The angle bisector of a triangle divides the triangle into two similar triangles sometimes true and sometimes not true. Because the sum of the angle of the triangle is 180 degrees. But all three angles are not equal.
TriangleTriangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
Given
Angle bisector of the triangle.
To find
The angle bisector of a triangle divides the triangle into two similar triangles always, sometimes, or never.
How to show the condition?The angle bisector of a triangle divides the triangle into two similar triangles sometimes true and sometimes not true. Because the sum of the angle of the triangle is 180 degrees. But all three angles are not equal.
More about the triangle link is given below.
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The angle bisector divides a triangle into two similar triangles Option B) sometimes, specifically when the triangle is isosceles.
1. Isosceles Triangle: In an isosceles triangle, two sides are equal in length. When the angle bisector of the vertex angle is drawn, it also bisects the base, creating two congruent triangles (by the Angle Bisector Theorem). Congruent triangles are always similar, so in this case, the statement holds true.
2. Scalene Triangle: In a scalene triangle, none of the sides are equal. When you draw the angle bisector of one of the angles, it won't necessarily bisect any other side into two equal lengths. Hence, the resulting triangles formed by the angle bisector won't necessarily be similar.
So, the angle bisector divides the triangle into two similar triangles sometimes (when it's an isosceles triangle) but not always (when it's a scalene triangle).
The intersection of two planes is a point and two lines intersect in a point. True or false
Statement: Two planes intersect to form a point
This is false. Two planes intersect to form a single straight line.
-----------------
Statement: two lines intersect to form a point
This is true assuming the two lines have different slopes
-----------------
Because the first statement is false, the overall argument is false.
Final answer:
The intersection of two planes is a line, not a point, which makes the statement false. Two lines intersecting in a point is true provided they are not parallel.
Explanation:
The statement that the intersection of two planes is a point is false. According to geometric principles, specifically the line of intersection of two planes, when two planes intersect, they do so along a line, not just a single point. This line of intersection is represented by the points where their respective great circles cross. The intersection of two lines, however, is indeed a point, provided that the lines are not parallel. This is in agreement with Theorem 1, which states that two straight lines of a plane have either one point or no point in common; similarly, two planes have no point in common or a straight line in common.
Relevant Theorems on Intersections
Theorem 1 and Theorem 2 outline the foundational concepts regarding intersections in geometry. Understanding these theorems helps explain why two intersecting planes result in a line and not a single point.
12-packs Of Skwunch apple juice cost $3.00 after a 40% discount. Which equation would allow you to find the original price of the 12-pack? PLEASE HELP!!!!!!
Answer:
3.00 = original price * (1-.4)
or
3 = original price*.6
Step-by-step explanation:
We know the cost after the discount.
Price after discount = original price - original price * discount rate
Factoring out the original price
Price after discount = original price (1- discount rate)
We know the price after discount = 3.00 and the discount rate =.40
Substituting these values in
3.00 = original price * (1-.4)
3 = original price*.6
Divide each side by .6
3/.6 = original price
5.00 = original price
The side of a square is 3 cm smaller than one of the sides of a rectangle and 2 cm greater than its other side. Find the side of the square, if it’s known that the area of the square is 30 cm2 less than the area of the rectangle.
Quickly 10 points
[tex]a-the\ side\ of\ square\\a^2-the\ area\ of\ square\\\\a+3-the\ one\ side\ of\ rectangle\\a-2-the\ second\ side\ of\ rectangle\\(a+3)(a-2)-the\ area\ of\ rectangle\\\\\text{The equation:}\\\\(a+3)(a-2)=a^2+30\qquad\text{use distributive property}\\\\(a)(a)+(a)(-2)+(3)(a)+(3)(-2)=a^2+30\\\\a^2-2a+3a-6=a^2+30\qquad\text{subtract}\ a^2\ \text{from both sides}\\\\a-6=30\qquad\text{add 6 to both sides}\\\\\boxed{a=36}\\\\Answer:\ \boxed{36\ cm}[/tex]
A swimming pool has 2.5 million liters of water in it. Some water evaporated and then the pool only has 2 millions liters in it. What percent of the water evaporated?
Answer:
20% was evaporated
Step-by-step explanation:
Formula:
((New value-old value)/(old value))*100
((2-2.5)/(2.5))*100 = 20
Answer:
20% of the water evaporated
Step-by-step explanation:
We know that 500,000 evaporated because 2,500,000-2,000,000 is 500,000.
100% - 2,500,000
500,000 - x%
2,500,000/500,000 = 100/x
x=(500,000)(100)/2,500,000
x= 20%
20% of the water evaporated.
What is the solution to the inequality −3x < 7.5?
Answer:
The solution of the inequality is [tex](-2.5,\infty)[/tex].
Step-by-step explanation:
The given inequality is
[tex]-3x<7.5[/tex]
If an inequality divided by a negative number,then the sign of inequality change. Divide both sides by -3.
[tex]\frac{-3x}{-3} >\frac{7.5}{-3}[/tex]
[tex]x >-2.5[/tex]
Therefore the solution of the given inequality is all real numbers greater than -2.5.
In interval notation it can be defined as
[tex](-2.5,\infty)[/tex]
Answer:
x > −2.5
Step-by-step explanation:
i got the correct answer
PLEASE!!!!!!!!!!!! HELPPPP!!!!!!!!!!!!!!!!!!
Which of the following inequalities matches the graph?
graph of an inequality with a solid vertical line through the point (5, 0) and shading to the left of the line
x less than or equal to 5
x greater than or equal to 5
y less than or equal to 5
y greater than or equal to 5
The graph described by the student shows a solid vertical line through the point (5, 0), with shading to the left. This corresponds to the inequality 'x less than or equal to 5'.
Explanation:The student is asking about a graph of an inequality which features a solid vertical line that passes through the point (5, 0). The graph has shading to the left of this line. A vertical line in coordinate geometry represents all points where the x-coordinate is a specific value, and if the shading is to the left, it indicates that the x-values are less than or equal to that specific value of the vertical line.
Therefore, the correct inequality that matches the described graph is x less than or equal to 5 (`x ≤ 5`). The other options do not correctly represent a vertical line or the indicated shading direction.
if f(x) = 3x-12, what is f(2)
A.18
B.-18
C.6
D.-6
f(2) This means that x is 2, so you can plug in 2 for "x" in the equation
f(x) = 3x - 12
f(2) = 3(2) - 12
f(2) = 6 - 12
f(2) = -6
Your answer is D
Answer:
D. -6
Step-by-step explanation:
Hi!!! You have to substitute 2 for f(x) & for the x next to 3!!!
f(x) = 3x- 12
f(2) = 3(2) - 12
= 6 - 12
= 6 -12
= -6
a sea bird is 28 meters above the surface of the ocean what is the elevation
91.8 ft above sea level
HELP ASAP : Find the largest value of n such that 5x^2+nx+48 can be factored as the product of two linear factors with integer coefficients
Answer:
[tex]n=241[/tex]
Step-by-step explanation:
We are given
[tex]5x^2+nx+48[/tex]
Let's assume it can be factored as
[tex]5x^2+nx+48=(5x-s)(x-r)[/tex]
now, we can multiply right side
and then we can compare it
[tex]5x^2+nx+48=5x^2-5rx-sx+rs[/tex]
[tex]5x^2+nx+48=5x^2-(5r+s)x+rs[/tex]
now, we can compare coefficients
[tex]rs=48[/tex]
[tex]5r+s=-n[/tex]
[tex]n=-(5r+s)[/tex]
now, we can find all possible factors of 48
and then we can assume possible prime factors of 48
[tex]48=-+(1\times 48)[/tex]
[tex]48=-+(2\times 24)[/tex]
[tex]48=-+(3\times 16)[/tex]
[tex]48=-+(4\times 12)[/tex]
[tex]48=-+(6\times 8)[/tex]
Since, we have to find the largest value of n
So, we will get consider larger value of r because of 5r
and because n is negative of 5r+s
so, we will both n and r as negative
So, we can assume
r=-48 and s=-1
so, we get
[tex]n=-(5\times -48-1)[/tex]
[tex]n=241[/tex]
A 24 foot ladder leans against the wall of a building. The foot of the ladder is 5 feet from the base of the wall. How many feet above the ground is the point where the ladder touches the wall?
Answer:
The answer is approximately about 23.5 feet about the ground touching the wall.
Step-by-step explanation:
The ladder makes a right triangle with the wall and ground, therefore you use pythagorean theorem. If you draw what is being described, you can see that the 24 ladder is the hypotenuse or "c", while the ground and wall are "a" and "b" for the equation.
you set it up like so:
√(24²-5²) = a²
which will result in √(551) or ≈23.5 feet
The number of feet above the ground where the ladder touches the wall is 23.47 ft.
The information above forms a right angle triangle. The base of the right angle triangle is 5 ft and the hypotenuse of the right angle triangle is 24 ft.
Let's find the height of the triangle to know how many feet above the ground where the ladder touches the wall.
Using Pythagoras theorem,
c² = a²+b²where
c =hypotenuse
a and b are either adjacent side or opposite sides.
Therefore,
b² = 24² - 5²
b² = 576 - 25
b = √551
b = 23.4733891886
b ≈ 23. 47 ft.
Therefore, the feet above the ground where the ladder touches the wall is 23.47 feet.
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what is the approximate value of y - x
Answer:
17.2°
Step-by-step explanation:
using the tangent ration in the right triangle
tan y° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{19.1}{14.1}[/tex], hence
y = [tex]tan^{-1}[/tex]([tex]\frac{19.1}{14.1}[/tex]) ≈ 53.6°
tan x° = [tex]\frac{14.1}{19.1}[/tex], hence
x = [tex]tan^{-1}[/tex]([tex]\frac{14.1}{19.1}[/tex]) ≈ 36.4°
y - x = 53.6° - 36.4° = 17.2°
Answer:
D) y -x = Approximate 17.1 degree.
Step-by-step explanation:
Given : Triangle .
To find : Approximate value of y - x.
Solution : We have given a right angle triangle with
Opposite side = 19.1 in.
Adjacent side = 14 .1 in.
Tan( y ) = [tex]\frac{Opposite}{adjacent}[/tex].
Plug the values
Tan( y ) = [tex]\frac{19.1}{14.1}[/tex].
tan(y) = 1.354.
Taking tan inverse both sides.
y = [tex]tan^{-1}(1.354)[/tex].
y = 53.55 degree.
Now, by the sum of angle of triangles is 180 degree.
Angle c + angle y + angle x = 180.
Plug the variable
90 + 53.55 + x = 180.
83.55 + x = 180
On subtracting both sides by 83.55
x = 36.45 degree
Then ,
y - x = 53 .55 - 36 . 45
y - x = 17.2
Approximate 17.1 degree
Therefore, D) y -x = Approximate 17.1 degree.
WEATHER The equation y=0.2x +3.5 can be used to find the amount of accumulated snow y in inches x hours after 5 P.M. on a certain day. Identify the slope and y- intercept of the graph of the equation and explain what each represents.
Answer:
Slope (m) = 0.2 and y-intercept (b) = 3.5.
Slope represents here the increase in snow 0.2 inches per hour and y-intercept represents here the initially 3.5 inches snow was there.Step-by-step explanation:
We are given weather equation y=0.2x +3.5 for finding the amount of accumulated snow y in inches x hours after 5 P.M. on a certain day.
We need to identify the slope and y- intercept of the graph of the equation .
Let us compare given equation y=0.2x +3.5 by slope-intercept form y=mx+b, we get
Slope (m) = 0.2 and y-intercept (b) = 3.5.
Slope represents here the increase in snow 0.2 inches per hour and y-intercept represents here the initially 3.5 inches snow was there.Rewrite the following without an exponent.
Answer:
[tex]\frac{1}{81}[/tex]
Step-by-step explanation:
Law of exponent
[tex]a^{-m} = \frac{1}{a^{m} }[/tex]
1) Applying the above rule, we have
[tex]9^{-2} = \frac{1}{9^{2} }[/tex]
= [tex]\frac{1}{9*9}[/tex]
= [tex]\frac{1}{81}[/tex]
Please help!!
3.5(x) + -20 + 1/2(x) = 40 - 2x
Answer:
x = 10
Step-by-step explanation:
First, we need to isolate all the x's on one side. To do this we need to move the -20 over to the other side making it a +20:
3.5x + 1/2x = 40 + 20 - 2x
Add the x's and the 40 and 20:
4x = 60 - 2x
Move the -2x over to the other side making it a +2x:
4x + 2x = 60
6x = 60
Divide both sides by 6:
x = 10
So x = 10
Answer:
10
Step-by-step explanation:
3.5(x) + -20 + 1/2(x) = 40 - 2x
3.5x - 20 + x/2 = 40 - 2x
3.5x + x/2 + 2x = 40 + 20
6x = 60
x = 60/6
= 10
at a constant speed a car travels 75 miles in 60 minutes how far does the car travel in 18 minutes
Answer:
22.5 miles
Step-by-step explanation:
first divide 75 by sixty and that will be your traveled per minute then multiply that by 18 and that is you answer. Good luck, please mark me brainliest.
Constant speed is the speed of the object witch does not changes with the time. With constant speed the body traveled the same distance for the each time interval. The distance traveled by the car in 18 minutes is 22.5 miles.
Given Information-
The car traveled with the constant speed is 75 miles in 60 minutes.
What is the constant speed?Constant speed is the speed of the object witch does not changes with the time. With constant speed the body traveled the same distance for the each time interval.
As the car traveled with the constant speed is 75 miles in 60 minutes. Let x the total miles traveled by the car in one minutes is.
[tex]x=\dfrac{75}{60}[/tex]
[tex]x=\dfrac{5}{4}[/tex]
Thus the the total miles traveled by the car in one minutes is 5/4 miles. Let n be the total miles traveled by the car in 18 minutes. Thus,
[tex]x=\dfrac{5}{4}\times 18[/tex]
[tex]x=\dfrac{45}{2}[/tex]
[tex]x=22.5[/tex]
Hence the distance traveled by the car in 18 minutes is 22.5 miles.
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Oliver is watching a farmer plant a vegetable garden. He notices two hours after they began that the farmer had planted seven rows of the garden. Three hours later, he noticed that the farmer had now planted seventeen and a half rows of the garden. Assume that the farmer works at a constant rate.
Part B)Create an equation to represent the rate at which the farmer plants his vegetables, where x equals the hours worked and y equals the number of rows planted.
Answer:
y = 3.5x
Step-by-step explanation:
The equation for a straight line is
y = mx +b
We know that when
x₁ = 2, y₁ = 7 and when
x₂ = 5, y₂ = 17.5
Step 1. Determine the slope
m = (y₂ - y₁)/(x₂ - x₁) Substitute values
m = (17.5 – 7)/(5 – 2) Remove parentheses
m = 10.5/3
m = 3.5
===============
Step 2. Determine the y-intercept.
y = 3.5x + b Insert x₁ and y₁
7 = 3.5×2 + b
7 = 7 + b Subtract 7 from each side
b = 0
===============
Step 3. Write the equation
y = mx + b
y = 3.5x + 0
y = 3.5x
The equation is y = 3.5x.
Which is the graph of x is greater than or equal to 2
Write the sentence as an equation.
384 subtracted from the quantity 35 times q is q times 225, decreased by 189
Answer:
35q-384 = 225q-189
Step-by-step explanation:
since its 384 subtracted from 35 times q it will be 35q-384 and then it says "is" which is an equal sign (=) and then q times 225 which is 225q decreased by 189 which is 225q-189 so it will be 35q-384 = 225q-189
PLEASE HELP ME ON NUMBER 13 I NEED IT!!!!!
Answer:
a. x+y=10, 2x+3y=24
b.this systems of equations have a unique solution since there is only one value for x and one value for y where each equation is present in. There is no same slope or y-intercept
c. 4 magnet gift boxes
Step-by-step explanation:
solve for a 1/4(20-4a)=6-a
[tex]1/4(20-4a)=6-a \ /\cdot4\\20-4a=24-4a\\-4a+4a=24-20\\0=4\\false[/tex]
Tate has 5 more than twice as many pennies as Mia. If Mia has x pennies, how many does Tate have
Answer:
Tate has 7x pennies.
Step-by-step explanation:
Tate has 2x pennies because Mia has x pennies and Tate has twice the pennies of Mia so
5+2x= 7x
I'LL GIVE BRAINLIEST! :D
How do you write these equations in slope intercept form?
y - 2x = -4
y - 3 = -1/2x
2x + 3y = 6
Answer:
y= 2x-4 , y= -1/2x +3 , y= -2/3x+2
Step-by-step explanation:
slope intercept form: y=mx+b
y-2x=-4
add 2x to both sides
y= 2x-4
y-3= -1/2x
add 3 to both sides
y= -1/2x +3
2x+3y=6
subtract 2x from both sides
3y= -2x+6
divide both sides by 3
y= (-2x+6)/3
y= -2/3x+2
NOTES:
Slope-Intercept form is y = mx + b ; where m is the slope and b is the y-intercept.
To convert an equation into slope-intercept form, solve for y
******************************************************************************************
Answer: y = 2x - 4
Step-by-step explanation:
y - 2x = -4
+2x +2x
y = 2x - 4
********************************************************************************************
Answer: y = [tex]-\frac{1}{2}x[/tex] + 3
Step-by-step explanation:
y - 3 = [tex]-\frac{1}{2}x[/tex]
+3 +3
y = [tex]-\frac{1}{2}x[/tex] + 3
********************************************************************************************
Answer: y = [tex]-\frac{2}{3}x[/tex] + 2
Step-by-step explanation:
2x + 3y = 6
-2x -2x
3y = -2x + 6
÷3 ÷3 ÷3
y = [tex]-\frac{2}{3}x[/tex] + 2
NEED HELP ASAP!!!! Daniel buys one bond each with a par value of $1,000 from Grath Oil, Ombor Medical Supplies, and Dwyn Horticulture. Grath Oil bonds are selling at 120.514, Ombor Medical Supplies bonds are selling at 90.773, and Dwyn Horticulture bonds are selling at 101.180. What is the total face value of Daniel’s bonds? a. $3,124.67 b. $3,000.00 c. $3,312.46 d. $312.47
Answer:the answer would be a i just did it but correct me if i was wrong
Step-by-step explanation:
Answer:
b. $3,000.00
Step-by-step explanation:
Daniel buys one bond each with a par value of $1,000 from Grath Oil, Ombor Medical Supplies, and Dwyn Horticulture.
Grath Oil bonds are selling at 120.514
Ombor Medical Supplies bonds are selling at 90.773
Dwyn Horticulture bonds are selling at 101.180.
These values have nothing to do here as we only have to find the face value.
The face value of 1 bond is $1000 so, the face value of 3 bonds will be = [tex]1000\times3=3000[/tex] dollars.
what is this song of 2.5 x 10 to the 4th power + 3.4 * 10 to the 4th power
simplify (b^9)^3
A.b^24
B.b^6
C.b^27
D.b^9
Answer:
C. b^27
Step-by-step explanation:
By the definition of exponents
[tex](b^9)^3=b^9*b^9*b^9[/tex]
And since for any real numbers [tex]r,x,[/tex] and [tex]y[/tex]
[tex]r^x*r^y=r^{(x+y)}[/tex]
This makes
[tex](b^9)^3=b^9*b^9*b^9=b^{{9+9+9}}=\boxed{b^{27}}[/tex]
Which is choice C.
Alternatively, we could use the identity
[tex](r^x)^y=r^{xy}[/tex]
in which case
[tex](b^9)^3=b^{(9*3)}= \boxed{b^{27}}[/tex]
which is the same answer.
Answer:b²⁷
Step-by-step explanation:
An author has 18 pages to send to a publisher. The author has only small envelopes and can't fit all the pages into a single envelope. It ends up taking 6 envelopes to hold all the pages. If each envelope has the same number of pages in it, how many pages are there in each envelope? A) 2 pages B) 3 pages C) 4 pages D) 5 pages
is this right i dont know smo help
Answer:
D. multiplication property
Step-by-step explanation
Am not so sure but i think its that
what is the equation
Graham and Max will meet at the same altitude after approximately 22 minutes.
Explanation:
To find out how many minutes it will take Graham and Max to meet at the same altitude, we need to set up an equation.
Let's assume that after t minutes, Graham and Max will meet at the same altitude. This means that the altitude of Graham is equal to the altitude of Max.
Equation: 14,040 - 50t = 12,500 + 20t
To find t, we can solve this equation:
14,040 - 50t = 12,500 + 20t
Subtract 20t from both sides: 14,040 - 70t = 12,500
Subtract 12,500 from both sides: 14,040 - 12,500 - 70t = 0
Combine like terms: 1,540 - 70t = 0
Subtract 1,540 from both sides: -70t = -1,540
Divide by -70 on both sides: t = -1,540/-70
Simplify: t ≈ 22 minutes
Therefore, it will take approximately 22 minutes for Graham and Max to meet at the same altitude.
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ANY HELP WITH THIS WOULD BE AMAZING TYSM!!!
Match the equation with its graph -2x+7y=14
Answer:
x= 1
Step-by-step explanation:
- = negative. so negative 2 blank + 7 equals 14.
x is 1 because the more you add positively to a negative number the close it gets to zero. negative 21 + 7 is negative 14 but I you got an 8ntegr the n it would be 14.
The graph of the function -2x + 7y = 14 is attached
How to plot the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
-2x + 7y = 14
We start by making the variable y the subject
-2x + 7y = 14
So, we have
7y = 2x + 14
Divide through by 7
y = 2/7x + 2
And it also means that the equation is a linear equation
A linear equation is represented as
y = mx + c
Where
m = slope
i.e. m = 2/7
Hence, the equivalent equation to plot is y = 2/7x + 2
See attachment for graph
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can someone please tell me what r^2 - 9 = is?
Answer:
The answer is (r + 3)(r - 3)
Step-by-step explanation:
There need to be two number that add together to get 0
and two number that multiply together to get -9
3 + -3 = 0
3 · -3 = -9
= (r + 3)(r - 3)