Answer:
72
Step-by-step explanation:
Since the triangle's area is 240, the base * height must equal 480 because for the area of a triangle it is half of that. Since you know that the base AC = 20, find out what you can multiply by 20 to get 480. This gives you a result of 24. Now that the height is found divide the triangle into two right triangles. Now Just use the pythagorean theorem to find the legs of the triangles. AB = BC = 26. 26 + 26 + 20 = 72 which is the perimeter.
The Perimeter of triangle ABC is 72 unit
What is isosceles triangle ?Isosceles triangles are those triangles that have at least two sides of equal measure. We know that triangles are three-sided enclosed polygons and they are classified as equilateral, isosceles, and scalene, based on the length of their sides. In this article, we will learn about the definition of an isosceles triangle and its properties.
We have
AC = 20 unit
Area of triangle {ABC} = 240 unit square
AB = BC
draw the altitude to AC, let’s call it BD (Construction)
Now,
we know the area of triangle = 1/2 × AC × BD
240 = 1/2 × 20 × BD
BD = 240 × 2/20
BD = 24 unit
AD=CD (Altitude to base of isosceles triangle)
2AD=AC
2AD=20
AD=10 (Parts-Whole Postulate, substitution)
in ∠ABC using Pythagorean theorem
[tex]AD^{2}[/tex] + [tex]BD^{2}[/tex] = [tex]AB^{2}[/tex]
[tex]AB^{2}[/tex] = [tex]10^{2}[/tex] + [tex]24^{2}[/tex]
AB = [tex]\sqrt{100 + 576}[/tex]
AB = [tex]\sqrt{676}[/tex]
AB=26
AB=BC=26 (Definition of Isosceles Triangle)
AC = 20
Perimeter of triangle ABC = AB+BC+AC (definition of Perimeter)
Perimeter of triangle ABC = 26 + 26 +20
Perimeter of triangle ABC = 72 unit
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what is the answer for n ?
Answer:
18
Step-by-step explanation:
The formula for interior angles in a ngon is
(n-2)*180
2880/180=16
n-2=16
n=18
The external angle of a regular polygon is 200 . How many sides does it have ? What is the measure of each interior angle? What is the total measure of its angles.
Answer:
An 18 sided shape.
Since the sum of the exterior angles of a polygon is 360° and an angle of the regular polygon is 20°, then 360° / 20° is the number of sides. We find the answer = 18, an octadecagon
Suppose that the weights of 5400 registered female Labrador retrievers in the United States are distributed normally with a mean of 62.5 lb and a standard deviation of 2.5 lb. Approximately how many of the Labrador retrievers weigh less than 65
I believe the normal distribution is symmetrical above and below
the mean. That tells us that in this kind of distribution, the mean
and the median are the same number ... 50% of the population
is below it, and 50% is above it.
So if the female Labs' weight actually follows a 'normal' distribution
with a mean of 62.5 lbs, then 2,700 of them weigh more than 62.5 lbs
and 2,700 of them weigh less than that.
The standard deviation doesn't matter.
What are the coordinates of the vertex of the graph of the absolute value function h(x) = 3|x + 5| + 2? A) (5,-2) B) (-5,2) C) (5,2) D) (2,-5)
Answer:
B) Vertex = (-5, 2)
Step-by-step explanation:
Vertex can be defined as defined as the point where two lines meet and form a particular angle with each other. It can also be described as the point where a line changes its direction
We can find vertex by two methods:
1) GRAPHWe can see in the graph attached below that the line changes its direction at point (-5, 2). So the vertex is (-5,2)
2) FORMULAGeneral form of equation of mod function is given by
y = a |x - h| + k
where Vertex = (h, k)
The given equation is
h(x) = 3 |x + 5| + 2
h(x) = 3 |x - (-5)| + 2
where h = -5 and k = 2
So the vertex is:
Vertex = (-5, 2)
Answer:
(–5, 2)
Step-by-step explanation:
Explain how you can use the inscribed angle theorem to justify its second corollary, that an angle inscribed in a semicircle is a right angle
Step-by-step explanation:
Explanation:
An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle. The other two endpoints define what we call an intercepted arc on the circle. The intercepted arc might be thought of as the part of the circle which is "inside" the inscribed angle. (See the pink part of the circle in the picture above.)
A central angle is any angle whose vertex is located at the center of a circle. A central angle necessarily passes through two points on the circle, which in turn divide the circle into two arcs: a major arc and a minor arc. The minor arc is the smaller of the two arcs, while the major arc is the bigger. We define the arc angle to be the measure of the central angle which intercepts it.
The Inscribed Angle Conjecture I gives the relationship between the measures of an inscribed angle and the intercepted arc angle. It says that the measure of the intercepted arc is twice that of the inscribed angle.
The precise statements of the conjectures are given below. Each conjecture has a linked Sketch Pad demonstration to illustrate its truth (proof by Geometer's Sketch Pad!). The linked activities sheet also include directions for further "hands on" investigations involving these conjectures, as well as geometric problems which utilize their results.
The precise statement of the conjectures:
Conjecture (Inscribed Angles Conjecture I ): In a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc..

Corollary (Inscribed Angles Conjecture II ): In a circle, two inscribed angles with the same intercepted arc are congruent.

Proof: The measure of each inscribed angle is exactly half the measure of its intercepted arc. Since they have the same intercepted arc, they have the same measure.
Corollary (Inscribed Angles Conjecture III ): Any angle inscribed in a semi-circle is a right angle.

Proof: The intercepted arc for an angle inscribed in a semi-circle is 180 degrees. Therefore the measure of the angle must be half of 180, or 90 degrees. In other words, the angle is a right angle.
Given the piecewise function shown, find the value of h(–6). A) 1 B) 26 C) -23 D) -6
Answer:
-22
Step-by-step explanation:
Which part of the function is valid when x = -6
The first part
h(-6) = 4x+2 and let x = -6
=4(-6) +2
= -24 +2
=-22
Answer:
-22
Step-by-step explanation:
Expand the binomial using Pascal's triangle
(3x+5)
Answer:
Step-by-step explanation:
0. 1
1. 1 1
2. 1 2 1
3. 1 3 3 1
4. 1 4 6 4 1
5. 1 5 10 10 5 1
6. 1 6 15 20 15 6 1
7. 1 7 21 35 35 21 7 1
8. 1 8 28 56 70 56 28 8 1
The graph below shows the distance in miles, m, hiked from a camp in h hours.
Which hourly interval had the greatest rate of change?
1) hour 0 to hour 1
3) hour 2 to hour 3
2) hour 1 to hour 2
4) hour 3 to hour 4
Answer:
Option 1) is correct
Step-by-step explanation:
Given: The graph shows the distance in miles, m, hiked from a camp in h hours.
To find: hourly interval that had the greatest rate of change
Solution:
Rate of change between two points refers to the vertical change divided by the horizontal change.
For hour 0 to hour 1:
rate of change = [tex]\frac{2-0}{1-0}=2[/tex]
For hour 2 to hour 3:
rate of change = [tex]\frac{4.5-3.5}{3-2}=1[/tex]
For hour 1 to hour 2:
rate of change = [tex]\frac{3.5-2}{2-1}=1.5[/tex]
For hour 3 to hour 4:
rate of change = [tex]\frac{5-4.5}{4-3}=0.5[/tex]
So, rate of change is greatest in interval: hour 0 to hour 1
The greatest rate of change between the interval 0 to 1 hour.
Given that,
The graph below shows the distance in miles, m, hiked from a camp in h hours.
We have to determine,
Which hourly interval had the greatest rate of change?
According to the question,
The greatest rate of change between the interval is determined by the rate of change between two points refers to the vertical change divided by the horizontal change.
1. The rate of change between 0 to 1 hours is,
[tex]\rm Rate \ of \ change = \dfrac{2-0}{1-0}\\\\ Rate \ of \ change= \dfrac{2}{1}\\\\ Rate \ of \ change= 2[/tex]
The rate of change between 0 to 1 hour is 2.
2. The rate of change between 2 to 3 hours is,
[tex]\rm Rate \ of \ change = \dfrac{4.5-3.5}{3-2}\\\\ Rate \ of \ change= \dfrac{1}{1}\\\\ Rate \ of \ change= 1[/tex]
The rate of change between 2 to 3 hours is 1.
3. The rate of change between 1 to 2 hours is,
[tex]\rm Rate \ of \ change = \dfrac{3.5-2}{2-1}\\\\ Rate \ of \ change= \dfrac{1.5}{1}\\\\ Rate \ of \ change= 1.5[/tex]
The rate of change between 1 to 2 hours is 1.5.
4. The rate of change between 3 to 4 hours is,
[tex]\rm Rate \ of \ change = \dfrac{5-4.5}{4-3}\\\\ Rate \ of \ change= \dfrac{0.5}{1}\\\\ Rate \ of \ change= 0.5[/tex]
The rate of change between 2 to 3 hours is 1.
Hence, The required greatest rate of change between the interval 0 to 1 hour.
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When the two crews start working together, what part of all
the garbage bins will the first garbage truck empty?
The crew of a garbage truck takes 5 hours to empty all the
bins in one neighborhood on pickup day. The city assigned
a second garbage truck to this neighborhood. During their
training, it took the crew from the second truck 8 hours to
empty all the bins.
0.6
0.5
0.7
Time
(hours)
t
Part of Bins
Emptied
Rate
(part/hour)
1
5
0.4
First Truck
500
(9
1
t
Second
Truck
1
8
8
This question is not properly written
Complete Question
When the two crews start working together, what part of all
the garbage bins will the first garbage truck empty?
The crew of a garbage truck takes 5 hours to empty all the bins in one neighborhood on pickup day. The city assigned a second garbage truck to this neighborhood. During their training, it took the crew from the second truck 8 hours to empty all the bins.
Options
• 0.6
• 0.5
• 0.7
Answer:
0.6
Step-by-step explanation:
Let us say that the total hours worked by both trucks = t hours
Number of hours worked by first truck = 5 hours
Number of hours worked by second truck = 8 hours
Let 1 = total number of bins.
For the 1st truck the rate at which work was carried out is
(1 ) ÷ (5 ) = 1/5
For the 1st truck the rate at which work was carried out is
( 1 ) ÷ (8 ) = 1/8
Then,
(1/5 + 1/8) × t =1
(1/5 + 1/8) × t= 1
(13/40)t = 1
t = 1÷ 13/40
t = 1× 40/13
t = 40/13 hours.
Hence, the total hours worked by both trucks = 40/13 hours
the part of all
the garbage bins that the first garbage truck will empty is calculated as:
1/5 × 40/13 hr
1/5 × 40/13
= 0.6153846154
Approximately = 0.6
Therefore, when the two crews start working together, the part of all
the garbage bins that the first garbage truck will empty is 0.6 of the total work done.
Answer:
A) 0.6
Step-by-step explanation:
What is the difference between (8y-7) and (1-3y)?
________________________________
Solution,
(8y-7)-(1-3y)
= 8y-7-1+3y
= 8y+3y-7-1
=11y-8
Hope it helps
Good luck on your assignment
_____________________________
the pair of figures is similar. find x. round to the nearest tenth if necessary.
A: 34cm
B: 29.6cm
C: 9.8cm
D: 21.9cm
Answer:
B
Step-by-step explanation:
For f(x)= 4x+1 and g(x) = x^2 -5, find (f g)(x).
O A. 4x2 -19
O B. 4x3 + x2 - 4x -6
O C. 4x3 + x2 - 20x-5
O D. 4x3 + x2 - 5x -5
Answer:
The answer is option c.
4x³ + x² - 20x - 5
Answer:
C
Step-by-step explanation:
This sphere has a diameter of 5 m. What is the volume of the sphere?
Answer:
65.46 meters cubed
Step-by-step explanation:
Answer: the answer is V= 125/6πm^3
Step-by-step explanation: edge 2021
I NEAD HELP ASAP The Lewis family dined at a restaurant. Their bill came to $52, and they plan on leaving a 19% gratuity. This means that the total amount they will pay is 119% of the bill. Which calculation results in the best estimate of the total amount they will pay in dollars? Assume there is no tax. (50) (110 percent) = (50) (100 percent + 10 percent) = (50) (100 percent) + (50) (10 percent) = (50) (1.0) + (50) (0.1) = 50 + 5 = 55 (50) (120 percent) = (50) (100 percent + 20 percent) = (50) (100 percent) + (50) (20 percent) = (50) (1.0) + (50) (0.2) = 50 + 10 = 60 (60) (110 percent) = (60) (100 percent + 10 percent) = (60) (100 percent) + (60) (10 percent) = (60) (1.0) + (60) (0.1) = 60 + 6 = 66 (60) (120 percent) = (60) (100 percent + 20 percent) = (60) (100 percent) + (60) (20 percent) = (60) (1.0) + (60) (0.2) = 60 + 12 = 72
Answer:
Step-by-step explanation:
multiply 52 times 90% +52
Answer:
Option B is the correct answer.
Explanation:
The image below is the correct answer.
Which line has a slope 3/4
Line C shown in the graph has a required slope of 3/4.
Given that,
A figure is shown we have to determine a line that has a slope of 3/4.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanФ where x in degrees.
m =(y₂ - y₁) / (x₂ - x₁) = tanФ
here,
The slope of the line A = ∞
The slope of the line D = 0
The slope of the line B = 4/ 3
The slope of the line C = 3/4
Thus, Line C shown in the graph has a required slope of 3/4.
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Simplify:
(3x3+5x2−9x−2)−(2x3+3x2−x−3)?
A. x3+8x2−8x+1
B. x3+8x2−10x−5
C. x3+2x2−8x+1
D. x3+2x2−10x+1
Step-by-step explanation:
Answer is;−
9
x
−
2
−
2
x
3
−
3
x
2
+
x
+
3
Simplify by adding terms.
Tap for more steps...
x
3
+
2
x
2
−
8
x
+
1
Mr. Smith paid $36.36 for a carpet. This amount includes a tax of 10%. What was the cost of the carpet before tax?
Answer:
32.72
Step-by-step explanation:
36.36/100
0.3636
0.3636 times 90 (I use 90 because 100-10=90) 10% tax, so 90% original cost.
32.72
if you need to exercise 4 hours per week, how many minutes do you need to exercise each day to achieve this goal?
Answer:
A approximation of 34 minutes and 30 seconds each day .
Step-by-step explanation:
First you would need to convert 4 hours to minutes , so 1 hour equals 60 minutes - 60 min = 1 hour, 60 min times 4 = 240 minutes in total. There are 7 days in total of the week, 240 minutes - 7 days of the week : 240 divided by 7 , equals a approaximation of 34 minutes and 30 seconds each day.
(-2ab+8a+8) - (7ab + 6)
Answer:
-9ab + 8a + 2
Step-by-step explanation:
Combine like terms and distribute the negative
_______________________________
Solution,
(-2ab+8a+8)-(7ab+6)
= -2ab+8a+8-7ab-6
= -2ab-7ab+8a+8-6
= -9ab+8a+2
Hope it helps..
Good luck on your assignment
__________________________
How many ways can the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members?
a.
Permutation; Subscript 28 Baseline P Subscript 4 Baseline = 491,400
b.
Permutation; Subscript 24 Baseline P Subscript 4 Baseline = 255,024
c.
Combination; Subscript 28 Baseline C Subscript 4 Baseline = 20475
d.
Combination; Subscript 24 Baseline C Subscript 4 Baseline = 10626
Answer:
A)[tex]^{28}P_4}=491400[/tex]
Step-by-step explanation:
Total number of members = 28
We are supposed to find the no. of ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members
When 1 member is selected for Chairman position
So, 27 members will be left for the selection for the position of Vice chairman
When 1 member out of 27 is selected for Vice chairman position
So,26 members will be left for the selection for the position of secretary
When 1 member out of 26 is selected for secretary position
So,25 members will be left for the selection for the position of treasurer
Permutation relates to the act of arranging all the members of a set into some sequence or order,
The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter.
So, we will use permutation over here
Formula [tex]^nP_r=\frac{n}{(n-r)!}[/tex]
Substitute n = 28 and r = 4
So,[tex]^{28}P_4=\frac{28!}{(28-4)!}=491400[/tex]
So, Option A is true
A)[tex]^{28}P_4}=491400[/tex]
Hence There are 491400 ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members.
The number of ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members is 491,400.
The given parameters
Number of members = 28 Number of positions = 4Total arrangement of the different positions available[tex]nP_r =\frac{n!}{(n- r)!}[/tex]
[tex]28 P4 = \frac{28!}{(28-4)!} = \frac{28!}{24!} = 491,400[/tex]
Thus, the number of ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members is 491,400.
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Solve for x and show all of your steps.
3x - 20 - 4x = 4x - (3x - 2)
Answer:
Step-by-step explanation:
3x -20 -4x =4x -(3x -2)
3x - 20 -4x = 4x -3x+2
-x-20 =x +2
-20-2=x +x
-22=2x
x= -22/2
x=-11
Please answerrrrrrr !!!! please
calculate the surface area of the following shape
1. 450cm2
2. 294cm2
3. 358cm2
4. 716cm2
Answer:
210cm2
Step-by-step explanation:
Area of rectangle: HxW
Area of Triangle: 1/2 x bx h
There are 3 rectangles with the length of 14x3
14x3x3
= 14x9
= 126cm2
There are two triangles with the height of 12 and base of 14.
1/2x 14x 12
= 1/2x 168
= 168/2
= 84cm2
Now finally add them together:
84+126
= 210cm2
Jesse drives to work. The distance Jesse’s car travels (d) on a number of gallons of gas (g) is given by the equation d = 15g. The constant of proportionality in terms of distance traveled per gallon of gas is ?.
Answer:
1/15
Step-by-step explanation:
Jesse drives to work. The distance Jesse’s car travels (d) on a number of gallons of gas (g) is given by the equation d = 15g. The constant of proportionality in terms of distance traveled per gallon of gas is 1/15.
the equation is...
d=15g
Now lets solve for 1 gallon of gas
d=15g
d=15(1)
d=15
This means that for every 1 gallon of gas, 15 (insert missing unit of distance here) can be driven.
15/1=15
1/15
please mark me brainliest :)
express 1.875 in the form p/q
Answer:
If the answer asks for improper fraction it is [tex]\frac{15}{8}[/tex]
If it asks for simplest form it is [tex]1\frac{7}{8}[/tex]
Step-by-step explanation:
Rewrite the decimal number as a fraction with 1 in the denominator
[tex]1.875=\frac{1.875}{1}[/tex]
Multiply to remove 3 decimal places. Here, you multiply top and bottom by [tex]10^3=1000[/tex]
[tex]\frac{1.875}{1} *\frac{1000}{1000} =\frac{1875}{1000}[/tex]
Find the Greatest Common Factor (GCF) of 1875 and 1000, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 125
[tex]\frac{1875/125}{1000/125} =\frac{15}{8}[/tex]
Simplify the improper fraction
[tex]=1\frac{7}{8}[/tex]
Can someone please help me on these two questions?
Answer:
Arc = angle/360° x 2πr
13) = 72/360 x 2π x 25
= 1/5 x 2π x 25 = 10π
14) 270/360 x 2π x 2
= 3/4 x 4π = 3π
A briefcase in the shape of a rectangular prism has a height of 10 cm and a volume of 4,875 Centimeters cubed. What is the area of the base of the briefcase?
243.75 centimeters squared
487.5 centimeters squared
2,437.5 centimeters squared
4,865 centimeters squared
Answer:
Step-by-step explanation:
the correct question is
A briefcase in the shape of a rectangular prism has a height of 10 cm and a volume of 4,875 cm³. What is the area of the base of the briefcase?
we know that
volume of a rectangular prism=area of the base*height
volume=4875 cm³
h=10 cm
area of the base=volume/height
area of the base=4875/10-----> 487.5 cm²
the answer is
the area of the base is 487.5 cm³
Answer:
487.5 cm³
Step-by-step explanation:
Anyone know the answer to this?
Answer:
3x-5+19-x+2x
5x-x=14
4x=14
Hope that helps
|x-1|=14 solve the equation
Answer:
x = 15 x = -13
Step-by-step explanation:
|x-1|=14
There are two solutions to the absolute value equation, one positive and one negative
x-1 = 14 and x-1 = -14
Add 1 to each side
x-1+1 = 14+1 x-1+1 = -14+1
x = 15 x = -13
Answer:
x= 13 or -13
Step-by-step explanation:
Substitute x for 13
|13+-1|=14
13+1=14
14=14
Now try -13
|-13+-1|=14
13+1=14
14=14
Use the drop-down menus to complete each statement to describe the relationship
between the number of inches and the number of centimeters.
Answer:
Step-by-step explanation:
2.54 centimeters = 1 inch
15.24 centimeters = 6 inches
I don't know what other relationships they want :)