11 The table below shows pairs of values that satisfy a linear function.2 -53 64 175 286 397 50What is the y-intercept of the graph of this function?
Answers
10)
we get the points from the table are (2,12) and (8,0).
Consider the line equation.
[tex]y=mx+b[/tex]where b is the y=intercept.
Substitute x=2 and y=12, we get
[tex]12=m(2)+b[/tex][tex]12=2m+b[/tex][tex]12-b=2m[/tex][tex]\frac{12-b}{2}=m[/tex]Substitute x=8 and y=0 in the line equation, we get
[tex]0=8m+b[/tex]Substitute m value in this equation to find the value of b.
[tex]0=8(\frac{12-b}{2})+b[/tex][tex]0=4(12-b)+b[/tex][tex]0=4\times12-4b+b[/tex][tex]0=48-3b[/tex][tex]3b=48[/tex]Dividing both sides by 3, we get
[tex]b=\frac{48}{3}=16[/tex]Hence the y-intercept is 16.
11)
we get the points from the table are (2,-5) and (4,17).
Consider the liner function.
[tex]y=mx+b[/tex]where b is the y-intercept.
Substitute x=2 and y=-5, we get
[tex]-5=2m+b[/tex][tex]-5-b=2m[/tex][tex]\frac{-5-b}{2}=m[/tex][tex]m=\frac{-5-b}{2}[/tex]Substitute x=4 and y=17 in the equation, we get
[tex]17=4m+b[/tex]Substitute the value of m in this equation to find the value of b.
[tex]17=4(\frac{-5-b}{2})+b[/tex][tex]17=2(-5-b)+b[/tex][tex]17=-10-2b+b[/tex][tex]17+10=-b[/tex][tex]b=-27[/tex]Hence the y-intercept is -27.
Related Questions
Please I need you to help me and show the steps please so I can understand it better
I will mark brainliest
Answers
Answer:
LM = √34
Step-by-step explanation:
L is at (-7, 4), and M is at (-2, 1).
LM
[tex] \sqrt{ {( - 7 - ( - 2))}^{2} - {(4 - 1)}^{2} } [/tex]
[tex] \sqrt{ {( - 5)}^{2} + {3}^{2} } = \sqrt{25 + 9} = \sqrt{34} [/tex]
how do I find a triangle congruence postulate that can be used to prove that the triangles are congruent if any with the options below?
Answers
First figure
we have that the triangles
ABC is congruent with triangle DCB by HL (hypotenuse leg)
Second figure
The triangles are congruent by Angle-Side- Angle
Third figure
The triangles are congruent by Side-angle -side
Please help me with this problem it’s 1 question of 3 please help me I will leave good feedback for you(((
Answers
tan T = 8/8 = 1
tan ^-1 T = 45°
angle T = 45°
2) angle J = tan J = 2/4
tan J = 1/2
tan^-1 J = 26.57
rounded J = 26.6
c=(5f-32)/9 solve for F
Answers
⇒They simply want you to make F the subject for the equation, since there are multiple variables in one equation we cannot solve for the exact values
[tex]c=\frac{(5f-32)}{9} \\c(9)=5f-32\\9c=5f-32\\5f-32=9c\\5f=9c+32\\\frac{5f}{5} =\frac{9c+32}{5} \\f=\frac{9c+32}{5}[/tex]
4) when Mrs. Oglethorpe sold her house recently, She received $210,000 for it, This was 40% more than she paid for it 10 years ago, What was the original purchase price?
Answers
the original purchase price was:
original purchase= 210,000- 0.4(210,000)=210,000-84,000=126,000
So the final answer will be that she paid $126,000, 10 years ago for her house.
we can check that our answer is correct by adding 126,000+84,000=210,000
Determine the slope and equation of a line passing through the point (2, –1) and parallel to the x-axis
Answers
Answer:
slope = 0
eq of line: y = -1
Step-by-step explanation:
A line parallel to the x-axis is a horizontal line. The equation of a horizontal line is " y = anumber". Horizontal lines have 0 slope. The point given is (2,-1). In the point (2,-1) the y is -1. The equation of the horizontal line thru (2,-1) is
y = -1
In the table below, replace a with a value that will make the relation a function: 1 3 5 b(n) 9 8 9 11 a
Answers
Function:
A function is a relation in which each input (x) has only one output (y).
If any one input (x) has more than one output (y) then it is not a function.
As you can see from the given table, the value of (a) must be anything other than (2)
So we can set a value of 4 for (a)
Now if you notice, each input will have exactly one output value so the criteria of a function is satisfied.
So, the answer is 4
start new workings.
What value of x makes the two expressions
below equal? Give your answer as a
decimal.
5x-8
First expression
3x+5
Second expression give ur answer as a decimal maths
Answers
The value of x that makes both expressions equal is 6.5.
What are expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.So, the value of x that makes both the expression equal.
So, we can write the expression as:
5x - 8 = 3x + 5
Now, solve for x as follows:
5x - 8 = 3x + 5
5x - 3x = 5 + 8
2x = 13
x = 13/2
x = 6.5
Therefore, the value of x that makes both expressions equal is 6.5.
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Determine algebraically ifthe function is even, odd, or neither. f(x)= -9
Answers
Background:
• Even ,functions are symmetric with respect to the ,y-axis,.
,• Odd ,functions are symmetric with respect to the origin.
,• Neither ,has no symmetry with respect to the origin or ,y-axis,.
Answer: Even
3. A car originally cost $16,000. The owner reduced the price of the car by 20%. After a few
weeks, the owner reduced the price of the car by another 20%, Belinda then purchased the
If a 3% sales tax was added, how much did Belinda pay for the car?
A. $9,600.80
B. $9,888,20
C. $10,240.00
D. $10,547.20
Answers
Answer:
the answer is D: $10547.20
Find the domain of the piecewise function and evaluate it for the given values. Then use the drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters. f(x) = \left\lbrace \begin{array}{cc} x+1 & x<-2 \\ -2x-3 & x\ge -2 \end{array}\right. The domain is:AnswerAnswer,AnswerAnswerf(-3)=Answerf(-2)=Answerf(-1)=Answerf(0)=Answer
Answers
SOLUTION
Let us make a graph of the function
[tex]\begin{gathered} f(x)=x+1\mleft\{x<-2\mright\} \\ f(x)=-2x-3\mleft\{x\ge-2\mright\} \end{gathered}[/tex]This is shown below
(a) The domain is usually determined from the x-axis. From the graph, the domain is all real numbers, that is, it is infinite for both positive and negative values for x, as you can see that if the graph is extended, there is no limit for x-values that it can contain. So the domain is (-infinity, infinity)
Hence the answer, Domain is
(-inf, inf)
(b)
[tex]f(-3)[/tex]In
[tex]\begin{gathered} f(x)=x+1\{x<-2\} \\ -3\text{ is less than -2, so -3 is valid here, so } \\ f(-3)=-3+1 \\ f(-3)=-2 \end{gathered}[/tex]Hence, the answer is -2
(c)
[tex]f(-2)[/tex]In
[tex]\begin{gathered} f(x)=-2x-3\{x\ge-2\} \\ -2\text{ is equal to -2, so we will put -2 for x here, so } \\ f(-2)=-2(-2)-3 \\ f(-2)=4-3 \\ f(-2)=1 \end{gathered}[/tex]Hence, the answer is 1
(d)
[tex]f(-1)[/tex]In
[tex]\begin{gathered} f(x)=-2x-3\{x\ge-2\} \\ -1\text{ is greater than -2, hence, it is valid, so we will put -1 for x here, so } \\ f(-1)=-2(-1)-3 \\ f(-1)=2-3 \\ f(-1)=-1 \end{gathered}[/tex]Hence, the answer is -1
(e)
[tex]f(0)[/tex]In
[tex]\begin{gathered} f(x)=-2x-3\{x\ge-2\} \\ 0\text{ is greater than -2, so we will put 0 for x here, so } \\ f(0)=-2(0)-3 \\ f(0)=0-3 \\ f(0)=-3 \end{gathered}[/tex]Hence, the answer is -3
A fish descends 4 meters per minute for 2 minutes. Then it ascends 3 meters per minute for 3 minutes. What is the total distance, in meters, the fish traveled?
Answers
Answer:
1 meter of dispalcement,
17 meters of path distance
Step-by-step explanation:
-4meters/min * 2min = -8meter
3 m/m * 3m = 9meters
-8+9 = 1 meter of displacement, it's looking for the total path's distance, then that is just |-8|+|9|=17 meters
I hope this helps
Answer:
The fish ascended a total of meter.
Step-by-step explanation:
distance= rate x time
D= -4(2)= -8m
A= 3(3)= 9m
-8m+9m= 1m
;)
y=-x^2-2x+3 what is the vertex of the graph? Answer an order pair.
Answers
Given:
[tex]y=-x^2-2x+3[/tex]a) To find the vertex:
Here, a=-1, b=-2, and c=3
We know that the formula to find the x- coordinate of the vertex is given by,
[tex]\begin{gathered} -\frac{b}{2a}=-\frac{(-2)}{2(-1)} \\ =-1 \end{gathered}[/tex]Substitute x=-1 in the given equation we get,
[tex]\begin{gathered} y=-(-1)^2-2(-1)+3 \\ =-1+2+3 \\ =4 \end{gathered}[/tex]Hence, the vertex of the graph is (-1, 4).
b) To find the range of the graph:
Let us find the y-intercept.
Put x=0, we get
[tex]\begin{gathered} y=-(0)^2-2(0)+3 \\ =3 \end{gathered}[/tex]From the figure, we observe that
The range of the graph is
[tex]\lbrack0,4\rbrack[/tex]c) To find the domain of the graph:
Let us find the x-intercept.
Put y=0, we get
[tex]\begin{gathered} -x^2-2x+3=0 \\ (x+3)(x-1)=0 \\ x=-3,1 \end{gathered}[/tex]From the figure, we observe that,
The domain of the graph is,
[tex]\lbrack-3,0)[/tex]Translate and solve. Twice a number plus 6 is -14
Answers
translation 2x + 6 = -14
2x = -14 - 6
2x = -20
x = -20/2
x = -10
Andrea labels ten cards with the numbers 1 through 10. She places the cards with prime numbers (2,3,5,7) in one box, and places the rest of the cards in another box. If Andrea draws one random card from the box of prime numbers and then one random card from the other box, how many different pairs of numbers are possible outcomes?
Answers
Box with prime numbers = 2, 3, 5, 7
Box with the other numbers = 1, 4,6,8,9, 10
Possible pairs
12 13 15 17 Four pairs
42 43 45 47 Four pairs
62 63 65 67 Four pairs
82 83 85 87 Four pairs
92 9 3 95 97 Four pairs
102 103 105 107 Four pairs
Total numbers of pairs 24 pairs
determine the miss term 3:5:7:?:25:
Answers
2. A bird flew from a point on the ground directly to the edge of the roof of a building. The height of the building is 40 feet, and the angle of elevation the bird's flight path made with the ground is 26°. Which expression models the total distance, in feet, the bird flew? А 40 cos 26 B 40 sin 26 с cos 26 40 D sin 26 40 I
Answers
We can draw the flight as:
We can use the trigonometric ratio that relates the sine of an angle with the opposite side and the hypotenuse:
[tex]\begin{gathered} \sin (26\degree)=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{h}{D} \\ D=\frac{h}{\sin (26\degree)} \\ D=\frac{40}{\sin (26\degree)} \end{gathered}[/tex]Answer: the distance can be expressed as 40 / sin(26 deg)
Answer:
Step-by-step explanation:
Write an equation in slope-intercept form for the line that passes through (0,4) and is parallel to the line described by y=3x-7
Answers
slope-intercept form of a line (L1): y = mx + b; where m is the slope and b the y - intercept.
If two lines are parallel, that means the slope of both equations are equal.
L2: y = 3x - 7, m = 3
So, m for L1 is m = 3.
Now we just need to find y - intercept, as follows:
L1 passes through (0,4), then:
4 = 3(0) + b
4 = 0 + b
b = 4
The equation for the line is y = 3x + 4
Answer the question thx
Answers
The height, h of the airplane to the nearest foot is 536 feet (option D).
What is the height of the airplane?The diagram shown is a right angled triangle. The take off point and the height of the plane form a right angled triangle.
Trigonometry would be used to solve of the height of the airplane. We are to determine the opposite side given the adjacent side and the angle of elevation.
Tan = opposite / adjacent side
Tan 15 = h / 2000
0.2679 = h / 2000
h = 2000 x 0.2679
h = 536 feet
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Gianna purchased 5\tfrac{1}{2}5
2
1
pints of ice cream for a party. If each guest will be served exactly \tfrac{1}{3}
3
1
pint of ice cream, what is the maximum number of guests Gianna can serve?
Answers
The maximum number of guests Gianna can serve will be 16.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers
From the information, Gianna purchased 5 1/2 pints of ice cream for a party. If each guest will be served exactly 1/3 pint of ice cream
The maximum number of guests Gianna can serve will be:
= 5 1/2 ÷ 1/3
= 11/2 ÷ 1/3
= 11/2 × 3
= 33/2
= 16.5
The maximum number will be 16.
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Complete question
Gianna purchased 5 1/2 pints of ice cream for a party. If each guest will be served exactly 1/3 pint of ice cream, what is the maximum number of guests Gianna can serve?
The question and the Triangle is in the same image. I'm on point 3
Answers
ANSWER
• Ratio: 2
,• Lengths of the sides of the new triangle: 6, 6√2
,• Circles: ,see explanation
,• Triangle: ,see explanation
EXPLANATION
• The ratio is the quotient between the length of segment DE and, for example, segment AB,
[tex]\frac{DE}{AB}=\frac{6}{3}=2[/tex]• Now, we have to multiply each side of triangle ABC by 2 to obtain the lengths of the sides of triangle DEF,
[tex]\begin{cases}DF=2BC=2\cdot3=6 \\ \\ EF=2AC=2\cdot\sqrt[]{3^2+3^2}=2\cdot\sqrt[]{2\cdot9}=6\sqrt[]{2}\end{cases}[/tex]• Next, draw the two circles mentioned,
• The intersection between the two circles is point F. The ,triangle is,
A firm has a monthly fixed cost of $2000, and the variable cost per unit of its product is $25. a. Determine the cost function. b. The revenue R obtained by selling x units is given by R(x) = 60x - 0.01x2. Determine the number of units that must be sold each month so as to maximize the revenue. What is the maximum revenue? c. How many units must be produced and sold each month to obtain a maximum profit? What is the maximum profit?
Answers
a) We can write the cost function (in function of the units made) as the sum of the fixed cost (2000) and the variable cost (25*x):
[tex]C(x)=2000+25x[/tex]b) The revenue R(x) is:
[tex]R(x)=60x-0.01x^2[/tex]To find the value of x that maximizes R(x) we derive R(x) and equal it to 0:
[tex]\frac{dR}{dx}=60(1)-0.01(2x)=60-0.02x[/tex][tex]\begin{gathered} \frac{dR}{dx}=0 \\ 60-0.02x=0 \\ 60=0.02x \\ x=\frac{60}{0.02} \\ x=3000 \end{gathered}[/tex]We can now calculate the maximum revenue as R(3000):
[tex]\begin{gathered} R(3000)=60\cdot3000-0.01\cdot(3000)^2 \\ R(3000)=180000-0.01\cdot9000000 \\ R(3000)=180000-90000 \\ R(3000)=90000 \end{gathered}[/tex]c) The profit function P(x) can be calculated as the difference between the revenue and the cost:
[tex]\begin{gathered} P(x)=R(x)-C(x) \\ P(x)=(60x-0.01x^2)-(2000+25x) \\ P(x)=-0.01x^2+60x-25x-2000 \\ P(x)=-0.01x^2+35x-2000 \end{gathered}[/tex]In the same way as we did in b), we can calculate the number of units x that maximize the profit by deriving P(x) and making it equal to 0:
[tex]\begin{gathered} \frac{dP}{dx}=-0.01(2x)+35(1)-2000(0)=0 \\ -0.02x+35=0 \\ 35=0.02x \\ x=\frac{35}{0.02} \\ x=1750 \end{gathered}[/tex]The maximum profit can be then calculated as P(1750):
[tex]\begin{gathered} P(1750)=-0.01(1750)^2+35(1750)-2000 \\ P(1750)=-0.01\cdot3062500+61250-2000 \\ P(1750)=-30625+61250-2000 \\ P(1750)=28625 \end{gathered}[/tex]We can graph R(x) and P(x) as:
Answer:
a) C(x) = 2000 + 25x
b) x = 3000 units
R(3000) = $90000
c) x = 1750 units
P(1750) = $28625
find the slope of 4x + 3y equals to
Answers
find the slope of 4x + 3y equals to
I will assume a value of a
so
4x+3y=a
Isolate the variable y
3y=-4x+a
y=-(4/3)x+a/3
therefore
the slope is -4/3Note: the value of the slope not depend of the value of a
The number of distinct right triangles with hypotenuse length 10 and a leg of length 5 is ____
1. Infinite
2. 0
3. 2
4. 1
Answers
According to the Pythagorean theorem we see that there are no distinct right triangles possible with hypotenuse length 10 and a leg of length 5. Thus, option 2 is correct.
It is given to us that -
Hypotenuse length = 10
Leg of length = 5
We have to find out the number of distinct right triangles that have the given hypotenuse length and leg of length.
For a right triangle, the Pythagorean theorem states that -
[tex]a^{2} +b^{2} =h^{2}[/tex] ---- (1)
where, a and b = Legs of the right triangle
and, h = hypotenuse of the right triangle
Substituting the given values of hypotenuse length and one leg of length in equation (1), we have
[tex]a^{2} +b^{2} =h^{2}\\= > 5^{2} +b^{2} =10^{2}\\= > b^{2} = 100-25\\= > b^{2} = 75\\= > b = 8.65[/tex]------ (2)
From equation (2), we see that another leg's length of the right triangle is equal to 8.65 which is not possible it is not a real number.
Therefore, applying the Pythagorean theorem we see that there are no distinct right triangles possible with hypotenuse length 10 and a leg of length 5. Thus, option 2 is correct.
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juanita makes leather lanyards to sell she charges a base fee and a cost per inch of the finished lanyard.
Answers
Answer
y = ½x + 5
If y is the total amount Juanita makes for x inches of finished lanyard,
Base fee = y-intercept = 5
Cost per inch = Slope = 0.5 = ½
Explanation
To write the expression for this, we need to write the equation for the line representing the whole function
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
From the gaph, we can easily see that
b = y-intercept = point where the line crosses the y-axis = 5
For the slope, for a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (2, 6) and (6, 8)
[tex]\text{Slope = }\frac{8-6}{6-2}=\frac{2}{4}=\frac{1}{2}=0.5[/tex]Recall,
y = mx + b
m = slope = 0.5 = ½
b = y-intercept = 5
y = ½x + 5
If y is the total amount Juanita makes for x inches of finished lanyard,
Base fee = y-intercept = 5
Cost per inch = Slope = 0.5 = ½
Hope this Helps!!!
Out of 40 students, 14 are taking English composition, 29 are taking Chemistry. If 5 students are in both class how many students are in neither classes.What is the probability that a randomly chosen student from this group is taking only chemistry class.
Answers
The probability that a randomly chosen student from this group is taking only a chemistry class will be 0.60.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
Out of 40 understudies, 14 are taking English organization, and 29 are taking chemistry. Assuming 5 understudies are in both classes the number of understudies that are in neither class.
The number of students in neither class will be given as,
⇒ 40 - (29 + 14 - 5)
⇒ 40 - 38
⇒ 2
The probability that a randomly chosen student from this group is taking only a chemistry class will be
P = (29 - 5) / 40
P = 24 / 40
P = 0.60
The probability that a randomly chosen student from this group is taking only a chemistry class will be 0.60.
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Proof Practice
Given: ∠ PQR and ∠ XYZ are complementary
m ∠ XYZ = 10 degrees
Prove: m ∠ PQR = 80 degrees
5 statements and Reasons needed
Answers
Answer:
1. Given (angle PQR and angle XYZ are complimentary)
2. Definition of complimentary angles (Complimentary means they are added to 90 degrees)
3. Definition of Complimentary angles (Complimentary angles only include two angles)
4. Subtraction postulate (90 degrees - 10 degrees= 80 degrees which proves they are complimentary)
5. Complimentary angles theorem (angle XYZ is 80 degrees)
Sorry if that's too vague, but I really hope this helps you! I bet someone elses answer would clear it up better, so more research or finding a different answer would probably help, just to confirm. I tried to explain as much as I could, I'm not good at teaching what I know.
help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Two numbers differ by 2, and their squares differ by 48. What are these numbers?
Answer needs to be: 11 and 13
Thank sou<3
Answers
Answer:
Below
Step-by-step explanation:
a - b = 2 so a = 2+b
a^2 - b^2 = 48 <===== substitute the value for 'a' underlined above
(2+b)^2 - b^2 = 48 expand L side
b^2 + 4b +4 - b^2 = 48 simplify
4b+4 = 48
4b = 44
b = 11 then a = 2+b = 13
pls help mepls pls pls pls pls pls
Answers
The expression with a coefficient of 10 and a constant of 5 is given by 10x + 5.
What is an equation? What is a coefficient?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. In a equation say : ax + b, [a] is called coefficient of [x] and [b] is independent of [x] and hence is called constant.
We have a expression with a coefficient of 10 and a constant of 5.
The expression with a coefficient of 10 and a constant of 5 is given by -
10x + 5
Therefore, the expression with a coefficient of 10 and a constant of 5 is given by 10x + 5.
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