The value of the trigonometric relation cos ∠O = 0.849
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔPQR
Now , the measure of ∠PQR = 90° and it is a right triangle
The measure of the hypotenuse PO = 53
The measure of adjacent side OQ = 45
The measure of opposite side QP = 28
Now , from the trigonometric relations ,
cos θ = adjacent / hypotenuse
cos θ = OQ / PO
Substituting the values in the equation , we get
cos θ = 45 / 53
cos θ = 0.849
Therefore , the value of cos ∠O is 0.849
Hence , the trigonometric relation cos θ = 0.849
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Work out 135% of 160
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{135\% of 160}}{\left( \cfrac{135}{100} \right)160}\implies \text{\LARGE 216}[/tex]
Does the set of even integers have the density property? Explain.
Answer:
No
Step-by-step explanation:
You want to know if the set of even integers has the density property.
Density propertyThe density property states that for any two elements of a set, there are additional elements of the set between them.
There are no even integers between any two consecutive even integers, so the set of even integers does not have the density property.
Use the graph at the right. Find the vertices of the image of QRTW for a dilation with center (0,0) and a scale factor of 5.
With dilation at center (0,0) and a scale factor of 5, the coordinates as we can see from given graph are Q(-3,4), R(-2,-1), T(3,1), W(3,5).
What exactly is dilation?
Dilation is the process of modifying the size of an item or form by reducing or expanding its dimensions according to specific scaling variables. A circle of radius 10 unit, for example, is reduced to a circle with radius 5 unit. This approach is utilised in photography, arts and crafts, and the creation of logos, among other things. There are four primary types of transformations in geometry. They are as follows:
RotationTranslationReflectionDilation or ResizingDilation Properties
Some characteristics of forms that stay constant during dilation changes are:
The figure's angles are all the same.The midpoints of the figure's sides stay the same as the midpoint of the dilated form.The figure's parallel and perpendicular lines stay the same as the dilated figure's parallel and perpendicular lines.The visuals stay unchanged.Now,
As we can see from properties that the image does not change in dilation it stays same and angles are also same.
So, we can see coordinates from the given graph
hence,
the coordinates as we can see from given graph are Q(-3,4), R(-2,-1), T(3,1), W(3,5).
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Using the F’(x) Graph shown, find the Integral from 0 to 1 F’(x)dx if f(5) = -7.8, and f(0) = 3.
Answer:
[tex]-22.8[/tex]
Step-by-step explanation:
[tex]\int^{1}_{0} f'(x) \text{ } dx=f(1)-f(0)=f(1)-3 \\ \\ \\ B=\int^{5}_{1} f'(x) \text{ } dx=12 \implies f(5)-f(1)=12 \\ \\ -7.8-f(1)=12 \implies f(1)=-19.8 \\ \\ \therefore f(1)-3=-19.8-3=-22.8[/tex]
If the water evaporates at the rate in a, for 12 hours, how many inches will evaporate?
On solving the provided question, we cans ay that inches will evaporate, the equation will be = 12x = 1/2y + 7.43
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
he water evaporates at the rate in a, for 12 hours.
inches will evaporate,
the equation will be = 12x = 1/2y + 7.43
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(x
Consider a sequence of transformations where
ALMN is translated (x, y) - (x - 3, y + 4),
reflected across the y-axis, and then reflected
across the x-axis.
Predict the effect of the second transformation.
The transformation of the triangle is the orientation changes and moves the triangle into Quadrant III
What is Reflection?Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.
The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Given data ,
Let the transformation of the triangle be represented as A
Now , the initial coordinates are ( x , y )
And , on transformation , we get ( x , y ) - ( x - 3 , y + 4 )
Now , the triangle is reflected across the y-axis
So , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
And , its orientation has changed and it is now in Quadrant III.
Hence , the triangle is now in Quadrant III
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Select the correct answer. Newspaper Advertisement on Front Page ABC 89. 4% JKL 86. 3% PQR 80. 5% TUV 88. 7% XYZ 89. 1% Total 82. 4% The probabilities of different newspapers having an advertisement on the front page are given in the table. What is the chance of seeing an advertisement on the front page if the newspaper is JKL? A. 82. 4% B. 86. 3% C. 88. 7% D. Insufficient data
The chance of seeing an advertisement on the front page if the newspaper is JKL is 86.3%.
Probabilities:
In science, the probability of an event is a number representing the probability that an event will occur. It is expressed as a number ranging from 0 to 1, or as a number ranging from 0% to 100% using percentage display. The more likely an event is to happen, the more likely it is to happen. The probability of an impossible event is zero. The probability of an event that must happen is 1. The probabilities of two complementary events A and B (A or B) add up to 1.
A simple example is a fair (unbiased) coin toss. When the coin is fair, the two possible outcomes (heads and tails) are equally likely. Since the two outcomes are complementary and the probability of heads is equal to the probability of tails, the probability of each of the two outcomes is 1/2.
Therefore,
After looking at the table, the percentage that represents JKL and a front page advertisement is 86.3%.
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I need to find the value of x and it's a horizontal line or whatever the cross over like a x (3x-3)°147°
Simplify (6x-15)/(4x^2-25)
Help ASAP................................
Answer:
Step-by-step explanation:
Top problem:
A = πr² = (22/7)(21)² = 1386 ft²
Bottom problem:
r = D/2 = 20/2 = 10 in
A = (22/7)(10)² = 314 in²
a) Hassan deposits $325 into an account that pays 4.7% annual interest compounded monthly. Write an equation to represent Hassanʼs account balance A after t years.
b) Use a system of equations to determine how many years it will take for the account reach $200. Round to the nearest year.
The equation will be written as [tex]A = 325[1.004]^{12t}[/tex]. The time taken to reach $200 will be 10 years.
What is compound interest?Compound interest is defined as the interest levied upon the interest. The formula to calculate the compound interest will be written as:-
[tex]A = P[1+\dfrac{r}{m}]^{rt}[/tex]
Given that Hassan places $325 into a savings account that offers a monthly compound interest rate of 4.7%.
The equation for the compounding on monthly basis,
[tex]A = 325[1+\dfrac{0.047}{12}]^{12t}[/tex]
[tex]A = 325[1.004]^{12t}[/tex]
The time will be calculated as:-
[tex]A = 325[1.004]^{12t}[/tex]
[tex]200 = 325[ 1.004]^{12t}[/tex]
log(0.615) = 12 x t x log(1.004)
12t = 121.77
t = 10 years
Therefore, the equation will appear as [tex]A = 325[1.004]^{12t}[/tex]. It will take 10 years for the price to reach $200.
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jayden measured a pen to be 20 cm long the actual length of the pen is 20.8
The percent error in a measure is given by the formula:
P = 100%*|real value - measure|/real value
Here we know that:
real value = 20.8 cm
measure = 20cm
Replacing that in the formula we will get:
P = 100%*|20.8 cm - 20cm|/20.8cm = 3.8%
That is the percent error.
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Complete question:
Jayden measured a pen to be 20 cm long the actual length of the pen is 20.8 cm, then what is the percentage error?.
f(x) = -x² + 5 and g(x) = -2x+2, find all values of x for which f(x) = g(x).
Answer:
The values of x for which f(x) = g(x) are:
x = -1x = 3Step-by-step explanation:
To find all the values of x for which f(x) = g(x), equate the given functions:
[tex]\implies f(x)=g(x)[/tex]
[tex]\implies -x^2+5=-2x+2[/tex]
Rearrange the equation so that it is in the quadratic form ax²+bx+c=0:
[tex]\implies -x^2+5+2x-2=0[/tex]
[tex]\implies -x^2+2x+3=0[/tex]
Divide both sides by -1:
[tex]\implies x^2-2x-3=0[/tex]
Factor the quadratic equation:
[tex]\implies x^2-3x+x-3=0[/tex]
[tex]\implies x(x-3)+1(x-3)=0[/tex]
[tex]\implies (x+1)(x-3)=0[/tex]
To solve for x, apply the zero-product property:
[tex](x+1)=0 \implies x=-1[/tex]
[tex](x-3)=0 \implies x=3[/tex]
Therefore, the values of x for which f(x) = g(x) are:
x = -1x = 3We can check the solutions by substituting each found value of x into the functions.
[tex]f(-1)=-(-1)^2+5=4[/tex]
[tex]g(-1)=-2(-1)+2=4[/tex]
[tex]f(3)=-(3)^2+5=-4[/tex]
[tex]g(3)=-2(3)+2=-4[/tex]
As f(-1) = g(-1) and f(3) = g(3), this proves that the values of x for which f(x) = g(x) are x = -1 or x = 3.
Equate Both equatios and find x
f(x)=g(x)-x²+5=-2x+2x²-5=2x-2x²-2x-3=0(x+1)(x-3)=0The points are -1,3
whay are mixed fractions
Answer:
hope this helps!! <3
Step-by-step explanation:
A fraction is represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
Sloan is going to make a berry salad for a party.
Her salad will include only blueberries, raspberries, and strawberries. She wants the ratio of blueberries to strawberries to be 2:5, and the ratio of blueberries to all berries to be 4:23. How many of each type of berry can she put in the salad?
The number of each type of berry that she can put in her salad would include the following:
Blueberry = 4
Blueberry = 4Strawberry = 10
Blueberry = 4Strawberry = 10Raspberry = 13
How to calculate the quantity of berries in the salad?The salad that was prepared by Sloan contains the following berries:
Ratio of Blueberry to strawberries = 2:5
The ratio of blueberry and others = 4:23
Therefore,
Since every 2 blueberry = 5 strawberry, 4 blueberry = 10 strawberry.
The quantity of raspberry = 23-10 = 13
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Kenji is deep-sea diving with two friends. Ezra is exploring a coral reef 12 meters in front of Kenji, and Tori is floating on the surface directly above Kenji. If Tori and Ezra are 20 meters apart, how far apart are Kenji and Tori?
Answer:
Step-by-step explanation:
We know that the hypotenuse is 20m and one leg is 12m.
Pythagorean Theorem= a^2 + b^2 = c^2
12^2 + b^2 = 20^20
144 + b^2 = 400
b^2 = 256
Square root of 256 = 16
Kenji and Tori are 16 meters away from each other.
PLEASE HURRY!! Which of the following statements are true regarding the graph of this linear function? Select all that apply.
By making linear equation for given graph, slope of line will be 9.75 which is the amount she makes in an hour i.e. E.
What exactly is a linear equation?
The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.
Now,
As given she has a debt of $25 that will be y-intercept.
and as we can see from graph she earns $39 in 4 hours that means $9.75 in an hour which will be slope of line also, then the line will be represented as
y=9.75x-25 where x=hours worked and y=amount earned
hence,
slope of line will be 9.75 which is the amount she makes in an hour.
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The area of the trapezoid is 36 ft².
Find the height of the trapezoid.
4 ft
8 ft
Answer:
6ft
Step-by-step explanation:
area of trapezoid formula: 1/2h(a+b)
height=x
x/2(4+8)=36
x/2*12=36
2 and 12 will get cancelled
6x=36
x=36/6
x=6
hope it helped!!!
convert 1hour 38 min 14 second to seconds
Answer:
5894 seconds
Step-by-step explanation:
Convert 1 hour 38 min 14 seconds to seconds
1 hour = 3600 seconds
1 min = 60 seconds
38 mins = 60 x 38 = 2280 seconds
Now add all numbers together
3600 + 2280 + 14 = 5894 seconds
So, 1 hour 38 minutes 14 seconds is 5894 seconds.
-2/5(15-5) is equivalent to what value?
PLEASE HELP 50POINTS!!!!!
Can you always use synthetic division for dividing polynomials?
Yes, we can use always the synthetic division for dividing polynomials since it is the easiest way in order to get the quotients of two polynomials.
Dividing Polynomials:We use the division of polynomials to find the quotients of two polynomials. Two polynomials can be divided by simply multiplying and dividing by the largest power in each term.
The two different ways to divide polynomials are 1. Long division method and 2. The synthetic division method. The synthetic division method is the quickest way to divide polynomials between these two approaches.
Advantages of performing a Synthetic Division:
Only if the divisor is a linear factor can we use the synthetic division approach. In contrast to the long division method, which uses division and subtraction, the synthetic division approach uses multiplication and addition. There are just a few calculations needed. There is no need for variables to do the calculation.This method is less prone to errors than the polynomial long division method.
Therefore,
We can say
Yes, we can use always the synthetic division for dividing polynomials since it is the easiest way in order to get the quotients of two polynomials.
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What percent of Jemma's answers did she get incorrect?
If Jemma got 2 out of 20 questions wrong on her most recent math quiz, then the incorrect percent is 10% .
Total number of questions in the Math's quiz is = 20 ;
Number of incorrect questions done by Jemma is = 2 ;
Number of correct questions done by Jemma are = 18 ;
So , to find the percentage she got incorrect, we divide ; (number of incorrect answers) by (total number of questions) and then multiply by 100 ;
that means ⇒ (2/20) × 100 = 10% ;
Therefore, Jemma got 10% of the questions incorrect on her most recent math quiz.
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The given question is incomplete , the complete question is
If Jemma got 2 out of 20 questions wrong on her most recent math quiz, what percent did she get incorrect ?
can rectangle corner perpendicular diagonal lines of the rectangle?
if so can you draw a picture
Answer:
yes
Step-by-step explanation:
Hey! I need help with these 2 questions! Thanks.
8. The depth of the water is solved to be = 2.9 cm (one decimal place).
9 The ratio r: s =√3 : 2.
How to find the depth of the waterThe depth of water is calculated by first using Pythagoras theorem to get the level between water level 7 cm and water level when completely full which is 10 cm
= √(10² - 7²)
= √(100 - 49)
= √51
The next step is to subtract from the radius
= 10 - √51
= 2.8586 cm
= 2.9 cm
9. The length of diagonal of a cube is given by the formula
= (√3)·s
The diameter of the sphere is equal to length of diagonal of a cube.
radius of a sphere = diameter / 2
r = (√3)*s / 2
r / s = √3 / 2
hence the ratio is
r : s = √3 : 2
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complete question is attached
Which is the graph of f(x) = 100(0.772)
It is not possible to graph f(x) = 100(0.772) without additional information. A function needs at least two points to graph a line. The expression f(x) = 100(0.772) represents a constant value, not a function of x, so it cannot be graphed on its own.
Answer: knvsvvs
Step-by-step explanation:
There were 10 games work out the mean number of goals per game
Answer:
Step-by-step explanation:
Add all the number of goals and then divide by 10.
solve for x -8= x+27/-6
Answer:
x=-7/2 (exact form)
x=-3.5 (decimal form)
x=-3 1/2 (mixed number form)
Step-by-step explanation: :)
Jack bought 5 pounds5 pounds5, start text, space, p, o, u, n, d, s, end text of Halloween candy. He gave out 3 pounds3 pounds3, start text, space, p, o, u, n, d, s, end text of the candy to trick or treaters and ate 10 ounces10 ounces10, start text, space, o, u, n, c, e, s, end text of the candy.
Number of candies that will be left with Jack is 1.375 pounds if the total candies were 5 pounds.
What is Subtraction?Subtraction can be done for any numbers or algebraic expressions.
It is the process of taking out certain value from a given amount of number.
The process of subtraction can also be called as finding the difference.
Given that,
Total candies that Jack bought = 5 pounds
Candies given to trick or treaters = 3 pounds
Candies left = 5 - 3 = 2 pounds
Amount of candies ate = 10 ounces
16 ounces = 1 pound
10 ounce = 10 / 16 pounds = 0.625 pounds
Amount of candies ate in pounds = 0.625 pounds
Candies left = 2 - 0.625 = 1.375 pounds
Hence the amount of candies left is 1.375 pounds.
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Your question is incomplete. The complete question is given below.
Jack bought 5 pounds of Halloween candy. He gave out 3 pounds of the candy to trick or treaters and ate 10 ounces of the candy. How many ounces of Halloween candy does jack have?
Write the quadratic equation whose roots are 3 and -3 and whose leading coefficient is 1 (use the letter x to represent the variables)
The quadratic equation whose roots are 3 and -3 is x² - 9 = 0.
What is the quadratic equation whose roots are 3 and -3 and whose leading coefficient is 1?Given the roots of the quadratic equation;
x = 3 and x = -3
The two real distinct solutions for the quadratic equation are x = 3 and x = -3.
Which means x - 3 and x + 3 are the factors of the equation.
Hence;
( x - 3 )( x + 3 ) = 0
Now, expand using FOIL method
x( x + 3 ) - 3( x + 3 ) = 0
x² + 3x - 3x - 9 = 0
x² - 9 = 0
Therefore, the equation is x² - 9 = 0.
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Identify the range of the function shown in the graph.
Range of the function shown by the graph is (-∞ , ∞)
What is range?Range is a statistical measurement of dispersion, or how much a given data set is stretched out from smallest to largest.
The range is the set of possible output values, which are shown on the
y -axis.
Given,
Graph of a function,
Range represents the y-coordinate of the function.
By the graph,
Range of the function is -∞ < y < ∞.
In interval notation,
Range = (-∞ , ∞)
Hence, (-∞ , ∞) is the range of the function shown by the graph.
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