Is the area of an equilateral triangle is 9 root 3 cm square then the semi perimeter of the triangle is?
The equilateral triangle has a 9 root 3 cm square area, and its semi-perimeter is 9 cm.
what is triangle ?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
given
area of equilateral triangle = [tex]9\sqrt{3}cm^{2}[/tex]
formula of area of equilateral triangle = [tex]\frac{\sqrt{3}a^{2} }{4} sq.units[/tex]
a = side of triangle
[tex]\frac{\sqrt{3}a^{2} }{4} sq.units[/tex] = [tex]9\sqrt{3}cm^{2}[/tex]
[tex]a^{2} = \frac{4* 9\sqrt{3} }{\sqrt{3} }[/tex]
[tex]a^{2} = 36\\ a = 6 cm[/tex]
since equilateral triangle all sides are equal
perimeter of triangle = 6 + 6 + 6
= 18cm
the semi perimeter of the triangle = 18 /2 = 9 cm
The equilateral triangle has a 9 root 3 cm square area, and its semi-perimeter is 9 cm.
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Jeanette took two tests. Find her z-score for each test. (Remember: The number of standard deviations between a score and the mean score is indicated by a z-score.) On which did she score better compared with others in her class
The z-score is compared as Test A : 3.25; Test B : 3.5; Test B.
What is the z-score to be compared?The Z-score is a statistical measure that describes the relationship of a value to the mean of a group of values. The Z-score is expressed in standard deviations from the mean. A Z-score of 0 indicates that the data point's score is the same as the mean score.Here given that,
Test A
Jeanette's score 90
Mean score 64
Standard deviation 8
Test B
Jeanette's score 95
Mean score 60
Standard deviation 10
The formula =
z = x - µ / σ
By substituting,
test A : z = (90 - 64) / 8 = 26 / 8 = 3.25
test B : z = (95 - 60) / 10 = 35/10 = 3.5
So Test A : 3.25; Test B : 3.5; Test B
The data of the question is attached below:
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Z-score in test A = 3.25, Z-score in test B = 3.5. She performed better in test B.
What is Z-score?Z-score represent the difference between a given value and standard deviation.
What is the Z-score of the above question?given, Jeanette scored 90 in the Test A
mean score of test A = 64
standard deviation = 8
we know, the Z-score is calculated by the following formula.
Z-score = (X - μ) /σ
where, σ denotes the standard deviation.
μ denotes the mean value
X is the actual value
Test A has Z- score = (actual score - mean score) / standard deviation
= (90 -64)/8
Z = 3.25
In the test B, she scored 95.
actual score = X = 95
mean score in test B = 60
standard deviation in test B = 10
hence, Z-score for test B = (X - μ)/ σ
= (95 -60)/ 10
Z-score = 3.5
Therefore, Jeanette scored better in her test B.
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In the sequence generated by the formula an=(-1)n+1(5)n , which of the following terms has the greatest value? Assume an > 0.
The term that have the greatest value is
aₙ₊₁₅How to find the term that will have the greatest valueThe knowledge of negative and positive number is necessary here.
numbers less than zero are negative while numbers greeter than zero are positive
Negative terms in an odd exponent remains negative hence less than zero in even exponent the negative changes to positive and becomes greater than zero
For the expression aₙ = (-1)ⁿ⁺¹(5)ⁿ the teem that determines whether the expression is greater that zero is (-1)ⁿ⁺¹. therefore
n + 1 must be even
n must be odd for n + 1 to be even hence the greatest number here is aₙ₊₁₅ a(n+15)
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NEED HELP ASAP
PLEASE REFER TO PICTURE
Radicals
How Do I Simplify
(3√5+√3)(√5+ √3)
Answer:
18 + 4√15
Step-by-step explanation:
(3√5+√3)(√5+ √3)
= 3√5 (√5+ √3) + √3 (√5+ √3)
= 3√5 √5 + 3√5 √3 + √3 (√5+ √3)
= 3√5 √5 + 3√5 √3 + √3 √5 + √3 √3
= 18 + 4√15
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An equilateral triangle has sides 12cm in length. Calculate the
perpendicular height of the triangle. (to the nearest mm)
Help please
Answer:
10 mm
Step-by-step explanation:
Draw an equilateral triangle. Label each side 12 mm.
Draw one altitude from one vertex perpendicular to the opposite side. Label the length of the altitude h.
The altitude divided the opposite side into two congruent segments, each one measuring 6 mm.
Now use the Pythagorean Theorem.
a² + b² = c²
(6 mm)² + h² = (12 mm)²
36 mm² + h² = 144 mm²
h² = 144 mm² - 36 mm²
h² = 108 mm²
h = 6√3 mm
h ≈ 10 mm
Answer: 3.5 cm or 35 mm
Step-by-step explanation:
12/3 =4 for each side of triangle
cutting the triangle in half, bottom side(a) 4 becomes 2
2^2 + b^2 = 4^2
4 + b^2 = 16
subtract 4 from both sides
b^2 = 12
b = 3.464 cm or 3.5 cm
convert 3.5 cm to 35 mm
The amount of money in a savings account is given by � = 580(1.03)" where t is the
time in years. After how many years will the account have reached $1000? Clearly
demonstrate your strategy for figuring it out.
An initial investment of $580, earning 3% annually-compounded interest, will take 18.429 years (investment period) to reach $1,000.
How the period is determined?The period for the investment to accumulate to $1,000 at 3% compounded interest is computed using an online finance calculator.
The parameters required include identifying the interest rate, compounding period, present investment, and future value., from the given formula:
A = 580(1.03)^t
$1,000 = 580(1.03)^18.429
Investment Period:I/Y (Interest per year) = 3%
PV (Present Value) = $580
PMT (Periodic Payment) = $0
FV (Future Value) = $-1000
Results:
N = 18.429
= 18 years and 5 months
Total Interest = $420
Thus, for the account to reach $1,000, it will take 18 years and 5 months.
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Question Completion:A = 580(1.03)^t
Function rules from equations
For a given input value q, the function f outputs a value r to satisfy the following equation.
11g 4= 3r6
Write a formula for f(g) in terms of q.
f(q) =
Stuck? Review related articles/videos or use a hint.
Report a problem
On solving the provided question, we can say that - 11g +4= 3r-6 the value of this equation is -10/3
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
here,
11g +4= 3r-6
g = 0
3r = -10
r = -10/3
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How many solutions exist for the given equation 3 x 10 6 3 x 12?
There are no solutions for the equation 3x106 3x12.
The equation 3x106 3x12 can be rearranged to 3x106 - 3x12 = 0. This is a linear equation and can be solved using the equation ax+b=0, where a is the coefficient of the variable and b is the constant.
In this case, a = 3 and b = -3x106. To solve this equation, we can use the quadratic formula, which states that x = -b ± √b2 - 4ac / 2a.
Substituting the values for a, b, and c yields x = -(-3x106) ± √(3x106)2 - 4(3)(-3x106)/2(3). Simplifying this yields x = 3x106 ± √9x1012 - 36x1012/6.
This simplifies to x = 3x106 ± √-27x1012/6. Since the square root of a negative number is not a real number, this equation has no real solutions. Therefore, there are no solutions for the equation 3x106 3x12.
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Define an exponential function, f(x), which passes through the points (0,125) and (3,8). Enter your answer in the form a*b^x
Answer:
Step-by-step explanation:
put (0, 125) in a*b^x, we get a = 125, then put (3,8) in 125*b^x, we get 125*b^3=8
b^3=8/125
b=2/5
then the answer is 125*(2/5)^x
3.) In a proportional relationship, y=2 when x = 8. Which of the following equations would describe this relationship? (1) y=1/4x (2) y = 4x (3) y=x-6 (4) y =1/2x-2
The correct option is y=1/4x.Because it holds the directly proportional relationships.
What is directly proportional?Two values x and y are said to be directly proportional to each other when the ratio x:y always remains the same. Directly proportional relationship between a quantity y and a quantity x that has a constant of proportionality k is represented by the equation y = kx.
How do you find if an equation is a proportional relationship?A relationship is proportional if each pair of data values are related in the same way by multiplying by a factor. You can recognize a proportional relationship by looking at data.When two quantities x and y are in direct proportion then they are written as x ∝ y. Symbol “∝” stands for 'is proportional to'.
NOW we find
according to directly proportion
y∝x
y=kx
y/x=k
2/8 =k
1/4 =k
Now we get
y = 1/4x
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The coordinate of A i -9 and the coordinate of C i 12. The ditance between A and B i 1/3 of AC. What i the coordinate of B?
The cordinate of point B is -2.
To find the coordinate of point B, we need to determine its distance from point A and then add that distance to the coordinate of point A. We are given that point B lies on a number line between points A and C, and that the distance between A and B is 1/3 of the distance between A and C.
First, we'll find the distance between points A and C. We know that the coordinate of A is -9 and the coordinate of C is 12. To find the distance between these two points, we simply subtract the coordinate of A from the coordinate of C. So, 12 - (-9) = 21. This tells us that the distance between points A and C is 21 units.
Next, we'll use this information to find the distance between points A and B. We know that this distance is 1/3 of the distance between A and C, so we'll multiply 21 (the distance between A and C) by 1/3. 21 * 1/3 = 7. This tells us that the distance between points A and B is 7 units.
Finally, we'll add this distance to the coordinate of point A to find the coordinate of point B. Since A is at -9, B is at -9 + 7 = -2. Therefore, the coordinate of B is -2.
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What is a binomial Class 8?
The Binomial Expression is defined as the type of algebraic expression that consists of exactly two terms .
What is Binomial Expression ?
The algebraic expression which contains exactly only two terms is termed as binomial expression . It is called a two term polynomial.
the binomial is also called a sum or a difference between two or more monomials. Binomial is the simplest form of a polynomial.
Some Examples of Binomial Expression are ⇒ [tex]4x^{2} +6y^{2}[/tex] , [tex]xy^{3} +xy[/tex] ;
Various Mathematical Operations can be performed on Binomial Expression such as Addition , Subtraction , Multiplication and Division .
and The Equation that contains one or more binomial expression is called as a Binomial Equation.
The given question is incomplete , the complete question is
What is a Binomial Expression ?
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Write the explicit formula for the sequence below:
The explicit formula for the sequence will be an = 10 + 5n. The correct option is C.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed as the arithmetic progression.
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Given series is 15,20,25,30,...,
The common difference is d = 20 - 15 = 5
First term is, 15
The formula can be written as,
an = a₁ + d(n-1)
an = 15 + 5 ( n - 1 )
an = 15 + 5n - 5
an = 10 + 5n
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Jeremiah completed a straight, 120 km drive in 1.5 hours. At one point during the drive, he saw that his speedometer read 105 km/h. Which of the following statements are accurate?
His average velocity was 105 km/h.
His instantaneous velocity was always 105 km/h.
His instantaneous velocity was always 80 km/h.
At one point, his instantaneous velocity was 105 km/h.
His average velocity was 80 km/h.
Jeremiah average velocity during the drive was 80 km/h while the instantaneous velocity at one point was 105 km/h
What is an equation?An equation is used to show the relationship between numbers and variables.
Average velocity is the ratio of total distance travelled to total time taken. Instantaneous velocity is the velocity at a particular point in time.
Jeremiah completed a straight, 120 km drive in 1.5 hours, hence:
Average velocity = total distance / total time
Average velocity = 120 km / 1.5 hours = 80 km/h
At one point during the drive, he saw that his speedometer read 105 km/h, hence:
Instantaneous velocity = 105 km/h
The average velocity is 80 km/h while the instantaneous velocity is 105 km/h
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An object is moving at a speed of 11 yards every 6 months. Express this speed in centimeters per hour.
Speed of the given object in centimeters per hour
= 0.23 cm / hour
What is unit conversion?Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters.
Like 1 yard = 91.44 cm
1 month = 730 hrs.
Distance covered by the object = 11 yards
Distance covered in cm = 11 × 91.44 = 1005.84 cm
Time taken to cover 11 yards = 6 months
Time taken in hours = 6 × 730 = 4380 hrs.
Speed of the object = distance covered by the object / Time taken
Speed of the object = 1005.84/4380 = 0.2296 ≈ 0.23 cm per hour
Hence, in centimeters per hour,
the speed of the object is 0.23 cm / hour.
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Based on the following calculator output, determine the population standard
deviation of the dataset, rounding to the nearest 100th if necessary.
1-Var-Stats
-
86.7142857143
Σæ = 607
Σχ2 = 59459
Sx= 33.72296095
o2 = 31.2213950714
n=7
minX = 52
Q₁ = 55
Med=87
Q3 = 110
maxX = 138
Therefore , the solution of the given problem of standard deviation comes out to be 67.15=σx .
Define standard deviation.It tells about how dispersed the data is is indicated by the standard deviation. It expresses the deviation of each observed variable from the mean. Any distribution will have roughly 95% of its values within two standard deviations of the mean.
Here,
We know population SD= Σ(xi-mu)2/n where mu is the population mean and n is the number of observation.
Here
we have n=7 and mu can be taken as x- =310.142
Standard deviation = SD=Σ(xi-mu)2/n
=>(Σxi2/n)-x-2
=>(704883/7)-(310.14)2=67.15=σx
Therefore , the solution of the given problem of standard deviation comes out to be 67.15=σx .
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HELP ASAP!!!!
A person is standing 19 feet from the base of a tree and there is a bird's nest in the tree 10 feet above the groundWhat is the angle off elevation from the person to the bird's nest? Round to the nearest tenth of a degree
Answer:
do your own work don't ask any question
(m-12)divided by 44=32
Answer: (m-12)
Step-by-step explanation:
(m-12)divided by 44=32
Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently.
Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300.
PLS HELP ME IM ABT TO CRY!!!! 100 PTS
Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn.
Salesman C does not earn any commission. His weekly salary is $900.
If Salesman A has exactly ____ sales, he will reach his maximum weekly commission.
Answer:
Sales = 20
Step-by-step explanation:
Simply make the equation "1300 = 65s" to solve the problem
1300 = 65s
Divide both sides by 65.
1300/65 = 65s/65
Divide 1300 by 65 to get 20.
20=s
Swap sides so that all variable terms are on the left-hand side.
s=20
Which set of ordered pairs (x, y) could represent a linear function?
A = {(-2,5), (0, 3), (2, 1), (5,-2)}
B = {(2,9), (4,5), (5,2), (6,0)}
C = {(-3,-8), (0,-4), (3,-1), (6,2)}
D = {(-2,3), (0, -1), (2,-4), (4,-7)}
Can you help me with this
The graph of the given equation y=2x+1 is attached below.
How to find the function which was used to make graph?There are many tools we can use to find the information of the relation which was used to form the graph.
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
For example, when the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
The equation y=2x+1 gives the following information:
The slope is 2
The line intercepts is 1 on the y axis
First, we would put a point or a dot on (0,1) on the y axis. Then start making 2 points above and below my original point. IT would do this by using the slope 2/1.
By using my slope we know that (1,3) and (-1,-1).
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Simplify the expression.
[tex](1+\frac{x}{y} )(\frac{4y^{2} }{x^{2} -y^{2} } )[/tex]
Answer:
4y / x-y
Step-by-step explanation:
First change 1 to y/y. This allows us to rewrite the first term as a single fraction.
We can also factor the denominator of the second term.
x^2 - y^2 factors into (x - y)(x + y)
The y cancels and also the term x+y cancels. See image.
Each square inch of your body has about 6. 5 × 10^2 pores. Suppose the top of your foot has an area of about 2. 0 × 10^1 in. ^2. About how many pores are on the top of your foot?
The number of pores that are on the top of your foot is approximately 13,000 pores on the top of your foot.
To find the number of pores on the top of your foot, we can multiply the area of the top of your foot in square inches by the number of pores per square inch.
The area of the top of your foot is 2.0 x 10^1 in^2 and each square inch of your body has about 6.5 x 10^2 pores. So, the number of pores on the top of your foot can be calculated as:
2.0 x 10^1 in^2 * 6.5 x 10^2 pores/in^2 = 130 x 10^2 pores = 13000 pores
So, there are approximately 13,000 pores on the top of your foot.
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y-int coordinates of y=x^2-5x+6, please explain
The y intercepts of the quadratic equation y = x² - 5x + 6 is given by (0 , 6)
and the x intercepts are ( 3 , 0 ) and ( 2, 0 )
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
y = x² - 5x + 6 be equation (1)
On simplifying the equation , we get
y = x² - 2x - 3x + 6
Taking the common factors of the equation , we get
y = x ( x - 2 ) - 3 ( x - 2 )
On factorizing the equation , we get
y = ( x - 3 ) ( x - 2 )
To find the y intercepts , substitute the value of x = 0 , we get
y = ( 0 - 3 ) ( 0 - 2 )
y = ( -3 ) ( -2 )
So , y = 6
Hence , the y intercepts of the equation is ( 0 , 6 )
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Is Y =- 3 vertical or horizontal?
According to the following graph, y = -3 makes the horizontal line on graph.
The term graph in math is known as a pictorial representation or a diagram that represents data or values in an organized manner and the points on the graph often represent the relationship between two or more things.
Here we have given the expression y = -3.
Now, we have to plot these on the graph, then we get the graph like the following.
While looking into the given graph, we have identified that y = -3 is a horizontal line, and that passes through y-axis, here at a distance of 3 units on the bottom of the origin and is parallel to x-axis.
Therefore, the expression y = -3 makes the horizontal line which crosses the y -axis at (0,−3).
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The game starts at 1830. They play four eight minute quarters, and half-time lasts for thirty minutes. What time should you tell your parents to pick you up? Give your answer in both 12 and 24 hour clock notation
Therefore , the solution to the given problem of time comes out to be the time to pick up by your parents is 7:32.
What is time?the idea that time was the fourth dimension and that space and time were therefore inseparably connected. According to his general theory of relativity (opens in new tab), the mass and momentum of adjacent matter influence how much space-time enlarges and compresses.
Here,
Given : The game starts at 18:30
Thus,
They play for eight minutes quarters and half time last for 30 minutes.
So,
To find the time to pick up by your parents:
=> 8*4 + 30
=> 32 + 30
=> 62
Thus time after 62 minutes is 7:32
Therefore , the solution to the given problem of time comes out to be the time to pick up by your parents is 7:32.
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the chicken coup at the petting farm is 10 feet by 14 feet. the farm would like to double the current area by adding the same amount, x, to the length and width.
Answer:
22 by 26
Step-by-step explanation:
10+10+14+14=48 (the perimeter)
48×2=96
10+12=22
14+12=26
22+22+26+26=96
Solve this problem?
step by step
The value of x is 9.32 after solving using the Pythagoras theorem.
What is Pythagoras 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, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
The diagram has 4 corners namely - A, B, C and D.
Draw a perpendicular through B.
The intersecting point at line AD is named as E.
It can be seen in figure that EDCB is a rectangle and falls under the category of parallelogram.
So, angle ADC = angle DEB = angle AEB = 90° .
Now, side BC = ED = 5.
So, side AE = 18 - 5 = 13.
Here, it can be seen that triangle ABE is a right-angled triangle.
So, to get the measurement of side BE, apply the Pythagoras theorem -
c^2 = a^2 + b^2
Where, a is perpendicular, b is base and c is hypotenuse.
So, according to the diagram -
(16)^2 = (13)^2 - (BE)^2
(BE)^2 = (16)^2 - (13)^2
(BE)^2 = 256 - 169
(BE)^2 = [tex]\sqrt{87}[/tex]
(BE)^2 = 9.32
Now, as EDCB is a rectangle so, side BE = side CD.
Therefore, the value for side CD = x = 9.32.
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At Clara's Beading Boutique, 9 out of the 18 beads on clearance are plastic. What percentage of beads on clearance are plastic?
The percentage of beads on clearance are plastic is 50%.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
So the percentage actually means a part per 100.
Total number of beads = 18
Number of beads which are plastic on clearance = 9
Percentage of beads which are plastic on clearance = (9 / 18) × 100
= (1/2) × 100
= 0.5 × 100
= 50%
Hence 50% of beads on clearance are plastic.
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