You do know that to get to the fifth term from the second term you had to add the common difference 3 times. (adding ones takes you to the 3d term, adding twice takes you to the 4th term, and adding 3 times takes you to the 5th term.
What is arithmetic sequence?An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k. This is in contrast to a geometric sequence where each term increases by dividing/multiplying some constant k. Example: a1 = 25. a(n) = a(n-1) + 5.
nth term=a+(n-1)d
Where a is the first term and d is the common difference.
Now,
2nd term=a+(2–1)d=a+ d——————(1)
5th term=a+(5–1)d=a+4d—————-(2)
Now, we take (2)-(1):
5th term-2nd term=(a+4d)-(a+ d)
5th term-2nd term=3d
So:
d=(5th term-2nd term)/3
Now as all the terms are known we can find out the common difference
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NO LINKS!!
Please help me with these proofs. Part 1
Given:
C is the midpoint of AE,∠BCA ≅ ∠DCE,∠A ≅ ∠EWe have two pairs of congruent angles and the included sides are congruent. It gives us ASA congruence. AB ≅ DE as corresponding parts of congruent triangles.
Statement Reason
C is the midpoint of AE Given∠BCA ≅ ∠DCE Given∠A ≅ ∠E GivenAC ≅ EC Definition of a midpointΔABC ≅ ΔEDC ASA congruence AB ≅ DE CPCTCProvedProblem 8Given:
AH bisects ∠BHT,AH ⊥ BTWe have two right triangles with common leg and the other pair of legs are congruent as bisected segment. We get SAS congruence with two sides and included right angle.
Statement Reason
AH bisects ∠BHT GivenAH ⊥ BT Given∠BAH ≅ ∠TAH = 90° Definition of perpendicularAH ≅ AH Reflexive property (common side)BA ≅ TA Definition of segment bisectorΔBAH ≅ ΔTAH SAS congruenceProvedProblem 10Given:
AB ⊥ AC,CD ⊥ BD,AC ≅ BDΔABC and ΔCDB are right triangles with common hypotenuse and congruent pair of legs. It gives us HL congruence and it proves the corresponding angles are congruent.
Statement Reason
AB ⊥ AC GivenCD ⊥ BD GivenAC ≅ BD Given∠A & ∠D are right angles Definition of perpendicularBC ≅ BC Reflexive property (common side)ΔABC ≅ ΔDCB HL congruence∠ABC ≅ ∠BCD CPCTCProvedThe Two-Steppers numbered 10 more than 5 times the number of waltzers. Also there were 10 times as many Two-steppers as waltzers. How many of each were there?
Answer: I think it is 1,200
Step-by-step explanation: search it up
demand curve's slope to P=2-0.0025Q
The demand curve slope to P = 2 - 0.0025·Q is -0.0025
What is the slope of a line?The slope of a line is the ratio of the rise of the line (vertical distance), divided by the horizontal distance of the line.
The equation of the demand curve is; P = 2 - 0.0025·Q
The possible question is to graph the demand curve.
Let P represent the price of the item in dollars, and let Q represent the quantity demanded, we get the following table, with which the graph of the demand curve can be plotted
Price($) [tex]{}[/tex] Quantity Demanded
2 [tex]{}[/tex] 0
1.75 [tex]{}[/tex] 100
1.50 [tex]{}[/tex] 200
1.25 [tex]{}[/tex] 300
1.00 [tex]{}[/tex] 400
0.75 [tex]{}[/tex] 500
0.5 [tex]{}[/tex] 600
0.25 [tex]{}[/tex] 700
0 [tex]{}[/tex] 800
The above points, obtained by using the equation function of MS Excel, can be used to plot the graph of the Demand function.
The slope of the graph, using any two points, is found as follows;
Slope = (1.75 - 2)/(100 - 0) = -0.0025
The required slope of the line is -0.0025The other characteristics of the line includes;
The x-intercept, the point at which P is 0 is obtained as follows;
P = 2 - 0.0025·Q = 0
At the x-intercept; 2 = 0.0025·Q
Q = 2/0.0025 = 800
The x-intercept is the point where the quantity, Q, is 800
The y-intercept, the point where, the quantity, Q, is 0 is found as follows;
P = 2 - 0.0025·Q
Q = 0, P = 2 - 0.0025 × Q = 2
The y-interceprt is the point where the price is $2
Please find attached the required graph of the demand function created with MS Excel.
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Triangle TRW will be dilated by a scale factor of n with the origin as the center of dilation to create triangle T′R′W′. Which ordered pair best represents the location of point R′?
An ordered pair which best represents the location of point R′ include the following: B. (−3n, −5n).
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
Next, we would have to dilate the coordinates of the preimage (Triangle TRW) by using a scale factor of n centered at the origin as follows:
Ordered pair T (-3, 5) → Ordered pair T' (-3 × n, 5 × n) = Ordered pair T' (-3n, 5n).
Ordered pair R (-3, -5) → Ordered pair R' (-3 × n, -5 × n) = Ordered pair R' (-3n, -5n).
Ordered pair W (4, -5) → Ordered pair W' (4 × n, -5 × n) = Ordered pair W' (4n, -5n).
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Complete Question:
Triangle TRW will be dilated by a scale factor of n with the origin as the center of dilation to create triangle T'R'W'. Which ordered pair best represents the location of point R′?
answer choices
(-3/n, -5/n)
(−3n, −5n)
(−3+n,−5+n)
(−3−n,−5−n)
Layla ate 3/8 of the pie her mother made. What part of the pie Layla not eat
Today only, a table is being sold for $237.80. This is 29% of its regular price. What was the price yesterday?
Answer:300
Step-by-step explanation:
Please simply 24/64
2/6
3/8
1/3
6/16
Gabe goes to the mall. If d is the number of items he bought, the expression 13.09 d plus 28 gives the amount he spent in dollars at one store. Then he spent 22 dollars at another store. Find the expression which represents the amount Gabe spent at the mall. Then estimate how much Gabe spent if he bought 4 items
Estimate the amount that Gabe spent if he bought 4 items will be $102.36.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Gabe goes to the mall. If d is the number of items he bought, the expression 13.09 d plus 28 gives the amount he spent in dollars at one store. Then he spent 22 dollars at another store.
Then the equation that represents the total amount is given as,
T = 13.09d + 28 + 22
T = 13.09d + 50
Then estimate the amount that Gabe spent if he bought 4 items will be given as,
T = 13.09(4) + 50
T = 52.36 + 50
T = $102.36
Estimate the amount that Gabe spent if he bought 4 items will be $102.36.
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What is the value of the expression below?
14+2+3(4)-(6-1-3)
1.10/2
2.15-12
3.30-1/
4.36-1/
THe value of the expression using BODMAS rule is 26
What is BODMAS rule ?The abbreviation BODMAS, which stands for "Brackets, Order of powers or roots, Division, and Multiplication," is followed by the BODMAS rule. A stands for addition and S for subtraction. According to the BODMAS rule, multi-step mathematical statements must be solved in the BODMAS order from left to right.
The order of operations, or BODMAS, is a method for carrying out operations in an arithmetic statement. Math is all about logic, and there are several established laws that help us with our calculations. BODMAS is one of the established rules for consolidating multiple operator expressions.
An expression or equation in mathematics has two parts:
NumbersOperatorsA character known as an operator joins two integers to form an expression or equation. The four most often used operators in mathematics are addition (+), subtraction (-), multiplication (*), and division (*/*). Finding the solution to mathematical statements or equations with just one operator is usually rather easy.
The expression is 14 + 2 + 3(4) - (6-1-3) = 14 + 2 + 12 - 2 = 26
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Given f(x)= 4x^2 - 4 + 1 and g(x)= 2x-1, which of the following are expression(s) for f•g? Select all that apply.
The value for the expression, (f * g)(x) is calculated as: C. 8x³ - 12x² - 6x -1
How to Evaluate the Expressions of Functions?
We are given the following functions,
f(x) = 4x² – 4x + 1 and g(x) = 2x – 1.
To find the value of the expression, (f * g)(x), it means we have to multiply the functions together. See the steps explained below.
(f * g)(x) = f(x) * g(x)
Plug in the values:
(f * g)(x) = f(x) * g(x) = (4x² – 4x + 1)(2x – 1)
(f * g)(x) = 4x²(2x – 1) - 4x(2x – 1) + 1(2x – 1)
Apply the distribution property of equality:
(f * g)(x) = 8x³ – 4x² - 8x² + 4x + 2x – 1
Combine like terms:
(f * g)(x) = 8x³ - 12x² - 6x - 1
Therefore, the answer is: C. 8x³ - 12x² - 6x - 1.
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A diver starts at a depth of 4m below sea level. After half an hour she is Fives Times as deep what is her depth
Answer:
Step-by-step explanation:
20 m i think
What is y ^ (5/8) in radical form.
Answer: ASK ONLINE
Step-by-step explanation:
According to the American Academy of Cosmetic Dentistry, 75% of adults believe that an unattractive smile hurts career success. Suppose that 25 adults are randomly selected. What is the probability that more than 22 of them would agree with the claim?
97.03% probability that 15 or more of them would agree with the claim.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
P(X = x) = [tex]C_{n,x} p^x (1-p)^{n-x[/tex]
where [tex]C _{n,x[/tex] = n! / r! (n-r)!
And p is the probability of X happening.
75% of adults believe that an unattractive smile hurts career success.
p = 0.75
and n = 75
Now, the probability that 15 or more of them would agree with the claim
P(X≥ 15) = 1 - P(X< 15)
So, P(X< 15) = P(X=0) + P(X=1) + P(X=2) + ..........................P(X=14)
and, P (X = 14) = [tex]C_{25, 14} (0.75)^{14} (0.25)^{11[/tex] = 0.0189
P (X = 13) = [tex]C_{25, 13} (0.75)^{13} (0.25)^{12[/tex] = 0.0074
P (X = 12) = [tex]C_{25, 12} (0.75)^{12} (0.25)^{13[/tex] = 0.0025
P (X = 11) = [tex]C_{25, 11} (0.75)^{11} (0.25)^{14[/tex] = 0.0007
P (X = 10) = [tex]C_{25, 10} (0.75)^{10} (0.25)^{15[/tex] = 0.0002
P (X = 9) = [tex]C_{25, 9} (0.75)^{9} (0.25)^{16[/tex] = 0
Then, P(X< 15)
= P(X=0) + P(X=1) + P(X=2) + ..........................P(X=14)
= 0.0002+0.0007+0.0025+0.0074+0.0189
= 0.0297
and, P(X≥ 15) = 1 - P(X< 15)
= 1- 0.0297
= 0.9703.
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If 1% of a number equals 5, find 2% of that number.
If 1% of a number equals 5, find 2% of that number is 2
What are algebraic expressions?Algebraic expressions are described as expressions composed of variables, constants, factors, coefficients and terms.
Arithmetic operations also make up these expressions, they are;
DivisionBracketAdditionParenthesesMultiplicationSubtractionAlso, fractions are described as part of a whole element, number or variable
From the information given, we have that;
1% of a number is 5
Let the number be x
1/2x = 5
Make 'x' the subject
x = 10
Substitute the value
2/10 of x
2/10 × 10
2
Thus, the value is 2
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Represent the table graphically. Does the graph represent a proportional relationship? How do you know? 0,1,2 50,100,150
Yes, the graph represent a proportional relationship.
What is a proportional relationship?
If one variable is always equal to a constant multiplied by the other variable(quantity), then we can say that those variables are in a proportional relationship.
Based on the type of relationship two or more quantities share, the proportion can be classified into different types. There are two types of proportions.
Direct Proportion relationship:-
This type describes the direct relationship between two quantities. In simple words, if one quantity increases, the other quantity also increases and vice-versa.
For example, if the speed of a car is increased, it covers more distance in a fixed amount of time. In notation, the direct proportion is written as y ∝ x.
Denoted by y = kx where k is the constant of proportionality.
Inverse Proportion relationship:-
This type describes the indirect relationship between two quantities. In simple words, if one quantity increases, the other quantity decreases and vice-versa.
It is represented as y ∝ 1/x. For example, increasing the speed of the car will result in covering a fixed distance in less time.
Denoted by y = k(1/x) or xy = k, where k is the constant of proportionality.
Now,
It is a direct proportional relationship because y-axis is increasing in multiples (50 multiple) of x.
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Find (g ○ f )(x ) where `f(x)=x2+8,g(x)=5x-2.
Answer:
(g ○ f)(x) = 5x² + 38
Step-by-step explanation:
to find (g ○ f)(x) substitute x = f(x) into g(x) , that is
g(f(x)
= g(x² + 8)
= 5(x² + 8) - 2
= 5x² + 40 - 2
= 5x² + 38
-58.8 ÷ -245 + (-3.5 x 2) ^3
Answer:
=−42.875x6+0.24
Step-by-step explanation:
−58.8
−245
+(−3.5x2)3
=0.24+−42.875x6
A bag of Halloween candy contains 4 Snickers, 3 Milky Ways and 5 Kit Kat bars. You reach into the bag, grab a bar and eat it. You reach into the bag, grab a second bar and eat it too. What is the probability of getting a Kit Kat and then a Milky Way?
The probability of getting a Kit Kat and then a Milky Way candy bars is the fraction 5/44
Probability of an event without replacementThe probability of an event without replacement implies that once an item is drawn, then we do not replace it back to the sample space before drawing another item.
total number of candy bars = 12
probability of first getting a Kit Kat candy bar = 5/12
probability of then getting a Milky Way candy bar = 3/11
probability of getting a Kit Kat and then a Milky Way candy bars = 5/12 × 3/11
probability of getting a Kit Kat and then a Milky Way candy bars = 5/44
Therefore, the probability of getting a Kit Kat and then a Milky Way candy bars is the fraction 5/44.
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n
2016
20162016, the city of Rio de Janeiro had a population density of
5377
people
km
2
5377
km
2
people
5377, start fraction, start text, p, e, o, p, l, e, end text, divided by, start text, k, m, end text, squared, end fraction .
What was the population density of Rio de Janeiro in people per square meter?
The population density of Rio de Janeiro in people per square meter is 5. 377 x 10 ⁻³ people per m²
How to find the population density ?To find the population density in meters squared when given the population density in kilometers squared, you first need to find the conversion factor between kilometer squared and meters squared.
1 kilometer squared is equal to 1, 000, 000 meters squared.
The population density of Rio de Janeiro in meters squared is therefore:
= Population density in kilometers squared / Conversion factor
= 5, 377 / 1, 000, 000
= 0. 005377
= 5. 377 x 10 ⁻³ people per m²
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The full question is:
In 2016, the city of Rio de Janeiro had a population density of 5377 people/km2.
What was the population density of Rio in people per square meter?
Which arrangement shows 26/4, 6.45, 6 2/5, and 50/8 in order from least to greatest?
A. 50/8, 6 2/5, 26/4, 6.45
B. 6 2/5, 50/8, 6.45, 26/4
C. 50/8, 6 2/5, 6.45, 26/4
D. 26/4, 50/8, 6 2/5, 6.45
20 points.
The arrangement of 26/4, 6.45, 6 2/5, and 50/8 in order from least to greatest is C. 50/8, 6 2/5, 6.45, 26/4.
How can the order be determined?The concept that will be used here is ordering of numbers using < signs.
To arrange the shows, we can convert 26/4, 6.45, 6 2/5, and 50/8 to decimal so this will help us to determine the order.
26/4=6.50
6.45=6.45
6 2/5=32/5 = 6.40
50/8 =6.25
Then 6.25<6.40 <6.45 <6.50 and this implies that the order that the arrangement follows is 50/8, 6 2/5, 6.45, 26/4
Therefore, option C is correct.
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←
Find a if XZ = 125,
XY = 3a and YZ = 2a.
Y is 275.Add any like terms together, combining x-terms with x-terms and constants with constants, on either side of the equation.
How can I locate expressions that are equivalent?Add any like terms together, combining x-terms with x-terms and constants with constants, on either side of the equation. The x-term is typically put before constants when arranging the terms in the same sequence. The two phrases are equal if each of the terms in both of them is the same.
Explanation:
x 2 + xy+xz=135; y 2 + yz+ xy=351; z 2 + xz+ yz=243; (iii)
When I (ii), and (iii) are added together, we obtain x 2 + y 2 + z 2 + 2(xy+yz+xz) = 729, which converts to (x+y+z) 2 = 27 2.
x+y+z=27
........
(iv)
According to equation I x 2 + x y + x z = 135 => x(x+y+z) = 135 => x27=135 => x=5
In equation (ii), we have y 2 + y z + x y = 351, which leads to y (x+y+z) = 351.
y×27=351 \s=>
y=13
Once more, we obtain the following from equation (iii): z 2 + x z + y z = 243; z (x + y + z) = 243; z 27 = 243.
z=9 \sx \s2 \s +y \s2 \s +z \s2 \s =5
2 \s +13 \s2 \s +9 \s2 \s =275.
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ryann has 80$ to spend on gifts. She already decided to use $25 for a scarf for her grandmother. She wants to spend the reaming money to purchase gifts for her four freinds. She will spend the same amount of money for each friend's gift. What is the most she can spend on each friend?
Answer:
Okay so since she has 80 dollars, and already spent 25, then she would have 55 dollars remaining.
Now that she has 55 dollars, she will divide it up evenly between her 4 friends.
55/4 = 13.75
The most that she would be able to give them is $13.75
Step-by-step explanation:
Hope it helps! =D
The ratio of 3 red marbles to every 2 blue marbles
Answer:
yes
Step-by-step explanation:
Please someone help me out.
How many x-intercepts does the graph of
y = x³ - 1 have?
JO
K
1
L 2
M 3
N An infinite number
-1 x-intercepts in the graph.
The quantity of x-intercepts on a graph can be determined in what way?We can graph lines using the x- and y-intercepts since any line is determined by two points. When y=0, solve for x to determine the x-intercept. With x=0, solve for y to determine the y-intercept. Due to its universal applicability to all equations, this technique for determining x- and y-intercepts will be employed throughout our algebra study.Any number of -intercepts, including none and infinitely many, can exist on the graph of a function.We can graph lines using the x- and y-intercepts since any line is determined by two points. When y=0, solve for x to determine the x-intercept. With x=0, solve for y to determine the y-intercept.Explanation:
Y = X^3 - 1
Put y = 0 , x = -1.
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Given the following graph a. Evaluate f (1). f(1) = f b. Solve for f(x) = 1. If there is more than one solution, enter the solutions separated by semicolons (e.g. 2; 4; 6). x
For f(x) = 1 the value of x is 0, -6, and the value of the function at x= 4 or f(4) is -3.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given, a function f(x) in the graph
f(x) = y
F(X) represents the function value at various values of x
From graph,
f(4) = -3
Because at x = 4, y = -3
at f(x) = 1
since f(x) = y
y = 1
satisfying at two values of x that are -6, 0
Therefore, For f(x) = 1 the value of x is 0, -6 and the value of f(4) is -3.
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Complete question:
Colleen's family is moving to a new home overseas. They will send their car two thousand miles across the ocean in a shipping container. Their shipping container is twenty feet long, eight feet wide, and eight feet tall. What is the volume of the shipping container?
Answer: The volume of a rectangular container is given by the formula:
Volume = length * width * height
In this case, the length of the container is 20 feet, the width is 8 feet, and the height is 8 feet.
So the volume of the shipping container can be calculated as:
Volume = 2088 = 1,360 cubic feet
So, the volume of the shipping container is 1,360 cubic feet
Step-by-step explanation:
Sheena needs 1 3/4 cups of sugar to make pancakes. She already has 5/8 cups of sugar. How much more sugar does she need?
Answer: 9/8
Step-by-step explanation:
What is the solution to √7x-4 = 2√x ?
Answer:
B
Step-by-step explanation:
take square on both sides,
7x-4 = 4x
so, x = 4/3
find the value of help
Please help
Answer:
[tex]x=29^{\circ}[/tex]
Step-by-step explanation:
Please refer to the picture attached as I labeled the angles.
Given
[tex]\angle{B}=90^{\circ}[/tex]
[tex]\angle{ADB}=58^{\circ}[/tex]
[tex]AD=CD[/tex]
[tex]\angle{ACD}=\angle{CAD}[/tex] which also equals x in your picture.
We need to use the Exterior Angle Property to evaluate x.
This property states that the exterior angle equals sum of two interior opposite angles.
[tex]\angle{ACD}+\angle{CAD}=58^{\circ}[/tex]
Substitute x for [tex]\angle{ACD}[/tex] and [tex]\angle{CAD}[/tex].
[tex]x+x=58^{\circ}[/tex]
Add x and x.
[tex]2x=58^{\circ}[/tex]
[tex]x=29^{\circ}[/tex]
Answer:
The angle is 32
Step-by-step explanation:
The formula for the sum of interior angles is [tex](n-2)180[/tex]
We have a triangle inside a triangle.
A triangle has 3 sides.
[tex](n-2)180\\(3-2)180\\1(180)\\180[/tex]
The picture shows us an angle of 90 and 58.
All 3 angles must add up to 180.
[tex]180-90-58[/tex]
[tex]x=32[/tex]
Zach solves the system below and finds the solution (8, -7).
x + y = -15
x + y = -1
Use a graph to complete the explanation for whether Zach's solution is reasonable.
<------------> x + y = -15
< -----------> = -1
The graph shows that the of the solution , so Zach's solution reasonable.