7. Determine the midpoint
a) A (-4,6) B (2,-3)
The coordinates of the midpoint of line segment A (-4,6) and B (2,-3) is M (-1 , 3/2).
What is a line segment?A line segment is a measurable route between two points. Line segments can make up any polygon's sides because they have a set length.
Given:
Points A (-4,6), and B (2,-3)
Calculate the midpoint of the line segment by the formula given below,
[tex]M [(x_1 + x_2) / 2 \ \ , (y_1 + y_2)/2][/tex]
Substitute the values,
M [(-4 + 2) / 2 , (6 + (-3) / 2)]
M [(-2 / 2) , (3 / 2)]
M (-1 , 3/2)
Therefore, the coordinates of the midpoint of line segment A (-4,6) and B (2,-3) is M (-1 , 3/2).
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X-Y=4
-2X+6(4-X)=3
-8X+24=3
-24 -24
-8X=-21
X=21/8
Y=11/8
(21/8,11/8)
find the error in the problem.
Answer: You did wrong at Y=11/8! It should be -11/8, not positive 11/8
Step-by-step explanation:
You solved it all right; just the y is wrong! The reason why y is -11/8 is that a negative and a negative will make a positive, and add an x positive, and you will get a positive answer. If y is negative, the answer would be negative!
Ruby and her children went into a movie theater and she bought $42 worth of bags of popcorn and drinks. Each bag of popcorn costs $6 and each drink costs $4. She bought a total of 8 bags of popcorn and drinks altogether. Determine the number of bags of popcorn and the number of drinks that Ruby bought.
Using system of linear equation the number of popcorn and drinks bought are 5 and 3 respectively
System of Linear EquationIn solving a system of linear equation, we have two unknown variables which we are to find. However, we can use either substitution, elimination or graphical method to solve them.
In this case, to solve this problem, we have to write out two equations and solve for the unknown variable;
let;
x = popcorny = drinksx + y = 8 ...eq(i)
6x + 4y = 42 ...eq(ii)
From eq(i)
x + y = 8
x = 8 - y ...eq(iii)
Put eq(iii) into (ii)
6(8 - y) + 4y = 42
y = 3
put y = 3 into eq(i)
x + 3 = 8
x = 5
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ASAP ASAP ASAP ASAP PLEASE
Which statement best explains why Kyle's survey may be biased?
• Two out of every three students entering Kyle's class didn't receive the survey.
• It wasn't possible for students to volunteer to take the survey.
• Only students who are taking one of Kyle's classes received the survey.
• Kyle gave the survey on paper instead of electronically.
Answer: the answer is c
Step-by-step explanation:
because Bru
Review the proof of the identity cos(π − A) = −cosA.
cos(π − A)
Step 1: = cosπcosA − sinAsinπ
Step 2: = (−1)(cosA) + (sinA)(0)
Step 3: = −1cosA + (sinA)(0)
Step 4: = −cosA + 0
Step 5: = −cosA
At which step was an error made?
step 1
step 2
step 3
step 4
In the proof of given identity, cos(π - A) = -cos A. Therefore, step 1 is error made.
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.
The given identity is,
cos(π - A) = -cos A.
Use formula for cos(a − b) = cosa . cosb + sina . sinb
cos(π - A) = cosπcosA + sinAsinπ
= (−1)(cosA) + (sinA)(0)
= −1.cosA + (sinA)(0)
= −cosA + 0
= −cosA
Since, in the step 1 the formula is wrongly used,
Therefore, step 1 is error made.
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Yoko is riding on a bike course that is 70 miles long. So far, she has ridden 42 miles of the course. What percentage of the course has Yoko ridden so far?
Answer: 60%
Step-by-step explanation:
Take 42 divided by 70, then times 100% = 60%
Yoko has ridden 60% so far!
The difference of the ages of a sister and her younger brother is 6 years. The
numerical value of the product of their ages is equal 4 times the sum of their
Find the present ages of the sister and her brother.
Answer:
bother = 6 years ; sister = 12 years
Step-by-step explanation:
s = sister
b = brother
s - b = 6
s * b = 4(s+b)
s = b + 6
b(b+6) = 4(b+6 + b)
b² + 6b = 4(2b + 6)
b² + 6b = 8b + 24
b² + 6b - 8b - 24 = 0
b² - 2b - 24 = 0
(b-6)(b+4) = 0
b = 6
b = -4 (impossible because an age can’t be negative)
s = 6 + 6
s = 12
Diego’s family car holds 14 gallons of fuel. Each day the car uses 0. 6 gallons of fuel. A warning light comes on when the remaining fuel is 1. 5 gallons or less.
Diego says the expression 14-0. 6t helps him understand this situation. In this situation, what does this expression represent, and what does the variable t stand for?
In the given expression 14 - 0.6t, variable t represents the number of gallons of fuel used by the car each day.
Explain the term variable of the equation?A term which includes at least one variable number, symbolized by one or maybe more letters, in an arithmetic operation, equation, or inequality. A symbol (often a letter) used in mathematics to represent an unknowable numerical value in such an equation or algebraic statement. A variable can be defined as a quantity that is changeable and not fixed. Variables are crucial since they make up a significant portion of algebra.For teh stated question-
The gasoline capacity of Diego's family automobile is 14 gallons. The automobile takes 0. 6 gallons of fuel every day. In the event that there are only 1.5 gallons of fuel left, a warning light will turn on.In the given expression 14 - 0.6t, t represents the number of gallons of fuel used by the car each day.
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I have a job that pays me 40 dollars an hour. However, it's far away and I pay $250
a week on gas. I have another job that's closer, but it only pays 25 dollars an hour
and I only spend 100 dollars on gas a week. What should I do? Use math to
support your answer. (Calculate this problem on a monthly basis. On both jobs, he
would work 160 hours per month.)
Answer: The first job seems better.
Step-by-step explanation:
If 1 month = 4 weeks:
40 x 40 = 1600 per week
40 x 160 = 6400 per month
250 per week on gas
250 x 4 = 1000 per month on gas
1600 - 250 = 1350
6400 - 1000 = 5400
You would earn $1350 per week on the first job, and $5400 on this job.
_____________________________________________________
25 x 160 = 4000 per month
25 x 40 = 1000 per week
100 per week on gas
100 x 4 = 400 per month on gas
1000 - 100 = 900
4000 - 400 = 3600
$900 per week on the second job, and $3600 per month on this job.
Hello,
I hope you and your family are doing well!
To compare the two jobs and determine which one is more financially advantageous, you need to calculate the total income and total expenses for each job on a monthly basis.
For the first job, the total income is 40 dollars per hour * 160 hours per month = 6400 dollars per month. The total expenses are 250 dollars per week * 4 weeks per month = 1000 dollars per month. The net income is 6400 dollars per month - 1000 dollars per month = 5400 dollars per month.
For the second job, the total income is 25 dollars per hour * 160 hours per month = 4000 dollars per month. The total expenses are 100 dollars per week * 4 weeks per month = 400 dollars per month. The net income is 4000 dollars per month - 400 dollars per month = 3600 dollars per month.
Based on these calculations, the first job is more financially advantageous because it has a higher net income. You would earn an additional 1800 dollars per month by working the first job instead of the second job.
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Happy Holidays!
Which word sentence represents the equation?
4y = y + 9
Responses
Four times a number plus 9 is 9.
Four times a number plus 9 is 9.
Four times a number equals the number increased by 9.
Four times a number equals the number increased by 9.
Four increased by a number equals the number increased by 9.
Four increased by a number equals the number increased by 9.
Four times the sum of a number and 9 is the number.
Here is a system of equations.
y=2x-2
y=2x-1
Graph the system. Then write its solution. Note that you can also answer "No solution" or "Infinitely many" solutions.
For the system of equations y = 2x -2 and y = 2x - 1, There is no solution.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given pair of set of equations,
y = 2x -2,
y = 2x - 1.
The graph of the equations is shown below,
To find the solution for the equations,
The value of x and y can not be determined because lines are parallel to each other.
Therefore, Equations have no solution.
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ABSTRACT REASONING In △EFG, the bisector of
∠F intersects the bisector of ∠G at point H. Explain
why FG — must be longer than FH — or HG . —
Which graph represents f of x equals square root of the quantity x plus 3 end quantity minus 2?
The graph that correctly represents the function f(x) = [√(x + 3)] - 2 is; Graph D
How to interpret the graph of the function?
We are given the function;
f(x) = [√(x + 3)] - 2
Remember that the argument of a square root must be zero or larger, then the minimum of the domain is the value of x such that:
x + 2 = 0
x = -2
Then the function starts at:
f(-2) = [√(-2 + 3)] - 2
f(-2) = 3
Then the graph should start at (-3, 2).
We can also identify another point by evaluating in x = 2.
f(2) = [√(2 + 3)] - 2
f(2) = -1
So the function also passes through (2, - 1).
Notice that the only graph that contains these two points is the last graph with x-intercept at 7.
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Please tell me what I should shade in!
Answer:
Hope this helps : )
You should shade in 1 whole rectangle on the the bottom left corner and the top half of the second rectangle the bottom right corner.
Step-by-step explanation:
This is because 1 1/2 is one whole rectangle and half of another rectangle. However, in this case the second rectangle on the bottom right corner is split into sixths. So half of it is 3/6 which is equal to 1/2.
= -x + 2. Find the remaining vertices
PERSEVERE A quadrilateral in the coordinate plane has exactly two lines of symmetry, y = x-1 and y
of the figure if there is a vertex at (-1,0). Graph the figure and the lines of symmetry on a separate sheet of paper.
List the coordinates of the vertices by starting with the vertex at (-1,0) and moving clockwise around the quadrilateral.
Answer:
wheres the photo?
Step-by-step explanation:
PLEASE HELP ME!!!!!!!!!!!!!
A state government borrows $2,000,000 at simple annual interest. Some of the money is borrowed at 6%, some at 7.5%, and some at 8.5%. Use a system of linear equations to determine how much (in dollars) is borrowed at each rate given that the total annual interest is $137,000 and the amount borrowed at 7.5% is four times the amount borrowed at 8.5%. Solve the system of linear equations using matrices.
If the amount borrowed at 7.5% is four times the amount borrowed at 8.5%. The amount borrowed is: $200,000, $800,000, $1,000,000.
How to find the amount borrowed?Now let find the amount borrowed
Let X+Y+Z = 2000000
0.06X + 0.075Y + 0.085Z = 137000
Y = 4Z
Substituting Y=4Z into the first and second equations:
X + 5Z = 2000000
0.06X + 0.075(4Z) + 0.085Z = 137000
X = 2000000 - 5Z
0.06X + 0.385Z = 137000
0.06(2000000 - 5Z) + 0.385Z = 137000
120000 - 0.3Z + 0.385Z = 137000
0.085Z + 120000 = 137000
0.085Z = 17000
Divide both side by 0.085Z
Z= 17,000/0.085
Z = 200000
So,
Y = 4Z
Y = 800000
X= 200,000 + 800,000
X = 1000000
Hence,
Z = 200000
Y = 800000
X = 1000000
Therefore the amount borrowed is: $200,000, $800,000, $1,000,000.
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Question in picture. Please answer quickly
Answer: [tex]\frac{2\sqrt{2}-1 }{2}[/tex]
Step-by-step explanation:
1. multiply both the numerator and denominator by [tex]2\sqrt{2}[/tex]
2. distribute on the top to get [tex]8\sqrt{2} - 4[/tex] ([tex]\sqrt{2} *\sqrt{2}[/tex] equals 2)
3. multiply the bottom to get 8
4. after getting [tex]\frac{8\sqrt{2}-4 }{8}[/tex], factor out a 4 from each term to get [tex]\frac{4(2\sqrt{2}-1)}{4(2)}[/tex]
5. the fours will cancel and the answer will be [tex]\frac{2\sqrt{2}-1 }{2}[/tex]
Literal Equations
help asap !!
Answer: y=13\3 or 4 1\3
Step-by-step explanation:
While hovering near the top of a waterfall in a national park at 5776 feet, a helicopter pilot accidentally drops his sunglasses. The height h(t) of the sunglasses after t second
is given by the polynomial function h(t)=-16t^2+5776. When will the sunglasses hit the ground?
Answer:
Step-by-step explanation:
set the height function = 0 and solve for t-16t2+6400=0t2 = -6400/(-16)=
∆abc and ∆def satisfy the aaa correspondence. ∆abc and ∆def . is not a criterion for congruency of any two triangles.
Triangles ABC and DEF might or might not be congruent since the angle-angle-angle (AAA) postulate is not a requirement for congruency of any two triangles. This is due to the fact that the angle-angle-angle postulate only takes into account the triangles' angles and does not specify their side lengths, hence congruency for these triangles may or may not be true.
What is a congruent triangle?
Therefore, if two triangles have the same number of sides on each side, they are said to be congruent.
Additionally, we can determine if they are congruent if we have a side, an angle between the sides, and then another side that is congruent, in that order: side, angle, side.
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Answer:
congruent
(AAA)
Step-by-step explanation:
Select all expressions that equal the distance between the points on the number line
| 3 | + | -2 |
| -2 + 3 |
| -3 - 2 |
3 - ( -2 )
| 3 - ( -2 ) |
The expressions that are equal to the distance between point A and point B would be
| 3 | + | -2 |
| -3 - 2 |
3 - ( -2 )
| 3 - ( -2 ) |
What is a number line?
In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
In the given number line, the distance between point A and point B is 5.
Now we have to check each option
| 3 | + | -2 | = 3 + 2 = 5
| -2 + 3 | = | 1 | = 1
| -3 - 2 | = | -5 | =5
3 - ( -2 ) = 3+ 2 = 5
| 3 - ( -2 ) | = |3 + 2| = 5
Hence, the expressions that are equal to the distance between point A and point B would be
| 3 | + | -2 |
| -3 - 2 |
3 - ( -2 )
| 3 - ( -2 ) |
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Find the area of the rhombus.
5m,10m,5m, and 10m
Please show your work.
The area of rhombus is 100m²
What is rhombus ?
A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.
A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is also referred to as a diamond or rhombus.
A quadrilateral with four equal sides that has the shape of a diamond is called a rhombus. In everyday life, rhombus-shaped objects can be seen. In the illustration below, two instances of rhombuses in nature are shown: a diamond and a kite.
The area of rhombus is
A = pq / 2
The value of p is 10 and q is 20
A = (10 * 20) / 2
= 100m²
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What’s the domain of this relation (-1,5) , (0,4), ( 1,2) , (3,-2)
Answer:
{-1, 0, 1, 3}
Step-by-step explanation:
A relation is a set of ordered pairs of numbers. The domain of a relation is the set of all the first elements (or x-values) in the ordered pairs. In this case, the relation is (-1,5) , (0,4), ( 1,2) , (3,-2), so the domain is the set of all the x-values in these ordered pairs, which is the set {-1, 0, 1, 3}. Therefore, the domain of the relation is {-1, 0, 1, 3}.
a fair die is rolled four times A4 is condsider success while all.other out comes are failures what is the probability of 2 succusses?
Answer:
P(Success1) =1/6
P(Success2) =1/6
P(2Success) =1/6 × 1/6 = 1/12
find the probability of the given event. a single fair die is rolled. the number on the die is greater than 2.
The probability to get the numbers greater than 2 from the outcomes of the event of rolling a single fair die is equal to P(A) = 2/3.
As given in the question,
Event is rolling a single fair die.
Number of fair die to be rolled = 1
Possible outcomes = { 1, 2, 3, 4, 5, 6 }
Total number of possible outcomes = 6
Numbers greater than 2 on rolling a single fair die = { 3, 4. 5,6 }
Number of favourable outcomes = 4
Probability of getting a number greater than 2
= (Number of favourable outcomes) / (Total number of outcomes)
= 4 / 6
= 2 / 3
Therefore, the probability of getting a number greater than 2 while rolling a single fair die is equal to 2 / 3.
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write the equation in slope -intercept form. What are the slope and y intercept?
-3x-10y=7
Answer: slope -intercept form = [tex]-\frac{3}{10} x-\frac{7}{10}[/tex] the slope = [tex]-\frac{3}{10}[/tex] and the y-intecept = [tex](0,-\frac{7}{10} )[/tex]
Step-by-step explanation: I used y=mx+b and filled it in with the infomation that I already knew. Hope this helps :)
find the probability for the experiment of drawing two marbles (without replacement) from a bag containing three green, three yellow, and four red marbles.
The probability for the experiment of drawing two marbles (without replacement) from a bag containing three green, three yellow, and four red marbles = 0.0111
In this question we need to find the probability for the experiment of drawing two marbles (without replacement) from a bag containing three green, three yellow, and four red marbles.
Total marbles in tha bag
= 3 green marbles + 3 yellow marbles + 4 red marbles
= 10 marbles
the probability of drawing one marble from a bag,
P1 = 1/10
Now there are 9 marbles in the bag.
So, the probability of drawing second marble would be,
P2 = 1/9
So, the required probability of drawing two marbles (without replacement) from a bag would be,
P = P1 * P2
P = 1/10 * 1/9
P = 1/90
P = 0.0111
Therefore, the probability of drawing two marbles (without replacement) from a bag = 0.0111
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PLEASE HELP!! WILL GIVE BRAINLIEST AND 25 POINTS!!
Solve for x. Round your answer to the nearest tenth.
A. 12
B. 14.4
C. 15.0
Answer: its is 12
Step-by-step explanation:
Lisa paid $46.58 for 16.7 gallons of gasoline. What was the cost per gallon, rounded to the nearest hundredth? It's a 100 points pls
Answer:
2.8
Step-by-step explanation:
First you need to divide the cost by the number of gallons dollars/number of gallons =cost per gallon
And then round it . I hope it helped
F(x)=2x+7 and g(x)=3x^2+2
Answer:
The answer for f(g(3)) is 65.