The point at which three or more lines intersect is the point of concurrency.
What is the point where three line intersect?The point were three lines meet or intersect is a point of concurrency.
In other words, a point of concurrency is where three or more lines intersect in one place.
This point of concurrency is a single point shared by three or more lines.
Perpendicular bisectors, and altitudes are concurrent in every triangle.
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Answer:
concurrency
Step-by-step explanation:
Look above for more
Question 8
Select the solution to the following system of equations:
3x+2y=0
-x-y=1
Answer:
-x-y=1
-x= 1+y
x= -1-y
3x+2y=0
3(-1-y) +2y=0
-3-3y+2y=0
-3-y=0
y= -3
x= -1-(-3)
x= -1+3
x= 2
Therefore, x= 2 and y= -3
how to find the length of sides using pythagorean theorem
Answer:
Pythagorean theorem is mainly used for finding the length of the third side of a right angled triangle if the lengths of other two sides are known.
For this, it is more useful if the theorem is stated in terms of the length of the sides of the triangle.
Consider a right angled triangle with sides of lengths p,b and h, where p,b and h are the lengths of perpendicular,base and hypotenuse respectively.
Draw squares on each of these sides.These squares have areas p²,b² and h².
For any right angled triangle with sides of length p,b and h;
[tex] \: \: \: \: \: \: \: {h}^{2} = {p}^{2} + {b}^{2} ....................(i)[/tex]
[tex] \therefore \: h = \sqrt{ {p}^{2} + {b}^{2} } [/tex]
From (i); p²=h²-b²
[tex] \therefore \: p = \sqrt{ {h}^{2} - {b}^{2} } [/tex]
Similarly,
[tex]b = \sqrt{ {h}^{2} - {p}^{2} } [/tex]
Step-by-step explanation:
[tex] \blue{ \frak{seolle_{aphr.odite} }}[/tex]
Question 4 of 10
If ƒ(x) = 3(x+5) +−, what is f(a+2)?
[tex]f(x) = 3(x+5)\\\\f(a+2) = 3(a+2 +5) \\\\~~~~~~~~~~~~=3(a+7)\\\\~~~~~~~~~~~~=3a+21[/tex]
what the volume of the soild
Answer:
A.264
Step-by-step explanation:
((Area Of triangle*height)=Volume
Area of triangle is the base of the triangle multiplied by height of triangle divided by 2
((8*6)/2)*11=264
The measure of an exterior angle of a regular polygon is 45º. How many sides does the polygon have?
Answer:The answer is 8 sides
Step-by-step explanation:
Esther gave the storekeeper a twenty dollar bill for a purchase of $14.51. How
much change should she have received?
Answer:
She would have received $5.49 change
Answer:
$5.49 ~$5.50
Explanation: $20 - $15.51 = $5.49 therefore you have to round off which would initially equal to $5.50
(07.03 MC)
Victoria used a probability simulator to pull 3 colored marbles from a bag and flip a coin 50 times. The results are shown in the tables below:
Color of
Marble Number of
Times Rolled
Blue
18
Green
20
Yellow
12
Heads Tails
20 30
Using Victoria's simulation, what is the probability of pulling a blue marble and the coin landing tails up?
48 over 50
38 over 50
540 over 2500
360 over 2500
The probability of pulling a blue marble and the coin landing tails up is 360/2500
How to determine the probability?The tables of values are given as:
Color Times
Blue 18
Green 20
Yellow 12
Heads Tails
20 30
The probability of obtaining a blue marble is:
P(Blue) = 18/50
The probability of landing tails up is:
P(Tail) = 20/50
The required probability is:
P = P(Blue) * P(Tail)
This gives
P = 18/50 * 20/50
Evaluate the product
P = 360/2500
Hence, the probability of pulling a blue marble and the coin landing tails up is 360/2500
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Eleanor is working her way through school. She works two part-time jobs for a total of 24 hours a week. Job A pays $5.80 per hour, and Job B pays
$7.40 per hour. How many hours did she work at each job the week that she made $158.40.
Step-by-step explanation:
a = hours at job A
b = hours at job B
a + b = 24
a = 24 - b
5.8a + 7.4b = 158.4
note we can use the a = 24 - b identity in the second equation :
5.8×(24 - b) + 7.4b = 158.4
139.2 - 5.8b + 7.4b = 158.4
1.6b = 19.2
b = 12 hours
a = 24 - b = 24 - 12 = 12 hours
she worked 12 hours on job A and 12 hours on job B.
6 x (3+2) divided by 10
x y
-1 -10
3 14
Complete the slope-intercept form of the linear equation that represents the relationship in the table.
to get the equation of any straight line, we simply need two points off of it, let's use the ones in the table.
[tex]\begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} -1&-10\\ 3&14\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{(-10)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{14 +10}{3 +1}\implies \cfrac{24}{4}\implies 6[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-10)}=\stackrel{m}{6}(x-\stackrel{x_1}{(-1)}) \\\\\\ y+10=6(x+1)\implies y+10=6x+6\implies y=6x-4[/tex]
there are 20 students 15 men and 5 women in a maths class,in how many different ways can a committee of 3 men and 2 women be choosen
[tex]\displaystyle\\\binom{15}{3}\cdot\binom{5}{2}=\dfrac{15!}{3!12!}\cdot\dfrac{5!}{2!3!}=\dfrac{13\cdot14\cdot15}{2\cdot3}\cdot\dfrac{4\cdot5}{2}=13\cdot7\cdot5\cdot2\cdot5=4550[/tex]
If 12,5 % discounted is offered on a R500,00 pair of shoes ,how much discount will you receive
Answer: R62,500
Step-by-step explanation:
To find the discount, simply multiply 12.5% (0.125 in decimal form) with 500,000
500,000 x 0.125 = 62,500
Answer:
₹62,50
Step-by-step explanation:
The amount of discount is found by multiplying the discount rate by the amount being discounted.
discount = 0,125 × ₹500,00 = ₹62,50
You will receive a discount of ₹62,50.
_____
Additional comment
Here, a comma is used to separate the units part of the number from the fractional part of the number. This decimal separator is an alternative to the use of a period or centered dot (·) for that purpose.
What represents vector t = –5i + 12j in trigonometric form?
t = 13 ❬cos 67.38°, sin 67.38°❭
t = 13 ❬sin 67.38°, cos 67.38°❭
t = 13 ❬cos 112.62°, sin 112.62°❭
t = 13 ❬sin 112.62°, cos 112.62°❭
The representation of the vector in trigonometry form is t = 13 ❬cos 112.62°, sin 112.62°❭
Complex numberThe representation of complex number in polar form is expressed as;
y = r(cosФ + isinФ)
where;
r is the modulus
Ф is the argument
Given the vector t = –5i + 12j, the modulus of the vector is given as;
r = √(-5)²+(12)²
r = √25 + 144
r = √169
r = 13
Determine the angle between the vectors
Ф = arctan(-12/5)
Ф = -67.38
Since tan is negative in the second quadrant, hence;
Ф = 180 - 67.38
Ф = 112.62°
The representation of the vector in trigonometry form is t = 13 ❬cos 112.62°, sin 112.62°❭
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39. What is the value of x?
Answer:
x = 15
Step-by-step explanation:
the sum of the exterior angles of a polygon = 360°
sum the 5 exterior angles and equate to 360
5x + 3 + 4x + 8 + 5x + 5 + 6x - 1 + 3x = 360 , that is
23x + 15 = 360 ( subtract 15 from both sides )
23x = 345 ( divide both sides by 23 )
x = 15
Select the best definition of repeating decimal.
A. any number that does not repeat, or terminate, that can not be written as a fraction.
B. a decimal that has a recurring sequence of numbers that follow a pattern
C. any number that can be written as a fraction, repeating or terminating decimal
D. a decimal which has digits that do not go on forever.
The correct option that defines repeating decimals correctly is Option B;
a decimal that has a recurring sequence of numbers that follow a pattern.
What is a Repeating Decimal?A repeating decimal is also called a recurring decimal and it is a decimal representation of a number whose digits are periodic and the infinitely repeated portion is not zero.
From the above definition, it means that the correct option that defines repeating decimals correctly is Option B.
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a puppy weighs 1 pound. what does the puppy weigh after 4 weeks
Cheng likes a modern lawn sculpture made of four identical solid right pyramids with square bases. He decides to create an exact copy of the sculpture, so he needs to know what volume of sculpting material to purchase.
2 identical solid right pyramids with square bases are connected at the square base. Another 2 are connected in the same way and are stacked on top of the other 2 pyramids. The length of the base edge is 2 feet and the height of the whole structure is 6 feet.
He measures each edge of each base to be 2 feet. The height of the whole sculpture is 6 feet.
Volume is a three-dimensional scalar quantity. The amount of sculpting material needed is 8 ft³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Since the pyramid is stacked one over the other, the total height of the sculpture is the sum of the four pyramid heights, therefore, the height of each pyramid is 1.5 ft.
The volume of the complete sculpture = 4(Volume of a single pyramid)
= 4[(1/3) × (2 ft)² × 1.5 ft]
= 4(2 ft³)
= 8 ft³
Hence, the amount of sculpting material needed is 8 ft³.
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Answer:
8ft.^3
Step-by-step explanation:
I just took the test on edge :)
A bicycle company is designing women's bicycle frames The frames can accommodate any woman taller than 54.5 inches. Given that the heights of adult American women are normally distributed, with a mean of 65 inches and a standard deviation of 3.5 inches, what percentage of American women CANNOT use the bicycles designed by this company?
Using the normal distribution, it is found that 0.13% of American women CANNOT use the bicycles designed by this company.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 65, \sigma = 3.5[/tex]
The proportion of women that cannot use the bikes(smaller than 54.5 inches) is the p-value of Z when X = 54.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{54.5 - 65}{3.5}[/tex]
Z = -3
Z = -3 has a p-value of 0.0013.
0.0013 = 0.13% of American women CANNOT use the bicycles designed by this company.
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Heart of algebra
If 5=a^x, then 5/a=?
Step-by-step explanation:
[tex]5 = {a}^{x} [/tex]
[tex] \frac{5}{a} = \frac{a {}^{x} }{a} [/tex]
[tex] \frac{5}{a} = {a}^{x - 1} [/tex]
help please, i need to turn this in
Answer:
a = -3
b = 9
c = -3
Step-by-step explanation:
[tex]a. (2^{5} )(2)^{-8} =2^{a} \\2^{(5-8)} =2^{a} \\2^{-3}=2^{a}[/tex]
[tex]a=-3[/tex]
[tex]b.\frac{4^{7} }{4^{-2} } =4^{b} \\4^{(7-(-2))} } =4^{b} \\4^{(7+2)} =4^{b}[/tex]
[tex]4^{9} =4^{b}[/tex]
[tex]b=9[/tex]
[tex]c. \frac{7^{9} }{7^{c} } =7^{12}[/tex]
[tex]7^{9-c} =7^{12}[/tex]
[tex]9-c=12[/tex]
[tex]c=9-12[/tex]
[tex]c=-3[/tex]
Hope this helps
Solve the system of equations
−5x−3y=−28 and x+2y=0 by combining the equations
Answer: (8, -4)
Step-by-step explanation:
-5x - 3y = -28
x + 2y = 0
1. Multiply both sides of the bottom system by 5 to cancel the x out
5(x+2y=0)
5x + 10y = 0
2. rewrite
-5x - 3y = -28
5x + 10y = 0
3. add
0x + 7y = -28
4. divide by 7
7y = -28
5. y = -4
6. plug in -4 for y in one of the original equations
x + 2(-4) = 0
7. simplify
x = 8
9. solution is
(8, -4)
answer asap giving max points and brainliest A projectile is launched at an angle of 30° and travels a distance of 400 meters. Gravitational acceleration equals 9.8 m/sec2 calculate the initial velocity.
answer choices:
67
87
57
Answer:
67 m/s
Step-by-step explanation:
Formula for range :
Range = u²sin2θ / gu = initial velocityθ = angle of launchg = gravitational accelerationSolving with the given values :
400 = u² x sin60° / 9.8u² x √3/2 = 3920u² = 7840/√3u² = 4526.4u = 67 m/s (approximately)Answer:
[tex]\sf u=67\:ms^{-1}[/tex]
Step-by-step explanation:
Assuming the distance traveled is the horizontal distance.
Horizontal Range Formula
[tex]\sf R=\dfrac{u^2 \sin 2\theta}{g}[/tex]
where:
R = horizontal rangeu = initial velocity[tex]\theta[/tex] = angle of initial velocityg = acceleration due to gravityGiven:
R = 400 m[tex]\theta[/tex] = 30°g = 9.8 m/s²Substituting the given values into the formula and solving for u:
[tex]\implies \sf 400=\dfrac{u^2 \sin 60^{\circ}}{9.8}[/tex]
[tex]\implies \sf 3920=u^2 \sin 60^{\circ}[/tex]
[tex]\implies \sf 3920=\left(\dfrac{\sqrt{3}}{2}\right)u^2[/tex]
[tex]\implies \sf u^2=\dfrac{7840}{\sqrt{3}}[/tex]
[tex]\implies \sf u=\sqrt{\left(\dfrac{7840}{\sqrt{3}} \right) }[/tex]
[tex]\implies \sf u=67.2787196...[/tex]
[tex]\implies \sf u=67\:ms^{-1}\:(nearest\:whole\:number)[/tex]
write an article for publication into the school's magazine on three effects of indiscipline and suggest about three ways of arresting the menace
Answer:
East West Point E.W English School's effects and solutions of indiscipline Effects.peer influence.Teacher's immoral relationship.Poor attitude of teachers to work Solutions .Review children's act to incorporate emerging issues.Indiscipline students be absorbed into correctional schools.That student involved in criminal activities be treated as criminals and dealt with in accordance with lawStep-by-step explanation:.......NEED HELP ASAP!!! PLEASE
The linear function that has a different rate of change from y = -3x+4 is A, a function with a y-intercept of -4 that passes through the point (-3,-13)
What is an intercept?An intercept is the point where a straight line or a curve meets with the x or y axes.
Analysis:
The rate of change is the same as slope. The slope of y = -3x + 4 is -3,
All other functions Except A have a slope of -3.
for linear function A,
if y = mx + c, c = -4, x = -3, y = -13
-13= -3m - 4
-3m = -9
m = 3
In conclusion, linear function A with a y-intercept of -4 passing through the point (-3,-13) has a different rate of change from y = -3x + 4
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Ted needs 2500 metres for job. What length is this in kilometres
Answer:
2.5 kilometers
Step-by-step explanation:
One kilometer is 1000 meters
To convert from metres to kilometers, we divide by 1000
2500 ÷ 1000 = 2.5km
Suppose the scores of seven members of a women’s golf team are 68, 62, 60, 64, 70, 66, and 72. Find the mean, median, and midrange.
a.
Mean = 64, median = 64, midrange = 64
b.
Mean = 65, median = 64, midrange = 66
c.
Mean = 66, median = 77, midrange = 65
d.
Mean = 66, median = 66, midrange = 66
Please select the best answer from the choices provided
A
B
C
D
The mean, median, and midrange of the given that are 66, 66 and 66 respectively.
Option D) Mean = 66, median = 66, midrange = 66 is the correct answer.
What is the mean, median, and midrange?Mean is the sum total of the number divided by number of terms
Median is the middle number when arranged in ascending or descending order.
Midrange is the average of the sum of the maximum number and the minimum number.
Given that;
Data set: 68, 62, 60, 64, 70, 66, and 72n = 7First, we arrange in ascending order.
60, 62. 64, 66, 68, 70, 72
Mean = ( 60 + 62 + 64 + 66 + 68 + 70 + 72 ) / 7
Mean = 462 / 7
Mean = 66
Median = 66
66 is the middle number.
Range = ( Max + Min ) / 2
Range = ( 72 + 60 ) / 2
Range = 132 / 2
Range = 66
Therefore, the mean, median, and midrange of the given that are 66, 66 and 66 respectively.
Option D) Mean = 66, median = 66, midrange = 66 is the correct answer.
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he graph of the function f(x) = –(x + 6)(x + 2) is shown below.
The domain of the function is all real numbers, the range of a function is y ≤ 4
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = –(x + 6)(x + 2)
If we plot this function on the coordinate plane, we will see it is a graph of a quadratic function.
Here the no other details are given.
But we can say:
The domain of the function is all real numbers.The range of a function is y ≤ 4The x-axis intercept will be at (-6, 0) and (-2, 0).Thus, the domain of the function is all real numbers, the range of a function is y ≤ 4
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Question 1: 5 pts
Bill wants to plant roses in his triangular plot. There will be 1 plant at a corner. Each row will have 6
additional plants. He wants the plot to have as many lows as possible with 150 rose plants. How many
rows will Bill's plot have?
O 7 rows
O 8 rows
O 6 rows
O 5 rows
The arrangement of the rose plants on the triangular plot is such that they
form a series or progression that is defined.
The number of rows on Bill's plot is; 8 rows
The given parameters for the triangular plot are;
Number of plants at the corner = 1 plant
Number of additional plants per row = 6 plants
Number of rose plants = 150 rose plants
The number of rows in the plot.
The difference between successive rows, d = 6
The number rose at the top vertex, a = 1
Therefore, the rose in the garden forms an arithmetic progression
The first term, a = 1
The common difference, d = 6
The number of rows Bill's plot will have, n is given by the sum of n in terms of
an arithmetic progression, Sn, is given as follows;
[tex]S_n=\frac{n}{2}[2a+(n-1)\times d[/tex]
When Sn = 150, we get;
[tex]150=\frac{n}{2} [2\times 1+(n-1)\times 6[/tex]
150 = 3·n² - 2·n
3·n² - 2·n - 150 = 0
Taking only the positive solution for n, we have;
[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:3\left(-150\right)}}{2\cdot \:3}[/tex]
[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \:2\sqrt{451}}{2\cdot \:3}[/tex]
[tex]n=\frac{1+\sqrt{451}}{3},\:n=\frac{1-\sqrt{451}}{3}[/tex]
The number of rows Bill's plot has, n ≈ 7.3965
Given that the 7th row is completed, an 8th row will be present on Bill's plot
The number of rows Bill's plot will have = 8 rows
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use mathematics to calculate [tex] Ilan \ ang \ asawa \ ni \ Sheryl [/tex]
[tex] 4x² - 12x + 9 = 0 [/tex]
[tex]~~~~~~~4x^2-12x+9=0\\\\\implies (2x)^2-2 \cdot 2x \cdot 3+3^2 = 0\\\\\implies (2x-3)^2 = 0\\\\\implies 2x -3 = 0\\\\\implies x =\dfrac 32[/tex]
Solve for X.
21
14
X
42
x = [?]
Enter the number that belongs in the green box.
Answer:
x = 28
Step-by-step explanation:
By Triangle Proportionality Theorem,
14/x = 21/42
14 * 42/21 = x
x = 28