinkage is 1% annually.
Explanation:The question pertains to the subject of compound interest in finance, but it appears that some of the figures and percentages are missing. However, generally speaking, continuous growth or shrinkage refers to the rate at which a quantity increases or decreases for a specific period of time. The effective growth rate is a term in finance that is used to compare the annual interest rates between financial products that have different compounding terms. For instance, if a quantity shrinks at a continuous rate of 3% per year, and its effective growth rate is 2% per year, it means that net shrinkage is 1% per year.
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Solve (x+1)2 =13/4 using the square root property
Answers
Answer:
Starting with the equation:
(x + 1)^2 = 13/4
We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.
Taking the square root of both sides, we get:
x + 1 = ±√(13/4)
Simplifying under the radical:
x + 1 = ±(√13)/2
Now we can solve for x by subtracting 1 from both sides:
x = -1 ± (√13)/2
Therefore, the solutions to the equation are:
x = -1 + (√13)/2 or x = -1 - (√13)/2
Step-by-step explanation:
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and do all 3. :) (Do the one highlighted)
Answers
(4ˣ/7)ˣ is not an exponential function, because the exponent is applicable to all the fractions.
Which of the following is not an exponential function?To determine which option is not an exponential function, we will apply general equation of an exponential function.
f(x) = aⁿ
where;
a is the base of the functionn is the exponentSo from the given options;
(³/₅)ˣ is an exponential function, because ³/₅ is the base while x is the exponent.
4ˣ is an exponential function, because 4 is the base while x is the exponent.
(4ˣ/7)ˣ is not an exponential function, because the exponent is applicable to all the fractions, so there is no one base.
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Calculator
What is the volume of this figure?
Enter your answer in the box.
ft³
4
3 ft
5 ft
6 ft
7 ft
2 ft
Answers
Answer:
The answer should be 1,260
Answer:
75
Step-by-step explanation:
.
What is the equation of the line shown in this graph?
Answers
Answer:
The equation is y=-3
Step-by-step explanation:
The line is horizontal, cutting across the y-axis, which means it will be a y= line. The point it hits the y-axis is -3, so it is y=-3.
Use mathematical induction to prove that the statement is true for all positive integers: 30 + 138 + 318...
Answers
The mathematical induction has been used to prove that the statement is true for all positive integers: 30 + 138 + 318.
What is mathematical induction?In mathematics, mathematical induction is a way of proving propositions. The method entails demonstrating that a statement is true for a base case, usually the smallest feasible value, and then demonstrating that if the statement is true for some value, it is likewise true for the next value.
The key to the proof is the inductive step. It is typically accomplished by assuming that the statement is true for some value and then utilizing that assumption to establish that the statement is true for the following value.
Check the attachment.
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Question 4 A study has been conducted to compare male and female test performance on a standardised science exam. In this hypothetical study, the researchers reported with a sample size of n = 50, the 95% confidence interval was found to be between 0.15 and 0.55.
What would happen to the 95% confidence interval if the sample size was increased?
The 95% confidence interval would remain the same Cannot be determined from the information provided The 95% confidence interval would decrease The 95% confidence interval would increase
Answers
If the sample size was increased, the 95% confidence interval would decrease. A larger sample size would provide more precise and accurate data, resulting in a narrower confidence interval.
A confidence interval is a range of values within which a population parameter is estimated to lie with a certain level of confidence. It is commonly used in statistical inference to estimate the true value of a population parameter based on a sample from that population.
If the sample size was increased, the 95% confidence interval would likely decrease. This is because a larger sample size typically leads to more precise estimates and less variability in the data, resulting in a narrower confidence interval. However, the exact size of the decrease would depend on various factors such as the amount of variability in the data and the level of statistical significance chosen for the study.
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Subtract t⁴-3t²+7 from 5t³-9.
Answers
Answer:
t⁴+5t³-3t²-2
Step-by-step explanation:
You can't subtract a variable with a different exponent:
Example:
CAN'T BE SUBTRACTED - 3x²-3x⁴
CAN BE SUBTRACTED - 4x²-2x²=2x²
[tex]\sf -t^{4}+5t^{3} +3t^{2} -16.[/tex]
Step-by-step explanation:1. Write the expression.[tex]\sf (5t^{3} -9)-(t^{4}-3t^{2} +7 )[/tex]
2. Remove the parenthesis.Beware of the terms of the right hand side parenthesis, as we'll have to change the symbol of all of them because of the minus (-) symbol infront of the parenthesis.
[tex]\sf 5t^{3} -9-t^{4}+3t^{2} -7[/tex]
3. Work with like terms.Like terms are terms that contain the same variables and can be added and subtracted simply. For example, 7x and 2x are like terms, because they are both expressed in terms of x. However, 7x and x² are not like terms, because one os expressed in terms of x and the ither in terms of x².
• Note: All natural numbers not being multiplied by any variables are like terms.
So now let's identify those like terms:
From this expression: [tex]\sf 5t^{3} -9-t^{4}+3t^{2} -7[/tex]
Only -9 and -7 are like terms. And, since -9-7= -16, the resulting expression should be the following:
[tex]\sf 5t^{3} -t^{4}+3t^{2} -16[/tex]
4. Order the terms correctly.So even though the last expression is the answer to this problem, we can polish it a little bit by ordering the terms. In math and other exact sciences, terms are normally ordered alphabetically and from greatest to least of it's the same variable with different exponents. Therefore, the final answer is:
[tex]\sf -t^{4}+5t^{3} +3t^{2} -16.[/tex]
Solve the following for θ, in radians, where 0≤θ<2π.
2cos2(θ)−8cos(θ)−1=0
Select all that apply:
1.07
1.69
4.59
2.49
2
2.33
Answers
Answer:correct answers 1.69
4.59
Step-by-step explanation:
We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
2u^2 - 8u - 1 = 0
Now we can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 2, b = -8, and c = -1. Substituting these values, we get:
u = (8 ± sqrt(8^2 - 4(2)(-1))) / 2(2)
u = (8 ± sqrt(72)) / 4
u = 2 ± sqrt(18)
Therefore, either:
POSSIBLE POINTS: 10
Find the area of the composite figure below. Area of Triangle = bh, Area of Rectangle = lb Use Pythagorean formula to find the length () of the
Rectangle.
7 mm
10.4 mm
15.3 mm
Answers
The total surface area of the composite figure is: 288.62 mm²
What is the area of the composite figure?From the attached image, we can see that the composite figure is made up of 2 triangles and one rectangle. Thus:
Formula for area of rectangle is:
A = Length * Width
Formula for area of triangle is:
A = ¹/₂ * base * height
Using Pythagoras theorem, length of rectangle is:
L = √(10.4² + 15.3²)
L = 18.5 mm
Thus:
TSA = (18.5 * 7) + 2(¹/₂ * 15.3 * 10.4)
TSA = 129.5 + 159.12
TSA = 288.62 mm²
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Pls help
The shape below contains a rectangle and four semi-circles.
Round your responses to two decimal places.
What is the perimeter of the shape above?
What is the area of the shape above?
Answers
Answer:
perimeter: 47.12 unitsarea: 151.60 square unitsStep-by-step explanation:
You want the perimeter and area of a figure consisting of a 4 × 11 rectangle with semicircles attached to each straight edge.
PerimeterIf you trace the perimeter of the figure, you see you are tracing the circumference of a circle 4 units in diameter and the circumference of a circle that is 11 units in diameter. The circumference of a circle is given by ...
C = πd
so the total circumference is ...
C1 +C2 = π(4) +π(11) = π(4+11) ≈ 47.12 . . . . units
The perimeter of the figure is about 47.12 units.
AreaThe area of two half-circles is the area of one whole circle of the same diameter. The area of a circle of diameter d is given by ...
A = (π/4)d²
The total area of the circles of diameters 4 and 11 is ...
A1 +A2 = (π/4)·4² +(π/4)·11² = (π/4)(4² +11²)
The area of the central rectangle is added to the areas of the semicircles. Its area is ...
A = LW
A = (11)(4)
TotalThe area of the entire figure is the sum of the circle areas and the rectangle area:
total area = (π/4)(4² +11²) +(4)(11) ≈ 151.60 . . . . square units
The area of the figure is about 151.60 square units.
__
Additional comment
You usually see the formula for the area of a circle as ...
A = πr²
Since r = d/2, we can express this using d as ...
A = π(d/2)² = π(d²)/(2²) = (π/4)d²
You may notice that a square that circumscribes the circle will have a side length of d, and an area of d². The fraction π/4 tells you the fraction of that enclosing square that is covered by the circle. This fact can help you estimate areas and volumes of circles and cylinders.
which equation represents a parabola opening downward with a vertex of the origin and a focus at (0,-1)?
y= -1/4x^2
y=1/4x^2
y=1/12x^2
y=-1/12x^2
Answers
y = -1/4x^2
The standard form of the equation of a parabola with vertex at the origin and focus (0, p) is given by:
y^2 = 4px
In this case, p = -1, so the equation becomes:
y^2 = -4x
Solving for y, we get:
y = ± √(-4x)
Since the parabola opens downward, we take the negative square root:
y = -√(-4x)
Simplifying, we get:
y = -2√(x)
Multiplying by a constant, we get:
y = -1/4(4√(x))^2
Therefore, the equation that represents a parabola opening downward with a vertex of the origin and a focus at (0,-1) is:
y = -1/4x^2.
So, the answer is "y = -1/4x^2."
2y+3y-18=-83?????????????
Answers
Answer:
-13
Step-by-step explanation:
Given the unit circle what is the value of y PLEASE HELP
Answers
Answer: √35/6
Step-by-step explanation:
see image for explanation
Which of the following is a statistical question that can result in numerical data?
What is the name of the librarian at your local library?
Which park is the best one to take your dogs to play?
What is the name of a local farm in your area?
How many students at your school ride horses?
Answers
Please help !!!!!!!!!!!!!!!!!!!!!!
Answers
2) The way the coordinates show the given scale factor is that the ratio of both x and y coordinates to the mapped coordinate before dilation are all equal.
3) The coordinates after dilation are: (5.4, 27)
How to use scale factor dilation?2) The coordinates transformed points after dilation are completed as:
B(2, 4) → B'(3, 6)
K(4, -4) → K'(6, -6)
N(-6, 0) →N'(-9, 0)
The scale factor is same because using the ratio of the x coordinates gives:
3/2 = 1.5
6/4 = 1.5
-9/-6 = 1.5
3) The point W of the vertex of the polygon has coordinates as (2, 10)
Thus, if dilated by a scale factor of 2.7, we have the new coordinates as:
(2*2.7, 10*2.7) = (5.4, 27)
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What meaning of the statement this?
Answers
We can see here that the statement means that H is a subgroup of a group, and aЄ H is an element of that subgroup.
What is a mathematical statement?We can define a mathematical statement to be a claim that, depending on the circumstances, may be true or false. It frequently incorporates mathematical objects and their relationships or characteristics, such as integers, sets, functions, or geometric shapes.
We can see here that it shows that a is an element of the subgroup of H.
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20x-12 factor out gcf in order to rewrite expression
Answers
20x - 12 = 4(5x - 3)
a 110 minute meeting should have a 10 minute break in the middle of two equal parts. How long after the meeting start should the break begin
Answers
Answer: 24 minutes and 30 seconds after the meeting as started
Step-by-step explanation:
110 minutes into 2 equal parts = 55 minutes in each section.
In the middle of 55 minutes = subtract the 10 minutes for a break from the 55 minutes that leaves you with 45 minutes. 24 minutes and 30 seconds before and after the 10 minute break.
Total session minutes - 110
Two equal parts of session: 55 minutes in each session
10 minute break in each session: 55-10 =45.
24 minutes and 30 seconds + 10 min break (in middle) + 24 minutes and 30 seconds
After 50 minutes the break will start.
The metting is 110 minutes long. According to the Question the metting have 'a'(only one) break of 10 minutes in between of two equal parts of metting.
so, duration of metting without the break=100 minutes
duration of each part=50 minutes
Now, the break should be after First part which is of 50 minutes.
=> The break should 50 minutes after the starting of metting.
prove the identity tan3x-tanx =2sinxsec3x
Answers
(Problem #1) 2sin(x)/cos(3x) = tan(3x) - tan(x)
Let's try to prove that 2sin(x) = sin(3x) - tan(x)cos(3x).
Using the identities sin(3x) ? 3sin(x) - 4sin³(x) and cos(3x) ? 4cos³(x) - 3cos(x),
sin(3x) - tan(x)cos(3x) = 3sin(x) - 4sin³(x) - tan(x)(4cos³(x) - 3cos(x))
= sin(x)(3 - 4sin²(x) - (4cos²(x) - 3))
= sin(x)(6 - 4(sin²(x) + cos²(x)))
= 2sin(x).
(The above is simpler than using the standard identity that gives tan(3x) in terms of tan(x).)
(Problem #2) (1 - tan²((?/4)-x))/(1 + tan²((?/4)-x)) = sin(2x)
Multiplying the numerator and denominator of the left-hand side by cos²((?/4)-x)) gives
(cos²((?/4)-x)) - sin²((?/4)-x)))/(cos²((?/4)-x)) + sin²((?/4)-x))),
which equals cos(2(?/4 - x))/1, i.e., cos(?/2 - 2x), i.e., sin(2x).
(Problem #3) (1 + sin(2x) - cos(2x))/(1 + sin(2x) + cos(2x)) = tan(x)
Hint: use the identities cos(2x) = 1 - 2sin²(x) = 2cos²(x) - 1 and sin(2x) = 2sin(x)cos(x) to express the left-hand side in terms of sin(x) and cos(x), then factorize the numerator and denominator.
(Problem #4) sin(2x) + (1/sin(2x)) = 5/2; for 0 ? x <2?
This is an equation you have to solve, not an identity. Start by treating it as a quadratic equation in sin(2x). The quadratic factorizes easily.
Pls help Thanks!!!!!!!!!!!
Answers
Answer:
Put your calculator in degree mode.
[tex] \cos(x) = \frac{12}{13} [/tex]
[tex]x = {cos}^{ - 1} \frac{12}{13} = 22.6[/tex]
Angle x measures 22.6°.
what are the coordinates of the point that corresponds to -5pi/4 on the unit circle
Answers
The coordinates of the point that corresponds to -5π/4 on the unit circle is (-1/√2, 1/√2).
Given that,
We have to find the coordinates of the point that corresponds to -5π/4 on the unit circle.
We know that any point on the unit circle can be defined as,
(cos θ, sin θ)
where θ is the angle formed with the X axis.
-5π/4 will be the point the corresponds to -225°.
Cos(-5π/4) = cos (5π/4)
= cos (π + π/4)
= -cos (π/4)
= -1/√2
sin (-5π/4) = -sin (5π/4)
= -sin (π + π/4)
= sin (π/4)
= 1/√2
Hence the coordinate of the unit circle is (-1/√2, 1/√2).
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what type of number is 15/10?
Answers
Answer:
1.5
Step-by-step explanation:
its a decimal number
Answer: the number 15/10 is a fraction.
Step-by-step explanation:
any two numbers that have a slash in the middle are fractons. :)
Need help with this 50 Points
Answers
Answer:
8.) is D
9.) is B
10.) is A
Step-by-step explanation:
mark brainliest
Answer: D, B, A
Step-by-step explanation:
When multiplying or dividing - and + numbers, rules are as follows:
If the signs are the same, your answer will be +
[tex]\frac{-a}{-b} =+\frac{a}{b}[/tex]
[tex]\frac{+a}{+b} =+\frac{a}{b}[/tex]
If the signs are different, your answer will be -
[tex]\frac{-a}{+b} =-\frac{a}{b}[/tex]
[tex]\frac{+a}{-b} =-\frac{a}{b}[/tex]
If there is no sign in front of number, it is positive
8.
a. 18 / -9 = -2 negative because signs are diff
b. -35 / -7 +5 signs same so +
c. -12 / -6 = +2 same signs so +
d. 70 / -10 = -7 diff signs so -
Order from least to greatest:
-7 -2 2 5
Answer: D
9. Follow rules from above:
Be careful with fractions 1/5 is not the same as 5/1.
With the fraction problems they do not divide into the number because 1 cannot be divided by 5 evenly, leave as a fraction and we are only taking care of the signs.
a. +1/5
b. -1/5
c. +1/10
d. +1/10
Order from least to greatest:
-1/5 1/5 1/10 1/10
Answer: B
10.
a. -2/3
b. +1/25
c. +3/25
d. +1/50
The smallest number is the negative number
Answer A
Determine which of the following statements is true concerning the values described in column #1 and column #2. (1 point)
Column #1
Column #2
The x-coordinate of the vertex of the graph of The x-coordinate of the vertex of the graph of
y=-2x² - 4x + 12
y=x²-4x+3
O The value found in column #1 is greater than the value found in column #2.
The value found in column #1 is less than the value found in column #2.
O The value found in column #1 is equivalent to the value found in column #2.
The relationship between column #1 and column #2 cannot be determined by the information given.
8
Answers
The statement which is true concerning the values described in column #1 and column #2 is: B. The value found in column #1 is less than the value found in column #2.
How to determine the x-coordinate of the vertex of the graph?In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:
Axis of symmetry, Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function f(x) = -2x² - 4x + 12, we have:
Axis of symmetry, Xmax = -(-4)/2(-2)
Axis of symmetry, Xmax = 4/-4 = -1.
For the vertex of f(x) = -2x² - 4x + 12, we have:
f(-1) = -2(-1)² - 4(-1) + 12 = 14.
For the given quadratic function f(x) = x²-4x+3, we have:
Axis of symmetry, Xmax = -(-4)/2(1)
Axis of symmetry, Xmax = 4/2 = 2.
For the vertex of f(x) = x²-4x+3, we have:
f(2) = (2)²-4(2) +3 = -1.
Therefore, 2 is greater than -1.
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You invest $4000 in an account to save for college.
a. Option 1 pays 5% annual interest compounded semi-annually. What would
be the balance in the account after 2 years?
b. Option 2 pays 4.5% annual interest compounded continuously. What would
be the balance in the account after 2 years?
c. At what time t (in years) would Option 1 give you $100 more than Option 2?
Answers
The answers to the given questions about annual interest are given below:
a. $4,415.25b. $4,376.70c. 2.27986 yearsHow to solvea.
A = 4,000 (1 + 0.05/2)^(2 x 2)
= $4,415.25
b.
A = 4,000 x e^(0.045 x 2)
= $4,376.70
c. $100 more than option 2 = 4,376.70 + 100
= $4,476.70
t (in years) = ln(4,476.70/4,000) / ln(1 + 0.05/2)
= 2.27986 years
Annual interest denotes the rate of interest levied or gained on a loan or investment for a duration of one year. This indicates the portion, expressed as a percentage, of the original amount that is utilized for interest payments or gained as a profit within a twelve-month period.
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a rock is thrown straight up with an initial velocity of 3m/s. The mass of the rock is approximately 0.2kg. Air resistance acts on the rock with a force numerically equal to 0.5v where v is the velocity of the rock. Acceleration due to gravity is 9.8 m/s^2. Set up and solve a differential equation to find the velocity of the rock as a function of time
Answers
The velocity of the rock as a function of time is given by:
[tex]v(t) = 3 - 4.9exp(-2t/0.2) m/s[/tex]
where 4.9 is the value of mg in SI units.
The forces acting on the rock are the force due to gravity and the force due to air resistance. The force due to air resistance is given by 0.5v, where v is the velocity of the rock.
The force due to gravity is given by the mass of the rock (0.2 kg) times the acceleration due to gravity [tex](9.8 m/s^2)[/tex]. Using Newton's second law, we can set up the following differential equation:
[tex]m(dv/dt) = -mg - 0.5v[/tex]
where m is the mass of the rock, g is the acceleration due to gravity, and v is the velocity of the rock as a function of time t.
We can simplify this differential equation by dividing both sides by m:
[tex]dv/dt = (-g - 0.5v/m)v[/tex]
This is a separable differential equation, which we can solve using the separation of variables:
[tex](1/(-g - 0.5v/m)) dv = dt[/tex]
Integrating both sides gives:
[tex]-2ln(-g - 0.5v/m) = t + C[/tex]
where C is a constant of integration.
Solving for v gives:
[tex]v(t) = -0.5mg + C'exp(-2t/m)[/tex]
where C' = exp(C).
We can find the value of C' using the initial condition that the initial velocity of the rock is 3 m/s:
[tex]v(0) = -0.5mg + C' = 3[/tex]
[tex]C' = 0.5mg + 3[/tex]
Substituting this into the equation for v(t) gives:
[tex]v(t) = -0.5mg + (0.5mg + 3)exp(-2t/m)[/tex]
Therefore, the velocity of the rock as a function of time is given by:
[tex]v(t) = 3 - 4.9exp(-2t/0.2) m/s[/tex]
where 4.9 is the value of mg in SI units.
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11. Which of the following are not meaningful?
(b) XXXI
(a) VXXIX
(C) XLIV
12. Write 'Divide the difference of 91 and 7 by 6' using brackets and solve.
(d) CXCLXV
Answers
The answer to question 12 is [(91 - 7) ÷ 6] = 14.
Consider the line y=8x-7
Find the equation of the line that is parallel to this line and passes through the point (5,-3)
Find the equation of the line that is perpendicular to this line and passes through the point (5,-3)
Answers
y - (-3) = 8(x - 5)
Simplifying this equation, we get:
y = 8x - 43
Therefore, the equation of the line that is parallel to y = 8x - 7 and passes through the point (5,-3) is y = 8x - 43.
Since the line we are looking for is perpendicular to the given line, its slope is the negative reciprocal of the slope of the given line. The slope of the given line is 8, so the slope of the line we are looking for is -1/8. Also, we know that the line passes through the point (5,-3). Using the point-slope form of a line, we can write the equation of the line as:
y - (-3) = (-1/8)(x - 5)
Simplifying this equation, we get:
y = (-1/8)x + (41/8)
Therefore, the equation of the line that is perpendicular to y = 8x - 7 and passes through the point (5,-3) is y = (-1/8)x + (41/8).
Answer:
Parallels lines:
y = 8x - 43
Perpendicular line:
y = [tex]\frac{-1}{8}[/tex]x - [tex]\frac{19}{8}[/tex]
Step-by-step explanation:
y = 8x -7
Parallel lines have the same slope.
The slope will be 8. We will use the x from the point (5,-3) and the y from the point (5,-3) to find the y-intercept (b)
y = mx + b Substitute in -3 for y, 8 for m, and 5 for x.
-3 = 8(5) + b
-3 = 40 + b Subtract 40 from both sides
-3 - 40 = 40 - 40 + b
-43 = b
Substitute in 8 for m and -43 for b to write the equation
y = mx + b
y = 8x - 43
Perpendicular slope are opposite reciprocals of each other, so the perpendicular slope is [tex]\frac{-1}{8}[/tex]
Substitute [tex]\frac{-1}{8}[/tex] doe m, -3 for y and 5 for x.
y = mx + b
-3 = [tex]\frac{-1}{8}[/tex](5) + b
-3 = [tex]\frac{-5}{8}[/tex] + b add [tex]\frac{5}{8}[/tex] from both sides
-3 + [tex]\frac{5}{8}[/tex] = [tex]\frac{-5}{8}[/tex] + [tex]\frac{5}{8}[/tex] + b
[tex]\frac{-24}{8}[/tex] + [tex]\frac{5}{8}[/tex] = b
[tex]\frac{-19}{8}[/tex] = b
Substitute [tex]\frac{-1}{8}[/tex] for m and [tex]\frac{-19}{8}[/tex] for b
y = mx + b
y = [tex]\frac{-1}{8}[/tex]x - [tex]\frac{19}{8}[/tex]
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Financial aid letters show your aid and costs of attendance for
one year
O four years
the entire time you plan on attending
a semester
Answers
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