Equations can be used to find the number of pencils (x) and pens (y) she bought are X+1.5Y = 21, and X+Y = 18
The correct option is C.
What is liner equation?One or two variables make up a linear equation. Neither the numerator nor the denominator of a fraction can be a variable in a linear equation raised to a power higher than 1. The lines that connect all the points on a coordinate grid when you identify the values that make a linear equation true are congruent.
According to the given information:Let x stand for the number of pencils Stella purchased, and y for the number of pens Stella purchased.
Since Stella purchased a total of 18 things, the quantity of pencils and pens purchased must equal 18 or one of the following:
x + y = 18
We also know she spent $21, that a pencil costs $1, and that a pen costs $1.50. Therefore,
1x + 1.5y = 21
Thus, the set of equations that may be utilized to determine the quantity of pencils (x) and pens (y) that she purchased is as follows:
X+1.5Y = 21, and X+Y = 18
equations can be used to find the number of pencils (x) and pens (y) she bought are X+1.5Y = 21, and X+Y = 18
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Walter used the iterative process to determine that √13 is between 3.61 and 3.62.Analyze Walter’s estimation. Is he correct? If not, what was his mistake?
A-Yes, Walter is correct.
B-No, 3.612 is less than 13.
C-No, both 3.612 and 3.622 are greater than 13.
D-No, both 3.612 and 3.622 are less than 13.
i need the right answer
The correct option is C no, both 3.61^2 and 3,62^2 are greater than 13.
Is he correct? If not, what was his mistake?To check this, we can just square both of the bounds that he found, and see if it makes sense.
Walter says hat:
3.61 < √13 < 3.62
Then we must have:
(3.61)^2 < 13 < (3.62)^2
The lower bound is 3.61, if we square it we get:
3.61*3.61 = (3 + 0.61)*(3 + 0.61) = 9 + 6*0.61 + 0.61*0.61 = 13.0321
Now, this is larger than 13, so the above inequality is false, which means that Walter is incorrect, because both 3.61 and 3.62 are larger than √13 , then the correct option is C.
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Answer:
c
Step-by-step explanation:
c
What is the area of parallegram ABCD
Answer:
c
Step-by-step explanation:
if you take the triangle off of the left side and attach it to the left side then you would have a 6 by 4 rectangle that has an area of 24 units squared.
Please help!!!!!!!!!!!!!!!!
The data which is most likely to be normally distributed is total points scored by a basketball team the whole season.
Given five statements:
1)Daily temperature highs for winter in 25 US cities.
2)Daily stock reports from the stock market.
3) Height of flowers.
4) Total points scored by a basketball team the whole season.
We are required to choose a statement whose data is most likely to be normally distributed.
A normal distribution is an arrangement of data set in which most values cluster in the middle of the range and the rest off symmetrically towards either extreme.It is basically a probability distribution that is most likely symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. Its graph is a bell curve.
So,the statement which is likely to be normally distributed is total points scored by a basketball team the whole season.
Hence the data which is most likely to be normally distributed is total points scored by a basketball team the whole season.
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Which if the following rational functions is graphed below?
A.F(x)=1/x+4
B.F(x)=1/4x
C.F(x)=1/x-4
D.F(x)=4/x
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Take note that there is a vertical asymptote at x = -4. This means that our function has the form:
▪ [tex]\longrightarrow \sf{F (x)=\dfrac{A}{x + 4} }[/tex]
[tex]\leadsto[/tex] By comparing it with the given options, the correct option is A.
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
◉ [tex] \bm{A. \: \: F(x)= \dfrac{1}{x + 4} }[/tex]
5. Betty claims the solution to the equation 4x - 5(x - 5) = 7x + 13 is x = 1.5. She shows her steps below to
justify her solution.
Given
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
4x5(x-5) = 7x + 13
4x5x + 25 = 7x + 13
-x+ 25 = 7x + 13
25 = 8x + 13
12 = 8x
1.5 = x
Select the all correct justifications for the given steps.
Step 1: Distributive Property
Step 2: Combining Like Terms
Step 3: Addition Property of Equality
Step 4: Subtraction Property of Equality
Step 5: Associative Property of Equality
Answer:
See attached image
Step-by-step explanation:
Every step holds except for step 5
In mathematics, it deals with numbers of operations according to the statements.
Here,
Step 1 is the result of the distribution of -5 while opening the parenthesis, So, Step 1 holds the distributive property.
Step 2, states adding like terms across each side, so combining as terms hold,
Step 3, Addition over the equal sign. So it also holds
Step 4, subtraction of 12 over the equal sign. So subtraction of the terms also holds.
Step 5, does not hold because the number 12 gets divided by 8 it is not an associative property.
Thus, Every step holds except for step 5.
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You are wearing a pair of cargo pants with six pockets. you put $10 on one of those pockets, but you cannot remember which one after checking two pockets without success, what is the possibility that the money will be in the next park view check?
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
According to the given information ,there still 4 pockets to check .
Then
the possibility that the money will be in the next pocket :
[tex]=\frac{1}{4}[/tex]
Answer: Answer above me is correct
what is the value of sin30°+cos60°
The answer is 1.
Here, we need to know the trigonometric values of sin 30° and cos 60°, which are :
sin 30° = 0.5cos 60° = 0.5Hence, sin 30° and cos 60° :
0.5 + 0.51Part 1 The main tank has a radius of 95 feet. What is the volume of the
quarter-sphere sized tank? Round your answer to the nearest whole number. You must explain
your answer using words, and you must show all work and calculations to receive credit.
Holding Tank Calculations: The holding tanks are congruent in size, and both are in the shape
of a cylinder that has been cut in half vertically. The bottom of the tank is a curved surface.
What is the volume of both tanks if the radius of tank #1 is 15 feet and the height of tank #2 is
120 feet? You must explain your answer using words, and you must show all work and
calculations to receive credit.
The volume of the quarter-sized tank is 14034 cubic feet and the volume of the holding tanks is 84857 cubic feet
The volume of the quarter-sized tankThe radius is given as;
r = 95 feet
For a quarter-sized tank, we divide the radius by 4.
So, we have
r = 95/4 feet
r = 23.75 feet
The volume is
V = 1/3 πr³
This gives
V = 1/3 * 22/7 * 23.75³
Evaluate
V = 14034
Hence, the volume of the quarter-sized tank is 14034 cubic feet
The volume of the holding tanksHere, we have
Radius, r = 15 feet
Height, h = 120 feet
The volume is
V = πr²h
This gives
V = 22/7 * 15² * 120
Evaluate
V = 84857
Hence, the volume of the holding tanks is 84857 cubic feet
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What is a simplified representation or abstraction of reality?
a) metric
b) project
c) consolidation
d) model
Answer:
That would be a model.
Step-by-step explanation:
Like climate scientists use a model of the Earth's processes to make predictions of climate change.
Look at the diagram below
Answer:
TRUE
Since , Angle ABD is congruent or equal to Angle CBD
we know that sides opposite to equal angles are also equal.
i.e AD and CD are opposite sides to angles ABD and CBD respectively.
So, AD = CD
Find the rule.
pattern:
[|(-1)|; |(0)|; |(1)| ; |(m)|; |(3)|]
[|(-3)|; |(-1)|; |(1)| ; |(3)|; |(n)|]
write down the rule in the form y= ...
The first series uses a linear function with - 1 as first element and 1 as common difference, then the rule corresponding to the series is y = |- 1 + x|.
The second series uses a linear function with - 3 as second element as 2 as common difference, then the rule corresponding to the series is y = |- 3 + 2 · x|.
What is the pattern and the function behind a given series?
In this problem we have two cases of arithmetic series, which are sets of elements generated by a condition in the form of linear function and inside absolute power. Linear functions used in these series are of the form:
y = a + r · x (1)
Where:
a - Value of the first element of the series.r - Common difference between two consecutive numbers of the series.x - Index of the element of the series.The first series uses a linear function with - 1 as first element and 1 as common difference, then the rule corresponding to the series is y = |- 1 + x|.
The second series uses a linear function with - 3 as second element as 2 as common difference, then the rule corresponding to the series is y = |- 3 + 2 · x|.
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Let R be the region bounded by
y
=
7
sin
(
π
2
x
)
,
y
=
7
(
x
−
2
)
2
, and
y
=
x
+
6
, and containing the point (2,7).
a. The area of [tex]R[/tex] is given by the integral
[tex]\displaystyle \int_1^2 (x + 6) - 7\sin\left(\dfrac{\pi x}2\right) \, dx + \int_2^{22/7} (x+6) - 7(x-2)^2 \, dx \approx 9.36[/tex]
b. Use the shell method. Revolving [tex]R[/tex] about the [tex]x[/tex]-axis generates shells with height [tex]h=x+6-7\sin\left(\frac{\pi x}2\right)[/tex] when [tex]1\le x\le 2[/tex], and [tex]h=x+6-7(x-2)^2[/tex] when [tex]2\le x\le\frac{22}7[/tex]. With radius [tex]r=x[/tex], each shell of thickness [tex]\Delta x[/tex] contributes a volume of [tex]2\pi r h \Delta x[/tex], so that as the number of shells gets larger and their thickness gets smaller, the total sum of their volumes converges to the definite integral
[tex]\displaystyle 2\pi \int_1^2 x \left((x + 6) - 7\sin\left(\dfrac{\pi x}2\right)\right) \, dx + 2\pi \int_2^{22/7} x\left((x+6) - 7(x-2)^2\right) \, dx \approx 129.56[/tex]
c. Use the washer method. Revolving [tex]R[/tex] about the [tex]y[/tex]-axis generates washers with outer radius [tex]r_{\rm out} = x+6[/tex], and inner radius [tex]r_{\rm in}=7\sin\left(\frac{\pi x}2\right)[/tex] if [tex]1\le x\le2[/tex] or [tex]r_{\rm in} = 7(x-2)^2[/tex] if [tex]2\le x\le\frac{22}7[/tex]. With thickness [tex]\Delta x[/tex], each washer has volume [tex]\pi (r_{\rm out}^2 - r_{\rm in}^2) \Delta x[/tex]. As more and thinner washers get involved, the total volume converges to
[tex]\displaystyle \pi \int_1^2 (x+6)^2 - \left(7\sin\left(\frac{\pi x}2\right)\right)^2 \, dx + \pi \int_2^{22/7} (x+6)^2 - \left(7(x-2)^2\right)^2 \, dx \approx 304.16[/tex]
d. The side length of each square cross section is [tex]s=x+6 - 7\sin\left(\frac{\pi x}2\right)[/tex] when [tex]1\le x\le2[/tex], and [tex]s=x+6-7(x-2)^2[/tex] when [tex]2\le x\le\frac{22}7[/tex]. With thickness [tex]\Delta x[/tex], each cross section contributes a volume of [tex]s^2 \Delta x[/tex]. More and thinner sections lead to a total volume of
[tex]\displaystyle \int_1^2 \left(x+6-7\sin\left(\frac{\pi x}2\right)\right)^2 \, dx + \int_2^{22/7} \left(x+6-7(x-2)^2\right) ^2\, dx \approx 56.70[/tex]
201
5. One flight took a total of 4.6 hours. Write this number as a mixed number
and as an improper fraction. Show your work in the space below. Remember
to check your solution.
The improper fraction is 25 / 6 hours
The mixed fraction is [tex]4\frac{1}{6}[/tex] hours.
What is the mixed fraction and the improper fraction?The time is written as a decimal. A decimal is a number that is made up of integers and non-integers. The integers are separated from the non-integers by a decimal point.
A mixed number is a fraction that is made up of a whole number and a proper fraction. A proper fraction is a fraction whose numerator is less than the denominator. An improper fraction is a fraction whose numerator is greater than the denominator.
In order to convert 4.6 hours to a mixed fraction, the proper fraction has to be determined. To determine this value, multiply 0.6 by the minutes in an hour
0.6 x 60 minutes = 10 minutes
The decimal becomes : [tex]4\frac{10}{60}[/tex] hours
[tex]4\frac{1}{6}[/tex] hours
To convert the mixed fraction to an improper fraction, multiply the denominator by the whole number and add the numerator, then divide by the denominator
The improper fraction is : 25 / 6 hours
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Daria pays x dollars for a pair of shoes. the tax on shoes is 5%. the expression representing her total cost is x+0.05x.
witch expression is equivalent and why?
A 1.05x because adding $5 to the cost of the shoes is the same as multiplying the cost by 1.05
B 1.05x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.05
C x(0.05) because the cost of the shoes can be factored out
D 1.5x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.5
The expression which represents Daria's total cost is; 1.05x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.05
PercentageAmount paid for shoes = $xTax = 5%Total cost = x + (5% of x)
= x + (0.05 × x)
= x + (0.05x)
Total cost = 1.05x
Therefore, the correct answer is; 1.05x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.05
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the volume of my sphere is 62.5/3 pi, with the radius being 2.5 and the height of each cylinder being 0.208. help pls this makes no sense
Based on the given parameters, the volume of the cylinder is 62.5/3 π cubic units
How to determine the volume of the sphere?From the question, the given parameters are:
Shape = Sphere
Volume = 62.5/3π
Radius = 2.5
Height of cylinder = 0.208
The volume of a cylinder is calculated using the following formula:
V = 4/3πr^3
Substitute the known values in the above equation
V = 4/3 * π * (2.5)^3
Evaluate the exponent
V = 4/3 * π * 15.625
Evaluate the product of 15.625 and 4
V = 1/3 * π * 62.5
Evaluate the product of 62.5 and 1/3
V = 62.5/3 π
This means that the volume of the cylinder is 62.5/3 π cubic units
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The circumference of the tree trunk is 7.85
feet. If the tree trunk is cut, what will be
the diameter of the tree stump?
Use 3.14 for π.
Hint: C = πd
diameter [?] feet please explain how you got this answer for future problems
Answer:
2.5 feet
Step-by-step explanation:
Since circumference is just pi(we're using 3.14 in this case) * diameter, which is our answer, we need to divide the circumference(which is 7.58) BY 3.14, which is pi. This leaves us with the diameter, which is 2.5. The unit is already feet, so we needn't do anything about that.
to set up a model linear equation to fit real world applications, what should always be the first step?
Answer:
Define the variables.
Step-by-step explanation:
Define the variables, then set up the equations, and finally solve the system using graphing, substitution, or elimination method.
To set up or model a linear equation to fit a real-world application, First, we have to determine the known amounts or quantities before defining the unknown quantity as a variable.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
To set up a model linear equation to fit real-world applications
In the first step determine known amounts or quantities.
Then, assign the unknown amount to a variable.
Now, find a method or approach to express the second unknown in terms of the first if there are many unknown quantities.
Create an equation that translates the words into mathematical functions.
Complete the equation. Make certain that the solution, including the system of measurement, can be expressed in words.
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Find the area of the shaded region
∆BOC is equilateral, since both OC and OB are radii of the circle with length 4 cm. Then the angle subtended by the minor arc BC has measure 60°. (Note that OA is also a radius.) AB is a diameter of the circle, so the arc AB subtends an angle measuring 180°. This means the minor arc AC measures 120°.
Since ∆BOC is equilateral, its area is √3/4 (4 cm)² = 4√3 cm². The area of the sector containing ∆BOC is 60/360 = 1/6 the total area of the circle, or π/6 (4 cm)² = 8π/3 cm². Then the area of the shaded segment adjacent to ∆BOC is (8π/3 - 4√3) cm².
∆AOC is isosceles, with vertex angle measuring 120°, so the other two angles measure (180° - 120°)/2 = 30°. Using trigonometry, we find
[tex]\sin(30^\circ) = \dfrac{h}{4\,\rm cm} \implies h= 2\,\rm cm[/tex]
where [tex]h[/tex] is the length of the altitude originating from vertex O, and so
[tex]\left(\dfrac b2\right)^2 + h^2 = (4\,\mathrm{cm})^2 \implies b = 4\sqrt3 \,\rm cm[/tex]
where [tex]b[/tex] is the length of the base AC. Hence the area of ∆AOC is 1/2 (2 cm) (4√3 cm) = 4√3 cm². The area of the sector containing ∆AOC is 120/360 = 1/3 of the total area of the circle, or π/3 (4 cm)² = 16π/3 cm². Then the area of the other shaded segment is (16π/3 - 4√3) cm².
So, the total area of the shaded region is
(8π/3 - 4√3) + (16π/3 - 4√3) = (8π - 8√3) cm²
Help me with this question
Answer:
s = 55 degrees
t = 35 degrees
Step-by-step explanation:
I am not sure what the question is, but I am assuming that you are trying to find the value for s and t
S and 125 are supplemental. That means that they add to 180. 180 - 125 = 55.
The two angles opposite of s together add up to 125. I know that one angle is 90, so t is 125 -90 or 35
The length of a parallelogram exceeds its breadth by 30 cm. If the perimeter of the parallelogram is 2 m 60 cm, find the length and breadth of the parallelogram.
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
[tex]\longrightarrow \sf{2(1 + b) = 260}[/tex]
[tex]\longrightarrow \sf{2(x+30+x) = 260}[/tex]
[tex]\longrightarrow \sf{ 2x+30 = \dfrac{260}{20} }[/tex]
[tex]\longrightarrow \sf{2x + 30 =130}[/tex]
[tex]\longrightarrow \sf{2x = 130 - 30}[/tex]
[tex]\longrightarrow \sf{2x = 100}[/tex]
[tex]\longrightarrow \sf{x= \dfrac{100}{2} }[/tex]
• [tex]\longrightarrow \sf{b= \underline{50cm}}[/tex]
[tex]\longrightarrow \sf{= x + 30}[/tex]
[tex]\longrightarrow \sf{= 50 + 30}[/tex]
• [tex]\longrightarrow \sf{ \underline{80cm}}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex]\large\bm{Breadth= \: 50cm}[/tex]
[tex]\large\bm{Length= \: 80cm}[/tex]
808, 408, 208,108, 68 find out wrong number.
68 is the wrong number in the sequence 808, 408, 208,108, 68
What is Number system?A number system is defined as a system of writing to express numbers.
Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The given sequence is 808, 408, 208,108, 68
Eight hundred eight, Four hundred and eight, two hundred and eight, one hundred eight and sixty eight.
808, 408, 208,108, 68
Let us find the difference between the consecutive numbers
400, 200, 100, 40
As we observe the first three terms having the common ratio where as 40 and 100 has different ratio.
Hence, 68 is the wrong number in the sequence 808, 408, 208,108, 68
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These values have an average of 6. What is the average distance of those values from that average of 6?
The average of the values from that average of 6 is 0
How to determine the averageWe have the numbers to be
0 2 4 10 14 and have an average of 6
To find their distances, we should substract each from the given average
We have;
6 - 0 =6
6 -2 = 4
6 -4 = 2
6 - 10 = -4
6 - 14 = -8
The average of this distances is
= pro
= [tex]\frac{0}{6}[/tex]
= 0
Thus, the average of the values from that average of 6 is 0
The complete question is
These values have an average of 6. What is the average distance of those values from that average of 6?
0 2 4 10 14
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
sub -2 into 12x^3 - 15
h(-2) = 12(-2)^3 -15
= -111
hope this helps!!!! If it's incorrect I'm sorry :(
Answer:
[tex]h(-2) =\boxed{ \bf -111}[/tex]
Step-by-step explanation:
The function [tex]h(x)[/tex] is defined as:
[tex]h(x) = 12x^3 - 15[/tex]
To calculate the value of [tex]h(-2)[/tex], we have to replace the [tex]x[/tex] in the definition of [tex]h(x)[/tex] with -2:
[tex]h(-2)[/tex] = [tex]12(-2)^3 - 15[/tex]
⇒ [tex]12(-8) -15[/tex]
⇒ -96 - 15
⇒ -111
Determine if the following infinite series converges or diverges
Using limits, it is found that the infinite sequence converges, as the limit does not go to infinity.
How do we verify if a sequence converges of diverges?Suppose an infinity sequence defined by:
[tex]\sum_{k = 0}^{\infty} f(k)[/tex]
Then we have to calculate the following limit:
[tex]\lim_{k \rightarrow \infty} f(k)[/tex]
If the limit goes to infinity, the sequence diverges, otherwise it converges.
In this problem, the function that defines the sequence is:
[tex]f(k) = \frac{k^3}{k^4 + 10}[/tex]
Hence the limit is:
[tex]\lim_{k \rightarrow \infty} f(k) = \lim_{k \rightarrow \infty} \frac{k^3}{k^4 + 10} = \lim_{k \rightarrow \infty} \frac{k^3}{k^4} = \lim_{k \rightarrow \infty} \frac{1}{k} = \frac{1}{\infty} = 0[/tex]
Hence, the infinite sequence converges, as the limit does not go to infinity.
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The series diverges by the comparison test.
We have for large enough [tex]k[/tex],
[tex]\displaystyle \frac{k^3}{k^4+10} \approx \frac{k^3}{k^4} = \frac1k[/tex]
so that
[tex]\displaystyle \sum_{k=0}^\infty \frac{k^3}{k^4+10} = \frac1{10} + \sum_{k=1}^\infty \frac{k^3}{k^4+10} \approx \frac1{10} + \sum_{k=1}^\infty \frac1k[/tex]
and the latter sum is the divergent harmonic series.
In a right angled triangle ABC with hypotenuse c and sides a and b. Find the unknown leangth
b = 5dm, a=5√7dm, c = ?
Step-by-step explanation:
since it has a hypotenuse C
using pythagoras theroem
hpy²=opp²+adj²
=(5)²+(5√7)²
=25+175
=200
hyp=√200
=10√2
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]3x + y = - 4 \\ 3x + 0 = - 4 \\ 3x = - 4 \\ x = \frac{ - 4}{3} = - 1.333[/tex]
It has to be the last line in the second picture since it intersects the x axis at approximately x=-1.333[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
◉ [tex] \bm{Last \: option \: (D.)}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Write the equation in slope-intercept form. Then solve y.
▪ [tex]\small\longrightarrow \sf{3x-3x + y = −3x -4}[/tex]
▪ [tex]\small\longrightarrow \sf{y= -3x-4}[/tex]
Identify the x-intercept,
[tex]\small \sf \longrightarrow{3x + 0 = - 4}[/tex]
[tex]\small\longrightarrow \sf{3x=-4}[/tex]
[tex]\small\longrightarrow \sf{x = - \dfrac{4}{3} }[/tex]
[tex]\small\longrightarrow \sf{x = -1.33}[/tex]
The graph has the next properties:
[tex]\small\longrightarrow \sf{Slope: \: 3}[/tex]
[tex]\small\longrightarrow \sf{x-intercept: \: (-1.33,0)}[/tex]
[tex]\small\longrightarrow \sf{y-intercept: \: (0,4) }[/tex]
What is the radius of the sector of the circle below, if the area is 30.39 m^2 and the central angle < AOB measures 43 °. (round answer to the nearest whole meter)
Answer:
a. 9m
Step-by-step explanation:
Pi = 3.14 = 22/7
formula :
Area of a Sector of a Circle = (central angle)/360 * πr² =
(central angle)/360 * πr² = Area of a Sector of a Circle
43/360 * Pi * r^2 = 30.39
r^2 = (30.39 * 360) / (Pi * 43)
r^2 = (30.39 * 360) / (22/7 * 43)
r = √ (30.39 * 360 * 7) / (22 * 43)
r = √76582.8/946
r = √80.9543340381
8.99746264444 which is roughly
9
The radius of the sector will be 9m. The correct option is A.
What is the arc length of the circle?The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc segment by simulating it as a network of connected line segments.
The radius will be calculated as below:-
Area of a Sector of a Circle = (central angle)/360 * πr² =
(Ф)/360 * πr² = Area of a Sector of a Circle
43/360 * Pi * r²= 30.39
r² = (30.39 * 360) / (Pi x 43)
r²= (30.39 x 360) / (22/7 x 43)
r = √ (30.39 x 360 x 7) / (22 x 43)
r = √76582.8/946
r = √80.9543340381
r = 9
Therefore, the radius of the sector will be 9m. The correct option is A.
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3 integers are in an arithmetic progression. their product is prime. what is the sum of their squares?
The sum of their squares is (x)^2 + (x-d)^2 + (x-2d)^2.
According to the statement
we have given that the 3 integers are in an arithmetic progression and their product is prime.
And we have to find the sum of their squares.
So, let the three integers which is A, B, C.
And according to the arithmetic progression the
A = x and B = x-d, C = x-2d. here d is the common difference and x is a 1st term.
So, there product is prime
then
(x) (x-d) (x-2d) = c -(1)
And
their sum of square is
(x)^2 + (x-d)^2 + (x-2d)^2 - (2)
So, The sum of their squares is (x)^2 + (x-d)^2 + (x-2d)^2.
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Need help look at attachment
Volume=
Help me please! Thank u so much I appreciate it
the volume of the oblique pyramid is 16 cubic units
How to determine the volumeThe formula for finding the volume of a oblique pyramid is given as;
Volume = [tex]\frac{1}{3}[/tex] × base area/ height
Where
base area = area of a right triangle
From the lengths of the triangle given, we can deduce that the opposite side is 24unit and the adjacent side or the base is 10 unit
let's put in the values to the formula
Base area = 10 × 24
Base area = 240 units
height = 5 units
Since we have both the height and the base area, let's find the volume
Volume = [tex]\frac{1}{3}[/tex] × [tex]\frac{240}{5}[/tex]
Volume = [tex]\frac{1}{3}[/tex] × [tex]48[/tex]
Find the division
Volume = 16 cubic units
Thus, the volume of the oblique pyramid is 16 cubic units
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