Select the correct responses in the table.
The relationship between two numbers is described below, where xrepresents the first number and y represents the second number.
The square of the first number is equal to the sum of the second number and 16. The difference of 4 times the second number and 1 is equal to
the first number multiplied by 7.
Select the equations that form the system that models this situation. Then, select the solution(s) of the system.
Equations
y² +16=x
x²=y+16
1-4y=7x
(2x)² =y+16
7y-1=4x
4y-1 =7x
(1,15)
(2.-12)
Solutions
(5,9)
(8,48)
(9,3)
Answers
The system that can help to model this are
x² = y + 164y - 1 = 7xHow to solve for the system of equationWe have the following equation. Remember that a good understanding of the question is what would help us to write the equation
The condition says:
The square of first number is equal to the sum of the second number and 16:
First number = x. Square of x = x²
second number = y + 16
For the second
The difference of 4 times the second number and 1 is equal to the first number multiplied by 7:
second number is y
4*y - 1= x*7
= 4y - 1 = 7x
Hence we would have the following as our equations
x² = y + 16
4y - 1 = 7x
The solution to the equation when graphed = 5, 9
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Related Questions
Building managers recently surveyed employees of three different companies regarding their method of transportation to work day. The results of the survey are shown in the two-way frequency table below.
Car Bus Walk Bike Subway Total
Tech company 10 16 14 38 20 98
Law firm 27 8 10 2 26 73
Finance group 18 22 12 8 34 94
Total 55 46 36 48 80 256
Which Conclusion can the building managers draw based on this data?
A: It is more common to find a bus rider who works at the tech company than a person on the subway who works at the law firm.
B: Walking to work is more common among employees at the finance group than employees at the law firm.
C: The percentage of walkers who are employers at the law firm is the same as the percentage of car drivers who are employees at the tech company.
D: Riding to work is more common among tech company employees than at the other modes of transportation.
Answers
The conclusion that the building managers can draw based on the given data is; D: Riding to work is more common among tech company employees than at the other modes of transportation.
How to Interpret Data Tables?The results of the survey are shown in the two-way frequency table below.
From the table we can see that;
Total Cars = 55
Total Number of Buses = 46
Total Number of Walks = 36
Total Number of Bikes = 48
Total Number of Subways = 80
Total Number of Tech company = 98
Total Number of Law Firms = 73
Total Number of Finance Groups = 94
Option A; There are 16 people who use buses from the tech company while there are 26 people who use subway from the Law firm. Thus, the statement is false.
Option B; There are 12 people who walk to work at the finance group while there are a total of 10 people who walk to work at the law firm. Thus the statement is false.
Option C; Percentage of walkers at law firm = 10/73 * 100% = 13.7%
Percentage of car drivers at the tech firm = 10/98 * 100% = 10.2%
Thus, the statement is false
Option D; This is true
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Answer:
It is more common to find a bus rider who works at the tech company than a person on the subway who works at the law firm.
Step-by-step explanation:
got it right on edmentum
Someone help me please
45-45-90 triangles
Answers
Answer:
Side AB = [tex]9\sqrt{2}[/tex]
Side AB = [tex]9\sqrt{2}[/tex]
Side CB = 36
Step-by-step explanation:
This is a special right triangle and it's also an isosceles triangle
therefore the measure of AC = AB and they are both = [tex]9\sqrt{2}[/tex]
for this special triangle the measure of hypotenuse (CB in here) is represented with [tex]x\sqrt{2}[/tex] and the legs are represented with x, each
since legs' lengths are given as = [tex]9\sqrt{2}[/tex] then x = [tex]9\sqrt{2}[/tex]
replace the x in front of [tex]x\sqrt{2}[/tex] with [tex]9\sqrt{2}[/tex]
[tex]9\sqrt{2}[/tex] * [tex]\sqrt{2}[/tex] = 36
Find the slope when y2=9, y1=13, x2=4, and x1=0.
Answers
Answer:
Formula=√(x2-x1)²+(y2-y1)² =√(4-0)²+(9-13)2 =√16+16 =√32
Answer: slope=-1
Step-by-step explanation:
9-13 -4
------ --------- -4/4=-1
4-0 4
PLS HELLP ITS SO HARD
Answers
Answer:
[3,0]
[0,9]
Step-by-step explanation:
9x+3y=27
9x+3(0)=27
9x=27
x=3
9(0)+3y=27
3y=27
y=9
A choir has 3 spots open for altos, and 8 altos are interested in them. in how many ways can the open spots be filled? 24 56 112 336
Answers
Answer:
56
Step-by-step explanation:
combinations
C(8,3)
What is the euclidean distance between x(3,2,5) and y(2,3,3) in three dimensional space?
a) 4
b) 2. 45
c) 3
d) 1. 5
Answers
Answer:
b) 2.45
Step-by-step explanation:
The Euclidean distance in 3-space is the root of the sum of the squares of the x-, y-, and z-differences between the points.
ApplicationFor the given points ...
[tex]x(3,2,5)=(x_1,y_1,z_1)\quad\textsf{and}\quad y(2,3,3)=(x_2,y_2,z_2)[/tex]
The distance between x and y is ...
[tex]d=\sqrt{(x_2-x_1)^2+(y_2=y_1)^2+(z_2-z_1)^2}\\\\d=\sqrt{(2-3)^2+(3-2)^2+(3-5)^2}=\sqrt{1+1+4}\\\\d=\sqrt{6}\approx2.45[/tex]
The degrees of freedom for a chi-square test applied to a cross-tabulation with 5 rows and 2 columns is equal to:
Answers
The degrees of freedom for a chi-square test applied to a cross-tabulation with 5 rows and 2 columns is equal to 6
How to determine the degrees of freedom applied to a cross-tabulation ?The given parameters are:
Rows = 5
Column = 2
The degrees of freedom is then calculated as:
df = Rows + Column - 1
Substitute the known values in the above equation
df = 5 + 2 - 1
Evaluate the expression
df = 6
Hence, the degrees of freedom for a chi-square test applied to a cross-tabulation with 5 rows and 2 columns is equal to 6
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3 tons of sawdust cost $5,700.00. What is the price per pound?
$
Answers
Answer:
$0.95/lb
Step-by-step explanation:
1 ton = 2000 lb
3 tons = 3 × 1 ton = 3 × 2000 lb = 6000 lb
$5700/(6000 lb) = $0.95/lb
Answer: $0.95/lb
Step-by-step explanation:
3 tons = 6000 pounds
Therefore, using ratio and proportion rules,
6000/5,700 = 1/x
x = 5700/6000 = 0.95
The price is $0.95, or 95 cents per pound.
If the graph of a budget function has an x-intercept at 2 and the y-intercept at 5, name two ordered pairs that would fall on this line.
(2, 0) (0, 5)
(0, 2) (5, 0)
(2, 0) (2, 5)
(0, 2) (2, 5)
Answers
Based on the graph of the budget function with the x-intercept and the y-intercept, the two ordered pairs that would fall on this line are (2, 0) (0, 5).
What points fall on this line?The x-intercept is the point on the graph where the budget function would cross the x-intercept.
At this point, the value of y would be 0 because the x-axis intersects the y-axis at y = 0.
An x-intercept of 2 would therefore have the point, (2,0).
The y-intercept would be the point where the y axis is crossed. At this point, x will be zero because the y-axis intercepts the x-axis at the value, x = 0.
A y-intercept of 5 would therefore yield a point of (0, 5).
In conclusion, option A is correct.
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LK=
Help please asap thx so much
Answers
Answer:
LK = 4[tex]\sqrt{2}[/tex]
Step-by-step explanation:
given point J (4, 4 )
then LJ = 4 and JK = 4
using Pythagoras' identity in right triangle LJK
LK² = LJ² + JK² = 4² + 4² = 16 + 16 = 32 ( take square root of both sides )
LK = [tex]\sqrt{32}[/tex] = [tex]\sqrt{16(2)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{2}[/tex] = 4[tex]\sqrt{2}[/tex]
6. Solve the system of equations.
x = 3y + 1
2x+4y= 12
O (10,3)
O (4,1)
(1,4)
(3,10)
Answers
Answer:
(4, 1 )
Step-by-step explanation:
x = 3y + 1 → (1)
2x + 4y = 12 → (2)
substitute x = 3y + 1 into (2)
2(3y + 1) + 4y = 12
6y + 2 + 4y = 12
10y + 2 = 12 ( subtract 2 from both sides )
10y = 10 ( divide both sides by 10 )
y = 1
substitute y = 1 into (1)
x = 3(1) + 1 = 3 + 1 = 4
solution is (4, 1 )
Line m contains the points (4, 16) and (0, 8). At what point will line m intersect with line n if the equation of line n is -8x+4y=24 ?
A) (0, 0)
B) (-4, 0)
C) The lines don't intersect
D) The lines intersect at an infinite number of points
Answers
The correct option regarding the point at which the linear functions intersect is given by:
C) The lines don't intersect.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For line m, we have that the y-intercept is of b = 8. When x changes by 4, y changes by 8, hence the slope is of 2, and the equation is:
y = 2x + 8.
Line n, in slope-intercept format, is given by:
-8x + 4y = 24
4y = 8x + 24
y = 2x + 6
Hence:
2x + 8 = 2x + 6
0x = -2
Which is impossible, hence they do not intersect and option C is correct.
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Instead of recording the number 1.23 cm for the radius of 2 tube, a student recorded 1.32cm.find the percentage error, correct to 1.DP
Answers
= 0.09
Percentage error = (0.09/1.23)* 100
= 9/1.23
= 7.317
= 7.3% to 1 do
X
3.
What is the value of x to the nearest tenth?
6
24
Answers
Answer:
C. 13.4=======================
Connect the center with one end of the chord, this gives us a right triangle with hypotenuse of x, one leg of 6 and another leg of 24/2 = 12.
Use Pythagorean to find the value of x:
x² = 6² + 12²x² = 36 + 144x² = 180x = √180x = 13.4 (rounded)Correct choice is C.
Answer:
x = 13.4
Step-by-step explanation:
Definitions
Radius: a straight line from the center of the circle to its circumference.
Chord: a straight line joining two points on the circle.
Perpendicular: at a right angle (90°).
Isosceles triangle: a triangle with 2 sides of equal length and 2 congruent base angles.
From inspection of the given diagram:
radius = xchord = 24 unitssegment of the radius perpendicular to the chord = 6 unitsIf lines are drawn from the center of the circle to the endpoints of the chord, an isosceles triangle is created with base of 24 units and height of 6 units.
The isosceles triangle is made up of two right triangles with base of 12 units and height of 6 units. The radii are the hypotenuse of these right triangles. Therefore, to calculate the radius of the circle (x), use Pythagoras Theorem.
Pythagoras Theorem
[tex]\sf a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right trianglec is the hypotenuse (longest side) of the right triangleTherefore:
[tex]\sf \implies 6^2+12^2=x^2[/tex]
[tex]\implies \sf x^2=36+144[/tex]
[tex]\implies \sf x^2=180[/tex]
[tex]\implies \sf \sqrt{x^2}=\sqrt{180}[/tex]
[tex]\implies \sf x=\pm 6\sqrt{5}[/tex]
As length is positive:
[tex]\implies \sf x = 6\sqrt{5}=13.4\:units\:(nearest\:tenth)[/tex]
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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices.
Josiah’s Music
Sample 1
Sample 2
R & B
5
R & B
4
Pop
4
Pop
3
Classical
3
Classical
5
Jazz
2
Jazz
4
Rock
6
Rock
4
Josiah’s work:
StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x.
He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.
He did not multiply the numerator and denominator by the correct number to equal 1,500.
His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion.
He can only solve the proportion by multiplying the numerator and denominator by a common multiple.
He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Answers
Based on the number of songs in each genre that Josiah listened to, the statements about his solution that are true are:
He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.He did not multiply the numerator and denominator by the correct number to equal 1,500.He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.What did Josiah do wrong?To find the average of the number of rock songs, he should have taken the average of rock songs he listened to which were 4 and 6:
= (4 + 6) / 2
= 5
Because he has a total of 1,500 songs on his player, he should have multiplied both the numerator and denominator by a number that would lead to 1,500 which is 75 and not 30.
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The nth term of a sequence is given by 3n² + 11 Calculate the difference between the 6th term and the 9th term of the sequence.
Answers
The difference between the 6th term and the 9th term of the sequence is 135
How to determine the difference
Given that the nth term is;
3n² + 11
For the 6th term, the value of n is 6
Let's solve for the 6th term
= 3( 6)^2 + 11
= 3 × 36 + 11
= 108 + 11
= 119
For the 9th term, n = 9
= 3 (9)^2 + 11
= 3( 81) + 11
= 243 + 11
= 254
The difference between the 6th and 9th term
= 254 - 119
= 135
Thus, the difference between the 6th term and the 9th term of the sequence is 135
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There are 3 red, 1 blue, and 2 yellow marbles in a bag. Once a marble is selected, it is not replaced. Find P(red and the yellow).
Answers
Answer:
5/6
Step-by-step explanation:
we add all the marbles together to get 6
then we seperate the marbles according to the question which would be yellow and red. that would make the probability of getting one of those to 5/6. Hope this helps :)
ts
The table below represents the concessions sold at the last three basketball games. The
games were held on different days and times.
Friday night
Saturday morning
Tuesday night
Total
Candy Hot Dogs
148
94
78
320
102
27
150
279
Nachos
108
42
97
247
Total
358
163
325
846
What is the approximately probability of a person going to a Saturday morning game and
buying nachos?
Answers
The approximately probability that a person will go to the Saturday morning game and buy nachos is 18%.
What does approximate mean?Anything similar to something else but not precisely the same is called an approximation. By rounding, a number can be roughly estimated. An estimated result can be obtained by rounding the values in a computation before carrying out the procedures.The word type "approximately" is an adverb.A value that is close to, higher than, as close to, and with the specified level of precision is known as an approximation value by the excess of a number.Approximately symbol ≈.The approximately probability of a person going to a Saturday morning game and buying nachos:
Probabaility= [tex]\frac{150}{846} *100[/tex]
=17.7%
Approximately=18%.
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What is the next term in the geometric sequence below?
3, -6, 12, -24, __, ...
A. 36
B. -48
C. -36
D. 48
Answers
Answer:
48
Step-by-step explanation:
48 because you are multiplying it by -2 each time. -24 x -2 = 48
When the shape of a bst approaches that of a perfectly balanced binary tree, what is the worst case performance characteristic of searches and insertions?
Answers
The shape of a bst approaches that of a perfectly balanced binary tree, (log2n) is the time complexity for a balanced binary search tree in case of insertions and search.
In computing, binary bushes are mainly used for looking and sorting as they offer a way to save statistics hierarchically. a few common operations that may be conducted on binary trees encompass insertion, deletion, and traversal.
A binary tree has a special situation that each node could have a most of two youngsters. A binary tree has the benefits of each an ordered array and a linked listing as search is as brief as in a taken care of array and insertion or deletion operation are as fast as in related listing.
In pc science, a binary tree is a tree information shape in which every node has at maximum two youngsters, that are known as the left baby and the proper toddler.
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Consider the incomplete paragraph proof.
Because triangle XYZ is a right triangle, the side lengths
Given: Isosceles right triangle XYZ (45°-45°-90°
must satisfy the Pythagorean theorem, a? + b2 c2
triangle)
which in this isosceles triangle becomes a2 + a? = c?. By
Prove: In a 45°-45°-90° triangle, the hypotenuse is V2
combining like terms, 2a? c2.
times the length of each leg.
Which final step will prove that the length of the
hypotenuse, c, is /2 times the length of each leg?
• Substitute values for and c into the original
Pythagorean theorem equation.
O Divide both sides of the equation by two, then
determine the principal square root of both sides of the
equation.
Determine the principal square root of both sides of
the equation.
O Divide both sides of the equation by 2.
Answers
The hypotenuse is [tex]c = a\sqrt{2}[/tex] times the length of each leg 'a'. Triangle XYZ is a isosceles right triangle, therefore the Pythagoras theorem becomes and this can be evaluated by using properties of isosceles triangle.
According to the statement
we have given that a theorem and we have to prove it.
So, For this purpose,
The given information is :
Isosceles triangle XYZ where [tex]Angle X = 45^{0}[/tex] [tex]Angle Y = 45^{0}[/tex] [tex]Angle Z = 90^{0}[/tex]
Let the sides of triangle XYZ be a, b, and c. Then side XY = c, YZ = b and ZX = a.
Now, it is given that triangle XYZ is isosceles triangle therefore, the shorter sides must be equal that is, a = b.
Now use Pythagoras theorem
[tex]a^{2} + b^{2} = c^{2}[/tex]
But here a= b then the equation become
[tex]a^{2} + a^{2} = c^{2}[/tex]
Then after solving it become
[tex]2a^{2} = c^{2}[/tex]
And here we have to find the value of the hypotenuse,
so we solve it for c.
Then
[tex]c = a\sqrt{2}[/tex]
From this it is clear that the
it can be concluded that the hypotenuse is times the length of each leg 'a'.
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Solve the following quadratic equation for all values of a in simplest form.
5(x − 6)² — 29 = −19
Answers
Answer:
[tex]X1 = 6-\sqrt{2} , X2 = 6+\sqrt{2}[/tex]
Step-by-step explanation:
Answer: x= √2 + 6, - √2 + 6
Step-by-step explanation:
Suppose the circumference of a crop circle is 150.7968 hectometers (hm). What's the radius of the circle? (Use π = 3.1416.)
Answers
The radius of the circle is 24 hectometers.
How to get the radius of the circle?Remember that the circumference of a circle of radius R is given by the equation:
[tex]C = 2*\pi*R[/tex]
In this case, we know that the circumference is: C = 150.7968 hm
And π = 3.1416
Replacing that and solving for R, we get:
[tex]R = \frac{C}{2*\pi} = \frac{150.7968hm}{2*3.1416} = 24hm[/tex]
The radius of the circle is 24 hectometers.
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‼️‼️‼️‼️HELP‼️‼️‼️
Ron is 3 years older than Sherry, who is 4
years less than twice as old as John. Which of
the following represents Ron's age, if J = John's age?
Answers
Answer:
2J - 1
Step-by-step explanation:
Let J = John's age. Sherry is 4 years less than twice as old as John, so Sherry is 2J - 4 years old. Ron is 3 years older than Sherry, so Ron is 2J - 4 + 3 = 2J - 1 years old.
10x(4-3x) pls someone help???
Answers
Answer: [tex]\Large\boxed{-30x^2+40x}[/tex]
Step-by-step explanation:
Given expression
10x (4 - 3x)
Expand the parenthesis by distributive property
= 10x · 4 - 10x · 3x
= (10 × 4)x - (10 × 3) (x × x)
[tex]\Large\boxed{=-30x^2+40x}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Hi :)
We'll use distributive property to solve this
————————[tex]\LARGE\boldsymbol{10x(\hfill\stackrel{\hfill\stackrel{10x}\curvearrowright}4-\hfill\stackrel{\hfill\stackrel{10x}\curvearrowright}{3x)}}}[/tex]
Thus
[tex]\large\boldsymbol{10x\cdot4-3x\cdot10x}[/tex]
Simplify
[tex]\Large\boldsymbol{40x-30x^2}[/tex]
[tex]\tt{Learn~More;Work~Harder}[/tex]
:)
What steps do you use to solve y=x+12 and y=-x+17 an unknown number y is 12 more than an u known number x the number y is also x less than 17 the equations to find x and y are show
Answers
Answer:
x=2.5
Step-by-step explanation:
Solve for x in this systems of equations, we already have two values which equal y so half the work is finished for us.
Starting with the equation:
[tex]x+12=17-x[/tex]
Add x to both sides to remove the negative x on the right side of the equation:
[tex]2x+12=17[/tex]
Subtract 12 from both sides to remove the 12 on the left side of the equation:
[tex]2x=5[/tex]
Divide both sides by 2 to cancel out the x coefficient
[tex]x=2.5[/tex]
I need the answers with the explanation!
Answers
Answer:
you need all of them?
Step-by-step explanation:
A standard deck of cards contains 52 cards. There are four suits (spades, clubs, hearts, and diamonds) and thirteen of each suit (2-10, jack, queen, king, ace). One card is selected at random from the deck. What is the probability the card selected is an Ace or a heart?
Answers
The probability of selecting an ace or a heart when one card is drawn from 52 cards is 1/52.
Given that there are 52 cards in which there are 13 cards each for spades,clubs,hearts and diamonds.
We are required to find the probability of getting an ace or a heart when one card is drawn from 52 cards.
Probability is basically the chance of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative. The probability can be calculated through following formula:
Probability=Number of items/total number of items.
Number of hearts=13
Number of ace=4
Probability of getting an ace or a heart when one card is drawn=P(X=heart)*P(X=ace)
=13/52 * 4/52
=52/(52*52)
=1/52
Hence the probability of getting an ace or heart when one card is drawn from standard deck of cards is 1/52.
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You purchase one microsoft july $72 put contract for a premium of $1. 32. what is your maximum possible profit?
Answers
The maximum possible profit = $7068
For given question,
One Microsoft July $72 put contract for a premium of $1.32
The payoff arise from put option is max (K - S, 0) - P
Now it would be maximum at S = 0
And, the maximum payoff is
K - 0 - P
= K - P
= 72 - 1.32
= $70.68
We assume that for each and every contract the number of shares is 100
So, the maximum profit gained from this strategy is
= $70.68 × 100 shares
= $7068
The maximum profit that will be gained from this strategy is $7068
Therefore, the maximum possible profit = $7068
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what is 4^-2. ................................
Answers
Answer:0.0625
Step-by-step explanation:
Answer:
1/16.
Step-by-step explanation:
4 ^-2 = 1 / 4^2
= 1/16.