Answer:
First Case:
[tex]\displaystyle p=\frac{5}{2}\text{ and } d=-2[/tex]
Second Case:
[tex]\displaystyle p=-\frac{5}{4}\text{ and } d=\frac{7}{4}[/tex]
Step-by-step explanation:
We know that the first three terms of an arithmetic series are:
[tex]6p+2, 4p^2-10, \text{ and } 4p+3[/tex]
Since this is an arithmetic sequence, each subsequent term is d more than the previous term, where d is our common difference.
Therefore, we can write the second term as;
[tex]4p^2-10=(6p+2)+d[/tex]
And, likewise, for the third term:
[tex]4p+3=(6p+2)+2d[/tex]
Let's solve for d for each of the equations.
Subtracting in the first equation yields:
[tex]d=4p^2-6p-12[/tex]
And for the second equation:
[tex]2d=-2p+1[/tex]
To avoid fractions, let's multiply the first equation by 2. Hence:
[tex]2d=8p^2-12p-24[/tex]
Therefore:
[tex]8p^2-12p-24=-2p+1[/tex]
Simplifying yields:
[tex]8p^2-10p-25=0[/tex]
Solve for p. We can factor:
[tex]8p^2+10p-20p-25=0[/tex]
Factor:
[tex]2p(4p+5)-5(4p+5)=0[/tex]
Grouping:
[tex](2p-5)(4p+5)=0[/tex]
Zero Product Property:
[tex]\displaystyle p_1=\frac{5}{2} \text{ or } p_2=-\frac{5}{4}[/tex]
Then, we can use the second equation to solve for d. So:
[tex]2d_1=-2p_1+1[/tex]
Substituting:
[tex]\begin{aligned} 2d_1&=-2(\frac{5}{2})+1 \\ 2d_1&=-5+1 \\ 2d_1&=-4 \\ d_1&=-2\end{aligned}[/tex]
So, for the first case, p is 5/2 and d is -2.
Likewise, for the second case:
[tex]\begin{aligned} 2d_2&=-2(-\frac{5}{4})+1 \\ 2d_2&=\frac{5}{2}+1 \\ 2d_2&=\frac{7}{2} \\ d_2&=\frac{7}{4}\end{aligned}[/tex]
So, for the second case, p is -5/4, and d is 7/4.
By using the values, we can determine our series.
For Case 1, we will have:
17, 15, 13.
For Case 2, we will have:
-11/2, -15/4, -2.
A shop sells 3 different types of tea
200 g of Kenyan tea costs £2.10
300 g of Columbian tea costs £3.45
150 g of Indian tea costs £1.70
a) Work out the cost of 100g of each type of tea
b) Which type of tea is the cheapest?
Answer:
The cheapest is the Kenyan tea which costs £1.05 for each 100g.
Step-by-step explanation:
A)
200 g of Kenyan tea costs £2.10
1. Calculate the rate of each gram, by dividing 2.10/200
0.0105 x 100 = £1.05 for each 100g
300 g of Columbian tea costs £3.45
1. Calculate the rate of each gram, by dividing 3.45/300
0.0115 x 100 = £1.15 for each 100g
1. Calculate the rate of each gram, by dividing 1.70/150
150 g of Indian tea costs £1.70
0.01133333333 x 100 = £1.133333333 for each 100g
B) The cheapest is the Kenyan tea which costs £1.05 for each 100g.
pls help worth a lot of points
Answer: Ordinarily, no, it wouldn't matter.
Step-by-step explanation: No matter in what order you add it up it will be the same answer in the end.
The graph of the function f(x) = (x – 4)(x + 1) is shown below.
On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1.75, negative 6.2), and goes through (4, 0).
Which statement about the function is true?
The function is increasing for all real values of x where
x < 0.
The function is increasing for all real values of x where
x < –1 and where x > 4.
The function is decreasing for all real values of x where
–1 < x < 4.
The function is decreasing for all real values of x where
x < 1.5.
the funcn is decreasing for all real values of x where x<1.5
A football field is 300ft long a sloth moving very quickly travels 60ft every 5 minutes based on this ratio how many minutes would it take a sloth to travel the length of a football field
Answer:
25 minute
Step-by-step explanation:
Speed is the ratio of the total distance traveled to the total time taken to reach this distance. The formula for speed is:
Speed = total distance / total time taken
The total distance covered by the sloth = 60 ft, and the time taken = 5 minutes, hence:
Speed = total distance / total time taken
speed of the sloth = 60 ft / 5 minutes = 12 ft per minute.
We can calculate the time taken for the sloth to travel the length of the football field (i.e. 300 ft)
speed = distance / time
12 ft/minute = 300 ft / time
time = 300 ft / (12 ft/minute)
time = 25 minute
Use the original price and the markup to find the retail price.
Original price: $60; Markup: 20%
Answer:
$72 would be the retail price
Step-by-step explanation:
In electronics, the formula V = IR is called Ohm's Law. It gives the relationship in a circuit between the voltage V (in volts), the current I (in amperes), and the resistance R (in ohms). Find R when I = 2 − 3i amperes and V = 34 + i volts.
Answer:
R = 5 + 8i (Ohm)
Step-by-step explanation:
R = V/I
= (34 + i)/(2 - 3i)
= 5 + 8i (Ohm)
Simplifyyyyyyyyyyyyyyyyy
Answer:
Here ya go:
Step-by-step explanation:
Answer:
ok, yea, the above answer is correct
Step-by-step explanation:
Can I get help on 1 and 2
Answer:
1.the slope is 1/2 and the y int is -4
2.the slope is -3 and the y int is 6
Determine whether each sum or product is even or odd.
10,481 + 4,569
Answer:
even
Step-by-step explanation:
11050 it's even because it ends in a zero
Does the rule y = 6x7 represent an exponential function?
yes
no
No , the rule y = 6x ^7 does not represent an exponential function.
The exponential function is a mathematical function of the form f(x) = a^x. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0. The exponential function is defined by the formula f(x) = a^x. where the input variable x is displayed as an exponent. An exponential curve depends on the exponential function and the value of x.
We have given y =6 x^7.
Here the variable is base & the exponent is an integer.
But an exponential function has a constant as its base and a variable as its exponent .
So, it does not represent an exponential function .
Learn more about exponential function here :
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Which graph represents the function fx) =|x–4?
The image below shows the graph f(x) = |x| – 4
Hope this helps! :)
2 tablets, 3x per day for 10 days
Answer:
60
Step-by-step explanation:
Simple
First you multiply 2 x 3 =6
Then you multiply 6 x 10 =60
That mean 60 is the answer you are looking for
Hope This Helps :)
1. Shlomo Benartzi begins his talk by outlining three things that we as a people are not
doing well. What are these three things? Do you agree or disagree with his evaluation of
these things?
According to Shlomo Benartzi's talk, the three things we humans do badly are risk taking, insurance and money management.
The biblical king who is most well-known for his wisdom is Solomon. When Solomon offered a sacrifice to God, God later asked him in a dream what he wanted from Him. Solomon prayed for wisdom in order to lead and govern his people more effectively.
The processes of setting up a budget, saving money, making investments, and spending are all examples of money management. To help you overcome the barriers to wealth, money management gives you a 360-degree view of your financial situation while putting important financial disciplines into practice. You have much more control over your financial future when you have a clear purpose for your money and sound money management principles behind it. Budgeting, investing, spending, and other types of capital usage oversight are all included in the definition of money management.
Learn more about money management here
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the question: a computer manufacturer built a new facility for assembling computers. there were construction and new equipment cost. the company paid for these cost and made combined profits of $80 million after four years as shown in the graft.
answers:
a: f(x)=60x-160
b:f(x)=-60x+160
c:f(x)=-80x +4
d: f(x)= 80x -4
Answer:
The equation that closely represents the graph is [tex]\mathbf{y=60x-160}[/tex]
Option A is correct.
Step-by-step explanation:
We need to find equation that represents the graph.
We can write equation in slope-intercept form: [tex]y=mx+b[/tex] where m is slope and b is y-intercept.
For finding the equation we need to find slope and y-intercept
Finding slope
The slope can be found using formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we can find [tex]x_1=0, y_1=-160, x_2=1, y_2=-100[/tex]
Putting values and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-100-(-160)}{1-0} \\Slope=\frac{-100+160}{1}\\Slope=-100+160\\Slope=60[/tex]
We get Slope = 60
Finding y-intercept
Using point (0,-160) and slope m = 60, we can find y-intercept
[tex]y=mx+b\\-160=60(0)+b\\b+0=-160\\b=-160[/tex]
Writing the equation
So, the equation for given graph having slope m = 60 and y-intercept b =-160 is:
[tex]y=mx+b\\y=60(x)+(-160)\\y=60x-160[/tex]
So, The equation that closely represents the graph is [tex]\mathbf{y=60x-160}[/tex]
Option A is correct.
Graph the image of this triangle after a dilation with a scale factor of 1/2 centered at (−5, 1).
Use the Polygon tool to graph the dilated triangle.
Answer:
Please see picture below.
Step-by-step explanation:
Convert 0.45 to a percent. Remember to add the percent sign.
0.45%
4.5%
45%
50%
Answer:
45%
Step-by-step explanation:
4y-7-(y-7) find answer
Answer:
3y
Step-by-step explanation:
4y-7-1(y-7)
4y-7-y+7
4y-y
3y
A device produces random 64-bit integers at a rate of one billion per second. After how many years of running is it unavoidable that the device produces an output for the second time? Round to the nearest number of years.
Answer:
3171 × 10^(44) years
Step-by-step explanation:
For each bit, since we are looking how many years of running it is unavoidable that the device produces an output for the second time, the possible integers are from 0 to 9. This is 10 possible integers for each bit.
Thus, total number of possible 64 bit integers = 10^(64) integers
Now, we are told that the device produces random integers at a rate of one billion per second (10^(9) billion per second)
Let's calculate how many it can produce in a year.
1 year = 365 × 24 × 60 × 60 seconds = 31,536,000 seconds
Thus, per year it will produce;
(10^(9) billion per second) × 31,536,000 seconds = 3.1536 × 10^(16)
Thus;
Number of years of running is it unavoidable that the device produces an output for the second time is;
(10^(64))/(3.1536 × 10^(16)) = 3171 × 10^(44) years
A shirt was marked down 25% which means you saved $15. What was the original cost of the shirt? What is the new price?
Solve the given equation for x.
2x-B = 10
Answer:
x=5+b/2
Step-by-step explanation:
move all terms that dont contain x to the right, and solve
Answer:
2 times 6-2+10
Step-by-step explanation:
Can you explain this question please??
Answer:
the answer is here.
Step-by-step explanation:
hope it will helps you
Mayfield Water Company manufactures two types of bottled water: regular and flavored. The company produces at least twice as many bottles of regular water as bottles of flavored water. The company can produce, at most, 1,500 bottles of water per week. Which of these combinations would be reasonable for the company to produce in one week’s time?
A. 750 flavored and 750 regular
B. 500 flavored and 1,000 regular
C. 750 flavored and 1,000 regular
D. 1,000 flavored and 2,000 regular
Answer:
the answer is A
Step-by-step explanation: it's a because if u add 750 + 750 it will give you 1,500
Is y=3x+5 a relation or not ?
the equation you have given is linear because x directly influences y
Theoretically, if the spinner is spun 150 times, how many times would you expect to get an even number?
150/2 = 75
The spinner would have to be spun 75 times to expect to get an even number.
The volume of a glass container is given to be 2x3+9x2-11x-30. If the height of the glass
container is given to be x - 2, what are the dimensions of the rectangular base of the glass
container?
Answer:
d
Step-by-step explanation:
if ummm its d
Simplify the expression. Explain each step 7(4y)
Answer:
28y
Step-by-step explanation:
7 x 4 =28
then just add the y to it
and you get
28y
A package of 15 batteries cost $14.25 what is the cost per battery
Answer: $0.95 per battery
Step-by-step explanation: Divide 14.25 and 15.
giving brainliest if correct!
There are 8 sprinters in the Olympic 100-meter finals. The gold medal goes to first place, silver to second, and bronze to third. In how many ways can the medals be awarded?
Answer:
I think it is 336 ways the medals can be given out.
Step-by-step explanation:
Pls graph and answer!
Answer:
Closed bracket “ ] “
at -5 facing the left then fill in the graph from -5 to -10
It’s facing left because -5 is greater than -x-4
Answer:
x ≥ 1
Step-by-step explanation:
Move all terms not containing x to the right side of the inequality.
−x ≤ −1
Divide each term in −x ≤ −1 by −1 and simplify.
x ≥ 1
Hope this helps! :)
Given two objects represented by the tuples (22, 1, 42, 10) and (20, 0, 36, 8):(a)Compute the Euclidean distance between the two objects. (b) Compute the Manhattan distance between the two objects.
Answer:
(a) 6.708
(b) 11
Step-by-step explanation:
Tuples ( 22, 1, 42, 10) and (20, 0, 36, 8)
Euclidian distance formula
[tex]D = \sqrt{(q1 -p1)^2 + (q2-p1)^2 + (q3 - p3)^2 + (q4 -p4)^2}[/tex]
D = [tex]\sqrt{(22-20)^2 + (1-0)^2 + (42 -36)^2 + (10 -8)^2 }[/tex]
= [tex]\sqrt{(2)^2 + (1)^2 + (6)^2 + (2)^2}[/tex]
= [tex]\sqrt{4 + 1 + 36 + 4 }[/tex]
= [tex]\sqrt{45}[/tex]
D = 6.708
Therefore the Euclidean distance between the tuples is 6.708
Manhattan Distance formula
D = |q1-p1| + |q2 -p2| + |q3 -p3| + |q4-p4|
= |22-20| + | 1-0| + | 42 -36| + | 10-8|
= |2| + |1| + |6| + |2|
D = 11
Therefore the Manhattan distance is equal to 11