A right triangle is formed by the provided sides 6 cm, 10 cm, and 8 cm
Given that a triangle has sides measuring 6 cm, 10 cm, and 8 cm.
The question is whether a right triangle is formed by the specified sides.
The Pythagorean theorem states that the sum of the squares of the base and height is equal to the square of the hypotenuse.
Hypothesis 2 Equals Base 2 plus (Altitude)2
Make the hypotenuse 10 cm long.
Specify 6 cm for the base and 8 cm for the perpendicular.
(Hypotenuse)2 LHS (Hypotenuse)
RHS: (Base)2 + (Altitude)2 (Base)2 + (Altitude)2 = (6)2 + 2 = (10)2 = 100 (8)
LHS = RHS: 2 = 36 + 64 = 100
The sides provided meet the requirements for a right triangle.
As a result, a right triangle is formed by the provided sides.
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Kate is putting mulch down in her circular shaped garden. The garden has a radius of 12 feet. How much mulch does she need?
Kate needs to buy 453.6 ft2 of mulch for her 12 ft radius garden, which is equal to 76.3 cubic feet when multiplied by the desired depth.
Kate needs to purchase 453.6 cubic feet of mulch for her garden. To figure this out, she needs to first calculate the area of her garden using the formula A = πr2, where A is the area of the garden and r is the radius. In this case, the area of Kate’s garden is 453.6 ft2. For example, if she wants to put down 2 inches of mulch, she would need to purchase 453.6 ft2 x 0.167 ft = 76.3 cubic feet. This calculation can be adjusted depending on the depth of mulch desired. For example, if Kate wants to put down 3 inches of mulch, she would need to purchase
453.6 ft2 x 0.25 ft = 113.4 cubic feet
A = πr2
A = π(12)2
A = 453.6 ft2
Mulch = A x depth
Mulch = 453.6 ft2 x 0.167 ft
Mulch = 76.3 cubic feet
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Which table shows a proportional relationship between x and y?
Answer:
C
Step-by-step explanation:
Put in the form y/x and you should have equivalent fraction
12/4 = 3
15/5 = 3
18/6 = 3
When the fractions are simplified, they all equal 3.
Find the distance between the two points rounding to the nearest
(if necessary)
tenth
(1, -6) and (-8, -4)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-8 - 1~~)^2 + (~~-4 - (-6)~~)^2} \implies d=\sqrt{(-8 -1)^2 + (-4 +6)^2} \\\\\\ d=\sqrt{( -9 )^2 + ( 2 )^2} \implies d=\sqrt{ 81 + 4 } \implies d=\sqrt{ 85 }\implies d\approx 9.22[/tex]
For how many integer values of $n$ between 1 and 349 inclusive does the decimal representation of $\frac{n}{350}$ terminate
The decimal form of n/350 terminates after 49 integer values of n between 1 and 349 inclusive.
What is prime factorization?The technique of expressing all numbers as a product of primes is known as prime factorization. As an example, suppose we have the number 20. We may divide this into two categories. "Well, that's 4 times 5," we may remark. Also, 5 is a prime number. The number four is not a prime number. All numbers are made up of prime numbers. "Factors" are numbers that are multiplied to generate another number. As an example. "Prime factorization" is the process of determining which prime numbers multiply to produce the original number.
Here,
first, find the prime factorization of 350. (2*5^2*7)
then we need to find all multiples of 7 that are between 1 and 350.
the first multiple of 7/350.
The first multiple of 7 between 1 and 350 is 7.
so 7/350=0.02.
Then, drop the two zeros and find out what is 100% (1 whole, ignoring the percent) /2.
Then, we get 49.
49 integer values of n between 1 and 349 inclusive does the decimal representation of n/350 terminate.
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what is the percent change from 99 to 71?
To calculate the percent change of two numbers such as 99 to 71, you use the Percent Change Formula, where a is the start value and b is the end value. When we insert a = 99 and b = 71 in the formula above, then we get the following that we can simplify and solve to get the percent change from 99 to 71.
Change ≈ -28.2828%
A sample of fish from a river showed
that of the fish were less than one
year old. If there are an estimated
8,000 fish in the river, about how
many of them are less than one year
old?
par teme
d
Bookwork code, 021
Cessss chance Review your workings and see if you can comes your make
Ria buys 19 textbooks, which cost £6.82 each,
By first rounding both numbers to 1 significant figure, estimate the total
amount of money Ria spends,
Give your answer in pounds (L),
Answer?
Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.
Define unitary method.By multiplying the value about one unit by the quantity of units required, one can apply the unit technique to solve a problem. The unit procedure is used to separate a single entity integer from a given many, to put it simply. One pen, or 400 rupees, would be needed to purchase 40 needle. There might be a common way to verify this. only one nation. Anything has a unique feature. Algebra, grid logic, and its laminates and reverse are all identical terms used to describe mathematical analysis.
Here,
Given : Ria purchases 19 books for £6.82 apiece.
Thus,
Total cost of book = 19 * 6.82
=> 129.58
Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.
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Solve the problem as directed. The force F of attraction between two bodies varies jointly as the weights of the two bodies and inversely as the square of the distance d between them. Express this fact as a variation using c as a constant. Use M1 and M2 for the weights of the two bodies.
Therefore, F = c * M1 * M2 / d^2 when the force F of attraction between two bodies varies jointly as the weights of the two bodies and inversely as the square of the distance between them using the C constant.
What is the distance?Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.
What is direction?Direction is characterized as the course that anything follows, the route that must be taken to go to a certain location, the direction in which something is beginning to take shape or the direction you are facing.
F = c * M1 * M2 / d^2
Where,
F is the force of attraction,
M1 and M2 are the weights of the two bodies,
d is the distance between the two bodies,
and c is the proportionality constant.
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i need help with this
*im second guessing*
Answer:
A) 5
B) X-3
C) 2X+Y
step by step:
base x height = area
A Height= (5x+20) ÷ (x+4)= 5
B Base= (8x-24) ÷ 8 = x-3
C Height= (12x+6y) ÷ 6 = 2x+y
The solution is
Parallelogram A : Base = x + 4 ; Height = 5
Parallelogram B : Base = x - 3 ; Height = 8
Parallelogram C : Base = 6 ; Height = 2x + y
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the area of the parallelogram be A = Base x Height
So , Substituting the values in the equation , we get
a)
Let the parallelogram be A
Now , Area = 5x + 20
Base = x + 4
So , the height = Area / Base
Height = 5
b)
Let the parallelogram be B
Now , Area = 8x - 24
Height = 8
So , the Base = Area / Height
Height = x - 3
c)
Let the parallelogram be C
Now , Area = 12x + 6y
Base = 6
So , the height = Area / Base
Height = 2x + y
Hence , the equations are solved
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Here are two points: (-3, 4), (1, 7). What is the slope of the line between them?
A.4/3
B.3/4
C.1/6
D.2/3
Answer:
B. 3/4
Step-by-step explanation:
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P = P ( -3 , 4 )
Let the second point be Q = Q ( 1 , 7 )
Now , the slope of the line between the two points is given by the formula ,
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 7 - 4 ) / ( 1 - ( -3 ) )
On simplifying the equation , we get
Slope m = 3 / 4
Type the correct answer in the box.
C
square units.
m
AADC is formed by reflecting AABC across line segment AC, as shown in the figure.
If the length of AC is 4 units, the area of AADC is
The area of ΔADC is equal to 6 unit².
What is the triangular area formula?The total area that is bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h.
A abc = A adc because the areas of the initial and reflected triangles are equal.
Using the formula area=1/2 base height, determine the area of triangle ABC.
ABC in a triangle:
base = 4 units + AC
height = 3 units + BE
AΔ= abc = 1/2×4×3 =6 unnit²
Hence,
ΔADC = 6 unit²
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classify the relationship between angles 1 and 2
Answer:
<1 and <2 are Complementary Angles
m<1 + <2 = 90 degrees
Step-by-step explanation:
<1 and <2 are Complementary Angles
m<1 + <2 = 90 degrees
Have a great day!
Since, angle 1 and 2 sums up to make 90 degrees, hence Angle 1 and 2 are complementary angles.
What is complementary angle?Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complementary angles.
What is a supplementary angle?Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. In the same way, complementary angles sum to 90 degrees.
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How do you identify an exponential graph?
Exponential graph is identified by its curve.
An exponential graph is a graph that shows a rapid increase or decrease of a value over time, where the rate of change is proportional to the current value. It is usually represented by a curve that bends upward or downward.
The key characteristic of an exponential graph is that the Y-axis is on a logarithmic scale, and the curve of the graph is a steep curve going either up or down. The equation of an exponential graph is usually of the form y = ab^x, where a is the initial value, b is the growth or decay factor, and x is the independent variable.
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Chee and her children went into a grocery store and she bought $12 worth of bananas and mangos. Each banana costs $0.50 and each mango costs $2. She bought twice as many bananas as mangos. Graphically solve a system of equations in order to determine the number of bananas, x,x, and the number of mangos, y,y, that Chee bought.
We get the number of bananas as 8 and the number of mangoes as 4.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is that Chee and her children went into a grocery store and she bought $12 worth of bananas and mangos. Each banana costs $0.50 and each mango costs $2. She bought twice as many bananas as mangos.
We can write the system of equations as -
x = 2y ..... (1)
(1/2)x + 2y = 12 ..... (2)
We can write equation (2) as -
(1/2) x 2y + 2y = 12
3y = 12
y = 4
then -
x = 8
Therefore, we get the number of bananas as 8 and the number of mangoes as 4.
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a population of rabbits doubles every year write an expression for the increase after five years as repeated multiplication. then write it as an exponential expression
Answer: An increase of a population doubling every year can be modeled using repeated multiplication. The expression for the increase after five years would be:
2 * 2 * 2 * 2 * 2 = 2^5 = 32
This can also be written as an exponential expression, with 2 as the base and 5 as the exponent:
2^5 = 32
This notation expresses that 2 is multiplied by itself 5 times to get 32, which represents the population size after 5 years with the rate of doubling every year.
It's also worth mentioning that exponential notation is used to represent the quantity of growth (doubling every year) , and using exponents makes it easy to see how much the population has grown over a certain period of time.
Step-by-step explanation:
Answer:
Step-by-step explanation:
2^5= 32
=2 x 2 x 2 x 2 x 2
= 2^5
= 32
Sandy ate 1/6 of the candy bar John ate 3/4 of it how much more of the candy bar did John eat then Sandy
Answer: 7/12
Step-by-step explanation:
Based on the given conditions, formulate: 3/4 - 1/4
Find the common denominator and write the numerators above the common denominator: 9/12 - 2/12
Calculate the product or quotient:
Write the numerators over the common denominator: 9-2
12
Calculate the sum or difference: 7/12
Answer: 7/12
If Brian could have bought exactly 12 pairs with the amount of money that was spent on apples and oranges find the cost of each pair incense in terms of x
Therefore the cost of each pair of incense is 2.4 in terms of x.
Define the unitary method.The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
What are ratios and proportions?An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
Let x be the cost of one pair of incense.
We know that the total amount spent on apples and oranges is the same as the total cost of 12 pairs of incense. Therefore:
(cost of apples + cost of oranges) = 12x
We also know that the cost of the apples is 3x the cost of the incense, and the cost of the oranges is 2x the cost of the incense. Therefore, we can substitute these values into the equation:
(3x + 2x) = 12x
5x = 12x
x = 12/5 or 2.4
So the cost of each pair of incense is 2.4 in terms of x.
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60 workers can complete a work in 21 days. How long will it take to complete the some work if 10 more workers were added?
Answer:
Step-by-step explanation:
set 1 is the work, then 60 works finish 1/21 per day. [tex]\frac{1}{21*60}[/tex] is the work for per workers. so, the days for 70 workers is [tex]\frac{21*60}{70}=18[/tex] days.
it will spend 18 days to complete
What are personal assets?
Personal assets are the list of things which are owned by any person for the present or the future use such as house , saving accounts, Cash etc.
Personal assets the list of things all of which are owned by any personal or a family for the present or the future use.When an individual want to take loan of any purpose then bank give the loan by considering the present value of the personal assets.It represent the total property and cash owned by any individual for the present or the future use.Example of personal assets are : house, any other property , cash, certificate representing some value, jewelry, any vehicle etc.Therefore, the personal assets represent the valuable items owned by any individual for present or the future use.
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(6 × 10^3) ÷ (3 × 10^2)
J31) what are the undefined values for sinx cosx / 1 - sin²x , where 0 ≤ x < 2pi ?
how?
Answer:Mathematics2 minutes ago
+5 pts
J31) what are the undefined values for sinx cosx / 1 - sin²x , where 0 ≤ x < 2pi ? how?
Step-by-step explanation:
A cooker is priced at £80 after a 20% reduction from the original price.
Answer: original price: £400
Step-by-step explanation:
20/100 × original price = £80
Original price = £80 ÷ 20/100
= £400
Help, please. 20 POINTS
Answer:
C. x=68 and y=112
Step-by-step explanation:
We can find that x=68 by adding 52 and 60 together which would get us 112. Then subtracting 112 from from 180 leaving us with our sum of 68, which means x=68. Then we find the value of y by adding the two interior angles on the opposite sides of the triangle. So 52+60=112. This makes y=112.
-Hope this helped
Answer:
x = 68
y = 112
Step-by-step explanation:
The interior angles of a triangle add to 180º.
Using this knowledge, we can solve for x:
52º + 60º + xº = 180º
↓ subtract 52º and 60º from both sides
xº = 180º - 52º - 60º
xº = 68º
x = 68
The interior and corresponding exterior angles of a triangle are supplementary (they add to 180º).
Using this knowledge, we can solve for y:
xº + yº = 180º
↓ substitute for solved x-value
68º + yº = 180º
↓ subtract 68º from both sides
yº = 112º
y = 112
-x+6=-2(x+2)-5
Solve for x
Answer:
x = -15
Step-by-step explanation:
-x+6=-2(x+2)-5
Solve for x
-x + 6 = -2(x + 2) - 5
-x + 6 = -2x - 4 - 5
x = -15
------------------------
check- (-15) + 6 = -2(-15 + 2) - 5
21 = 21
the answer is goodx = -15
To be able to walk to the center $C$ of a circular fountain, a repair crew places a 16-foot plank from $A$ to $B$ and then a 10-foot plank from $D$ to $C$, where $D$ is the midpoint of $\overline{AB}$ . What is the area of the circular base of the fountain
The area of the circular base of the fountain is 179 square feet.
What is the area of the circular base ?A circle's area is equal to its radius, r, squared, then multiplied by the mathematical constant pi: A = pi x r2.
A cylinder has two bases that are two congruent circles at the top and bottom. The radius r of a cylinder is only the radius of the circular bases, and the height h of a cylinder is the perpendicular distance between these bases.
Combined area of the walkway and fountain: (3.14)112=379.94 ft2.
Fountain area: (3.14)8*2=200.96 feet
Walkway area: 379.94-200.96=178.98 square feet, which is also rounded to 179 square feet.
The area of the circular base of the fountain is 179 square feet.
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How many numbers among 1000-2000 are multiples of any two but not three of the first three odd prime numbers?
Hint: the first three odd prime numbers are 3,5,7
Answer: The first three odd prime numbers are 3, 5, and 7. A number is a multiple of two but not three of these prime numbers if it is divisible by two of them, but not the third.
To find the number of numbers between 1000 and 2000 that are multiples of two but not three of the first three odd prime numbers, we can count the number of multiples of each pair of prime numbers and subtract the number of multiples of all three prime numbers.
There are 200 multiples of 3 and 5 between 1000 and 2000 (200 numbers for each, for a total of 200 * 2 = 400). There are 133 multiples of 3 and 7 between 1000 and 2000 (133 numbers for each, for a total of 133 * 2 = 266). There are 80 multiples of 5 and 7 between 1000 and 2000 (80 numbers for each, for a total of 80 * 2 = 160). There are no multiples of all three prime numbers between 1000 and 2000.
Thus, the total number of numbers between 1000 and 2000 that are multiples of two but not three of the first three odd prime numbers is 400 + 266 + 160 = 826.
Step-by-step explanation:
A weight is suspended from a spring is set into oscillating
motion by compressing it into a point 3 cm above its resting
position and releasing it. It will displace 3 cm past its resting
point. From the time it is released it will bounce at a rate of 3
cycles per second.
a. Draw a graphical representation and give the equation
involving the situation.
b. What is the displacement of the spring after 2.5
seconds?
a. The graphical representation of the oscillation of the weight suspended from a spring is a sine wave, with the displacement of the weight on the y-axis and time on the x-axis. The equation involving the situation would be y = Asin(2pift + phi) where A is the amplitude of the oscillation (3 cm in this case), f is the frequency of oscillation (3 cycles per second in this case), t is the time elapsed since the weight was released, and phi is the phase offset (0 in this case).
b. To find the displacement of the spring after 2.5 seconds, we can substitute 2.5 seconds for t in the equation: y = Asin(2pift + phi) = 3sin(2pi32.5 + 0) = 3sin(15pi) = 3*0 = 0 cm. So the displacement of the spring after 2.5 seconds is 0 cm.
What is an oscillation period?By definition, period of oscillation of an oscillator is the time interval that the oscillating object needs to pass through its equilibrium position with velocity in the same direction.
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What is called composite function?
A composite function is a type of function that is made up of two or more other functions. It is created by combining two or more functions together. The resulting function can be written as a single expression, or as a composition of multiple functions.
A composite function is a type of function that is formed by combining two or more other functions. It is created by combining two or more functions together using the mathematical operations of addition, subtraction, multiplication, division, or composition. The resulting function can be written as a single expression, or as a composition of multiple functions. A composite function is often used to simplify a complex problem, or to manipulate and analyze data. For example, if a data set contains two sets of data, a composite function could be used to combine the two sets of data into a single expression. Additionally, composite functions can be used to solve problems that involve multiple variables, as the resulting function can be used to represent the relationship between the variables. Furthermore, composite functions can be used to create graphs, which can be used to further analyze the data.
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You have a 5 inch by 7 inch picture that you framed. When you hung the picture, you found that the entire area is 69.56 inches squared. What is the width of the frame?
The width of the frame is 2.4 inches
How to determine the width of the frame?
Let w represent the width of the frame
Then the area of the frame is:
(w + 5)(w + 7) = 69.56
Rewrite it in Standard form of a quadratic equation:
w² + 12w + 35 = 69.56
w² + 12w - 34.56 = 0
Use Quadratic Formula to solve for w:
w = (-b±√(b²-4ac))/(2a)
w = (-12±√(12²-4×1×(- 34.56)))/(2×1)
w = (-12±√(144+138.24))/(2)
w = (-12±16.8)/2
w = -6 ± 8.4
w = -6 + 8.4 or -6-8.4
w = 2.4 or w = -14.4
Since the width cannot be negative.
Thus, w = 2.4 inches
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find the values of X, Y, and Z
On applying the midpoint theorem the values of x, y, and z are 2, 10 and 8 respectively.
What is the mid-point theorem?
According to the midpoint theorem, the line segment connecting any two triangle sides' midpoints is parallel to and equal to half of the third side.
The outer triangle is ABC and the inner triangle is DEF.
It can be seen that sides AB, BC and AC are equally divided such that AD=DB,
BE=EC and
CF=FA.
So, this proves that point D, E and F are the middle points of AB, BC and AC respectively.
Now, according to the midpoint theorem -
DF = 1/2(BC)
Plugging in the values -
x = (5x-6)/2
2x = 5x-6
2x-5x = -6
-3x = -6
x = 2
Now, for side DE -
DE = 1/2(AC)
Plugging in the values -
12 = (2z+8)/2
24 = 2z+8
24-8 = 2z
16 = 2z
z = 8
Now, for side EF -
EF = 1/2(AB)
Plugging in the values -
y = 20/2
y = 10
Therefore, the values obtained are x=2, y=10 and z=8.
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