The mathematical form of perimeter and area formulas allows us to find obtain the same values from triangles not congruent to each other due to commutative property for addition and multiplication.
Is it possible to obtain the same perimeter and area from triangles with same sides but not congruent to each other?
The perimeter is equal to the sum of the lengths of the three sides of the triangle and the Heron's formula allows us to calculate the areas in term of the three side lengths:
A = √[s · (s - a) · (s - b) · (s - c)]
s = 0.5 · (a + b + c)
Where:
s - Semiperimetera, b, c - Side lengthsThe mathematical form of perimeter and area formulas allows us to find obtain the same values from triangles not congruent to each other due to commutative property for addition and multiplication.
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The ratio of good guys to bad guys was 15 to 4. If there were 75 good guys, how many bad guys were there ?
\(\begin{array}{ccll} \stackrel{guys}{good}&\stackrel{guys}{bad}\\ \cline{1-2} 15&4\\ 75&x \end{array}\implies \cfrac{15}{75}=\cfrac{4}{x}\implies \cfrac{1}{5}=\cfrac{4}{x}\implies x = 20\)
Number of bad guys = 12
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given,
Ratio of good to bad guys = 15:4 = 15/4
No. of good guys = 75
Let the no. of guys be x
⇒ 15:4 = 75:x
⇒ 15/4 = 75/x
Cross multiplying
15 x = 75×4
x = (75/15)×4
No. of bad guys = (75/15)×4
= 3 × 4
No. of bad guys = 12
Hence, there are 12 bad guys.
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What is the simplified form of
Answer:
Step-by-step explanation:
2pi
____
3
Answer:
A) \(\frac{2\pi }{3}\)
Step-by-step explanation:
Subtract \(2\pi \sqrt{5}\) from \(4\pi \sqrt{5}\)
Cancel the common factor of \(\sqrt{5}\)
To get \(\frac{2\pi }{5}\)
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HELPPP PLEASE!!!!!!!!!
The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion differs from 30%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is 2.5. Find the P-value for a two-tailed test of hypothesis.
The probability of observing such an extreme result by chance alone is 0.0124.
To find the P-value for a two-tailed test of hypothesis, we need to first determine the significance level (alpha) of the test. Let's assume a significance level of 0.05, which is a common choice.
Since this is a two-tailed test, we need to find the probability of observing a test statistic as extreme or more extreme than 2.5 in either direction. We can find this probability using a standard normal distribution table or a calculator.
Using a standard normal distribution table, we can find that the probability of observing a z-score of 2.5 or greater is 0.0062. The probability of observing a z-score of -2.5 or smaller is also 0.0062. Therefore, the P-value for the two-tailed test of hypothesis is:
P-value = 2 * 0.0062
P-value = 0.0124
This means that if the true proportion of business students who have personal computers at home differs from 30%, with a significance level of 0.05, and we obtain a test statistic of 2.5, then the probability of observing such an extreme result by chance alone is 0.0124.
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Oceanside Bike Rental Shop charges a $15 flat fee plus $6 an hour for renting a bike. Dan paid $39 to rent a bike. Which equation can be used to find how many hours he rented the bike for?
a 15x + 39 = 6
b 39x + 6 = 15
c 6x + 15 = 39
d 15x + 6 = 39
e6x + 39 = 15
f 39x + 15 = 6
Answer:
c. 6x + 15 = 39
Step-by-step explanation:
hope this helps
how to solve this 3x³+x-11x+1
Answer:
You can’t solve but you can simplify to
3x^3-10x+1
Step-by-step explanation:
Answer:
3x^3-10x+1 ?
Step-by-step explanation:
HELPPPP WILL MARK BL!!!!!
The quadratic equation y = 4 · x² + 28 · x + 49 is an example of a perfect square trinomial.
There are two configurations for the dimensions of the rectangle:
Configuration 1: b = 6 · (x - 1 / 2), h = x + 4 / 3
Configuration 2: b = 6 · (x + 4 / 3), h = x - 1 / 2
Is a given quadratic equation a perfect square trinomial?
In this problem we find the quadratic equation y = 4 · x² + 28 · x + 49 and we need to check if the expression represent a perfect square trinomial. A quadratic equation is a perfect square trinomial if and only if the following formula is fulfilled:
a · x² + b · x + c = r₁² · x² + 2 · r₁ · r₂ · x + r₂² = (r₁ · x + r₂)²
That is,
r₁² = a
r₁² = 4
r₁ = 2
r₂² = c
r₂² = 49
r₂ = 7
2 · r₁ · r₂ = b
2 · 2 · 7
28
The quadratic equation y = 4 · x² + 28 · x + 49 is a perfect square trinomial.
Finally, we determine the dimensions of a rectangle whose area is the quadratic equation A = 6 · x² + 5 · x - 4. The area formula for a rectangle is described by the following formula:
A = b · h
Where:
b - Baseh - HeightThen, the factored form of the quadratic equation is:
A = 6 · x² + 5 · x - 4
A = 6 · [x² + (5 / 6) · x - 2 / 3]
A = 6 · (x - 1 / 2) · (x + 4 / 3)
There are two possible configurations for the rectangle:
Configuration 1: b = 6 · (x - 1 / 2), h = x + 4 / 3
Configuration 2: b = 6 · (x + 4 / 3), h = x - 1 / 2
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Find the volume of a cone with radius 5 yards and height 8 yards. Round your answer to two
decimal places
The volume of a cone will be 209.41 yard³.
What is volume of cone?
The area or volume that a cone takes up is referred to as its volume. Cones are measured by their volume in cubic units such as cm3, m3, in3, etc. By rotating a triangle at any of its vertices, a cone can be created. A cone is a robust, spherical, three-dimensional geometric figure.. Its surface area is curved. The perpendicular height is measured from base to vertex. Right circular cones and oblique cones are two different types of cones. While the vertex of an oblique cone is not vertically above the center of the base, it is in the right circular cone where it is vertically above the base.
So the
V = (1/3)πr²h.
Given, data r = 5yards
h = 8 yards
Volume = 1/3 * π * r ²* h
= 1/3 * 3.141*25*8
=209.41 yard³
Hence, the volume of a cone will be 209.41 yard³.
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Mindy has 5 blue markers, 3 pink markers, and 4 green markers.
What is the probability she draws a blue marker, puts it on the table, and draws another blue marker?
Answer:
4/12 and 3/12
the simplified version is 1/3 and 1/4
Step-by-step explanation:
Jim buys a vase. The diameter of the vase is 14 cm. What is the circumference?
Step-by-step explanation:
To find circumfrence you use the equation:
\(C=2\pi r\)
Since you were given the diameter so you divide by half to get the radius.
14/2 = 7
your radius is 7 and all you do is plug into the equation
\(C=2\pi 7\)
C= 43.98 or 44 rounded
Answer:
To find circumfrence you use the equation:
Since you were given the diameter so you divide by half to get the radius.
14/2 = 7
your radius is 7 and all you do is plug into the equation
C= 43.98 or 44 rounded
Step-by-step explanation:
A local congressman must decide whether or not to vote for a bill to reduce the speed limit.
Supporters of the bill claim that the gas mileage improves at lower speeds! The congressman was given the data about the Toyota Camry gas usage - presented in the table below. (Picture Attached.)
Note: MPG stands for miles per gallon of gas.
IDENTIFY THE INDEPENDENT VARIABLE FIR THIS DATA AND WHY.
The independent variable in this data is the speed of the car. This is because the congressman is trying to determine whether or not the gas mileage improves at lower speeds.
How to explain the variablesThe dependent variable is the gas mileage, because it is the variable that is being measured and that is affected by the independent variable.
The other variables in this data are the weight of the car, the type of engine, and the year of the car. However, these variables are not being changed in this experiment, so they are not considered to be independent variables.
The data shows that the gas mileage of the Toyota Camry improves as the speed of the car decreases. This supports the claim of the supporters of the bill to reduce the speed limit.
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Donte is planning on repairing bikes and skateboards to save up money for
college. He can repair up to 2 bikes per day and 4 skateboards per day. If b
represents the number of bikes and s represents the number of
skateboards, write the expression that represents the total number of
things Donte can repair in a single day. *
Answer:
y=2b+4s
Step-by-step explanation:
Solve for b
10, b, 150degrees, 12degrees
Hello!
We have all angles of the triangle:
We will use the law of cosines. This relation is valid for all sides of any t
We have:
angle A = 12°
côté a = 10
angle B = 150°
This is therefore the first case of application of the sine law.
So:
\(\sf \dfrac{b}{sin~B} = \dfrac{a}{sin~A}\)
\(\sf b =\dfrac{sin~B~*~a}{sin~A} = \dfrac{sin~150~*~10cm}{sin~12} = \dfrac{arcsin~0.5~*~10cm}{arcsin~0.2079116908} = \dfrac{30~*~10cm}{12} = \dfrac{300cm}{12} = \boxed{\sf25cm}\)
b = 25cmFind the value of x in the rhombus
Answer:
Your answer is.....
x= 37
Mark it as brainlist answer . follow me for more answer.
Step-by-step explanation:
help me please, thank you
Answer:
your chance is 3/10
Step-by-step explanation:
add how many marble then count how many pink and make a fraction
factorise x³-4x²+x+6
The binomial factors of x³- 4x²+x+6 are (x+2), (x+3), and (x-1).
Using the splitting and grouping the terms:
x³ + 4x² + x - 6
= x³ + 2x² + 2x² + x - 6 [Splitting 4x² = 2x² + 2x²]
= (x³ + 2x²) + (2x² + x - 6)
= x² (x + 2) + (2x² + 4x - 3x - 6)
= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]
= x² (x + 2) + (x + 2) (2x - 3)
= (x + 2) ( x² + 2x - 3)
= (x + 2) ( x² + 3x - x - 3)
= (x + 2) [x (x + 3) - 1 (x + 3)]
= (x + 2) (x + 3) (x - 1)
Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)
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Can someone please explain this if you can please tell how to do a future problem like this on
Point S is between points R and T. If RS = 16, ST = 2x, and RT = 5x + 10, what is the length of RT? Hint: draw a diagram with point S between points R and T. Then label it.
20
40
211.67
2
Answer:
Down below
Step-by-step explanation:
I hope this can help
I provided a url
https://www.lcps.org/cms/lib4/VA01000195/Centricity/Domain/3768/Unit%202%20Day%202%20Notes.pdf
is 3.4567 irrational or rtional
Answer:
3.4567 is a rational number
Step-by-step explanation:
An irrational number has no ending while a rational number does. An irrational number can not be written as a fraction while a rational number can. Basically, all you have to do to figure out if a number is rational or irrational is to figure out if it has an ending.
For example, if you had 234.888888888 irrational but if the number was 234.98989654 then it would be rational
what is the fifteenth term in the sequence 12, 24, 36, 48, 60,...? A72 B76 C96 D180
Answer:
D)180
you go 12+ so the nth term is 12n, then substitute the n with the term you're looking for, in this case it is 15: 12(15) = 180
Answer:
180
Explanation:
Please help me with this proof.
Answer:
See below
Step-by-step explanation:
For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.
Please help me find the angle of these, Also show work if possible so i can use it for future lessons.
Answer:
1=60 degrees, 2=60 degrees, 3=120 degrees 4=67 degrees, 5=23 degrees 6=37 degrees
Step-by-step explanation:
180 degrees in any triangle
1: 180-(49+71)
2: 1 and 2 are opposite and opposite angles are equal
3: 360 -(angle 1+angle 2) then divide by 2
4: 180-(53 + angle 2)
5: 180-(angle 3+angle 6)
6: 90 degrees in a right angle so 90 degrees - 53 degrees
Solve the inequality:
p ÷ (-5) ≥ - 9
⮜|-------|--------|➤
Hello there!
p:(-5)=9
Multiply both sides by -5:
p=9*(-5)
p=-45
When we mutliply a positive times a negative, we get a negative.
Hence, p=-45 (Answer)
Hope it helps. Please mark branliest.
~An emotional teen who helps others with joy
Good luck.
write the inequality shown -4x+y=-3
The inequality corresponding to the equation -4x + y = -3 is either y > 4x - 3 or y < 4x - 3, depending on the relationship between 4x - 3 and 0.
To write the inequality represented by the equation -4x + y = -3, we first need to manipulate the equation to express y in terms of x.
Starting with -4x + y = -3, we isolate y by adding 4x to both sides:
y = 4x - 3
Now we have y expressed in terms of x. To form the inequality, we consider the relationship between x and y. The inequality depends on whether the expression 4x - 3 is greater than or less than 0.
If 4x - 3 is greater than 0, then y is greater than 0, and we can write the inequality as:
y > 4x - 3
If 4x - 3 is less than 0, then y is less than 0, and we can write the inequality as:
y < 4x - 3
The inequality represents a region in the coordinate plane where the y-values are either greater than or less than the expression 4x - 3, depending on the direction of the inequality sign.
For example, if we choose a point (x, y) in the region above the line y = 4x - 3, where y is greater than 4x - 3, the inequality y > 4x - 3 will hold true. On the other hand, if we choose a point below the line, where y is less than 4x - 3, the inequality y < 4x - 3 will be satisfied.
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Aliana cuts a wire with a length of 56.88 inches into 5 equal parts. Whatis the length of each part?(Round off the answer)
17 inches
11 inches
10 inches
7 inches
The length of each part when the wire is cut into 5 equal parts is 11 inches.
To find the length of each part when a wire with a length of 56.88 inches is cut into 5 equal parts, we divide the total length by the number of parts.
Dividing 56.88 inches by 5, we get 11.376 inches per part.
Now, we need to round off the answer.
The general rule for rounding is to look at the digit immediately to the right of the desired decimal place.
If that digit is 5 or greater, we round up; if it is less than 5, we round down.
In this case, the digit immediately to the right of the desired decimal place is 3.
Since 3 is less than 5, we round down the desired decimal place.
Therefore, rounding 11.376 inches to a whole number, the length of each part is 11 inches.
Thus, the length of each part when the wire is cut into 5 equal parts is 11 inches.
Please note that rounding off the answer introduces some degree of approximation, and the actual lengths may vary slightly.
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Scenario: The Cannon
Instructions:
• View the video found on page 1 of this Journal activity.
• Using the information provided in the video, answer the questions below.
• Show your work for all calculations.
The Cannon: Ernest's friend Nik is about to be shot out of a cannon. The path he will
travel follows a parabolic arch that can be described by this polynomial.
((x) = -0.05(x° - 26x - 120)
He is supposed to land on a safety net 30 feet away. Does the function give you
enough information to tell you where he will land? If so, how far from the cannon will
he land?
Answer:
The given polynomial that describes the path of the cannonball is:
h(x) = -0.05(x^2 - 26x - 120)
where h(x) represents the height of the cannonball at a horizontal distance of x feet from the cannon.
To find where Nik will land, we need to find the value of x when h(x) = 0, since this indicates that the cannonball has landed on the safety net.
So we need to solve the equation:
-0.05(x^2 - 26x - 120) = 0
Simplifying this equation, we get:
x^2 - 26x - 120 = 0
We can use the quadratic formula to solve for x:
x = (-(-26) ± sqrt((-26)^2 - 4(1)(-120))) / 2(1)
x = (26 ± sqrt(976)) / 2
x = 13 ± 2sqrt(61)
So the cannonball will land either 13 + 2 sqrt (61) feet from the cannon or 13 - 2 sqrt (61) feet from the cannon.
Since 30 feet is the only distance given in the problem, we can't determine which solution is correct. Therefore, we can conclude that the function does not give us enough information to tell us where Nik will land.
Step-by-step explanation:
Overview
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Question Progress
Homework Progress
22/44 Marks
Round the number 125.3546 to 1 decimal place.
Answer:
125.4
Step-by-step explanation:
Given
\(Number = 125.3546\)
Required
Round to 1 decimal place
Up till the first decimal place, the number is:
\(Number = 125.3\)
The digit after .3 is 5
The conditions for approximation are:
If n > 4, approximate to 1Else: approximate to 0In this case: 5 > 4, so we approximate to 1
Add this "1" to the last digit of 125.3. This becomes 125.4
Hence: when the number is approximated to 1 decimal place, the digit is 125.4
What is the meaning of "\( \mathbb{N}=\bigcap \left \{X:X inductive \right \}\)"?
The meaning of \(\( \mathbb{N}=\bigcap \left \{X:X inductive \right \}\) is that the set of natural numbers is the intersection of all inductive sets.
What does the set show ?The set of natural numbers is inductive because it satisfies both of these conditions. The set is non-empty because it contains the number 1. And if x is a natural number, then x+1 is also a natural number.
In other words, a set is inductive if it satisfies the following two conditions:
The set is non-empty.If x is an element of the set, then x+1 is also an element of the set.The concept of an inductive set is important in mathematics because it allows us to define the set of natural numbers.
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Distance-Time Graph for an Object Moving at Constant Speed Distance Timc 9) A tennis ball was hit and was traveling at a constant speed. The graph above shows the distance the tennis ball traveled from its starting point in 5 seconds. What was the tennis ball's speed? a) 0.5 m/s b) 1 m/s c) 1.5 m/s d) 2 m/s
Let's first make a table of the data that the graph represents.
Time (seconds) Distance (meter)
1 0.5
2 1
3 1.5
4 2
5 2.5
To be able to get the speed of the tennis ball, let's use one of the data and apply the formula in getting the speed.
\(\text{Speed = }\frac{Dis\tan ce}{Time}\)At 1 second, the distance covered is 0.5 meters.
We get,
\(\text{Speed = }\frac{0.5\text{ meters}}{1\text{ second}}\)\(\text{Speed = 0.5 meter/second}\)Therefore, the speed of the tennis ball is 0.5 meters/second or m/s.
The answer is letter A.
TWO DVDs and one videocassette tape cost $72. One DVD and two videocassette tapes
cost $57. What is the price of each item?
Answer:
dvd cost 36 dollars
casette costs 10.5 dollars
please see picture for question