To find the length of the side opposite the angle, multiply the hypotenuse by sin(). Alternatively, to obtain the side next to the angle, multiply the hypotenuse by cos()
What is Hypotenuse triangle?The term "hypotenuse" refers to a right-angled triangle's longest side as compared to the base and perpendicular lengths. The right angle, the largest angle of the three angles in a right triangle, is opposite the hypotenuse side. In essence, only the right triangle possesses the hypotenuse feature, not any other triangles. When we study the right-angled theorem, Pythagoras Theorem, or Pythagorean Theorem, this is better understood.
Hypotenuse TheoramPythagoras theorem defines the hypotenuse theorem. This theorem states that the square of a right-angled triangle's hypotenuse side is equal to the sum of its base and perpendicular squares, so that;
Hypotenuse2 = Base2 + Perpendicular2
The square root of the sum of the base and perpendicular squares of a right-angled triangle provides the formula to get the hypotenuse. The hypotenuse formula is represented as follows:
Hypotenuse = √[Base2 + Perpendicular2]
Length of the hypotenuse:Hypotenuse length: In the scenario where the square root is not a perfect square, we take an approximation of the root here in order for the solution to appear.Additionally, the squares of the base and the height should always be added to establish the value, however this does not provide a perfect square.Due to the imperfect square-root number, we must therefore approximation the solution.To know more about Hypotenuse Triangle refer to:
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Eleven is 20% of what number?
55
11 = 20% × y
11 = 20/100 × y
multiply both sides by 100 and divide both sides by 20
y = 11 x 100/20
y = 11 × 100 ÷ 20
y = 55
Select the correct answer from each drop-down menu. the function has been transformed, resulting in function h. to create function h, function f was translated 2 units , translated 4 units , and reflected across the _______.
Across the y-axis, translated 2 units to the right and four units to the left, the new function is now h(x) = -(x + 2)3 - 4
Step (i): The type of transformation change of the function
a) The translated left "c" units are x - c;
b) The translated right "c" units are x + c
Step (ii) The given function is translated "2" units right side, then the new function is
h(x) = (x + 2 )3followed by the translated "4" units left sides and reflected across the y-axis.
Now the new function is h(x).
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9. Expand :
(i) (3x - 4y + 5z)² (ii) (2a-5b-4c)²
(iii)
(5x + 3y)³
(iv) (6a - 7b)³
Write an equation in slope-intercept form for the line that passes through the given
point and is perpendicular to the graph of the equation.
24. (−5, 2), y = ¹⁄2x − 3
Please explain how to get the answer too.
Answer:
Step-by-step explanation:
perp. -2
y - 2 = -2(x + 5)
y - 2 = -2x - 10
y = -2x - 8
Could someone help me
[tex]\cfrac{6a^2 + 21a}{3a^2}\implies \cfrac{6a^2 }{3a^2}+\cfrac{21a}{3a^2}\implies 2+\cfrac{7}{a}[/tex]
In a random sample of 70 people, it was found that 44 of them were fans of the New York Yankees. What is the margin of error for the true proportion of all individuals who are fans of the New York Yankees? A. 0.0088 B. 0.058 C. 0.063 D. 0.116 E. 0.173
The margin of error for the true proportion of all individuals who are fans of the New York Yankees is 0.058.
The Correct option is (B).
How to find the margin of error?The formula to calculate the margin of error for the true proportion is;
M = √[p(1 - p)/n]
Given:
n= 40
p = 44/70
Now, The general formula for the margin of error would be:
z x √[p (1-p) ÷ n]
where:
z = values for selected confidence level
p = sample proportion
n = sample size
Since the confidence level is not given,
√[p (1-p) ÷ n]
=√[44/70 (1 - (44/70) ÷ 70]
=√[0.6286 (0.3714)] ÷ 70
=√0.2335 ÷ 70
= √0.0033357
= 0.05775 or 0.058
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Why do the Iroquois perform rituals?
The Iroquois perform rituals in "The World on Turtle's Back" to honour the twins, demonstrating their belief that they must carry out specific rituals in order to preserve the Earth.
What is rituals?A ritual is a set sequence of actions involving gestures, words, actions, or objects. The customs of a group, including a religious group, may dictate rituals. Formalism, traditionalism, invariance, rule-governance, sacral symbolism, and performance are characteristics of rituals but not what defines them.
All known human societies have rituals. In addition to the rites of passage, atonement, and purification, oaths of allegiance, dedication ceremonies, coronations, presidential inaugurations, marriages, funerals, and other ceremonies, they also include the worship rites and sacraments of organised religions and cults. Even routine behaviours like shaking hands and saying "hello" can be categorised as rituals.
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Questions:
1. What did you do to the numerators? What did you do too to the denominators?
2. Did you find like terms among the collected terms of the numerator? What did you do
to terms?
3. What factoring techniques did you apply?
4. How did you simplify your sum?
The answers to all the subparts are shown:
(1) The numerator is simply added. The denominator is copied.
(2) Yes, it has; yet, we include them since that is what needs to be done.
What is numerator and denominator?In a fraction, the number above the line is the numerator.
For instance, the numerator of the fraction 3/5 is 3.
A fraction's numerator displays the number of pieces that make up the whole while the denominator, or a number of equal parts, is displayed below the line.
So, we have the equation:
2x² + x/2x - 2 + x - 4/ 2x - 2
Now, answering questions taking the above-given equation into consideration:
(1) The numerator is simply added. The denominator is copied.
(2) Yes, it has; yet, we include them since that is what needs to be done.
(3) We complete the square, but we can also use the straightforward factoring approach.
(4) We eliminate or simply cancel the factors in the numerator that are also present in the denominator to simplify the sum.
Therefore, the answer to all the subparts are shown:
(1) The numerator is simply added. The denominator is copied.
(2) Yes, it has; yet, we include them since that is what needs to be done.
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CORRECT ANSWER WITH **STEPS** GETS BRAINLIEST
for the following questions, determine what values of x makes the rational expression equal to zero.
1. x+6 / x-4
2. (x+4)(x-2) / (x+6)
3. 2x+10 / 3x-12
thanks.
Answer:
see explanation
Step-by-step explanation:
if the denominator of a rational expression is zero then the expression will be undefined.
the numerator is the part of the rational expression that makes it zero.
solve the numerators in each to find values of x
1
[tex]\frac{x+6}{x-4}[/tex]
x + 6 = 0 ( subtract 6 from both sides )
x = - 6 ← value that makes expression equal to zero
2
[tex]\frac{(x+4)(x-2)}{x+6}[/tex]
(x + 4)(x - 2) = 0
equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x - 2 = 0 ⇒ x = 2
x = - 4 and x = 2 make the expression equal to zero
3
[tex]\frac{2x+10}{3x-12}[/tex]
2x + 10 = 0 ( subtract 10 from both sides )
2x = - 10 ( divide both sides by 2 )
x = - 5 ← value that makes expression equal to zero
Answer:
1) x = -6
2) x = -4 and x = 2
3) x = -5
Step-by-step explanation:
A rational expression is undefined when the denominator equals zero.
A rational expression equals zero when the numerator equals zero.
Question 1Given rational expression:
[tex]\dfrac{x+6}{x-4}[/tex]
Set the numerator to zero and solve for x:
[tex]\implies x+6=0[/tex]
[tex]\implies x=-6[/tex]
Question 2Given rational expression:
[tex]\dfrac{(x+4)(x-2)}{x+6}[/tex]
Set the numerator to zero:
[tex]\implies (x+4)(x-2)=0[/tex]
Apply the zero-product property and solve for x:
[tex]\implies x+4=0 \implies x=-4[/tex]
[tex]\implies x-2=0 \implies x=2[/tex]
Question 3Given rational expression:
[tex]\dfrac{2x+10}{3x-12}[/tex]
Factor the numerator and denominator:
[tex]\dfrac{2(x+5)}{3(x-4)}[/tex]
Set the numerator to zero and solve for x:
[tex]\implies 2(x+5)=0[/tex]
[tex]\implies x+5=0[/tex]
[tex]\implies x=-5[/tex]
need help with this screenshot
The quadratic equation in vertex form is y = -(x - h)² + k
The parabola passed through points (-1, -3), (0, 0), (1, 1), (2, 0) and so on
How to write the equation of parabola in vertex formFor a vertical parabola, the vertex form of the equation is written as
y = a(x - h)² + k
where:
a = 1/4p
h and k are points of the vertex = v(h, k)
The vertex
v (h, k) = (1, 1)
h = 1
k = 1
y = a(x - 1)² + 1
using point (0, 0)
0 = a(0 - 1)² + 1
-1 = a
hence a = -1
the equation is written as y = -(x - h)² + k
The points the graph passed is read from the graph to be
(-1, -3), (0, 0), (1, 1), (2, 0) and so on
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1. From the information given in the triangles, are these triangles always, sometimes, or never congruent?
A. always
B. sometimes
C. never
D. cannot be determined
On solving the provided question, we can say that - the both triangle similar triangle ABC and triangle DEF
What is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
here,
AB = DE
BC = EF
AC = DF
so, by SSS both triangles are similar
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How do you find the sides of an isosceles triangle given the angles?
To find the sides of an isosceles triangle given the angles, use the Law of Cosines to calculate the length of each side.
An isosceles triangle has two angles and two sides that are both equal.. To find the sides, you will need to use the Sine Law. The Sine Law states that the ratio of the length of a side of a triangle to the sine of its opposite angle is equal for all sides and angles of the triangle.
For example, if you have the angles A and B, and you know that they are both equal (i.e. they are the angles of an isosceles triangle), then you can use the Sine Law to calculate the length of the sides:
Side AB = Side BC = (Side AC) x (Sin A / Sin B)
Where A and B are the angles of the triangle and Side AC is the known side length.
Once you have calculated the length of the two equal sides, you can then use the Pythagorean Theorem to calculate the length of the third side (the base).
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WHAT IS THE OPPSIT OF 0
Answer:
0
Step-by-step explanation:
The zero is in the middle.it is a special number by being its opposite because it doesn't have it's partner.
find four consecutive odd integers such that 4 times the sum of the first and third is 4 larger than 4 times the fourth
The four consecutive odd integers = 15, 17, 19, 21
What are integers ?Positive, negative, and zero are all examples of integers.
The Latin word "integer" signifies "whole" or "intact."
As a result, fractions and decimals are not included in integers.
All whole numbers and negative numbers are considered integers.
This means that if we combine negative numbers with whole numbers, a collection of integers results.
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.
Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043. a collection of numbers, denoted by the symbol Z.
According to our question-
First digit: x
Second digit: x + 2
Three-digit number Equals x + 4
Fourth digit: x + 6
The difference between the opposite of the third and the first two sums up to 55.
x + x + 6 = -(x + 4) + 55
x + x+6 = (-x - 4) + 55
2x + 6 = -x + 51
assemble similar terms
2x + x = 51 - 6
3x = 45
x = 15
Therefore,
First digit: x = 15
Second digit: 15 + 2 + x = 17
Third number: 15 + 4 + 4 = 19
Fourth digit: x+6 = 15+6 = 21
The four odd numbers in a row equal 15, 17, 19, and 21.
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5-115. Let us consider the difference between t(n) = 2 · 3" and f(x) = 2. 3
a) Is f(x) = 2 · 3 a function? Is t(n) = 2 · 3" a function? Why or why not?
Both f(x) = 2.3 and t(n) = 2.3" is not a function as they does not has any input variable.
f(x) = 2.3 is not a function because it's a constant value, it doesn't have any input x that could be used to produce a different output. It's just a number, and it's not a mathematical function.
t(n) = 2 · 3^n also doesn't represent a function because, again, it doesn't have any input n that could be used to produce a different output. It's also just a number, and it's not a mathematical function.
A mathematical function is a set of ordered pairs (input, output) such that for each input, there is only one output. A function must have at least one variable that can take different values and the output must depend on the input value. In other words, for each value of the independent variable, there is only one value of the dependent variable.
So, in the case of f(x) = 2.3 and t(n) = 2 · 3^n, there is no input variable that can produce different output, so they're not functions.
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How do you write an expression in factored form?
To write an expression in factored form, its products needs to be deduced.
What is an expression?
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
Factoring is the process of representing a given number or algebraic statement as the product of its components.
For example - Consider the binomial 3x^2-9x.
On simplifying it -
3x^2-9x = 3x(x-3)
So, here 3x^2-9x is the expanded form and 3·x·(x-3) is the factored form.
Another example is - Consider y^2-100.
The terms used here can all be expressed as squares.
y^2 − 100 = y^2 − 10^2
(y + 10)(y − 10)
The factors in this case are (y + 10) and (y - 10).
Therefore, the products are the factors of an expression.
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(2x+6y) exponent 2 with solution po thanks
Answer: (2x+6y)^2 = (2x+6y)(2x+6y) = 4x^2 +12xy + 12yx + 36y^2 = 4x^2 + 24xy + 36y^2
So the result of (2x+6y)^2 is 4x^2 + 24xy + 36y^2
Which expression is equivalent to –3 – 3x – 1 x? 2x – 4 –2x 4 –2x – 4? 4 – 2x
The expression equivalent to -3 - 3x -1x is 4 - 2x.
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
To get to this you can combine like terms:
-3 - 3x - 1x = -3 - (3x + 1x)
= -3 - (4x)
= -3 - 4x
= -4x - 3
= 4 - 2x
Hence 4 - 2x is equivalent to -3 - 3x -1x
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What are the roots of the equation 2x^2 3x 5 0?
The roots of the equation 2x² - 3x - 5 = 0 are 5/2 and -1.
The quadratic formula is a formula that can be used to find the solutions (or roots) of a quadratic equation. For a quadratic equation written in the form ax² + bx + c = 0, where a, b, and c are constants, the quadratic formula is given by:
x = (-b ± √(b²- 4ac))/(2a)
Where x is the solution, a, b, and c are the coefficients of the equation.
Plug in the coefficients of the equation 2x² - 3x - 5 = 0 to the quadratic formula to find the roots.
x = (-b ± √(b²- 4ac))/(2a)
x = (3 ± √((-3)²- 4(2)(-5)))/(2)(2)
x = (3 ± 7)/4
x = 5/2 ; x = -1
Hence, the roots of the equation are 5/2 and -1.
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Zendaya has $540 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $269.88.
She buys 4 bicycle reflectors for $10.57 each and a pair of bike gloves for $17.76.
She plans to spend some or all of the money she has left to buy new biking outfits for $65.65 each.
Write and solve an inequality which can be used to determine
x
x, the number of outfits Zendaya can purchase while staying within her budget.
Plsss help!!
Answer:
269.88 +4(10.57) +17.76 +65.65x ≤ 540x ≤ 3.2; 3 outfits or lessStep-by-step explanation:
After spending $269.88, 4 times $10.57, and $17.76 of her $540 budget, you want to know how many (x) outfits Zendaya can buy at $65.65 each.
InequalityThe total of Zendaya's spending must be no more than her budget amount:
269.88 +4(10.57) +17.76 +65.65x ≤ 540
SolutionSimplifying the inequality gives ...
329.92 +65.65x ≤ 540
65.65x ≤ 210.08 . . . . . . . . . . subtract 329.92
x ≤ 3.2 . . . . . . . . . . . . . divide by 65.65
Zendaya can purchase up to 3 outfits while staying within her budget.
Two cards are chosen at random from a standard 52-card deck. What is the probability that the first card is a heart and the second card is a 10
The probability that the first card is a heart and the second card is a 10 is 1/51.
What is the probability?Probability with Replacement is used for questions where the outcomes are returned to the sample space again. This means that once the item is selected, it is replaced in the sample space, so the number of elements of the sample space remains unchanged.
The following combinations are possible:
When we choose first card, total no. of card is 52 and card of heart is 13
so the probability of the first card to be heart is
P(1)= 13/52
= 1/4
When we choose second card, total no. of card is 51 and card of 10 is 4
so the probability of the first card to be 10 is
p(2)= 4/51
So the final probability is
= P(1)* P(2)
= 1/4 * 4/51
= 1/51
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How do you prove irrational rational and irrational?
Rational and Irrational numbers can be depicted as the number that can be communicated as p/q are reasonable and which can't be communicated are called Unreasonable Numbers.
Rational Numbers are characterized as a number that can be addressed as p/q where q isn't equivalent to zero.
We can likewise, say that the part where the denominator and the numerator are whole numbers and the denominator isn't equivalent to zero is called Reasonable Numbers.
For Instance: 2/3, 3/9, addresses Rational numbers.
Irrational Numbers are characterized as genuine numbers that can't be communicated as a proportion of whole numbers.
For Instance: [tex]\sqrt{2}[/tex], [tex]\sqrt{3}[/tex] addresses an Irrational number.
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Use the diagram to help you solve the equation 4x-12=16 how to do it
How do you simplify 3 ratios?
To simplify 3 ratios, divide each part of the ratio with the same amount and keep diving numbers in the ratio until they are as small as possible but they remain as whole numbers.
To simplify or reduce a fraction, first, we need to find a common factor between the ratio numbers. When we have multiple ratio numbers, we must find a common factor between all of them.
The greatest factor between all the ratio numbers (greatest common factor) will be utilised to divide or reduce the ratios down to their lowest form.
For example reduce the ratio 350: 250: 125
The first step is to determine a common factor between all of the ratio numbers. In this example, we can see that all of the numbers end in either 5 or 0. This means that each number should have 5 as a factor.
If numbers are large and we are not sure of the greatest common factor between them all, we can reduce by a common factor and then reduce again.
Now divide each number by 5 and see what we get.
350/5: 225/5: 125/5
70: 45: 25
When we divide each one by 5 again, we can see that each number again ends in 5 or 0 which means that 5 is still a factor of each number.
Now divide each number by 5 again and get a final ratio of 14: 9: 5.
70/5: 45/5: 25/5
14: 9: 5
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# Morgan is making two cookie recipes. Recipe A calls for one-third less than twice the number of cups
of sugar that Recipe B calls for. If she needs four and one-sixths cups of sugar in all, how many cups will she need for Recipe A?
Answer: 2 2/3
Step-by-step explanation:
Brittany practices hitting softballs for 2/3 of an hour each day for three days.For how many hours does she practice hitting softballs?
Step-by-step explanation:
2/3 hours every day for 3 days.
so, for the total hours we need to multiply 2/3 by 3 (3 times 2/3 hours) :
3 × 2/3 = 2 hours
you can get there directly by saying that the factor of 3 and the denominator of 3 are canceling each other out. what is left is 2 in the numerator.
or you can do the full calculation and say
3 × 2/3 = 3×2/3 = 6/3 = 2
Two children take turns breaking up a rectangular chocolate bar 6 squares wide by 8 squares long. They may break the bar only along the divisions between the squares. If the bar breaks into several pieces, they keep breaking the pieces up until only the individual squares remain. The player who cannot make a break loses the game. Who will win
The player who goes first will win.
This is because the chocolate bar can be broken up into 6*8=48 squares, and the player who goes first can always ensure that the second player is left with one square on their turn (by breaking the bar into two pieces that leave one square for the second player to take). This means that the second player will always be the one who cannot make a break, and thus loses the game.
Therefore, The player who goes first will win.
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What is the 3 example of quadratic equation?
The three examples of quadratic equations are x(x - 2) = 4, x(2x + 3) = 12 and 3x(x + 8) = -2
The term quadratic equation also known as quadratic expression referred as an equation containing one term in which the unknown is squared and no term in which it is raised to a power higher than 2.
Here the examples of quadratic equations in other forms is written as follows:
=> x(x - 2) = 4
Here we have to multiply and then moving the 4, then we get the quadratic expression as,
=> x² - 2x - 4 = 0
Another example like the following,
=> x(2x + 3) = 12
Here we have to multiplying and moving the 12, then we get the resulting expression as,
=> 2x² - 3x - 12 = 0
Final example for quadratic expression is written as
=> 3x(x + 8) = -2
When we multiplying and moving the -2, then we get the simplified form as
=> 3x² + 24x + 2 = 0
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Complete the following function table for the linear equation y=4x-1
First we can find value of x and. When x=0 then y=-1 and x=1 then y= 3
What is linear equation explain?A linear equation is an algebraic equation of the form y=mx+b involving only a constant and a first-order (linear) term where m is the slope and b is the y-intercept.So the above given equation is called a "linear equation of two variables," where y and x are the variables.
How do you find the value of Y?Finding the y value is easy if you know the slope of the line and the x coordinate. Review the equation for the slope of a line. The equation for finding the slope is: m = [y1 - y2] / [x1 - x2]. If you know x, you can solve for y to find the y value for the slope of the line.
Now we have y= 4x-1
lets x=0 then y= -1
x=1 then y=3
x=2 then y=7
To find slope
y=mx+c
y= 4x-1
so by comparing we can find m=4
Then we can evaluate given equation y=4x-1
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Acellus Geometry Question in picture