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the sum of three consecutive integers if the last integer is z.
a.) 3z+3
b.) 3z+6
c.)3z-3
d.)3z
The sum of three consecutive integers where the last integer is z is 3z - 3.
Explanation:The sum of three consecutive integers can be derived using the concept of arithmetic series. For instance, if z represents the last of the three consecutive integers, we know that the numerals preceding it are z-1 and z-2. Hence, the sum of these three integers would be (z-2) + (z-1) + z.
Simplifying this, we get 3z - 3 which corresponds to option c.)3z-3 in the question's list.
Remember, an important aspect of sequences and series is that the numbers are arranged in a specific order.
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A homeowner is draining her swimming pool. The volume of water in the pool changes by −12 gallons every minute.
What is the change in volume over 60 minutes?
So, water decreases by 12 gallons EVERY minute.
How much water will decrease in 60 minutes?
[tex]12*60=720[/tex] gallons
So, the volume changes by 720 gallons in 60 minutes.
ANSWER: Volume decreases 720 gallons in 60 minutes.
If total liabilities are $200,000 and total assets are $325,000, owner's equity would be: 2)
a. $525,000
b. $200,000
c. $125,000
d. impossible to determine from the given data
You and your frend step into identical row-boats. you notice that your boat sinks into the water twice as far as your friends. what can you say about your friend's weight compared with yours? your friend weighs twice as much as you your friend weighs the same as you your friend weighs half as much as you your friend weighs one fourth your weight
Write an equation of the line that passes through (0, 5) and (−1.5, 1)
The equation of the line that passes through (0, 5) and (−1.5, 1) is y = 8/3 x + 5
The equation can be represented as follows:
y = mx + b
where
m = slope
b = y-intercept
lets find the slope
(0, 5) (−1.5, 1)
m = 1 - 5 / -1.5 - 0 = - 4 / -1.5 ≈ 8 / 3
we multiplied the numerator and denominator by 2
b = 5, b is the value of y when x = 0.
Therefore, the equation will be as follows:
y = 8/3 x + 5
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What is 0.69 expressed as a fraction in simplest form?
Construct a polynomial function of least degree possible using the given information.
Real roots: -2, 1/2 (with multiplicity 2) and (-3, f(-3))=(-3,5)
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For the x-values 1,2,3, and so on, y-values...
Answer:
decreasing linear
Step-by-step explanation:
what are the term in the expression 4x^2-2x-x^2+3x+1
the line L1 has equation 2x + y = 8. The line L2 passes through the point A ( 7, 4 ) and is perpendicular to L1 . Find the equation of L2.
Answer: [tex]x-2y+7=0[/tex]
Step-by-step explanation:
Given : The line[tex]L_1[/tex] has equation [tex]2x + y = 8[/tex]
In intercept form : [tex]y =-2x+8[/tex]
The slope of [tex]L_1[/tex] =-2 [in intercept form equation of line [tex]y =mx+c[/tex], m is slope ]
Let p be slope of [tex]L_2[/tex]
We know that when two lines are perpendicular then the product of their slopes is -1.
[tex]\Rightarrow\ -2\times p=-1\\\\\Rightarrow\ p=\dfrac{1}{2}[/tex]
The equation of line having slope 'm' and passing through (a,b) is given by :-
[tex](y-b)=m(x-a)[/tex]
Then , equation of line [tex]L_2[/tex] will be :-
[tex](y-7)=\dfrac{1}{2}(x-7)\\\\\Rightarrow\ 2y-14=x-7\\\\\Rightarrow\ x-2y+7[/tex]
You can buy 4 pounds of peaches for $5.96. What do 4 1/2 pounds of peaches cost?
Write the equation in standard form
x^2+y^2+6x+14y+37=0
how many meters does it take to make 1 kilometer
Harry worked seven hours last week this is 1/3 as many hours as Aiden worked how many hours did Aidan work
A small train at an amusement park is carrying passengers. Half of the passengers are 6 years old, 1 over 10 are 7 years old, 1 fifth are 8 years old, and 1 fifth are 9 years old.
What is the expected age for one of the passengers on the train?
6 years
7.1 years
8 years
8.5 years
The expected age for one of the passengers on the train is 7.1 years. This can be explained by following steps:
Following are the calculation for the expected age given
½ = 6 years old
1/10 = 7 years old
1/5 = 8 years old
1/5 = 9 years old
With the help of the above information, expected age can be calculated as follows:
Expected age = ½*6+1/10*7+1/5*8+1/5*9
= 6/2+7/10+8/5+9/5
=3+0.7+1.6+1.8
= 7.1
Therefore, the correct answer is 7.1 years old.
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Veronique and Lily compare their investment accounts to see how much they will have in the accounts after seven years. They substitute their values shown below into the compound interest formula. Compound Interest Accounts Name Principal Interest Rate Number of Years Compounded Veronique $1,000 5% 7 Once a year Lily $1,800 9% 7 Once a year mc017-1.jpg Which pair of equations would correctly calculate their compound interests? Veronique: mc017-2.jpg, Lily: mc017-3.jpg Veronique: mc017-4.jpg, Lily: mc017-5.jpg Veronique: mc017-6.jpg, Lily: mc017-7.jpg
Answer:
A
Step-by-step explanation:
The pair of equations that would correctly calculate their compound interests are:
Veronique's interest = A = 1000(1 + 0.05/1)⁷ - 1000 = 407.10
Lily's interest = 1800(1 + 0.09/1)⁷ - 1800 = 1,490.47.
What is the compound interest rate?Compound interest is computed as interest on the principle of an account plus any accrued interest.
Compound interest can be calculated using the following formula:
x = P (1+r/n)^(nt)
,where x = compound interest
P = principal (the initial deposit or loan amount)
r = annual interest rate
n = the number of compounding periods per unit of time
t = the number of time units the money is invested or borrowed for
For Veronique, we have:
A = 1000(1 + 0.05/1)⁷ = $1,407.10
For Lily, we have:
A = 1800(1 + 0.09/1)⁷ = $3290.47
To calculate the compound interest for each account, we subtract the principal amount from the final amount:
For Veronique:
Interest = A - P = $1,407.10 - $1,000 = $407.10
For Lily:
Interest = A - P = $3,290.47 - $1,800 = $1,490.47
Therefore, the pair of equations that would correctly calculate their compound interests are:
Veronique's interest = A = 1000(1 + 0.05/1)⁷ - 1000 = 407.10
Lily's interest = 1800(1 + 0.09/1)⁷ - 1800 = 1,490.47.
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In two or more complete sentences, explain whether the sequence is finite or infinite. Describe the pattern in the sequence if it exists, and if possible find the sixth term. 2a, 2a2b, 2a3b2, 2a4b3. . .
Answer:
a). it is an Infinite Sequence.
b). This sequence is Geometric Progression.
c). [tex]6th\,term\,of\,this\,GP\,=\,2a^6b^5[/tex]
Step-by-step explanation:
Given: A Sequence 2a , 2a²b , 2a³b² , [tex]2a^4b^3[/tex]
To find: a). Given Sequence is finite or infinite
b). Pattern of the sequence
c). Sixth term
a). Since, there is no detail about no. of terms of the sequence.
Therefore, It implies it is an Infinite Sequence.
b). Given 1st term = 2a , 2nd term = 2a²b , 3rd term = 2a³b²
First we find the difference of 1st and 2nd term
d = 2a²b - 2a ⇒ d = 2a (ab - 1)
Now, Difference of 2nd and 3rd term,
d = 2a³b² - 2a²b = 2a²b (ab - 1)
So, This Sequence is not a Arthematic Progression.
Now, we find the ratio of 2nd term to 1st term,
[tex]r\:=\:\frac{2a^2b}{2a}\,=\,ab[/tex]
Ratio of 3rd term to 2nd term,
[tex]r\:=\:\frac{2a^3b^2}{2a^2b}\,=\,ab[/tex]
Since, the ratio is common.
This sequence is Geometric Progression.
So, Pattern is next term of this sequence has 1 more in power of a and b
⇒ [tex]nth\,term\,of\,this\,GP\,=\,2a^{n}b^{n-1}[/tex]
c). [tex]6th\,term\,of\,this\,GP\,=\,2a^{6}b^{6-1}[/tex]
[tex]6th\,term\,of\,this\,GP\,=\,2a^6b^5[/tex]
Therfore, a). it is an Infinite Sequence.
b). This sequence is Geometric Progression.
c). [tex]6th\,term\,of\,this\,GP\,=\,2a^6b^5[/tex]
Michael did 45 pushups in 3 minutes. Michelle did 36 pushups in 2 minutes.Who did pushups at a faster rate? How much faster was that person? Answer with supporting work.
The perimeter of a rectangle is 36 yards. The width is 18 yards less than twice the length. Find the length and the width of the rectangle
The length of the rectangle is 12 yards and the width is 6 yards. The problem is solved with algebra using the formulas for the perimeter of a rectangle and given relation between the length and width.
Explanation:This problem involves the use of algebra in solving geometrical problems. The question provides information about the perimeter and the relationship of length to width using algebraic expressions. To find the length and the width, we can use the formulas for the perimeter of a rectangle (P=2L + 2W) and the given width (W=2L-18).
Let L represent the length. Then, 2L+W=18 represents the width. Setting 2L + 2W equal to the given perimeter of 36, we get 2L + 2(2L - 18) = 36.
Solving this equation gives: L = 12, and substituting L=12 into W=2L - 18, we get: W=6. Hence, the length is 12 yards and the width is 6 yards.
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Please answer ASAP: Use cross products to determine which of the following proportions are equivalent to each other.
Select all situations that apply.
a/b=c/d
a/c=b/d
a/d=c/b
b/a=d/c
d/a=c/b
If the coordinates of point A are (-3, 2) and the coordinates of point B are (7, 6), the x-intercept of is . Point lies on .
Rya uses 4 gallons of gas ro drive 120 miles on the highway. If she gets that samw gas mileage, how many miles can she drive on 1 gallon of gas?
Curve passes through the point (0,8)(0,8) and has the property that the slope of the curve at every point pp is four-times the y-coordinate. what is the equation of the curve
Suppose investment of $6200 doubles in value every 13 years how much is the ivestment worth after 78 years
find the y-intercept of the line represented by 6x-7y=12
A vendor sold 72 hotdogs and hamburgers during a football game if the ratio of hotdogs to hamburgers sold was 8:1 how many of each food did vendor sell?
Stu is laying brick down to make a patio. He plans for the patio to be 12.5 feet by 18.3 feet. He orders enough brick for 247 square feet. Which statement about the amount of brick is correct?
Answer:
Stu estimated correctly by rounding up.
He ordered enough brick.
The exact area is [tex]228.75[/tex] square feet
Step-by-step explanation:
we know that
the area of the patio is equal to
[tex]A=bh[/tex]
In this problem we have
[tex]b=12.5\ ft, h=18.3\ ft[/tex]
substitute in the formula
[tex]A=12.5*18.3=228.75\ ft^{2}[/tex]
[tex]228.75\ ft^{2}< 247\ ft^{2}[/tex]
Write a function perfect that determines whether parameter number is perfect number
Factor the following