Answer: 74.98cm
Step-by-step explanation:
Step 1: Find out radius of Circle A. [We use circumference of circle A to find its radius].
Circumference of circle A = 2πr; where r is radius.
To better viewing we change sides, we get:
2πr = Circumference of circle A
2πr = 25
r = [tex]\frac{25}{2\pi }[/tex]
r = [tex]\frac{25}{3.14}[/tex]
r ≈ 3.98
Step 2: Calculate the diameter of circle A.
diameter of circle A = 2r = 2(3.98) = 7.96
Step 3: Finding diameter of circle B.
diameter of circle B = 3(diameter of circle A) = 3(7.96) = 23.88
Step 4: Converted diameter of circle B to r.
diameter of circle B = 2r
23.88 = 2r
divided 2 from both sides, we get:
11.94 = r
Step 5: Substitute radius of circle B into the circumference formula, where C = 2πr.
C = 2πr
C = 2(3.14)(11.94)
C ≈ 74.98
Alice was having a conversation with her friend Trina, who had a discovery to share:
Pick any two integers. Look at the sum of their squares, the difference of their squares,
and twice the product of the two integers you chose. Those three numbers are the
sides of a right triangle.
a. Write an equation that models this conjecture using the variables x and y.
b. Investigate this conjecture for at least three pairs of integers. Does her trick
appear to work in all cases, or only in some cases? Explain.
c. Use Trina’s trick to find an example of a right triangle in which all of the sides
have integer length, all three sides are longer than 100 units, and the three side
lengths do not have common factors.
BONUS: If Trina’s conjecture is true, use the equation found in part a to prove the
conjecture. If it is not true, modify it so it is a true statement, and prove the new
statement
Answer:
a. (x² + y²)² = (x² - y²)² + (2xy)²
b. The conjecture works in all cases.
c. Sides of 119, 120, and 169
Step-by-step explanation:
a. Equation that models this conjecture
x² + y² = sum of squares
x² - y² = difference of square
2xy = twice the product of the integers
If these are the sides of a right triangle then
(x² + y²)² = (x² - y²)² + (2xy)²
b. Test the conjecture
(i) Try x = 2, y = 1
(2² + 1²)² = (2² - 1²)² + (2×2×1)²
5² = 3² + 4²
25 = 9 + 16
(ii) Try x = 3, y = 1
(3² + 1²)² = (3² - 1²)² + (2×3×1)²
10² = 8² + 6²
100 = 64 + 36
(iii) Try x = 3, y = 2
(3² + 2²)² = (3² - 2²)² + (2×3×2)²
13² = 5² + 12²
169 = 25 + 144
The conjecture appears to work in all cases.
c. A possible triangle
We must have one side greater than 100. That means,
x² > 100 or x >1 0.
Let x = 12
One side = 12² + y²
The second side = 12² - y²
The third side must have 2xy > 100
24y > 100
y > 4.2
Try y = 5
(12² + 5²)² = (12² - 5²)² + (2 × 12 × 5)²
169² = 119² + 120²
So, one right triangle could have sides of 119, 120, and 169.
Furthermore, these sides have no common factors.
Check:
169² = 119² + 120²
28561 = 14161 + 14400
28561 = 28561
The perimeter of a rectangular pool is 246 m.
If the width of the pool is 52 m, what is its length?
Friday’s temperature was 40 degrees and the temperature increased by 130% by Sunday evening. What was the temperature on Sunday evening?
Answer:
By Sunday evening the temperature would be 92 degrees
Step-by-step explanation:
Find 130% of 40
40 × 1.3 = 52
Add the product to your original temperature (40)
40 + 52 = 92
Are Figures A and B congruent? Explain your reasoning.
Answer:
no bc the two figures need to be exactly the same size
Step-by-step explanation:
What is the domain of the given function?
Answer:
b or c
Step-by-step explanation:
tttttttttttttttttttttttttttttttttttttttttttttttttt
We know that:
[tex]x - 11 \space\ and \space\ 2x + 8 \space\ are \space\ a \space\ linear \space\ pair. \space\ (Refer \space\ to \space\ attachment.)[/tex]This means that:
[tex](x - 11) + (2x + 8) = 180[/tex]Step-by step calculations:
Open the parenthesis:
[tex](x - 11) + (2x + 8) = 180[/tex]=> [tex]x - 11 + 2x + 8 = 180[/tex]Combine like terms:
=> [tex]x - 11 + 2x + 8 = 180[/tex]=> [tex](x + 2x) + (-11 + 8) = 180[/tex]Simplify the LHS:
=> [tex]3x - 3 = 180[/tex]Add 3 both sides:
=> [tex]3x - 3 = 180[/tex]=> [tex]3x - 3 + 3 = 180 + 3[/tex]=> [tex]3x = 183[/tex]Divide 3 both sides:
=> [tex]\frac{3x}{3} = \frac{183}{3}[/tex]=> [tex]x = 61[/tex]Same side exterior angles are linear pair and have sum 180°
[tex]\\ \rm\Rrightarrow x-11+2x+8=180[/tex]
[tex]\\ \rm\Rrightarrow 3x-3=180[/tex]
[tex]\\ \rm\Rrightarrow 3x=183[/tex]
[tex]\\ \rm\Rrightarrow x=61[/tex]
how do i do 21 divided by 18
Answer:
Hello~Step-by-step explanation:
[tex]21 \div 18[/tex]
if you will use calculator you'll simply get the answer 1.16666667but simply you can put 1.1666A baby is b weeks old. How old will it be in five weeks time
Answer:
b(5)
Step-by-step explanation:
pls I am not sure
pls I really don't want any bad comment I already feeling bad
Can some help me please
Answer:
Your answer is 140
Step-by-step explanation:
Rectangle:
16 x 8 = 128
Triangle:
1/2(6 x 4)
1/2(24)
24 / 2 = 12
Add areas:
128 + 12 = 140
Tucker deposited $20,000 in a savings account with simple interest. Five years later, he had earned $14,000 in interest. What was the interest rate? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer:
the interest rate should be 14%
a grocery store sells a 6-pack of bottled water for $3.79, a 9- pack for $4.50, and a 12-pack for $6.89. which package cost the least per bottle explain your reasoning ?
Answer:
Cost per bottle. Therefore cost/bottle. Set 1: 3.79/6=.63 Side note, don’t forget to round each time to the nearest cent. Set 2: 4.50/9=.50 Set 3: 6.89/12=.57 The second package (9-pack for $4.50) is the costs least per bottle.
Step-by-step explanation:
Mr. Campbell decides that too many students are getting a pass on homework. He adds 10 yellow marbles to the jar. Tell whether each part of the probability model does or does not change.
The sample space change.
Each event within the sample space change. The probability of each event
change.
Answer:
The new probability of drawing a red marble is ()=.
Step-by-step explanation:
The sample space change. Each event within the sample space change. The probability of each event changes.
can you help me understand this
Answer:
For the small boxes on the side, drag the one that you think is correct to the grey spaces. Your supposed to enter the fraction in the simpliest form
Step-by-step explanation:
Please assist!!!! No links
Answer:
The choice C.
Step-by-step explanation:
[tex] {( \frac{ {2}^{ - 10} }{ {4}^{2} } )}^{7} = \frac{ {(2}^{ - 10}) ^{7} }{ {( {4}^{2}) }^{7} } = \frac{ {2}^{ - 10 \times 7} }{ {4}^{2 \times 7} } = \frac{ {2}^{ - 70} }{ {4}^{14} } \\ \\ = \frac{1}{ {2}^{70} \times {4}^{14} } [/tex]
What value belongs next to the 1 in the table? What does it mean in this context?
Answer:
The number next to 1 is 2.5.
It means 2.5 dimes are in 1 quarter (1 quarter = 2.5 dimes)
Step-by-step explanation:
The value next to 1 in the table above = number of dimes we have in 1 quarter.
Let the value next to 1 be "x".
That is:
1 quarter = x dimes
If 4 quarters = 10 dimes, then,
Cross multiply to find, how many dimes, x is equal to.
Thus:
1*10 = 4*x (cross multiplication)
10/4 = 4x/4 (dividing both sides by 4)
2.5 = x
The number next to 1 is 2.5.
It means 2.5 dimes are in 1 quarter (1 quarter = 2.5 dimes)
Helppp with this question plzz
Answer:
306
Step-by-step explanation:
There are 102 triangles, a triangle has 3 sides, each side is 1 cm. 102 x 3=306
(PLS HELP)The diameter of a cylindrical water tank is 12 ft, and its height is 17 ft. What is the volume of the tank?
Use the value 3.14 for л, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer.
Answer: The volume is equal to 1922.65.
Step-by-step explanation:
Diameter is 12 ft, height is 17 ft.
V = πr2h
V = πr2h = π·62·17≈ 1922.65
The volume of the tank is approximately 1814 cubic feet.
What is a cylinder?A cylinder is a 3-D figure that has a radius and a height.
The volume of a cylinder is given as πr²h.
Example:
The volume of a cup with a height of 5 cm and a radius of 2 cm is
Volume.
= 3.14 x 2 x 2 x 5
= 62.8 cm³
We have,
The formula for the volume of a cylinder is:
V = πr²h
where V is the volume, r is the radius, h is the height, and π is a constant equal to approximately 3.14.
We are given the diameter of the tank, which is 12 feet.
The radius is half the diameter, so:
r = 12/2 = 6 feet
We are also given the height of the tank, which is 17 feet.
Substituting these values into the formula, we get:
V = πr²h
V = 3.14 × 6² × 17
V ≈ 1814
Therefore,
The volume of the tank is approximately 1814 cubic feet.
Learn more about cylinder here:
https://brainly.com/question/15891031
#SPJ2
What is the value of x in the equation -5/8x=-160
Answer:
x=256
Step-by-step explanation:
Answer:
x=256
Step-by-step explanation:
Miguel measured a house and its lot and made a scale drawing. The backyard, which is 40 feet wide in real life, is 20 inches wide in the drawing. What scale did Miguel use?
1 inch :
feet
Answer:
1 inch:2 feet
Step-by-step explanation:
Please Help Me In Math
Will mark U Brainliest
!!!
#soconfused
Answer:
[tex]\tt volume=\boxed{6}\: units^3[/tex]
Step-by-step explanation:
[tex]\tt volume=(\frac{9}{2})(\frac{4}{3} )[/tex]
[tex]\tt volume=\frac{36}{6}[/tex]
[tex]\tt volume=6[/tex]
~
zachary has six times as many nickels as dimes and four times as many quarters as dimes. zachary has a total of ninety-nine nickels, dimes, and quarters. The total value of the coins is $12.60. How many of each coin does he have?
Answer:
nickels: 54dimes: 9quarters: 36Step-by-step explanation:
The ratio of nickels to dimes to quarters is given as ...
N : D : Q = 6 : 1 : 4
The total number of ratio units is 6 +1 +4 = 11. The total number of coins is given as 99, so each "ratio unit" must represent 99/11 = 9 coins. That is, the actual coin count ratios are ...
N : D : Q = 54 : 9 : 36
Zachary has 54 nickels, 9 dimes, and 36 quarters.
__
Check
The value of the coins is ...
$0.05 × 54 +$0.10 × 9 +$0.25 ×36 = $2.70 +0.90 + 9.00 = $12.60
please answer this
9²+5x2+ 1³
Answer: your answer would be 92 .
Step-by-step explanation: all you have to do is add . hope this helped <3 .
50 POINTS FOR CORRECT AWNSER!
Answer: y > x + 4
Step-by-step explanation:
First lets find a linear equation for the dividing line, in the form:
y = mx + b
We know that b is 4, since this is the y-intercept
lets use any point on the graph, I'll use (-4, 0):
y = mx + 4
0 = m(-4) + 4
-4 = -4m
m = 1
So the slope is 1. Our completed formula for the line is:
y = x + 4
Since the left side of this graph is shaded, we know it will either be > or ≥. Since the line is also dotted we know it is denoted by a simple ">" sign.
So our completed inequality equation is: y > x + 4
Hope this helped!
Answer:
[tex]\sf y > x+4[/tex]
Step-by-step explanation:
Choose 2 points on the line: (-4, 0) and (0, 4)
Let [tex]\sf (x_1,y_1)=(-4,0)[/tex]Let [tex]\sf (x_2,y_2)=(0,4)[/tex][tex]\sf slope=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-0}{0-(-4)}=1[/tex]
point-slope form of linear equation: [tex]\sf y-y_1=m(x-x_1)[/tex]
[tex]\implies \sf y-0=1(x-(-4))[/tex]
[tex]\implies \sf y=x+4[/tex]
Solid line : ≤ or ≥
Dashed line: < or >
Therefore as the line is dashed, and the shading is above the line,
[tex]\implies \sf y > x+4[/tex]
Sammy scored an 80% on her math quiz. She answered 12 correctly. How many questions were on her quiz?
Answer:
15 questions
Step-by-step explanation:
If Sammy got 80%, we can see that 12/15=0.8, and 0.8 as a percentage is 80%.
Hope it helps!!
Carpet Plus installs carpet for $100 plus $8 per square yard of carpet. Carpet World charges $75 for installation and $10 per square yard of carpet. Find the number of square yards of carpet for which the cost including carpet and installation is the same.
Answer:
12.5 square yards.
Step-by-step explanation:
Let a square yard of carpet = x
The cost of installing a carpet is given by;
100 + 8x
The charge for installation
75 + 10x
The number of square yards of carpet for which the cost including carpet and installation is the same is given by;
100 + 8x = 75 + 10x
100 - 75 = 10x - 8x
25 = 2x
x = 25 / 2
x = 12.5 square yards.
Answer:
old post so answering for points
Step-by-step explanation:
To get an A, you need more than 200 points on a two-part test. You score 109 points on the
first part. How many more points do you need?
Answer:
91 more points are needed
Step-by-step explanation:
Answer:91
Step-by-step explanation:
Please Help!!!
simplify (x-4)(6x^2+2x-1)
Answer:The solution is in the attached file
Step-by-step explanation:
need this asap so if you know it please let me know quickly
Answer:
Step-by-step explanation:
-20d + 12
4(d + 9) - 8(-3d - 3)
4d + 36 - 24d - 24
4d - 24d + 36 - 24
-20d + 12
Can some Please help me with this please please :(((( (The Image is In The Question)
When Hana goes to the mall, she always buys the same lunch and also buys some books. The table shows the number of books she buys, x, and the total amount of money she spends, y.
If this data were displayed in a scatter plot, select ALL statements that would be true about a good trend line summarizing the data.
SELECT GROUP OF ANSWER CHOICES
A. The y-intercept approximates the average cost of one book.
B. The y-intercept approximates the cost of Hana's lunch.
C. The slope approximates the cost of Hana's lunch.
D. The trend line goes through the origin.
E. The slope approximates the average cost of one book.
Solve for T
V = x + at
Answer:
t=V‒x/a
Step-by-step explanation:
V=x+at (add ‒x in both side)
V‒x=x+at‒x
V‒x=at
V‒x/a=at/a
V‒x/a=t
so the formula is t=V‒x/a