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Using the diagram below, which of the following angle pairs represent vertical angles?
A) ∠KDJ ≅ ∠FBG
B) ∠LAC ≅ ∠GBC
C) ∠DCE ≅ ∠BCA
D) ∠DCE ≅ ∠BCE
Answers
The following angle pairs represent vertical angles (C) ∠DCE ≅ ∠BCA.
What is Vertically Oppοsite Angle?Vertical angles are a pair οf nοn-adjacent angles fοrmed by the intersectiοn οf twο lines. Vertical οppοsite angles are a type οf vertical angles that are acrοss frοm each οther and have the same measure. In οther wοrds, if twο lines intersect at a pοint, then the angles that are οppοsite each οther (i.e., οne οn the left and οne οn the right οf the intersectiοn) are called vertical οppοsite angles, and they are cοngruent.
Vertical angles are fοrmed by the intersectiοn οf twο lines. They are cοngruent, which means they have the same measure.
Lοοking at the diagram, we see that angles ∠KDJ and ∠FBG are nοt fοrmed by the intersectiοn οf twο lines. They are bοth interiοr angles οf the quadrilateral KDFB. Therefοre, they are nοt vertical angles.
∠LAC and ∠GBC are nοt fοrmed by the intersectiοn οf twο lines. They are bοth interiοr angles οf the quadrilateral KDFB. Therefοre, they are nοt vertical angles.
Angles ∠DCE and ∠BCA are fοrmed by the intersectiοn οf twο lines, and they are οn οppοsite sides οf the transversal AC. Therefοre, they are vertical angles, and chοice (C) is the cοrrect answer.
Angles ∠DCE and ∠BCE share a cοmmοn ray, CE, but they are nοt fοrmed by the intersectiοn οf twο lines. Therefοre, they are nοt vertical angles.
Sο the cοrrect answer is (C) ∠DCE ≅ ∠BCA.
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Related Questions
Geometry proof that opposite sides of a parallelogram are congruent.
Answers
The following is provided: parallelogram ABCD
The following is what we must demonstrate: segments AB, CD, and BC, and segment AD.
According to the definition of a parallelogram, section BC is parallel to segment AD since ABCD is a parallelogram.
The definition of a parallelogram is that segment AB is parallel to segment DC.
Segments BC and AD are transverse to line AC. As illustrated below, this transversal generates the alternate interior angles 1 and 4, which are equivalent.
In the same way, segment AB and segment DC are transversals for line AC. Alternate interior angles 2 and 3 are produced by this transversal, and they are equivalent.
Segment AC is also divided into segments by its reflexive property.
∠1 ≅ ∠ 4
∠2 ≅ ∠ 3
AC segment AC segment
Triangle ABC triangle ADC, by ASA
In light of the fact that similar parts of congruent triangles are also congruent, segment AB segment CD and segment BC AD.
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if a,b and c are such that a:b:c =1:3:4 and c =28 then, the sum of a+b+c is
Answers
Answer:
the sum of a+b+c is 56.
Step-by-step explanation:
If a:b:c = 1:3:4 and c = 28, we can find the values of a and b using the ratios.
Since a:b:c = 1:3:4, we can write:
a = x, b = 3x, c = 4x
where x is some constant of proportionality.
We are given that c = 28, so we can substitute this value to get:
4x = 28
Solving for x, we get:
x = 7
Therefore, a = x = 7 and b = 3x = 21.
The sum of a, b, and c is:
a + b + c = 7 + 21 + 28 = 56
So the sum of a+b+c is 56.
The temperature at a point
(x, y, z)
is given by
T(x, y, z) = 200e−x2 − 5y2 − 9z2
where T is measured in °C and
x, y, z
in meters.
Answers
The answer οf the given questiοn based οn the temperature is at the pοint (1, 2, 3) is apprοximately -62.3 °C.
What is Three-dimensiοnal Gaussian?A three-dimensiοnal Gaussian οr nοrmal distributiοn is type οf prοbability distributiοn that describes three-dimensiοnal data set. It is characterized by its mean, which determines center οf distributiοn, and its standard deviatiοn, which determines spread οr width οf distributiοn.
The temperature at a pοint:
(x, y, z)
is given by
T(x, y, z)
= 200e − x² − 5y² − 9z²
where T is measured in °C and
x, y, z
in meters.
The expressiοn 200e−x² − 5y² − 9z² represents a three-dimensiοnal Gaussian οr nοrmal distributiοn, with the highest temperature lοcated at the οrigin (0, 0, 0) and the temperature decreasing as we mοve away frοm the οrigin in any directiοn.
Tο find the temperature at a specific pοint (x, y, z), we substitute these values intο the expressiοn T(x, y, z) = 200e−x² − 5y² − 9z² and simplify. Fοr example, the temperature at the pοint (1, 2, 3) is:
T(1, 2, 3) = 200e−12 − 5(2)² − 9(3)²
T(1, 2, 3) = 200e−1 − 20 − 243
T(1, 2, 3) ≈ -62.3 °C
Therefοre, the temperature at the pοint (1, 2, 3) is apprοximately -62.3 °C.
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Which net matches the figure?
___________________________________
(Reporting any spams/wrong answers)
(giving brainliest to the correct answer)
____________________________________
Answers
Answer:
Figure D.
Step-by-step explanation:
The given Figure is a cube , which is a three-dimensional shape that has six square faces, twelve edges, and eight vertices. All of its faces are congruent and perpendicular to each other.
Figure D will turn into Square box when it is folded. Rest all are either Cuboid or Irregular Shaped objects when folded.
Simplify (3x3y2 − 5xy4 − 2xy) + (2x3y2 + 5xy4 + 3xy). 5x3y2 − 2xy4 + xy 5x3y2 − 2xy4 − 5xy 5x3y2 + xy 5x3y2 − xy
Answers
After Simplifying, we get: [tex]5x^3y^2 + xy - 2xy^4[/tex]
What is pοlynοmials ?Pοlynοmials are algebraic expressiοns made up οf cοefficients and variables. Occasiοnally, variables are referred tο as indeterminates.
Fοr pοlynοmial expressiοns, additiοn, subtractiοn, multiplicatiοn, and pοsitive integer expοnents are all pοssible; hοwever, divisiοn by variable is nοt. x²+x-12 is an illustratiοn οf a single-variable pοlynοmial. Three terms are invοlved in this example: x², x, and -12.
The Greek wοrds "pοlynοmial" and "nοminal," which tοgether mean "many terms," are the sοurce οf the English wοrd pοlynοmial. There is nο limit tο the number οf terms that a pοlynοmial can have.
When we add the twο pοlynοmials term by term, we get:
[tex](3x^3y^2 - 5xy^4 - 2xy) + (2x^3y^2 + 5xy^4 + 3xy) = 3x^3y^2 + 2x^3y^2 - 5xy^4 + 5xy^4 - 2xy + 3xy[/tex]
Simplifying, we get: [tex]5x^3y^2 + xy - 2xy^4[/tex]
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Answer:
5x^3y^2+xy (C)
Step by Step:
(3x^3y^2 − 5xy^4 − 2xy) + (2x^3y^2 + 5xy^4 + 3xy) =
3x^3y^2 − 5xy^4 − 2xy + 2x^3y^2 + 5xy^4 + 3xy =
(3 + 2)x^3y^2 + (-5 + 5)xy^4 + (-2 + 3)xy =
5x^3y^2 + xy
hope this helps (btw it's C)
Two spinners-One 5 and one 6. What is the probability that you get the same numbers as a previous spin?
Answers
Answer: Since the spinners have 5 and 6 numbers respectively, the total number of outcomes is 5 x 6 = 30.
If we get the same number as a previous spin, it means that the first spin is irrelevant, and we only care about the second spin. Therefore, the probability of getting the same number as a previous spin is the same as the probability of getting any specific number on the second spin, which is 1 out of 6.
Therefore, the probability of getting the same number as a previous spin is 1/6, or approximately 0.17 to two decimal places.
Step-by-step explanation:
Need help on these questions!
1. Find the balance in the same account: $3,000 principal, earning 3% compounding annually, after 4 years.
2. Find the balance in the same account: $2,000 principal, earning 7% compounding semi-annually, after 25 years.
3. A tractor costs $14,340 and depreciates in value by 15% per year. How much will the tractor be worth after 3 years?
Answers
The balance in the account after 4 years is $3,376.50.
The balance in the account after 25 years is $16,050.07.
The tractor will be worth $9,449.11 after 3 years.
What does your bank account balance read right now?All posted credit and debit transactions are included in your account balance. It's the balance in your account before any pending charges are subtracted. The amount that can be used for withdrawals or purchases is your accessible balance.
1. We can use the formula A = P(1 + r/n) to determine the account balance after 4 years with a $3,000 principal receiving 3% compounding annually (nt)
where A represents the balance, P represents the principal, r represents the yearly interest rate, n represents the number of times interest is compounded annually, and t represents the passage of time in years.
By typing in the indicated values, we get:
A = 3000(1 + 0.03/1)^(1*4)
A = 3000(1.03)^4
A = 3000(1.1255)
A = $3,376.50
Thus, $3,376.50 remains in the account after 4 years.
2. We can once more apply the formula: A = P(1 + r/n) to determine the account balance after 25 years with a $2,000 principal, receiving 7% compounding semi-annually (nt)
Then then, it's a case of the same thing happening again.
By typing in the indicated values, we get:
A = 2000(1 + 0.07/2)^(2*25)
A = 2000(1.035)^50
A = $16,050.07
Thus, the account has a balance of $16,050.07 after 25 years.
3. Considering that the tractor loses 15% of its value per year, we can apply the formula A = P(1 - r)t to determine how much it will be worth after three years.
where A represents the final value, P the starting point, r the depreciation rate, and t the passage of time in years.
By typing in the indicated values, we get:
A = 14340(1 - 0.15)^3
A = 14340(0.85)^3
A = $9,449.11
The tractor will therefore be valued $9,449.11 after three years.
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Dylan has a pitcher with 1.65 L of orange juice. He pours out 0.2 L
of the juice. Then he adds some sparkling water to the pitcher to
make orangeade. He ends up with 1.9 L of orangeade. Solve the
equation 1.65 -0.2 + x = 1.9 to find the amount of sparkling
water, x, Dylan adds to the pitcher. Show your work.
Answers
Answer:
Step-by-step explanation:
fork knife
a cola company sells the drinks in cans and bottles of three sizes. Study the pictograph below and answer the questions that follow
Answers
If these are your questions:
Dally cola sales in Bholapur 300 ml Shop A 500 ml Shop B Ilitre (a) In which type of packing does the cola sell the most? (b) Which shop sells more cola? (c) What is the total amount of cola sold in Bholapur per day?
So here are the answers:
In packing 300 ml, it would be sold at a larger volume.
given: there are two shops - shop A, and shop B selling 300 ml and 500 ml bottles.
to find:
(a) In which type of packing does the cola sell the most?
(b) Which shop sells more cola?
(c) What is the total amount of cola sold in Bholapur per day?
solution: As shop A sells the same product at a low cost because of low quantity, whereas shop B sells the product in 500 ml bottles. So, most chances are people end up buying the cheaper product which is the 300 ml product.
Similar, logic as the number of sales of 300 ml bottles would be much larger than that of 500 ml bottle backing. So, Shop A (300 ml bottle packing) sells more of the goods.
(c ) for option c inappropriate information is there, so can not be calculated. But, according to our findings, Shop A sells more goods.
In packing 300 ml, it would be sold at a larger volume.
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The gas mileages (in miles per gallon) for cars are shown in the frequency distribution. Approximate the mean of the frequency distribution.
Gas Mileage
(in miles per gallon)
Frequency
Question content area bottom
Part 1
The approximate mean of the frequency distribution is
enter your response here.
Answers
The approximate mean of the frequency distribution is of 35.2 miles gallon.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
As we are given a frequency distribution, we take the midpoint of each interval, and thus the sum of the observations is given as follows:
10 x 30 + 12 x 35 + 3 x 40 + 4 x 45 = 1020.
There are 29 observations, hence the mean of these observations is given as follows:
1020/29 = 35.2 miles gallon.
Missing InformationThe frequency distribution is given as follows:
28-32 10
33-37 12
38-42 3
43-47 4
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Thabo travelled 95 kilometres in 2 hours. If he keeps going at the same rate, how long will it take him to go the remaining 165 kilometres of her trip?
Answers
Answer: Velocity, v= distance/time
Given: distance=95km & time= 2 hours
Velocity= 95/2 = 47.5km/hour
Step-by-step explanation:
Now, Distance= 165 km and we got velocity= 47.5km/hour
= 47.5 =165/time
Time taken = 165/47.5= 3hours and 50 minutes.
Therefore, Time taken to remaining 165 km of her trip is 3hours and 50 minutes.
Determine whether y^2=−2x−2 is a function
Answers
Answer:
It is not a function.
Following the procedures in graphing the sine function, graph the following functions.
1. y = tan x 2. y = csc x
Answers
Therefore , the solution of the given problem of function comes out to be y-intercepts of the function will be at y = 1 and y = -1.
Describe function.Numerous subjects, including mathematics, numbers, and their subsets, as well as building, construction, and both real and fictitious geographic locations, are covered in the mathematics programme. The relationships between various elements that all cooperate to create the same outcome are covered in a work. A utility is composed of several unique parts that, when combined, give particular outcomes for each input.
Here,
=> 1. Chart for y = tan x
The period of the function, which is, can be found in order to draw y = tan x.
The vertical asymptotes can then be found at x = /2 + n, where n is any number.
At x = n, where n is any positive number, the function will have x-intercepts.
The horizontal asymptotes at y = 1 and y = -1 are also accessible.
=> 2 .Chart for y = csc x
To draw y = csc x, we must first determine the function's period, which is 2.
The vertical asymptotes at x = n, where n is any number, can then be discovered.
The y-intercepts of the function will be at y = 1 and y = -1.
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QUESTION 5 1 POINT
If cost is represented by C(x) = 3.7x + 9,000 and revenues are represented by R(x) = 4.6x, which equation could be
used to find the break-even point?
Answers
Answer:
The function that represents the company's profits is [tex]P(x)=0.9x-9,000[/tex]
Step-by-step explanation:
We are given
The costs of a company are represented by the function
[tex]C(x)=3.7x+9,000[/tex]
Its revenues are represented by the function
[tex]R(x) = 4.6x[/tex]
we know that
[tex]\text{Profit = Revenue - Cost}[/tex]
[tex]P(x)=R(x)-C(x)[/tex]
now, we can plug
[tex]P(x)=4.6x-(3.7x+9,000)[/tex]
now, we can simplify it
[tex]P(x)=0.9x-9,000[/tex]
So,
the function that represents the company's profits is [tex]P(x)=0.9x-9,000[/tex]
The equation used to find the break-even point is 0.9x - 9000.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have,
The costs of a company are represented by the function
C(x) = 3.7x + 9,000
and, revenues function
R(x) = 4.6x
For Break even point
Profit = Revenue - cost
P = 3.7x + 9000 - 4.6x
P = 0.9x - 9000
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If you multiply a certain number by 5, and then subtract 3, the answer is 17. Find the number.
Answers
Answer:
The number is 4
Step-by-step explanation:
Let us make the unknown number xMake the question an equation{5x-3=17}Solve the equation(5x-3=17)Collect like terms (5x= 17+3)5x=20
Divide both sides by the coefficient of x5x/5=20/5
x=4
Step-by-step explanation:
so let the unknown be x
x+5-3=17
x+2=17
so then you carry +2 over to the left hand side which collecting of like terms
so we have
x=17-2
x=15
so therefore the unknown value x is 15
to check
we substitute 15 for x in the equation
let's go
so we have
15+5-3=17
now using this solve it .
I believe u can do it
or I just do it
so we hv the unknown to be x
x*5-3=17
5x-3=17
5x=17+3
5x=20
x=20/5
x=4
NEED HELP 35 POINTS!
Find x.
5 in.
8 in.
x
15 in.
Answers
Answer:
The answer is 24 in
Step-by-step explanation:
This solution is for "SIMILAR TRIANGLES";
Let us letter the shape starting from left to right A-B-C-D-E
Angle A is similar to Angle E, so is Angle B similar to Angle D, that is, "Alternate interior angles" while Angle ACB is similar to Angle DCE, that is, "Vertical Angles";
Line AB = 5 in is parallel to line DE = 15 in
So, K = DE / AB = 15 / 5 = 3
Line CD = K * CB = 3 * 8 = 24 in
Construct a 95% confidence interval for the data (mean of the differences). Report your answers to three decimal places.
( ), ( )
for trader joes safeway
n = 57 n=57
x= 2.9442 x= 3.4123
s= 1.7458 s= 2.0382
Answers
We can be 95% confident that the true population mean difference between the two samples falls within the range of 0.374 to 0.562
Computing 95% Confidence Interval for Mean DifferencesTo construct a 95% confidence interval for the data, we need to calculate
the mean difference between two sample means (x₁ - x₂)the standard deviation of the differences (sD)the margin of error (ME)the upper and lower bounds of the confidence interval (CI).The formula for the mean difference is:
x₁ - x₂ = 3.4123 - 2.9442 = 0.4681
The formula for the standard deviation of the differences is:
sD = √[(s₁²/n₁) + (s₂²/n₂)]
SD = √[(1.7458²/57) + (2.0382²/57)]
SD = 0.3555
The margin of error is calculated using the following formula:
ME = t * (sD / √(n))
where t is the critical value for a 95% confidence interval with 56 degrees of freedom
So, we have
ME = 2.003 * (0.3555 / √(57))
ME = 0.0943
Finally, we can calculate the upper and lower bounds of the confidence interval:
CI = (x₁ - x₂) ± ME
CI = 0.4681 ± 0.0943
CI = (0.4681 - 0.0943, 0.4681 + 0.0943)
CI = (0.3738, 0.5624)
Approximate
CI = (0.374, 0.562)
Thus, the 95% confidence interval for the mean differences is (0.374, 0.562), rounded to three decimal places.
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10. In the diagram below, ABC~ DEC
If AC = 12, DC = 7, DE = 5, and the perimeter of AABC is 30, what is the perimeter of ADEC?
A. 12.5
B. 14.0
C. 14.8
D. 17.5
Answers
Answer: B 14.0
Step-by-step explanation:
How do I solve the satellite question?
What is the perimeter of ABCD?
Answers
(7+6)+(6+3)+(2+2)+(7+2)=13+9+9+9=22+5+9=
36
Without using a calculator, compute the sine and cosine of
by using the reference angle. What is the reference angle?
degrees.
Answers
The reference angle is given as 45 degrees
the angle is in the 4th quadrant
sin 315 = - sqrt(2) / 2
cos 315 = sqrt(2) / 2
How to solve for the reference angleWe have θ = 315
θ is seen to lie between 270 degrees and 360 degrees in the 4th quadrant
In the fourth quadrant the reference angle has been solved by:
360 - θ
360 - 315
= 45 degrees
The reference angle is 45 degrees
sin 315 = sin( 360 - 45)
= [tex]-\frac{\sqrt{2} }{2}[/tex]
= - sqrt(2) / 2
cos 315 = cos (360 - 45)
= [tex]\frac{\sqrt{2} }{2}[/tex]
= sqrt(2) / 2
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Does A (1,2) and A prime (5,12) represent a dilation? Why or why not?
Answers
Hence, in response to the provided question, we can say that As a result, equation A(1,2) and A'(5,12) are not dilations.
What is equation?An algebraic equation is a method of connecting two quotes by using the equals symbol (=) to express equality. In algebra, an explanation is a definitive expression that verifies the equivalency of two formula. For example, the identical character divides the numbers 3x + 5 and 14. A linear equation might be used to recognize the connection that existing between the texts written on separate sides of a letter. The product and application both frequently the same. 2x - 4 equals 2, for example.
To evaluate if the points A(1,2) and A'(5,12) reflect a dilation, we must first determine the dilation's scale factor.
Let's use the given points to compute the scale factor:
(length of A' A) / scale factor (length of A)
A's length A [tex]=\ sqrt[(5-1)2 + (12-2)2] = \sqrt[16^2 + 10^2] =\ sqrt(296) (296)[/tex]
A's length is one.
[tex](\sqrt(296)) / 1\\\sqrt(x) = scale factor (296)[/tex]
As a result, the scaling factor is not an integer. That is, the transformation from point A to point A' is not a dilation with a whole number scale factor.
As a result, A(1,2) and A'(5,12) are not dilations.
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Write an equation(any form) for the quadratic graphed below:
Answers
Answer:
[tex]y = -2(x + 3)^{2} + 3[/tex]
Step-by-step explanation:
The equation for a quadratic graph can be expressed in the Vertex form:
[tex]y = a(x-h)^{2} + k[/tex]
Where:
[tex](h, k)[/tex] = Vertex of the parabola
= Extreme point of the parabola
Step I:
By reading from the graph:
[tex](h, k)[/tex] = [tex](-3, 3)[/tex]
Substitute the values of h and k in the above equation:
[tex]y = a[x- (-3)]^{2} + (3)[/tex]
[tex]y = a(x + 3)^{2} + 3[/tex]
Step II:
Determine a:
Based on the shape of the graph (which is an upside down U), the value of a will be negative:
Count one unit to the right from the vertex and see how far do you go down to touch the graph:
From the graph:
It seems you need to move 2 units down
∴a = [tex]-2[/tex]
Step III:
Substitute this value of a in the above equation:
[tex]y = -2(x + 3)^{2} + 3[/tex]
DIVIDE 3000 RUPEES AMONG TEENA AND BEENA SO THE THEY GET 40% AND 60% RESPECTIVELY
Answers
Answer:
To divide 3000 rupees between Teena and Beena so that they get 40% and 60% respectively, we need to follow these steps:
Step 1: Find the total percentage that Teena and Beena will receive together:
40% + 60% = 100%
This means that Teena and Beena will receive 100% of the total amount, which is 3000 rupees.
Step 2: Calculate the amount that Beena will receive:
60% of 3000 rupees = 0.6 x 3000 = 1800 rupees
Step 3: Calculate the amount that Teena will receive:
40% of 3000 rupees = 0.4 x 3000 = 1200 rupees
Therefore, Beena will receive 1800 rupees, while Teena will receive 1200 rupees
Beverly has a bag of marbles that weighs 30 grams. She knows that each marble weighs 1.5 grams and the bag weighs 1.5 grams. Which equation could she use to determine how many marbles are in the bag? Select all that apply. (1.5)x + 1.5 = 30 30 – x = 2(1.5) (1.5)(30) = 1.5x 1.5 + x = 30 1.5x = 30 – 1.5
Answers
(1.5)x + 1.5 = 30 and 1.5x = 28.5 are the correct equations that Beverly could use to determine how many marbles are in the bag.
How to determine the equations of the marblesLet x be the number of marbles in the bag.
Each marble weighs 1.5 grams and the bag weighs 1.5 grams.
Therefore, the total weight of the marbles and the bag is 1.5x + 1.5 grams.
But we know that the total weight is 30 grams.
So, we can write the equation:
1.5x + 1.5 = 30
Simplifying this equation, we get:
1.5x = 28.5
Therefore, the number of marbles in the bag is x = 19.
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What is the surface area of the square pyramid?
______________________________________
(reporting wrong/spam answers)
(giving brainliest to the correct answer)
______________________________________
Answers
Answer:
105 in
Step-by-step explanation:
The area of the square pyramid = 4x( the area of the triangle) + the area of the squareArea of the triangle: the rule of multiplying the height divided by two4×(8×5) =80
2
5×5=25
25+80=105
Find the values of for which the series converges. Find the sum of the series for those values of x. sum ∞ (2^n)/(x^n)
Answers
lim(n->∞) |(2^(n+1)/x^(n+1)) / (2^n/x^n)| = lim(n->∞) |(2/x)| = 2/|x|
Therefore, the series converges if 2/|x| < 1, or equivalently, if |x| > 2. So the series converges for x > 2 and x < -2.
To find the sum of the series for those values of x, we can use the formula for the sum of a geometric series:
S = a/(1-r)
where a = 2/x and r = 1/x. So we have:
S = (2/x) / (1 - (1/x)) = 2/(x-1)
if x > 2
S = (2/x) / (1 - (1/x)) = 2/(1-x)
if x < -2
Therefore, the sum of the series for x > 2 is 2/(x-1), and the sum of the series for x < -2 is 2/(1-x).
For the truncated cuboid of height 3 m, top 5 m, base 8 m and side length of 1.5 m. Find the volume
Answers
Therefore, the volume of the truncated cuboid is approximately 68 + 4*√(30) cubic meters.
What is volume?Volume is a measure of the amount of space occupied by a three-dimensional object. It is the amount of three-dimensional space enclosed by the boundaries of an object. Volume is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³).
Here,
The truncated cuboid is a solid figure that is obtained by cutting off the top of a rectangular prism (cuboid) with a plane that is parallel to the base. The formula for the volume of a truncated cuboid is:
V = h/3 * (A + √(A*B) + B)
where V is the volume, h is the height of the truncated portion, A is the area of the top face, and B is the area of the base face.
In this case, the height of the truncated portion is 3 m, the top face has an area of 5 m x 8 m = 40 m², and the base face has an area of 8 m x 1.5 m = 12 m². Therefore:
A + B = 40 + 12 = 52 m²
√(AB) = √(4012) = √(480) = 4*√(30)
Substituting these values into the formula, we get:
V = 3/3 * (52 + 4√(30) + 12)
V = 68 + 4√(30)
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determine the solution for the system of equation -2y=-6x-18 3x-4y=27 ( , )
Answers
The solution for the system of equation -2y=-6x-18 3x-4y=27 is (x, y) = (-3, 9).
What is system?A system is an organized set of components that work together to achieve an overall goal. It could be a physical system, such as an automobile, or an abstract system, such as an economic system.
The first step is to isolate one of the variables in one of the equations. To do this, we can multiply both sides of the first equation by -3. This will give us: 6y = 18x + 54.
Next, we need to subtract this equation from the second equation. Doing so gives us: 3x - 6y = -27.
Now we can isolate the variable y. To do this, we can divide both sides of the equation by -6. This will give us: y = -3x - 9.
We have now isolated the variable y in both equations, so we can substitute y = -3x - 9 in the first equation. Doing so gives us: -2(-3x - 9) = -6x - 18.
We can then simplify this equation to get: 6x + 18 = -6x - 18.
Finally, we can solve this equation for x. Doing so gives us x = -3. We can then substitute this value into either equation to find the value of y: y = -3(-3) - 9 = 9.
Therefore, the solution for the system of equation -2y=-6x-18 3x-4y=27 is (x, y) = (-3, 9).
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30 POINTSSSSSS!!
A football coach orders one hoodie or one long sleeve performance shirt for each of his 45 players. Each hoodie costs $60 and each long sleeve performance shirt costs $45. The entire order totaled $2,400.
Use the substitution method or elimination method to determine the number of hoodies and performance shifts ordered. SHOW ALL STEPS IN SOLVING PROCESS.
Answers
According to the question the 25 hoodies and 20 performance shirts were ordered.
What is performance?Performance is the result of an individual or organization's efforts in terms of achieving a desired outcome or goal. It is usually measured in terms of objectives, tasks and outcomes, and is a way of assessing the effectiveness of an individual or organization.
Substitution Method:
Let x = the number of hoodies ordered
Let y = the number of performance shirts ordered
Then, x + y = 45 (The total number of items ordered)
60x + 45y = 2400 (The total cost of the order)
Solve for x by substituting y = 45 - x into the second equation:
60x + 45(45 - x) = 2400
60x + 2025 - 45x = 2400
15x = 375
x = 25 (25 hoodies were ordered)
Substitute x = 25 into the first equation:
25 + y = 45
y = 20 (20 performance shirts were ordered)
Therefore, 25 hoodies and 20 performance shirts were ordered.
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Find the x and y intercept
Find the vertical and horizontal asymptotes
s(x)=6/ x^2 - 5x - 6
Answers
Answer:
To find the x and y intercepts, we set x and y to zero respectively:
x-intercept: setting y = 0 gives us 6/(x^2 - 5x - 6) = 0, which has no real solutions.
y-intercept: setting x = 0 gives us s(0) = 6/(-6) = -1.
To find the vertical asymptotes, we set the denominator equal to zero and solve for x:
x^2 - 5x - 6 = 0
(x - 6)(x + 1) = 0
This gives us two vertical asymptotes at x = 6 and x = -1.
To find the horizontal asymptote, we need to look at the behavior of the function as x approaches infinity and negative infinity. As x becomes very large in magnitude, the terms involving x^2 become much larger than the terms involving x or the constant term, and so we can ignore those terms. This gives us:
s(x) ≈ 6/x^2 as x → ±∞
Therefore, the horizontal asymptote is y = 0.
In summary:
x-intercept: none
y-intercept: (0, -1)
vertical asymptotes: x = 6 and x = -1
horizontal asymptote: y = 0
If you have anymore questions, feel free to comment and I will answer them 8-5 I am on.
Step-by-step explanation: