Right angled triangle is formed by the points (3, 2), (-2, -3) and (2,3).
Let the given points be,
A = (3, 2), B = (-2, -3) and C = (2, 3)
The formula for the distance between two points:
The length of the line segment bridging two points on a plane is known as the distance between the points.
The formula to find the distance between the two points is usually given by [tex]D = $$\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}$$[/tex].
Therefore,
A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), B = [tex](x_{2} , y_{2} )[/tex] = (-2, -3)
[tex]& \mathrm{AB}=\sqrt{(3+2)^2+(2+3)^2}=\sqrt{50}=5 \sqrt{2}[/tex] units
B = [tex](x_{1} , y_{1} )[/tex] = (-2, -3), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)
[tex]& \mathrm{BC}=\sqrt{(-2-2)^2+(-3-3)^2}=\sqrt{52}=2 \sqrt{13}[/tex] units
A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)
[tex]& \mathrm{AC}=\sqrt{(3-2)^2+(2-3)^2}=\sqrt{2}[/tex] units
By using the Pythagorean theorem:
According to Pythagoras's Theorem in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides.
Now, we can see that,
[tex]& (2 \sqrt{13})^2=(5 \sqrt{2})^2+(\sqrt{2})^2 \\[/tex]
[tex]& \mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2[/tex]
Therefore, the given triangle is a right angled triangle.
Therefore, option(A) s correct.
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What type of triangle do the points (3, 2), (-2, -3) and (2,3) form a triangle? If so, name the type.
A. right triangle
B. equilateral triangle
C. isosceles triangle
D. none of these
The rate of growth dP / dt of a population of bacteria is proportional to the square root of t, where P is the population size and t is the time in days (0 ? t ? 10) as shown below.
dP/dt=k \sqrt{t}
The initial size of the population is 300. After 1 day the population has grown to 600. Estimate the population after 8 days. (Round your answer to the nearest whole number.)
The population of bacteria after 8 days is 7088
Here, we have been given an equation for the rate of growth of a population of bacteria
dP/dt = k√t
where P is the population size
and t is the time in days (0 ≤ t ≤ 10)
We rewrite above equation as,
dP = k√t dt
Integrating both sides, we get,
P = (2/3) × kt^(3/2) + C
We find the value of C.
For t = 0, P = 300 as the initial size of the population is 300.
Substitute t = 0 in above equation.
300 = 0 + C
C = 300
So, the above equation becomes,
P = 300 + (2/3) × kt^(3/2) .......(1)
Now we find the value of k.
After 1 day the population has grown to 600.
substitute t = 1, P = 600 in equation (1)
600 = 300 + (2/3) × k
(2/3)k = 300
k = 900/2
k = 450
So, the equation of population of bacteria after time t is:
P = 300 + [(2/3) × 450 × t^(3/2)]
P = 300 + 300 × t^(3/2)
P = 300 (1 + t^(3/2))
To find the population after 8 days, substitute t = 8
P = 300 (1 + 8^(3/2))
P = 7088.22
P ≈ 7088
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The tables show the prices for ordering team jerseys from two different companies. You can use the information to write ratios showing the relationship between the cost and the corresponding number of jerseys. 1/5=5 25/5=5 50/10=5 75/15=5. 5/1=5 20/5=4 40/10=4 69/15=4. These ratios are all equivalent. These ratios are not all equivalent. This relationship is proportional. This relationship is not proportional. Explain how you can tell whether a group of ratios represents a proportional relationship.
Even though this relationship is proportional, not all of these ratios are equal.
What is the solution to the 3 to 5 ratio?Verify that the ratios provided are equal. The ratios of 3:5 and 15:25 are both equal. Because the first ratio 3: 5 can be derived by multiplying the ratio 15: 25 by 5 on both the numerator and denominator. The initial ratio of 3: 5 can be multiplied by 5 to get the ratio 15: 25, and vice versa.
What is an illustration of a 4:1 ratio?This indicates that you would require an 8 fl oz can (a quarter of a quart) of Part B if you were ordering a quart of Part A. You will have 1.25 after combining Parts A and B.
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How do you find the third side?
The third side of a triangle can be found using the Pythagorean Theorem.
This states that the sum of the squares of the two shorter sides of a triangle must equal the square of the longest side (the hypotenuse).
Let's say you have a triangle with sides a, b, and c, where c is the longest side. To find c, you can use the following formula:
c = √(a2 + b2)
For example, if you have a triangle with sides a = 4 and b = 5, then c = √(42 + 52) = √41 = 6.4. Therefore, the third side of the triangle is 6.4.
To calculate this using steps, you would first square the two shorter sides of the triangle:
a2 = 4 x 4 = 16
b2 = 5 x 5 = 25
Then, add the two squares together:
16 + 25 = 41
Finally, take the square root of the sum to find the length of the third side:
√41 = 6.4
Therefore, the third side of the triangle is 6.4.
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Jamila deposits $800 in an account that earns yearly simple interest at a rate of 2.65%. How much money is in the account after 3 years and 9 months?
Answer:
$821.2
Step-by-step explanation:
cause 2.65 percentage of 800 dollars is 800/100=8*2.65=21.2dollars.+800 =$821.2
NEED HELP ASAP
PLEASE REFER TO PICTURE
Why will the speedup of a parallel algorithm will eventually reach some limit?
The advantages of adding additional processors will decrease as more are added because some portions are always still sequential, and eventually the speedup approaches a limit.
What is a parallel algorithm's speedup factor?The ratio of the compute time for the sequential method to the time for the parallel algorithm represents the speedup of a parallel algorithm over a matching sequential algorithm. n-fold speedup is what we refer to if the speedup factor is n. For instance, if a sequential approach needs 10 minutes to compute while a parallel algorithm needs just 2, then the speedup is 5 times.
The observed speedup is dependent on every aspect of the implementation. For instance, more processors frequently result in speedups that are greater; but, if other programmer are running on the processors concurrently with a programmer using a parallel technique, the speedup may be reduced by those other applications.
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Consider sequences of positive real numbers of the form , in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of does the term 3000 appear somewhere in the sequence ?
a. 1
b. 2
c. 3
d. 4
e. more than 4
No two values of x in the computation we just did are equal, there are 4 different values of x for which the sequence contains the value 2001.
What is meant by sequences?An ordered list of numbers is all that a sequence is. Number series are collections of numbers that adhere to a pattern or guideline. An arithmetic sequence is one where the rule is to add or take away a number each time.
To estimate a few terms of the sequence in order to obtain a feel how it looks like.
In our case, the definition is that [tex]$\forall$[/tex] (for all) [tex]$n > 1: a_n=a_{n-1} a_{n+1}-1$[/tex].
This can be rewritten as [tex]$a_{n+1}=\frac{a_n+1}{a_{n-1}}$[/tex].
We have [tex]$a_1=x$[/tex] and [tex]$a_2=2000$[/tex], and we estimate:
[tex]$& a_3=\frac{a_2+1}{a_1}=\frac{2001}{x} \\[/tex]
[tex]$& a_4=\frac{a_3+1}{a_2}=\frac{\frac{2001}{x}+1}{2000}=\frac{2001+x}{2000 x} \\[/tex]
[tex]$& a_5=\frac{a_4+1}{a_3}=\frac{\frac{2001+x}{2000 x}+1}{\frac{2001}{x}}=\frac{\frac{2001+2001 x}{2000 x}}{\frac{2001}{x}}=\frac{1+x}{2000} \\[/tex]
[tex]$& a_6=\frac{a_5+1}{a_4}=\frac{\frac{1+x}{2000}+1}{\frac{2001+x}{2000 x}}=\frac{\frac{2001+x}{2000}}{\frac{2001+x}{2000 x}}=x \\[/tex]
[tex]$& a_7=\frac{a_6+1}{a_5}=\frac{x+1}{\frac{1+x}{2000}}=2000[/tex]
At this point we see that the sequence will become periodic: we contain [tex]$a_6=a_1, a_7=a_2$[/tex], and each subsequent term exists uniquely determined by the previous two.
Hence 2001 appears, it contains to be one of [tex]$a_1$[/tex] to [tex]$a_5$[/tex].
As [tex]$a_2=2000$[/tex], we only have four possibilities left.
Clearly [tex]$a_1=2001$[/tex] for x = 2001, and [tex]$a_3=2001$[/tex] for x = 1.
The equation [tex]$a_4=2001$[/tex]
solves to [tex]$x=\frac{2001}{2000 \cdot 2001-1}$[/tex], and the equation [tex]$a_5=2001$[/tex] to [tex]$x=2000 \cdot 2001-1$[/tex]
There are four alternative values of x for which the sequence contains the value 2001 since no two values of x are equal in the computation we just performed.
Therefore, the correct answer is option (D) 4.
The complete question is:
Consider sequences of positive real numbers of the form x, 2000, y, ........ in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of x does the term 2001 appear somewhere in the sequence?
(A) 1
(B) 2
(C) 3
(D) 4
(E) more than 4
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Tamika is ordering a taxi from an online taxi service. The taxi charges $3. 50 just for the pickup and then an additional $0. 75 per mile driven. How much would a taxi ride cost if Tamika is riding for 5 miles? How much would a taxi ride cost that is m miles long?
Cost for 5 miles:
Cost for m miles:
If the pickup charge for taxi is $3.50 and additional charge of $0.75 per mile , then the cost for riding 5 miles is $7.25 and cost for riding m miles is $[tex]3.50+0.75m[/tex] .
The pickup charge that taxi service charges is = $3.50 ;
the additional charge for per miles driven is = $0.75 ;
we have to find the cost for riding 5 miles ;
So , the total cost for riding 5 miles is = [tex]Pickup Charge + (Additional Charge)\times(Number Of Miles Driven)[/tex] ;
substituting the values , the total cost equation becomes ;
[tex]Total Cost = 3.50 + 0.75\times5[/tex]
= [tex]3.50+3.75[/tex]
= 7.25
So , the cost for 5 miles is = $7.25 ;
to find cost for driving "m" miles ,we substitute the number of miles = m;
[tex]Total Cost = 3.50+0.75\times m[/tex]
= [tex]3.50+0.75m[/tex]
Therefore , the cost for riding m miles is $ [tex]3.50+0.75m[/tex] .
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Solve 3x^2 - 6x - 9?
Answer:
3(x+1)(x-3)
Step-by-step explanation:
Well, this isn't an equation, but we can factor it like this:
[tex]3x^2-6x-9=3(x^2-2x-3)=3(x+1)(x-3)[/tex]
Given that K is the midpoint of segments RM and JL, and prove Δ RKJ ≅ Δ MKL.
Statements
Reasons
1. K is the midpoint of segments RM and JL
1. Given
2.
2.
3. and
3.
4. RK = MK and JK = LK
4. Definition of Congruent Segments
5. Δ EGF ≅ Δ EGH
5.
What is Reason #3?
a
Given
b
Definition of Midpoint
c
CPCTC
d
SSS Congruence Postulate
The complate table is,
Statement Reasons
1) K is the midpoint of segments Given
RM and JL.
2) RJ ≅ ML SSS Congruence Postulate
3) RK ≅ MK , JK ≅ LK Definition of Midpoint
4) RK = MK , JK = KL Definition of Congruence
Segments
5) Δ EGF ≅ Δ EGH CPCTC
What is Line segment?A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.
Given that;
K is the midpoint of segments RM and JL.
Now,
Since, K is the midpoint of segments RM and JL.
Hence, We get;
Statement Reasons
1) K is the midpoint of segments Given
RM and JL.
2) RJ ≅ ML SSS Congruence Postulate
3) RK ≅ MK , JK ≅ LK Definition of Midpoint
4) RK = MK , JK = KL Definition of Congruence
Segments
5) Δ EGF ≅ Δ EGH CPCTC
Thus, The complete table is shown above.
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In the figure, JKLM-EFGH. Complete the following table,
type your answer
Value of x
Value of y
Scale factor of JKLM to EFGH
type your answer.
type your answer
Value of z
type your answer.
The values of x , y and z are 80,2,110 respectively from the given figure where JKLM ~ EFGH
What is Quadrilateral ?
Quadrilateral can be defined as the type of the polygon in which it contains four sides.
Given ,
JKLM ~ EFGH
Since , JKLM ~ EFGH
3/30 = 11/z
z = 30*11/3
z =110
3 / 30 = 8/ x
3 * x = 8 * 30
x = 80
3 / 30 = y/ 20
y = 20 * 3 / 30
y = 2
Hence the values of x , y and z are 80,2,110 respectively.
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Find the area of the right triangle below.
9m
4m
18 m²
Step-by-step explanation:The area is the size of a 2-dimensional shape.
Area of a Triangle
The formula for the area of a triangle is [tex]\frac{1}{2}bh[/tex], where b is the base and h is the height.
This formula comes from the fact that a triangle is half of a rectangle. Remember that the area of a rectangle is the base times the height, so a triangle would be half of this.
Solving for Area
The base of the triangle is 9 meters. Then, the height is 4 meters. So, we can plug these values into the formula.
[tex]A=\frac{1}{2}*4m*9m[/tex]So, A = 18. Then, since meters are being multiplied by each other, the units are meters squared. The final answer is 18 m².
Determine the prices for which quantity demanded is greater than quantity supplied.
The prices where the quantity demanded is greater than quantity supplied are :
$ 2$ 1$ 0When is quantity demanded greater than quantity supplied ?Quantity demanded refers to the amount of goods and services that people and businesses in an economy demand.
This amount of goods and services demanded will be more than the quantity supplied when the price of the good or service is less than the equilibrium price.
The equilibrium price here is $ 3 and so the prices less than $ 3 are $2, $1, and $ 0.
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Shay and Nadine solve this problem in two different ways.
Mark has $25 in his bank account.
He makes $7 per hour babysitting.
How many hours must he babysit to have a total of $165 in his account?.
Use the drop-down menus to complete the sentences below.
Shay's
Assignment
25+7h-165
25-25 7h-165-25
7h-140
7h-140
7h 7h
A-20
Nadine's
Assignment
166-25-140
You need to make
$140 babysitting
140
-20
You need to babysit
for 20 hours
Please Help!
On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.
What is proportionality?When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.
Here,
U/5 = 17/11
U = 17/11 X 5
U = 7.72
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Mitchell made a scale drawing of a house. A rug in the hallway is 5 inches wide in the drawing. The actual rug is 3 feet wide. What is the drawing's scale factor?
Simplify your answer and write it as a ratio, using a colon.
Answer:
Step-by-step explanation:
a.Scale factor = distance on the plot / actual distance
b.3 feet = 12 inchs.
so scale factor = 5/12
How does the mean absolute deviation (MAD) of the data in set 1 compare to the mean absolute deviation of the data in set 2
On solving the provided question, we can say that 12,12,12,22,23,32,43 Mean Absolute Deviation (MAD): 8.8979591836735
what is mean absolute deviation?The average of the absolute deviations from the center point within a dataset is called the mean absolute deviation. This statistic summarizes the statistical spread or variability. Each data point's average distance from the mean is known as the dataset's mean absolute deviation. This gives a sense of the dataset's variability. To determine the absolute value, take the mean from each integer in the dataset and then subtraction. Take the total of the absolute values next. Subtract the aforementioned sum from the total number of items in the dataset to obtain the mean absolute deviation.
12,12,12,22,23,32,43
Mean Absolute Deviation (MAD): 8.8979591836735
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Answer:
On solving the provided question, we can say that 12,12,12,22,23,32,43 Mean Absolute Deviation (MAD): 8.8979591836735
Step-by-step explanation:
Graph the line with 1 passing through the point (3, -4)
Answer:y=1x-7
Step-by-step explanation:
How do you find the y-intercept without a calculator?
In the equation y = mx + c if we substitute the value of x as zero we will get a point on the y axis given by y =(m × 0) + c ⇒ y = c. Therefore the point of the line on the y axis is (0, c) and so c is also called the y -intercept of the line.
Now, According to the question:
i) from the general equation of line we know that any line can be represented in the form y = mx + c , where m is a constant and is called the slope of the line and c is also a constant and is the y-intercept.
ii) In the equation y = mx + c if we substitute the value of x as zero we will get a point on the y axis given by y =(m × 0) + c ⇒ y = c. Therefore the point of the line on the y axis is (0, c) and so c is also called the y intercept of the line.
iii) If for example we have the line 3y = 6x + 12 then we first get this equation of the line to match the general form of the equation of the line, that is y = mx + c. Therefore dividing both the left and the right sides of the given equation of the line by 3 we get y = 2x + 4 which matches with the general form of the equation for line and we see that the slope of the given line is m = 2 and the y intercept is given by c = 4.
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•35 POINTS• don’t explain.
SSS
SAS
ASA
SAA
HL
Reason:
The tickmarks tell us that the pair of hypotenuses are congruent.
The shared horizontal sides at the bottom are the pair of congruent legs of the right triangles. Therefore, we can use the hypotenuse leg (HL) theorem. This theorem only works for right triangles.
what is the total cost with sales tax? price 120.00 tax 5%
Answer:
5% of 120 is 6, so you would add that 6 to 120.
120 + 6 = 126.
The total cost will sales tax would be $126.00.
Step-by-step explanation:
Hope it helps! =D
(I NEED THIS RIGHT AWAY!) (PLS HELP) Lynette earns $5 by delivering newspapers. She saves $3 and she spends the rest. If she saved $27 one month, how much did she spend?
Answer:
$18
Step-by-step explanation:
To find how many times she has saved money, you would do 27/3=9. This means that she worked 9 times. Since she worked 9 times, she earned $45 in total. To find how much she saved you would do 45-27=$18
What type of triangle is 70 70 40?
70-70-40 is an isosceles triangle.
The isosceles triangle has three acute angles, which means that the angles are less than 90°.The summation of three angles of an isosceles triangle is always 180°. In an isosceles triangle, if two sides are equal, then the angles opposite to the two sides correspond to each other and are also always equal.The two equal sides are defined as the legs and the third side is defined as the base of the triangle.The two angles opposite the legs are equal and are always acute, so the categorization of the triangle as acute, right, or obtuse depends only on the angles between its two legs.Read more about the isosceles triangle:
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PLS HELP
using factorisation solve
E=(a+1)(a-1)-3(a+1)²
Answer:
Step-by-step explanation:
factoring
e =
(a+1)(a-1-3(a+1))
= (a+1)(a-1-3a-3)
= (a+1)(-2a-4)
= -2(a+1)(a+2)
The null and alternative hypotheses divide all possibilities in to:
a. two sets that may or may not overlap .
b. as many sets as necessary to cover all possibilities c. two non-overlapping sets d. two sets that overlap reset selection
Answer:
Step-by-step explanation:
b
Solve each system by graphing
I’m looking for the answer but also a explanation of how you solved it so I can solve the other 1s without help
Answer: its hard to give an answer but read explanation
Step-by-step explanation: so the first number (1/3x) is your slope and the second number is the y-intercept (5). so for example, you're going to put positive 5 on the y-axis and because you slope is a fraction, rise/run will make you go 3 to the right and 1 up. Then you do the same with the second equation except, the slop is negative and you'll have to go down.
help please (photo attached)
Answer:
slope = -1
Step-by-step explanation:
any 2 points:
(2,2) (0,4)
to find the slope we use the formula:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
slope is:
2/-2 = -1
Answer:
The slope is =
2/-2 = -1
Step-by-step explanation:
Also i hope you have a wonderful day !
HELP ME NOW PLEASE DESCRIBE AND CREATE FRACTION PATTERNS
find the rule
1 3/8, 1 3/4, 2 1/8, 2 7/8
The missing term of the arithmetic sequence is 2 1/2
What is Arithmetic Progression?An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the arithmetic sequence be represented as A
Now , the equation will be
A = 1 3/8 , 1 3/4 , 2 1/8 , x , 2 7/8
The first term a₁ = 1 3/8
The second term a₂ = 1 3/4
The common difference d of the arithmetic sequence d = second term - first term
Common difference d = 1 3/8 - 1 3/4 = 3/8
Now , the fourth term of the arithmetic sequence is given by
Tn = a + (n - 1) d
Substitute the values in the equation , we get
a₄ = 1 3/8 + ( 4 - 1 ) ( 3/8 )
a₄ = 11/8 + 9/8
a₄ = 20/8
a₄ = 2 4/8
a₄ = 2 1/2
Therefore , the fourth term is 2 1/2
Hence , it is an arithmetic sequence and the fourth term is 2 1/2
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Calculate the size of angle ABC
Therefore , the solution of the given problem of trigonometry comes out to be B = arcsin(9/14) - 180° = 140.0°.
Describe trigonometry.Correlations between triangles' angles and sides are studied in the branch of mathematics known as trigonometry. Since every straight-sided form may be reduced to a collection of triangles, trigonometry can be found throughout geometry. The relationships between trigonometry and other branches of mathematics, in particular calculus, real or complex, infinite series, logarithms, and infinite series, are astonishingly complicated.
Here,
There are two potential solutions because the supplied angle is opposite the given side that is the shortest.
Using the sine law,
B = b/asin(A)arcsin(9/7sin(30°))arcsin(9/14)
Angle B may take on the following values:
B is equal to arcsin(9/14) = 40.0°.
B = arcsin(9/14) - 180° = 140.0°
Therefore , the solution of the given problem of trigonometry comes out to be B = arcsin(9/14) - 180° = 140.0°.
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How do you know if 3 lengths will make a triangle?
If three lengths can make a triangle by using the Triangle Inequality Theorem which states . that any two triangle sides added together must exceed the third side If the sum of any two sides is equal to or less than the third side, then the lengths cannot make a triangle.
The Triangle Inequality Theorem can be used to determine if a triangle can be formed from three lengths. According to this theorem, any two triangle sides must add up to more than the third side. To put it to use, add up the lengths of the first two sides and compare them to the third side's length. The lengths cannot form a triangle if the total of the first two sides is more than or equal to the third side. The lengths can form a triangle if the product of the first two sides is bigger than the product of the third side.
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Need the answer for these
Answer:
Step-by-step explanation:
2A. 3x=6 ⇒ x=2
2B. 3n=2(n-3) ⇒ 3n=2n-6 ⇒ n= -6
1. cross multiplication method