:. In the diagram below, AC is congruent to CE and D is the midpoint of CE. If CE = 10x + 18, DE = 7x - 1, and BC = 9x - 2, find AB.
Answers
Answer:
25
Step-by-step explanation:
Since AC is similar to CE, we can say that they have equal lengths. We are given CE, DE, and BC. To solve this, we can solve for the length of CE (equal to AC) and then subtract that from BC.
To solve for CE, we are given DE and CE. We know that DE is 1/2 of CE because D is the midpoint of CE. Therefore,
7x-1 = 1/2(10x+18)
expand
7x-1 = 5x + 9
add 1 to both sides to separate the 7x
7x = 5x + 10
subtract 5x from both sides to separate the x
2x = 10
divide both sides by 2 to separate the x
x=5
Therefore, DE = 7(5)-1 = 34 and CE = 10(5) + 18 = 68 = AC.
Using x=5, we know that BC = 9(5) -2 = 43
Therefore, AB = AC-BC = 68-43 = 25
D is the midpoint of CE, so if you draw a line with those three points, it'll look like C-D-E.
Since DE = 7x-1, which also means CD = 7x-1.
CD + DE = CE, so (7x-1)+(7x-1) = 10x+18.
Therefore, x = 5 and CE = 68.
Since AC is congruent to CE, AC = 68.
Assuming the point B is somewhere between AC.
Since BC = 9x-2 and x = 5, which means BC = 43.
AC - BC = AB, so 68 - 43 = 25.
Therefore, AB = 25
Related Questions
What Is the factored form of the polynomial
x^2-12x+27
Answers
Step-by-step explanation:
The Answer is (x-9) (x-3) Factor 12 and 27 out.
Answer:
[tex]x^{2} -12x+27=[/tex]
[tex](x-3)and\:(x-9)[/tex]
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hope it helps...
have a great day!!
Jacob and sumalee each improved their yards by planting daylilies and geraniums. They bought their supplies from the same store. Jacob spent $107 on 11 daylilies and 4 geraniums. Sumalee spent $60 on 4 daylilies and 12 geraniums. Find the cost of one daylilies and the cost of one geranium.
Answers
Answer:
Daylily: $9
Geranium: $2
Step-by-step explanation:
1 daylily costs x.
1 geranium costs y.
11x + 4y = 107
4x + 12y = 60
Multiply the first equation by 3 and subtract the second equation from it.
29x = 261
x = 9
4x + 12y = 60
4(9) + 12y = 60
12y = 24
y = 2
Answer:
Daylily: $9
Geranium: $2
Answer:
1) Set up a system of equations. Assign each plant a variable. I used X for Daylillies and Y for Geraniums. In this case:
11x + 4y = 107
4x + 12y = 60
2) Get one variable by itsef. You can choose to either get the X or the Y by itself. For the sake of ease, I'll go with achieving X.
3) Using the equation 4x + 12y = 60, isolate the 4x.
4x = -12y + 60
4) Divide both sides by 4.
x = -3y + 15
5) X is isolated. Now plug in that isolated X into another remaining equation in order to isolate Y. Don't forget to combine like terms.
11(-3y + 15) + 4y = 107
-33y + 165 + 4y = 107
-29y + 165 = 107
-29y = -58
y = 2
6) You have your Y, which means that each Geranium costs $2 each. Now, you need to find X. Plug in Y into any of the first two equations that we started with.
4x + 12(2) = 60
4x + 24 = 60
4x = 36
x = 9
7) You now have both X and Y. Daylillies cost $9 each, and Geraniums cost $2 each.
8) You can double-check your answers by plugging in your final X and Y values into any of the first equations you wrote. If it comes out equal, it works.
A high school held an election for class president. Exactly 1,000 votes were cast and they were all for either Gillian or Clive. Gillian received 100 more votes than Clive. What percent of the 1,000 votes were for Gillian?
Answers
Answer: 60%
1000÷2=500
Clive: 500-100= 400
Gillian: 500+100= 600 (Because Gillian has 100 more votes than Clive)
[tex] \frac{600}{1000} \times 100\% = 60\%[/tex]
If Gillian received 100 more votes than Clive, Gillian received 55% of the 1,000 votes.
To determine the percentage of votes for Gillian out of the total 1,000 votes, we need to calculate the proportion of votes that Gillian received.
Given that Gillian received 100 more votes than Clive, we can set up the equation:
Votes for Gillian = Votes for Clive + 100
Let's denote the number of votes for Clive as C. Therefore, the number of votes for Gillian is C + 100.
The total number of votes is 1,000, so we have the equation:
C + (C + 100) = 1,000
Simplifying, we find:
2C + 100 = 1,000
2C = 900
C = 450
Therefore, Clive received 450 votes and Gillian received 450 + 100 = 550 votes.
To calculate the percentage of votes for Gillian, we divide her votes by the total votes and multiply by 100:
(550 / 1,000) * 100 = 55%
To learn more about percentage click on,
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A jug holds 10 pints of milk. If each child gets one cup of milk, it can serve children. (Hint: 1 cup = 8 fluid ounces and 1 pint = 16 fluid ounces.)
Answers
Answer:
20 children
Step-by-step explanation:
We can see that 1 pint is equal to 2 cups. Since the jug holds 10 pints of milk, we can convert that to cups by multiplying by 2. We realize that the jug holds 20 pints of milk.
Since each child needs one cup of milk to be satisfied, we can state that the jug can satisfy 20 children.
Answer:
20 childrenyjvvvvggguggggyg
How many fives makes 6 tens
Answers
Answer:
12 fives
Step-by-step explanation:
6 tens is 60, so 60÷5 is 12
Answer:
12
Step-by-step explanation: 60 divided by 12 is 5 and 12 times 5 is 60 so there you go.
You sunk my battleship...The hms petticoat and uss junction are being monitored on a tracking screen where each ship is measured in millimeters from the lower left corner. The linear path of the hms petticoat is given by y=2x+50. If x=3t, express y as a function of t minutes
Answers
Answer:
y = f(t) = 6t + 50
Step-by-step explanation:
Given:
y = 2x + 50
Where,
x = 3t
Substitute x = 3t into the equation
y = 2x + 50
y = 2(3t) + 50
Open parenthesis
y = 6t + 50
y = f(t) = 6t + 50
pls help- the question kept cutting off before:
If cos(πr) = 2 cos(πr) and 0 < r < 3, what is one possible value of r?
Answers
Answer:
r can be 0.5
Step-by-step explanation:
Here, we want to get a possible value of r
From the question, the value of r is between 0 and 3
Mathematically, we know that in degrees pi is the same as 180 degrees
In a case where we have r = 1/2
we have it that;
cos(pi/2) = 2 cos (pi/2)
Since pi/2 is 90 and cos 90 is zero; then we have it that the two sides of the equation is the same and r can be 1/2
Jahlil is 6 inches shorter than 4 times his sister’s height. Jahlil’s height is 70 inches.
Answers
Answer:
x = his sister's height = 19 inches
Step-by-step explanation:
Let
x = his sister's height
Jahlil's height is given by the equation:
4x - 6 = 70
4x = 70 + 6
4x = 76
x = 76/4
x = 19 inches
x = his sister's height = 19 inches
Check:
4x - 6 = 70
4(19) - 6 = 70
76 - 6 = 70
70 = 70
Expansion (2x-3y+4z)^2
Answers
Answer:
Step-by-step explanation:
(a+b+c)²=a²+b²+c²+2ab+2bc+2ca
(2x-3y+4z)²=(2x)²+(-3y)²+(4z)²+2(2x)(-3y)+2(-3y)(4z)+2(4z)(2x)
=4x²+9y²+16z²-12xy-24yz+16zx
We know that,
→ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
Now Putting 2x = a, -3y = b and 4z = c , we get
→ (2x - 3y + 4z)²
→ (2x)² + (- 3y)² + (4z)² + 2 × 2x × (- 3y) + 2 × (- 3y) × 4z + 2 × 4z × 2x
→ 4x² + 9y² + 16z² - 12xy - 24yz + 16zx
Arranging according to the like terms, we get
→ 4x² - 12xy + 16zx + 9y² - 24yz + 16z²
▬▬▬▬▬▬▬▬▬▬▬▬What is the median of the data set given below?
19, 22, 46, 24, 37, 16, 19,33
A. 24
B. 23
C, 19
D. 27
Answers
Answer:
B. 23
Step-by-step explanation:
16, 19, 19, 22, 24, 33, 37, 46
Median = n/2
= 8/2
= 4//
(22 + 24)÷2 = 46 ÷ 2
= 23
help please
1 2 3 4 5 6 7 8 9 10
Answers
Answer:
place it 2 3 4 5 6 7 8 9 10 1 then is come 18
Answer:
2 3 4 5 6 7 8 9 10 1 then come 18
What is the solution to the equation below?
√2x/√x-1=2
A. 4 B. 2 C. 5 D.3
Answers
Given:
The given equation is:
[tex]\dfrac{\sqrt{2x}}{\sqrt{x-1}}=2[/tex]
To find:
The solution for the given equation.
Solution:
We have,
[tex]\dfrac{\sqrt{2x}}{\sqrt{x-1}}=2[/tex]
On simplification, we get
[tex]\sqrt{2x}=2\sqrt{x-1}[/tex]
Squaring both sides, we get
[tex]2x=4(x-1)[/tex]
[tex]2x=4x-4[/tex]
[tex]2x-4x=-4[/tex]
[tex]-2x=-4[/tex]
Divide both sides by -2.
[tex]x=\dfrac{-4}{-2}[/tex]
[tex]x=2[/tex]
Therefore, the correct option is B.
a ratio equivalent to 10:15
Answers
Answer:
3/2, 6/4, 9/6, 12/8, 15/10, 18/12, 21/14, 24/16, 27/18, 30/20, 33/22, 36/24, 39/26, 42/28, 45/30, 48/32, 51/34, 54/36, 57/38, 60/40
Step-by-step explanation:
Answer:
20 : 30
Step-by-step explanation:
Given Ratio :-
10 : 15Equivalent Ratio :-
10 : 15 10 / 15 10 * 2 / 15 *2 20 / 30 20 : 30can someone help me with this?
Answers
Answer:
-64 is the 26th number
it's an arithmetic sequence because the difference between the number is constant : -3
they are all -3 in difference
Step-by-step explanation:
an = a1 + (n-1)d
an = the nᵗʰ term in the sequence
a1=the first term in the sequence
d=the common difference between terms
-64 = 11 + (n - 1)-3
-64=11 -3n+3
-78 = -3n
n = 26
help i’m so confused
Answers
Answer:
-27/7
Step-by-step explanation:
put x into the equation
Find the measure of the indicated side
Answers
Answer: X = 8
Step-by-step explanation:
Lim x->-5(((1)/(5)+(1)/(x))/(10+2x))=
correct answer 1/10x = -1/50
explain:
Answers
Given:
The limit problem is:
[tex]lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}[/tex]
To find:
The value of the given limit problem.
Solution:
We have,
[tex]lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}[/tex]
It can be written as:
[tex]=lim_{x\to -5}\dfrac{\dfrac{x+5}{5x}}{2(5+x)}[/tex]
[tex]=lim_{x\to -5}\dfrac{x+5}{5x}\times \dfrac{1}{2(5+x)}[/tex]
[tex]=lim_{x\to -5}\dfrac{1}{5x\times 2}[/tex]
[tex]=lim_{x\to -5}\dfrac{1}{10x}[/tex]
Applying limit, we get
[tex]lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{10(-5)}[/tex]
[tex]lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{-50}[/tex]
Therefore, the value of given limit problem is [tex]-\dfrac{1}{50}[/tex].
Which equations are true?
Choose All Answers That Apply (10 Points)
Answers
Answer:
B
Step-by-step explanation:
Two negatives is a positive, and you want your outcome to be a positive x, therefore b is the correct answer.
Answer:
second one
A negative multiplied by a negative is a positive.
- (-x) is multiplication.
Thank you very much you can help me with the others that I am uploading to my profile and there is more in case you can please
Answers
Answer: y = 2x + 20; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.
Step-by-step explanation:
Because it's time, it don't have to be just integers. Seconds are fractions of minutes.(0,20) is the y-intercept and there will be no smaller y-values because x(time) cannot go negative.He goes at a rate of a problem per 2 minutes, so 2 is his slope.Answer:
The second one is the answer.
Step-by-step explanation:
Objective: Linear Equation Problems.
Let model the equation given to us.
Vlad spent 20 minutes on his homework already and he complete x math problems every 2 minutes so we represent this as
[tex]y = 2x + 20[/tex]
X can be any real number greater than or equal zero because time isnt negative so anything below zero is wrong.
Y can be any real number but however since Vlad spent 20 mins on his homework already, he must spend over or equal to 20 minutes completing the total homework.
The second one is the answer
Please help I will mark brainliest- I already know it’s not the last two- please help!
Answers
Answer:
Traversable because it has exactly two odd nodes
Step-by-step explanation:
There is a rule that says it is traversable if it has exactly 2 odd nodes. The are other rule where it can be traversable is if has no odd nodes.
Also if we let the starting point be D and the ending point be B we can travel the network in such way that each edge is only traveled once which is the definition that the network is traversable.
So I will do this by starting at D, then travel to A using the outside edge, then travel to back to D using inside edge, then travel to C, then travel to B, then travel to A using outside edge, and then back to B from A using inside edge.
W=VI. Make V the subject of formula
Answers
Answer:
hope that is helpful
Step-by-step explanation:
W= VI
W= VI
I. I
V= W
I
Answer:
V = [tex]\frac{W}{I}[/tex]
Step-by-step explanation:
Given
W = VI ( isolate V by dividing both sides by I )
[tex]\frac{W}{I}[/tex] = V
In ΔOPQ, the measure of ∠Q=90°, OQ = 39, QP = 80, and PO = 89. What ratio represents the cosine of ∠P?
Answers
Answer:
The cosine of angle P = opposite / adjacent = 39 / 80
Step-by-step explanation:
What is the gradient of the graph shown? In its simplest form
Answers
Answer:
1
Step-by-step explanation:
the line passes point (-3,0) abd (0, 3)
so, the gradient = (3-0)/(0+3) = 3/3 = 1
Find slope if a line pass through the original and (3,2)
Answers
heyy im not sure if you meant origin instead of original but the origin would be (0,0)
Answer:
2/3
Step-by-step explanation:
the slope form equation is : y2 - y1/ x2-x1 (aka change in y divided by change in x)
so it would be 2-0/ 3-0 = 2/3
the slope is 2/3
Helpppp ,I will mark you brainlist
Answers
Answer:
Okay
Step-by-step explanation:
Can someone please help me with this?
Answers
Answer:
p = 1.2
Step-by-step explanation:
Bring 3.9 to the other side of the equation.
-10.9p = -13.08
p = 1.2
Sarah finds herself with 9 different cheeses and 9 different wines. In how many ways can she pair one cheese to one wine
Answers
Answer:
She has 9 choices for each different cheese.
For each of these cheeses there are 9 different wines,
So 9 * 9 = 81 and there are
81 possible different choices
Which formulas can be used to find the surface area of a right prism where p is the perimeter of the base, h is the height of the prism, BA is the area of bases, and LA is the lateral area? Check all that apply.
A. SA = BA - LA
B. SA = p + LA
C. SA = BA + LA
D. SA = BA + ph
E. SA = 1 / BA + LA
Answers
Answer:
SA=BA+LA and SA=BA+ph
Step-by-step explanation:
I just looked it up
The correct formulas to find the surface area of a right prism are:
SA = BA + LA and SA = BA + ph.
Options (A), and (D) are the correct answer.
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
The correct formulas to find the surface area of a right prism are:
1)
SA = BA + LA, where SA is the total surface area, BA is the area of the two identical bases, and LA is the lateral area (the sum of the areas of all the rectangular sides).
2)
SA = BA + ph, where SA is the total surface area, B is the area of one base, p is the perimeter of the base, h is the height of the prism, and ph is the area of all the rectangular sides (the lateral area).
Therefore,
The correct formulas to find the surface area of a right prism are:
SA = BA + LA and SA = BA + ph.
Learn more about prism here:
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Please help me asap!
Answers
Answer:
Its 48
Step-by-step explanation:
subtract 69 and 56 from 173, what you have left is your answer
48
Step-by-step explanation:
total 176 subtract 69 and 58 since they are given.
176 - 69 -56 = 48
find the volume of the rectangular prism. plz answer this lol
Answers
Answer:
.....how when the dimensions are not even clear lol
Answer:
48 cm³
Step-by-step explanation:
the volume of a rectangular prism= length × breadth × height
= 8× 3 × 2
= 48 cm³
