Donald graphs the distance he walks over time the graph passed through the points (3, 12) and (4, 16)
Answers
Using a proportional relationship, it is found that:
A. The slope of the line is of 4.
B. The slope is the same over both segments.
What is a proportional relationship?A proportional relationship is modeled as follows:
y = kx.
Hence a proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.
For the presented case, the two variables x and y are direct proportional, and thus the output variable y is obtained as the multiplication of the input variable x by the constant of proportionality k.
In this problem, the relationship has two points presented as follows:
(3, 12) and (4, 16).
Hence the slope, which is the constant of the relation, is given as follows:
k = 12/3 = 16/4 = 4.
Given two points, the slope is given by the change in y divided by the change in x. Hence, over each segment, the slopes are given as follows:
(1,4) and (3,12): m = (12 - 4)/(3 - 1) = 8/2 = 4.(3, 12) and (4,16): m = (16 - 12)/(4 - 3) = 4.Which are the same slopes.
Missing InformationThe problem is given by the image at the end of the answer.
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Related Questions
a box contains 22 red apples and 3 green apples. three apples are selected at random, one after the other, without replacement. (a) the first two apples are green. what is the probability that the third apple is red? (b) what is the probability that exactly two of the three apples are red?
Answers
(a) Probability that third apple is red from three selected apple one after one is 22/23.
(b) Probability that exactly two of the three apples are red is 0.3012
In the question we have,
total number of apples in a box = 25
number of red apples in a box = 22
number of green apples in a box = 3
Now, three apples are selected at random,one after other without replacement and first two apples are green .
(a) Then number of apples remained in a box after two green apples withdraw = 23
probability that third apple is red = 22/23
(b) The following are possible number of sample spaces for exactly two of the three apples are red
RGRRRGGRRwhere , R--> red apple and G--> green apple
For first sample space , RGR i.e first and last apples are red
probability that first and last apples are red from three withdraw apples or P(RGR) = 22/25× 3/24× 21/23 = 0.1004
similarly, P(RRG) = 22/25×21/24×3/23 = 0.1004
P(GRR) = 3/25×22/24×21/23 = 0.1004..
Probability that exactly two apples are red = P(RRG)+ P(RGR)+ P(GRR) = 3(0.1004) = 0.3012
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The table of ordered pairs (x, y) gives an exponential function.
Write an equation for the function.
X
-1
0
1
2
y
1
3
2
12
72
Answers
Answer:
y=2·6^2
Step-by-step explanation:
Use formula y=a[tex]b^x[/tex], plug in two different points.
72=ab^2
12=ab^1
isolate one so that a is on one side
a=[tex]\frac{12}{b}[/tex]
plug in a into the other equation
72=[tex]\frac{12}{b}[/tex][tex]b^2[/tex]
72=[tex]\frac{12b^2}{b}[/tex]
72=12b
b=6
complete solving for a now
a=2
now put it back into [tex]y=ab^x[/tex]
y=2·6^2
Which equation represents a line which is perpendicular to the line y=-4x-5?
A. x+4y=-32
B.4x+y=3
C.4x−y=−4
D.4y−x=4
Answers
Answer:
D.4y−x=4
Step-by-step explanation:
Perpendicual lines have a slope that is the negative inverse of the referenced line. The reference here is:
y = -4x-5
The slope is -4
The negative inverse of -4 would be +(1/4). Any line that has a slope of +(1/4) will be perpendicular to y=-4x+5.
The equations in the answer options are not arranged according to the standard format of y=mx+b, where m is the slope and b the y-intercept.
We could graph all the equations and look for the one(s) that are perpendicualr, but it might be safer, and faster, to rearrange them in the standard format, and then note the slope:
Slope =+(1/4)?
A. x+4y=-32
4y= -x-32
y = -(1/4)x-8 -(1/4) NO
B.4x+y=3
y = -4x + 3 -4 NO
C.4x−y=−4
y = 4x + 4 4 NO
D.4y−x=4
4y=x+4 +(1/4) <==YES
y=(1/4)x+1 [Option D has a slope of +(1/4). It will be perpendicular]
See the attached graph.
Peter, Bridget and Caroline share some sweets in the ratio 4:3:1. Peter gets 20 sweets. How many sweets are there altogether?
Answers
This means there are 20 + 15 + 5 = 40 sweets
Noah runs a farm stand that sells bananas and raspberries. Each pound of bananas
sells for $3 and each pound of raspberries sells for $2.25. Noah made $72 from
selling a total of 28 pounds of bananas and raspberries. Graphically solve a system of
equations in order to determine the number of pounds of bananas sold, a, and the
number of pounds of raspberries sold, y.
Answers
There is no possible solution for the weight of raspberries sold, given that 28 pounds of banana were sold.
What is Co-ordinate Geometry?
Graphs and coordinates are utilised in coordinate geometry to discover information about various geometric figures. A description of the coordinate plane must be included in a definition of coordinate geometry. A coordinate plane, also known as a coordinate graph, is a grid system formed by the intersection of two number lines known as axes. The x-axis is the horizontal number line, and the y-axis is the vertical number line. These axes meet at a position known as the origin.
Solution:
let, the total weight of banana sold be x pounds
and total weight of raspberries soldd be y pounds.
From the data given in the question, the equation formed is
3x + 2.25y = 72
(See Graph)
at x = 28 we will get the value of y as -5.34
which is not a possible solution
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Find 40th term for 4,8,12
Answers
Answer: 160
Step-by-step explanation:
because you times 40 by 4 as 4 is the first term and 4x10=40 <3
hope this helped <3
NSPECTIONS Mrs. Sanchez is inspecting a shed to determine if it is safe to use for storing football equipment. Mrs. Sanchez mapped the top view of the ceiling walls of the shed on a coordinate plane. If one of the walls lies from (–6, 11.5) to (2, 9.5) and the second wall lies from (–1, –2.5) to (2, 9.5), are the walls perpendicular? Explain your reasoning.
Answers
Answer:
Step-by-step explanation:
Answer:Yes, because the line that represents the first wall has a slope of -.25 and the line that represents the second wall has a slope of 4
Step-by-step explanation:
check the slope of both points
(-6,11.5) to (2, 9.5)
11.5-9.5= 2
-6-2=-8
2/-8
m=-1/4
(-1, -2.5) to (2,9.5)
-2.5=9.5=-12
-1-2=3
-12/-3
m=4
Yes, because the line that represents the first wall has a slope of -.25 and the line that represents the second wall has a slope of 4
Reese made a deposit into an account that earns 8% simple interest after 8 years Reese had earn $400 how much was Reece's initial deposit?
HELP
Answers
The principle investment necessary to obtain a total sum of $400.00 from simple interest at an annual rate of 8% for 8 years is $243.90.
What is arithmetic operation?Arithmetic operations is a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics. It consists mostly of operations like addition, subtraction, multiplication, and division. Arithmetic Operator is used to conduct mathematical operations on the supplied operands such as addition, subtraction, multiplication, division, modulus, and so on.
Here,
First, converting R percent to r a decimal
r = R/100 = 8%/100 = 0.08 per year.
Solving our equation:
P = 400 / ( 1 + (0.08 × 8)) = 243.90243902439
P = $243.90
The principal investment required to get a total amount, principal plus interest, of $400.00 from simple interest at a rate of 8% per year for 8 years is $243.90.
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Does the point (-2, 7) lie on the graph of y = -2x+1
Answers
The point (-2, 7) is not on the graph of y = -2x + 1
How to determine if the point is on the graph?From the question, we have the following equation
y = -2x + 1
This equation represents the equation of the graph
Also, we have the following points
(-2, 7)
This point implies that
(x, y) = (-2, 7)
Substitute (x, y) = (-2, 7) in the equation y = -2x + 1
So, we have
7 = -2 x -2 + 1
Evaluate
7 = 5
This is false
Hence, the point is not on the graph
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Each costume for a dance group in a talent show requires 2 yards of black material and 3 yards of red material. The dance group has 30 yards of black material and 60 yards of red material.
What is the greatest number of costumes they can make?
Answers
The greatest number of costumes the dance group can make is 15.
What is the greatest number of costumes they can make?The mathematical operation that would be used to determine the answer is division. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.
The first step is to determine the number of costumes that can be made given the total yards of black material.
Total costumes that can be made = total length available / length required for each costume
30 / 2= 15
The second step is to determine the number of costumes that can be made given the total yards of red material.
Total costumes that can be made = total length available / length required for each costume
60 / 3 = 20
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pls help me with algebra
Answers
a bike path is 12.5 miles. Dominic is 70% of the way to the end how far is Dominic on the path
Answers
Dominic is on the 8.75 mile of the bike path
How to determine how far on the path is the distance?From the question, the given parameters are:
Proportion of distance = 70% of the bike path Bike path = 12.5 milesThe above parameters implies that
Dominic's position = 70% of the total distance
Represent the total distance with x
So, we have the following representation
Dominic's position = 70% * x
Where
x = 12.5
So, we have
Dominic's position = 70% * 12.5
Evaluate the products
Dominic's position = 8,75
Hence, Dominic's position is 8,75 miles
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omg !!! please help so much !
Answers
Answer:
75
Step-by-step explanation:
15*3=45
6*5=30
45+30=75
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Allie is playing basketball. She takes a shot 17 ft away from the basket. When the ball is 2 ft away from her, it is at a height of 10 ft above the floor. The ball reaches its highest height of 17 ft above the
floor when it is 9 feet away from her.
a. Find the value of a.
b. If the hoop is 10 ft high, how close would Allie have to be in order to make the basket?
a. The value of a is
(Simplify your answer.)
Answers
According to the vertex form of the parabola,
a) The value of a is -1/7.
b) And If the hoop is 10 ft high, the distance close to Allie have to be in order to make the basket should be 16 feet.
Vertex form of the parabola
The vertex form of the parabola can be given as,
y = a(x - h)² + k
Where
h,k are the coordinates of the vertex.
Given,
Allie is playing basketball. She takes a shot 17 ft away from the basket. When the ball is 2 ft away from her, it is at a height of 10 ft above the floor. The ball reaches its highest height of 17 ft above the floor when it is 9 feet away from her.
Here we need to find the following:
a. The value of a
b. If the hoop is 10 ft high, how close would Allie have to be in order to make the basket?
We know that, Allie takes a shot of 17 ft away and at the distance of 2 feet the ball achieve the height of 10 feet from the ground.
And the greatest height achieved by the ball is 17 ft above the floor.
Then the value of a is calculated by using the point that is obtained thorough the given details is,
=> (2, 10)
And the vertex of the equation are (9, 17)
When we apply these on the vertex form, then we get,
10 = a(2 - 9)² + 17
-7 = a(-7)²
49a = -7
a = -1/7
Therefore, the value of a is 1/7.
Now we have to find if the hoop is 10 ft high, The distance close to Allie have to be in order to make the basket-
Here the value of y is 10 and x is not known.
Now, we have to put these values on the equation then we get,
=> 10 = -1/7 (x - 9)² + 17
=> -7 = -1/7 (x -9)²
=> 49 = (x - 9)²
=>√49 = x - 9
=> x = 16
Therefore, if the hoop is 10 ft high, the distance close to Allie have to be in order to make the basket should be 16 feet.
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How many kilometres is 6.5cm
Answers
Answer:
0.000065 km
Step-by-step explanation:
To get from cm to km you need to divide 6.5 by 0.000001 which equals 0.000065km
If J is the centroid of CDE, DE = 52, FC = 15,
and HE = 14, find each missing measure.
Answers
The measure of missing line segments will be:
DG = 26; GE = 26; DF = 15; CH = 14; CE = 28
What is centroid?The centroid of a triangle is the place where the three medians of the triangle connect. It is sometimes defined as the point at where the three medians cross. A median line connects the middle of a side to the opposing vertex of a triangle. The centroid of a triangle is the point at where the triangle's three medians coincide (each median connecting a vertex with the midpoint of the opposite side).
Here,
IF If J is the centroid of CDE, this means that J divides CG, FE, DC, CE and DH into two equal parts.
The following expressions are therefore true
DG + GE = DE and DG = GE
Substituting
DG + DG = DE
2DG = DE
Given DE = 52
2DG = 52
DG = 52/2
DG = 26
Since DG = GE, hence GE = 26
Also DF + FC = DC and DF = FC
Since FC = 15, hence DF = 15
Also CH + HE = CE and CH = HE
Since HE = 14, hence CH = 14
CE = 14+14
CE = 28
The missing line segment count will be: DG = 26; GE = 26; DF = 15; CH = 14; CE = 28.
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You go out to eat with 3 friends and your meal was $72.50. There is 6.75% sales tax and you plan to tip the server 15%. How much should each person pay?
Answers
The amount that each person should pay is $22.06 .
in the question ,
it is given that
total number of persons = 3 person + 1 = 4 persons
cost of the meal = $72.50
sales tax percent = 6.75%
tip percent = 15%
So , the amount of sales tax = 6.75% of cost = 0.0675 * 72.50 = $4.89
and , the amount of tip is = 15% of cost
= 0.15 * 72.50
= 10.87
So , the total amount payable is = cost + sales tax + tip
= 72.50 + 4.89 + 10.87
= 88.26
since the total number of persons is 4 ,
the amount per person is = 88.26/4 = 22.06
Therefore , The amount that each person should pay is $22.06 .
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Capital social 2.000.000 banco caixa 20.000 imovel 1.000.000 50% a vista 50% a prazo moveis 90.000 a vista transferencia bancaria veiculo 150.000 a prazo mercadoria a prazo 200.000
Answers
3/8=15/5x-2 please help me find x
Answers
Answer x = 19/24
Step-by-step explanation:
f(x) = x +4
g(x) = 3x
What is the value of fg(7)?
Answers
Answer: 105 (altough im not entirely sure sry...)
Step-by-step explanation:
I believe since it is "fg" then only the g gets the 7 (g(7)) and the f is just f(1)
This is quite difficult so you this may not be correct
I hope
The internal radius of a cylindrical bucket of height 50 cm is 21 cm. It is filled with water completely. If the water is poured into a rectangular vessel with internal length 63 cm and breadth 44 cm and it is completely filled with water, find the height of the vessel.
Answers
The height of the rectangular vessel into which the volume of water that completely fills the cylindrical bucket is poured is approximately 25 centimeters
What is the relation between height and volume of a cylinder?
The volume of a cylinder is the product of the base area of the cylinder and the height of the cylinder.
Height of the cylindrical bucket, h = 50 cm
Radius of the bucket, r = 21 cm
The level of water in the cylindrical container = The container is filled completely with water
The shape of the vessel into which the water is poured = Rectangular vessel
Length of the rectangular vessel into which the water in the cylinder is poured, L = 63 cm
Breadth of the rectangular vessel, B = 44 cm
Level to which the water fills the rectangular vessel = The rectangular vessel is completely filled with the water poured in from the cylinder
Volume of water in the cylinder, V = Volume of the cylinder = π·r²×h
Therefore;
V = π × 21² × 50 = 22050·π
The volume of water transferred from the cylinder = 22050·π cm³
Volume of the rectangular vessel, [tex]V_s[/tex] = L × B × H
[tex]V_s[/tex] = V = 22050·π cm³
Therefore;
The height of the rectangular vessel, H = [tex]V_s[/tex]/(L × B)
H = 22050·π/(63 × 44) = 24.9899415626 ≈ 25
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5 The table shows the weights of different packages.
What is the approximate total mass of packages A, B,
and D? (Hint: 1 lb ≈ 0.45 kg)
Package | Weight (lb)
A | 0.25
B | 0.8
C | 1
D | 1.75
answers:
F 1.26 g
G 2.8 g
H 280 g
J 1260 g
Answers
Answer:
1710 grams (not on the answer list)
Step-by-step explanation:
The total weight of the 4 packages is 3.8 pounds (lbs). The conversion factor is (0.45 kg/lb).
(3.8 lbs)*((0.45 kg/lb) = 1.71 kg or 1710 grams. Pease check the numbers provided.
Can someone please help with five?
Answers
Answer:
-3,-2,-1,0,1
Step-by-step explanation:
Just replace x with the x value to find the y value
y=x-1
y=-2-1
y=-3
Y=-1-1
y=-2
y=0-1
y=-1
y=1-1
y=0
y=2-1
y=1
hopes this helps please mark brainliest
All y values will be equal to the x value given in the table minus 1.
For example, -2 minus 1 equals -3. So, for the y value in the first column of the table, your answer is -3.
30% of the tickets sold at a school carnival were early-admission tickets. If the school sold 100 tickets in all, how many early-admission tickets did it sell?
Answers
The number of early-admission tickets that it sells is 30.
How to calculate the number of early admission?From the information, 30% of the tickets sold at a school carnival were early-admission tickets and the school sold 100 tickets in all.
Therefore, the number of early admission will be:
= Percentage for early admission × Total number of tickets
= 30% × 100
= 0.3 × 100
= 30
Therefore, there are 30 early admission.
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Brad had a small gathering at a local steakhouse. The steakhouse offers three dinner platters which vary by size and price. They ordered 4 of the 6-ounce platters, 3 of the 8-ounce platters, and 2 of the 11-ounce platters.
Steak Platter Prices
• 6-ounce $9.95
• 8-ounce $12.95
• 11-ounce $15.95
If a gratuity of 18% was added to the bill, which of the following is closest to the total of the steak platters and gratuity, ignoring sales tax?
Answers
Hello!
If Brad had a small gathering at a local steakhouse where they ordered 4 of the 6-ounce platters, 3 of the 8-ounce platters, and 2 of the 11-ounce platters. After adding an 18% gratuity their total before sales tax should have been $130.45
Step-by-step explanation:
[tex]4[/tex] x [tex]9.95=39.80[/tex]
[tex]3[/tex] x [tex]12.95=38.85[/tex]
[tex]2[/tex] x [tex]15.95=31.90[/tex]
[tex]31.90+[/tex][tex]38.85+[/tex][tex]39.80=[/tex][tex]110.55[/tex]
[tex]110.55[/tex] x [tex]0.18[/tex] [tex]=19.899[/tex]
[tex]110.55+19.90[/tex][tex]=130.45[/tex]
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Step-by-step explanation:
we have 11k + 4k.
this is like saying "I have 11 apples and then get 4 more apples - how many apples do I have ?"
in other words, how many "k" do I have ?
11 + 4 = 15.
we have 15k.
and then there is -3 + 8 = 5
so, the answer is
15k + 5
Answer:
15k + 5
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The expression is,
→ 11k - 3 + 4k + 8
Let's simplify the expression,
→ 11k - 3 + 4k + 8
→ 11k + 4k - 3 + 8
→ (11k + 4k) + (-3 + 8)
→ (15k) + (5)
→ 15k + 5
Hence, the answer is 15k + 5.
if the 90% confidence limits for the population mean are 45 and 55, which of the following could be the 99% confidence limits a) [48, 55] b) [49, 53] c) [42, 58] d) [46, 51] e) [49, 51] f) none of the above
Answers
The 99% confidence limit will be option B which is (45, 55)
90% confidence limits for the population mean are (46,54)
mean = 46+54 / 2 = 50.
the margin of error E = 54-46/2 = 4
For 90% Confidence Z- Critical value is = 1.645
But the margin of error
E = ZS/√n
4=(1.645)S/√n
S/√n = 4 / 1.645
= 2.4316
For 95% confidence Z-critical value is 1.96
A 95% confidence interval is = mean ± E
(50 ± 1.96) S/√n = (50 ± 1.96)×2.4316
= 50+ 4.7660
= 45.2340, 54.7660
= (45, 55)
Hence the correct option is B which is (45, 55) as the 99% confidence limit.
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What are the x and y intercepts? What do they mean in terms of the graph?
Answers
Step-by-step explanation:
these intercepts are the points where the graph intersects with the coordinate axes (x and y).
the x-intercept is a point on the x-axis, meaning when y = 0.
the y-intercept is a point on the y-axis, meaning when x = 0.
so, the x-intercept here is 14 at the point (14, 0).
the y- intercept is 7 at the point (0, 7).
that means the object started falling from a height of 7 meters and hit the ground after 14 seconds.
the falling speed was then
7 meters / 14 seconds = 0.5 meters / second
what are we talking about ? an asteroid with very little gravity ?
Can anyone state the vertex of the graph?
Answers
The graph has no vertex
The transformations from the parent function are
Vertical shift down 2Horizontal shift left 4How to determine the vertex?The graph represents the given parameter
As a general rule, the maximum or the minimum of a graph is the vertex
However, the graph has no maximum or minimum
This means that there is absence of a vertex in the graph
The transformationHere, we have:
The graph is translated 4 units to the left of the origin The graph is translated 2 units below the originThis transformation can be represented as (x - 4, y - 2)
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Help me on this please.
Answers
The steps and reason to prove the angle theorems is; Table 3
What is the proof of the angles in the triangle?The internal angles of the given triangle are given as;
a, b, c and d.
Now, we know that the sum of interior angles in a triangle is equal to 180°;
∠a + ∠b + ∠c = 180°
Now, ∠c and ∠d are angles that form a straight line and as such they sum up to 180° as they are supplementary angles.
∠c + ∠d = 180°
Thus, by transitive properties, we can say that;
∠a + ∠b + ∠c = ∠c + ∠d
Therefore by subtraction property of equality we have;
∠a + ∠b = ∠d
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