If B is the midpoint of AC, solve for x, and find the lengths of AB, BC, and AC.
Please show all work and not just the answers.
Answers
Answer:
x = 2
AB = 15
BC = 15
AC = 30
Step-by-step explanation:
Given that B is the midpoint of AC, then AB = ½ of AC.
AB is given as 3(3x - 1),
AC = 5(2x + 2),
Therefore:
[tex] 3(3x - 1) = \frac{1}{2}*5(2x + 2) [/tex]
Solve for x
[tex] 9x - 3 = \frac{5}{2}(2x + 2) [/tex]
Multiply both sides by 2
[tex] 2(9x - 3) = \frac{5}{2}(2x + 2)*2 [/tex]
[tex] 18x - 6 = 5(2x + 2) [/tex]
[tex] 18x - 6 = 10x + 10 [/tex]
[tex] 18x - 10x = 6 + 10 [/tex]
[tex] 8x = 16 [/tex]
Divide both sides by 8
[tex] x = 2 [/tex]
[tex] AB = BC = 3(3x - 1) [/tex]
Plug in the value of x
[tex] AB = BC = 3(3(2) - 1) [/tex]
[tex] = 3(6 - 1) = 3(5) = 15 [/tex]
[tex] AC = 5(2x + 2) [/tex]
[tex] AC = 5(2(2) + 2) [/tex]
[tex] AC = 5(4 + 2) = 5(6) = 30 [/tex]
Related Questions
Name the sets of numbers to which
3/5
belongs
Answers
Answer:
Fractions , Rational numbers ,Real numbers
Step-by-step explanation:
-3/5 is arguably a real number
Given g(x) = x2-4
Find g(-3)
Answers
Answer:
-10
Step-by-step explanation:
g(-3)=3×3 -4
=9-4
=5
Answer: 5
Step-by-step explanation:
g(x)=x²-4
g(-3)=(-3)²-4
g(-3)=9-4
g(-3)=5
Hope this helps!! :)
Please let me know if you have any question or need any further explanation
Sebastien hand-crafts circular braided rugs. The graph shows the prices of various sizes of his rugs. A customer ordered 3 identical rugs for a total of $1,350. Use the graph to determine the radius of each rug in the order. (Enter numerical answer only). Please help.
Answers
The correct answer is 6 ft
Explanation:
It is known the customer bought 3 identical rugs, which means the size and radio of each rug was the same. Moreover, the total this customer paid for the rugs was $1350, which is equivalent to $450 for each rug as $1350 ÷ 3 = $450.
Besides this, the black line in the graph shows at $450 (between 400 and 500 in the y-axis) the rugs have a ratio of 6 feet, which is shown in the x-axis as these two values intersect or align to form the black line. This means a carpet with a radius of 6ft costs $450, and therefore each of the rugs the customer bought had a radius of 6ft.
The length of a rectangle is 2 m more than twice its width. Find the length and width of the rectangle, if its perimeter is 28 m.
Please use algebra.
Answers
Answer:
Length is 10
Width is 8
Step-by-step explanation:
The formula for the perimeter of a rectangle is:
[tex]P=2l+2w[/tex]
We are told that the length l is 2 more than twice the width w. In other words:
[tex]l=2+2w[/tex]
Also, we are given that the perimeter is 28. Therefore:
[tex]P=2l+2w\\28=2(2+2w)+2w[/tex]
Distribute:
[tex]28=4+4w+2w[/tex]
Combine like terms:
[tex]28=4+6w[/tex]
Subtract 4 from both sides:
[tex]6w=24[/tex]
Divide by 6:
[tex]w=4[/tex]
So, the width is 4.
And the length is 2 more than twice the width. Thus:
[tex]l=2+2(4)\\l=2+8=10[/tex]
The length is 10.
And we are done :)
What is this answer ?
Answers
Answer:
its a bit cut off can u add the whole screen pls
Step-by-step explanation:
Answer:
KL NM
Step-by-step explanation:
that is the answer
Deshaun and Isabel each have opened a savings account today. Deshaun opened her account with starting amount of $590 and she'll take out $35 each month Isabel opened here with a start of $790 and she'll take out $55 per month (A) For each account write an expression for the amount of zkids in the account after x months (B) Write an equation to show when the two accounts would have the same amount of money
Answers
Answer:
Deshaun = $590 - $35x
Isabel : $790 - $55x
$590 - $35x = $790 - $55x
Step-by-step explanation:
For Deshaun :
Amount in her account = $590
Amount she would have withdrawn by month x = $35 × x = $35x
The amount she would have in her account = $590 - $35x
For Isabel :
Amount in her account = $790
Amount she would have withdrawn by month x = $55 × x = $55x
The amount she would have in her account = $790 - $55x
Let x be the time when the money in their account would be equal =
$590 - $35x = $790 - $55x
The members of a cooking club are making cakes, which they will sell at a street fair for $9 apiece. It cost $50 for a booth at the fair, and the ingredients for each cake cost $4. At some point, the club members will sell enough cakes so that their sales cover their expenditures. How much will the sales and expenditures be?
Answers
Answer:
Sales= $90
Expenditures= $90
Step-by-step explanation:
The members of a cooking club are making cakes.
The cakes will be sold at a street fair price of $9 for each cake.
It cost $50 for a booth at the fair.
The ingredients for each cake cost $4
Let y represent the number of cakes that was sold
Since the price of each cake is $9 then,
Sales = $9y
Since the booth cost $50 and ingredients cost $4 then,
Expenditures = $50 + $4y
Sales = Expenditures
9y= 50 + 4y
Collect the like terms
9y-4y= 50
5y= 50
Divide both sides by the coefficient of y which is 5
5y/5= 50/5
y= 10
Sales= 9×10
= $90
Expenditures= $50 + 4(10)
= $50+$40
= $90
Hence the sales is $90 and the expenditures is $90
what number sets or set does 11 belong to?
Answers
Answer:
Prime number
Step-by-step explanation:
Because it cannot be be multiplied by any other number less then it.
50 divided by a number y
Answers
What is the meaning of the
word arch"
Answers
Simplify the algebraic expression. (m - 7) + 5(m - 3)
Answers
Answer:
6m -22
Step-by-step explanation:
(m - 7) + 5(m - 3)
= m - 7 + 5m - 15
= 6m -22
Answer: 6m-22
Step-by-step explanation:
Given
(m-7)+5(m-3)
Take off parentheses/distributive property
= m-7+5m-15
Move like terms together
=m+5m-7-15
Combine like term
=6m-22
Hope this helps!! :)
Please let me know if you have any question
brainleist find the set of which -8/9 belongs to A integers b whole numbers c irrational numbers d real numbers e rational numbers f natural numbers
Answers
The sum of two numbers is 180. If one number is 40% more than the other, find the numbers
Answers
Answer:
We have 2 values to work with, both in terms of x. the first value is just x, our first number. The second value is 40% higher than the original.
x + (x + .4x) = 180
x + 1.4x = 180
2.4x = 180
x = 180/2.4
x = 75 1.4(75) = 105
Check:
75 * .4 = 30
75 + 30 = 105
Answer:
75, 105
Step-by-step explanation:
Let's let the two numbers be a and b.
The sum of them is 180. Thus:
[tex]a+b=180[/tex]
One of the number is 40% more than the other. In other words, let's let a be the bigger number:
[tex]a=1.4b[/tex]
Substitute this into the first equation:
[tex]1.4b+b=180[/tex]
Combine like terms:
[tex]2.4b=180[/tex]
Divide everything by 2.4:
[tex]b=75[/tex]
So, b is 75.
And their sum is 180. Thus, a is 180-75 or 105.
And we're done!
6. Write 1.12 repeating as a mixed number.
Answers
Answer:
3
1 -----
25
Step-by-step explanation:
Write the function g(x) as a transformation of the parent function
f(3) = |sc|, where the graph has been vertically compressed by a factor of
ş, shifted right 2 units, and shifted up 10 units.
A g(x) = 12 +2] +10
B g(x) = {\2 + 101 – 2
C g(x) = - +2] + 10
D g(x) = 42-2/+10
Answers
Which table represents a linear function? sorry im dumb ;w;
Answers
Answer:
Your answer is the third option
A linear function has to be added or subtracted by the same number every time. The independent variable is x and the dependent variable is y.
So for side "x" 1 is being added to each number and for side "y" is being subtracted by 2
You have to simplify this expression.
-2x+3-(5-6x)
Answers
Answer:
4x−2
Step-by-step explanation:
Answer:
4x -2
Step-by-step explanation:
-2x+3-(5-6x)
Distribute the minus sign
-2x+3-5+6x
-2x+6x +3-5
4x -2
An instructional video is 1.8 minutes long. How long is the video in seconds? How long is it in hours?
Answers
Answer:
108 seconds and 0.03 hours
Laurissa rolls two number cubes, each with the numbers 1 through 6. Laurissa adds the numbers that appear on the roll Which two sums have an equal chance of occurring?
Answers
Answer:
2 and 12;
4 and 10;
5 and 9
6 and 8
Step-by-step explanation:
Given
Roll of two number cubes
Required
Determine the sums which have equal chance
Represent the sample space of both number cubes with S1 and S2
[tex]S_1 = \{1,2,3,4,5,6\}[/tex]
[tex]S_2 = \{1,2,3,4,5,6\}[/tex]
Next, get the outcome of roll two number cubes
Outcome = [tex](1,1)(1,2)(1,3)(1,4)(1,5)(1,6)\ (2,1)(2,2)(2,3)(2,4)(2,5)(2,6)\ (3,1)(3,2)(3,3)(3,4)(3,5)(3,6)[/tex][tex](4,1)(4,2)(4,3)(4,4)(4,5)(4,6)\ (5,1)(5,2)(5,3)(5,4)(5,5)(5,6)\ (6,1)(6,2)(6,3)(6,4)(6,5)(6,6)[/tex]
Next, get the sample space;[tex]S = \{2,3,4,5,6,7, 3,4,5,6,7,8, 4,5,6,7,8,9, 5,6,7,8,9,10, 6,7,8,9,10,11, 7,8,9,10,11,12\}[/tex]
Reorder from lowest to highest[tex]S = \{2,3,3,4,4,4,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12 \}[/tex]
Next, form a frequency table
Sum -- Frequency
2 ---- -- 1
3 ---- -- 2
4 ---- -- 3
5 ---- -- 4
6 ---- -- 5
7 ---- -- 6
8 ----- -- 5
9 - ------ 4
10 --- -- 3
11 --- ---- 2
12 ------ 1
From the above table, we can now determine the two sums that have equal probability;
The two sums that have equal probability have the same frequency;
Hence;
2 and 12 have the same chance of occurring
4 and 10 have the same chance of occurring
5 and 9 have the same chance of occurring
6 and 8 have the same chance of occurring
Answer:
5 and 8
Step-by-step explanation:
I NEED THIS ANSWER ASAP!!!! The height of tower A is 644 feet more than tower B. The two towers have a combined height of 1590 feet. What are the heights of each tower?
Answers
Answer: oop ;-;
Step-by-step explanation: We have two basic equations
A = B + 826 A is 826ft taller than B
A + B = 1516 Combined height is 1516 ft
Replace A with B+826 in 2nd equation and solve for B
B + 826 + B = 1516 Combine like terms
2B + 826 = 1516 Subtract 826 from both sides
2B = 690 Divide both sides by 2
B = 690/2
B = 345 ft
We know that A = B + 826 so you simply need to do
that addition to have the height of both towers.
how to do this question plz answer me step by step plzz
Answers
Answer:
The four angles are;
30 degrees, 85 degrees, 95 degrees , and 150 degrees
Step-by-step explanation:
Call the four angles of this quadrilateral A, B, C, and X (being X the smallest angle)
Then angle A is 55 degrees larger than X , therefore we can write it as X+55
Angle B is 65 degrees larger than X , therefore we can write it as X+65
Angle C is 120 degrees larger than X , therefore we can write it as X+120
Then we know that the addition of all four angles of a quadrilateral must give 360 degrees , so we have:
X + X + 55 +X + 65 + X + 120 = 360
that is:
4 X + 240 = 360
4 X = 360 -240
4 X = 120
X = 120/4
X = 30 degrees
and the other angles are:
30 + 55 = 85 degrees
30 + 65 = 95 degrees
30 + 120 = 150 degrees
Prove theorems about triangles examine each triangle
Answers
Answer:
not possible
Step-by-step explanation:
[tex]a^{2} + b^{2} = c^{2}[/tex]
25 + 196 = 400
221=400
Chocolate and peanut butter cookies are randomly chosen from a cookie jar and placed onto a plate. The first plate had four chocolate chip cookies and one peanut butter cookie. A second plate was prepared with 2 chocolate cookies and p peanut butter cookies. If the probability of drawing a chocolate cookie from each plate is 8/25, how many peanut butter cookies, P, are on the second plate?
Answers
Answer:
Step-by-step explanation:
Which is the better buy, 6 bagels for $3.29 or 8 bagels for $4.15? Justify your answer by giving the cost per bagel for each offer in order to get full credit.
Answers
ex. 3.29/6= 0.5483 = 0.55
Answer: The better buy would be 8 bagels for $4.15
explanation: If you were to buy 6 bagels for $3.29, It would be about $.54 per bagel. but if you were to buy 8 bagels for $4.15, it is about about $.52 per bagel which makes it a better deal.
Match the statement to the property it shows.
If MN = XY, and XY = AB, then MN = AB.
If AB = CD, then CD = AB.
Segment CD is congruent to segment CD.
Answers
Answer:
If MN = XY, and XY = AB, then MN = AB. Transitive Property
If AB = CD, then CD = AB. Symmetric Property
Segment CD is congruent to segment CD. Reflexive Property
Step-by-step explanation:
Transitive property states that for all reall numbers a, b, and c, if a = b, b = c, then a = c.
Symmetric Property states that for all real numbers a and b, if a = b, then b = a.
Reflexive Property states that for every real number a, a=a
1. Transitive property
2. Symmetric property
3. Reflexive property
What are equivalence properties ?The equivalence properties are Reflexive property, Symmetric property & Transitive property.
Reflexive Property : For every real number a, a=a
Symmetric Property : For real numbers a & b, if a=b then b=a
Transitive Property : For real numbers a, b, c, if a=b & b=c then a=c
What are the perfect matches ?1. If MN = XY, and XY = AB, then MN = AB ⇒ Transitive property
2. If AB = CD, then CD = AB ⇒ Symmetric property
3. Segment CD is congruent to segment CD ⇒ Reflexive property
Learn more about equivalence properties here :
https://brainly.com/question/2273381
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4.32x+1=17.8929 Sole for x
Answers
Answer:
x = 3.91039
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
4.32x + 1 = 17.8929
Step 2: Subtract 1 on both sides
4.32x = 16.8929
Step 3: Divide both sides by 4.32
x = 3.91039
Solve in fraction form.
3
Angela has 7 cups of rice and she buys another 2 cup. How much rice does Angela have in all?
Answers
Answer:
Hey there!
Angela will have 7+2, or 9 cups of rice.
Let me know if this helps :)
Answer:
7/2
Step-by-step explanation:
You have r red balls, w white balls in a bag. If you keep drawing balls out of the bag until the bag now only contains balls of a single color (ie you run out of a color) what is the probability you run out of white balls first
Answers
Answer:
[tex] \frac{w}{w + r} [/tex]
Analyze the logical statements to fill in the missing information.
1. If a line is horizontal, then it has a slope of 0.
Hypothesis:
Conclusion:
2. A vertical line has an undefined slope.
The statement in equivalent "if-then" form would be:
Hypothesis:
Conclusion:
Answers
Answer:
1,2,2,1,2
Step-by-step explanation:
on edg
Conclusion: a slope of 0
Hypothesis: is there is a vertical lineConclusion: then it has an undefined slope.
What is Hypothesis?
A hypothesis, in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.
given:
1. If a line is horizontal, then it has a slope of 0.
Hypothesis: line is horizontal
Conclusion: a slope of 0.
2. . A vertical line has an undefined slope.
Hypothesis: is there is a vertical line
Conclusion: then it has an undefined slope.
Learn more about hypothesis here:
https://brainly.com/question/13025783
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Pick any number and add 5 to it. Find the sum of the new number and the original number. Add 5 to the sum. Divide the new sum by 2 and subtract the original number from the quotient. What is the final number?
Answers
Answer: The final number is 5
Step-by-step explanation:
Picked number: 10
STEP are all according to what you stated
10+5=15 (first sentence)
15+10=25 (second sentence)
25+5=30 (third sentence)
30÷2-10=5 (fourth sentence)
The final number is 5.