Answers
Answer:
a +7d = 11
Step-by-step explanation:
The sum of an arithmetic series is given by the formula ...
Sn = (n/2)(2·a1 +d(n -1))
where n is the number of terms, a1 is the first term, and d is the common difference.
__
Here, you are given n=15, S = 165, a1=a, and asked to find a relation for 'a' and 'd'. Substituting the known values, we have ...
165 = (15/2)(2a +d(14))
11 = a +7d . . . . . . . . simplify and divide by 15
We have found the relation to be ...
a +7d = 11 . . . . . as required
Related Questions
how many solutions does the following have? 3 (2x-4) = 2 (3x-6)
Answers
Answer: There are infinite solutions.
Step-by-step explanation:
3(2x-4) = 2(3x-6)
6x - 12 = 6x - 12
-12 = -12
0 = 0
Guys, Can you please help me with these questions
Answers
Answer:
a) [tex]w^{13} x^{5} y^{6}[/tex]
b) [tex]\frac{x}{3y^{6} }[/tex]
Step-by-step explanation:
a) [tex](w^{2} xy^{3} )^{2}(w^{3}x )^{3}[/tex]
1. Distribute the second power (2) outside the first pair of parenthesis:
[tex](w^{2(2)} x^{2} y^{3(2)} )[/tex]
= [tex]w^{4} x^{2} y^{6} (w^{3}x )^{3}[/tex]
2. Distribute the third power (3) outside the second pair of parenthesis:
[tex](w^{3(3)} x^{3} )[/tex]
= [tex]w^{4} x^{2} y^{6} w^{9} x^{3}[/tex]
3. Combine like terms:
[tex]w^{13} x^{5} y^{6}[/tex]
--------------------------------------------
b) [tex]\frac{2x^{2} y^{5} }{6xy^{11} }[/tex]
1. Factor the number 6 (= 2 · 3):
[tex]\frac{2x^{2} y^{5} }{2(3)xy^{11} }[/tex]
2. Cancel the common factor (2):
[tex]\frac{x^{2} y^{5} }{3xy^{11} }[/tex]
3. Cancel out [tex]xy^{5}[/tex] in the numerator an denominator:
[tex]\frac{x}{3y^{6} }[/tex]
hope this helps!
In the diagram, AD = 5, BD = 4, and the area of triangle ACD is 15. Find the area of triangle ABC.
Answers
Answer:
√20 =4.47
Area =4.47*4.5
Area =20 unit ^2
can you answer I need help
Answers
A reduction means that the original figure is made smaller.
An englargement means that the original figure is made larger.
The new figure (shown by the ' next to each letter) is smaller than the original. Therefore, the dilation was a reduction.
Hope this helps!
Hello Please Find The Answer To This Question (easy)
Answers
Answer:
y=-2x-4
Step-by-step explanation:
by using this website
its a graphing calculator
desmos. com/calculator
Where does the energy stored in coal originally come from?
A. The Earth's Core
B. Minerals
C. The Sun
D. Radioactive material in the crust
Answers
Answer: The Sun
Step-by-step explanation:
Energy has existed from the beginning of time. The sun was the initial source of energy, providing heat and light during the day. People used light to wake up and sleep, depended on wood and dung for heat, and water power to run primitive mills.
Please help so lost, it is not making any sense
Answers
????????
Step-by-step explanation:
1,1,1
Find the slope of the given line please see attached photo thank you
Answers
Answer:
2/5
Step-by-step explanation:
Find two integer coordinate sets ( use the two points labelled)
slope = m = (y1-y2)/(x1-x2) =
= ( 1 - -1 ) / (3- - 2) = 2/5
(NOTE: it does not matter which point you choose to be x1,y1 or x2,y2 )
Five runners need to be arranged in 5 lanes for a race so that there is a runner in each lane. How many unique ways are there to arrange the runners in the 5 lanes?
Answers
Answer:
25
Step-by-step explanation:
When answer questions about unique combinations, there are usually two ways people go about finding the solutions.
First, sometimes it can take a while, but it often helps people visualize the question if they jot down or sketch each different combination. Then, they can just count them up at the end to find there answer.
The easeier way is to use a quick math trick. If you have 5 runners, with 5 potential lanes each runner could start in, you can just multiply these two variables together to get your answer of the number of possible options.
So,
5 runners * 5 lanes = 25 possible combinations for each lane and runner
The number of unique ways that the runner can be arranged in 5 lanes for a race is 120.
What are Combinations?Combinations are defined as the arrangement of objects or numbers in a way such that the order of the arrangement does not matter.
Total number of runners = 5
Total number of lanes = 5
Number of ways that 5 runners can be arranged = 5! = 120
Hence the number of ways is 120.
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Plss I need help with this
Answers
Step-by-step explanation:
Since TRIANGLE BAD is an isosceles traingle you know line BA is equal to line AD
and since C is the given midpoint of line BD you know BC is equal to CD
both triangles share line AC so the third side is also the same
so now you know traingles BAC, and CAD have three sides which all measure the same making ABC equal to ADC
Triangle XYZ is equilateral with vertices located on circle W.
Circle W is shown. Line segments W Y, W Z, and W X are radii. Lines are drawn to connect the points on the circle to form a triangle. Sides Z X, X Y, and Z Y are congruent.
Which measurements are correct? Select two options.
mArc X Y = 60°
mArc Y Z = 120°
mArc Z X = 180°
m∠XWZ = 60°
m∠YWZ = 120°
Answers
Based on the inscribed angle theorem, the measurements that are correct are: B. m(arc YZ) = 120°; E. m∠YWZ = 120°.
What is the Inscribed Angle Theorem?The inscribed angle theorem states that the measure of an inscribed angle in a circle equals the twice the measure of the intercepted arc or twice the measure of the central angle.
In the circle given, since the triangle is an equilateral triangle, therefore, all its angles each equals 60°. Therefore:
m(XY) = m(YZ) = m(ZX) = 2(60°) = 120°.
The central angles, m∠XWZ = m∠XWY = m∠YWZ = 120°.
Therefore, the correct measurements are: B. m(arc YZ) = 120°; E. m∠YWZ = 120°.
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Answer:
B&E
Step-by-step explanation:
Trust me bruv
Evaluate the expression when a=7 and b=-6.
7a-b
Answers
Answer:
54
Step-by-step explanation:
7*a-b , a = 7 , b = - 6
7*7 - (-6)
49 + 6 = 54
If its 7 * (a - b)
7*(7 - (-6))
7 * 13
91
-x^+22+54 help me with this
Answers
Answer:
11
Step-by-step explanation:
answer these questions and show working out.
(extra points for all)
Answers
Answer:
See below
Step-by-step explanation:
We can find the Highest Common Factor (HCF) by the prime factorization of the terms.
===============================================================
a) 4 and 5
⇒ 4 = 4 x 1
⇒ 5 = 5 x 1
⇒ HCF (4, 5) = 1
=============================================================
b) 8 and 13
⇒ 8 = 2 x 2 x 2 x 1
⇒ 13 = 13 x 1
⇒ HCF (8, 13) = 1
=============================================================
i) 80 and 120
⇒ 80 = 40 x 2
⇒ 120 = 40 x 3
⇒ HCF (80, 120) = 40
Hugo received $100 dollars for his birthday which he uses to make an initial deposit in
a saving account. He gets an allowance of $20 per week which he deposits in his saving
account. Write an equation to represent the balance of his saving account over time.
Which amount represents the slope?
Which amount represents the y-intercept?
v
The equation would be written as:
y=
X+
<
The x in this equation represents:
The y in this equation represents:
Answers
The linear equation for his balance over time is given by:
y = 20x + 100.
The x-intercept is of 20, which is the amount by which the balance increases each week.The y-intercept is of 100, which is the initial balance.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, he stats the balance with the birthday present of $100, and gets an allowance of $20 a week, hence the equation for the balance after x weeks is given by:
y = 20x + 100.
Hence:
The x-intercept is of 20, which is the amount by which the balance increases each week.The y-intercept is of 100, which is the initial balance.More can be learned about linear functions at https://brainly.com/question/24808124
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write the decimal equivalent for this fraction 7/100
Answers
Answer:
0.07
Step-by-step explanation:
To convert from fractions into decimals, you have to divide the numerator by the denominator. The numerator is the number on top of the fraction, and the denominator is the number on the bottom of the fraction.
7/100 = 0.07
Please mark brainliest!
write a event that has a probability of 1
Answers
A probability of 1 means that the event will happen. If the probability of a road traffic accident was 1 there would be nothing you could do to stop it.
that's my answer
how to solve a pair of equations
Answers
1 + 2 x 3 + 4
Or,
3 x 4 + 6 /div 5
--
What you'd do:
1+2 x 3+4 First, add either 1+2 or 3+4 which is 3 & 7. then, youd multiply your answers as, 3 x 7 which is, 21.
--
Please ask if you have any questions
1 . The ratio of 3 1/3 to 2 1/4 is equal to the ratio of?
Answers
Answer:
40 : 27
Step-by-step explanation:
[tex]3\frac{1}{3} : 2\frac{1}{4}[/tex]
Turn into improper fractions:
[tex]\frac{10}{3} : \frac{9}{4}[/tex]
Make them integers by multiplying them by 12:
40 : 27
The ratio of 3 ¹/₃ and 2 ¹/₄ is 40 : 27.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b.
The given numbers are,
3 ¹/₃ and 2 ¹/₄
To find the ratio of the given numbers,
First simplify the numbers,
3 ¹/₃ = 10 / 3
2 ¹/₄ = 9 / 4
Divide 10 / 3 and 9 / 4
= (10 / 3) / (9 / 4)
= (10 x 4) / (9 x 3)
= 40 / 27
= 40 : 27.
The required ratio is 40 : 27.
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I need help with this
Answers
Answer:
Step-by-step explanation:
Remark
The longer the line, the larger the arc is. So
How to put in order.
It can be shown that the angle opposite the chord is related to the arc length by α = arc length / r Since r never changes, you are left with
α = k * chord length.
So what you conclude is that the larger the angle, the larger the arc length.
The largest angle is Q so the length of the arc opposite Q is the largest. The other two lines are handled the same way.
Answer:
Arc length PR is the largest.Arc Length PQ is the second largest.Arc Length RQ is the Smallest.Which of the following describes a simple event?
A. Drawing a three from a deck of cards and rolling 2 on a die
B. Tossing 3 coins and getting tails once
C. Rolling a die and getting a 2
D. Spinning red on a spinner and rolling an odd number on a die
Answers
Answer: c
Step-by-step explanation:
C is the only that gave us a single outcome so it’s a simple event
Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for full credit. Total score: ____ of 15 points (Score for Question 1: ___ of 4 points) 1. What is the value of x? Show all of your work. Answer:
Answers
To solve this equation we must find the value of x using the other values provided in the operation.
What is an equation?An equation is a type of mathematical operation that is characterized by expressing an equality between two expressions, each of these expressions involved in an equation are called members and are separated by the equal sign.
On the other hand, equations are characterized by having elements or known and unknown values related by mathematical operations.
According to the above, it can be inferred that we must use an equation to calculate the value of x using the other values provided by the situation.
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Graph a line representing the proportional relationship with slope 3 containing the point (2, 6).
To graph the line, plot two points on the line.
Answers
Answer:
(1, 3) and (0, 0)
Step-by-step explanation:
y = mx + b
m is the slope which is 3 (given)
b is the y intercept
(x, y) → (2, 6)
6 = 3(2) + b
6 = 6 + b
b = 0
so the equation is y = 3x
one point:
y = 3(1)
y = 3 when x = 1
(1, 3)
y = 3(0)
y = 0 when x = 0
(0, 0)
which graph represents y=3x-5
Answers
Answer:
(it won't let me paste a graph here)
(but it a / line on the graph.)
Step-by-step explanation:
Use Desmos Graphic Calculator, plot this equation in and it should show up a graph of that. : )
A car's speed is 80 2/3 miles in one hour. Going at the same speed, how far (in miles) will it travel in 2 1/4 hours?
Answers
Answer:
181.5 miles
Step-by-step explanation:
80 2/3 m/hr * 2 1/4 hr = 181. 5 miles
[100 POINTS!!] Consider this cone and pyramid, which have the same height, h. Planes parallel to the base cut through each solid at equal heights, as shown.
Answers
#Circle 1
π12²144πunits²#Circle 2
6²π36πunits²#Circle 3
3²π9πunits²#Triangle 1
1/2(12π)(24)6π(24)144πunits²#Triangle 2
1/2(6π)(12)36π units²#Triangle 3
1/2(3π)(6)9π units²The area of each cross section of the cone and pyramid is the same which is 2[tex]\pi[/tex].
This is because the cone and pyramid are similar solids, and the cross sections are taken at equal heights.
The similarity of the cone and pyramid can be seen by comparing the triangles formed by the apex, a point on the base, and the intersection of the plane with the solid. These triangles are similar because they have the same angles.
The fact that the cross sections are taken at equal heights means that the triangles are similar in size as well. This means that the areas of the triangles are also the same.
Therefore, the area of each cross section of the cone and pyramid is the same.
[tex]\pi[/tex][tex]h^2[/tex] / (1/2) h*h = 2[tex]\pi[/tex][tex]h^2[/tex] / [tex]h^2[/tex] = 2[tex]\pi[/tex]
The cross sections of the cone and pyramid are both triangles. The triangles are similar because they have the same angles. The fact that the cross sections are taken at equal heights means that the triangles are similar in size as well. This means that the areas of the triangles are also the same. Hence, the answer is 2[tex]\pi[/tex].
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Surface area of cubes and rectangular prisms
Answers
Answer:
130 square yards
Step-by-step explanation:
5 x 4 = 20
5 x 5 = 25
20 x 4 = 80
25 x 2 = 50
80 + 50 = 130
The surface area for this cube and rectangular prisms is 75 cubic square inches.
How do you find the surface area of a square and rectangular prism
Surface area of a prism is the sum of the area of the 2 polygonal bases and the area of the lateral faces. The surface area of a prism is measured in terms of square units. The Surface Area of a Prism Formula is given as, Surface Area Of A Rectangular Prism is A = 2 (wl + lh + hw)
B x W x HSo [tex]5[/tex] · [tex]4[/tex] · [tex]5=75[/tex] [tex]cubic[/tex] [tex]inches[/tex]
Therefore, The surface area for this cube and rectangular prisms is 75 cubic square inches.
At Goodies restaurant the quantity of large pizza sold is 200 at the unit price of $15. suppose the price elasticity of demand for pizza is $1.5, and you would to increase the quantity sold to 250,then the new price must be?
Answers
The new price of pizza when the quantity sold is increased to 250 is $12.45.
What is the new price of pizza?Price elasticity of demand measures the responsiveness of quantity demanded to changes in price of the good.
Price elasticity of demand = percentage change in quantity demanded / percentage change in price
Percentage change in quantity demanded = (250 / 200) - 1 = 25%
Percentage change in price = 25% / 1.5 = 16.67%
New price = (0.1667 x 15) - 15 = $12.45
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Marcus is rolling a number cube will show 10 is?
Answers
Answer:
no
Step-by-step explanation:
The cube has only 6 sides,
so it has only 6 numbers : 1, 2, 3, 4, 5 & 6.
ASAP!!!
Every day, Jorge buys a lottery ticket. Each ticket has a probability of 0.2 of winning a prize. After seven days, what is the probability that Jorge has won at least one prize? Round your answer to four decimal places.
(a) The probability that Jorge has won at least one prize is ____.
Answers
Step-by-step explanation:
the probability to win is 0.2.
the probability to lose is 1-02 = 0.8.
there is no sure win after at least n trials.
on day 1 the probability to win is 0.2.
on day 2 the probability to win at least once is
the probability to have won on day 1 but not on day 2, plus the probability to have won on day 2 but not on day 1 plus the probability to have won on both days :
0.2×0.8 + 0.8×0.2 + 0.2×0.2 = 0.32 + 0.04 = 0.36
...
on day 7 we have
the probability to have won on one day but not on 6 days times the combination of picking 1 day out of 7,
plus the probability to have won on 2 days but not on 5 days times the combinations to pick 2 out of 7,
plus the probability to have won on 3 days but not on 4 days times the combinations to pick 3 out of 7,
...
plus the probability to have won on all 7 days.
that is
0.2.×0.8⁶ × 7 +
+ 0.2²×0.8⁵ × C(7, 2) +
+ 0.2³×0.8⁴ × C(7, 3) +
+ 0.2⁴×0.8³ × C(7, 4) +
+ 0.2⁵×0.8² × C(7, 5) +
+ 0.2⁶×0.8 × 7 +
+ 0.2⁷
but before we lose ourselves in tons of little operations, this is the same as the opposite of having lost on all 7 days.
that is
1 - 0.8⁷ = 1 - 0.2097152 = 0.7902848 ≈ 0.7903
so, the probability that Jorge has won at least one prize is
0.7903
