Answers
On applying the midpoint theorem the values of x, y, and z are 2, 10 and 8 respectively.
What is the mid-point theorem?
According to the midpoint theorem, the line segment connecting any two triangle sides' midpoints is parallel to and equal to half of the third side.
The outer triangle is ABC and the inner triangle is DEF.
It can be seen that sides AB, BC and AC are equally divided such that AD=DB,
BE=EC and
CF=FA.
So, this proves that point D, E and F are the middle points of AB, BC and AC respectively.
Now, according to the midpoint theorem -
DF = 1/2(BC)
Plugging in the values -
x = (5x-6)/2
2x = 5x-6
2x-5x = -6
-3x = -6
x = 2
Now, for side DE -
DE = 1/2(AC)
Plugging in the values -
12 = (2z+8)/2
24 = 2z+8
24-8 = 2z
16 = 2z
z = 8
Now, for side EF -
EF = 1/2(AB)
Plugging in the values -
y = 20/2
y = 10
Therefore, the values obtained are x=2, y=10 and z=8.
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Related Questions
Use algebra tiles to solve 2x + 1 = 9 on IXL
Answers
Answer: 4
Step-by-step explanation:
1. Question: 2x+1=9
2. Subtract 1 from the 9
Answer to step 2: 2x=8
3. Divide 8/2 (4x2)
4. Answer: x=4
Answer: X= 4; look below for the explanation of algebra tiles
Step-by-step explanation: First, we need to determine the value of x. We can use the rule of inverse operations. So, the opposite of addition is subtraction, and the opposite of multiplication is division. Now, using that, we start with the inverse operations of 1 + 9. That'd be 9 - 1. So, that's 8. Now, according to the order of inverse operations, we divide the 2 by 8. So, 8 divided by 2 is 4. Therefore x = 4.
Now, using the tiles, we need to get 8 tiles, + 1 tile, which should get you your answer. I hope this helped!
An office manager is planning to set up three computer workstations
and a file cabinet in a space that is 27 feet wide. The file cabinet takes up
3 feet. What is the width of the space available for each computer work
station?
PLEASE HELP
Answers
Explanation: Since we start with 27 feet, and 3 feet is taken, then we have 24 feet to work with. If we want to evenly distributed the remaining space for 3 computer work stations, we can say 24 feet / 3 to get 8 feet to use for each computer work station.
Cheers.
1. Are the triangles shown below similar? Explain.
Answers
Answer:
Step-by-step explanation:
These are the tests for similar triangles:
AA - if 2 pairs of corresponding angles are equal.
SSS - if corresponding sides have the same ratio.
SAS - if 2 pairs of corresponding sides have the same ratio and the included angles are equal.
This diagram does not indicate any of these relationships exist.
Therefore the triangles are not similar.
Help with question 3
Answers
Answer:
All real numbers for both Range and Domain
R
or
(−∞,∞)
Explain how finding the area of a
rectangle with whole-number side lengths compares to finding the are
of a rectangle with fractional side lengths.
Answers
The area of rectangle with side whole number = ab sq. units,
and area of rectangle with fraction side = ac/bd sq. units.
What is rectangle?A quadrilateral with four right angles is a rectangle. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°). A square is a rectangle with four equally long sides.
Given to find the area of rectangle,
Area of rectangle is given by product of length and width.
A = l x b
Let the dimensions of a rectangle are all whole numbers, a by b
Area = a x b
A = ab sq. units
another rectangle with dimensions all fractions say, a/b by c/d .
Area = a/b x c/d
A = ac/bd sq. units
In all situations, the area of the rectangle must be calculated by multiplying its length and breadth.
Hence the area of rectangle is product of length to width in both cases.
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In 2010, the population of a city was 237,000. From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?
Answers
The population of the city grew from 2010 to 2020 by 13.37%.
What is percentage?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.
We have to given that;
In 2010, the population of a city was 237,000.
And, From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.
We know that;
Where, A = P (1+r)ⁿ
A = final population.
P = Initial population.
r = rate
n = time
Hence, The population in 2015 is, =
A = 237,000(1 + 0.076)⁵
A = 341829.629
And, The population in 2020 =
A = P (1 - r)ⁿ
A = 341829.629 (1 - 0.047)⁵
A = 268704.047
So, Percent grow = (268704.047 - 237,000) / 237,000 × 100
= 31704.047 / 237,000 × 100
= 13.37 %
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There are 200 students, where 86 of them were in the athletics team. Therefore, ___% of the students were in the athletics team.
Answers
Answer:
43%
Step-by-step explanation:
calculate percentage as
( number of students in athletics team ÷ total students ) × 100%
= ( 86 ÷ 200) × 100%
= 0.43 × 100%
= 43%
86 divided by 200=0.43
0.43 times 100= 43
Is this a perfect square trinomial X² 6x 9?
Answers
x² + 6x + 9, this is a perfect square trinomial, which is expressed as
(x + 3)².
What is trinomial?Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."
An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.
A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.
Given that,
x² + 6x + 9
= (x)² + 2(3x) + 9
= (x)² + 2(x)(3) + 3²
This is similar to a² + 2ab + b² = (a + b)²
so, we can write:
= (x + 3)²
= (x +3) (x + 3)
so, this is a perfect square trinomial.
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PLS HELP!!!! Will give brainliest (multiple answers) 40PTS
Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weekly salary is $900. The following table shows the number of sales each salesman had during the first three weeks of this month.
Week 1 Week 2 Week 3
Salesman A 11 14 16
Salesman B 14 15 13
Salesman C 16 12 11
In which week(s), did Salesman C have a larger paycheck than both of the other salesmen? Select all that apply.
Week 3
None of the weeks.
Week 2
Week 1
Answers
Salesman C have a larger paycheck than both of the other salesmen in
None of the weeks.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Here, we have,
Salesman A works earns $65 per sale, with a maximum weekly commission of $1,300
Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale.
Salesman C does not earn any commission. His weekly salary is $900. Now we have that, A is getting $1300 commission,
and, salary of C is $900, he has no commission.
i.e. C can't earn more than A
Hence, Salesman C have a larger paycheck than both of the other salesmen in None of the weeks.
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The solution is Option D.
The week 1 is when Salesman C have a larger paycheck than both of the other salesmen and is given by the equation C = $ 900
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of sales be represented as x
Let the maximum weekly salary of Salesman C be = $ 900
Now , the weekly salary of Salesman A = $ 65x
where x is the number of sales
And , the weekly salary of Salesman B = $ 300 + $ 40x
Now , on week 1,
Salesman A made 11 sales
Substitute the value of x = 11 in the equation , we get
So , the salary of Salesman A on week 1 = 65 ( 11 )
On simplifying the equation , we get
The salary of Salesman A on week 1 = $ 715
And , Salesman B made 14 sales
Substitute the value of x = 14 in the equation , we get
The salary of Salesman B on week 1 = 300 + 40 ( 14 )
On simplifying the equation , we get
The salary of Salesman B on week 1 = 300 + 560
The salary of Salesman B on week 1 = $ 860
So , Salary of Salesman C on week 1 > salary of Salesman B on week 1 > salary of Salesman A on week 1
And , $ 900 > $ 860 > $ 715
Hence , the solution to the equation is week 1
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Jared’s monthly income is 4500 Jared spend 11%of his income on grocies
Answers
Answer:
Jared's groceries = 495
Step-by-step explanation:
We calculate 11% from Jared monthly income:
11% x 4500 = 495
Jared's groceries = 495
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Claire keeps track of the miles per gallon her car gets per week. She has accumulated the following data: (1, 22.42), (2, 22.84), (3, 23.26), (4, 23.68) What is the common difference or ratio
Answers
The common difference is 0.42. The comparison of each ratio's successive values over time for a single firm.
Now, According to the question:
What is meant by ratio?
When expressed in numbers or amounts, a ratio is a relationship between two things. For example, if a room contains ten boys and thirty girls, the boy-to-girl ratio is 1:3, or one to three.A ratio, or getting rationed, on the occurs when replies to a tweet vastly outnumber likes or retweets. This means that people are reacting negatively to the tweet's content.It usually means that your comment has received more replies than likes. This implies that there are more people who disagree with your comment than agree with it.Therefore, simplifying the equation then we get,
if you take the ranges (y) and subtract one from the other you get 0.42.
(22.84 - 22.42)/(2 - 1) = 0.42/1 = 0.42
(23.26 - 22.84)/(3 - 2) = 0.42
(23.68 - 23.26)/(4 - 3) = 0.42
Hence, The common difference is 0.42
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Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-7,-6)
(6,3)
(4,-4)
Answers
The fourth point is (-6.5, -14)
Vertices of a parallelogram?
The three vertices you've provided are (-7,-6), (6,3), and (4,-4). To find the fourth vertex of a parallelogram, we can use the fact that opposite sides of a parallelogram are parallel and congruent, meaning they have the same length and the same slope.
The three vertices you've provided are (-7,-6), (6,3), and (4,-4). To find the fourth vertex of a parallelogram, we can use the fact that opposite sides of a parallelogram are parallel and congruent, meaning they have the same length and the same slope.
One way to find the fourth vertex is to use the vector that connects one vertex to another. The vector from (-7,-6) to (6,3) is (13,9), and from (6,3) to (4,-4) is (-2,-7)
If we use the vector which is opposite of (-2,-7) that is (2,7) and add it to the third point (4,-4) , we will get the fourth point.
(2,7) + (4,-4) = (6,3)
so the fourth point is (6,3)
Another way is to find the midpoint of the diagonal of the parallelogram which are (-7,-6) and (4,-4) and then add the vector which is opposite of (6,3) to (4,-4) that is (-6,-9) which is also the vector from (6,3) to (4,-4)
Midpoint of (-7,-6) and (4,-4) = (-0.5,-5)
(-0.5,-5) + (-6,-9) = (-6.5, -14)
Hence, the fourth point is (-6.5, -14)
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The perimeter of a square is 48. If the perimeter is 4 times than before then find the number of times the area becomes of what it was before.
Answers
Answer:
12?
Step-by-step explanation:
Lowkey don't understand the last part of your q but if it's 4 times then if the original was 12 48 is four times bigger
if you do 44 push ups in 4 minutes how many will he do in 5 minutes
Answers
Answer:
55
Step-by-step explanation: i think
Answer:
Step-by-step explanation:
it would be 55 because he does 11 each minute.
2x+5=2x+6
equations please help
8th grade math
Answers
Answer:
Step-by-step explanation:
Subtract 5 from both sides:
2x=2x+6-5
2x=2x+1
Subtract 2x from both sides:
2x-2x=1
0=1
Therefore, this is a false statement, so there are no solutions.
Hi, please help ! (see image)
Answers
Answer:
R = 144400000/59 [this is a fraction]
PLEASE HELP !!
Find the value of x
picture attached
Answers
Answer:
x = 11
Step-by-step explanation:
The two angles are consecutive interior angles so they add up to 180
13x -26 + 5x + 8 = 180
13x + 5x -26 + 8 = 180
18x - 18 = 180
18x = 180 + 18
18x = 198
x = 11
The ratio of the four sides of a trapezoid is 2:1:1:1.$ The area of the trapezoid is 27*sqrt3. Find the length of the median of the trapezoid.
Answers
The length of the median = 6[tex]\sqrt{3}[/tex]
If we call the longer base "a" and the shorter base "b", then we know that:
a:b = 2:1
Since the ratio of the four sides is 1:1:1:1, we know that the height, median and the longer base are all equal.
We can use that information to determine the area of the trapezoid. The formula for the area of a trapezoid is:
Area = (a + b) * h / 2
We know that the area is 27[tex]\sqrt{3}[/tex] and the height and median are equal, so we can set up the equation:
(a + b) * h / 2 = 27[tex]\sqrt{3}[/tex]
We also know that a:b = 2:1, so we can substitute that in:
(2b + b) * b / 2 = 27[tex]\sqrt{3}[/tex]
Simplifying, we get:
3b^2 = 54 * [tex]\sqrt{3}[/tex]
So the length of the median (h) is b
= [tex]\sqrt{(54 * \sqrt{3} / 3) }[/tex]
= 6[tex]\sqrt{3}[/tex]
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What is the y-intercept at 0 4?
Answers
The y-intercept of (0,4) is 4.
A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.
The y-coordinate of the y-intercept is determined by computing f(0) if the curve in question is supplied as y=f(x), y=f(x), etc. There is no y-intercept for functions that have an value at x = 0.
The constant term a is the y-coordinate of the y-intercept if the function is linear and is written in slope-intercept form as f(x)=a+bx"
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prove that the value of the expression does not depend on the value of x. (x-5)(x+8)-(x+4)(x-1)
Answers
The value of the expression is -44 and thus does not depend on the value of x
What are algebraic expressions?An algebraic expression can be described as a mathematical expression made up of variables, terms, factors, coefficients and constants.
They are also made up of mathematical or arithmetic operations, which includes;
MultiplicationSubtractionAdditionBracketParenthesesDivision, etcFrom the information given, we have that;
(x-5)(x+8)-(x+4)(x-1)
expand the bracket
x² + 8x - 5x - 40 - (x² -x + 4x - 4)
x² + 8x - 5x - 40 - x² + x - 4x + 4
collect like terms
3x - 3x - 40 - 4
add or subtract like terms
0 - 44
Hence, the expression does not depend o x
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What quadrant does (-a,b) belong
Answers
Coordinate (-a , b ) belongs to second quadrant.
What is a Quadrant?The axes (x-axis and y-axis) of a two-dimensional Cartesian plane system divide the plane into four infinite regions called quadrants. The horizontal line or x-axis and vertical line or y-axis intersect each other at the right angle. The intersection of two lines is known to be the reference point. All the measurement is done by taking this point as the reference (or starting point) in the coordinate system.
"A quadrant is simply defined as the region of a cartesian plane formed when the x-axis and y-axis intersect each other."
Given, Coordinate ≡ (-a , b)
1st Quadrant: The upper right-hand corner of the graph is the first quadrant. In this quadrant the values of x and y both are positive.
2nd Quadrant: The upper left-hand corner of the graph is the second quadrant. In this quadrant, the value of x is negative whereas the value of y is positive.
3rd Quadrant: The lower left-hand corner of the graph is the third quadrant. It contains the negative values of both x and y.
4th Quadrant: Finally, the fourth quarter is at the lower right-hand corner, which has a positive value of x and a negative value of y.
Hence, by the above observation, given coordinate (-a, b) belongs to the 2nd quadrant.
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What is the value of the expression shown below?
-28+42-12+(-16) + 7
A.14
B. 7
C.-7
D.-14
Answers
-28 + 42 - 12 +(-16) + 7
14 - 12 +(-16) + 7
2 +(-16) + 7
-14 + 7
-7
Given
A
B
‾
∥
D
C
‾
AB
∥
DC
and
B
C
‾
∥
A
D
‾
BC
∥
AD
, prove
△
A
B
C
≅
△
C
D
A
△ABC≅△CDA by filling out the flowchart below.
Answers
The second row's third box AC = AC ( common side ) ( common side ) box last. Therefore, by applying the ABCD ASA congruence axiom.
What is triangle ?Three sides, three angles, and three vertices make up the closed, two-dimensional shape of a triangle. Polygons include triangles. Triangle ABC is depicted in the above figure. Triangular polygons in geometry are those with three sides and three vertices. There are three straight sides to this two-dimensional figure. Three-sided polygons include triangles. A triangle's three angles add up to a full 180 degrees. A single plane contains the triangle. Triangulus, which means "three-cornered" or "having three angles," is a Latin word with roots in tri-, "three," and angulus, "angle or corner."
given
AB||DC , BC||AD
To show that
ΔABC≅ ΔCDA
First box
AB || DC (given )
below box to the first box
∠BAC = ∠DCA ( parallel lies cut by the transverse form congruent alternate interior angles )
Second box
BC||AD ( given )
Below box to the second box
∠DAC = ∠BCA ( parallel lies cut by the transversal form congruent alternate interior angles )
Third box in the second row
AC = AC ( common side )
Last box
So by using ASA congruence axiom
ΔABC ≅ΔCDA
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Blake uses 2 gallons of gas to drive 34.6 miles in his car. Find the rate of change.
Answers
Answer:
17.3 miles / gallon
Step-by-step explanation:
RatesRates can be represented in different forms, such as speed (meters per second) or water flow rate (liters per minute or second)
SolutionGiven information from the question,
2 gallons = 34.6 miles
1 gallon = 34.6 ÷ 2 = 17.3 miles / gallon
Please Help me find the area of the figure round to the nearest hundredth nessary
Answers
Answer:
912 cm²
Step-by-step explanation:
Formula for area of triangle: 1/2bh
So you'll first multiply the base by the height of the triangle
48 x 38 = 1,824
Then you'll multiply 1,824 by 1/2(which is the same as dividing it by 2)
1,824 ÷ 2 = 912
Help me pls I’m struggling and I can’t solve it
Answers
The perimeter of the rectangle is 4y + 6 (cm).
How can the perimeter equation be found?All four side lengths must be added up in order to get the perimeter, or the distance around the rectangle. Since there are two of each side length, it is simple to multiply the total of the length and the breadth by two in order to do this task effectively. The formula for perimeter is perimeter=(length Plus width)2.
The diagram shows a rectangle. All measurements are in centimetres an expression in terms of y, for the perimeter of the rectangle.
The perimeter of the rectangle is
2(y+3)+24
=2y + 6 + 2y = 4y + 6 (cm)
{ the perimeter:
2 * width + 2 * Length}
The perimeter of the rectangle is 4y + 6 (cm).
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The average scores on Mrs. Wilson's test and Mr. Lewandowski's test were normally distributed on the last Algebra 2 test they gave. The average in my class Mrs. Wilson's class, was 86 with a standard deviation of 2. The average in my friend's class, Mr. Lewandowski's class was an 82 with a standard deviation of 2. If I made an 88 on the test and my friend made an 85 on their test, who had the better score relative to the rest of their class?
Answers
You had a better score relative to the rest of your class.
To compare the scores of you and your friend relative to the rest of their classes, we need to calculate the standard deviation of your score and your friend's score from the average of their respective classes.
A standard deviation of 2 means that 68% of the scores in the class fall within 1 standard deviation of the mean, or between 84 and 88 in the case of Mrs. Wilson's class. Since 88 is greater than 86 (the mean) and less than 2 standard deviations away (88-86 < 2*2=4) , so your score of 88 is better than the average score in your class.
On the other hand, 85 is less than 82 (the mean) and more than 1 standard deviation away (85-82 > 2) so your friend's score of 85 is less than the average score in their class.
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Abdul made $162 for 9 hours of work.
At the same rate, how much would he make for 12 hours of work?
Answers
Answer:218
explanation: 162 divided by 9 = 18 and 18 multiplied by 12 =218
Gcf of -28, 60, and 72
Answers
Answer:
4
Step-by-step explanation:
-28 = ±2^2 x ±7
60 = ±2^2 x ±3 x±5
72 = ±2^3 x ±3^2
=> Gcf of -28, 60, 72: 2^2 = 4
Answer: 12
Step-by-step explanation:
Therefore, the highest common factor of 60 and 72 is 12.
:) I know somebody already answered but like..im answering some stuff today, hope this helped by the way!
What is the GCF of 20x^76 and 8x^92
Answers
The GCF of the given expressions is 4x⁷⁶
What is the greatest common factor?The greatest common factor, abbreviated as GCF, of two numbers is the largest number that is a factor of, or divides evenly into, both of the numbers. When two numbers are relatively small, we have a quick and simple way to calculate their greatest common factor. We do this by listing all of the factors of each number, and then identifying the largest number that is in both lists.
Given here, The expressions 20x⁷⁶ and 8x⁹² and GCF(20,8)=4
and x⁷⁶ is a factor of 8x⁹²
∴ GCF(20x⁷⁶ , 8x⁹²) =4x⁷⁶
Hence, The GCF of the given expressions is 4x⁷⁶
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