The length of the unknown side of this right angled triangle is 12cm.
This is a question about the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem can be written as c^2 = a^2 + b^2, where c is the hypotenuse, and a and b are the other two sides.
In this case, we know that the base of the triangle is 8cm and the length is 9cm.
So we can use the formula c = √(a^2 + b^2)
c = √(8^2 + 9^2)
c = √(64 + 81)
c = √(145)
c = 12cm
Therefore, the length of the unknown side of this right angled triangle is 12cm.
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-12 + 3m=m - 2
Thank u
Answer:
m = 5
Step-by-step explanation:
-12 + 3m=m - 2
3m = m + 10
2m = 10
m = 5
Let's check
-12 + 3(5) = 5 - 2
-12 + 15 = 3
3 = 3
So, m = 5 is the correct answer.
Hey um can somone help me out please i dont know what is correct and wrong
Re-write the quadratic function below in Standard Form
-(x-3)(x+7)
Answer:
[tex]-x^{2}[/tex] -4x + 21
Step-by-step explanation:
-(x-3)(x+7)
(-x + 3) ( x + 7)
[tex]-x^{2}[/tex] - 7x + 3x + 21
[tex]-x^{2}[/tex] -4x + 21
What is the definition of the sine ratio in a right triangle?.
The ratio of the side of a right-angled triangle opposite to a specified angle to the hypotenuse; when expressed as a real number between 0 and 1, it defines the sine of the angle.
What is the sine ratio in a right triangle?.Whenever the ratio is found by using the opposite side and the hypotenuse, we call it sine ratio.
We then say that sine 45 degrees is equal to 0.707. In short, we can use the symbol sin instead of sine and write sin (45 degrees) = 0.707
In general, sine of angle A = length of leg opposite angle A / hypotenuse
sin(A) = opposite/hypotenuse
In a right triangle, the sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.
The ratio of the side of a right-angled triangle opposite to a specified angle to the hypotenuse; when expressed as a real number between 0 and 1, it defines the sine of the angle.
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what is the probability of selecting a 2 and then a number divisible by 4?
The probability of selecting a 2 and then a number divisible by 4 will be C. 1/24.
How to calculate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur
The probability of selecting 2 is 1/6.
The probability of selecting a number divisible by 4 will be 1/4.
The probability of selecting a 2 and then a number divisible by 4 will be:
= 1/6 × 1/4
= 1/24
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PLEASE HELP!!! I PUT IN EXTRA POINTS!!!!
Which equation is an equation of a circle with a radius of 4 and its center is at (3, -2)?
Responses
(x - 3)² + (y + 2)² = 16
(x - 3)² + (y + 2)² = 4
(x + 3)² + (y - 2)² = 4
(x + 3)² + (y - 2)² = 16
Answer:
A. (x - 3)² + (y + 2)² = 16
Step-by-step explanation:
The formula for a circle plotted on the Cartesian coordinate system is:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
where [tex](a,b)[/tex] is the center of the circle, and [tex]r[/tex] is the length of the circle's radius.
Since the center of the circle in this problem is (3, -2), we know that the left side of the equation should be:
[tex](x - 3)^2 + (y - (-2))^2[/tex]
which can be simplified to:
[tex](x - 3)^2 + (y + 2)^2[/tex]
The radius of the circle is given as 4, so we know that the right side of the equation is:
[tex]4^2[/tex], which is the same as [tex]16[/tex].
Finally, to answer this question, we can put the two sides of the equation together to get:
[tex](x - 3)^2 + (y + 2)^2 = 16[/tex]
Please answer this. Thank you! :)
Protein of [tex]125 g[/tex] Yoghurt A is [tex]6,5 g[/tex]
Protein of [tex]150 g[/tex] Yoghurt B is [tex]4,0 g[/tex]
How many grams of protein are provided by [tex]100 g[/tex] of yoghurt A?
First, find the ratio of the weight of the yogurt A
[tex]125 g : 100 g[/tex]
125 and 100 have the same factor is 25. then divide both numbers by 25 to simplify it.
[tex]\frac{125}{25}:\frac{100}{25} =5:4[/tex]
Find grams of protein are provided by [tex]100 g[/tex] of yoghurt A use comparison [tex]5:4[/tex]
[tex]\frac{4}{5}(4)=\frac{16}{5}=3,2 g[/tex]
[tex]3,2g[/tex] of protein are provided by [tex]100 g[/tex] of yoghurt A.
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Subtract (2x - 2y) from the sum of (10x - 2y) and (-3y)
The value of (10x - 2y) + (-3y) - (2x-2y) is 8x-3y (option A)
What is subtraction?In math, to subtract means to take away from a group or a number of things. When we subtract, the number of things in the group reduces or becomes less. The minuend, subtrahend, and difference are parts of a subtraction problem.
For example, if 5 mangoes were taken from a basket filled with 20 mangoes, the number of mangoes left in the basket is calculated by subtracting 5 from 20 i.e 20-5 = 15 mangoes.
(10x-2y) + (- 3y) - (2x-2y)
10x +2y -3y-2x +2y
collect like terms
10x -2x+2y-3y-2y
8x-3y
= 8x - 3y
Therefore the value of Subtracting (2x - 2y) from the sum of (10x - 2y) and (-3y) is 8x+3y
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A store has a 25% discount now the cost is 34.50 what was the original price of the item
Answer:
$46
Step-by-step explanation:
We already have our first value of 34.5 and the second value of 75. Let's assume the unknown value is Y which answer we will find out.
As we have all the required values we need, Now we can put them in a simple mathematical formula as below:
STEP 1
34.5 = 75% × Y
STEP 2
[tex]34.5 = \frac{75}{100} *Y[/tex]
Multiplying both sides by 100 and dividing both sides of the equation by 75 we will arrive at:
STEP 3
[tex]Y = 34.5 *\frac{100}{75}[/tex]
STEP 4
Y = 34.5 × 100 ÷ 75
STEP 5
Y=46
Answer:
The original price is 46
Step-by-step explanation:
The x be the original price of the item.
The discount is 25%
x - .25x = 34.50
.75x = 34.50
Divide each side by .75
x = 34.50/.75
x = 46
The original price is 46
How to write a system of linear inequalities represented by the graph?.
To write a system of linear inequalities represented by the graph solution boundary line dashed for > and < and solid for ≤ and ≥ is used.
These steps will be used to graphically solve a set of linear inequalities:
1. Find y's inequality solution.
2. Represent the inequality as a linear equation and, depending on the inequality sign, graph the line as either a solid line or a dashed line.
a. Draw the line as a dashed line if the inequality symbol is missing an equals sign ( or >).
b. Draw the line as a solid line if the inequality sign contains an equals sign (or ).
3. Darken the area when the inequality is satisfied.
4. For every disparity, repeat steps 1 through -3.
5. The region where all of the inequalities intersect will be the solution set.
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How do you write 1 more than a number?.
To write 1 more than a number, we use the mathematical operation of addition and the notation 1 + Number = N+1.
To write 1 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.
In this case, we are given the number 1 and we are asked to find the number that is 1 more than it. To do this, we can use the mathematical notation: 1 + Number = N+1.
This notation means that we are adding 1 to a number, which results in N+1. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+1.
Another way to write 1 more than a number is to use the phrase "1 plus a number". This phrase indicates that we are adding 1 to a number to get N+1.
Therefore, In short, to write 1 more than a number, we use the mathematical operation of addition and the notation 1 + Number = N+1. This means that we are adding 1 to a number, resulting in N+1. It can also be written as "1 plus N", indicating the same operation.
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What is the symmetry of a quadratic function?.
The symmetry of a quadratic function is a vertical line that is x = − b/2a.
Quadratic function is defined as the function of the form f(x) = ax² + bx + c, where a, b and c are real numbers with a = 0 and it has the domain of a quadratic function is (−∞,∞).
Here we have given that we need to find the symmetry of a quadratic function.
As we all know that When a quadratic function is graphed in the coordinate plane, then the resulting parabola and corresponding axis of symmetry are vertical.
Here we have also know that in order to find the symmetry we have to replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.
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Mr. Johnson is going to buy an 1834 18 3 4 pound turkey for Thanksgiving. The turkey costs $2.95 $ 2.95 per pound at the grocery store. Which is the closest estimate to total cost of Mr. Johnson's turkey (before taxes)?
Answer:
The closest estimate to the total cost of Mr. Johnson's turkey (before taxes) is $54.67.
Step-by-step explanation:
You can calculate this by multiplying the weight of the turkey (18 3/4 pounds) by the price per pound ($2.95).
(18 3/4) * ($2.95) = 54.67
What is 1 4 plus 1 4 as a fraction?.
Fraction value for 1/4 plus 1/4 is 1/2.
The same denominator and different numerators are considered equivalent fractions in mathematics. For instance, since 2/4 and 3/6 both equal 1, they can both be considered similar fractions. A fraction is a portion of a whole. Equivalent fractions depict identical sections of the total.
It is possible to determine the equivalent fraction of any fraction by multiplying the numerator and denominator by the same integer. Equivalent fractions are those that represent the same value despite having different visual characteristics. For instance, if you cut a piece of cake in half and eat one of the pieces, you will have eaten half of the cake.
= 1/4+1/4
= 2/4
= 1/2
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Correct Question:
What is 1/4 plus 1/4 as a fraction?.
The average of a list of 4 numbers is 85. A new list of 4 numbers has the same first 3
numbers as the original list, but the fourth number in the original list is 105, and the
fourth number in the new list is 115. What is the average of this new list of numbers?
According to the solving the average of this new list of numbers is 60.
What is the average in math?The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
According to the given information:The sum of the original list's four numbers, whose average is 90, is as follows:
4 × 85 = 232
Since 80 is the fourth number inside the original list, the first three numbers in the original list add up to:
232 − 105 = 127
The total of these updated first 3 numbers is also: if the first 3 numbers inside the new list are the same as those in the old list:
127
The total of the first four numbers with in new list, if the fourth number is 96, is:
127 + 115 = 242
As a result, the new list of four numbers' average is:
242 ÷ 4 = 60
According to the solving the average of this new list of numbers is 60.
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Complete each congruency statement, and name the rule used.
If you cannot show the triangles are congruent from the given information, leave the triangle's name blank and write CNBD for "CanNot Be Determined" in place of the rule.
△SAT ≅ △____ by ____
A
O
S
T
The triangles SAT and SAO are congruent by the Side-Angle-Side (SAS) congruence theorem.
What is the Side-Angle-Side congruence theorem?The Side-Angle-Side congruence theorem states that if any of the two sides on a triangle are the same, along with the angle between them, then the two triangles are congruent.
For the triangles SAT and SAO in this problem, we have that:
Angles ASO and AST are the sime.Side SA is common to both triangles, hence the same.Sides ST and SO are the same.The common angle are between the common sides, hence the SAS congruence theorem was used to determine the congruence of the two triangles.
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What is the highest decimal value a byte can represent?
Answer:
255 is the highest decimal value a byte can represent.
Step-by-step explanation:
Tony bakes a casserole for 25 5/12 minutes. He decides it needs to bake longer. He bakes it for another 2 3/6 minutes. How long does the casserole bake altogether?
The total time that Tony bakes the casserole is calculated by adding the two times together.
The first time the casserole bakes for 25 5/12 minutes and the second time it bakes for 2 3/6 minutes. The two times can be written in fractions as 25 5/12 + 2 3/6. To add fractions with different denominators, the denominators must first be made equal.To accurately calculate the total amount of time the casserole bakes, the fractions must be converted to their equivalent value in the same unit. 5/12 minutes is equal to 10/24 minutes and 2 3/6 minutes is equal to 8/6 minutes. To add the two fractions, 10/24 and 8/6, they must be converted to have the same denominator. The least common denominator is 24, so 10/24 is equal to 5/12, and 8/6 is equal to 16/24. To make the denominators equal, the common denominator of 12 must be used. 25 5/12 can be rewritten as 225/12 and 2 3/6 can be rewritten as 15/12. 225/12 + 15/12 = 240/12. The fraction 240/12 can be reduced to 20/1. Therefore, the total time that Tony bakes the casserole is 20 minutes. The formula used to calculate this time is (25 5/12) + (2 3/6) = (225/12) + (15/12) = (240/12) = (20/1).
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What equation has many solutions?.
An equation with infinite solutions has both sides equal.
We know that a solution of an equation is a value that satisfies given equation.
As we know the system of equations has infinitely many solutions if the system of lines are coincident, and if they have the same y-intercept.
In some equations, any value for the variable makes the equation true. This means, an equation has infinitely many solutions.
Consider the equation 5x + 13 = 3x + 13 + 2x
5x + 12 = 5x + 12 .....(combine like terms)
13 = 13 ........(subtrsct 5x from each side)
As we know 13 = 13 is always true.
To check that above equation has an infinite number of solutions, we try substituting some different values for x
For x = 3
5(3) + 13 = 3(3) + 13 + 2(3)
15 + 13 = 9 + 13 + 6
28 = 28
The statement 28 = 28 is always true. So, x = 3 is a solution.
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What is an XYZ triangle?.
A formed angle has been created between the two sides. Two of the sides of XYZ are the same length if XY = YZ. It will be an isosceles triangle as a consequence.
An isosceles triangle in geometry is a triangle with two equal-length sides. There are two ways to describe it: either as having precisely two sides of equal length or at least two sides of equal length, with the equilateral triangle being an exception to the second definition. The two sides have come to an agreement.The base of the triangle is the third side of an isosceles triangle, which is not equal to the other two sides.
The two angles are exactly aligned with the equal sides.
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How do you graph y 2x 4 on a graph?.
The curve's y-intercept is 4, and its slope is 2.
To depict the curve, we will make use of the idea of slope and intercept in linear equations.
A line's slope and y-intercept are represented by the equation y = mx + c, where m represents the slope and c represents the y-intercept.
When y = 2x - 4 is put into comparison with the generic form, we get
The curve has a slope of 2 and a y-intercept of -4.
Picking two points on the line y = 2x – 4 will make it easier for us to plot the graph.
Since the supplied line's y-intercept is 4, the line y = 2x - 4 must pass through (0, -4).
Put y = 0
0 = 2x - 4
x = 2
Line passes through (2,0).
Draw a line passing through (0,4) and (2,0) and we get the graph.
Correct question :
How do you graph y = 2x - 4 on a graph?
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Use this equation for the questions below: y=log(5x+10)+8
Create a real-life application problem involving your chosen function type
Explain how to determine all of the key properties of your specific function and how to sketch the graph
Ask two interesting, realistic questions about the situation in context.
Question 1: Determine the value of the dependent variable given a value of the independent
Question 2: Determine the value of the independent variable given a value of the dependent
Show how you would solve both problems using only algebra. Show all of the steps.
Question 1: The value of the dependent variable given a value of the independent is 11.54 (thousands of people)
Question 2: The value of the independent variable given a value of the dependent is 1998 (5 years after 2000)
How do we get the values?Real-life application problem: The population of a city is growing at a rate modeled by the equation y = log(5x + 10) + 8, where y is the population in thousands and x is the number of years since the year 2000.
To determine the key properties of the function and sketch its graph:
The function is a combination of a logarithmic and an exponential function.
The domain of the function is all real numbers (since the logarithm function is defined for all positive numbers)
The range of the function is all real numbers greater than or equal to 8 (since the minimum value of the function is 8)
The graph of the function will be a smooth, continuous curve that starts at the point (0,8) and increases without bound as x increases.
Question 1: Determine the value of the population (y) given a value of x = 5 (number of years since 2000)
Solution:
y = log(5x + 10) + 8
y = log(5(5) + 10) + 8
y = log(25 + 10) + 8
y = log(35) + 8
y = 3.54 + 8
y = 11.54 (thousands of people)
Question 2: Determine the value of x (number of years since 2000) given a population of y = 12 (thousands of people)
Solution:
y = log(5x + 10) + 8
12 = log(5x + 10) + 8
4 = log(5x + 10)
5x + 10 = 10^4
5x = 9990
x = 1998 (5 years after 2000)
Note that this is not a realistic scenario, as the population of a city cannot be negative except in the case of extinction.
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Eric and Willow collect baeball card. Eric ha 350 baeball card and collect 10 card per week. Willow ha 250 baeball card and collect 15 card per week. After how many week will Eric and Willow have the ame number of baeball card? Explain the meaning of the olution
Eric and willow will have the same number of baseball cards (when they initially have 350 and 250 cards respectively ) after 20 weeks.
Given,
Number of baseball cards Eric has = 350
Eric collects 10 cards per week.
Number of baseball cards Willow has = 250
Willow collects 15 cards per week
Let after [tex]x[/tex] weeks both eric and willow have the same number of baseball cards .
According to the question,
[tex]350 + 10x = 250 + 15x\\5x = 100\\x=20[/tex]
Therefore, after 20 weeks both eric and willow have the same number of baseball cards.
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Which point represents the ordered pair (2, -4)?
Responses
A
B
C
D
What is a linear equation in two variables Class 10?.
A linear equation in two variables is an equation that can be written in the form of:
ax + by = c,
where a, b, and c are constants, and x and y are variables.
Linear equations in two variables are also called a system of linear equations in two variables. In this type of equation, the variables are related linearly, meaning that the highest power of the variables is 1. This is in contrast to non-linear equations, which have variables with powers greater than 1.
For example,
2x + 3y = 6 is a linear equation in two variables.
4x - 6y = 10 is also a linear equation in two variables.
A system of linear equations in two variables can have one unique solution, infinitely many solutions, or no solution. The solution of the system can be found by different methods such as graphing, substitution, elimination, matrix method, and numerical methods, as mentioned in the previous answers.
Linear equations in two variables are used to model many real-world situations such as in finance, physics, economics, and many more. The study of linear equations in two variables is a fundamental part of algebra and is a stepping stone to more advanced mathematical concepts.
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1234568x0987654321x12345678890
Answer:
1.5053412e+25
Step-by-step explanation:
use a calculator dude
What is the rule of parallel lines?.
The rule of parallel lines: they never intersect each other.
We know that two lines are parallel to each other if they lie in the same plane and never intersect each other.
Parallel lines are always equidistant from each other.
Also, the parallel lines are coplanar.
Mathematically, the parallel lines are represented by the symbol, ‘||‘.
If two lines l₁ and l₂ are parallel to each other then they are represented as l₁ || l₂.
Two lines parallel to a third line are parallel
As we know, the slopes of parallel lines are equal.
Let us assume that m₁ be the slope of line l₁ and m₂ be the slope of line l₂.
If line l₁ and l₂ are parallel to each other then m₁ = m₂
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The endpoints of GH are G(10,1) and H(3,5). What is the midpoint of GH?
Answer:
C
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = G (10, 1 ) and (x₂, y₂ ) = H (3, 5 ) , then
midpoint = ( [tex]\frac{10+3}{2}[/tex] , [tex]\frac{1+5}{2}[/tex] ) = ( [tex]\frac{13}{2}[/tex] , [tex]\frac{6}{2}[/tex] ) = ( [tex]\frac{13}{2}[/tex] , 3 )
Is 36 and 49 are co-prime?.
The prime factorization of 36 is (2 2 3 3) while that of 49 is (7 7), respectively. As can be seen, the prime numbers 36 and 49 have no common prime factors, making them co-prime.
What is the prime factorization process?Finding the prime factors of a given number, such as a composite number, is done through the process of prime factorization. The prime numbers are the only components in these factors. A number with just the number itself and factor 1 is said to be a prime number. As an illustration, the prime number 2 contains two factors, 2 and 1.
What does a math prime factor mean?The prime numbers that divide a positive integer exactly are said to be its prime factors. Integer factorization, often known as prime factorization, is the process of locating these integers. According to the basic theorem of mathematics, each positive integer has a distinct prime factorization.
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Using the formula, Quantity= Percent x Whole, 20 is what percent of 40? 20 = p(40) Find what is p by dividing both sides by 40.
By using the formula, Quantity = Percent × Whole, 20 is 50% percent of 40.
What is a percentage?In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
How to calculate the percentage of a number?In order to determine the percentage which 20 is of a whole number (40), we would apply the following mathematical expression (formula);
Quantity = percent × whole number
Substituting the given parameters into the percentage and quantity formula, we have the following;
20 = percent × 40
Percent = 20/40
Percent = 0.5
Next, we would multiply the resulting decimal value by 100 as follows;
Percentage = 0.5 × 100
Percentage = 50%.
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