The relation is not a function it is not a function because there are multiple y-values paired with a single x-value. Option B.
Is the relation a function?A relation is a function only if every input is mapped into a single output.
Here we have the relation {(3,7), (3,8), (3,-2), (3.4),(3,1)}
Remember that the first number of each pair is the input, so we can see that all the inputs are the same one
So the input x = 3 is mapped into different outputs, thus, this is not a function.
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The correct option is B) it is not a function because there are multiple y-values paired with a single x-value.
To determine if a relation is a function, one must check if each x-value is associated with exactly one y-value. In other words, for every x, there should be one and only one y. This is known as the vertical line test in the context of graphs.
Let's examine the given set of ordered pairs: {(3,7), (3,8), (3,-2), (3,4), (3,1)}.
We can see that the x-value of 3 is repeated with different y-values: 7, 8, -2, 4, and 1.
This means that the x-value of 3 is associated with multiple y-values, which violates the definition of a function.
Therefore, the relation is not a function because it fails to satisfy the condition that each x-value must correspond to exactly one y-value.
The presence of multiple y-values for a single x-value is the key indicator that the relation is not a function.
Glenn has a beginning balance of $840 in his checking account. He has a deposit of $375 and withdraws $250 from the ATM. If the ATM fee is $3, what is his new balance?
$718
$212
$962
$572
Marcus solved for x in the quadratic equation x2 – 10x + 25 = 0.
Answer:
Option 1,3 and 4 are correct.
Step-by-step explanation:
Given is a quadratic equation
[tex]x^2-10x+25=0[/tex]
Marcus used quadratic formula to solve this
The correct use of formula is
[tex]\frac{-b+/\sqrt{b^2-4ac} }{2a}[/tex]
for the quadratic equation [tex]ax^2+bx+c=0[/tex]
Comparing we have a =1, b =-10: c=25
The student should have substituted -10 for b but he wrong did only 10
II option is wrong since 2 is substituted correctly
III option is right -4ac i.e. the product x 4 must have been subtracted
IV option is right since repeated root is there so only one solution
What is 7/50 in decimal form?
Question 1: Describe how you would use the distributive property to simplify (39 x 5). Question 2: Your best friend tells you the solution of 375 = x - 28 is 347. Explain your best friend's error.
What is the result of isolating y2 in the equation below?
(x - 2)^2 + y2 = 64
A. y2 = -x2 + 4x + 60
B. y2 = -x2 + 4x + 4
C. y2 = 64 - x2
D. y2 = x2 + 4x + 60
Answer with explanation:
The given equation which represents a circle having center at, (2,0) and radius =8 is,
[tex](x - 2)^2 + y^2 = 64\\\\y^2=64 - (x-2)^2\\\\y^2=64 - (x^2-4 x +4)\\\\ y^2=64 -x^2+4 x-4\\\\y^2=60+4 x-x^2[/tex]
Result of isolating y² in the equation below, gives
Option A
[tex]y^2=60+4 x-x^2[/tex]
Multiply. (x – 4)(x2 – 3x + 5) ...?
Answer:
Answer is
[tex]x^3-7x^2+17x-20 \\ [/tex]
Step-by-step explanation:
We need to find
[tex](x-4)(x^2-3x+5) \\ [/tex]
Using distribution rule.
[tex](x-4)(x^2-3x+5)=x^3-4x^2-3x^2+12x+5x-20\\\\(x-4)(x^2-3x+5)=x^3-7x^2+17x-20 \\ [/tex]
So the answer is
[tex]x^3-7x^2+17x-20 \\ [/tex]
There are 35 students going to the zoo each vans can hold 6 students how many vans are needed
Which is the better buy, 6 bagels for $3.29 or 8 bagels for $4.15?
A highway makes an angle of 6 with the horizontal. This angle is maintained for a horizontal distance of 5 miles.
To the nearest hundredth of a mile, how high does the highway rise in this 5-mile section? Show the steps you use to find the distance.
Within a specific stretch spanning 5 miles, the roadway inclines approximately 0.53 miles or 2771.64 feet, rounded to the nearest hundredth of a mile.
Trigonometric principles aid in determining the elevation gained by the highway over this distance.
Given:
An angle of ascent (θ) of 6 degrees and a horizontal distance (adjacent side) of 5 miles, our objective is to ascertain the vertical distance (opposite side).
Utilizing the tangent function in trigonometry:
[tex]\[ \tan(\theta) = \frac{{\text{{opposite}}}}{{\text{{adjacent}}}} \][/tex]
[tex]\[ \tan(6^\circ) = \frac{{\text{{height}}}}{{5}} \][/tex]
The calculation for the height is:
height = 5 × tan(6°)
Plugging in the values:
height ≈ 5 × 0.1051
height ≈ 0.5255 miles
To convert this to feet (1 mile = 5280 feet):
height ≈ 0.5255 × 5280
height ≈ 2771.64 feet
Thus, within this 5-mile segment, the roadway ascends approximately 0.53 miles or 2771.64 feet, rounded to the nearest hundredth of a mile.
The triangles below are similar. Find the value of x.
9
8
10.5
11
Factor the GCF first and then factor the trinomial: 2x2 + 20x + 50
A. 2(x + 5)(x + 5)
B. 2(x + 5)(x + 10)
C. 2(x + 2)(x + 25)
D. prime Factor the GCF first and then factor the trinomial: 2x2 + 20x + 50
A. 2(x + 5)(x + 5)
B. 2(x + 5)(x + 10)
C. 2(x + 2)(x + 25)
D. prime
Which is the largest religion in india? zoroastrianism hinduism daoism judaism?
Write the decimal 0.063 as a percent. Answer choices: 0.0063 0.063 0.63 6.3 MY ANSWER: 0.063
The decimal 0.063 can be represented as 6.3% in the percent form.
Thus, option (D) is correct.
Given decimal: 0.063.
As, to convert any decimal into the percentage then multiply the the decimal with 100.
So, to convert 0.063 to a percent multiply it by 100:
= 0.063 x 100
= 6.3
Therefore, 0.063 as a percent is 6.3%.
Thus, option (D) is correct.
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Straight-line depreciation is a method of calculating an asset’s value by subtracting its salvage value from its acquisition or purchase price divided by the estimated useful life of the asset. suppose a manufacturing robot cost $1.5 million in 2005 and is sold in 2010 for $50,000. what is the linear equation representing the value of the robot?
Answer:
Linear equation is V(t) = 1500 - 290t
Step-by-step explanation:
To find the linear equation representing the value of the robot we will calculate per year depreciation in the cost of the robot.
Rate of depreciation = [tex]\frac{\text{(Manufacturing cost in 2005-selling price in 2010)}}{5}[/tex]
= [tex]\frac{[(1.5)(10^{6})-50000]}{5}[/tex]
= [tex]\frac{(1500000-50000)}{5}[/tex]
= [tex]\frac{1450000}{5}=290000[/tex]
If depreciation is represented by V(t) (in $000) then equation will be
V(t) = 1500 - 290t
Simplify
sqrt(3 + 2 sqrt 2) ...?
Answer:
[tex]1+\sqrt{2}[/tex]
Step-by-step explanation:
We have been given a radical expression [tex]\sqrt{3+2\sqrt{2}}[/tex]. We are asked to simplify the given expression.
We will add [tex](\sqrt{2})^2-2[/tex] to our given expression as after adding and subtracting same quantity the value of our expression will be same.
[tex]\sqrt{3+2\sqrt{2}+(\sqrt{2})^2-2}[/tex]
[tex]\sqrt{3-2+2\sqrt{2}+(\sqrt{2})^2}[/tex]
[tex]\sqrt{1+2\sqrt{2}+(\sqrt{2})^2}[/tex]
Using perfect square formula [tex](a+b)^2=a^2+2ab+b^2[/tex] we can rewrite our expression as:
[tex]\sqrt{1^2+2\sqrt{2}\cdot 1+(\sqrt{2})^2}[/tex]
[tex]\sqrt{(1+\sqrt{2})^2}[/tex]
Applying radical rule [tex]\sqrt[n]{x^n} =x[/tex], we will get,
[tex](1+\sqrt{2})^{\frac{2}{2}}=1+\sqrt{2}[/tex]
Therefore, the simplified form of our given expression would be [tex]1+\sqrt{2}[/tex].
Erica bought 3 1/2 yards of fabric. If she uses 2/3 of the fabric to make a curtain, how much will she have left?
Final answer:
Erica will have 1 1/6 yards of fabric left after using 2/3 of the 3 1/2 yards she purchased to make a curtain.
Explanation:
The student's question is about how much fabric Erica will have left after using 2/3 of the 3 1/2 yards she bought to make a curtain. To solve this problem, we first need to convert the mixed number of yards of fabric to an improper fraction. We start by multiplying the whole number, 3, by the denominator of the fraction, 2, and then adding the numerator, 1. This gives us (3 × 2) + 1 equals 7, so Erica has 7/2 yards of fabric.
Next, we determine how much fabric she uses by multiplying 7/2 yards by 2/3. Doing the multiplication, (7/2) × (2/3), we can cancel out the common factor of 2 to simplify the calculation. The result is 7/3 yards of fabric used for the curtain.
To find out how much fabric is left, we subtract the used fabric from the total amount Erica originally had, which is 7/2 yards. So, we calculate 7/2 - 7/3 yards. To subtract these fractions, they need to have a common denominator. Multiplying 7/2 by 3/3 and 7/3 by 2/2 gives us equivalent fractions with a common denominator of 6. We now have (21/6) - (14/6) yards, and subtracting these gives us 7/6 yards of fabric remaining. This can also be represented as 1 1/6 yards, which is how much Erica will have left after making the curtain.
What is the converse of the following true conditional? If the converse is true, rewrite the statements as a bioconditional. If either is false, give a counter example. If two lines are parallel, they do not intersect
The converse of the statement 'If two lines are parallel, they do not intersect' is 'If two lines do not intersect, they are parallel', which is false. A counterexample to this converse is skew lines that do not intersect but are not parallel. Thus, we can't write both statements as a biconditional
Explanation:The subject of your question is regarding conditional statements and their converses in mathematics. A conditional statement is often expressed in the form: 'If p, then q', where p is a hypothesis and q is a conclusion. The converse of a conditional statement switches the hypothesis and the conclusion, i.e., 'If q, then p'.
In the context of your question, the conditional statement given is 'If two lines are parallel, they do not intersect'. The converse of this statement is 'If two lines do not intersect, they are parallel'. However, this converse is not true. A counterexample can be two lines that do not intersect but are not parallel because they are skew lines, which exist in three dimensions and do not lie in the same plane. Thus, the statements can't be written as a biconditional as one is not a valid conditional.
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what is the area of a park that is 100 yards square?
1,119.85 is estimate to what number
Will calculators or computers be needed to perform some calculations?
Answer:
yes
Step-by-step explanation:
When performing certain statistical calculations, finding roots, or working with powers, calculators or computers are necessary for the calculations; otherwise, more traditional methods will be sufficient.
Line segment AB has a length of 4 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A'B'. What is the length of A'B'?
Answer:
it 2 units
Step-by-step explanation:
Ariel wants to write 8 entries for her blog. After 2 hours, she has 5 entries left. After 4 hours, she has 2 entries left. Which graph represents Ariel's remaining entries?
graph of line going through (0, 0) with a slope of 1.5
graph of line going through (0, 2) with a slope of 2
graph of line going through (0, 8) with a slope of 1.5
graph of line going through (0, 3) with a slope of 3
Answer:
Graph of line going through (0, 8) with a slope of 1.5 represents Ariel's remaining entries
Step-by-step explanation:
Ariel wants to write 8 entries for her blog.
After 2 hours, she has 5 entries left. [tex](x_1,y_1)=(2,5)[/tex]
After 4 hours, she has 2 entries left. [tex](x_2,y_2)=(4,2)[/tex]
So, now using two point slope form:
[tex]y-y_1=m(x-x_1)[/tex] ---1
where [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
So , substituting the given points we get the equation that represents the given situation .
[tex]m = \frac{2-5}{4-2}[/tex]
[tex]m = \frac{-3}{2}[/tex]
[tex]m = -1.5[/tex]
Now,
[tex]y-5 = -1.5(x-2)[/tex]
[tex]y-5 = -1.5x+3[/tex]
Thus the slope of the given situation is 1.5
Now at x = 0
[tex]y-5 = -1.5*0+3[/tex]
[tex]y=8[/tex]
So, at 0 hour 8 entries left .
So, graph of line going through (0, 8) with a slope of 1.5 represents Ariel's remaining entries
what is 999 divided by 3
The manager of a convenience store wishes to determine how many cartons of eggs are damaged in shipment and delivery. For ten shipments of 1000 cartons of eggs, she examines every 50th carton to see how many cartons contain cracked eggs.
How large is the sample?
a.200 cartons
b.the 50th carton
c.1000 cartons
d.cannot determine from this information
Answer:
Option a is correct
200 cartons is the sample size
Step-by-step explanation:
As per the statement:
For ten shipments of 1000 cartons of eggs, she examines every 50th carton to see how many cartons contain cracked eggs.
First examine how many cartons are examined per shipment.
For every 50th cartons, 1 are examined
For every 100th cartons, 2 are examined
then;
For 1000 cartons , we have 20 are examined.
Examined per shipment = 20 cartons
We have to find how large is the sample.
Since, there are total 10 shipment
then;
For 10 shipment, we have
[tex]20 \times 10 = 200[/tex] cartons
Therefore, 200 cartons is the sample size
ryan makes 6 backpacks he uses 3/4 of cloth to make each backpack what is the total amount cloth ,in yards ryan use to make all 6 backpacks
Answer:
Ryan use 4. 50 yards of cloth to make 6 backpack.
Step-by-step explanation:
Given : ryan makes 6 backpacks he uses 3/4 of cloth to make each backpack.
To find : what is the total amount cloth ,in yards ryan use to make all 6 backpacks.
Solution : We have given that
Ryan make a backpack to use = [tex]\frac{3}{4}[/tex] of a cloth.
Ryan make such 6 backpack = [tex]6*\frac{3}{4}[/tex]
= [tex]\frac{18}{4}[/tex] .
= 4. 50 yards.
Therefore, Ryan use 4. 50 yards of cloth to make 6 backpack.
1) The data in the table below represents the pressure of the gas as the temperature changes. Plot a graph of the data, using the space below. Draw a trend line and calculate its slope. How are the variables related? What will he pressure of the gas be at 0C?
the graph looks like this
Temperature Pressure
10 723
25 763
40 800
55 845
80 900
Answer:
The pressure of the gas 0°C is about 699.
Step-by-step explanation:
The given table of values is
Temperature Pressure
10 723
25 763
40 800
55 845
80 900
The general form of a trend line is
[tex]y=a+bx[/tex]
where, b is slope and a is y-intercept.
[tex]b=\frac{\sum_{i=1}^nx_iy_i-n\overline{x}\overline{y}}{\sum_{i=1}^nx_i^2-n\overline{x}^2}[/tex]
[tex]a=\overline{y}-b\overline{x}[/tex]
Using graphing calculator, we get
[tex]a=699.006826[/tex]
[tex]b=2.552218[/tex]
The equation of line of best bit is
[tex]y = 2.552218x + 699.006826[/tex]
where, y is pressure at x°C.
We need to find the pressure of the gas at 0°C.
Substitute x=0 in the above equation.
[tex]y = 2.552218(0) + 699.006826[/tex]
[tex]y =699.006826[/tex]
[tex]y \approx 699[/tex]
Therefore the pressure of the gas 0°C is about 699.
Please help 3 questions will Upvote
1.Write the equation of a line with a slope of 3 and a y-intercept of 1.
y = x + 3
y = 3x + 1
3x + y = 1
x + 3y = 1
2.Write the equation of the line that passes through (1, 3) and has a slope of 2 in point-slope form.
y – 1 = 2(x – 3)
y – 3 = 2(x – 1)
x – 1 = 2(y – 3)
x – 3 = 2(y – 1)
3.Write the equation of the line that passes through (–2, 6) and (2, 14) in slope-intercept form.
y = 2x – 2
y = 2x + 10
y = 0.5x + 7
y = 0.5x – 4
carl is paid $10 plus $8 an hour he was paid $66 how many hours did he work?
jill sold half her comic books then bought 16 more she now has 36 how many did she start with? help me plz ...?
The function c(x)=35x+75 r
If the repair took 5 hours, the total cost would be $250.
To find the total cost if the repair took 5 hours, we need to evaluate the function[tex]\(C(x)\) at \(x = 5\).[/tex]
Given that [tex]\(C(x) = 35x + 75\),[/tex] we substitute [tex]\(x = 5\)[/tex] into the function:
[tex]\[C(5) = 35 \times 5 + 75\]\[C(5) = 175 + 75\]\[C(5) = 250\][/tex]
So, if the repair took 5 hours, the total cost would be $250.
Complete correct question:
The function C(x) = 35x + 75 represents the labor cost (in dollars) for Bob's Auto Repair to replace our alternator, where x is the number of hours of labor. What would be the total cost if the repair took 5 hours?