Please help
A line intersects the point (-8, -1) and
has a slope of 2. What is the
slope-intercept equation for this line?
y =
母
EX+
x+
Answers
Answer:
\( \displaystyle \large{y = \frac{1}{4} x + 1}\)
Step-by-step explanation:
Whenever you solve a word problem, our first step is to read and gather the information we find.
"A line intersects the point (-8,-1) and has a slope of 1/4. What is the slope-intercept equation for this line?"
After reading the question, I am going to highlight or bold the contexts that are important to our problem-solving.
"A line intersects the point (-8,-1) and has a slope of 1/4. What is the slope-intercept equation for this line?"
First, let's understand that slope-intercept equation is in the form of y = mx+b where m = slope and b = y-intercept
After reading the context, what do we know?
a slope of 1/4a line passes through (-8,-1)write in slope-intercept formWe finally have the information — our first step is to write our slope-intercept equation.
\( \displaystyle \large{y = mx + b}\)
We know that m is slope which is 1/4 — substitute in the equation.
\( \displaystyle \large{y = \frac{1}{4} x + b}\)
We have used the two information which are a slope of 1/4 and slope-intercept equation.
That only leaves to one information which is a line that passes through (-8,-1).
Since the graph has to pass through the point, we substitute x = -8 and y = -1.
\( \displaystyle \large{ - 1= \frac{1}{4} ( - 8)+ b}\)
After using all information, it seems that we are solving for b-term or y-intercept.
\( \displaystyle \large{ - 1= \frac{1}{1} ( - 2)+ b}\)
From above — cross-division.
\( \displaystyle \large{ - 1= 1( - 2)+ b} \\ \displaystyle \large{ - 1= - 2+ b}\)
Add both sides by 2 to isolate b-term.
\(\displaystyle \large{ - 1 + 2= - 2 + 2+ b} \\ \displaystyle \large{ 1= b}\)
Therefore, the value of b is 1. From the equation:
\( \displaystyle \large{y = \frac{1}{4} x + b}\)
Substitute b = 1 in the equation.
\( \displaystyle \large{y = \frac{1}{4} x + 1}\)
And we're done!
ANSWER
\(\sf{\red{y = \frac{1}{4}x + 1}}\)EXPLANATION
The slope-intercept equation of a straight line is of the form\(\sf{}y = mx + b\)
Where,
'm' is the slope
'b' is the y-intercept
From the question we have slope to be
\(\sf{}m = \frac{1}{4}\)
We substitute the slope into the slope-intercept equation and obtain:
\(\sf{}y = \frac{1}{4}x + b\)
To find the value of 'b' we plug in the point (-8,-1) into our current equation.
\(\sf- 1= \frac{1}{4}( - 8)+ b\)
\(\sf- 1= - 2+ b\)
\(\sf- 1 + 2 = b\)
\(\sf{}b= 1\)
The complete equation is
\(\sf{}y = \frac{1}{4}x + 1\)Related Questions
Solve the following equation. Write your answer in reduced fraction form, if necessary.(3x)(x + 4) = 0AnswerKeyboSeparate multiple entries with commas.X=
Answers
Given :
The equation is given as
\(3x(x+4)=0\)Explanation :
To find the value of x for the given function.
\(3x(x+4)=0\)\(3x=0,x+4=0\)\(x=0,x=-4\)Answer :
The values of x are obtained as x=0,-4.
Help me please!!! will give brainiest if right
Answers
9514 1404 393
Answer:
-3, -1, 8
Step-by-step explanation:
The quadratic factor can be found by dividing f(x) by (x -8). Synthetic division is good for that. The result in the attachment shows the quadratic factor to be x² +4x +3. That factors as ...
x² +4x +3 = (x +1)(x +3)
Then the factors of f(x) are (x -8), (x +1), (x +3). The zeros of f(x) are the values of x that make these factors zero:
x -8 = 0 ⇒ x = 8
x +1 = 0 ⇒ x = -1
x +3 = 0 ⇒ x = -3
The zeros of f(x) are x = -3, -1, and 8.
_____
The graph in the second attachment confirms these zeros.
Can someone help with number 4 please
Answers
Answer:
.(0,4,3,1,2,5)..............
Triangles FEG and FDH are similar. If segment DH is 28 units, what is the
measure of segment EG?
Answers
What are the slope and the y-intercept of the linear function that is represented by the graph? On a coordinate plane, a line goes through points (0, negative 2) and (3, 0). The slope is Two-thirds, and the y-intercept is –2. The slope is Two-thirds, and the y-intercept is 3. The slope is Three-halves, and the y-intercept is –2. The slope is Three-halves, and the y-intercept is 3.
Answers
Answer:
the slope is 2/3 and the y-intercept is -2
The slope and the y-intercept of the linear function represented by the graph are 2/3 and -2, respectively.
What is meant by linear function?A linear function is one that, when graphed, produces a straight line. Thus, non-linear functions are any non-linear functions. Although graphing is the quickest way to determine whether a function is linear or non-linear, we can also determine linearity from its input/output table or equation.
So the way to describe linear functions is that for any given change in x, the change in y will always be the same value. You're dealing with a linear function if it always returns the same value.
Therefore,
Any line's slope - intercept form is
y = mx + c
Where m = Slope of the line
c = y - intercept of the line
The given points in this case are (0, - 2) and
The equation of the line passing through the points (0, - 2) and (3, 0) is now complete.
\(&\frac{y+2}{x-0}=\frac{0+2}{3-0} \\\)
\(&\Longrightarrow \frac{y+2}{x}=\frac{2}{3} \\\)
\(&\Longrightarrow y+2=\frac{2}{3} x \\\)
\(&\Longrightarrow y=\frac{2}{3} x-2\)
Which of the slope - intercept form y = mx + c
Where m = 2/3 and c = -2
Thus, Two/thirds is the slope, and -2 is the y-intercept.
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5 is 1/2% of what number
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Question 4 of 10 What is the scale factor from ABC to DEF? A BO 72 42 35 65 B 66 O A. 2 OB. O O D. 6 Ico
Answers
Answer:
C
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original, so
scale factor = \(\frac{EF}{BC}\) = \(\frac{11}{66}\) = \(\frac{1}{6}\)
Find the area of a circle with a diameter of 15 feet
Answers
Answer:
15\(\pi\)
Step-by-step explanation:
with diameter
A=\(\pi\)d
A=\(\pi\)(15)
A=15\(\pi\)
Because...
The diameter is two times the radius and the formula for the area is pi r squared. So multiply half of the diameter, ( 7.5 ) by itself to square it and then multiply that by pi I did it by 3.14 so it’s approximately 176.625
Enrique is 7 years older than Erin. In 3 years the sum of their ages will be 57. How old is Enrique now?
Answers
ok
Enrique = e
Erin = n
e = n + 7
e + n = 57 - 6
e + n = 51
Solve by substitution
n + 7 + n = 51
2n = 51 - 7
2n = 22
n = 22/2
n = 11
e = n + 7
e = 11 + 7
e = 18
Right now Enrique is 18 years old
Write an equation of a line passing through the point (9, 3) that is perpendicular to the line y= -5x + 11.
Answers
Explanation: This equation is in the form y=mx+b, where m (-5) is the slope. To find the slope of a line perpendicular to this one, you have to take the negative reciprocal of the slope, which is 1/5. The point, (9, 3), doesn’t really matter to this problem because it is automatically on the line with the perpendicular slope.
Points A, B, and C are collinear. Point B is
between A and C. Find the length indicated. AB=
1) Find AB if AC = 12 and BC = 3.
Answers
Answer:
9
Step-by-step explanation:
\(AB+BC=AC \\ \\ 3+AB=12 \\ \\ AB=9\)
Which statements are true? Select each correct answer. Responses Only some triangles are plane figures. Only some triangles are plane figures. All triangles are polygons. All triangles are polygons. All triangles have 3 right angles. All triangles have 3 right angles. All triangles are closed figures. All triangles are closed figures. All triangles have 3 straight sides.
Answers
The three true statements are as follows:
All triangles are polygons.All triangles are closed figures. All triangles have 3 straight sides.What are the true statements?In the list, there are several true statements and some of them include the facts that all triangles are polygons, they are closed figures and they have three straight sides.
A polygon is a shape with two or more sides. Triangles ahve three sides, so we can easily address them as polygons. Also, all triangles are closed figures and they also have three straight sides.
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The graph of the function rule that models the volume of the sphere has symmetry with respect to ____?
Answers
The correct option D: the origin, has the symmetry of the volume of sphere for the graph of the function rule.
Explain the term symmetry along origin?About the Origin: Symmetry. If a point appears on a graph at every time, then the graph is symmetric having respect to the origin. When seen in relation to the origin, this graph is symmetric.A function having a single term which is the sum of a real number, the coefficient, as well as a variable raised to something like a fixed real number is called a power function. (A coefficient is a number which multiplies a variable by an exponent.) Think of equations like area or volume as an illustration.For the stated question.
The volume of the sphere is modeled by the power function with respect to the radius as;
V = f(r) = 4/3πr³
As, r is independent of any of the coordinate axis.
Thus, the function rule's graph, which describes the volume of the sphere, is symmetric with regard to the origin.
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Consider the following specifications: "Whenever the system software is being upgraded, users cannot access the file system. If users can access the file system, then they can save new files. If users cannot save new files, then the system software is not being upgraded." The goal of this exercise is to determine whether the given specifications are consistent. To do this, we express the given specifications in terms of the statements: u. The software system is being upgraded. a: Users can access the file system. s: Users can save new files. Identify a set of truth values that make the three specification true. (You must provide an answer before moving to the next part.) Multiple Choice FFF, TFF, FTF, and FTT FFT, TFT, FFF, and FTT FFT, TFT, TFF, and TTT o o O FTF, TTF, TFF, and ITT
Answers
The set of truth values that make the three specifications true is FFT, TFT, TFF, and TTT.
Let's break it down step by step:
u: The software system is being upgraded.
a: Users can access the file system.
s: Users can save new files.
The given specifications are as follows:
Whenever the system software is upgraded, users cannot access the file system.
If users can access the file system, then they can save new files.
If users cannot save new files, then the system software is not being upgraded.
Given these specifications, we can set up the following truth table:
The set of truth values that make the three specifications true is therefore FFT, TFT, TFF, and TTT.
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Can someone help me pls
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In a chemical plant, 24 holding tanks are used for final product storage. Suppose that six of the tanks contain high viscosity material. Four tanks are selected at random and without replacement. What is the probability that exactly one tank in the sample contains high-viscosity material
Answers
Answer:
The probability is 0.461
Step-by-step explanation:
Since six tanks contain high viscosity material, it means that 18 does not contain since the total number of tanks is 24.
Now, here, we know that we are selecting a total of 4 tanks.
out of the tanks with high viscosity materials, we will be selecting one only while out of the others without viscosity materials we shall need selecting three.
Thus,
the number of ways we can select one tank with viscosity material from a total of six tanks will be 6C1 = 6 ways
Now, we want to select three from the remaining 18 tanks
The number of ways we can do this is 18C3 = 816 ways
Finally, we are selecting 4 out of 24 tanks.
The number of ways we can do this is 24C4 = 10,626 ways
Now, we proceed to calculate the probability.
Kindly note that we are selecting 1 from 4 and 3 from 18
The term ‘and’ in probability means we are multiplying the probabilities of these events together and thus, that means that we are going to combine our numbers of selections.
So the total number of ways in which we can select 1 out of 3 and 3 out of 18 will be = 6 * 816 = 4,896 ways
The probability would now be 4896/10626 = 0.461
What is the pattern for the sequence 1.3, 8.3, 27.3, 64.3,…?
Answers
The pattern for the sequence 1.3, 8.3, 27.3, 64.3,… is f(n) = (n)³.3
Calculating the pattern for the sequenceThe pattern in the question is given as
1.3, 8.3, 27.3, 64.3,…
In the above expressions and pattern, we can see that
The decimal part remain unchangedThe digit before the decimal is the cube of its positionFrom the above, we have the following
Current term = (n)³.3
Note that the decimal does not represent product
And also the pattern is a geometric sequence
Hence, the pattern for the sequence is f(n) = (n)³.3
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If \(a\ \textless \ b\), there are three ordered pairs of positive integers \((a,b)\) that satisfy \(a^{2}+b^{2}=10(123)^{2}\) If two of these ordered pairs are \((39,387)\) and \((201,333)\). What is the third such ordered pair?
Answers
The third ordered pair positive integers that satisfies the equation is (123, 369).
The given parameters;
\(a^2 + b^2 = 10(123)^2\)First pair of the equation, = (39, 387)Second pair of the equation = (201, 333)The third ordered pair of the equation can be determined by using general equation of a circle;
\(a^2 + b^2 = r^2\\\\a^2 + b^2 = (123\sqrt{10} )^2\\\\a^2 + b^2 = (\sqrt{151290} )^2\\\\a^2 + b^2 = 151290\\\\a^2 = 151290- b^2\\\\ a= \sqrt{151290 - b^2}\)
The radius of the circle is calculated as;
\(r^2 = 151290\\\\r = \sqrt{151290} \\\\r = 388.96\)
The value of a can be obtained by randomly choosing numbers less than the radius as values of b.
\(b < r\\\\b < 388.96\)
\(a = \sqrt{151290 \ - \ (387)^2} \\\\a = 39\\\\(39, \ 387)\\\\a = \sqrt{151290 \ - \ (333)^2}\\\\a = 201\\\\(201, \ 333)\\\\a = \sqrt{151290 \ - \ (369)^2}\\\\a = 123\\\\(123, \ 369)\)
Thus, the third ordered pair positive integers that satisfies the equation is (123, 369).
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Which excerpt from "The Treasure of Lemon Brown" would provide strong evidence that Greg feels upset and resentful
at the beginning of the story?
O The dark sky, filled with angry, swirling clouds, reflected Greg Ridley's mood as he sat on the stoop of his building.
His father's voice came to him again, first reading the letter the principal had sent to the house, then lecturing
endlessly about his poor efforts in math.
O Report cards were due in a week, and Greg had been hoping for the best. But the principal had ended the suspense
early when she sent the letter saying Greg would probably fail math if he didn't spend more time studying.
O There was a room a few feet from the door, and from where he stood in the entrance, Greg could see a squarish
patch of light on the floor. He entered the room, frowning at the musty smell
. It was a large room that might have beer
someone's parlor at one time.
O From this spot he could see the blinking neon sign over the bodega on the corner. He sat a while, watching the sign
blink first green then red, allowing his mind to drift to the Scorpions, then to his father.
Answers
Answer:
I just took my test on edge and it’s a
Does anyone know how to find the mean of one number?
For example, what is the mean of 44?
Answers
Answer:
It's just the number itself, therefore, it's just 44.
Step-by-step explanation:
Finding the mean of many numbers is just adding up all of the values and then dividing the sum by how many numbers there in the list. Since it is just one number and you divide it by the count, which in this case it's 1, it will be the number itself, 44. As there is only one number, this calculation is always the number itself. I hope this helps! Let me know if I am wrong! :D
The city of Ventura would like to build a seawall to protect the city from the threat of tsunamis. Each additional inches of height further protects the city and the 100 residents are each willing to pay $10 per inch of seawall height, regardless of how many inches are provided. The cost of building a wall that is i inches high is given by c(i) = 6i^2. What is the Pareto Optimal height for the seawall?
Answers
Answer:
The Pareto Optimal height is \(i = 100 \ inch\)
Step-by-step explanation:
The Pareto Optimal height is a height of the seawall at which an increase in wall height will exceed the amount the resident are willing to pay and a decrease will affect the protection of the city
The number of residents is \(n = 100\)
The amount each are willing to pay is \(z=\)$10 per inch
The cost of building a wall that is i inches high is given by \(c(i) = 6i^2.\)
The total amount the residents are willing to pay is
\(n = 100 * 10\) = $1000
The maximum cost is mathematically represented as
\(\frac{dc(i)}{di} = 10i\)
which implies that
1000 = 10i
Hence the Pareto Optimal height is
=> \(i = \frac{1000}{10}\)
\(i = 100 \ inch\)
Square root of 214 show work thanks
Answers
Calculator maybe??
e the function.
R
ƒ(x) = −x² – 10x + 16
Find f(-7)
Submit Answer
Answers
Answer
37
Step by Step explanation
replace x with -7
which gives
-(-7)^2-10(-7)+16
= 37
Question 6 (5 points)
Which of the following pairs of triangles can be proven similar through SSS
similarity?
Answers
The pairs of triangles can be proven similar through SSS similarity is given by Third pair.
We know that the SSS similarity criteria will have the ratio of three corresponding sides of both triangles congruent.
1. KL / EG = HL / DG = HK / DE
3/6 = 6.5/13 ≠ 4/10
Thus, SSS similarity does not follow.
2. KL / EG = HL / DG = HK / DE
3/10 ≠ 6.5/13 ≠ 4/10
Thus, SSS similarity does not follow.
3. KL / EG = HL / DG = HK / DE
3/6 = 6.5/13 = 5/10
Thus, SSS similarity follow.
4. All three angles are congruent.
Thus, SSS similarity does not follow.
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Rewrite 13/25 and 11/20 so that they have a common denominator
Answers
The fractions are rewritten as so that they have a common denominator as 107/100
What is a fraction?A fraction can be described as the part of a whole element, variable or number.
The several types of fractions are;
Complex fractionsSimple fractionsMixed fractionsProper fractionsImproper fractionsFrom the information given, we have that;
13/25 and 11/20
To rewrite the fractions, we have to determine the lowest common multiple
13/25 + 11/20
52 + 55 /100
Add the numerators , we have;
107/100
Hence, the fraction is 107/100
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Match each strength of association with the correct scatter plot.
1. Weak. 2. Moderate. 3. Strong
Answers
Answer:
Step-by-step explanation:
The closer together the points are to a line that can be drawn, the stronger the association.
1. weak is B, the points are all over the place and a clear line can't even be drawn
2. moderate is A, if you drew a line between the points, a line can be drawn and they points are somewhat close to the line
3. strong is C because you can draw a line through points are they are pretty closely clustered near the line.
During a baseball game, a player hits a ball while a bird is flying across the field. Let t be the time in seconds since the ball is hit and h be the height in feet. The height of the baseball over time is modeled by the equation h = –16t2 + 65t and the height of a bird over time is modeled by the equation h = 8t + 20. What do the intersection points of the equations represent?
the height of the bird and the ball when the ball and the bird are the same distance from the player
the height of the bird and the ball when the player hits the ball
the time when the height of the ball and the bird are the same
the time when the ball and the bird hit the ground
Answers
If a player hits a ball while a bird is flying across the field. The intersection points of the equations represent: C the time when the height of the ball and the bird are the same.
What is intersection points?Intersection points can be defined as the points in which two parallel lines meet each other.
Given data:
Height of the baseball over time = h = –16t² + 65t
Height of a bird over time = h = 8t + 20
Where:
t = time in seconds
h = height in feet
–16t² + 65t = 8t + 20
-16t² +57t -20 =0
So,
t = -57 ±√57² -4×(-16) × (-20) / 2× (-16)
t = -57±√3249 -1280/ -32
t = -57 ±√1969 /-32
t = -57 + 44.373 / -32
t = -12.627 /-32
t =.395
And
t = -57 - 44.373 / -32
t = -101.373 /-32
t =3.168
Based on the above of the height of both the baseball and the bird, the time when the height of the ball and the bird are the same are the points were the two lines intersect.
Therefore the correct option is C.
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Reduce 2a/5a. Thanks!!!!
Answers
Hey there!
ANSWER: \(\frac{2}{5}\)EXPLANATION.\(2a/5a\)
Simplfy and remove a to solve.
\(\frac{2a}{5a} =\frac{2}{5}(ANSWER)\)
Hope this helps!
\(\text {-TestedHyperr}\)
The reduction of 2a/5a will be 0.4.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
Given the expression,
2a/5a
Now by the law of multiplication
(2a/5a) = (2/5)(a/a)
(2a/5a) = 0.4
Hence "The reduction of 2a/5a will be 0.4".
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EMERGENCY! HELP NUMBER 5 PLEASE!!!!! WILL GIVE BRAINLY TO THE FIRST PERSON WHO IS CORRECT! THANK YOU!
Answers
Answer:
WHERE IS THE QUESTION
Step-by-step explanation:
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Write 20 as a product of 3 primes
Answers
Answer:
2×2×5=20
2 is prime number and 5 is prime number