A direct variation with nonzero numbers is if y varies directly as x, and y = 6 when x = 2,
What is direct variation?The relationship between two variables in which the variables have a constant ratio, k, where k is not equal to 0.
K is known as the constant. Assume the variables are x and y, and that y varies directly with x. We can say that the y/x ratio is equal to k, where k is not equal to zero.
This formula can also be written as y = kx where k is not equal to 0.
It's critical to understand that we can use these two ratios interchangeably depending on the problem at hand.
In the example given, the constant of variation is k = = 3. Thus, the equation describing this direct variation is y = 3x.
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How many liters of a 25% saline solution
must be mixed with 4 liters of a 40% saline
solution to make a 30% saline solution?
The required amount of 25% saline solution is 8 liters.
Finding unknown quantity using Linear equation:In mathematics, the equation that used to find an Unknow quantity is known as Linear Equation. Here we use different types of variables to represent the unknown value like x, y, z or a, b, c.. etc.
Here we have
4 liters of a 40% saline
we need to make it a 30% of saline solution by adding a mount of 25% saline solution
Let us assume that we added x L of 25% of saline solution
After adding x L of 25% saline into 4 liters of 40% saline to get 30% saline solution then the resultant solution is “x+4” liters of 30% saline.
The mathematical representation for the above line will be
⇒ x litres 25% saline + 4 litres 40% saline = (x+4) litres 30% saline
⇒ x(25%) + 4(40%) = (x+4)(30%)
⇒ 25x/100 + 4(40/100) = (x+ 4)30/100
⇒ 25x + 160 = (x +4)30
⇒ 25x + 160 = 30x + 120
⇒ 30x - 25x = 160 - 120
⇒ 5x = 40
⇒ x = 8
Therefore
The required amount of 25% saline solution is 8 liters
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Describe how the graph of g(x)= –||x+2||+4 is related to the graph of the parent function.
The graph of g(x) = -|x + 2| + 4 is obtained after these following transformations from the parent function f(x) = |x|.
Reflection over the x-axis.Shift left of 2 units.Shift up of 4 units.Which transformations were used?The parent function in this problem is defined as follows:
f(x) = |x|.
The transformed function in this problem is defined as follows:
g(x) = -|x + 2| + 4
The transformations are listed and described as follows:
The multiplication by -1 represents a reflection of the parent function over the x-axis.The addition by 2 in the domain, that is, x -> x + 2, represents a shift right of two units of the parent function.The addition by 4 in the range, that is, y -> y + 4, represents a shift up of four units of the parent function.More can be learned about transformations at https://brainly.com/question/28792248
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Draw the dilation of ABC with center P scale factor 2. label the dilation GHI
Using dilation rules, the dilated triangle whose coordinates of the vertices are as follows: A'(-2 , 2), B'(-1,0), C'(1 , 2).
What is the rule for a dilation?
To dilate a figure by a factor of a, each coordinate of each vertex of the image is multiplied by a, that is, the following rule is applied:
(x, y) -> (ax, ay).
suppose the coordinates of the vertices of ABC are given as follows:
A(-6,6), B(-3,0), C(3,6).
After a dilation with a scale factor of 1/3, the coordinates of the vertices of A'B'C' will be given as follows:
A'(-2 , 2), B'(-1,0), C'(1 , 2).
These coordinates are derived multiplying the coordinates of A, B and C by 1/3.
For the image of triangle DEF, each of the coordinates of D, E and F will be multiplied by 2 to generate the dilated triangle.
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For community service, Ben is picking
up litter along Avondale and Bedford
Way. Adam is picking up litter along
Oakley Street.
Avondale
39 yds
Oakley Street
52 yds
Bedford Way
How many more yards of roadside is
Ben cleaning than Adam?
Samson says Ben is
cleaning 65 more
yards than Adam.
Sheridan says Ben
is cleaning 26 more
yards than Adam.
The yards of roadside that Ben is cleaning more than Adam is 26 yards. Sheridan is correct.
Who is correct?The first step is to determine the length of Oakley Street. Pythagoras theorem would be used to determine the length. Oakley Street is the hypotenuse of the right triangle that is formed by the streets.
The Pythagoras theorem: a² + b² = c²
where:
a = lengthb = basec = hypotenuse39² + 52² = c²
1,521 + 2704 = c²
c² = 4,225
c = √4225
c = 65 yards
Total yards Ben picked = 39 + 52 = 91 yards
Yards picked by Adam = 65 yards
Difference in the yards of litters picked = 91 - 65 = 26 yards
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Graph the point on the graph.
Answer:
see below
Step-by-step explanation:
To graph this equation, start at the origin (0,0) since there is not y-intercept.
Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.
Because the rise (up and down, numerator) is 1, we know that we will go up one unit.
The run (side to side, denominator) is 4, so we will go to the right 4 units.
This makes the first point (4, 1).
Continue doing this until you get an idea of the line and connect the points to get the graph
Answer:
Info down in Explaination
Step-by-step explanation:
To graph this equation, start at the origin (0,0) since there is not y-intercept.
Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.
Because the rise (up and down, numerator) is 1, we know that we will go up one unit.
The run (side to side, denominator) is 4, so we will go to the right 4 units.
This makes the first point (4, 1).
Continue doing this until you get an idea of the line and connect the points to get the graph
An online streaming service charges a monthly fee as well as a one-time sign-up fee. The cost for this online streaming service is modeled by the following function where m represents the number of months the service is subscribed to and C(m) represents the total cost given that amount of time:
C(m) = 11.99m + 7
In the above function, what is the slope?
What is the y-intercept?
How do we interpret the slope of this function?
How do we interpret the y-intercept of this function?
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
C(x) = 11.99 + 7
The slope of the function is 11.99.
The y-intercept of the function is 7.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
C(m) = 11.99m + 7
The equation is in the form of y = mx + c
So,
m = 11.99
c = 7
The slope of the function is 11.99.
The y-intercept of the function is 7.
Thus,
The slope of the function is 11.99.
The y-intercept of the function is 7.
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Enter an inequality that represents this graph
The inequality that represents the graph is y < 4
The graph is shown in the figure
The graph is the pictorial representation of the collection of data. It has 2 axis . The x axis and y axis
Consider the each block of the graph as 1 units
At y = 4 there is dotted line parallel to the x axis of the graph
The dotted line represents the inequality symbol less than, Therefore the value of y is less than 4
From the graph, the entire region of the graph that y less than 4 are shaded therefore for all the value of x the value of y is less than 4
The inequality will be
y < 4
Hence, the inequality that represents the graph is y < 4
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Please help on two geometry questions!!!
Considering the two figures the value of x is
8) x = 12degrees9) x = 8.25 degreesHow to determine the value of xThe value of x is found by the external angle theorem which states that the sum of the two opposite internal angels of a triangle gives the external angle
The value of x is calculated as below
8) 70 + 5x = 9x + 22
70 - 22 = 9x - 5x
48 = 4x
x = 12
9) 65 + 8x + 11 = 16x + 12
65 + 11 - 12 = 16x - 8x
66 = 8x
x = 8.25
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3. If, over a few months, Jane saw 92 mayflies,
how many flying insects did she see ?? Need awnsers
The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers.
x + (x + 1) + (x + 2) = 42
x + (x + 2) + (x + 4) = 42
(x minus 1) + x + (x + 1) = 42
(x minus 2) + x + (x + 2) = 42
x + 2 x + 3 x = 42
Answer:
A and C are correct choices========================
The difference between two consecutive integers is 1.
Test it with the given choicesA) x + (x + 1) + (x + 2) = 42,
YesB) x + (x + 2) + (x + 4) = 42
No, the difference between the pairs is 2 not 1.C) (x minus 1) + x + (x + 1) = 42
YesD) (x minus 2) + x + (x + 2) = 42
No, the difference between the pairs is 2 not 1.E) x + 2 x + 3 x = 42
No, here is the multiples of integers and the difference between the pairs is x not 1.Answer:
x + (x + 1) + (x + 2) = 42
(x minus 1) + x + (x + 1) = 42
Step-by-step explanation:
Integer: A whole number that can be positive, negative, or zero.
Consecutive integer: Integers that follow each other in order.
Let x be an integer.
Consecutive integers of x are one more or one less than each other in order.
x + (x + 1) + (x + 2) = 42This equation represents 3 consecutive integers as each value is one more than the previous value.
x + (x + 2) + (x + 4) = 42This equation does not represent 3 consecutive integers as each value is 2 more than the previous value.
(x minus 1) + x + (x + 1) = 42This equation represents 3 consecutive integers as each value is one more than the previous value.
(x minus 2) + x + (x + 2) = 42This equation does not represent 3 consecutive integers as each value is 2 more than the previous value.
x + 2 x + 3 x = 42This equation does not represent 3 consecutive integers as each value is x more than the previous value.
4) A recipe that makes 3 dozen chocolate chip cookies calls for 2 and 2/5 cups of flour.
a) Exactly how much flour would you need for half the recipe?
b) Exactly how much flour would you need to make 5 dozen cookies?
As per the unitary concept,
a) There are 5/8 cups of flour would you need for half the recipe
b) There are 6 1/4 cups of flour would you need for 5 dozen cookies.
Unitary method:
The method by which first we find the value of single unit and then the value of the required number of units is known as the Unitary Method.
Given,
Here we have given that, A recipe that makes 3 dozen chocolate chip cookies calls for 2 and 2/5 cups of flour.
So, here we need to find the following:
a) Exactly how much flour would you need for half the recipe?
b) Exactly how much flour would you need to make 5 dozen cookies?
In order to find these value, we have to calculate the amount of flour need for 1 dozen.
In order to calculate that, one we need to divide the total amount by the cups of flour need.
Then we get,
=> 3/ (2 2/5)
=> 3/ (12/5)
=> 15/12
=> 1.25
So, for half dozen cookies, we need
=> 1.25/2
=> 0.625
Which is in the fraction form of,
=> 5/8
And for 5 dozen of cookie we need.
=> 5 x 1.25
=> 6.25
The fraction equivalent is
=> 6 1/4 cups.
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Sally can paint a room in 6 hours while it takes Steve 8 hours to paint the same room. how long would it take them to paint the room if they work together
Answer:
It will take them 3.5 hours to paint the room.
Step-by-step explanation:
Step 1: Add the number of hours it takes them together
A. 6 + 8
Step 2: Divide the total number of hours by two (since two people are working together)
B. 12 / 2 = 7 hours
Step 3: Divide by two again since you now have twice the speed
C. 7 / 2 = 3.5 hours
A normal distribution has a mean of 61 and a standard deviation of 15. What is the median?
Answer: median = 61
Reason:
A normal distribution is perfectly symmetric. Such distributions have mean = median = mode.
4/7 of a group of children are boys, if they are 18 more boys than girls how many children are there altogether
Answer:126 children
Step-by-step explanation:
first you want to multiply 18 times 4 (72) then 18 times 3 (54) and then you add 72+54=126
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Richard bought 3 slices of cheese pizza and 2 sodas for $8.75. Jordan bought 2 slices of cheese pizza and
4 sodas for $8.50. How much would an order of 1 slice of cheese pizza and 3 sodas cost?
• $3.25
O $5.25
• $7.75
• $17.25
The cost of 1 slice of cheese pizza and 3 sodas cost will be;
⇒ $5.25
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Richard bought 3 slices of cheese pizza and 2 sodas for $8.75.
And, Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50.
Now,
Let the cost of 1 slices of cheese pizza = x
And, The cost of 1 slices of soda = y
Since, Richard bought 3 slices of cheese pizza and 2 sodas for $8.75.
Hence, We get;
⇒ 3x + 2y = $8.75 ..(i)
And, Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50.
So, We get;
⇒ 2x + 4y = $8.50 ..(ii)
Multiply by 2 with (ii);
⇒ 2 (3x + 2y) = 2 × $8.75
⇒ 6x + 4y = $17.5
Subtract from (ii), we get;
⇒ 6x + 4y - 2x - 4y = $17.5 - $8.50
⇒ 4x = $9
⇒ x = $2.25
And, ⇒ 2x + 4y = $8.50
⇒ 2 × $2.25 + 4y = $8.50
⇒ $4.5 + 4y = $8.50
⇒ 4y = $8.50 - $4.5
⇒ 4y = $4
⇒ y = $1
Thus, The cost of 1 slice of cheese pizza and 3 sodas cost will be;
⇒ $2.25 + 3 × $1
⇒ $2.25 + $3
⇒ $5.25
Therefore, The cost of 1 slice of cheese pizza and 3 sodas cost will be;
⇒ $5.25
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Ashley has a $80 gift card to her favorite coffee shop. Each day, she uses her gift *
card to buy a coffee for $4.50, Aaron has a $60 gift card to the same coffee shop.
Each day, he uses his gift card to buy an iced tea for $2.50. For what number of
drinks purchased will Ashley's gift card balance be greater or equal to Aaron's?
Step-by-step explanation:
I assume this means that both purchase one item every day.
so, their number of purchases are the same (x).
80 - 4.5x >= 60 - 2.5x
20 - 4.5x >= -2.5x
20 >= 2x
10 >= x
our
x <= 10
after 10 purchased drinks their balances will be equal.
before that, Ashley's card balance will be greater than Aaron's.
after that, Aaron's card balance will be greater than Ashley's.
so, for up to 10 purchased drinks Ashley's card balance will be greater or equal to Aaron's.
Select all symmetries that apply
Answer:
graph 1
symmetry about the x and y axes
graph 2
symmetry about the y axis
graph 3
symmetry about the y axis
Step-by-step explanation:
try to imagine that you folded the graph by the x axis or y axis. If the to side of the graph are overlapping, the graph is symmetry across the axis you folded.
Hope this helps.
The scores of the students on a standardized test are normally distributed, with a mean of 500 and a standard deviation of 110. What is the probability that a randomly selected student has a score between 350 and 550? Use the portion of the standard normal table below to help answer the question. z Probability 0.00 0.5000 0.25 0.5987 0.35 0.6368 0.45 0.6736 1.00 0.8413 1.26 0.8961 1.35 0.9115 1.36 0.9131 9% 24% 59% 91%
Answer:
0.5867 (or 58.7%)
Step-by-step explanation:
The probability that a randomly selected student has a score between 350 and 550 is 59%.
What is z score?Standard score or z score in statistics is defined as the number of standard deviations by which that the value of a score is above or below the mean value.
Given that,
The scores of the students on a standardized test are normally distributed.
Mean, μ = 500
Standard deviation, σ = 110
z score = (x - μ) / σ
For x = 350,
z = (350 - 500) / 110 = -1.36
Probability = 1 - 0.9131 = 0.0869
For x = 550,
z = (550 - 500) / 110 = 0.45
Probability = 0.6736
Probability that a randomly selected student has a score between 350 and 550 is,
P = 0.6736 - 0.0869 = 0.5867 ≈ 59%
Hence the required probability is 0.5867 or 58.67%.
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Which parts of the triangles are congruent in the image? If you don’t know skip.
Answer:
angle LHJ is congruent to angle IKL
Answer:
segment JL is congruent to segment JK
segment HL is congruent to segment KI
Angle LJH is congruent to angle KJI
Step-by-step explanation:
we flip the triangles to look for the corresponding sides
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A sailboat is headed due north, and its sail is set perpendicular to the wind, which is from the south of west. The component of the force of the wind in the direction of the heading is 480N, and the component perpendicular to the heading (the drift component) is 650 N. What is the force exerted by the wind, and what is the direction of the wind?
The direction of force is [tex]53.6^0[/tex] South of West and force exerted by the wind is 596.4N.
What are the component of force?
If a force acting at some angle [tex]\theta[/tex] with respect to x axis then the force can be resolved into two perpendicular forces ([tex]Fcos\theta[/tex] and [tex]Fsin\theta[/tex]). These perpendicular forces are known as component of forces.
Consider the following diagram of the sialboat.
The component of force along the heading direction is 480N and the component of force perpendicular to the heading is 650N.
If F is the foce the direction of wind then then component of force in the East direction will be [tex]Fcos\theta[/tex] and the component of force in the heading direction is [tex]Fsin\theta[/tex]. Now, take the ratio of these two compnents to find the angle [tex]\theta[/tex] as follows:
[tex]tan\theta=\frac{Fcos\theta}{Fsin\theta}\\tan\theta=\frac{650N}{480N}\\\\\theta=tan^{-1}(1.354)\\=53.6^0[/tex]
Now, calculate the force exerted by the wind. Equate the force in heading direction to find the force.
[tex]Fsin\theta=480N\\F=\frac{480N}{sin\theta}\\=\frac{480N}{sin53.6^0}\\=596.4N[/tex]
Hence, the direction of force is [tex]53.6^0[/tex] South of West and force exerted by the wind is 596.4N.
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(y − 1)(y + 10)(y-6) < 0
Solve for y by simplifying both sides of the inequality, then isolating the variable.
Inequality Form:
y<−10 or 1<y<6
Interval Notation:
(−∞,−10)∪(1,6)
y = 3x + 18
y = 15
..............................
Answer: " x = 1 ".
The answer for this 'system of equations' is: " [1, 15] ".
_________
Step-by-step explanation:
To solve for x :
Given:
y = 3x + 18
y = 15 ;
_________
We know that:
3x + 18 = 15 ; Now, subtract 18 from Each Side of the equation:
3x + 18 − 18 = 15 − 18 ;
to get:
3x = 3 ; Now, divide Each Side of the equation by 3 ;
to isolate x on one side of the equation;
and to solve for x :
3x / 3 = 3 / 3 ;
to get: x = 1
_________
The answer is: " x = 1 " ;
The answer for this 'system of equations' is:
" [1, 15] " <== { written as: " [x, y] "} ;
in which: " y = 15 " ; is given in the problem.
_________
Hope this answer is helpful.
Best wishes!
_________
Copy the triangle. Start at any vertex and label the triangle as WVU.
.
What sides include
is the line through points P(-8, -10) and Q(-5, -12) perpendicular to the line through points R(9, -6) and S(17, -5) explain
Answer:
No, the lines are not perpendicularStep-by-step explanation:
Perpendicular lines have opposite-reciprocal slopes.
It means the product of the slopes is - 1.
Let's find the slopes of the two lines and their product.
m(PQ) = (- 12 - (-10)) / (- 5 - (-8)) = - 2/3m(RS) = (- 5 - (-6)) / (17 - 9) = 1/8Find the product of slopes:
- 2/3*1/8 = - 1/12This is not - 1, therefore the lines are NOT perpendicular.
Does X have a binomial distribution? Give your reasons
Opinion polls find that 45% of teens say that their parents put at least some pressure on them to get into a good college. If you take an SRS of 980 teens, X has a distribution of the number in your sample who say they feel at least some pressure from their parents to get into a good college.
The variable X has a binomial distribution, as:
It has a fixed number of observations.The trials are independent.For each outcome, there are only two possible outcomes.What are the requirements for the binomial distribution?There are three requirements for the binomial distribution to represent a variable, as follows:
Fixed number of trials.The result of each trial is independent of the result of any other trial.Two possible outcomes for each trial, one representing a success and the other representing a failure.In the context of the variable X, these requirements are respected as follows:
Fixed number of 980 trials.For each trial, there is a 45% probability that the teen says that their parents put some pressure on him/her to get on good college, and 55% that the parents do not put pressure.For each trial, there are only two possible outcomes, either the parents put pressure, or they do not.Hence yes, the variable X has a binomial distribution.
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An element with a mass of 800 g to Cave by 28% per minute. To the nearest minute how long will it take until they were 140 g of the element remaining?
The first three terms of a sequence are given. Round to the nearest thousandth. 10, 5, 5/2. Find the 6th term
Answer:
0.3125
Step-by-step explanation:
10 / 2 is 5
5 / 2 is 2.5
2.5 / 2 is 1.25
1.25 / 2 is 0.625
0.625 / 2 is 0.3125
Solve by factoring.
6x^2 - x - 12 = 0
Answer:
x = 3/2 and -4/3
Step-by-step explanation:
[tex] \rm \implies 6 {x}^{2} - x - 12 = 0 \\ \\ \rm \implies 6 {x}^{2} - 9x + 8x - 12 = 0 \\ \\ \rm \implies 3x(2x - 3) + 4(2x - 3) = 0 \\ \\ \rm \implies (2x - 3)(3x + 4) = 0 \\ \\ \rm \implies 2x - 3 = 0 \: \: and \: \: 3x + 4 = 0 \\ \\ \rm \implies 2x = 3\: \: and \: \: 3x = - 4 \\ \\ \rm \implies x = \frac{3}{2} \: \: and \: \: x = - \frac{4}{3} [/tex]
Start with the graph of
f(x) = 6x.
Then write a function
g(x)
that results from the given transformation.
shift f(x) 5 units downward
g(x) =
The number of students in nine faculties of a university are given as 168, 285, 397, 331, 383, 359, 366, 280 and 369 Find the mean number of students per Faculty
The mean number of students per Faculty is 326.
What is mean?Mean simply means the average of a set of numbers.
In this case, the number of students in nine faculties of a university are given as 168, 285, 397, 331, 383, 359, 366, 280 and 369. The mean will be:
= Total values / 9
= (168 + 285 + 397 + 331 + 383 + 359 + 366 + 280 + 369) / 9
= 2938 / 9
= 326.44
The mean is 326.
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