3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).
Given that,
The perimeter of a triangle 12cm.if the lengths of the three sides are all integers (in cm).
We have to find how many such difference triangle are possible.
We know that,
Perimeter of the triangle is 12cm.
p=12
a+b+c=12
a+b≥c
b+c≥a
So,
a+b+c≥2c
12≥2c
c≤6
So,
a≤6,b≤6,c≤6
We get,
a=6,b=3,c=3
a=5,b=4,c=3
a=4,b=4,c=4
Therefore, 3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).
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Plot 5/6 and 2 2/3
on the number line below.
The points with black dots on the number line represent the fractions.
What is a number line?In elementary mathematics -
A number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.Given are the fractions -
5/6 and 2[tex]\frac{2}{3}[/tex]
We can write -
2[tex]\frac{2}{3}[/tex] = 8/3
5/6 = 5/6
Refer to the number line attached. The points with black dots represent the numbers.
Therefore, the points with black dots on the number line represent the fractions.
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in the general formulation of fourier's law (applicable to any geometry), what are the vector and scalar quantities? why is there a minus sign on the right-hand side of the equation?
The scalar quantities in Fourier's law is the temperature and the conductivity whereas heat flux is vector.
Heat moves from a higher temperature to a lower temperature, which is explained by the minus sign.
Fourier's law
q = -k ▽T
Where,
q is the local heat flux density in W.m2
k is the conductivity of the material in W.m-1.K-1
▽T is the temperature gradient in K.m-1
The terms "force," "speed," "velocity," and "work" are frequently used, and they all refer to scalar or vector quantities. Physical quantities like mass and electric charge are examples of scalar quantities because they only have magnitudes. In contrast, a vector quantity is a physical quantity like force or weight that has both magnitudes and directions.
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Write an equation to model the situation:
Tyler withdraws $35 from his bank account every week until he runs out of
money. He started the year with $3245 in his bank account.
In his account balance now $3215
What is the explanation?Tyler withdraws $35 from his bank account every week until he runs out of
money. He started the year with $3245 in his bank account.
Tyler withdraws $35.
He started with $3245.
In his account balance now
Tyler withdraws -His started accound.
$3245 - $35 = $3215
Till he runs out of money, Tyler takes out $35 per week from his bank account. He had $3245 in his bank account before the year began.Tyler takes out $35.He had $3245 to start.Tyler is now making withdrawals from his beginning account amount. $3245 - $35 = $3215Currently, he has $3215 in his account.
In his account balance now $3215
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10. If 4n = 3.60, which is the value of n? A 0.09 B 0.9 C 9 P 6.5 D 90
Answer: The answer is B: 0.9
a ________ contains the actual values that are plotted on the chart.
A data series contains the actual values that are plotted on the chart. So the option c is correct.
In the given question, we have to find the answer to fill in the blanks.
The given statement is:
"A ________ contains the actual values that are plotted on the chart."
As we know that;
A data series, such as a list of quarterly corporate profits, is a row or column of figures that are input in a worksheet and plotted in your chart. Even if you generated your chart in a different software, like Word, Office automatically associates charts with an Excel-based worksheet.
A data series contains the actual values that are plotted on the chart.
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The complete question is:
A ________ contains the actual values that are plotted on the chart.
(1) data source
(2) category values
(3) data series
(4) legend
Select the graph for the solution of the open sentence. Click until the correct graph appears.
|x - 1| < 4
Answer:
graph D
Step-by-step explanation:
x - 1 ≥ 0
x ≥ 1
if x ≥ 1
x - 1 < 4
x < 4 + 1
x < 5
1≤ x < 5
if x < 1
-x + 1 < 4
-x < 4 - 1
- x < 3
x > -3
-3 < x < 1
final solution
-3 < x < 5
You buy the following from Amazon:
25 flash drives for $10 each
What is the Subtotal: $
Today only they are 25% off, how much do you save: $
What is the new Subtotal: $
Sales tax is 4%: $
I
What is the total: $
Answer:
Subtotal: $250.00
Savings: $62.50
New Subtotal: $187.50
Total: $195.00
Step-by-step explanation: First, multiply 25 by 10. You'd get 250. Then, recall the formula to find the worth after a percent is applied:
Worth = Whole number * part percent / 100
Plug in the numbers:
Worth = 250 * 25 / 100
6250 / 100
= 62.50
Now, since it's a discount we need to subtract the discount price from the current subtotal. This would look like this:
250 - 62.50 = 187.50
Now, use the same formula to find the sales tax:
187.50 * 4 /100
750 / 100
= 7.5
So, since we need to pay the tax, we add the amount to our current subtotal:
187.50 + 7.5 = 195
So, our total is $195.00
the larger circle has center $o$ and passes through $d$. the smaller circle has diameter $od$. what percent of the larger circle's area is gray?
25% is the larger circle area is gray.
Area of a Circle: The area of a circle is pi times the radius squared.
To calculate the area of the circle we have the formula:
A = π r²-----(1)
where
A=area
r=radius.
First, we have to analyze the given data, the large circle center o passes through d, so
Gray circle area=π*(radius)^2----(2)
The radius of the smaller circle = OD/2 substitute in (2)
Gray circle area=π*(OD/2)^2
Gray circle area=π*OD^2/4
Larger circle area=π*(radius)2
radius of the larger circle = OD
larger circle area=π*OD^2
To know the percentage of a large circle we have a small formula:
gray circle area/large circle area--------(3)
=π*OD^2/4/π*OD^2
=π*OD^2/4*1/π*OD^2=1/4
=25/100
=25%
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Which is a solution for the equation y= 6x + 6
Answer:
Step-by-step explanation:
Which is a solution for the equation y= 6x + 6
solve for yy = 6x + 6 (there is no possibility to simplify)
solve for xy = 6x + 6
6x + 6 = y
6x = y − 6
divide both side by 6
x = (1/6)y - 1you are standing at the point x = 300 m, y = 400 m in a reference frame with synchronized clocks.
The time on clock shows at the instant you see the clock at the origin showing 3.80 μs is 5.47 × [tex]10^{-6[/tex] s.
As per the given data the values of x and y are as follows:
x = 300 m
y = 400 m
Here you are standing at the point (300, 400) in a reference frame with synchronized clocks.
Here we have to determine the time on clock shows at the instant you see the clock at the origin showing 3.80 μs.
The point where you're standing (300, 400) is 500 m from the origin.
Therefore my distance from the origin is 500 m
Speed of light , c = 3 × [tex]10^8[/tex] m/s
The clock at the origin showing, [tex]T_0[/tex] = 3.80 μs
[tex]T_0 = 3.8 \times 10^{-6}[/tex] s
Time shown by my clock , T = distance ÷ c + [tex]T_0[/tex]
T = [tex]\frac{500}{(3 \times 10^8)} + 3.8 \times 10^{-6[/tex]
T = 5.47 × [tex]10^{-6[/tex] s
Therefore the time shown by my clock is 5.47 × [tex]10^{-6[/tex] s.
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in a triangle abc AB=12, AC=14 and angle BAC=68° find angles and side
Answer: The measures of the angles in triangle ABC are BAC = 68°, BCA = 50.6°, and ABC = 61.4°. The lengths of the sides are AB = 12, AC = 14, and BC = 13.68.
Step-by-step explanation:
To find the angles and sides of a triangle, you need to know at least three pieces of information about the triangle. In this case, you are given the lengths of sides AB and AC, and the measure of angle BAC.
You can use the Law of Sines to find the measure of the third angle and the length of the third side. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all sides and angles in the triangle. In other words, if we let a, b, and c represent the lengths of the sides of the triangle and A, B, and C represent the measures of the angles opposite those sides, then the following equation holds:
a/sin A = b/sin B = c/sin C
In triangle ABC, we are given the lengths of sides AB and AC and the measure of angle BAC. We can use the Law of Sines to find the measure of angle BCA and the length of side BC.
First, we can find the measure of angle BCA using the equation:
a/sin A = b/sin B = c/sin C
Substituting the known values, we get:
14/sin BAC = 12/sin BCA
Solving for sin BCA, we get:
sin BCA = 14/12 * sin BAC
Plugging in the given value for sin BAC, we get:
sin BCA = 14/12 * sin 68°
Using a calculator, we find that sin 68° = 0.906308
So sin BCA = 0.763696
To find the measure of angle BCA, we can use the inverse sine function on our calculator. The inverse sine of 0.763696 is about 50.6°.
Now that we know the measures of angles BAC and BCA, we can use the fact that the angles in a triangle sum to 180° to find the measure of angle ABC:
BAC + BCA + ABC = 180°
Substituting the known values, we get:
68° + 50.6° + ABC = 180°
Solving for ABC, we get:
ABC = 180° - 68° - 50.6°
This simplifies to:
ABC = 61.4°
Now that we have found the measures of all three angles, we can use the Law of Sines again to find the length of side BC.
We can use the equation:
a/sin A = b/sin B = c/sin C
Substituting the known values, we get:
14/sin BAC = 12/sin BCA = BC/sin ABC
Solving for BC, we get:
BC = 14/sin BAC * sin ABC
Plugging in the values we found earlier, we get:
BC = 14/0.906308 * sin 61.4°
Using a calculator, we find that sin 61.4° = 0.875
So BC = 14/0.906308 * 0.875 = 13.68
The measures of the angles in triangle ABC are BAC = 68°, BCA = 50.6°, and ABC = 61.4°. The lengths of the sides are AB = 12, AC = 14, and BC = 13.68.
a cyclist rides at an average speed of 24 miles per hour. if she wants to bike 180 km , how long (in hours) must she ride? express your answer using two significant figures.
4.66 hours is the required riding time (in hours) if she wants to cycle 180 km when cyclist travels at a speed of 24 miles per hour on average.
Given that,
A cyclist travels at a speed of 24 miles per hour on average.
We have to find what is the required riding time (in hours) if she wants to cycle 180 km.
We know that,
The velocity is a vector quantity (has magnitude and direction) that is calculated by dividing the distance by the amount of time needed to travel the distance in question.
So, the distance is 180 km, and the speed is 24 miles per hour.
To calculate the amount of time needed to travel the distance, we divide the distance by the speed.
The distance is first converted to miles as 1 mile is equal to 1.6098 kilometers,
180 kilometers are equal to 111.84681 Miles.
111.84681 miles traveled in 24 hours
111.84681/24
4.66 hours.
Therefore, 4.66 hours is the required riding time (in hours) if she wants to cycle 180 km when cyclist travels at a speed of 24 miles per hour on average.
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Select the statement that best justifies the conclusion based on the given information.
I is in plane M,
x is on line I
Conclusion: xis in plane M.
A) A plane contains at least three points not all on the same line.
B) Exactly one plane contains a given line and a point not on the line.
C) If a plane contains a line, it contains the points on the line.
D) If two points lie in a plane, then the line containing them lies in that plane.
The statement that best justifies the conclusion based on the given information is given as follows:
C) If a plane contains a line, it contains the points on the line.
How to justify the statement?We are given these two pieces of information:
Line l is in plane M.Point x is on line l.When a line belongs to a plane, as is the case in this problem, with Line l belong to plane M, then all the points of the line will belong to the plane.
Hence, point x belongs to the plane M in this problem, as the plane M contains the line l for which point x belongs, and thus statement c is correct.
(basically, the transitive property can be applied to conclude that every point on a line belonging to a plane also belong to the plane).
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What is the area of △mnp? 40 m2 60 m2 68 m2 127.5 m2
Although part of your question is missing, you might be referring to this full question: Right triangles MNP and QRS are congruent. What is the area of △MNP? (Picture as attached)
The area of △MNP is 60 m².
Since △MNP and △QRS are congruent, then SQ = MP, NM = RQ, and RS = NP.
The formula to find the area of a triangle is:
= 1/2 * base * height
As shown in the picture, height = 15, and base is unknown.
To find the base, we use Pythagoras theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle), or, in familiar algebraic notation, a² + b² = c².
So, MP = √ 17² – 15²
MP = 8m = the base
Hence, area of △MNP:
= 1/2 * 8 * 15
= 60 m²
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What are the endpoint coordinate for the midegment of △PQR that i parallel to PR¯¯¯¯¯?
point coordinates for the mid segment of the parallel to PQ segment of the PQR is ST point is (-3.5, 0.5) and (-1, -0.5).
Given that,
We have to find what are the endpoint coordinates for the middle portion of the parallel to PQ segment of the PQR.
We know that,
First we write the co-ordinates of the triangle in the given graph.
P is (-3,3)
Q is (2,1)
R is (-4,-2)
The triangle's midpoint, which is parallel to section PQ, must be located. As a result, we would need to locate the midpoints of the segments PR and QR before joining the points to obtain the mid segment.
Midpoint Formula is
(x₁+x₂/2, y₁+y₂/2)
So,
The midpoint of the side PR is
(-3+(-4)/2, 3+(-2)/2)
(-3-4/2, 3-2/2)
(-7/2,1/2)
So, S point is (-3.5, 0.5)
The midpoint of the side QR is
(2+(-4)/2, 1+(-2)/2)
(2-4/2, 1-2/2)
(-2/2,-1/2)
So, T point is (-1, -0.5)
Therefore, The endpoint coordinates for the mid segment of the parallel to PQ segment of the PQR is ST point is (-3.5, 0.5) and (-1, -0.5).
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Not everyone pays the same price for
the same model of a car. The figure
illustrates a normal distribution for the
prices paid for a particular model of a
new car. The mean is $21,000 and the
standard deviation is $1000.
Use the 68-95-99.7 Rule to find what
percentage of buyers paid between
$20,000 and $21,000.
Number of Car Buyers
-99.7%-
-95%-
68%-
18
19 20. 21 22 23 24
Price of a Model of a New Car (Thousands)
The percentage of buyers who paid between $20,000 and $21,000 is%.
(Type an exact answer.)
The figure illustrates a normal distribution for the prices paid for a particular model of a new car. The mean is $21,000 and the standard deviation is $1000. Use the 68-95-99.7 Rule the percentage of buyers that paid between $20,000 and $21,000 is 68%
What does the statistical 68-95-99.7 rule mean?68 percent of the data falls within one standard deviation of the mean,
95 percent falls within two standard deviations, and
99.7 percent falls within three standard deviations.
In the problem, it was given that the mean is $21 000 and the standard deviation is $1 000
The deviation between $20,000 and $21,000
= $21,000 - $20,000
= $1,000
The standard deviation is $1000 hence buyers within $20,000 and $21,000 are within one standard deviation. according to the 68-95-99.7 Rule they are 68%
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Here the points.
Good luck in the finals
Edit: 3 minutes later, no one wants it?!
Answer: good luck to you!
Step-by-step explanation:
Answer:
tysm for the points <33
Step-by-step explanation:
:)
Given that D i the midpoint of AB and K i the midpoint of BC, which tatement mut be true?
Option D is the correct answer. AK + BK = AC is not a true statement.
All the statements are not true except:
AK + BK = AC
Since BK = KC, so
AK + KC = AC
DB=BK is not necessarily true since it is not stated whether AB = BC
B is the midpoint of AC is not necessarily true since again it's not stated that AB = BC
D bisects AK is not necessarily true since it is not stated that D and K lie on the same line.
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Which angles are coterminal with 3π2?
Select each correct answer.
Answer:
Step-by-step explanation: : 630°, 990°, -90°, -450°
please solve
8x +9 ≤ 5x+3x-6
Choose the proportion that correctly represents the similar figures.
A. 5/x = 3/8
B. 8/5 = 3/x
C. 8/3 = x/5
D. x/3 = 8/5
The proportion that correctly represents the similar figures is the one in option B:
8/5 = 3/x
Which proportion correctly represents the similar figures?If two figures are similar, then the quotient between the correspondent sides must be equal.
Then we can write the equation:
8ft/3ft = 5ft/x
8/3 = 5/x
Now we can divide both sides by 5 and multiply both sides by 3, then we will get:
8/5 = 3/x
That is the proportion we wanted, then we conclude that the correct option is B.
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Each marble bag sold by Ahmad's Marble Company contains 5 green marbles for every 8 orange marbles. If a bag has 25 green marbles, how many orange
marbles does it contain?
Answer:
40 orange marbles
Step-by-step explanation:
Set up and solve this proportion:
[tex] \frac{5}{8} = \frac{25}{x} [/tex]
[tex]5x = 200[/tex]
[tex]x = 40[/tex]
What’s the surface area of this prism ?
Hence the required surface area is 228cm²
What is surface area?
The surface area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.
Given:
A triangular prism and its net.
To find:
Side lengths for the net.
Surface area of the triangular prism.
Solution:
Side lengths for the net:
A= 4 cm
B= 10 cm
C= 6 cm
D= 8 cm
Surface area:
[tex]sa = bh +(b1 +b2+b3)l\\\\sa=6(8) +(6+4+8)\times10\\\\sa= 48 +18(10)\\\\sa=48+180\\\\sa=228 cm^2[/tex]
Hence the required surface area is 228cm²
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In 2014 , a salesman was paid a basic monthly salary of rs 25 000. At the end of the year ,he was also paid a bonus of 6.5 % of the value of the sales that he had made during the year . his sales for the year was rs 100 000. calculate his totasl income that he receives in 2014.
x as his total income
x = 12(25 000) + 0.065(100 000)
x = 300 000 + 6 500
x = 306 500
CHECKING:
12(25 000) = 300 000 (12 months salary)
0.065(100 000) = 6 500 (bonus)
= 306 500
Therefore, the salesman total income is 306 500 in 2014.
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-HELP i ned help with this please
The length of BR is 40 cm.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
YN is parallel with BR.
Triangle HYN is congruent with Triangle HBR.
HN = 5 cm
NR = 15 cm
YN = 10 cm
Now,
HR = HN + NR
HR = 5 + 15 = 20 cm
YN/HN = BR/HR
10/5 = BR/20
2 = BR/20
BR = 20 x 2
BR = 40 cm
Thus,
The value of BR is 40 cm.
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What is the remainder when f(x) = 3x3 + 24x2 − 45x − 162 is divided by (x + 8)?
The remainder when f(x) = 3x³ + 24x² − 45x − 162 is divided by (x + 8) is 198.
How to find the remainder when dividing polynomial?A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.
Therefore, the remainder when f(x) = 3x³ + 24x² - 45x - 162 is divided by (x + 8) is as follows:
The dividend is x + 8.
Hence, let's Set the dividend to 0
x + 8 = 0
x = -8
Substitute x = - 8 in f(x) = 3x³ + 24x² - 45x - 162
f(-8) = 3(-8)³ + 24(-8)² - 45(-8) - 162
f(-8) = - 1536 + 1536 + 360 - 162
f(-8) = 198
Therefore, the remainder is 198.
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a parabola opening up or down has vertex (0,0) and passes through (6,9). write its equation in vertex form. simplify any fractions.
A parabola is a graph of a quadratic equation of the form
y = ax^2 + bx + c.In order to write the equation of a parabola in vertex form, we need to first determine the values of a, b, and c.
To find the vertex of the parabola, we know that the vertex lies at the point (0,0), so the x-coordinate of the vertex is 0. The y-coordinate of the vertex is the value of y at x = 0, which we can find by plugging 0 in for x in the equation
y = ax^2 + bx + c.So the vertex of the parabola is (0, c).
Since the parabola passes through the point (6,9), we can plug in these values for x and y into the equation y = ax^2 + bx + c to find the values of a, b, and c. We get the equation
9 = 36a + 6b + c.We can now write the equation of the parabola in vertex form. In vertex form, the equation of a parabola is y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola. In our case, the vertex is (0,c), so we can write the equation as y = a(x - 0)^2 + c. Plugging in the values we found earlier, we get
y = 36a(x - 0)^2 + c.Finally, we can simplify the equation by dividing both sides by 36a. This gives us
y = (x - 0)^2 + c/36a.Since c/36a is a constant, we can simplify the equation even further by letting d = c/36a, so the final equation is
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Please help!! And explain the work you did!! 60 points and brainliest!
3x²-12x+27= 0
Distinguish the discriminant and number of solutions for the equation. Show your work and explain the steps you
used to solve.
Elise is sewing doll blankets to sell at a craft fair. She has 25 full spools of thread in her new sewing kit, and she needs 0.2 spools of thread for each doll blanket she sews. If Elise makes 9 blankets, how many spools of thread will remain?
Answer: 23 spools of thread
Step-by-step explanation:
0.2 times 9 = 1.8 spools of thread
25 - 1.8 = 23.2 spools of thread
Shade 3 circles. Shade 4/3 more