The claim that is being made by Fabian is wrong and this can be proven by the steps below.
What is percentage of a number?The percentage of a number is the part of the number that is being represented by per hundred when it is divided by the whole and multiply by 100.
The 25% of a number can not always be greater than the 10% of any other number and this can be proven by using two different numbers.
For example, the 25% of 150 = 25/100 ×150 = 3750/100
= 37.5
Using another number such as 1500, the 10% of the given number is calculated as follows:
10/100 × 1500 = 15000/100 = 150
From the given examples, the 25% of 150 is not greater than the 10 percent of 1500, therefore, 25% of a number can not always be greater than the 10% of any other number and this can be proven by using two different numbers.
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Determine the relationship between the two triangles and whether or not they can be proven to be congruent
Side, Side, Side (SSS)
Are Congruent
Step-by-step explanation:Using the relationships between triangles based on the sides and angles we can determine whether or not triangles are congruent.
Congruent Sides
The diagram shows 2 triangles, and the sides of the triangles have tick marks to show that it is congruent to one of the sides of the other triangle. For example, both triangles have one side that has one tick mark. This means that these sides are congruent. Additionally, the sides with 2 tick marks are congruent and the same for the sides with 3 tick marks. Thus, it can be said that the sides of the triangles are congruent to each other.
Side, Side, Side
One of the most common relationships is side, side, side. This relationship occurs when 2 triangles have 3 sides that are congruent to each other. Side, side, side is usually shortened to SSS. This relationship will always prove congruency because triangles cannot have equal sides without the angles also being congruent.
estimate the quotient to the nearest whole number. 45.68 divided by 5.97 PLEASE HELP
When we divide the given decimal numbers and round off the answer to the nearest whole number, The answer is 8.
What are whole numbers?Whole numbers are the set of non-negative integers including 0, 1, 2, 3, 4, 5, and so on. They are numbers that can be counted and do not have fractions or decimals. Whole numbers are often used to count discrete objects and are an important foundation for many areas of mathematics, including number theory and combinatorics. They are opposite of the negative numbers and called Non-negative integers.
What do you mean by round off ?Round off is a method of approximating a number to a certain number of significant figures or decimal places. It involves replacing the least significant digits in a number with a 0 or a 5, depending on the next digit, in order to make the number simpler or more manageable. This can be done with the help of mathematical functions (e.g. round(), floor(), ceil() etc) in various programming languages. It is used to simplify large and complex numbers for ease of calculation, or to present data in a more readable form.
45.68/5.97
=7.65
rounding off to the nearest whole number , We get 8.
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Solve the equation below using factorising. 10y² – 11y − 6 = 0 - Give each answer as an integer or as a fraction in its simplest form.
Answer:
y = - [tex]\frac{2}{5}[/tex] , y = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
10y² - 11y - 6 = 0
consider the factors of the product of the y² term and the constant term which sum to give the coefficient of the y - term
product = 10 × - 6 = - 60 and sum = - 11
the factors are - 15 and + 4
use these factors to split the y- term
10y² - 15y + 4y - 6 = 0 ( factor the first/second and third/fourth terms )
5y(2y - 3) + 2(2y - 3) = 0 ← factor out (2y - 3) from each term
(2y - 3)(5y + 2) = 0 ← in factored form
equate each factor to zero and solve for y
5y + 2 = 0 ⇒ 5y = - 2 ⇒ y = - [tex]\frac{2}{5}[/tex]
2y - 3 = 0 ⇒ 2y = 3 ⇒ y = [tex]\frac{3}{2}[/tex]
Every pupil in class either swims or dances or both. Three fifths of the class swim and three fifths dance. Five pupil both swim and dance. How many pupils are there in the class?
Five pupils both swim and dance. Then the number of pupils in the class will be 25.
What are Sets?Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Every pupil in class either swims or dances or both. Three-fifths of the class swim and three-fifths dance. Five pupils both swim and dance.
Let 'x' be the total number of pupils. Then the equation is given as,
A∪B = A + B - A∩B
x = (3/5)x + (3/5)x - 5
x = (6/5)x - 5
(1/5)x = 5
x = 25
Then the number of pupils in the class will be 25.
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Factor completely using the distributed law 42m+ 56n
Answer:
14(3m + 4n)
Step-by-step explanation:
Now we have to,
→ factor the given expression.
The expression is,
→ 42m + 56n
Let's factorise the expression,
→ 42m + 56n
→ (14 × 3m) + (14 × 4n)
→ 14(3m) + 14(4n)
→ 14(3m + 4n)
Hence, answer is 14(3m + 4n).
16. A building has more than 2 stories but fewer than 10 stories. Each story of the building has the same number of windows. The. building has 25 windows. Complete the sentence. Then explain how you found your answer.
Based on the figure on the graph, match the describe transformation with the transformed figures.
The series of the transformation will be reflected across the x-axis, translating 9 units to the Right and 2 units down. Then the correct options are A and C.
What is a transformation of a shape?A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position. Picture, after translation, refers to the object's ultimate organization and placement.
The translation does not change the shape and size of the geometry. But changes the location.
The reflection does not change the shape and size of the geometry. But flipped the image.
The series of the transformation will be reflected across the x-axis, translating 9 units to the Right and 2 units down. Then the correct options are A and C.
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The complete question is attached below.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Based on the figure on the graph, match the described transformations with the transformed figures.
Reflected across the x-axis
Rotated 180° clockwise
Translated 9 units to the Right and 2 units down
Reflected across the y-axis
The graph of a function must be linear if it has what characteristic?
The graph of a function must be linear if it has ''a constant slope.''
What is linear expression?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The graph of a function must be linear.
Now,
We know that;
A linear function graphs as a straight line if It will have a constant rate of change.
Thus, The graph of a function must be linear if it has ''a constant slope.''
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You and your friend each deposit $50 in separate savings accounts. Your account earns 4% simple annual interest. Your friend’s account earns 6% simple annual interest. How long does it take for you to earn $12 in interest? How long does it take for your friend to earn $12 in interest?
I need help! Needs answers quick
I can earn simple interest $12 in 6 years and My friend can earn simple interest $12 in 4 years.
What is simple interest?
The principal of a loan or the initial deposit into a savings account serves as the foundation for simple interest. Because simple interest doesn't compound, a creditor will only pay interest on the principal sum, and a borrower will never have to pay interest on the interest that has already accrued.
Principle = $50
Rate of Interest I1 = 4%
Interest = $12.
Interest = [tex]\frac{PNR}{100}[/tex]
=> 12 = [tex]\frac{50\times 4\times N}{100}[/tex]
=> N = [tex]\frac{12}{2}= 6[/tex] years.
Rate of Interest I2 = 6%
=> 12 = [tex]\frac{50\times 6\times N}{100}[/tex]
=> N = [tex]\frac{12}{3}[/tex] = 4 years.
Hence I can earn $12 in 6 years and My friend can earn $12 in 4 years.
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p and q are integers and p*q denotes the remainder when the product pq is divided by 10. Find a value p, greater than 4, such that p*p = (8*p) + 3
The required value of the given equation is p = √3 + 8.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
If we let x = p - 8, then p = x + 8 and p × p = (x + 8) × (x + 8) = x² + 16x + 64.
We can substitute this expression for p × p in the given equation to get x^2 + 16x + 64 = (8 × (x + 8)) + 3 = 8x + 64 + 3 = 8x + 67.
Subtracting 64 from both sides gives us x² + 16x = 8x + 3, and if we subtract 8x from both sides, we get x² = 3.
The only positive value of x that satisfies this equation is x = √3, so p = √3 + 8.
Since √3 is approximately 1.73, p is approximately 9.73, which is greater than 4.
Therefore, a value of p that satisfies the given equation is p = √3 + 8.
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distance between the following numbers on the real number line. a=-10b=-15
The distance between the following numbers on the real number line is -5.
What is a number line?
A straight line with numbers positioned along it at equal intervals or segments. Positive and negative numbers are listed on each side of zero and continue forever on a number line, which is a straight line with a "zero" point in the center.
Here, we have
Given: a = -10, b = -15
We have to determine the distance between the following numbers on the real number line.
According to the given question, we have
= b - a
= -15 - (-10)
= 15 + 10
= -5
Hence, the distance between the following numbers on the real number line is -5.
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What is the length of the added metal bar?
The length of the added metal bar is exactly 5cm.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
In the given cuboid the length is of 4 meters
The height is 3 meters.
We need to find the length of the added metal bar.
We can find this by using pythagoras theorem
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
In the given figure the added metal bar is the hypotenuse.
4²+3²=d²
25=d²
d=5
Hence, the length of the added metal bar is exactly 5cm.
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Confused on the answers to #7, #8
Will give votes!
Question 7
[tex]3(2+x)=-3 \\ \\ 2+x=-1 \\ \\ \boxed{x=-3}[/tex]
Question 8
[tex]4(5+x)=-4 \\ \\ 5+x=-1 \\ \\ \boxed{x=-6}[/tex]
Find the growth/decay rate given the exponential function. *
f(x) = 5(1.34)'
The growth/decay rate of an exponential function can be found by taking the derivative of the function with respect to the independent variable.
K in terms of growth and decay?
The growth rate is represented by the constant k. When viewed in terms of exponential DECAY, it is NEGATIVE. The length of time since then is t. If the time information is provided as dates, you must convert it to the amount of time that has passed from the starting point.
Given the function f(x) = 5(1.34)^t, the derivative with respect to t is:
f'(x) = 5(1.34)^t * ln(1.34)
The derivative represents the instantaneous rate of change of the function, and it is also the growth/decay rate.
So the growth/decay rate of the function f(x) = 5(1.34)^t is 5ln(1.34) * (1.34)^t.
In this function, the growth/decay rate is directly proportional to the function value, and it is a constant times the function value. This means that the function is growing or decaying at a constant rate, the rate being 5ln(1.34) which is the coefficient of (1.34)^t.
This constant rate of change is the growth/decay rate. In this case it is a growth rate of 5ln(1.34) which is approximately 1.99.
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One angle of a right triangle measures 69∘. What is the measure of the third angle?
21°.
In a right-angle triangle, there is always a 90° angle. Because of this, and our knowledge about a 69° angle, when we add 90° + 69° and get 159° as a result, we just subtract this from the area of a triangle, which is 180°. 180° - 159° = 21°, hence the missing and third angle is 21°.
Use 3.14 for the value of , and round your answers to two decimal places, where applicable. A rectangle is 11 inches long and 7 inches wide. What is its area?
Answer: 77
Step-by-step explanation:
Area of a rectangle is length * width
Area = 7*11 so the answer is 77
In kite WXYZ, m < XYW = 23 deg and m < 7WY = 41 deg What is the m < WXY ? Help please help me due tonight
Answer:
Step-by-step explanation:
118.5
Sum of all angles in the kite is 360.
XYW = 23
XYZ = 46
ZWY = 41
ZWX = 82
We'll make the 2 angles left 2x in the equation because they are congruent.
2x+82+41=360
I got 118.5. This is a weird number, I'm not sure if it's right, but I don't have time to check.
What are the explicit equation and domain for an arithmetic sequence with a first term of 3 and a second term of 5?
The explicit equation for the arithmetic sequence whose first term and second term are 3 and 5 respectively is; a (n) = 3 + 2 (n - 1).
The domain of such an arithmetic sequence includes the set of all positive integers, n.
What is the explicit equation of the arithmetic sequence as described?Recall that the explicit equation of an arithmetic sequence takes the form;
a (n) = a (1) + d (n - 1).
where; a (n) is the nth term of the sequence.
a (1) = the first term of the sequence.
and d = common difference between each successive terms.
On this note, the required explicit equation of the arithmetic sequence is; a (n) = 3 + 2 (n - 1) since the common difference, d = 5 - 3 = 2.
The domain is the set of all possible values of n which includes all positive integers.
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Mini muffins cost $3.00 per dozen.
Andre says, “I have $2.00, so I can afford 8 muffins.”
Elena says, “I want to get 16 muffins, so I’ll need to pay $4.00."
Do you agree with either, both, or neither of them?
What is the next step in solving the equation 10x+5=-4x+47 for x after we have combined x variables to one side of the equation?
a. Once x variables have been combined we need to combine the constants using opposite operations.
b. Once x variables have been combined we need to divide the remaining numbers by our new x variable from combining it in step 1.
c. Since we have combined the x variables together we have completed the necessary steps to solve the equation and have the answer.
d. The problem cannot be solved for x.
The next step in solving the equation 10x+5=-4x+47 for x after we have combined x variables to one side of the equation is once x variables have been combined we need to combine the constants using opposite operations and is denoted as option A.
What is an Equation?This is referred to as a mathematical statement that shows that two mathematical expressions are equal.
The equation 10x+5=-4x+47 is solved by combining x variables to one side of the equation and combining the constants using opposite operations which is denoted below:
10x+5=-4x+47
10x + 4x = 47 - 5
14x = 42
x = 42/14 = 3
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Use the table below to answer the question. How many more grapes do 8 people eat than 5 people?enter your answer in the box.
The number of grapes that 8 people eat more than 5 people, given the table attached, is 34 kg of grapes
How to find the amount of grapes ?To find the amount of grapes that 8 people eat more than 5 people, the formula would involve subtracting the amount of grapes eaten by 5 people from the amount of grapes eaten by 8 people.
From the graph, the amount of grapes eaten by 8 people would be 74 kg of grapes. The amount of grapes eaten by 5 people was 40 kg of grapes.
The amount of grapes that 8 people eat more than 5 people, is therefore :
= Grapes eaten by 8 people - Grapes eaten by 5 people
= 74 - 40
= 34 kg of grapes
In conclusion, the amount of grapes that 8 people eat more than 5 people, is 34 kg of grapes.
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If there is 8 apple and 8 oranges how many is in total?
Answer:
16
Step-by-step explanation:
8+8=16
Calculate the power of a man weight 40m in 15minutes assume G=9.87m~2
The power of man weight 40 m in 15 min is 394.8 N x distance / 900 seconds the distance is not provided in the question, so it's impossible to calculate the power.
What is the step by step calculation?To calculate the power of a man who weighs 40 kg and walks for 15 minutes, we can use the following formula:Power = Work / TimeWork = force x distancewhereforce = mass x gravity (F = mg)distance = velocity x timeThe force exerted by the man is:force = 40 kg x 9.87 m/s^2 = 394.8 NIf we assume that the man is walking at a constant velocity, we can calculate the distance he travels using the formula:distance = velocity x timeThe power exerted by the man is:Power = (394.8 N x distance) / (15 minutes x 60 seconds/minute) = 394.8 N x distance / 900 secondsThe distance is not provided in the question, so it's impossible to calculate the powerTo learn more about power refer:
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an adult ticket costs 24$ a senior citizen ticket costs 16$ and a students ticket costs 12$. Today only, tickets will cost 3/5 of the original price. what is the discounted price to buy 4 adult tickets, 2 senior citizens ticket, and 3 student tickets?
Answer:
The total discounted price to buy 4 adult tickets, 2 senior citizen tickets, and 3 student tickets is 96$ + 32$ + 18$ = 146$
Step-by-step explanation:
The discounted price for each ticket type is 3/5 of the original price, so for 4 adult tickets the discounted price is 4 * 24 * 3/5 = 96$, 2 senior citizen tickets is 2 * 16 * 3/5 = 32$, and 3 student tickets is 3 * 12 * 3/5 = 18$. Summing these together gives us 96$ + 32$ + 18$ = 146$.
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Tahlia deposited $6800 into a savings account that earns 3.2% simple
interest each year, calculated annually. What will be the value of Tahlia's
account after 7 years?
OA. $15,232.00
OB. $1523.20
OC. $7017.60
OD. $8323.20
SUBMIT
Answer:
Simple interest= Principle × Rate× Time then you divide by 100
in this case the principle is $6800, rate is 3.2% and time is 7years
So $6800×3.2×7=152320
then you divide 152320 by 100 to get $1523.20
as the interest
but now to get the value the will be in the account, you will add the principle+ interest that will be gained
$6800+ $1523.20= $8323.20
Which unit would be best for measuring the thickness of a coin?
I
kilometer
meter
millimeter
centimeter
Done
The thickness of a coin will be measured in millimeters.
What is Units conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
For the Conversion to Millimeter
1 meter = 1000 millimeter.
1 centimeter = 10 millimeter,
1 kilometer = 1000000 millimeter
We know that the thickness of the coin is too small. To be measured in meters or kilometers of the coin.
Hence, the thickness will be measured in millimeters.
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If it is a given that the base angle of an isosceles triangle is a right angle, what do you know about this triangle? Why?
Answer:
Step-by-step explanation: so first you know how we have a right and left with our hands so that’s the same thing with the triangle is southern on the right and nothing left I’m not sure.
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Answer:
the Pythagorean Theorem
√73 = 8.544
a leg
hypotenuse
√89 ≈ 9.434
Step-by-step explanation:
Use the Pythagorean theorem since you are finding the hypotenuse of a right triangle.
AC = √(8² + 3²) = √73 ≈ 8.544
CG is a leg of right triangle ACG
AG = √(73 + 16) = √89 ≈ 9.434
See the Image below.
Answer:
21 inches
Step-by-step explanation:
The perimeter of a square is given by
P = 4s where s is the side of a square
P = 4 ( 5 1/4)
= 4 * 5 + 4 * 1/4
= 20 + 1
= 21
evelyn is making two rectangular table tops. the dimensions of both are shown. if both designs have the same area, what is the value of x? the dimensions of table one is x+4 and x. the dimensions of table two is 2x+3 and x-2
The value of x is for the two rectangular table to have the same area is 6 or -1.
How to solve an equationThe dimensions of table one is x+4 and x, hence the area is:
Area = length * breadth
A = (x + 4)(x)
A = x² + 4x
The dimensions of table two is 2x + 3 and x - 2, hence the area is:
Area = length * breadth
A = (2x + 3)(x - 2)
A = 2x² - 4x + 3x - 6
A = 2x² - x - 6
Since both tables have same area, hence:
x² + 4x = 2x² - x - 6
x² - 5x - 6 = 0
x² - 6x + x - 6 = 0
x(x - 6) + 1(x - 6) = 0
(x + 1)(x - 6) = 0
x = -1 or 6
The value of x is 6
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