After the dimensions of an equilateral triangle are increased by a scale factor of 2.5, the perimeter is 45 units. What were the side lengths of the original triangle?
Answer:
Original side of triangle = 6 units
Step-by-step explanation:
Given:
Perimeter = 45 units
Scale factor = 2.5 (Increase)
Find:
Original side of triangle = ?
Computation:
Original Perimeter = Perimeter / Scale factor
Original Perimeter = 45 units / 2.5
Original Perimeter = 18 units
Perimeter of an equilateral triangle = 3 (Side)
18 units = 3 (Side)
Side = 6 units
Original side of triangle = 6 units
Find the volume of this figure
Answer:
74
Step-by-step explanation:
you find the volume of each one by doing length * width * height and once you find the volume of all of them which is 36, 2, 36 you add them all together and you get 74
Answer:
74 ft
Step-by-step explanation:
Volume = length x width x height
For the 1st square - 3 x 3 x 4
For the rectangle in the middle - 1 x 1 x 2
For the last big square - 3 x 3 x 4
___________________________________
3 x 3 x 4 = 36
3 x 3 x 4 = 36
1 x 1 x 2 = 2
___________________________________
36 + 36 + 2 = 74
___________________________________
The volume of this figure is 74 ft
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Prove for any value of y the value of expression y^4−(y^2−9)(y^2+9) is divisible by 9.
Answer:
Step-by-step explanation:
y4−
(y2−9)(y2+9)
9
Distribute:
=y4+
−1
9
y4+9
Combine Like Terms:
=y4+
−1
9
y4+9
=(y4+
−1
9
y4)+(9)
=
8
9
y4+9
Answer:
=
8
9
y4+9
The polynomial expression is divisible by 9
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
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 polynomial be represented as A
Now , A = y⁴ - (y² - 9)(y² + 9)
To prove that the expression y⁴ - (y² - 9)(y² + 9) is divisible by 9 for any value of y, we can use algebraic manipulation and factorization.
First, we can simplify the expression inside the parentheses:
y² - 9 = (y - 3)(y + 3)
y² + 9 = (y + 3i)(y - 3i)
where i is the imaginary unit, i.e., i² = -1.
Substituting these expressions back into the original equation, we get:
y⁴ - (y² - 9)(y² + 9) = y⁴ - (y - 3)(y + 3)(y + 3i)(y - 3i)
Now, we can factor out (y − 3)(y + 3) from the second term:
y⁴ - (y² - 9)(y^2 + 9) = y⁴ - (y² - 9)(y² + 9) + 9(y - 3)(y + 3)
= y⁴ - (y² - 3^2)(y² + 3²)
= (y²)² - (3²)²
= (y² + 3²)(y² - 3²)
= (y² + 9)(y² - 9)
= (y + 3i)(y - 3i)(y + 3)(y - 3)
Now, we can see that the expression is equal to the product of four factors: (y + 3i), (y - 3i), (y + 3), and (y - 3). Note that either (y + 3i) and (y - 3i) or (y + 3) and (y - 3) must have the same residue modulo 3, since there are only three residues modulo 3 (0, 1, and 2) and four factors. In either case, the product of the two factors that have the same residue modulo 3 is divisible by 3, and therefore the entire expression is divisible by 3.
Moreover, since (y + 3) and (y - 3) are both odd or both even, the product of (y + 3) and (y - 3) is divisible by 8, which implies that the entire expression is also divisible by 8.
Hence , the expression y⁴ - (y² - 9)(y² + 9) is divisible by both 3 and 8 for any value of y, and therefore it is also divisible by their least common multiple, which is 9
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In the diagram, the circle will be dilated by a scale factor of 3 about the origin. The points C, A and B map to C, A and B'after the dilation. What
is the length of CB? Use the distance formula to help you decide: d = (x2-x)+(y2 - y.)?
18+
164
A = (8.15)
B = (12, 13)
12
101
C = (8.10)
The length of line segment CB is 5 units.
What is distance formula?The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].
Given that, A=(8, 15), B = (12, 13) and C = (8, 10)
Here, substitute (x₁, y₁)= (8, 10) and (x₂, y₂)=(12, 13) in distance formula, we get
CB = √[(12-8)²+(13-10)²]
= √(4²+3²)
= √(16+9)
= √25
CB= 5 units
Therefore, the length of CB is 5 units.
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Are the graphs of the lines in the pair parallel ? Explain.
Y=2/3x-17
3-x - y = -6
A.)Yes, since the slopes are the same and the y-intercepts are different.
B.)No, since the slopes are different.
C.)No, since the y-intercepts are different.
D.)Yes, since the slopes are the same and the y-intercepts are the same.
So the right answer is of option D
Look at the attached picture
Hope it will help you...
Good luck on your assignment
Enter the value of the 8 in the following number. 438.13
Answer:
8
Step-by-step explanation:
It is in the one's place, so it is just 8x1, which is 8
I NEED HELP PLZZZZZZ!!! I NEED TO WRITE SOMETHING...……..
Bob withdrew money from an ATM, put the receipt in an envelope, and filled in the information in his check register.
Explain why it is important for Bob to keep the receipt and record the information in his check register.
Answer:
It is important for bob to keep the receipt and record in the register so he can monitor how much money he has in the account. It prevents being overdrawn. Recording debits and deposits helps with budgeting.
Alina has been collecting video games for a year. The table below shows how many games she has received over
the year.
Amount of video games
4
Birthday
Holidays
School trades
8
6
At the end of the year, she went to a store and sold half of her video games.
Which numerical expression shows the amount of video games Alina has left after selling half?
Choose 1 answer:
(4+8) + (6 + 2)
2 : (4 +8+6)
© (4+8+6) : 2
The numerical expression shows the amount of video games Alina has left after selling half will be (4 + 8 + 6):2. Then the expression C is correct.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Alina has been collecting video games for a year. The table below shows how many games she has received over the year.
Amount of video games
Birthday 4
Holidays 8
School trades 6
Then the total number of the video games will be
⇒ 4 + 8 + 6
At the end of the year, she went to a store and sold half of her video games.
⇒ (4 + 8 + 6) / 2
⇒ (4 + 8 + 6) : 2
Then the expression C is correct.
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My phone rang midway between 10:53 A.M. one day and 1:05 P.M. the next day. It rang at
a) 11:58 P.M.
b) 11:59 P.M.
c) 12:59 A.M.
d) 1:59 A.M.
Step-by-step explanation:
So lets count the time between 10:53 and 1:05
7 Mins to 11
2 Hours to one
5mins to 1:05
Total 2 hours 12 mins divided by 2 to find the middle
1 hour 6 mins. We add 1 hr 6 mins to 10:53.
10:53 + 6mins equals 11:59
11:59 + 1hour = 12:59
Answer c
find the missing angle in the triangle
Answer:
45
Step-by-step explanation:
Because this is an isosceles triangle, two of the angles must be equal. Since the third angle is 90 degrees, the other two must be 90/2=45 degrees. Hope this helps!
asap-worth 25% of overall
Answer:
ummm
Step-by-step explanation:
what is the question
Is this SAS or Not SAS
Answer:
yes it is sas
Step-by-step explanation:
because one side is shared, they both have right angles and the other side is a given.
Answer:
SAS
Step-by-step explanation:
The sides are all equivalent so it is indeed a SAS triangle.
I need help with this please!
Answer:
The equation of a circle using the center [tex](2,0)[/tex] and the radius [tex]7[/tex]
[tex](x-2)^2+(y-0)^2= 49[/tex]
Step-by-step explanation:
-Directions:
To determine the following circle on a graph, you need the to look for a point that lands exactly on the center of the circle and to find the radius, you need look for a point that lands exactly on the outline of the circle and start counting from the center, to the point. Then, use both the center and the radius for the equation of a circle. After putting the center and radius on the equation of a circle, simplify the radius by the exponent [tex]2[/tex], because according to the equation of a circle, the radius is [tex]r^2[/tex].
-The equation of a circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]
-Finding the center and the radius for the equation of a circle:
Center: [tex](2,0)[/tex] Radius: [tex]7[/tex]
[tex](x-2)^2+(y-0)^2= 49[/tex]
I will give you brainliest if you answer correctly!!
Answer:
The answer is B.
Step-by-step explanation:
Percentages equal to 100% and how?
Answer:
2 or more percents add up to 100% or one percent is 100%
Step-by-step explanation:
The grades on a geometry midterm at Springer are roughly symmetric with u = 73 and 0 = 3.0.
Umaima scored 72 on the exam.
Find the z-score for Umaima's exam grade. Round to two decimal places.
Answer:
z = - 0.33
Step-by-step explanation:
Given that:
Mean (μ) = 73, standard deviation (σ) = 3.0
Z score is a measure in statistics to determine the number of standard deviation a value is above or below the mean of what is measured. If the value is above the mean it is positive but if it is below the mean it is negative. It is given by the equation:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
To calculate z-score for Umaima's exam grade, we need to calculate the z score of 72
For x = 72, the z score is:
[tex]z=\frac{x-\mu}{\sigma}=\frac{72-73}{3} =-0.33[/tex]
z = - 0.33
Answer:
−0.33
Step-by-step explanation:
just did it oh khan
PLS HELP ME FULL WORK SHOWN DUE
To solve this system of equations, we have to cancel out a variable:
12x-4y+28=0
16y-110=48x
Reorder:
12x-4y=-28
-48x+16y=110
Multiply first equation by 4:
4(12x-4y=-28)
-48x+16y=110
=>
48x-16y=-112
-48x+16y=110
0x+0y=-2
0=-2
This can never be true, therefore there are NO SOLUTIONS
Answer:
No Solutions
Angela is using a number cube for a game with faces labeled 1, 2, 3, 4, 5, and 6. Is the number cube fair? Explain why or why not.
Answer: Yes
Step-by-step explanation: It is equal because each side has a chance of it rolling on either 1,2,3,4,5, and 6.
Can someone help me and show how to write the perimeter equation for x to this polygon.50 points Find x for full 70 points
Answer:
10x + 8 = 21
x = 1.3
Step-by-step explanation:
a)
In pentagon ABCDE,
AB = DE = 2x + 3 and BC = CD = x + 1
Perimeter of pentagon ABCDE = 21
4x + 2(2x + 3) + 2(x + 1) = 21
4x + 4x + 6 + 2x + 2 = 21
[tex] \purple {\boxed {\bold{10x + 8 = 21}}} [/tex]
b)
10x = 21 - 8
10x = 13
[tex]x = \frac{13}{10} \\ x = 1.3 \: cm [/tex]
Which line segment is a diameter of T?
Answer:
[tex] \overline{UZ}[/tex]
Step-by-step explanation:
[tex] \overline{UZ}[/tex] is passing through the center of the circle with center T. Therefore [tex] \overline{UZ}[/tex] is the diameter
Answer:
Line UZ
Step-by-step explanation:
This is Beacause Line UZ passes thru T which is the center of the circle.
The diameter is the length of the line through the center that touches two points on the edge of the circle.
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What is the numerator of the next term in the arithmetic sequence?
1/2 2/2 3/2 4/2
Answer:
5
Step-by-step explanation:
The numerator is the value on top, above the denominator. In an arithmetic sequence you are increasing by the same amount each time. In this case, you are increasing by 1/2 each time. 4/2 plus 1/2 is 5/2, so your numerator is 5.
2x - 3 > 15 or 3 + 7x < 17
Answer:
2x-3>15 and 3-7x>17 =
3-7x>17
-7x>14
x<-2
Step-by-step explanation:
Sorry this is not a proper equation. I think you meant this equation.
2x-3>15 and 3-7x>17
for this equation the answer is
3-7x>17
-7x>14
x<-2
f(x) = 5x^2 - x + 8
g(x) = 9x - 1
Answer:
Step-by-step explanation:
But there is not a question?
PLEASE ANSWER QUICKLY. I GIVE BRAINLIEST AND I FOLLOW YOU.
Please do #1 and 2 and show work
Answer:
1= 5x and 7x
2= 3x and 2x
Step-by-step explanation:
its hard to explain you just add them or minus them
Answer:
1) x = 7 y = 19 2) x = 1 y = 3
Step-by-step explanation:
1) y = 4x - 9
y = 2x + 5 Since the equations are equal to y, set them equal to each other
4x - 9 = 2x + 5
-2x - 2x Subtract 2x from both sides
2x - 9 = 5
+ 9 + 9 Add 9 to both sides
2x = 14 Divide both sides by 2
x = 7
Plug this into the first equation
y = 4(7) - 9 Multiply
y = 28 - 9 Subtract
y = 19
2) -3x + 6 = x + 2
+3x +3x Add 3x to both sides
6 = 4x + 2
-2 - 2 Subtract 2 from both sides
4 = 4x Divide both sides by 4
1 = x
Plug this into the second equation
y = 1 + 2 Add
y = 3
The marked price of a water cooler is $ 4500. The shopkeeper offers an off-season discount of 18% on it. Find its selling price.
Answer:
$3690
Step-by-step explanation:
Let's first find what percent of the original price it is being sold for.
100%-18%=82%
The water cooler is being sold for 82% of its original price.
Let's now find 82% of 4500.
0.82*4500=3690
The selling price is $3690
Answer:
3690
Step-by-step explanation:
the original price is 4500
for decreasing or discount we use this formula x discount upo 100 multiply by the original price. so for this question if we apply the formula it will be
18upon 100 x4500. the answer comes as 810. noww we subtract the original price from the discounted price. so 4500-810=3690. comes as ur selling price
The equations 4 x minus 5 y = 5, 3 x + 10 y = 20, 4 x minus 5 y = negative 5, and 3 x + 10 y = negative 20 are shown on the graph below. On a coordinate plane, there are 4 lines. Green line goes through (0, 1) and (2.5, 3). Orange line goes through (0, negative 1) and (2.5, 1). Blue line goes through (0, 2) and (3.5, 1). Pink line goes through (0, negative 2) and (3.5, negative 3). Which system of equations has a solution of approximately (–2.7, –1.2)? 4 x minus 5 y = negative 5 and 3 x + 10 y = negative 20 4 x minus 5 y = 5 and 3 x + 10 y = 20 4 x minus 5 y = 5 and 3 x + 10 y = negative 20 4 x minus 5 y = negative 5 and 3 x + 10 y = 20
Answer:
First one:
4 x minus 5 y = negative 5 and 3 x + 10 y = negative 20
Step-by-step explanation:
4 x - 5 y = -5 (1)
3 x + 10 y = -20 (2)
Multiply (1) by 2 and add to (×)
8x - 10y = -10
3x + 10y = -20
11x = -30
x = -30/11 = -2.727272
x = -2.7
4(-30/11) - 5y = -5
5y = -65/11
y = -13/11 = -1.18181818
y = -1.2
Answer:
4 x - 5 y = - 5 and 3 x + 10 y = - 20
Step-by-step explanation:
4 x - 5 y = -5 (1)
3 x + 10 y = -20 (2)
Multiply (1) by 2 and add to (×)
8x - 10y = -10
3x + 10y = -20
11x = -30
x = -30/11 = -2.727272
x = -2.7
4(-30/11) - 5y = -5
5y = -65/11
y = -13/11 = -1.18181818
y = -1.2
hope this helps..
A circle with circumference 6 has an arc with a
340º central angle.
Answer:
17.80236
Step-by-step explanation:
What is the median of the data in this stem-and-leaf plot?
a 21
b 22
c 23
d 24
Answer:
23
Step-by-step explanation:
The median is the middle number
There are 10 number so the median is between 5 and 6
Take the 5 and 6th terms and average them
(22+24)/2 = 23
Answer
23 (Answer c is correct)hope this helps
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Which values are solutions to the inequality below
Check all that apply
There are two groups of people, three in each, for painting a wall. The numbers in the next two sentences express the time (in hours) spent on painting. In group A, Alex 2.5, Adam 3.6, and Antimo 4.7. In group Z, Zairo 2.2, Zeno 3.2, and Zubro 4.9. Estimate the total time for group A and for group Z when all three workers in each group work together. Which group can paint the wall faster and why do you think so?
(your answer is two numbers
(two estimates) in one sentence where you will explain your reasoning)
Answer:
1. The total time taken for group A to paint the wall together is 1.12 hours
2. The total time taken for group Z to paint the wall together is 1.03 hours
3. group Z can paint the wall faster
Step-by-step explanation:
The time spent on painting are;
Group A
Alex = 2.5 hours
Adam = 3.6 hours
Antimo = 4.7 hours
1. We have for group A
Alex's paint rate = 1 wall in 2.5 hours = 1/2.5 wall/hour
Adam's paint rate = 1 wall in 3.6 hours = 1/3.6 wall/hour
Antimo's paint rate = 1 wall in 4.7 hours = 1/4.7 wall/hour
When the three workers work together, we have;
1/2.5 wall/hour + 1/3.6 wall/hour + 1/4.7 wall/hour = 3767/4230 wall/hour
Therefore, the time for the three workers of group A to paint one wall is given as follows;
[tex]Time \ to \ paint \, one \, wall = \frac{1 \, wall}{\frac{3767}{4230} wall/hour} = 1\tfrac{463}{3767} hours[/tex]
The total time taken for group A to paint the wall together = 1.12 hours
2. The data for group Z is as follows;
Zairo = 2.2 hours
Zeno = 3.2 hours
Zubro = 4.9 hours
We have for group Z
Zairo's paint rate = 1 wall in 2.2 hours = 1/2.2 wall/hour
Zeno's paint rate = 1 wall in 3.2 hours = 1/3.2 wall/hour
Zubro's paint rate = 1 wall in 4.9 hours = 1/4.9 wall/hour
When the three workers work together, we have;
1/2.2 wall/hour + 1/3.2 wall/hour + 1/4.9 wall/hour = 8375/8624 wall/hour
Therefore, the time for the three workers of group Z to paint one wall is given as follows;
[tex]Time \ to \ paint \, one \, wall = \frac{1 \, wall}{\frac{8375}{8624} wall/hour} = 1\tfrac{249}{8375} hours[/tex]
The total time taken for group Z to paint the wall together = 1.03 hours
3. Since the total time for group A to paint the wall which is 1.2 hours is more than the total time for group Z to paint the wall which is 1.03 hours, group Z can paint the wall faster.
