Therefore , the solution of the given problem of equation comes out to be the error range for x is [1250, 1350].
Explain the equation.A mathematical equation is a formula that uses the equal sign (=) to connect two statements and express equality. A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The equal sign is a crucial part of mathematical formulas, especially equations. Algebra is frequently utilized in equations. Algebra is used in mathematics when it is difficult to determine a precise quantity.
Here,
Given: Some material has a length of 8.3 meters
We have provided a number, x, that has been rounded to two significant numbers with the supplied error.
Next, we must determine the x error interval.
It is necessary for x to have a value that is both bigger than or equal to 1250 and less than or equal to 1300.
i.e.,1250 ≤ x ≤ 1300 ---(1)
2. The value of x is more than 1300 but not equal to 1350.
1300 ≤ x ≤ 1350--- (2)
When (1) and (2) are combined, we obtain
1250≤ x ≤ 1350
As a result, 1350 is not part of the error-interval for x.
As a result, the interval notation is [1250, 1350].
As a result, the error range for x is [1250, 1350].
Therefore , the solution of the given problem of equation comes out to be the error range for x is [1250, 1350].
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An equilateral triangle with side lengths of 8.7 centimeters is shown. An apothem has a length of a and the radius has a length of 5 centimeters. The apothem and radius form a triangle with a base length of b. Which statements about finding the area of the equilateral triangle are true
The options (a),(b) and (d) are true regarding the apothem of equilateral triangle.
What is an apothem of a polygon?
A line segment from a regular polygon's centre to one of its sides is known as the apothem.
The given options are the following:
a)The apothem can be found using the Pythagorean theorem.
b)The apothem can be found using the tangent ratio.
c)The perimeter of the equilateral triangle is 15 cm.
d)The length of the apothem is approximately 2. 5 cm.
e)The area of the equilateral triangle is approximately 65 cm².
Now we will see if each option is true or not
a) From below figure,
b = 8.7 / 2 = 4.35 cm
From right angled triangle ΔABD,
Using Pythagorus Theorem,
a² + b² = 5²
a² + 4.35² = 5²
a = [tex]\sqrt{5^{2} - 4.35^{2} }[/tex] = 2.5 cm
Apothem can be found using Pythagorus Theorem.
b) From the figure, the radius divide the angle 60° of equilateral triangle to two 30° angles.
So from ΔABD,
tan 30° = a / 4.35
0.577 = a / 4.35
a = 2.5 cm
The apothem can be found using tangent ratio.
c) Perimeter of given equilateral triangle = 3 × side length
= 3 × 8.7 = 26.1 cm
This option is false.
d) From options (a) and (b) we found that length of apothem a = 2.5 cm
Therefore this option is true.
e) The area of given equilateral triangle = [tex]\frac{\sqrt{3} }{4} } * side^{2}[/tex] = [tex]\frac{\sqrt{3} }{4} * 8.7^{2}[/tex]
= 32.8 cm²
Therefore this option is false.
Therefore options (a),(b) and (d) are true regarding the apothem of equilateral triangle.
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The area of a sector of a circle is
18 pie cm². The radius of the circle is
6 cm. The angle in the sector is
Answer:
The angle in the sector is 180°.
Because the area of circle is 36 pie cm². So the angle is the half of 360°.
[tex]\boxed{\begin{array}{l} \\ \sf\huge{ \quad \underline{Answer} } \\ \\ \underline{ \underline\textsf{ Area of sector is given by : }} \\ \\ \dashrightarrow \sf{ A = \dfrac{ \theta}{360 \degree} \times \pi {r}^{2} } \\ \\ \dashrightarrow\sf{18 \pi = \dfrac{ \theta}{360 \degree} \times \pi {(6)}^{2} } \\ \\ \dashrightarrow \dfrac{ \theta}{360 \degree} = \dfrac{18 \pi}{ \pi(36)} \\ \\ \dashrightarrow \theta = 360 \degree \times \dfrac{1}{2} \\ \\ \dashrightarrow\theta = 180 \degree \\ \\ \end{array} } [/tex]
A karate studio offers a 6 week session for
$175. How much would you expect to pay for
a 9 week session?
Answer:
262.5 $
Step-by-step explanation:
A karate studio offers a 6 week session for
$175. How much would you expect to pay for
a 9 week session?
find the cost of 1 session175 : 6 = 29.16
multiply by the number of weeks29.16 x 9 = 262.5
or
175 : 6 = x : 9
x = 175 x 9 : 6
x = 262.5
Two sides of a triangle have lengths 15 and 20. The length of the third side can be any number greater than A and less than
The third side of the triangle will be less than 35.
What is a triangle?A polygon with three angles, sides and angles is called a triangle.
Given that, Two sides of a triangle have lengths 15 and 20. The length of the third side can be any number greater than A and less than
We know that, triangle inequality theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.
Therefore, length of the third side < 15+20 < 35
Hence, the third side of the triangle will be less than 35.
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What is 42a - 16 ?????
Answer:
2 (21a−8)
Step-by-step explanation:
Answer:
2(21a - 8)
Step-by-step explanation:
42a - 16
The gcf of 42, 16 is 2
=> 2(21a-8)
The population of a city is 5876000 in 1980. By 1990 it increased by 10.8%. In the 1990s it increased a further 4.7%. What was the population in the year 2000?
Answer: I think it's 6816606.576
Step-by-step explanation: Hope this helps?
What are equivalents in a reaction?
In a reaction the amount f a substance which react with another substance is known as it's equivalent.
The definition of equivalent is "weight in grams of a substance that displaces or combines with one gram of hydrogen."
It is an important part of chemistry and comes under stoichiometry. In every reaction there is a reactant which forms the suitable product and the amount of that is calculated using stoichiometry.
The mole ratio is a typical sort of stoichiometric relationship that compares the amounts in moles of any two components in a chemical process.
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How much of a radioactive kind of barium will be left after 39 days if you start with 52,256 grams and the half-life is 13 days?
Answer:
Step-by-step explanation:
Answer:
6,532
Step-by-step explanation:
ixl
What does r equal?
Answer: r = ________
If the area of Square 3 is 80cm and the area of square 2 is 100cm, what is the area of square1
The area of square 1 is 180 sq cm
What is the area of square?The area of a square is calculated with the help of the formula: Area = s × s, where, 's' is one side of the square. Since the area of a square is a two-dimensional quantity, it is always expressed in square units
Square 1 formed on hypotenuse of the triangle, squares 2 and 3 are formed on the perpendicular legs of the triangle. Thus, by Pythagoras Theorem, A(square 1) will be equal to the sum of the areas of (square 2) and (square 3).
Area of square 1 = Area of square 2 + Area of square 3
Area of square 1 = 100 + 80
Area of square 1 = 180cm^2
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The UTM coordinates of Enchanted Rock State Natural Area in Fredericksburg, Texas, are 517266.07 E, 3374884.58 N, Zone 14R. How far is it from the zone's central meridian
Enchanted Rock State Natural Area is located at latitude 30.506130 and longitude -98.820064. The geographic coordinates of Enchanted Rock State Natural Area in Fredericksburg, United States, are 30° 30' 22.068" N and 98° 49' 12.2304" W. Enchanted Rock State Natural Area falls under the Mysterious Sites category.
Where can measurements be made using the WGS84 datum?The standard datum used by default for GPS devices used for commercial and recreational purposes is WGS84. GPS users are advised to always verify the datum of the maps they are utilising.
What datum does US Navstar GPS employ?WGS 84, also known as the datum, is now in use by US forces.
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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
g Suppose that the retail price of a product has a normal distribution with a mean of $37 and a standard deviation of $20. Approximately, what is the probability that the price grows beyond double the mean
Retail price of the product will be double its mean will have a prbability of 0.0401.
What is Normal Distribution ?An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.
A probability distribution that is symmetric around the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.
The value of the product considering = $37*2 = $74(x)
Mean = $37
Standard Deviation (SD)= $20
here z= [tex]\frac{x - mean}{SD}[/tex] = [tex]\frac{74 - 37}{20} = \frac{37}{20} = 1.75[/tex]
P(z>1.75) = 1 - [tex]\phi(1.75)[/tex] = 1 - .9599 = 0.0401
Retail price of the product will be double its mean will have a prbability of 0.0401.
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How do parallel algorithms differ from sequential?
The capacity to complete complex tasks quickly enough to make them useful is the main benefit of choosing a parallel method over a sequential one.
Differences between Sequential and Parallel ComputingSequential Computing: One instruction is delivered at a specific time, and the subsequent instruction must wait for the first instruction to complete before it can be executed. This is known as sequential computing. Because all the instructions are carried out in order, it is often referred to as a conventional computing technique. It has a single CPU that performs poorly and has a heavy workload. The biggest drawback of employing this computing is that it requires more time because just one instruction is being processed at a time.
Parallel Computing: A computing method known as parallel computing involves running numerous calculations or processes simultaneously in parallel. Parallel computing is a kind of computing in which multiple processes can run at once.
Due to the simultaneous execution of the operations, time is saved. It resolves more complex issues. There are many processors with high performance and little work being put on each of them.
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PLEASE HELP 10 POINTS
Answer:
9.75
Step-by-step explanation:
3/4 |1/3x+2| < 6
you can turn the < into a =
then subtract 3/4 from 6 which leaves you with 5.25. And since you know 2 will always be positive because it's in an absolute value bracket 5.25-2=3.25. Which leaves you with
|1/3x| = 3.25
then do 3.25/(1/3) which leaves you with 9.75
:)
A colony of 100,000 bacteria doubles every 31 minutes. To the nearest whole number, what will the population be 124 minutes from now?
Answer:
Below
Step-by-step explanation:
How many times will the colony double ? 124 / 31 = 4 times
2^4 * 100 000 = 1 600 000
Write f(x)=1/2x^2+1/2x-10 in intercept form. Then find the x-intercepts, the vertex, and the axis of symmetry of the graph of f.
f(x)=1/2x^2+1/2x-10 in intercept form is (1/2)(x+4)(x-3)
The x-intercepts are x=-5 and x=4.
The vertex of symmetry is (-1/2, -81/8).
The axis of symmetry is: x = -1/2
What is intercepts?A vertical intercept is a point where the graph of a function or relation meets the y-axis of the coordinate system in analytical geometry,
f(x) = 1/2x^2+1/2x-10
= (1/2)(x² + x - 20)
= (1/2) (x² + 5x - 4x - 20)
= (1/2) { x(x+5) -4(x+5)
= (1/2) (x+5)(x-4)
Hence, Intercept form: f(x) =(1/2) (x+5)(x-4)
The x-intercepts will be where the factors = 0
x + 5 = 0 ⇒x = -5
x - 4 = 0 ⇒ x = 4
Therefore, the x-intercepts are x=-5 and x=4
To find the axis of symmetry, take the average of intercepts (to find the center of parabola)
(-5 + 4)/2 = -1/2
Axis of symmetry ⇒ x = -1/2
To find the vertex, put the axis of symmetry into the equation
f(x) = (1/2)(x + 5)(x - 4) = (1/2)(-1/2 + 5)(-1/2 - 4) = (1/2)(9/2)(-9/2) = -81/8
vertex is (-1/2, -81/8)
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The x-intercepts, vertex, and axis of symmetry will be - 5 & 4, (-0.50, -10.125), and x = - 1/2, respectively.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation is given below.
f(x) = (1/2)x² + (1/2)x - 10
2f(x) = x² + x - 20
2f(x) = x² + x + 1/4 - 1/4 - 20
2f(x) = (x + 1/2)² - 81/4
f(x) = 1/2 (x + 0.50)² - 10.125
The x-intercepts are given as,
f(x) = 0
1/2 (x + 0.50)² - 10.125 = 0
(x + 0.50)² = 20.25
x + 0.50 = ± 4.50
x = - 0.50 ± 4.50
x = - 0.50 - 4.50, - 0.50 + 4.50
x = - 5, 4
The equation of the axis of symmetry is given as,
x + 1/2 = 0
x = - 1/2
The graph is attached below.
The x-intercepts, vertex, and axis of symmetry will be - 5 & 4, (-0.50, -10.125), and x = - 1/2, respectively.
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Solve the following system of equations graphically on the set of axes below.
y = x + 8
y = -1/2x+5
Plot two lines by clicking the graph. Click a line to delete it.
By graphing both equations on the same axis and findin where do they intercept, we willsee that the solution is (-2, 6).
How to solve the system of equations?Here we have the following system of equations:
y = x + 8
y = -(1/2)x+5
And we want to solve it graphically.
To solve it in that way, we just need to graph both equations on the same coordinate axis and find the ponit where the graphs intercept, that point will be the solution for the system.
The graph of the system of equations can be seen in the image below:
There, we can see that the lines intercept at the point (-2, 6), so that is the solution of our system.
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Gaya buys 2 oranges and 1 cauliflower she pays £2.00
Esteben buys 4 oranges and 1 cauliflower he pays £2.90
Work out the price of one orange
Answer:
Step-by-step explanation:6
vivian and her dad drive from Boston to niagara falls it takes them 9 hours to drive 495 miles what is their driving rate in miles per hour.
Answer:
55 miles per hour
Step-by-step explanation:
The equation is:
R = d / s
We know
d = 495 miles
s = 9 hours
Let's solve
R = 495 / 9
R = 55 miles per hour
So, their driving rate is 55 miles per hour
On a certain hot summer day, 481 people used the public swimming pool. The daily prices are $1. 25 for children and $2. 25 for adults. Receipts for admission totaled $865. 25. How many children and how many adults swam at the public pool that day?
There were 481 people that utilized the public swimming pool that day, including 217 children and 264 adults.
what is equation ?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter.
given
The number of children =X=217
The number of adults=264
Let say the number of children are denoted by X
Then the number of adults are (481-X)
Price for children =1.25X
Price for adults=2.25(481-X)
Price for children +Price for adults=865.25
1.25X+2.25(481-X)=865.25
Solving for X:
1.25X+1082.25-2.25X=865.25
-X=865.25-1082.25
-X=-217
X=217
The number of children =X=217
The number of adults=(481-X)
The number of adults=(481-217)
The number of adults=264
There were 481 people that utilized the public swimming pool that day, including 217 children and 264 adults.
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What if Aya and Sakura could only afford a monthly payment of $1800?
What would be the maximum mortgage amount they could afford to borrow from the bank, if all the other conditions were the same?
What is the total amount that would be paid to the lender over 25 years?
a) The maximum mortgage amount they could afford to borrow from the bank, if all the other conditions were the same = $369,181.93.
b) The total amount that would be paid to the lender over 25 years = $540000
To find the maximum mortgage amount they could afford to borrow if they could only pay $1800.
Here, future value = 0
number of periods = 25 years
= 25 × 12 months per year
= 300
payment amount = -1800 dollars
interest rate = 4.25% per year
= 0.3542% per month
the maximum mortgage amount they could afford = $369,181.93.
And the total payments would be equal to 300 × 1800 = 540000
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The complete question is:
Aya and Harumi would like to buy a house and their dream house costs $500,000. They have $50,000 saved up for a down payment but would still need to take out a mortgage loan for the remaining $450,000 and they're not sure whether they could afford the monthly loan payments. The bank has offered them an interest rate of 4.25%, compounded monthly.
What if Aya and Harumi could only afford a monthly payment of $2,000?
What would be the maximum mortgage amount they could afford to borrow from the bank if all the other conditions were the same?
What is the total amount that would be paid to the lender over 25 years?
How do you solve a math problem step by step?
Reading a math word problem through to the end will help you comprehend what you need to do in order to solve it. After reading it, you may determine which components of the issue that need to be resolved are the most important and which are not.
There are few basic steps to be followed while solving any mathematics problem:
1. Read and understand the problem.
2. Identify what is given and what is needed to solve the problem.
3. Choose an appropriate strategy to solve the problem.
4. Carry out the strategy.
5. Check your answer to make sure it is correct.
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PLEASE HELP ME I REALLY NEED IT!!!!!!!!
Answer: for A it is: 3 and 4 represent the number values for X and Y.
Step-by-step explanation:
Sorry, but you B and C you did not give enough information
write an equation that represents the relationship between x and y shown in the table
An equation that represents the relationship between x and y shown in the table is y = 1.5x.
How to write an equation?In order to write an equation that represents the relationship between x and y shown in the table, we would have to find the slope from the table and then write the required equation based on the data points by using the point-slope form.
Mathematically, the point-slope form of a line is given by this mathematical equation:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.By substituting the given parameters into the point-slope formula, an equation for the data points contained in this table is given by;
y - y₁ = m(x - x₁)
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 21 = (96 - 21)/(64 - 14)(x - 14)
y - 21 = 75/50(x - 14)
y - 21 = 1.5(x - 14)
y = 1.5x - 21 + 21
y = 1.5x
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A triangle has sides with lengths that are
consecutive even integers. The perimeter of the
triangle is 72 centimeters. Sketch the triangle
and label the lengths of the sides, using the
variable. Find the length of the largest side.
Show work
The largest side of the length is 26cm.
Now, According to the question:
Three consecutive even numbers can be expressed in terms of n. If n is an even number then,
(n -2), (n), (n + 2)
are three consecutive even numbers.
Therefore,
(n -2)+ (n)+ (n + 2) = 72cm.
We can simplify so...
3n + 2 - 2 = 72 cm.
3n + 0 = 72 cm.
3n = 72cm.
Divide both sides by 3 to solve for n
n = 24 cm.
24 is an even integer. Input 24 into the original equation.
(n -2)+ (n)+ (n + 2) = 72cm.
(24 - 2) + 24 + (24 + 2) = 72cm
22 + 24 + 26 = 72
72 = 72
Hence, The largest side of the length is 26cm.
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Identify an irrational number between 7 and 8
BRAINLIEST IF U MAKE UR OWN AND ORIGINAL ANSWER!
Question 2(Multiple Choice Worth 1 points)
(01.06 MC)
An equation is shown:
−np − 6 = 3(c − 5)
Which of the following solves for n?
n = the quantity 3 times c minus 21 all over negative p
n = the quantity 3 times c minus 9 all over negative p
n = the quantity 3 times c minus 21 all over p
n = the quantity 3 times c minus 9 all over p
Answer:
Option 2
Step-by-step explanation:
Hello!
We can solve the equation for n by isolating the variable.
Solve for n:-np - 6 = 3(c - 5) Add 6 to both sides-np = 3(c - 5) + 6 Divide both sides by p-n = [tex]\frac{3(c - 5) + 6}{p}[/tex] Expand the parenthesis-n = [tex]\frac{3c - 15 + 6}{p}[/tex] Combine Like terms-n = [tex]\frac{3c - 9}{p}[/tex] Divide both sides by -1n = [tex]-\frac{3c - 9}{p}[/tex]The answer would be the second option: "n = the quantity 3 times c minus 9 all over negative p."
What is the formula for vector direction?
The formula for vector direction is: Direction = arctan (y/x) , Where x is the x component of the vector and y is the y component of the vector.
1. Find the x and y components of the vector
2. Divide the y component by the x component
3. Calculate the arctan (inverse tangent) of the result
4. The result is the direction of the vector in radians (or degrees if you prefer).
If you want to convert the result from radians to degrees, you can use the following formula:
(in degrees) = arctan (y/x) * (180/π)
Where π (pi) is approximately equal to 3.14.
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△ABC, BD &CE are the altitude of the ide AC & AB and BD=CE. Prove that △BCD≅△CBE
We have proved that △BCD≅△CBE.
What are congruent triangles?
Congruent triangles are triangles that have the same size and shape. They have the same angles and corresponding side lengths.
By the RHS congruence condition if the hypotenuse and one side of one right triangle are equal to the hypotenuse and one side of another right triangle then both right triangles are congruent.
It is given that BD=CE and BC is the hypotenuse of small triangles CEB and BDC
So, In right triangles BCD and CBE
BC=CB=common side⋯⋯[hypotenuse]
And BD=CE=given⋯⋯[sides of right triangles]
So, by RHS condition
△BCD≅△CBE.
Hence, we have proved that △BCD≅△CBE.
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We have proved that △BCD≅△CBE.
What are congruent triangles?
Congruent triangles are triangles that have the same size and shape. They have the same angles and corresponding side lengths.
By the RHS congruence condition if the hypotenuse and one side of one right triangle are equal to the hypotenuse and one side of another right triangle then both right triangles are congruent.
It is given that BD=CE and BC is the hypotenuse of small triangles CEB and BDC
So, In right triangles BCD and CBE
BC=CB=common side⋯⋯[hypotenuse]
And BD=CE=given⋯⋯[sides of right triangles]
So, by RHS condition
△BCD≅△CBE.
Hence, we have proved that △BCD≅△CBE.
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