The answers are as follows -
Relation 3y=x represents direct variation.Relation {(2,6),(3,9),(5,15)} represents direct variation.Relation - {(1,16),(2,8),(4,4)} reflects inverse relation.What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
Given are the following relations -
3y = x
{(2,6),(3,9),(5,15)}
{(1,16),(2,8),(4,4)}
We can write -
x = 3y
as
y = (1/3)x
m = 1/3
Relation 3y=x represents direct variation.
For the relation - {(2,6),(3,9),(5,15)}, we can write -
We can write it as -
y = 3x
Relation {(2,6),(3,9),(5,15)} represents direct variation.
For the relation - {(1,16),(2,8),(4,4)} , as [x] increases, [y] decreases, so it is a inverse relation.
Therefore -
Relation 3y=x represents direct variation.Relation {(2,6),(3,9),(5,15)} represents direct variation.Relation - {(1,16),(2,8),(4,4)} reflects inverse relation.To solve more questions on proportional relationship, visit the link below-
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[tex]\left \{ {{y=x^2+x-1} \atop {y + 2 x = 3}} \right.[/tex]
Solve the following system of equations algebraically or by graphing, and give the answer as points. Which method did you pick and why?
How could you check your answer afterwards?
Solving the system of equations using the algebraic method gives x = 1 or x = -4
How to solve the system of equations algebraically?Given: y = x²+x-1 and y+2x=3
In order to solve the system of equations algebraically
First, rewrite y+2x=3 to make y the subject:
y = 3-2x
Then, equate the two y of the equations and solve for x:
x²+x-1 = 3-2x
x²+x-1-3+2x = 0
x²+3x-4 = 0 (factorize)
x²+4x-1x-4 = 0
(x-1)(x+4) = 0
x-1 = 0 or x+4 = 0
x = 1 or x = -4
Therefore, the solution of the system of equations is x = 1 or x = -4
I pick the algebraic method because it is easier, faster and more accurate
I can check my answer by substituting the values of x into the equation
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Answer:
(-4, 11) and (1, 1)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=x^2+x-1\\y+2x=3\end{cases}[/tex]
The solutions to the given system of equations are the points of intersection of the two graphs.
To solve the given system of equations algebraically, first rearrange the second equation to make y the subject:
[tex]\implies y=3-2x[/tex]
Substitute the found expression for y into the first equation:
[tex]3-2x=x^2+x-1[/tex]
Rearrange to a quadratic equation and factor:
[tex]x^2+3x-4=0[/tex]
[tex]x^2+4x-x-4=0[/tex]
[tex]x(x+4)-1(x+4)=0[/tex]
[tex](x+4)(x-1)=0[/tex]
Apply the zero-product property to solve for x:
[tex](x+4)=0\implies x=-4[/tex]
[tex](x-1)=0\implies x=1[/tex]
To find the y-values of the solutions, substitute the found x-values into the rearranged second equation:
[tex]x=-4 \implies y=3-2(-4)=11[/tex]
[tex]x=1\implies y=3-2(1)=1[/tex]
Therefore, the solutions to the given system of equations are:
(-4, 11) and (1, 1)Find the measurement of V.
Answer:
60°
Step-by-step explanation:
As we can conclude from the equal measured side lengths, this is an equilateral triangle so all angles have equal measurement.
Since the sum of interior angles in a triangle is equal to 180 to find the measure of angle V we need to divide 180 by 3:
180 ÷ 3 = 60
From a set of whole numbers less than 25, what is the probability of getting a number either divisible by 5 or
divisible by 3?
A.) 3/5
B.) 14/25
C.) 1/5
D.) 11/25
From a set of whole numbers less than 25, the probability of getting a number either divisible by 5 or divisible by 3 is 11/25
The set of whole numbers = {0, 1,2,3,4,5.....}
The set of whole numbers less than 25 = {0,1,2,3,4,......,24}
The numbers divisible by 5 = {5, 10, 15, 20}
The numbers divisible by 3 = {3, 6, 9, 12, 15, 18, 21, 24}
The common term is 15
The probability = Number of favorable outcomes / Total number of outcomes
The number of favorable outcome = 11
Total number of outcomes = 25
Substitute the values in the equation
The probability = 11/25
Hence, from a set of whole numbers less than 25, the probability of getting a number either divisible by 5 or divisible by 3 is 11/25
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Find the value of x in the triangle below:
The value of x in the given triangle is x = 12 .
Angle Sum Property of the Triangle states that the sum of measure of all three sides of the triangle is 180° .
In the question ,
a triangular figure is given
in which , the measure of angle A is (6x - 19)°
the measure of angle B is [tex]=[/tex] 84°
the measure of angle C is [tex]=[/tex] (3x + 7)°
So , By Angle sum property ,
we get
∠A + ∠B + ∠C [tex]=[/tex] 180°
substituting the values of angle A, B and C ,
we get
(6x - 19)° [tex]+[/tex] 84° + (3x + 7)° [tex]=[/tex] 180°
6x - 19 [tex]+[/tex] 84 [tex]+[/tex] 3x + 7 [tex]=[/tex] 180
9x + 72 = 180
9x = 180 - 72
9x = 108
x = 108/9
x = 12
Therefore , the value of x is [tex]=[/tex] 12
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a grocery store has an average sales of $7,100 per day. the store introduced several advertising campaigns in order to increase sales. to determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 100 days of sales was selected. it was found that the average was $7,275 per day. from past information, it is known that the standard deviation of the population is $1,500. we know that the test statistic is 1.1667. find the p-value.
The P value of the question in the given condition is less than 0.05 hence it reject the null hypothesis.
What is null hypothesis?According to the null hypothesis, an independent variable and a dependent variable have no association with one another. The results might be the result of an experimental or sampling error if the hypothesis indicates a link between the two factors. There is a relationship in the measured phenomena, but, if the null hypothesis is incorrect.
First we find the value of small z
z = (x - μ) / (α / [tex]\sqrt{100}[/tex])
z = (7275 - 7100) / (1500/[tex]\sqrt{100}[/tex])
z = (175) / 150
z = 1.1667
As we have verified the test statistic value and it matched.
Then,
P value approach
Hence P value must be equal to 0.0013
As p value is less than 0.05 , Reject the null hypothesis.
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Write the equation of the line that passes through the points (8, –1) and (2, –5) in standard form, given that the point-slope form is y + 1 = (x – 8).
x +
y
The equation in standard form is x - y = 9
How to determine the equation in standard form?From the question, we have the following parameters that can be used in our computation:
Points = (8, –1) and (2, –5)
Point-slope form is y + 1 = (x – 8).
Recall that the point-slope form is y + 1 = (x – 8).
So, we have
y + 1 = (x – 8)
Open the brackets
y + 1 = x – 8
Subtract 1 from both sides
y = x - 9
Rewrite as
-x + y = -9
Multiply through by -1
x - y = 9
Hence, the equation is x - y = 9
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What are the coordinates of the centroid of a triangle with vertices X(−4, 0) , Y(−1, 4) , and Z(2, 2) ?
Enter your answer by filling in the boxes.
(
,
)
The coordinates of the centroid of a triangle with vertices X(−4, 0) , Y(−1, 4) , and Z(2, 2) is; (x, y) = (-1, 2)
What are the coordinates of the triangle centroid?Centroid of a Triangle states that the center of the triangle can be calculated as the point of intersection of all the three medians of that same triangle, and that this median is a line drawn right from the midpoint of one side to the opposite vertex.
We are given the coordinate of the vertices of the triangle as;
X(−4, 0) , Y(−1, 4) , and Z(2, 2)
Now, the formula to find the coordinates of the centroid of the triangle is; (x, y) = (x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3
Thus, the coordinates of the Centroid is;
(x, y) = (-4 + (-1) + (2))/3, (0 + 4 + 2)/3
(x, y) = (-1, 2)
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in a multiple regression problem involving two independent variables, if b1 is computed to be 2.0, it means that
In a multiple regression problem involving two independent variables, if b1 is computed to be 2.0, it means that For every unit increase in x1, the predicted mean of Y rises by 2 units holding [tex]x_{2}[/tex] constant.
Given data,
Slope b1 = +2
Mutiple regression which means,
Use multiple linear regression to determine the relationship between two or more independent variables and one dependent variable.
The value of the dependent variable at a specific level of the independent variables (For instance, the crop's anticipated yield at specific levels of temperature, rainfall, and fertilizer application).
[tex]y = b_{0} +b_{1}x_{1}+b_{2}x_{2}+b_{3}x_{3}+....[/tex]
[tex]b_{1}[/tex]=2 means
The estimated mean of Y increases by 2 units for each increase of 1 unit of [tex]x_{1}[/tex], holding [tex]x_{2}[/tex] constant.
Hence, the expected mean of Y increases by two units for every unit increase in x1.
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10. Coach deposits $4250 in the bank and gets 2.3% simple interest. He keeps the money in the
bank for 42 months without any deposits or withdrawals. How much money will he have in the
bank after 42 months? Round to the nearest cent.
With the help of some mathematical operations, we can conclude that after 42 months, coach will have a total amount of $8,356 in his bank account.
What exactly are mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.The order of operations is a rule that outlines the proper steps to take when analyzing a mathematical equation.We can recall the PEMDAS steps in the following order: Parentheses, Exponents, Multiplication, Division (from Left to Right), Addition, and Subtraction (from left to right).So, we know that coach gets 2.3% simple interest monthly.
Now, calculate the total amount after 42 months as follows:
4250/100 × 2.3 = $97.75Then, on monthly basis, the coach gets $97.75 as interest.
Then, for 42 months:
97.75 × 42 = $4,105.5Hence, the total amount after 42 months:
4250 + 4,105.5 = $8,355.5Rounding off: $8,356Therefore, with the help of some mathematical operations, we can conclude that after 42 months, coach will have a total amount of $8,356 in his bank account.
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Correct question:
Coach deposits $4250 in the bank and gets 2.3% simple interest monthly. He keeps the money in the bank for 42 months without any deposits or withdrawals. How much money will he have in the bank after 42 months? Round to the nearest cent.
Joh rent a kayak at a nearby tate park. He pay a fee of 12. 99 plu 3. 75 for each hour that he pend in the water. How much did Joh pend if he wa on the river 4 1/2 hour
The total amount Joh spend when he was in the river for 4(1/2) hours is 29.865.
Given, Joh rent a kayak at a nearby state park.
He pay a fee of 12.99 plus 3. 75 for each hour that he spend in the water.
We have to find the amount he spend when he was in the water for 4(1/2) hours.
Total amount = 12.99 + hourly amount
Hourly amount = 3.75×4(1/2)
Hourly amount = 3.75×9/2
Hourly amount = 16.875
Total amount = 12.99 + 16.875
Total amount = 29.865
Hence, the total amount Joh spend when he was in the river for 4(1/2) hours is 29.865.
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When parallel lines are cut by a transversal, then
Answer:
If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
What is the least common multiple of 8, 29, and 22?
Answer:
1
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Write an expression to represent:
8 less than the product of 2 and x.
Answer:
(2x)-8 is the correct answer
Step-by-step explanation:
Hope this helps
Compare the graph of -6 ≤ x ≤-4 with the graph of x ≤-6 or x ≥-4.
Answer: By compare the graph of -6 ≤ x ≤-4 with the graph of x ≤-6 or x ≥-4 we can see that in first graph value is x belongs to [-6,-4] and in second graph we can see that x belongs to (-∞,-6] ∪ [-4,∞)
What does a coordinate mean in math?
a pair of values used to specify a point's position on a coordinate plane using the horizontal and vertical breakups from the two reference axes. typically represented by the pair of x-values and y-values (x,y).
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At a math convention, nine out of eleven people are bored by cable news. If there 122 at the convention who are not bored by cable news, then how many people at the convention are bored by cable news?
A total of 549 of people at the convention are bored by the cable news
How to determine the number of people at the convention that are bored?From the question, we have the following parameters that can be used in our computation:
Not bored = 122
Bored = 9/11 of the people
This means that
Not bored = 1 - Bored
So, we have
Not bored = 1 - 9/11
Evaluate
Not bored = 2/11
Recall that Not bored = 122
So, we have
2/11 * x = 122
Where x = the number of people
This gives
x = 122 * 11/2
Evaluate
x = 671
Recall that
Bored = 9/11 of the people
So, we have
Bored = 9/11 * 671
Evaluate
Bored = 549
Hence, the number of people at the convention that are bored is 549
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the mean of a population of iq scores is 100. what is the mean of the distribution of sample means for samples of size 64?
The mean of the distribution of sample means is 100.
Considering the values provided in the question,
Population mean = 100
We know that,
The sample mean is a reliable indicator of the population mean.
That is, E( sample mean)=Mean(sample mean)= population mean
Here population mean is 100, therefore mean of distribution of sample means is also 100.
The total of all the values in a sample is known as the Sample Mean. It is a statistical metric used to examine different variables throughout time. It is calculated by statisticians and researchers by dividing the total sum of all data fragment values by the total number of data sets.
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What is the equation of the line that passes through the point (7,4) and has a slope of 1?
Answer:
y = x - 3
Step-by-step explanation:
Consider the equation "y = mx + b" :
y = mx + b
Since the slope is 1, you could input that into the equation:
y = (1)x + b
The variable "b" represents the y-intercept, therefore, to find the y - intercept, you would have to subtract 7 from each side of the coordinate points to get 0 as the x - coordinate to find the y - intercept:
(7 4)
-7 || -7
(0, -3)
Therefore, the y - intercept would be -3 and the equation would be:
y = x - 3
PLEASEE HELP ME !! Find the volume of each shape and then compare do not reduce your fractions.
Answer:
1.) 150/512 in.
2.) 64/125 in.
Step-by-step explanation:
1.) V = l x w x h That's the formula to find the volume of a rectangle
V = 6/8 x 5/8 x 5/8 in. Plug in the numbers
V = 150/512 in. Multiply
V = 75/256 in. Simplify
Since you're asked to not reduce don't write this answer. I only put it to show that it can be simplified.
2.) V = l^3 This is the formula to find the volume of a cube
V = (4/5)^3 in. Plug in the numbers
V = 64/125 in. Miltuply
PLEASE HELP plsssssss
A gigameter is 1.0×10^6 kilometers. How many square kilometers are in 5 square gigameters?
Write your answer in scientific notation.
The number of kilometers in 5 square gigameters is 5. 0 × 10^18
What is proportion?Proportion can be described as an expression or equation in which two ratios are made equal to each other.
It is also known as the mathematical comparison between two numbers or elements.
From the information given, we have;
1 gigameter = 1.0×10^6 kilometers
But,
5 square gigameters = 5. 1.0×10^6 . 1.0×10^6
Add the powers
5 square gigameters = 5..0×10^12
If 1 gigameter = 1.0×10^6 kilometers
Then 5. 1.0×10^12 gigameter = x
cross multiply
x = 5.0×10^12 × 1.0×10^6
x = 5. 0 × 10^18 kilometers
Hence, the value is 5. 0 × 10^18 kilometers
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Ms. Patel purchased some pliers, wrenches, and chisel sets for her shop. She bought twice as many pliers that cost $17. 50 each as wrenches that cost $21. 50 each. She bought 3 fewer chisel sets than pliers. How many of each tool did Ms. Patel buy if she paid a total of $141 and each chisel set costs $28?
NEED ASAP!
This comes to $141, indicating that Ms. Patel spent that money on four sets of pliers, two wrench sets, and a chisel set.
Define the meaning of the term ratios?A ratio is the relationship and comparison involving two numbers belonging to the same unit in order to determine how much larger one number is than the other.The given condition states that;
For her shop, Ms. Patel bought some sets of chisels, wrenches, and pliers. She purchased twice as many wrenches, which were $21.50 each, as she did pliers, which were $17.50 each. She purchased 3 fewer sets of chisels than pliers.Make a ratio first.
This ratio might be expressed as 4:2:1 (in pliers, wrenches, and chisels).
Then, multiply every one of these sums by their respective prices before adding them all up.
Pliers : 4 times 17.50 equals $70
Wrenches : $2 x $21.5 = $43
Chisels : 1 x 28 equals $28
Thus,
Sum = $70 + $43 + $28
Sum = $141
This amounts to $141, proving that she purchased a chisel set, two wrench sets, and four pairs of pliers.
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what is the future amount of 12,000 invested for 5 years at 14% compounded monthly?
Answer:
$24,067.32
Step-by-step explanation:
If you look up a compound interest calculator and put in the data correctly you should get $24,067.32
I need help like asap !!!
only numbers and decimal points
Answer:
b = 8 ft
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (10)² = b² + (6)²
→ 100 = b² + 36
→ b² = 100 - 36
→ b = √64
→ [ b = 8 ft ]
Hence, value of b is 8 ft.
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Maximum height of 32 feet after 1.25s
Step-by-step explanation:
2. Beth and Reena opened Basic Savings accounts on the same day. Reena's initial deposit was twice as much as Beth's. After 5 years, their combined interest earned was $21.00. What was the amount of Reena's initial deposit?
Answer:
Step-by-step explanation:
A=P(1+r/n)^nt
Let the Beth deposite is x.Here r and n will be 1.
A=x(1+1/1)^5
Similarly
B=2x(1+1/n)^nt
B=2x(1+1/1)^5
There combined interest is:
A+B=x(1+1/1)^5+2x(1+1/1)^5
21=32x+64x
21=96x
x=21/96 is the beth deposite.
2x=2*21/96 is the Reena deposite
How many inches are in 5 1/4 feet?
Answer: 63 inches
Step-by-step explanation:
Answer:
63 inches
Hope this helps :)
consider the matrix
what is the value of |C|
If the matrix C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex], then the determinant of the matrix |C| = -12
The given matrix is
C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex]
The matrix is defined as the set of numbers that arranged in rows and columns to form a rectangular array. The numbers in the matrix are called the elements of the matrix.
Here we have to find the determinant of the matrix C
The determinant of the matrix is defined as the scalar value calculated for a given square matrix.
The determinant of C is represented by |C|
Then,
C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex]
|C| = -6×4 - 6×-2
= -24 -(-12)
= -24 + 12
= -12
Hence, if the matrix C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex], then the determinant of the matrix |C| = -12
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Describe the relationship as parallel intersecting or skew AB or BC
Based on the image attached, the relationship are:
a). AB and BC - Both the segments are said to be perpendicular and they are intersecting at the point B.
b). AE and BF - Both segments are said to be parallel
c). EF and ED - Both are skew
d). Plane ABC and plane ABF - Both of the planes do intersect at point AB
e). Plane AED and plane BFC - Both of the given planes are known to be parallel
How do you know if lines are parallel intersecting or skew?if the ratio equality is accurate, parallel. If the lines are not parallel or if you can solve them as a system of simultaneous equations, the lines will intersect. If two crossing lines have a zero dot product, they are perpendicular.
If the lines are not parallel or intersecting, they are said to skew. Lines that are parallel never cross.
Therefore,
if lines are in the same plane, do not intersect, and are parallelif lines only meet at one point, then they are intersecting.If lines are on two distinct planes and don't intersect, they skew.Learn more about parallel intersection from
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Use number properties to simplify the following expression.
-5 + (5 + 3)
In the box below, show each step in simplifying the expression and explain which property you used in each step.
Please help me!
Also please try to make the answer as clear as you can. Thank You! <3
Answer: 3
I used PEMDAS in this explanation: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. Also known as the order of operations
Step-by-step explanation:
-5 + (5+3) :
First, add 5+3 =8
-5+8
When adding a negative to a positive, first, switch the -5 and 8 around like so.
8 + (-5)
then turn the -5 into it's opposite and subtract ---> 5
8-5=3
Unworded explanation:
-5 + (5+3) :
-5 + 8
8 + (-5)
8-5 = 3
∠1 ​ and ∠2 are complementary. m∠1=x°m∠2=(3x 30)° what is the value of x? select from the drop-down menu to correctly answer the question.
The value of x is 15
If two angles sum to 90 degrees, they are said to be complimentary angles. In other terms, a right angle is created when two complementary angles are combined (90 degrees). If the sum of angles 1 and 2 equals 90 degrees (i.e., angle 1 plus angle 2 = 90°), then the angles are complementary and are referred to as one another's complements.
∠1 and ∠2 are complementary angles i.e the sum of ∠1 and ∠2 is 90° .
Thus
∠1 + ∠2 = 90°
x° + (3x+30)° = 90°
x + 3x + 30 = 90
4x = 90-30
4x = 60
x = 15
Therefore the value of x is 15.
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