[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{8}}} \implies \cfrac{-4 +4}{-6} \implies \cfrac{ 0 }{ -6 } \implies \text{\LARGE 0}[/tex]
Find values of a and b that make the following equality into identity:
(2x+5)/(x-8)(2x+1)=a/(x-8) + b/(2x+1)
Giving 30+ points!
The values of a and b in the fraction are 21/17 and -8/17
How to determine the values of a and bFrom the question, we have the following parameters that can be used in our computation:
(2x+5)/(x-8)(2x+1)=a/(x-8) + b/(2x+1)
Take the LCM
So, the expression can be expressed as
(2x+5)/(x-8)(2x+1)=a(2x+1) + b(x-8)/(x-8)(2x+1)
Multiply both sides by (x-8)(2x+1)
(2x+5) = a(2x+1) + b(x-8)
Open the brackets
2x + 5 = 2ax + a + bx - 8b
By comparison, we have
2a + b = 2
a - 8b = 5
Make a, the subject in a - 8b = 5
a = 5 + 8b
Substitute a = 5 + 8b in 2a + b = 2
10 + 16b + b = 2
Evaluate the like terms
17b = -8
Divide by 17
b = -8/17
Substitute b = -8/17 in a = 5 + 8b
a = 5 + 8 * -8/17
Evaluate
a = 5 - 64/17
So, we have
a = 21/17
Hence, the values are 21/17 and -8/17
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What is the length of a leg of a 45 45 90 right triangle if the hypotenuse measures 5 square root of 2?
If the leg of the triangle is equal to a, then:
The second leg is also equal to a.
the given hypotenuse is a√2.
The given area is equal to a²/2; and
The perimeter equals a (2 + √2).
Now, looks easy, but from where does it come? There are various of methods to prove that equation, the most popular of them are:
By using the Pythagorean theorem, we can do that.
As you know one leg length a, then you know the length of the other as well, as both of them are equal.
The given 45 45 90 triangle shows the remaining parameters. Now you know that:
hypotenuse length is - 9 in * √2 = 12.73 in.
area is - 9 in * 9 in / 2 = 40.5 in²; and
perimeter - 9 in + 9 in + 9 in * √2 = 30.73 in.
Find the hypotenuse from the Pythagorean theorem:
a² + b² = c² => a² + a² = c² so c = √(2a²) = a√2
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Which statement is correct?
Answer:
B. ST and TK intersect at a 90 degree angle.
I know this because you can see that in between STK, there is a square in the corner indicating a 90 degree angle.
Step-by-step explanation:
Hope it helps! =D
can someone help me find two true statements!
1. In a triangle line parallel to one side will divides other two sides in the same ratio
2. 8/x = 12/18
x = 12
How do you find a linear equation from two points?Finding the slope between two points on a line and solving for the y-intercept in the slope-intercept equation y=mx+b allows us to formulate an equation for that line.
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).
Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.
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Look down below for the question
Answer:
1.centre
2.chord
3.chord
4.radius
5.diameter
BRAINLY ME PLEASE IF HELPFUL!!!
How to do plotting points?
Place a dot at the origin, sometimes referred to as the center of the Cartesian coordinate axis, to begin. We may then plot a point on the graph after placing the necessary points there.
An x-y (or bivariate) plot is any graph or plot with two axes.
The "x-axis" is often the horizontal axis, whereas the "y-axis" is typically the vertical axis.
However, if you have a data set with two sets of related data, you may utilize any variable for either one.
There are a few procedures you may take when plotting data on a graph to make sure you don't neglect anything:
Make sure you are working with two variables (two columns of data).
Make a decision on which variable will be represented on the x-axis and which on the y-axis.
Your plot's axes should be identified, and the scale should be chosen (if the graph is not already labeled).
Plot the first two pairs of numbers first (the top row of numbers).
Plot pairs of points repeatedly until all the points have been plotted.
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What does 5 mean in maths?
5 (five) is a number, numeral, and digit.
It is a prime number and the natural and cardinal number that comes after 4 and before 6. Because most people have five digits on each hand, it has gained significance throughout history.
5 is the second super-prime and third-smallest prime number. It is the first of three known Wilson primes, the first good prime, the first balanced prime, and the first safe prime. The number five is also the third Catalan number, the third Sophie Germain prime, the third exponent of the third Mersenne prime, and the second Fermat prime.
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Division of mixed numberrss
Answer:
1. 99/104
2. 4/3
3. 6/5
4. 52/25
5. 57/58
6. 33/100
7. 1/2
8. 8/5
9. 4
10. 4/3
hope this helps any
Can u please helppppppppp
Answer:
Draw a vertical line that goes through the point given. This will make the two lines perpendicular. The line given is horizontal, a vertical like would be 90° o the horizontal line.
Step-by-step explanation:
Click on the solution set graphic until the correct one is displayed.
Answer: I can't answer that because it's not a question
Step-by-step explanation:
F the altitude of a triangle meet at one of the triangles vertices then the triangle is
When the given altitude of the triangle meet at one of the vertices of the given triangle then it represents the option 1. right angled triangle.
As given in the question,
Given is the altitude of the triangle.
Given Condition is :
Altitude of the triangle meet at one of the vertices of the triangle.
⇒ This means altitude is representing the height of the triangle.
Height is always represented by perpendicular line.
⇒One of the side having altitude forms a angle of measure 90°.
⇒Given triangle is right angled triangle.
Therefore, when the altitude of the triangle meet at one of the vertices of the given triangles it represents the option 1. right angle triangle.
The above question is incomplete, the complete question is :
If the altitudes of a triangle meet at one of the triangle’s vertices, then the triangle is
1) a right triangle
2) an acute triangle
3) an obtuse triangle
4) an equilateral triangle
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26 °
100°
X=
help anyone ?
Answer:
Step-by-step explanation:
26° + 100°
= 126°
360° - 126°
234°
Write the standard equation of the circle.
Geometry b
The standard equation of the circle will be;
⇒ (x - 3)² + (y + 5)² = 16
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The circle is shown in figure.
Now,
Here, By the figure;
The radius of the circle = 7 - 3
= 4 units
And, The center of circle = (3, - 5)
We know that;
The standard equation of the circle is,
⇒ (x - h)² + (y - k)² = r²
Where, (h, k) = center and r is radius.
So, We get;
The standard equation of the circle is,
⇒ (x - 3)² + (y - (-5))² = 4²
⇒ (x - 3)² + (y + 5)² = 16
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Determine the vertical distance and the horizontal distance of point P and point Q. (a) P=4m Q=6m.
if you dog like something
Evaluate the expression (-243)1/5
[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ (-243)^{\frac{1}{5}}\implies \sqrt[5]{(-243)^1}\implies \sqrt[5]{(-3)(-3)(-3)(-3)(-3)} \\\\\\ \sqrt[5]{(-3)^5}\implies -3[/tex]
The ff. test scores were recorded by job applicants: 65, 68, 70, 75, 88, 90, 90, 91, 92. What is the mode
In the recorded test scores 90 is the mode, as it appears most frequently in the set of ff test scores.
What do you meant by mode?Job applicants submitted their ff test results, which were as follows: 65, 68, 70, 75, 88, 90, 90, 91, and 92. Following that, the Mean (Average) is 81, Median (Middle) is 88, and Mode (Most Common) is 90. The mode can be calculated quite easily.
After sorting the numbers in a set according to their order—lowest to highest or highest to lowest—count how many times each number appears in the group.
The mode is the one that is most prevalent. the quantity that happens the most frequently, or the quantity that appears the most frequently overall. The mode of the numbers 4, 2, 4, 3, 2, and 2 is 2, since it appears three times, more than any other number. The most frequent number in a set of numbers is called the mode.
To find the mode, we first need to put the test scores in order from lowest to highest:
65, 68, 70, 75, 88, 90, 90, 91, 92
Then we can count how many times each number appears:
65: 1 time
68: 1 time
70: 1 time
75: 1 time
88: 1 time
90: 2 times
91: 1 time
92: 1 time
As we can see, the number 90 appears the most with 2 times, so the mode of this set of data is 90.
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What is the frequency of the function f(x)? f(x)=3cos(πx)−2 Express the answer in fraction form
Answer:
1/2
Step-by-step explanation:
You want to know the frequency of the function f(x) = 3cos(πx) -2.
FrequencyFor frequency f, the basic function (before vertical scaling or translation) will be written ...
f(x) = cos(2πfx)
That is, we can find the frequency by comparing the arguments of the cosine function:
πx = 2πfx
f = (πx)/(2πx) = 1/2
The frequency of the function is 1/2.
__
Additional comment
You will notice in the attached graph that there is 1/2 period in 1 horizontal unit. A full period takes 2 horizontal units, so the frequency is ...
(1 period)/(2 units) = 1/2 periods/unit.
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A rescue boat just picked up some sailors in a lifeboat. Now the rescue boat is heading north at 14 miles per hour. The lifeboat, which they abandoned, is drifting south at a speed of 3 miles per hour. How long will it be before the rescued sailors are 57 miles from their lifeboat?
The time it will take for the rescued sailors to be 57 miles from their life boat is given as follows:
3.35 hours.
What is relative velocity?Relative velocity is obtained considering the direction in which the objects are traveling, as follows:
Opposite direction: the relative velocity is given by the sum of the velocities of each object.Same direction: the relative velocity is given by the subtraction of the velocities of each object.For this problem, the sailors and the lifeboat are traveling in opposite directions, hence the relative velocity, considering each of their velocities is given as follows:
v = 14 + 3 = 17 miles.
(meaning that they get 17 miles farther each hour).
Velocity is distance divided by time, hence the time it will take for them to be 57 miles apart is given as follows:
17 = 57/t
17t = 57
t = 57/17
t = 3.35 hours.
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The table below shows the number of animals at a local petting zoo.
Animal
Goats
Number
3
8:20 =
Ponies
3
Write the ratio of ponies to goats.
You may write the ratio in ANY of the three forms. Remember to REDUCE the ratio,
possible.
T
123 f() ∞*E ABC αβγ
Rabbits
8
21
7
8
O
1.
Sheep
6
a
DG
Answer: 1:1
Step-by-step explanation:
We will write a ratio of ponies to goats;
ponies : goats
3 : 3
Next, 3:3 can be simplified to 1:1. This gives us our fully reduced ratio.
Three runners are training for a marathon. One day, they all run about ten miles, each at their own constant speed. • The equation that relates Runner #2’s distance (in miles) with time (in minutes) is `t=8. 5d`. Find the slope/rate of ch
If the equation that relates the Runner 2’s distance (in miles) with time (in minutes) is [tex]t=8.5d[/tex] then the slope/rate of change of Runner 2 is 8.5 minutes for 1 mile .
The three runners are training for the marathon ,
The equation that relates the Runner 2’s distance (in miles) with time (in minutes) is ⇒ [tex]t=8.5d[/tex] ,
to cover the distance of 2 miles Runner2 will take [tex]t= 8.5 \times 2[/tex] minutes ;
So , [tex]t=17[/tex] minutes ;
the first point will be (2,17) .
and to cover the distance of 4 miles the runner 2 will take [tex]t= 8.5 \times 4[/tex]
So , [tex]t=34[/tex] minutes ;
the second point will be (4,34) .
we have to find the rate of change/slope of runner 2 ,
that can be written as : [tex]Slope = \frac{34-17}{4-2}[/tex]
On simplifying ,
we get ;
[tex]Slope = \frac{17}{2}[/tex] ;
So , [tex]Slope = 8.5[/tex].
Therefore , the rate of change of Runner 2 is 8.5 .
The given question is incomplete , the complete question is
Three runners are training for a marathon. One day, they all run about ten miles, each at their own constant speed. The equation that relates the Runner 2’s distance (in miles) with time (in minutes) is "t = 8.5d". Find the slope/rate of change of Runner 2 ?
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Erin combined 1 17/18 pounds of peanuts with 1 5/6 pounds of M&M's to create trail mix, then evenly distributed the mix in 8 bags. how many pounds of trail mix are in each bag?
There are 17/36 pounds of trail mix in each bag.
Finding out how much pounds of trail mix are in each bagTo find out how many pounds of trail mix are in each bag,you need to first add the weight of the peanuts and M&M's together.
1[tex]\frac{17}{18}[/tex] + 1 [tex]\frac{5}{6}[/tex] =([tex]\frac{35}{18}[/tex]) +([tex]\frac{11}{6}[/tex]) = [tex]\frac{35+33}{18}[/tex] =[tex]\frac{68}{18}[/tex]
which can be simplified to 3 [tex]\frac{14}{18}[/tex]
So there are 3 [tex]\frac{14}{18}[/tex]pounds of trail mix altogether.
To find out how many pounds of trail mix are in each bag, you will divide the total weight of the trail mix by the number of bags.3 [tex]\frac{14}{18}[/tex]÷ [tex]\frac{8}{1}[/tex] =
[tex]\frac{68}{18}[/tex] ÷ [tex]\frac{8}{1}[/tex]=[tex]\frac{68}{144}[/tex]
which can be simplified to [tex]\frac{17}{36}[/tex]
So there are [tex]\frac{17}{36}[/tex]pounds of trail mix in each bag.
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How do you calculate F G and G of f?
You will be calculate the function F(G) = f(g(x)) and G(F) = g(f(x)).
What is function ?
A function is a kind of rule that, for one input, it gives you one output. Image source: by Alex Federspiel. An example of this would be y=x2. If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.
Have given ,
Two functions , f(x) and g(x)
The composition of two functions g and f is the new function we get by performing f first, and then performing g. For example, if we let f be the function given by f(x) = x2 and let g be the function given by g(x) = x + 3, then the composition of g with f is called gf and is worked out as gf(x) = g(f(x)) .
So , You will be calculate the function F(G) = f(g(x)) and G(F) = g(f(x)).
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Lenny paid $13 for 4 1/3 pounds of apples.
How many pounds of apples can he buy
for $29?
Answer: 9 2/3
Step-by-step explanation:
you take 29 and divide by 13 to get 2.23076923077 and you then take that times the 4 1/3 to get 9 2/3
Answer:
Step-by-step explanation:
13(X-4 1/3)=29
13X-56.3=29
+56.3 = +56.3
13X=85.3
X=6.56
Find the 7th term of the geometric sequence whose common ratio is 3/2 and whose first term is 5
The 7th term of the geometric sequence is 3675/64.
A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant called the common ratio.
The 7th term of a geometric sequence can be found using the formula:
a_n = a_1 * (r)^(n-1) where a_1 is the first term of the sequence, r is the common ratio, and n is the position of the term in the sequence.
Given that the common ratio is 3/2 and the first term is 5, we can substitute these values into the formula:
a_7 = 5 * (3/2)^(7-1)
After solving the expression we get:
a_7 = 5 * (3/2)^6 = 5* (243/64) = 15*243/64 = 3675/64
So the 7th term of the geometric sequence is 3675/64.
Therefore, the 7th term of the geometric sequence is 3675/64.
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Determine the missing angle measure.
Answer:
38°
Step-by-step explanation:
We have supplementary angles, which mean they add up to 180°, so we can simply solve for x° by doing 180°-142°=38°
Answer:
X=38 degrees
Step-by-step explanation:
A straight line is 180 degrees so to find the missing part you can do 180-142.
That way you get the missing angle measurement.
50 POINTS!!!! urgent!!!!!!
Mary is collecting cup cakes for the school fair. She will make 12 cupcakes to start it off. She plans to collect 24 cupcakes each
day from her surrounding neighborhood for the next 3 days. If you model this word problem for Mary as y=mx+b then match the
corrects pairs.
a. 12
b. 84
c. 3
d. 24
1. m
2. y
3. x
4. b
Since the problem is about linear equation in the form of y = mx + b, initial number represents the value of b = 12, the number of days represents the value of x = 3, the daily collection of cupcakes represent the slope m = 24, then the value of y is:
y = 24*3 + 12 = 72 + 12 = 84So the matching pairs are:
a ⇔ 4, b ⇔ 2,c ⇔ 3,d ⇔ 1 .on the main floor of the Kodak halll at the easement they're the number of seats per row increase at a constant rate Steven counts 31 Seaton Rd. three and 37 Seaton Rd. six how many seats are there in a row 20
65 seats in 20th row.
What is direct proportion?Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. It is represented by the proportional symbol, ∝. In fact, the same symbol is used to represent inversely proportional, the matter of the fact that the other quantity is inverted here.
Given,
No. of seats in 3rd row = 31
No. of seats in 6th row = 37
Seats increase at a constant rate
Let k is the rate of increment.
Difference between no. of seats = k × difference between no. of rows
Difference of seats in 3rd and 6th rows = k difference between the no. of rows
37 - 31 = k ×(6-3)
6 = 3k
k = 2
Thus, we can determine
Difference between the no. of seats is twice the difference between the no. of rows.
Difference between 6th and 20th row = 14 rows
Hence the difference between number of seats = 2 × 14 = 28 seats.
No. of seats in 20th row = No. of seats in 6th row + 28 seats
No. of seats in 20th row = 37 + 28 = 65
Hence, there will be 65 seats in 20th row.
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Terms nd coefficients and constants of 6+n2 + 1/2d
Lucy ran the triangular route represented by ABDF. Kaitlyn starts from point H and wants to run the same distance as Lucy. What triangular route can Kaitlyn run? Explain.
Answer: Kaitlyn can run the triangular route represented by HEDF. This route is the same distance as Lucy's route, ABDF, because it is composed of three sides of the same length. H is the starting point, E is the midpoint, and F is the endpoint. The route starts at point H, travels to point E, then to point D, and finally to point F, completing the triangle.
If sin 0<0 and cos0>0, then the terminal point determined by 0 is in :
Answer: The statement "if sin 0 < 0 and cos 0 > 0" is not true, as both the sine and cosine of an angle of 0 degrees are equal to 0. Therefore, the statement is not meaningful and the question cannot be answered.
It is important to note that sine, cosine, and all the trigonometric functions are defined in radians and not degrees and the value of sin(0) and cos(0) is not zero but 1
Please provide more context or specify what you are asking about in order to give a more accurate answer.
Step-by-step explanation: