The equation of line is y=-9x-69.
To solve this problem we need to know the concept of slope of line and equation of straight line.
Writing the standard form of line is in the form of y= mx+ c where m is the slope of line.
And we also know that the product of slope of a line perpendicular to the line is equal to -1.
Let us assume that the slope of required line is m'
So, m' × 9 = -1
⇒ m'= -9
Now, the equation of line will be;
[tex](y-3)=-9(x+8)[/tex]
⇒ y-3=-9x-72
⇒ y=-9x-69 is the standard equation of line perpendicular to the given line y=9x-8.
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Use this information to find the value of b
c = 25
s = 9
b = 4c - s2
Answer:
Step-by-step explanation:
b=4c-s2
4(25)-9(2)
100-18=82
b=82
Find a cofunction equivalent to sin
5π
12
Cofunction equivalent to [tex]$\sin (5 \pi / 12)=\cos (1 \pi / 12)$[/tex].
You use the formula for the sine of a sum:
[tex]$$\sin (a+b)=\sin a \cos b+\cos a \sin b$$[/tex]
Think of a pie divided into twelve slices. Three of them form one quarter, two more form one sixth of the pie. So, thinking of the "pie" as [tex]$\pi$[/tex]:
[tex]\frac{5 \pi}{12}=\frac{\pi}{4}+\frac{\pi}{6}[/tex]
With that in mind, put [tex]$a=\frac{\pi}{4}, b=\frac{\pi}{6}$[/tex] into the sine formula given above:
[tex]$$\sin \left(\frac{5 \pi}{12}\right)=\sin \left(\frac{\pi}{4}\right) \cos \left(\frac{\pi}{6}\right)+\cos \left(\frac{\pi}{4}\right) \sin \left(\frac{\pi}{6}\right)$$[/tex]
Plug in the familiar values [tex]$\sin \left(\frac{\pi}{4}\right)=\cos \left(\frac{\pi}{4}\right)=\frac{\sqrt{2}}{2}, \cos \left(\frac{\pi}{6}\right)=\frac{\sqrt{3}}{2}$[/tex], [tex]$\sin \left(\frac{\pi}{6}\right)=\frac{1}{2}$[/tex], and you get the answer given above. And, yes, putting that expression into a calculator gives [tex]$0.9659$[/tex] (four significant digits).
The cofunction of an angle θ is the trigonometric complement of an angle. It shows the relationship between trignometric functions:
List the cofunction formula for [tex]$\sin$[/tex]
[tex]$$\sin (\theta)=\cos (\pi / 2-\theta)$$[/tex]
Plug in [tex]$\theta=5 \pi / 12$[/tex] for our cofunction formula:
[tex]$$\sin (5 \pi / 12)=\cos (\pi / 2-5 \pi / 12)$$[/tex]
Determine common denominator in radians
We use a common denominator of [tex]$(12 \div 2)=6$[/tex]
[tex]$\sin (5 \pi / 12)=\cos (6 \pi / 12-(5 \pi / 12))$[/tex]
[tex]$\sin (5 \pi / 12)=\cos (1 \pi / 12)$[/tex]
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Identify the segment bisector of
__
XY
The segment bisector of line segment XY is line n.
The length of the line segment XY is 6 units.
How do you define the line segment?A line segment is a section of a line with two endpoints. A line segment, unlike a line, has a fixed length.
A line segment's length can be measured in metric units including such millimeters and centimeters, or in customary units such as feet or inches.A bisector is a line that separates a straight line or perhaps an angle into two equal parts. A segment's bisector always contains the segment's midpoint.As per the given diagram in the question.
It is clear that the line segment XY is being divided by another line named n.
Thus,
The two segment of the line segment XY must be equal.
XM = MY
Substitute the values from the diagram;
5x + 8 = 9x + 12
Simplifying;
4x = -4
x = -1
Put the values in each segment;
XM = 5x + 8
XM = 5(-1) + 8
XM = 3 units.
Put the value in MY
MY = 9x + 12
MY = 9(-1) + 12
MY = 3 units.
As, it is clear from above values that the both segment are equal of 3 units each.
XY = XM + MY
XY = 3 + 3 = 6
Therefore, the value of XY is 6 units.
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Solve for x on the triangle
The value of x in given diagram is x=3;
The entire area filled by a triangle's three sides on a two-dimensional plane is referred to as the triangle's area. The fundamental equation for a triangle's area is A = 1/2 b h, where b and h are the product of the triangle's base and height. All triangle shapes, including scalene, isosceles, and equilateral triangles, may be calculated using this formula. It is important to keep in mind that a triangle's base and height are perpendicular to one another.
Area of triangle SXY = 1/2 × SX × (x-2);
Area of triangle STR = 1/2 × ST × (x+3);
Area of trapezium XTRY = 1/2 × (x+3+x-2) × XT;
Area of triangle SXY = Area of triangle STR - Area of trapezium XTRY;
SX × (x-2) = ST × (x+3) - (2x + 1) × XT;
As; SX = TX = ST/2;
(x-2)/2 = (x+3) - (2x+1)/2;
x - 2 = 2x + 6 -2x -1
x = 3;
A triangle is a closed figure that has three vertices, three sides, and three angles. It is one of the most fundamental geometric forms, and it is represented by the symbol△. Triangles in mathematics can be categorized according to their sides and angles into many categories.
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9×8 no using cocalator
Answer:
9x8=72
Step-by-step explanation:
I didn't use a calculator I memorized it?
Foundational Concepts Unit Test
22. What is the simplified form of the following expression? (1 point)
11[(92-52)+2248]
0224.5
0242
051.3
0110
The simplified form of the following expression is 51.3.
Given,
11(9²-5²)/(2²+8)
= 11(81-25)/(4+8)
= 11(56)/(12)
= 51.3
Expressions are simplified when they are rewritten in a concise manner and without any similar phrases. When simplifying an expression, we combine all similar terms and, if necessary, solve all of the supplied brackets, leaving just the, unlike words that cannot be further reduced.
Combining like terms together and leaving unlike terms alone is the fundamental principle for simplifying phrases. The following is a list of some of the guidelines for simplifying expressions:
Add the coefficients of two or more similar terms together, then include the common variable in the equation.
In the phrase a (b + c) = ab + ac, open the brackets using the distributive property.
Change the sign of all the phrases placed inside that bracket if there is a negative sign right outside the parenthesis to make things simpler.
Simply remove the bracket and put the words as they are, keeping the terms' original signs if there is a "plus" or other positive sign outside of it.
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Amy printed a square picture that was 225% the size of the original picture. The length of the side of her original picture was 4 inches. What is the length of the side of Amy’s printed picture
The length of the side of Amy’s printed picture is 6 inches.
What is defined as a square?A square is a two-dimensional closed shape with four equal sides.
A square is made up of four sides and four vertices.A square's sides are all the same length.All interior angles are identical and correct.The total of all interior angles is 360°.Now, as per the given question;
The original length of the side of the square was 4 inches.
Thus, the area of the old photo was;
A = side²
A = 4²
A = 16 square inch.
Now, as the picture is increased by 225%.
Then, increase the area by 225%.
New area = 225% of old area
= (16×225)/100
New area = 36
The length of the side of the new photograph is;
New area = length²
length = √New area
length = √36
length = 6 inches.
Therefore, the length of the side of Amy’s printed picture is 6 inches.
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A student's essay is 3 pages long. Page 1 contains M words. Page 2 contains 43 fewer words than page 1. Page 3 contains one-third as many
words as page 1.
Which expression represents the number of words on all three pages?
OM+(M-43) - M
O 3M+ (M-43) + M
O 3M+ (M+43) + M
OM+ (M-43) + M
OM-(M +43) + M
3m+(m-43)+m
3m=page 3
m-43=page 2
m=page 1
An airplane is flying at a speed of 300 mi/h at an altitude of one mile. The plane passes directly above a radar station at time
t = 0.
The horizontal distance that the plane has flown can be represented as a function of t d(t) = 300t.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
It is given that:
An airplane is flying at a speed of 300 mi/h at an altitude of one mile.
As we know,
From the relation between time-distance-speed
distance = time×speed
Speed = 300 mi/h
let distance be d and time be t
d = 300t
We can write the above equation as:
The horizontal distance that the plane has flown:
d(t) = 300t
Thus, the horizontal distance that the plane has flown can be represented as a function of t d(t) = 300t.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
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y = ²√x - 3
X
-10
-4
-2
4
y
Answer:
di mo po alam yan
oh di po kayo makain tindi tagalog
What’s the length of AZ. If A is between Y and Z, Y A = 22, AZ = 16x, and Y Z = 166
A) 9
B) 22
C) 144
D)188
Answer:
c) 144
Step-by-step explanation:
Since A is between Y and Z,
[tex]YZ = YA + AZ[/tex]
[tex]116 = 22 + 16x\\16x = 116 - 22\\16x = 144\\x = 9[/tex]
however, the question asks for [tex]the length of AZ[/tex], not the value of x.
Thus,
[tex]AZ = 16x[/tex]
[tex]AZ = 16\\[/tex] × [tex]9[/tex]
[tex]AZ = 144[/tex]
26. Julie says that sin A/cos A = tan A and sin B / cos B = tan B. Use the triangle shown to prove
Julie's statements true or false. Make sure you enter your work
-confused as to what this even means.
Julie is correct because:
[tex]\frac{\sin A}{\tan A}=\frac{a/c}{b/c}=a/b=\tan A \\ \\ \frac{\sin B}{\cos B}=\frac{b/c}{a/c}=b/a =\tan B[/tex]
PLEASE ANSWERING THIS QUESTION!!!
Riley drove home from college traveling an average speed of 65.1 mph and drove back to the college the following week at an average speed of 69.6 mph. If the total round trip took 12 hours, how much time did it take Riley to drive from home back to college? Express the time in hours and minutes. Round to the nearest minute.
(Blank) hours (Blank) minutes
Rules answering these questions:
Explain your answer!
Do not spam answers!
Show your work!
Nonsense answers will be reported and delete your answers.
Thanks!
Answer:
5 hours and 48 minutes
Step-by-step explanation:
The equation for finding average speed is: [tex]\frac{\text{Total Distance}}{\text{Total Time}}[/tex]
Let x represent the distance for both the journey from Riley's college to home and back. We can use one variable to represent this because both distances are the same.
We also know that the total round trip took 12 hours. Let y represent the time it took for Riley to drive from college to home. Therefore the time it takes for Riley to drive from home to college is 12 - y.
Using this information, we can set up a system of equations.
Setting up a System of Equations[tex]65.1=\frac{x}{y}\\\\69.6=\frac{x}{12-y}[/tex]
Multiply both sides of the first equation by "y" and both sides of the second equation by "12 - y".
[tex]65.1y=x\\\\835.2-69.6y=x[/tex]
Since both 65.1y and 835.2-69.6y are equivalent to x, we can set them equal to each other.
[tex]65.1y=835.2-69.6y[/tex]
Now, we have to solve the equation for time or "y".
Solving for Time[tex]65.1y=835.2-69.6y[/tex]
Add 69.6y to both sides
[tex]65.1y+69.6y=835.2[/tex]
[tex]134.7y=835.2[/tex]
Divide both sides by 134.7
[tex]y\approx6.2 $ hours = Six hours Twelve Minutes[/tex]
This is the time it took for Riley to drive from college to home, therefore the time it took for Riley to drive from home back to college is:
[tex]12-6.2=5.8=5$ hours and 48 minutes[/tex]
5 hours and 48 minutes
Please help I’m having trouble
Point K is between Points J and L. KL = 9x + 2, KJ = 5x 8 and JL= 12x. Find KL.
The length of KL is 35 units
How to determine the length KL?The given parameters are:
Point K is between Points J and L. KL = 9x + 2, KJ = 5x 8JL= 12x.The above means that
JL = JK + KL
So, we have
5x - 8 + 9x + 2 = 12x
Evaluate the like terms
2x = 6
Divide by 2
x = 3
Substitute x = 3 in KL = 9x + 2,
KL = 9 x 3 + 8
Evaluate
KL = 35
Hence, the length of KL is 35 units
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Identify the pair(s) of congruent angles in the figure. Explain how you know they are congruent.
by the Congruent Complements Theorem
$\angle NSP\cong\angle QSR$ by the Congruent Complements Theorem
$\angle MSP\cong\angle PSR$ by the Right Angles Congruence Theorem
$\angle MSP\cong\angle PSR$ by the Right Angles Congruence Theorem
$\angle MSN\cong\angle PSQ$ because they have the same measure
$\angle MSN\cong\angle PSQ$ because they have the same measure
$\angle MSN\cong\angle QSR$ by the Vertical Angles Congruence Theorem
$\angle MSN\cong\angle QSR$ by the Vertical Angles Congruence Theorem
$\angle NSP\cong\angle PSQ$ because they have the same measure
$\angle NSP\cong\angle PSQ$ because they have the same measure
$\angle NSQ\cong\angle MSP$ by the Right Angles Congruence Theorem
$\angle NSQ\cong\angle MSP$ by the Right Angles Congruence Theorem
$\angle NSQ\cong\angle PSR$ by the Right Angles Congruence Theorem
∠NSP ≅ ∠QSR, ∠MSP ≅ ∠PSR, ∠MSN ≅ ∠PSQ, ∠NSQ ≅ ∠MSP, ∠NSQ ≅ ∠PSR are the congruent angles.
∠NSP ≅ ∠QSR by the Congruent Complements Theorem. Because both are complementary to ∠PSQ.
∠MSP ≅ ∠PSR by the Right Angles Congruence Theorem. Because both ∠MSP = ∠PSR = 90°.
∠MSN ≅ ∠PSQ because they have the same measure. ∠MSN = ∠PSQ = 50°. Angles with same measure are congruent to each other.
∠NSQ ≅ ∠MSP by the Right Angles Congruence Theorem. Because ∠NSQ = ∠MSP = 90°.
∠NSQ ≅ ∠PSR by the Right Angles Congruence Theorem. Because ∠NSQ = ∠PSR = 90°.
Congruent Complements theorem states that if two angles are complementary (sum = 90°) to the same angle, then they are congruent.
Right Angles Theorem states that two right angles(90° angles) are congruent to each other.
Vertical Angles Congruence theorem states that two opposite angles formed between intersection of two lines are congruent. Here, ∠MSN is not congruent to ∠QSR because they are not vertical opposite angles.
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In the 2009-2010 school year in country A, there were 138,000 foreign students from country B. This number is % more than the number of students from country C. How many foreign students were from country C?
The number of students from country C using mathematical operations is 113,115.
What are the mathematical operations?The mathematical operations are addition, subtraction, multiplication, and division.
These mathematical operations are used to determine the output value, given some input values.
Data and Calculations:The number of foreign students from country B = 138,000
Students from country B are 22% more than the number of students from country C.
Assume that the number of students from country C = 100%
Then the number of students from country B = 122% (100 + 22)
If the number of foreign students from country B is 138,000, which is 22% more, then the number of students from country C is as follows:
The number of students from country C = 113,115 (138,000/1.22)
Thus, the number of students from country C using mathematical operations is 113,115.
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Question Completion:This number is 22% more than the number of students from country C.
help me i need to do this
Answer: 4.5
Step-by-step explanation:
To break even, we need the total profit to be equal to 0. If we make x dollars in 2012, then we need to solve
2.5 + 1.75 + (-3.3) + (-1.4) + x = 0
This gives us x = 0.45 in thousands.
Since the question asks us to give the answer in hundreds, we multiply by 10 and get 4.5. Thus the profit in 2012 must be 4.5 (in hundreds) to break even.
Find the domain and range of the relation. Also determine whether the relation is a function.
{(6,3), (8,5), (-4,-4), (5,5)}
The domain is:
D: {-4, 5, 6, 8}
The range is:
R: {-4, 3, 5}
And yes, the relation is a function.
How to determine the domain and range?
For a relation that maps elements x into elements y (in the form (x, y)), we define the domain as the set of the inputs (values of x) and the range as the set of the outputs (values of y).
Here our relation is defined by: {(6,3), (8,5), (-4,-4), (5,5)}
The domain is the set of the first values of each pair, so we have:
D: {-4, 5, 6, 8}
The range is the set of the second values of each pair:
R: {-4, 3, 5}
Now, is this a function?
Yes, it is a function, because each input is mapped into only one output.
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An athlete is throwing a javelin on an open field, and the image below shows the path, or arc of the javelin's
path, on its journey from his hand to the ground. The path is measured in feet. This example is modeled
by a quadratic function. What are the domain and range of the function, and what do they represent?
Total path coered by the javelin in horizontal direction is domain
Maximum height achieved by the javelin is its range
The polynomial equations of degree two in one variable of type f(x) = ax² + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f(x). The roots of the quadratic equation are the values of x that fulfill the equation (α,β ).
It is a given that the quadratic equation has two roots. Roots might have either a real or imaginary nature.
Total path coered by the javelin in horizontal direction is domain
Maximum height achieved by the javelin is its range
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the question is in the picture below
Answer: Answer 2, Triangle A is dilated from the origin by a scale of 1/2 to obtain triangle B
Step-by-step explanation:
11. Descartes
has $9. He works 5 hours
and earns $8 each hour. Write an
expression
to represent the situation
Answer: y = 8x + 9
Step-by-step explanation: Descartes begins with only $9.00, so 9 is the y-intercept. He makes $8.00 every hour, so that is the slope.
y = mx + b
m is the slope, and b is the y-intercept.
y=8x + 9
The expression that represents the given situation is y = $49.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now it isgiven that,
Descartes has Money = $9
Each hour earning = $8
Total time of work = 5 hours
So, total money earned in 5 hours = 8*5 = $40
Let y be the total money Descartes has.
So total money Descartes has = Money + total money earned in 5 hours
⇒ y = $9 + $40
⇒ y = $49
This is the required expression for the present situation.
Thus, The expression that represents the given situation is y = $49.
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Find the midpoint of the segment with the given endpoints.
(6,-6) and (1,2)
The midpoint of the line segment of the endpoints (6,-6) and (1,2) is given as:
(3½,-1)
What is the midpoint of a line segment in geometry?
The midpoint of a line segment is simply the centre point of a give segment that cuts or divides it into two congruent segments.
That is for example, if there are two points with coordinates (x1,y1) and (x2,y2), then their midpoint will be ; [(x1+x2)÷2,(y1+y2)÷2]
From the given question!
x1=6, x2=1 and y1=-6,y2=2
Thus, the midpoint is derived as;
[(6+1)÷2,(-6+2)÷2]
[(7)÷2,(-4)÷2]
(3½,-1).
compare the following numbers
2.7×1012;1.5×108
2.7×1012 (i.e.2,732.4) is greater than 1.5×108 (i.e. 162)
Given two numbers
1)2.7×1012
2) 1.5×108
Two numbers can be equal or one is greater than the other or one is less than the other. there will be no other case rather than these three.
1)2.7×1012=2,732.4
2) 1.5×108=162
The value of the 1st number is 2,732.4 and the value of the 2nd number is 162
1st given number is greater than the 2nd number i.e. 2,732.4>162
Therefore,2.7×1012 (i.e.2,732.4) is greater than 1.5×108 (i.e. 162)
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if a package of cupcake liners contain 75 liners how many liners are there in 13 package
∠1 and ∠2 form a linear pair. If m ∠1 is eight more than m ∠2 find the measures of both angles
A linear pair is formed of ∠1 and ∠2. The measures of the angle ∠1 is 20 and ∠2 is 160.
Given that,
A linear pair is formed of ∠1 and ∠2.
We have to find the measurements of both angles if m∠1 is eight more than m∠2.
When they refer to something as "linear," they mean that two angles create a straight line (or, 180 degrees). In other words, the two angles add up to 180.
Let us take the ∠1 as x
Then ∠2 will be 8x.
Now, we can write as
x+8x=180
9x=180
x=180/9
x=20
Therefore, the measures of the angle ∠1 is 20 and ∠2 is 8×20=160.
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You invested $27,000 in two accounts paying 4% and 7% annual interest, respectively. If the total interest earned for the year was $1440 how much was invested at each rate?
a = amount invested at 4%.
b = amount invested at 7%.
we know that whatever "a" and "b" may be, they total 27000, so we can say that a + b = 27000, likewise we can say that b = 27000 - a.
how much will it be for 4% of "a"? well, that's just (4/100) * a, or 0.04a.
how much will it be for 7% of "b"? well, that's just (7/100) * a, or 0.07b.
we also know that the earned interest by those two interest amounts is 1440, so
[tex]\begin{cases} a + b = 27000\\ b = 27000 - a \end{cases}\hspace{5em}0.04a~~ + ~~0.07b~~ = ~~1440 \\\\\\ \stackrel{\textit{substituting "b"}}{0.04a~~ + ~~0.07(27000-a)~~ = ~~1440}\implies 0.04a+1890-0.07a=1440 \\\\\\ 1890-0.03a=1440\implies -0.03a=-450\implies a=\cfrac{-450}{-0.03} \\\\\\ 15000=\textit{\LARGE a}\hspace{15em}\stackrel{27000~~ - ~~15000}{\textit{\LARGE b}=12000}[/tex]
A parallelogram has an area of 7 square units. If the height that corresponds to a base is 1/4 unit, what is the base?
Answer: 28 units
Step-by-step explanation:
A=area of parallelogram. h=height. b=base
A=h*b
7=1/4 *b
(7=1/4 *b)*4 ==>Multiply both sides by 4 to get rid of fractions
28=b
b=28 units
Janayea wanted to change 0.079 to a percent. She changed it to 79%. Which statement is true?
A) Janayea Is Correct?
B) Janayea should have moved the decimal point 0.079 two places to the left to get 0.00079%.
C) Janayea should have moved the decimal point of 0.079 two places to the right to get 7.9%.
Answer:
Janayea should have moved the decimal point 0.079 two places to the left to get 0.00079%.
Which table had a constant of proportionality between y and x of 1/6
Answer: Table which had a constant of proportionality between y and x of 1/6
is table C
Step-by-step explanation:
The meaning of constant proportionality is very simple and that is
ratio of y and x
here
y/x=1/6;
therefore we have to check various options
checking option C
first part:
3/18=1/6;
second part:
(9/2)/27=1/6;(convert mixed fraction into improper fraction)
third part:
(11/2)/33=1/6;
hence ;
Table which had a constant of proportionality between y and x of 1/6
is table C
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