The measures of the sides of a triangle are 20 24 and 30. Find the measures of the segments former where the bisector of the smallest angle meets the opposite side.
Answer:
One segment is 8.89 long and the other one is: 11.11 long
Step-by-step explanation:
Recall that the bisector of a triangle divides the opposite side it intersects into two segments that are proportional to the other two sides of the triangle.
In our case the bisector is generated on the angle opposite to the size 20 side (it is the smallest angle in the triangle since it is opposite to the smallest side). This bisector divides the side of length 20 into a segment of length x and a segment of length 20-x.
The proportionality indicated by the bisector theorem gives;
[tex]\frac{20-x}{x} =\frac{30}{24}[/tex]
and we can solve for "x":
[tex]\frac{20-x}{x} =\frac{30}{24}\\24\,(20-x)=30\,x\\480-24\,x=30\,x\\480=54\,x\\x=480/54\\x\approx8.89[/tex]
Then the other segment is: 20 - 8.89 = 11.11
which one is it ?
substitution property of equality
reflexive property of equality
transitive property of equality
symmetric property of equality
what number is between 0.40 and 0.47 as a fraction
Rectangle ABCD has a length of 8n – 8 and a width of 3n - 1.
Find the Area of Rectangle ABCD. Write the answer in Standard
Form.
All of the following represent the same concept except _____. 47 take away 28 47 minus 28 47 less than 28 47 subtract 28
Answer:
C. 47 less than 28
Step-by-step explanation:
A. 47 take away 28
Equivalent to counting 47 and taking away 28
= 47 - 28
= 19
B. 47 minus 28
Simply
47 - 28
= 19
C. 47 less than 28
47 < 28
The less than sign is <
D. 47 subtract 28
= 47 - 28
= 19
Answer:47 less than 28
Step-by-step explanation:the rest are subtracting 28 from 47 , 47 less than 28 is subtracting 47 from 28.
the average number of spectators at a football competition for the first five days was 3144.the attendance on the sixth day was 3990.find the average attendance for the 6 days
Answer:
3285
Step-by-step explanation:
5x3144=15720
3990
15720+3990=19710
19710/6=3285
Amir wants to create a 4-digit password for his phone.
He wants to choose 4 different numbers between 1 and 5 inclusive.
Calculate the total number of 4-digit passwords that Amir can create.
Answer:
360
Step-by-step explanation:
Given that Amir wants to create a 4-digit password for his phone.
He wants to choose 4 different numbers between 1 and 5 inclusive.
The total number of 4-digit passwords that Amir can create will be achieved by using permutation
6P4 = 6!/ ( 6 - 4)!
6P4 = (6 × 5 × 4 × 3 × 2!)/2!
6P4 = 6×5×4×3 = 360
Therefore, the total number of 4-digit passwords that Amir can create is 360 different passwords.
Which list is in order from least to greatest?
|−9|, |4.2|, |−3.5|
|−3.5|, |−9|, |4.2|
|−3.5| , |4.2|, |−9|
|−9|, |−3.5|, |4.2|
Answer: C
Step-by-step explanation: Absolute value means all the values in the | | are positive so make them positive and you will see it’s 3.5, 4.2, and 9 in order from least to greatest.
What is the value of the following expression? 6p + 5 when p = 9
Answer:
I think the answer is 59
Step-by-step explanation:
6p+5
6(9)+5
54+5=59
Manny owns a home with a front and back lawn. The front lawn is ⅓ the size of the back lawn. If she mows ½ of her front lawn and ⅔ of her back lawn, what fraction of her entire lawn was left unmowed?
Answer:
[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
The computation of the fraction of her overall lawn remaining unmowed is shown below:
Let us assume that the back lawn be x
So the front lawn would be
[tex]= \frac{1}{3}\times x\\\\ = \frac{x}{3}[/tex]
So, the total lawn is ................... (i)
[tex]= x + \frac{x}{3}\\\\ = \frac{4x}{3}[/tex]
The back lawn mowed is [tex]\frac{2x}{3}[/tex]
Front lawn moved is [tex]\frac{x}{6}[/tex]
So, the total mowed is ....................(ii)
[tex]= \frac{2x}{3} + \frac{x}{6}\\\\ = \frac{5x}{6}[/tex]
So, the total unmowed is
[tex]= \frac{4x}{3} - \frac{5x}{6} \\\\= \frac{x}{2}[/tex]
Now the fraction is
[tex]= \frac{x}{2} \times \frac{3}{4x} \\\\ = \frac{3}{8}[/tex]
The fraction of the entire lawn unmoved is 3 / 8
What is a fraction?The fraction is defined as the division of the whole part into an equal number of parts. The computation of the fraction of her overall lawn remaining unmowed is shown below:
Let us assume that the back lawn is x
So the front lawn would be
[tex]=\dfrac{1}{3}\times x[/tex]
[tex]=\dfrac{4x}{3}[/tex]
So, the total lawn is ................... (i)
[tex]=x+\dfrac{x}{3}[/tex]
The back lawn mowed is
The front lawn moved is
So, the total mowed is ....................(ii)
[tex]=\dfrac{2x}{3}+\dfrac{x}{6}[/tex]
[tex]=\dfrac{5x}{6}[/tex]
So, the total unmowed is
[tex]=\dfrac{4x}{3}-\dfrac{5x}{6}[/tex]
[tex]=\dfrac{x}{2}[/tex]
Now the fraction is
[tex]=\dfrac{x}{2}\times \dfrac{3}{4x}[/tex]
[tex]=\dfrac{3}{8}[/tex]
Therefore the fraction of the entire lawn unmoved is 3 / 8
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Hannah has a small square shaped garden with an area of 196 square feet. If she wants to put a fence around the garden, how many feet of fencing will she need?
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A square is a quadrilateral that has the same length on every side.
The area of the garden is 196 square feet. To find the area of a garden, you have to multiply the length times the width. Since you know that both widths are the same, you can simply just calculate the square root of 196. The square root of 196 is 14. So you know that one side is 14 feet in length.
Now you will need to find the perimeter. The perimeter of any polygon is the lengths of all sides added up. Since there are 4 sides on a square, and each side is the same length, you can just add 14, 4 times. 14+14+14+14 equals 56. So the perimeter of the garden is 56 feet.
Hannah will need 56 feet of fencing.
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she needs to put 56 feet of fencing materials around ground
What is square?A quadrilateral which has four equal sides and four equal angles is known as a square.
According to the question,
To find the fencing material means to calculate the length around the square garden, or the perimeter of the square shaped garden.
Area , A is given as 196 square feet.
Formula for Area of a square (A )= Side × side
196 = side × side
This can be written as
Side × Side = 196
[tex]side^{2}[/tex] = 196
Take the square root of both sides,
[tex]\sqrt{side^{2} }[/tex] = [tex]\sqrt{196}[/tex]
side = 14 feet
The perimeter of a square can be calculated, P = 4(s), because all the four
sides are equal
P = 4 × side
= 4 × 14
= 56 feet
Hence, she needs 56 feet of fencing materials.
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n/3 - 2 = 4 2, 6, 14, or 18?
Answer:
Step-by-step explanation: all yu need to do is plug in each number option you have to replace in for until you get what it equals aka 4
for ex.
18/3-2=4 so that means 18 is your answer
Answer:
n = 18Step-by-step explanation:
In algebra, there is always an orderly progression of steps. Once we get an answer for the value of x, we must test it in the original question to make sure it is correct.
___________________________________________________Step 1: Add 2[tex]\frac{n}{3} - 2 + 2= 4 + 2 \\\\ \frac{n}{3} = 6[/tex]___________________________________________________Step 2: Multiply by 3n/3 × 3 = 6 × 3
n = 18
___________________________________________________Step 3: Check18/3 - 2 = 4
6 - 2 = 4
4 = 4 ✓
___________________________________________________I AM ALWAYS HAPPY TO HELP :)Which number Producing we are rational number When multiplied 0. 25
Answer
So changing 1/4 by multiplying top and bottom by 9 gives 9/36 and changing 2/9 by multiplying top and bottom by 4/4 gives 8/36 and adding 9/36 to 8/36 gives 17/36 - a rational number.
Step-by-step explanation:
|1-12| simlify tthe expression
Answer:
11
Step-by-step explanation:
|1 - 12| = |-11| = 11
Answer:
11
Step-by-step explanation:
If x is a rational number and y is a rational number than x + y is a rational number.
Answer:
True.
Step-by-step explanation:
The sum of two rational numbers is rational.
By definition, a rational number can be expressed as a fraction with integer values in the numerator and denominator (denominator not zero). So, adding two rational numbers produces another rational number.
Which of these numbers is irrational?
Answer:
[tex] \sqrt{5} [/tex]
Step-by-step explanation:
decimal repeats without a pattern
The transformation (x,y) -> (y,-x) is what degree rotation for a counter-clockwise turn?
Answer:
270°
Step-by-step explanation:
For example,
(x, y) is in 1st quadrant (x- coordinate is positive, y - coordinate is positive) , then
(y, - x) is in 4th (x- coordinate is positive, y - coordinate is negative).
x and y changed places, so clockwise is 90°,
and counter-clockwise 360-90= 270°.
would you rather have cheez its to cover a rectangle with a length of 9 and a perimeter of 22 or a length of 5 and a perimeter of 20
Answer:
A length of 5 and a perimeter of 20
Step-by-step explanation:
Personally, I'm lactose intolerant so I wouldn't take any Cheez-Its, but oh well.
Everyone wants the most Cheez-its, right? So we need to find the rectangle with the greatest area.
Let's look at the first one, a rectangle with a length of 9 and a perimeter of 22.
The perimeter of a rectangle can be expressed as [tex]2l+2w[/tex], where l is the length and w is the width.
We know the length and area, so let's solve for w (the width).
[tex]2\cdot9+2w=22\\\\18+2w=22\\\\2w=4\\\\w=2[/tex]
So the width is 2. The area of a rectangle is the length times the width.
[tex]9\cdot2=18[/tex]
So the first rectangle has an area of 18.
Using the same concept for the second statement, a length of 5 and a perimeter of 20, we can find the area.
[tex]2l+2w=20\\\\2\cdot5+2w=20\\\\10+2w=20\\\\2w=10\\\\w=5\\\\5\cdot5=25[/tex]
So the area of the second one is 25.
The greatest area is 25, so you'd want this one.
Hope this helped!
Answer:
The second one
Step-by-step explanation:
yaaaaaaaa
Rita needs to solve 3/4 divided by 2/3, she plans to multiply 3/4 times 3/2 will Rita’s strategy work
Answer:
Yes, I think so!
Step-by-step explanation:
3*3=9
4*2=8
So i will be 9/8
Hope this helps!
(pls mark brainiest!)
Find the difference: 3.45 - 0.12 =
Answer:
3.33
Step-by-step explanation:
3.45
- 0.12
______
3.33
DeMario has two ltimes and four quarters. Pratima has five dimes and two quarters. They have $2.20 altogether. Write an expression or equation that matches this situation.
Answer:
8 x2.20 = Answer
Step-by-step explanation:
Answer:
7d+6q=2.20
Step-by-step explanation:
Which diagram represents the postulate that states exactly one line exists between any two points?
Answer:
C with points A and B on the line
The diagram that supports the postulate is line option (c).
What are lines and points?Lines and points are both undefined terms in geometry.
The given postulate states that;
Exactly one line exists between any two points.
This means that the line must pass through the two points.
From the given options, Only option (c) is true because the line passes through points A and B.
Hence, the diagram that supports the postulate is line option (c).
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Use the following function rule to find f(16.36).
f(x) = 0.77x + 8.64
Write your answer as a decimal or whole number.
f(16.36) =
The angle of elevation of the top of a tower from a point 100m away is 45 degrees. What is the height of the tower to the nearest metres?
===========================================
Explanation:
If you draw out the diagram, then you'll find that a 45-45-90 triangle forms. The nice thing about this type of triangle is that the two legs are always the same length. The horizontal leg is 100 meters, so the vertical leg must also be 100 meters.
Side note: this type of triangle is an isosceles right triangle.
---------
You could use the tangent rule to get the same thing
tan(angle) = opposite/adjacent
tan(45) = 100/x
1 = 100/x
1*x = 100
x = 100
In this case, the opposite leg is the vertical leg since it is furthest from the angle of elevation.
Answer:
[tex]\Huge \boxed{\mathrm{100 \ meters}}[/tex]
Step-by-step explanation:
The base of the right triangle created is 100 meters.
The angle between the base and the hypotenuse of the right triangle is 45 degrees.
We can use trigonometric functions to solve for the height of the tower.
[tex]\displaystyle \mathrm{tan(\theta) = \frac{opposite }{adjacent} }[/tex]
[tex]\displaystyle \mathrm{tan(45) }= \frac{x }{100}[/tex]
Multiplying both sides by 100.
[tex]\displaystyle \mathrm{100 \cdot tan(45) }= x[/tex]
[tex]\displaystyle \mathrm{100 }= x[/tex]
The height of the tower is 100 meters.
Complete the missing parts of the paragraph proof.
By the definition of angles, the sum of the measures of angles 1 and 2 is 180 degrees. Likewise, the sum of the measures of angles is 180 degrees. By the property, mAngle1 + mAngle2 = mAngle3 + mAngle2. Subtract the measure of angle from each side. You get mAngle1 = mAngle3, or Angle1 Is-congruent-to Angle3, by the definition of congruence
Answer: Supplementary, 3 and 2, substitution, 2.
Step-by-step explanation: just did it .
The ∠1 is congruent to ∠3 by definition of congruency.
What is an angle?An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and scalene.
m∠1 + m∠2 = 180° (given)
m∠2 + m∠3 = 180° (given)
Hence:
m∠1 + m∠2 = m∠2 + m∠3 (equality property)
Subtract m∠2 from both sides to get:
m∠1 = m∠3
The ∠1 is congruent to ∠3 by definition of congruency.
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James is learning to type at the end of the first month games could type 9 words per minute at the end of the second month of practice James could type 18 words per minute after another month of practice James could type 27 words per minute James continued to practice at the end of five months how many worlds could James type per minute?
36?
45?
54?
52?
Decide whether is true or false.
2/11 < 5/22
=======================================
Explanation:
For now, assume the inequality is true
We can cross multiply to get
2/11 < 5/22
2*22 < 11*5
44 < 55
Since the last inequality is true (44 is smaller than 55), this means the first inequality is also true.
------------
We could use a calculator to see that
2/11 = 0.1818 approximately
5/22 = 0.2273 approximately
Since 0.1818 is smaller than 0.2273, this means 2/11 is smaller than 5/22.
In other words, 0.1818 < 0.2273 leads to 2/11 < 5/22
------------
An alternative is to multiply 2/11 by 2/2 to get 4/22
So 2/11 < 5/22 would update to 4/22 < 5/22. Both have the same denominator so we just compare the numerators. Because 4 < 5 is true, this makes 4/22 < 5/22 true, and consequently 2/11 < 5/22 true as well.
Simplify the exponential express
(-1)3 =
Answer:
-1
Step-by-step explanation:
(-1) ^3
This is (-1) multiplied together 3 times
(-1) * (-1) * (-1)
-1
20 points to whoever gets the correct answer uwu
Answer:
Angle EFG = 104 degrees
Angle GFH = 76 degrees
Step-by-step explanation:
Angle EFG and Angle GFH are a linear pair, which means that they add up to 180 degrees.
Angle EFG = 4n + 20 and Angle GFH = 2n + 34, so 4n + 20 + 2n + 34 = 180.
We can then combine like terms, getting 6n + 54 = 180.
Then, we can subtract both sides by 54, getting 6n = 126.
Lastly, we can divide both sides by 6, getting n = 21.
EDIT - solve for EFG and GFH:
Angle EFG = 4n + 20 = 4(21) + 20 = 104 degrees
Angle GFH = 2n + 34 = 2(21) + 34 = 76 degrees
Answer:
∠EFG = 104°
∠GFH = 76°
Step-by-step explanation:
∠EFG + ∠GFH = 180
(4n + 20) + (2n + 34) = 180
6n + 54 = 180
6n = 180 -54
n = 126 / 6
n = 21
plug in values to ∠EFG
∠EFG = 4(21) + 20
∠EFG = 104°
plug in values to ∠GFH
∠GFH = 2(21) + 34
∠GFH = 76°
a lightbulb manufacturer would like to increase production from 1.4 million to 3.9 million lightbulbs per year. find the percent increase of the production expectation. ( round your answer to one decimal place)
Answer:
The percentage increase of the production expectation to 1 decimal place is 178.6%
Step-by-step explanation:
Here in this question, we are interested in finding the percentage increase in the production capacity of the hypothetical company;
We can make or have a formula for this to make our workings easier;
% increase = (new value - old value)/old value * 100%
From the question;
The old value is the former productive capacity which is 1.4 million
The new productive capacity is 3.9 million
Thus;
The percentage increase in the production capacity would be;
(3.9 million - 1.4 million)/1.4 million * 100%
= 2.5 million/1.4 million * 100% = 178.57%
But the question asks we should have our answer in one decimal place;
Thus; 178.57% becomes 178.6%