The ratio of red grapes to blueberries in simplest form is 3/4.
What is ratio?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
Given:
Matthew made a fruit salad, in which the ratio of blueberries to red grapes is 8:6.
We have to find the ratio of red grapes to blueberries in simplest form.
Let there are 6 red grapes and 8 blueberries.
So, the ratio is
Red grapes / blueberries = 6/ 8
Reduces the ratio,
6 / 8 = (2 x 3) / (2 x 4) = 3 /4
Hence, the ratio of red grapes to blueberries in simplest form is 3/4.
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What will be the roots of the equation 3x² 7x 5 0?
The roots of the Given quadratic equation are 0.57 and -2.9 solved using the algebraic method.
The given equation is a quadratic equation because the degree of the given equation is 2.
How can one tell whether or not a given equation is a quadratic equation?
A quadratic equation is a two-variable polynomial equation of degree two of the form [tex]f(x) = ax^2+bx+c = 0[/tex] with the variables a, b, and c being real numbers and a not equal to 0. With "a" denoting the leading coefficient and "c" denoting the absolute term of f, it is a quadratic equation in its general form (x). The values of x that fulfil the quadratic equation are known as the roots.
The given equation is 3x²+7x - 5 = 0 a =3,b=7, c =-5
lets roots of the given equation is (α, β).
roots can be found using Shreedhara Acharya's formula.
[tex](\alpha, \beta) = [-b \± \sqrt(b^2 - 4ac) ]/2a[/tex]
α = [-b + √(b^2 – 4ac)]/2a
β = [-b - √(b^2 – 4ac)]/2a
b^2 – 4ac = 49-4*3*(-5) = 49+60 = 109
α = (-7+[tex]\sqrt{109}[/tex])/2*3
α = (-7+10.44)/6
α = 0.57
β = (-7 - 10.44)/6
β = -2.9
So the roots of the Given quadratic equation are 0.57 and -2.9.
-- The given question is incomplete, the complete question is
"What will be the roots of the equation 3x^2+7x-5=0" --
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x^2+4x-7 in the form (x+a)^2-b
The equation x² + 4x - 7 can be written in the form (x + a)² - b as (x + 2)² - 11.
How to write equation in another form?It follows from the task content that the equation x² + 4x - 7 is to be written in the vertex form; (x + a)² - b.
Since the given equation is; x² + 4x - 7 in which case, b is a constant.
b = constant
x² + 4x - 7
We therefore have an equivalent expression using the completing the square method as follows;
(x + 2)² - 4 - 7
= (x + 2)² - 11
Hence,
x² + 4x - 7 = (x + 2)² - 11
To Check:
= (x + 2) (x + 2) - 7
= x² + 2x + 2x + 4 - 11
= x² + 4x - 7
Therefore, the obtained equation; (x + 2)² - 11 is another form the equation x² + 4x - 7 can be written.
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Which theorem has two sides and a non-included angle?
Angle-Angle-Side (AAS) Theorem has two sides and a non-included angle.
What is Angle-Angle-Side (AAS) Theorem?The triangles are congruent if two angles and a non-included side in one triangle are congruent with two angles and the corresponding non-included side in another triangle, according to the Angle-Angle-Side (AAS) Congruence Theorem.The side-angle-side (SAS) theorem is the first such theorem. The triangles are congruent if two sides and the included angle of one triangle are equivalent to two sides and the included angle of another triangle.When two angles and an unincluded side of one triangle are equal to two angles and the corresponding unincluded side of the other triangle, two triangles are said to be congruent (AAS=AAS).To learn more about Angle-Angle-Side (AAS) Theorem refer to:
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What additional information is needed to establish the congruence?
To establish congruence between two geometric figures, it is necessary to have information about their size and shape. This includes information about the lengths of their sides and the measures of their angles. It may also be necessary to know the relative positions of the figures, such as whether they are oriented in the same way or whether one is a reflection of the other.
To show that two figures are congruent, it is usually necessary to use one or more of the following techniques:
Superimpose the figures: This involves placing one figure directly on top of the other so that corresponding parts are aligned. If the figures are congruent, they will fit exactly on top of each other and no gaps or overlaps will be visible.
Use a ruler or other measuring tool: By measuring the lengths of the sides and angles of the two figures, it is possible to determine whether they are congruent. If all of the measures are the same, the figures are congruent.
Use transformations: Congruent figures can be obtained from each other through translations, rotations, and reflections. By applying these transformations to one of the figures, it is possible to determine whether it can be made to match the other figure.
Use geometric principles: There are various geometric principles that can be used to establish the congruence of two figures. For example, the AA (Angle-Angle) Congruence Postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are congruent.
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if the odds for a certain event are 11 to 28, what is the probability of the event occuring? write your answer as a simplified fraction.
The probability of the event occurring at odds of 11 to 28 is 11/39.
What is Odds and Probability?The odds of an event are other way of expressing the likelihood of an event occurring. Use the below formula for converting the probabilities and odds .
Probability = odds/(1+ odds)
We have, the odds for a certain event = 11 to 28 i.e, 11/28
The probability of the event occuring say, P =
= odds/(1+ odds) = (11/28)/( 1 + 11/28 )
=> P = (11/28 )/(( 28+ 11)/28)
=> P = (11/28 )/(39/28)
=> P =( 11/28)× 28/39
=> P = 11/39
Since 11 is prime number, this fraction cannot be reduced. Hence, required fraction is 11/39.
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Find the coordinates of point P along the directed line segment AB so that
AP to PB is in the ratio 3 to 7] Round your answer to the nearest tenth.
B(4, 5)
A(-2, 1)
-4
-2
Ay
61
-4-
Coordinates: P
N.
2
4 x
(1+x)
2-3
x) = 8 bris E= SVIÐ
V/22
Answer:
P(-0.2, 2.2)
Step-by-step explanation:
You want the coordinates of point P that divides AB into segments with the ratio AP/PB = 3/7. The end points are A(-2, 1) and B(4, 5).
Dividing pointThe point that divides AB in the ratio m/n is ...
P = (mB +nA)/(m+n)
P = (3(4, 5) +7(-2, 1))/(3+7) = (12 -14, 15 +7)/10
P = (-0.2, 2.2)
Evaluate the following
-(-4)+3
Answer:
7
Step-by-step explanation:
-(-4) + 3
= 4 + 3
= 7
The circle below has centre O.
BC and DE are tangents to this circle.
Work out the size of angle 0.
Give reasons for your answer.
A
56°
B
O
D
21°
0
C
Answer:
Step-by-step explanation:
Tangent is perpendicular to radius at point of contact.
So, ∠ABO=∠ACO=90
∘
In a quadrilateral, the sum of the angles is 360
∘
.
∠BAC+∠BOC+∠ABO+∠ACO=360
∘
∴∠BAC+∠BOC=180
∘
∠BOC=180
∘
−40
∘
∠BOC=140
∘
So, option C is the answer
points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.
Points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.
True
which expressions represent the length of side \overline{hi} hi start overline, h, i, end overline? choose 2 answers: choose 2 answers:
The expressions represent the length of side, HI are sqrt(161) and 15 sin(90°- 75°) . So, option (a) and (c) are right answers.
What is Pythagoras theorem?A geometry theorem : the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides ( i.e base and prependicular) .
Mathematically, (GH)² + (HI)² = (GI)²
We have , provide a triangle GHI , since measure of angle H is 90° so it is a right angled triangle.
We have to calculate the length of side HI , for this we can use either triangular formulae or Pythagoras theorem. Here, we are using Pythagoras theorem,
As we have, GH (prependicular) = 8 unit , GI (hypotenuse) = 15 unit , HI ( base) = ?
(prependicular)²+( base)² = (hypotenuse)²
=> (GH)² + (HI)² = (GI)²
=> (8)² + (HI)² = (15)²
=> (HI)² = (15)² - (8)²
=> (HI)² = 225 - 64 = 161
=> HI = sqrt(161) = 12.68
Using Trigonometric functions,
measure of angle G = 180° - 90° - 75° = 15°
In right triangle GHI, sin 15° = HI /15
=> HI = 15 sin 15° = 15 sin(90°- 75°)
So, the length of side HI is sqrt(161) or 15 sin 15° .
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Complete question:
Consider right triangle ∆GHI present above. Which expressions represent the length of side HI? Choose 2 answers:
a)15 sin(90° - 75°)
b)15 cos(90° - 75°)
c) sqrt(161)
d)tan(90° -
A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers placed an ad online asking for volunteers to participate in the study. One hundred subjects replied and were informed that one group would receive the new cream and the other group would receive a cream with no active ingredient. All 100 subjects were exposed to poison ivy. Fifty were then randomly assigned to the group with the new cream, and 50 were randomly assigned to the group with the cream with no active ingredient. After three days, the subjects’ level of irritation was measured.
Which of the following accurately describes the benefit of comparison in the experiment?
The overall level of irritation can be compared to see if the new cream had a significant effect.
The level of irritation for both groups can be compared to see if the new cream had a significant effect.
The level of irritation in the treatment group only can be compared to see if the new cream had a significant effect
Since one group received a cream with no active ingredient, the researchers will not be able to determine of the new cream is effective.
Answer:
The level of irritation for both groups can be compared to see if the new cream had a significant effect.
Step-by-step explanation:
In this experiment, the purpose of having two groups is one being the control group, and one being the group being experimented on. The control group is needed in order to know for sure that it is the cream that is beneficial, instead of an outside factor such as the poison ivy being bad.
By comparing the level of irritation for both groups, it will become apparent if the new cream has a side effect.
Answer:
The level of irritation for both groups can be compared to see if the new cream had a significant effect.
Step-by-step explanation:
the phrasing is a bit strange.
but I think the first one means "overall" in the sense of outside and inside the 2 test groups.
the third one would object compare results only inside the group that got the active ingredient.
the 4th one is just nonsense.
so, only the second answer option makes sense. these 2 groups are created so that their results can be compared. that is the whole point.
Damian plans to repaint some classroom bookcases. All of the bookcases are the same size and each requires \
5
3
gallon of paint. If he's going to paint 19 bookcases, how many gallons of paint does he need? Express your answer in simplest form.
Answer: 95/3 gallon of paint
Step-by-step explanation:
I guess you mean each requires 5/3 gallon of paint
If so, we take 5/3 times 19 = 95/3 gallon of paint
95/3 = 31 2/3
2.3.4 In a game between two equal teams; the home team wins with probability p > 1/2_ In a best of three playoff series; a team with the home advantage has a game at home, followed by a game away, followed by a home game if necessary The series is over as soon as one team wins two games. What is P[H], the probability that the team with the home advantage wins the series? Is the home advantage increased by playing a three-game series rather than a one-game playoff? That is, is it true that P[H] > p for all p > 1/2?
The team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.
For the team with the homecourt advantage, let [tex]Wi[/tex] and [tex]Li[/tex] denote whether the game '[tex]i[/tex]' was a win or a loss. Because games 1 and 3 are home games and game 2 is an away game.
The probability that the team with the home-court advantage wins is
P [H] = P [[tex]W1W2[/tex]] + P [[tex]W1L2W3[/tex]] + P [[tex]L1W2W3[/tex]]
= [tex]p(1-p)[/tex] + [tex]p3[/tex] + [tex]p(1-p){2}[/tex]
Note that P[H] ≤ pfor 1/2≤p≤1.
Since the team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.
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For the team with the homecourt advantage, let and denote whether the game '' was a win or a loss. Because games 1 and 3 are home games and game 2 is an away game.
The probability that the team with the home-court advantage wins is
P[H] ≤ pfor 1/2≤p≤1.
Since the team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.
use the following normal-form game to answer the questions below. suppose the players do not know exactly how many times this game will be repeated. what is the maximum level of probability of the game ending that would make collusion more profitable than cheating? g
If the player do not know exactly how many times the game will be repeated the maximum level of probability can be predicted through Nash equilibria.
The concept, Nash equilibrium in game theory where the optimal outcome is when there is no incentive for players to deviate from their initial strategy. The players have knowledge of their opponent’s strategy and still will not deviate from their initial chosen strategies because it remains the optimal strategy for each player. Overall, an individual can receive no incremental benefit from changing actions, assuming that other players remain constant in their strategies. A game may have multiple Nash equilibria or none at all. The Nash equilibrium is a decision making theorem within game theory that states a player can achieve the desired outcome by not deviating from their initial strategy.
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Which function is continuous function?
A continuous function in mathematics is a function without discontinuities, or any sudden changes in value.
How to know a continuous functionA function must be defined there, have a limit there, and have the value of the function there equal the value of the limit there in order for it to be continuous at that place.
Discontinuities can be categorized as being removable, jump, or infinite.
If we have a corresponding output value for any input value, the function graph will be continuous.
Without removing the pencil from the paper, we could continue the graph in both the negative and positive directions without the graph becoming broken.
Any breakage in the graph marks discontinuity
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a car is being driven at a rate of 40 mph when the brakes are applied. the car decelerates at a constant rate of 10 ft/sec2. how long, in seconds, before the car stops? (round your answer to two decimal places.)
A car is being driven at a rate of 40 mph when the brakes are applied. the car decelerates at a constant rate of 10 ft/sec2.The car will stop after 5.87 seconds.
1 mile = 5280 ft (approx)
1 hr = 3600 sec
The car is driven at a rate of 40 mph when the breaks are applied , then,
v(0)=40 m/hr
v(0)=40 5280 / 3600
v(0)=58.67 ft/sec2 [rounded to two decimal places] .............. (i)
The car decelerate at a constant rate of 10 ft/sec²
So, acceleration function,
a(t)=-10 m/sec2
Now, velocity function,
v(t)= a(t) dt (ft/sec²)
v(t)= -10 dt (ft/sec²)
v(t)=-10t+C1 (ft/sec²) [where c is integrating constant]............ (ii)
Putting t=0 in this function,
v(o)=-10(0)+C1 (ft/sec²) (ft/sec²)
v(0)=C1 (ft/sec²)
58.67=C1
C1=58.67
Putting this value of C1 in equation (ii) velocity function becomes,
v(t)=-10t+58.67 ......... (iii)
Car will stop when v(t) =0 . Then,
-10t+58.67=0
10t=58.67
t=58.67/10
t=5.867 [rounded to 2 decimal places]
So after 5. 87 sec the car will stop.
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100 POINTS HELP PLEASE ILL GIVE BRAINLIEST
Answer:
A. It is a decrease in assets.
Step-by-step explanation:
The business paid $700,000 to the Loans Payable via cash, reducing their assets by 700,000 dollars AND increasing the credits. The business increased its credit score since it paid the exact amount it got a loan for back to the Loan Company.
That money was the payable loan depicted in the Debit section.
Answer:
OptionA) Decrease in assets
Step-by-step explanation:
The business paid $700,000 to the Loans Payable via cash, reducing their assets by 700,000 dollars AND increasing the credits.
How do you find median in 7th grade?
The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.
To find the median:
1-Arrange the data points from smallest to largest.
2-If the number of data points is odd, the median is the middle data point in the list.
3-If the number of data points is even, the median is the average of the two middle data points in the list.
Finding the middle number requires sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers).
Example: The median of 4, 1, and 7 is 4 because when the numbers are put in order (1,4,7)the number 4 is in the middle.
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I need help on these questions, I will give you brainliest if it lets me!
Carlos attempted correctly.
What is Temperature Conversion?Formulas for converting temperature values between different units are referred to as temperature conversions. There are numerous ways to convert temperatures. The most popular units of measurement among these are Kelvin, Celsius, and Fahrenheit.
Given:
We know the formula
F= 9/5 C + 32
Now, writing in the equation form
5F = 9C + 160
5F- 9C = 160
As, per the given Information Carlos attempted the right form and
Mikala made a mistake in transferring 5/9.
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Given m\parallel nm∥n, find the value of x and y.
m
n
(6x+19)°
(3x+8)°
(2y+1)
Based on the definition of supplementary angles, the values of x and y are:
x = 17; y = 29.
What are Supplementary Angles?If two angles are supplementary angles, then they will be equal to 180 degrees.
Since lines m and n are parallel, then:
(6x + 19) + (3x + 8) = 180 [supplementary angles]
Solve for x:
6x + 3x + 19 + 8 = 180
9x + 27 = 180
9x + 27 - 27 = 180 - 27
9x = 153
Divide both sides by 9
9x/9 = 153/9
x = 17
(6x + 19) + (2y + 1) = 180 [supplementary angles]
6x + 19 + 2y + 1 = 180
6x + 2y + 20 = 180
Plug in the value of x:
6(17) + 2y + 20 = 180
102 + 2y + 20 = 180
122 + 2y = 180
2y = 180 - 122
2y = 58
y = 58/2
y = 29
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Jim invests $5,000 in an account that
pays 2.5% annual interest,
compounded semi-annually.
What is
his balance, to the nearest cent, at the
end of 5 years?
The balance after 5 years would be near around 5661 dollars.
What is compound interest?
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
First, convert R as a percent to r as a decimal
r = R/100
r = 2.5/100
r = 0.025 rate per year,
Then solve the equation for A
[tex]A = P(1 + r/n)^{nt}\\\\A = 5,000.00(1 + 0.025/2)^{(2)(5)}\\\\A = 5,000.00(1 + 0.0125)^{10}\\\\A = 5,661.35[/tex]
Hence the balance after 5 years would be near around 5661 dollars.
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x and y are integers, y>_ 2, x +y <_ 4 and y <_ 2x +2
The true values of x and y in the system of inequalities are (2/3, 10/3)
How to determine the values of x and y?From the question, we have the following parameters that can be used in our computation:
y ≥ 2
x + y ≤ 4
y ≤ 2x + 2
Express the inequalities as equations
So, we have the following representation
x + y = 4
y = 2x + 2
Substitute y = 2x + 2 in the equation
x + y = 4
So, we have the following representation
x + 2x + 2 = 4
Evaluate the like terms
So, the equation becomes
3x = 2
Divide by 3
x = 2/3
Substitute x = 2/3 in y = 2x + 2
y = 2 x 2/3 + 2
Evaluate
y = 10/3
In y ≥ 2, we have
10/3 ≥ 2
The above inequality is true
Hence, the values of x and y are (2/3, 10/3)
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Write a system of inequalities to represent this
situation.
The Washington family is hosting a cookout. They
decide to serve chicken and pork. They determine
that they will need at most 20 pounds of meat, and
they want to have at least twice as much chicken as
pork.
Answer:
c + p <= 20
2c >= p
Step-by-step explanation:
We can declare our variables as:
c = pounds of chicken
p = pounds of pork
The total meat can be expressed as c + p, and at most signifies that the family needs 20 pounds or less. Putting this together, one equation becomes c + p <= 20.
The family additionally wants at least 2 * c as p, which means that 2*c is greater than or equal to p, or 2c >= p.
hope this helps :)
How do you find the asymptotes and holes of a rational function?
To find the asymptotes and holes of a rational function, factor the denominator of the function and set it to zero. This will give you the x-values of the holes. To find the asymptotes, take the degree of the numerator and subtract it from the degree of the denominator. This will give you the degree of the asymptote.
To find the asymptotes and holes of a rational function, you must first factor the denominator of the function and set it to zero. This will give you the x-values of the holes, or the values where the function is undefined. To find the asymptotes, take the degree of the numerator and subtract it from the degree of the denominator. This will give you the degree of the asymptote. For example, if the numerator is a second degree polynomial and the denominator is a third degree polynomial, the asymptote will be a first degree polynomial. To find the equation of the asymptote, divide the numerator and denominator by the highest degree term of the denominator. The resulting quotient will be the equation of the asymptote. The asymptotes will be straight lines, so the equation will be in the form of y = mx + b. The holes will be the x-values of the points where the denominator equals zero. The asymptotes and holes will divide the graph of the rational function into distinct regions, and can be used to analyze the behavior of the function.
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At a local sandwich shop, 45% of customers preferred white bread over whole wheat bread. Of those who chose whole wheat bread, 52% preferred ham for the protein, and 43% of those who chose white bread preferred turkey.
What percentage of customers chose whole wheat bread with turkey? Round your answer to the nearest whole percentage.
52%
37%
29%
26%
If at a local sandwich shop, 45% of customers preferred white bread over whole wheat bread. The percentage of customers chose whole wheat bread with turkey is: D. 26%.
How to find the percentage?First step is to find the percentage of customers who preferred ham with whole wheat bread
Percentage = ( 1- .45)
Percentage = .55
Second step is to find the percentage of customers who preferred whole wheat bread
Percentage = (1- .52)
Percentage = .48
Now let find the percentage of customers chose whole wheat bread with turkey
Percentage = .48 × .55
Percentage = .26 ×100
Percentage =26%
Therefore the correct option is D.
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How do you verify a congruence transformation?
By using several transformations, including reflection, translation, rotation, and stretching, geometry may be changed into congruent geometry.
What is congruence?
A "matching" figure is one that can be placed perfectly on another. The bread has the same size and form when it is stacked. Match refers to objects that are precisely the same size and form. If one of two geometric figures can be consistently overlaid on the other, they are said to be congruent or to be in a congruent relationship.
congruence: Two forms are congruent if they have comparable sides and corresponding angles. By using transformations, including reflection, translation, rotation, and stretching, geometry may be changed into congruent geometry.
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What is the difference between apply function and transform function?
The difference between the apply and the transform function is explained below.
In order to differentiate these function, first we have to know the definition of each of the function.
The apply function is used to operate on different types of data.
Where as the transform function is used to convert an equation transforming into one equation to another whose given roots are inverse to the roots present in an equation that is given
According to the definition, the difference between these function is defined as the transform() can take a function and string function then list of functions finally a dict.
Where as the apply() is only allowed a function and on the other hand it works with multiple Series at a time. Where as the transform function is only allowed to work with a single Series at a time.
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The graph shows the proportional relationship between the number of gems collected and the number of levels that have been completed in a video game.
Graph with x axis labeled game levels and y axis labeled gems collected. A line begins at 0 comma 0 and goes through points 6 comma 480 and 8 comma 640.
Determine the constant of proportionality for the relationship.
p = 160
p = 80
p equals 2 over 160
p = 0.0125
The constant of proportionality for the data is 80. The correct option is B.
What is the constant of proportionality?The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, and even the rate of change.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the points are (6,480) and (8,640). The value of the proportionality constant will be calculated as,
y =kx
480 = k x 6
k = 480 / 6
k = 80
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The graph of which function has an axis of symmetry at x = 3?
The graph of which the function has an axis of symmetry at x = 3 is the graph of
y = x² - 6x - 1How to find the graph with axis of symmetry x = 3The axis of symmetry of a quadratic function is the line that bisects the curve into two.
The formula for the axis of symmetry is of the form
x = -b / 2a
for the function y = x² - 6x - 1
b = -6
a = 1
the axis of symmetry, x = -(-6/(2 * 1))
= - (-3)
= 3
hence the axis of symmetry is x = 3
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What is the range of real numbers?
The optimal response is The ranges below encompass all real numbers: From 0 through all actual numbers. The domain of this function is all real numbers since x can be entered with any value.
What is Range?Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.
answer to the question is that all real numbers or (−∞,∞)
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