WXYZ is an isosceles trapezoid with legs WX and YZ and a base XY. If the length of WX is 6x+5, the length of XY is 10x+4 and the length of YZ is 8x-3, find the value of x.
Answers
Since it is an isosceles trapezoid, the legs are congruent; that means
6x + 5 = 8x - 3
When solving this equation, we do not want a variable on both sides. We will cancel the 6x to avoid negatives:
6x + 5 - 6x = 8x - 3 - 6x
5 = 8x - 3 - 6x
Combine like terms:
5 = 2x - 3
Cancel the 3 by adding:
5 + 3 = 2x - 3 + 3
8 = 2x
Cancel the 2 by dividing:
8/2 = 2x/2
4 = x
See answer in attachment.
Hope it helps you.
Related Questions
These data show the ring sizes for a sample of 8 men. 12 10 11.5 11.5 12 9 9 11 What is the best approximation of the standard deviation for the ring size data?
Answers
The mean (average) = (12 +10+ 11.5 +11.5 +12 +9 +9 +11)/8
= 10.75
Standard deviation is the square root of variance, it is one of the measures of central dispersion, that is a measure of by how much the values in the data set are likely to differ from the mean.
In this case, Standard deviation, s= √(∑(x-m)²)/(n-1)
= 1.172
Thus, best approximation of the standard deviation is 1.17
Answer:
The answer should be 1.10
Step-by-step explanation:
The reason being is that I took the test. I hope you do well iA
Algebra 1 B Exponents and Exponential Functions Unit Portfolio?
Task 1?
Task 2?
Task 3?
Need an
Exponents and Exponential Functions Table?
Would be nice if you could help with all of it though. After all it is (30)points!!!
Answers
y=$500(in billions)
x= the number of years that have passed since 2009
percentage of decrease: 1 - % =
so your formula will look like this: y(1 - %)^x
Exponents multiply a number by itself, while exponential functions contain variables in the exponent. Algebra 1B tasks involving these could include simplifying exponents, solving problems with exponential functions, and creating or interpreting an Exponential Functions Table. Studying, understanding rules, and practicing problems will aid success.
Explanation:It seems like you need help with understanding Exponents and Exponential Functions. Exponents are a way of multiplying a number by itself. For example, 2^3 means 2 is multiplied by itself twice (2 * 2 * 2).
On the other hand, exponential functions are a special type of functions where the variable is in the exponent. For instance, the function f(x) = 2^x is an exponential function.
For your Algebra 1B tasks, here's a sample process: for Task 1, you might be required to simplify numbers or expressions using exponents. Task 2 may require you to solve problems using exponential functions. And Task 3 could involve creating or interpreting an Exponential Functions Table, which is a table showing the values of an exponential function for different x-values.
Remember to follow your study guides, textbooks, and your teacher's instructions for each task. Practicing problems and understanding the rules of exponents and exponential functions will help you earn those 30 points!
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If x = −4 is a zero of the polynomial function f(x) = 2x3 + 13x2 + 23x + 12, which of the following is another zero of f(x)
A. X=4
B. X=-1
C. X= 1
D. X=12
Answers
A “zero” is the number x has to be for the equation to equal 0. So, looking at the equation, x HAS to be negative, because the whole equation has +’s, which will never amount to 0 unless X is a negative number.
You can also plug -1 in for X as so:
2(-1)3 + 13(-1)2 + 23(-1) + 12
Which simplifies:
-2 +13 - 23 + 12
Which equals 0
I hope this Helps!
Jasmine and Carlotta are sisters and each have their own savings together they borrowed $28 from their brother to go to the movies.Each girl has to pay back an equal amount.Carlotta also owes her brother $6,which expression represents the change in Carlotta’s savings after she repays her brother
Answers
hopes this helps :)
The expression which shows the change in Carlotta's savings is x-8 if her she owes her brother $6.
What is expression?An expression is a combination of numbers, symbols and variables but not in equal to form.
How to form an expression?In the problem Jasmine and Carlotta borrowed $28 from their brother. Since both need to pay back equally so Carlotta needs to pay back $14 but she owes 6 from her brother so she now has to pay only 8.
Let the savings be x
in this way only $8 needs to be subtracted from savings.
The expression will be = x-8.
Hence the expression which shows the change in savings is x-8.
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Trucks are delivering gravel to a construction site each truck hold 7.5 cubic yards of gravel. The weight of 1 cubic yard of gravel is 1.48 tons. The gravel will be placed in containers that each hold 3.7 tons of gravel. how many contaoners of this size are needed to hold all the gravel from one truck
Answers
If the weight of 1 yard³ is 1.48 tons, then the weight of 7.5 yards³ is:
w=7.5x1.48 tons
w=11.1 tons
The problem says that the gravel will be placed in containers that each hold 3.7 tons of gravel,so, If they need 1 cotainer to place 3.7 tons, how many containers they need to place 11.1 tons?
1 container-------3.7 tons of gravel
x-------11.1 tons of gravel
x=(11.1x1)/3.7
x=11.1/3.7
x=3 containers
How many containers of this size are needed to hold all the gravel from one truck?
The answer is: 3 containers.
PLEASE HELP STEP BY STEP
Answers
[tex]= \frac{z^{2}-6}{z-5} \times \frac{z^{2}+z-18}{z+2}[/tex]
[tex]= \frac{(z^{2}-6)(z^{2}+z-18)}{(z-5)(z+2)}[/tex]
Ordinarily, with a problem of this sort, there would be factors that would cancel, making the result simpler than what you get by multiplying things out. Here, there are no common factors and the numerator factors are all irrational. Of course, the denominator cannot be zero, so the restrictions are
.. z ≠ -2 or +5
[tex]= \frac{z^{4}+z^{3}-24z^{2}-6z+108}{z^{2}-3z-10}[/tex]
Isabella spends $4.87 on paintbrushes and paint. How many of each item does she buy? Explain how you found your answer. Paint brush=$0.95Paint=$0.75
Answers
Let
x-----------------> number of paintbrushes----------- > $0.95 each
y---------------- > number of jar of paint-------------- > $0.99 each
we know that
0.95x+0.99y = $4.87
using a graph tool
the solution will be a pair of coordinates that are whole numbers -- > see the attached figure
the solution is the point (2,3)
x=2---------------------- > number of paintbrushes
y=3---------------------- > number of jar of paint
the answer is
number of paintbrushes=2
number of jar of paint=3
Find the surface area of a sphere with a radius of 8cm.
(use 3.14 for pi and round to the nearest tenth)
A. 267.9 cm^2
B. 803.8 cm^2
C. 2143.6 cm^2
D. 201.0 cm^2
Answers
By definition, the surface area of a sphere is given by:
[tex] A = 4 * \pi * r ^ 2
[/tex]
Where,
r: sphere radius
Substituting values in the given equation we have:
[tex] A = 4 * 3.14 * 8 ^ 2
[/tex]
Doing the calculations we have:
[tex] A = 803.84
[/tex]
Rounding to the nearest tenth:
[tex] A = 803.8 cm ^ 2
[/tex]
Answer:
The surface area of a sphere with a radius of 8cm is:
B. 803.8 cm ^ 2
Is this statement true? Why?
Answers
Let's find the inverse function:
We apply arctan to both sides:
arctan (y) = arctan (tan (x- (pi / 2)))
arctan (y) = (x- (pi / 2)
Then, we clear x:
x = arctan (y) + (pi / 2)
Finally we make the change y = x
y = arctan (x) + (pi / 2)
Answer:
False, y = tan ^ -1 (x + (pi / 2)) is not the inverse of y = tan (x- (pi / 2)).
The inverse is:
y= arctan (x) + (pi / 2)
Is my answer correct ?
I believe it’s either (B) or (C)
Answers
------------------------------------------------------------------
Divide 77 over 4 to get
77/4 = 19 remainder 1
The remainder 1 tells us that i^77 = i^1 = i
So in short, i^77 = i
a cylinder shaped paint can has a diameter of 10 cm and a height of 30. what is the volume of the paint can when it is 30% full? use 3.14 to approximate pi
WILL pick brainliest if correct!!!
Answers
.. = 3.14*(5 cm)^2*(0.30*30 cm)
.. = 706.5 cm^3
What are debit cards?
Answers
So if you are much more richer, and do not want to pay interest rates, you might want to get a debit card
hope this helps
What is the product? (2x-1)(x+4)
Answers
Answer:
[tex]2x^{2}+7x-4[/tex]
Step-by-step explanation:
We are given to find the product of (2x-1) and (x+4).
So, we have,
[tex](2x-1)(x+4)[/tex] = [tex]2x^{2}+8x-x-4[/tex] = [tex]2x^{2}+7x-4[/tex].
Thus, the product of (2x-1) and (x+4) is [tex]2x^{2}+7x-4[/tex].
i.e. [tex](2x-1)(x+4)[/tex] = [tex]2x^{2}+7x-4[/tex].
hhhhhhheeeeeeeeellllllllllpppppppppppp
Answers
sine (60) = (z) / (a + b)
Clearing z we have:
z = (a + b) * sine (60)
Substituting:
z = (15) * sine (60)
z = 15 * (root (3) / (2))
Answer:
z = 15 * (root (3) / (2))
blake is signing a lease for a studio apartment that rents for $425/month. how much will blake pay to move in if he must pay the first and last months rent and a security deposit equal to 50% of his monthly rent?
Answers
Total amount he needs to pay is $1,062.5
Sum of money based problem:Given that;
Rent of apartment = $425 / month
Security deposit = 50% monthly rent
Find:
Total amount he needs to pay
Computation:
Total amount of rent he needs to pay = 425 + 425 + 50%[425]
Total amount he needs to pay = 425 + 425 + 212.5
Total amount he needs to pay = $1,062.5
Find out more information about ' Rent'
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Why do you switch the inequality sign when multiplying or dividing by a negative?
Answers
Karen is buying pens and pencils for the new school year. She wants to have no more than 25 writing utensils in all. She also wants the number of pencils to be greater than or equal to the square of 3 less than the number of pens. Create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.
Answers
Karen's situation can be modeled by the following system of inequalities:
Total number of utensils: p + n ≤ 25 (p = number of pens, n = number of pencils)
Pencils vs. pens: n ≥ (3 - p)^2 (pencils must be at least the square of 3 less than the number of pens)
Viable solutions: All solutions within this system are viable.
Explanation:First inequality: This ensures that the total number of writing utensils (pens + pencils) doesn't exceed 25, Karen's desired maximum.
Second inequality: This accounts for Karen's preference for having at least as many pencils as the square of 3 less than the number of pens. It avoids solutions with fewer pencils than the squared difference.
Viable solutions: Since both inequalities are valid and independent, any solution that satisfies both is acceptable. This leaves a broad range of viable combinations of pens and pencils, allowing Karen flexibility within her limits.
Therefore, all solutions within the system of inequalities are valid possibilities for Karen's purchase. She can choose any combination of pens and pencils as long as their total is 25 or less and the number of pencils is greater than or equal to the square of 3 less than the number of pens.
Graph image 1 for translation. one unit to the right
Answers
(x, y) = (x + 1, y)
We have then:
M (-3, 1) ---> M '(- 2, 1)
O (1, 4) ---> O '(2, 4)
P (3, -1) ----> P '(4, -1)
Answer:
The new vertices are
M '(- 2, 1)
O '(2, 4)
P '(4, -1)
Graph five (last from left to right) is the correct one.
what is perimeter is that you count the out side of a shape
Answers
The graph of y = srtqx is translated. The translation is defined by (x + 1, y – 2). Which is the graph of the translated image?
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Answer with explanation:
The graph of Original function is:
[tex]y=\sqrt{x}[/tex]
The function is translated by the rule (x+1, y-2).
After translation Point (a,b) is obtained.
a=x+1
,→x=a-1
b=y-2
→y=b+2
Substituting the value of x and y in the above function and obtaining the graph of the translated image
[tex]\rightarrow b+2=\sqrt{a-1}\\\\\text{Replacing a and b by x and y}\\\\\rightarrow y+2=\sqrt{x-1}[/tex]
Answer:
Graph B
Step-by-step explanation:
hope this helps!
(plz mark as brainliest if correct)
Rachael is a nurse. She earns 12 vacation days after working 768 hours. How many hours does Rachael need to work to earn 1 vacation day? Remember to include units! (Example: 12 hours)
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Sasha and Mona practiced swimming every day. They increased the number of minutes of swimming every week as described below: Sasha: Practiced swimming for 10 minutes every day in the first week, 20 minutes in the second week, 40 minutes in the third week, and 80 minutes in the fourth week. Mona: Practiced swimming for 10 minutes every day in the first week, 20 minutes in the second week, 30 minutes in the third week, and 40 minutes in the fourth week. Which statement best describes the methods used by Sasha and Mona to increase the time they practiced swimming? Mona's method is linear because the number of minutes increased by an equal factor every week. Sasha's method is exponential because it increases by an equal number every week. Mona's method is exponential because it increases by a fixed factor, and Sasha's method is linear because it increases by a fixed number. Sasha's method is exponential because it increases by a fixed factor, and Mona's method is linear because it increases by a fixed number.
Answers
Final answer:
Sasha's method of increasing swimming time is exponential, doubling each week, while Mona's method is linear, adding a fixed number of 10 minutes each week.
Explanation:
The question asks about the methods Sasha and Mona used to increase their swimming practice times over several weeks. Sasha's method is exponential because each week, the number of minutes she practices doubles, which is a fixed factor of increase. Every week, Sasha's swimming time increases by a factor of 2. Therefore, her increase is exponential. Mona's method is linear because she increases her swimming time by a fixed number of 10 minutes each week. Her increments are consistent and add the same amount each time, defining a linear pattern of increase.
How many terms are in 8y+7z
Answers
there are 2 terms.
hope it helps
the equation of the quadratic function represented by the graph is y=a(x-3)^2-1. What is the value of a?
Plz help I don't understand how to solve.
Answers
Answer:
Value of a is 2
Step-by-step explanation:
Given the equation of the quadratic function represented by the graph is [tex]y=a(x-3)^2-1[/tex]. we have to find the value of a.
As seen in the figure, parabola cuts the graph at point (2,1) implies point (2,1) is one of the solution of the given quadratic equation i.e of given parabola.
∴ Point (2,1) satisfies the given equation.
Hence, we can find the value of a by putting the value of x and y, we get
[tex]1=a(2-3)^2-1[/tex]
⇒ [tex]2=a[/tex]
Hence, the value of a is 2
Answer:
2
Step-by-step explanation:
Have a good day :)
PLEASE someone help me on this!!
BRAINLIEST AVAILABLE
Answers
what set of transformations could be applied to rectangle ABCD to create A’B’C’D’?
A)Reflected over the x-axis and rotated 180 degrees
B)Reflected over the y-axis and rotated 180 degrees
C)Reflected over the x-axis and rotated 90 degrees counterclockwise
D)Reflected over the y-axis and rotated 90 degrees counterclockwise
Answers
Answer:
C)Reflected over the x-axis and rotated 90 degrees counterclockwise
Step-by-step explanation:
Reflection over the x-axis move point C from (-1, 1) to (-1, -1), point D from (-1, 2) to (-1, -2), point A from (-4, 2) to (-4, -2) and point B from (-4, 1) to (-4, -1). As can be seen, y-coordinate changes sign, so that, the distance between the original point and its reflection respect x-axis remains the same.
Rotation 90 degrees counterclockwise around origin means that x-coordinate and y-coordinate switches and x-coordinate is multiplied by -1. So, point (-1, -1) transforms into (1, -1) - point C' -, (-1, -2) transforms into (2, -1) - point D' -, point (-4, -2) transforms into (2, -4) - point A' - and point (-4, -1) transforms into (1, -4) - point B'.
Determine whether the given measures can be the lengths of the sides of a triangle. write yes or no. explain. 9.2, 14.5, 17.1
Answers
h²=a²+b²
h=√(a²+b²)
h: It is the hypotenuse (The opposite side of the right angle and the longest side of the triangle).
a and b: They are the legs (The sides that form the right angle).
The result of h=√(a²+b²), should be 17.1 (The longest side given in the problem). So, let's substitute the values of the legs into the Pythagorean equation:
h=√(a²+b²)
h=√((9.2)²+(14.5)²)
h=17.1
Therefore, the answer is:
Yes, the given measures can be the lengths of the sides of a triangle.
Answer with explanation:
If the length of three segments are, 9.2, 14.5 and 17.1 ,it can be sides of triangle if , Sum of two segments is greater than the third segment.
1.→ 9.2 +14.5=23.7 >17.1
2.→ 14.5 +17.1=41.6 > 9.2
3.→17.1 +9.2=26.3 >14.5
As, sum of any two segment is greater than third segment, so the following measurements can be the the lengths of the sides of a triangle.
Denise and Stacey went to a carnival. The admission fee was $6 per person. Each ride at the carnival costs c dollars. The game booths charged g dollars for each game. Both Denise and Stacey went on 7 rides each. Stacey played 3 games, while Denise played 2 games. Which expression represents the total amount of money that Denise and Stacey spent at the carnival? 7c + 5g + 6 7c + 5g + 12 14c + 5g + 6 14c + 5g + 12
Answers
This makes a total of $12,-
(Since 6 x 2 = 12).
Next up, the ride at the carnival. This costs c dollars.
This makes a total of 14c
(Since they have made a total of 14 rides (7 each), and we multiply it by 'c')
Finally the game boots, which costs g dollars a game.
Denise and Stacey played a total of 5 games, hence the total cost of the boots will be 5g.
The total cost will therefore be: 14c + 5g + 12
This makes the fourth answer (in your question) the correct answer.
The correct answer is D. 14c + 5g + 12.
The entry fee is $6 each. 6 + 6 = 12
Each girl goes on 7 rides which cost c dollars. 7c + 7c = 14c
The number of games both girls play totals 5. And each game costs g dollars. 2g + 3g = 5g.
Add all the costs up and you get 14c + 5g + 12 as their total cost for going to a carnival.
Subtract and polynomials (3x^2+5x+7)-(-4x^2+3x-6 please help ASAP
Answers
Steps:
Rewrite Problem
Change all signs in the second parenthesis to the opposite sign
Combine Like Terms
If rectangle WXYZ is slid three units to the right what will be the coordinates of point W?
A) (0, 2)
B) (3, -1)
C) (3, 5)
D) (6, 2)
Answers
The correct answer is (D) (6, 2).
To find the new coordinates of point W after sliding the rectangle three units to the right, you need to add 3 to the x-coordinate of point W.
Given the initial coordinates of rectangle WXYZ, if the point W is at (x, y), then after sliding three units to the right, the new coordinates of W will be (x + 3, y).
Therefore, the correct answer is (D) (6, 2).