a. How many non-degenerate scalene triangles with integer sides have a
perimeter of 27?
b. A square is inscribed in an equilateral triangle of side length 2 so that
two adjacent corners of the square lie on two sides of the triangle, and
the third side of the triangle contains one side of the square. The area of
the region inside the triangle and outside the square can be expressed as
a√b − c. What is a + b + c?
Answer:
Hello,
a)18
Step-by-step explanation:
\(p=27, int[p/2]=13\\\\\begin{array}{c|c|c|c|c}a&p-a&b&c\\---&---&---&---\\1&26&13&13\\2&25&12&13\\3&24&12&12\\4&23&10&13\\&&11&12\\5&22&9&13\\&&10&12\\&&11&11\\6&21&8&13\\&&9&12\\&&10&11\\7&20&7&13\\&&8&12\\&&9&11\\&&10&10\\8&19&8&11\\&&9&10\\9&18&9&9\\---&---&---&---\\\end{array}\)
number of triangle=18
b)
Side of the equilateral triangle =2
Height=√3 (using Pythagorean's theorem) (tr ACP)
Triangle ABJ has the same area as the triangle ABC
Uisng Thalès's theorem,
\(\dfrac{2-v}{2}=\dfrac{v}{\sqrt{3} } \\\\\\v=\dfrac{2\sqrt{3} }{2+\sqrt{3} } \\\\\\v=\dfrac{2\sqrt{3}*(2-\sqrt{3}) }{1} } \\\\v=4\sqrt{3}-6\\\\v^2=84-48\sqrt{3} \\Area =a\sqrt{b}-c= \sqrt{3} -(84-48\sqrt{3} )=49\sqrt{3} -84\approx{0,87049...}\\\\So:\\b=3\\a=49\\c=84\\\\a+b+c=3+49+84=136\\\)
How do you solve this?
Write the expression as a number in scientific notation.
Pls help me or I'm gonna fail :(
Answer:
(5 x 10^7)(6 x 10^4)= 3 x 10^12 is the answer in scientific notation
Answer:
As a professional failure, I shall try this.
3.5 * 10^3
Mu is walking laps to raise money for charity. For each lap she walks, her sponsors will donate $7. Mu has walked l laps and raised a total of $150
Write an equation to describe this situation.
Answer:
7\(l\)=150
Step-by-step explanation:
Each lap is worth $7, so if Mu walked \(l\) laps and the total is $150, then the equation would be
7\(l\)=150
Which choice when added to | −5 + 7 | will equal zero?
| +5 − 7 | [ 2] − | −5 + 7 | [3] | −( −5 + 7 ) | [4] | 7 − 5 |
i know the anwser is two but how do you get it
i need it by 5/1/23 at 8pm
Answer:
[ 2] − | −5 + 7 |
Step-by-step explanation:
Since we know that | −5 + 7 | is an absolute value, we know that the answer will be positive no matter what.
Step 1) Solve. | −5 + 7 | = 2.
Step 2) Find which other absolute value is equal to -2.
After solving [2], − | −5 + 7 | = -2, we know that the answer is choice 2.
We know this because | −5 + 7 | = 2, however, since it is multiplied by (-), it becomes -2. And 2 + (-2) = 0
Please help me. Please
Answer:
im pretty sure that the answer would be B
Step-by-step explanation:
Answer:
it would be B bc u will replace 2 with 6
Step-by-step explanation:
hope this helps
Three equivalent ratios are shown on the graph.
On a coordinate plane, points (1, 0.5), (2, 1), and (5, 2.5) are plotted.
Starting on one of the plotted points, how can you plot more equivalent ratio points?
Move up one and right one and one-half.
Move up one and one-half and right three.
Move up two and right three.
Move up one and right two
Move up one and right one and one-half.
Move up one and one-half and right three.
Move up two and right three.
Move up one and right two
It would be the 4th one
It would be D, Move up one, and right two. *
Answer:
D option
Step-by-step explanation:
Move up and right two
Because according to the pattern before, (2, 1) is one up and two right to (1, 0.5)
Similarly, for equivalent ratio, we'll apply the same pattern.
Hope it helps. Pls mark it the BRAINLIEST!
Explain how got got the answer :) tysm
The action of the object is 127cm.
How to find the action of the object?To find the action of an object in centimeters if it is 50 inches long, let the action of the object be \(x\)
\(\frac{15}{6} =\frac{x}{50}\)
\(15.4 * 50 = 6 * x\)
\(\frac{762}{6} =\frac{6x}{6}\)
\(x=127\)
Therefore, the action of the object is 127cm.
A grocery store sells 6 oranges for $2. How much would it cost to buy 10 oranges? Round to the nearest cent if necessary.
cost per orange: $2/6 = $0.3333
cost of 10 oranges: $0.3333 x 10 = $3.3333 ($3.33 rounded up to the nearest cent)
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What is the area of a rectangle with a length of Four and two-fourths meters and a width of Seven and five-sixths meters? 50 POINTS
Thirty-five and six twenty-fourths m2
Twenty-eight and ten twenty-fourths m2
Twenty-eight and seven-tenths m2
Twenty-two and ten-twelfths m2
Answer:
.
Step-by-step explanation:
.
The area of the rectangle will be 35⁵/₂₄ square meters.
What is the area of the rectangle?
The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
The area of the rectangle is calculated by the formula below:-
Area = Length x Width
Area = 4⁴/₄ x 7⁵/₆
Area = (18 / 4) x ( 47 / 6 )
Area = 141 / 4
Area = 35⁵/₂₄ square meters
Therefore, the area of the rectangle will be 35⁵/₂₄ square meters.
due tomorrow!!!!!!!!
Just 17, 18, and 19
in order if possible
Distributive property with variables (negative numbers)
5 stars to correct answers
Have a wonderful day!
C is your answer.
Thank you and have a splendid day as well!
Pls help! Will give brainliest!!
Considering area (A) of garden as 30 square feet:
30 = x(2x+7)
Now we need to expand it:
x(2x+7) = 2x^2 + 7x
2x^2 + 7x = 30
Adding this into an Algebra calculator gives us 5/2 or 2.5
So x = 2.5
To prove this:
2(2.5) + 7 = 12
14 * 2.5 = 30
I NEED QUADRATIC EQUATION!PLEASE!URGENT QUIZ!A rectangular poster has an area of 190 square inches. The height of the poster is 1 inch less than twice its width. Find the dimensions of the poster.
I'm going to ask this question again because no one really explained it to me 'clearly.' So if you could do that it would be much appreciated! I'll also give u a brainly <3
Question: What is the value of r.
(20 POINTS) This diagram shows an origami fish. The fish has been labeled to show several line segments. Which pair of line segments appears to be parallel?
Answer:
C
Step-by-step explanation:
J6K4 × 7 = L9M98
Each of J, K, L, and M is a different digit.
Find the values of J, K, L, and M.
Step by step pls thx
I appreciate your answer
WILL PICK BRAINLIEST
Answer:
5463
Simplify ————
20
Equation at the end of step 1 :
5 5463
k - ((— • (f - 32)) + ————) = 0
9 20
Step 2 :
5
Simplify —
9
Equation at the end of step 2 :
5 5463
k - ((— • (f - 32)) + ————) = 0
9 20
Step 3 :
Equation at the end of step 3 :
5 • (f - 32) 5463
k - (———————————— + ————) = 0
9 20
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 9
The right denominator is : 20
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
3 2 0 2
2 0 2 2
5 0 1 1
Product of all
Prime Factors 9 20 180
Least Common Multiple:
180
Calculating Multipliers :
4.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 20
Right_M = L.C.M / R_Deno = 9
Making Equivalent Fractions :
4.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 5 • (f-32) • 20
—————————————————— = ———————————————
L.C.M 180
R. Mult. • R. Num. 5463 • 9
—————————————————— = ————————
L.C.M 180
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
5 • (f-32) • 20 + 5463 • 9 100f + 45967
—————————————————————————— = ————————————
180 180
Equation at the end of step 4 :
(100f + 45967)
k - —————————————— = 0
180
Step 5 :
Rewriting the whole as an Equivalent Fraction :
5.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 180 as the denominator :
k k • 180
k = — = ———————
1 180
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
5.2 Adding up the two equivalent fractions
k • 180 - ((100f+45967)) 180k - 100f - 45967
———————————————————————— = ———————————————————
180 180
Equation at the end of step 5 :
180k - 100f - 45967
——————————————————— = 0
180
Step 6 :
When a fraction equals zero :
6.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
180k-100f-45967
——————————————— • 180 = 0 • 180
180
Now, on the left hand side, the 180 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
180k-100f-45967 = 0
Equation of a Straight Line
6.2 Solve 180k-100f-45967 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 180k-100f-45967 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when k = 0 the value of f is 45967/-100 so this line "cuts" the f axis at f=-459.67000
f-intercept = 45967/-100 = -459.67000
Calculate the X-Intercept :
When f = 0 the value of k is 45967/180 Our line therefore "cuts" the k axis at k=255.37222
k-intercept = 45967/180 = 255.37222
Calculate the Slope :
Slope is defined as the change in f divided by the change in k. We note that for k=0, the value of f is -459.670 and for k=2.000, the value of f is -456.070. So, for a change of 2.000 in k (The change in k is sometimes referred to as "RUN") we get a change of -456.070 - (-459.670) = 3.600 in f. (The change in f is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 3.600/2.000 = 1.800
Geometric figure: Straight Line
Slope = 3.600/2.000 = 1.800
k-intercept = 45967/180 = 255.37222
f-intercept = 45967/-100 = -459.67000
Step-by-step explanation:
hope this helps
The simplified form of \(\frac{\sqrt[3]{81} }{\sqrt[3]{-3} }\)
Answer:
-3
Step-by-step explanation:
\(\frac{\sqrt[3]{81} }{\sqrt[3]{-3}}\\\)
the index of both the numerator and denominator are "3", so they cancel each other out:
\(\frac{\sqrt{81} }{\sqrt{-3}} \\=\frac{9}{-3}\\ =-3\)
Hope this helps! :)
Answer:
-3
Step-by-step explanation:
pls help w/math i have so many more questions so yeah thx needed by 2pm
PLSSSSS HELP ME, I WILL GIVE BRAINLIEST!!!
Answer:
Step-by-step explanation: The answer would be
10
A box contains $20$ blue markers and $12$ red markers.
What is the ratio of blue markers to red markers?
A $3:5$
B $3:8$
C $5:3$
D $5:8$
Answer:
C.
Step-by-step explanation:
20/4=5
12/4=3
5:3
Enter 52.16 in expanded form.
Answer:
50 + 2 + 0.1 + 0.06
Find the perimeter of this shape.
Answer:
draw a line that makes a triangle and rectangle.
hypotenuse= 30
3k-4k-5k triangle
18-24-30
so the short part of triangle is 18 cm
10+10+18+24+30 equals 92
sorry for language I am not familiar with English
the perimeter of this shape is
24+10+10+30+\(\sqrt{30^{2} -24^{2} }\) = 92 cm
Sorry about all the math Questions. I suck at math
Answer:
It loses 5/48 ml per minute.
Step-by-step explanation:
-1.25/12 = -5/48
Check:
-5/48 * 12 = 1.25
Should be correct, tell me if not or if you need something else.
using the ordered pairs (x, y) in the table
what is the proportionality constant or the rate of change?
Charlie’s mom set the timer for her to complete her homework. She has 24 minutes remaining of the 60-minute timer. What percentage of her allotted time has she used?
60% of her allotted time has she used.
Here, we have,
given that,
Charlie’s mom set the timer for her to complete her homework.
She has 24 minutes remaining of the 60-minute timer.
so, we get,
total time = 60 minutes
she has remaining = 24 minutes
then, she has used = 60 - 24 = 36 minutes
now, we need to find the percentage of her allotted time has she used.
so, we have,
she used 36 minutes of 60 minutes
so, she has used = 0.6
= 60%
Hence, 60% of her allotted time has she used.
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A photo of a beetle in a science book is increased to 778% as large as the actual size. If the beetle is 15 mm, what is the size of the beetle in the photo
Answer:
Step-by-step explanation:
If the beetle is 15 mm in actual size, and the photo is increased to 778% of the actual size, then we can find the size of the beetle in the photo by multiplying its actual size by 7.78:
Size of beetle in photo = Actual size of beetle x 7.78
Substituting the given value of the actual size, we get:
Size of beetle in photo = 15 mm x 7.78
= 116.7 mm
Therefore, the size of the beetle in the photo is 116.7 mm.
Question is in the picture:)
Answer: It would probably be 30
Step-by-step explanation:
The ratio is 10:0 , 20:10 , 30:20 , 40:30 , 50:40, 60:50 , etc…
so basically you just need to know the ratios!
Hope I could help :)
What is the angle made by the hour hand and the minute of the clock at 8:57
Answer:
85 degrees
Step-by-step explanation:
please help me i will give brainliest to first person to anwser.
Answer:
The first option, V ≈ 1607.7 in²
Step-by-step explanation:
Find the volume of the given cylinder.
\(\begin{center}\framebox{\parbox{4cm}{\textbf{Volume of a Cylinder:}\\[2ex]The volume of a cylinder with radius $r$ and height $h$ is given by the formula:\\[2ex]\center{$V = \pi r^2 h$} \\ \\}}\end{center}\)
Given:
r = 8 in
h = 8 in
π = 3.14
Find:
V = ?? in³
\(\hrulefill\)
Now solving,
Substitute the given values into the formula:
=> V = (3.14)(8)²(8)
Using a calculator to simplify:
=> V = 1607.68 in²
Rounded to the nearest tenth:
∴ V ≈ 1607.7 in²
Thus, the first option is correct.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP PLEASE
Answer:
use formula
area = 1/2 *Height *(side 1 + side 2)
Answer:
use the equation of area of parallelogram = height ×base