Answer:
a)6,7,8,9 and 10th term is 15.
b)1,3,5,7 and 10th term is 19.
Step-by-step explanation:
Given a) n+5
b)2n-1
Solution for a) n+5
Taking the value of n is 1 we get the first term of the sequence;
[tex]n+5=1+5=6[/tex]
Similarly taking the value of n 2,3,4 we get;
[tex]2+5=7\\3+5=8\\4+5=9[/tex]
And for 10th term we take the value of n is 10 and get;
[tex]n+5=10+5=15[/tex]
So the solution for 1st sequence is 6,7,8,9 and 10th term is 15.
Solution for b)2n-1
Taking the value of n is 1 we get the first term of the sequence;
[tex]2n-1=2\times1-1=2-1=1[/tex]
Similarly taking the value of n 2,3,4 we get;
[tex]2n-1=2\times2-1=4-1=3\\2\times3-1=6-1=5\\2\times4-1=8-1=7[/tex]
And for 10th term we take the value of n is 10 and get;
[tex]2n-1=2\times10-1=20-1=19[/tex]
So the solution for 2nd sequence is 1,3,5,7 and 10th term is 19.
Final answer:
The first 4 terms and the 10th term of sequence (a) n + 5 are 6, 7, 8, 9, and 15, respectively. For sequence (b) 2n - 1, they are 1, 3, 5, 7, and 19, respectively.
Explanation:
For each sequence, we need to find the first 4 terms and the 10th term. The sequences are given by (a) n + 5 and (b) 2n - 1.
Let's start with sequence (a) n + 5. The first 4 terms, where n starts at 1, will be:
1 + 5 = 62 + 5 = 73 + 5 = 84 + 5 = 9The 10th term can be found by substituting n = 10 into the expression, so the 10th term is:
10 + 5 = 15
Moving on to sequence (b) 2n - 1. The first 4 terms are:
2(1) - 1 = 12(2) - 1 = 32(3) - 1 = 52(4) - 1 = 7The 10th term is calculated as:
2(10) - 1 = 19
3х – 2 y = 0
I need some help idk why but I just can’t remember how to do this one
Answer:
y=3x/2
Step-by-step explanation:
first you want to get the -2y alone so you move the 3x. since it's adding now the opposite of addition is subtraction. now your left with -2y= -3x. since your trying to solve for y now you divide -2 on both sides and your gonna be left with y= -3x/-2. since their both negatives it turns to postive. that's why the answer would be y= 3x/2.
Step-by-step explanation:
this line will cross the origin
to help I'm just going to explain something real quick.
make it into y intercept form (y=mx+b)
-2y=0-3x
y=3/2x +0
the m (3/2) is the slope
and b (0) is the y intercept
if you want to check it then imput a point on the line into the x and y variables
Simplify each expression. (a2b-3/a-2b2)2 a=/0 b=/0
Answer:
The answer is C.
Step-by-step explanation:
Just failed hah stream fancy
Answer:
Answer is a^8/b^10
Option C
Step-by-step explanation:
((a²b-³)/(a-²b²))² where b and a are not equal zero
To solve this equation we start solving the equation from inside the bracket. And for simplicity we solve the numerator and solve the denominator before dividing them with each other. Now let get started
((a²b-³)/(a-²b²))²
Recall from indices that
a ^ -b = 1/a^b
I.e b-³ = 1/b³... We will apply this here.
((a²b-³)/(a-²b²))²
=((a²* 1/b³)/(b²*1/a²))²
=((a²/b³)/(b²/a²))²
Also recall that
(a/b) / (c/d) = (a/b) * (d/c)
Therefore
=((a²/b³)/(b²/a²))²
=(a²/b³ * a²/b²)²
Recall that: a^b * a^c = a^(b+c)
= (a ^ (2+2) / b ^ (2+3))²
= (a^4/b^5)²
Recall that: (a^b)^c = a^(b+c)
Therefore:
=™(a^4/b^5)²
=(a^(4*2)/b^(5*2))
= a^8/b^10
Formulate the recursive formula for the following geometric sequence.
{-16, 4, -1, ...} Show all your work please:)
The recursive formula for given sequence is:
[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]
Step-by-step explanation:
Given sequence is:
-16, 4, -1, ...
First of all, we have to find the common ratio. common ratio is the ratio between two consecutive terms of a geometric sequence
Here
[tex]a_1 = -16\\a_2 = 4\\a_3 = -1\\Now\\r = \frac{a_2}{a_1} = \frac{4}{-16} = -\frac{1}{4}\\r = \frac{a_3}{a_2} = \frac{-1}{4} = -\frac{1}{4}[/tex]
The recursive of geometric sequence is:
[tex]a_n = r * a_{n-1}[/tex]
Putting the value of r
[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]
Hence,
The recursive formula for given sequence is:
[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]
Keywords: Geometric sequence, Recursive formula
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53 pts!! The function f(x)= 7^x+1 is transformed to function g through a horizontal compression by a factor of 3. What is the equation of function g? Substitute a numerical value for k into the function equation.
The value of k will be 3 if the function is transformed by compression factor of 3
Step-by-step explanation:
The horizontal stretch or compression for a function f(x) is given by g = f(bx) where b is a constant. If b> 0 then the graph of function is compressed.
As it is given in the question that he function is transformed by a compression factor of 3.
Given function
[tex]f(x) = 7^x+1\\To\ transform\\g = f(bx)\\g = 7^{3x}+1[/tex]
The value of k will be 3 if the function is transformed by compression factor of 3
Keywords: Functions, Transformation
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Please help me I need help quick
!!!!
Jim’s new car has 150 miles on the odometer. He takes a trip and drives an average of m miles each day for three weeks. Which expression represents the mileage on Jim’s car after his trip?
Answer:
[tex](150+21m)\ miles[/tex]
Step-by-step explanation:
we know that
[tex]1\ week=7\ days[/tex]
Remember that the speed is equal to divide the distance by the time
Let
s ---> the speed in miles per day
d ---> the distance in miles
t ---> the time in days
[tex]s=\frac{d}{t}[/tex]
[tex]d=st[/tex]
we have
[tex]s=m\ miles/day[/tex]
[tex]t=3\ weeks[/tex]
Convert to days
[tex]t=3(7)=21\ days[/tex]
Find the distance covered in the trip
[tex]d=st[/tex] ----> [tex]d=m(21)=21m\ miles[/tex]
To find out the mileage on Jim’s car after his trip, sum the mileage before his trip (150 miles) plus the mileage of the trip
[tex](150+21m)\ miles[/tex]
. In an encyclopedia of language, the author presents five sentences that make a reasonable paragraph regardless of their order. The sentences are listed below. Mark had told him about the foxes. John looked out of the window. Could it be a fox? However, nobody had seen one for months. He thought he saw a shape in the bushes. In how many different orders can the five sentences be arranged?
Answer:
the 1st & last paras are fixed.
that leaves 3 to be put in any order
there are 3 choices for the 1st,
2 choices left for the 2nd
and just 1 choice for the last
multiply to get
3*2*1
= 6 ways
We want to find the total number of orders in which we can order the given sentences.
We will see that there are 120 different orders.
There are 5 sentences, let's define them as:
s₁ = Mark had told him about the foxes.s₂ = John looked out of the window.s₃ = Could it be a fox? s₄ = However, nobody had seen one for months.s₅ = He thought he saw a shape in the bushes.We know that we can order these in any order, so we can think of the situation as 5 empty slots, in each slot, we can put one of the previous statements.
Let's count the number of options for each one of these slots.
On the first one, we have 5 options (5 sentences)
On the second one we have 4, because we already used one on the first slot.
On the third, we have 3 options.
On the fourth, we have 2 options.
On the fifth, we have 1 option.
The total number of combinations is given by the product of these numbers of options.
Combinations = 5*4*3*2*1 = 120
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What is the answer ?
Answer:
126
Step-by-step explanation:
621 - x = 495
Subtract 621 from both sides.
-x = -126
Divide by -1
x = 126
Determine the next three terms in the following sequence:
1, 2, 5, 10,
a 17, 26, 37
b. 19, 30, 43
c50, 500, 25,000
d. 15, 25, 40
The correct sequence is a. 17, 26, 37.
To determine the next three terms in the sequence, we must first identify the pattern governing the sequence. Let's examine the differences between consecutive terms:
- The difference between the second term (2) and the first term (1) is 1.
- The difference between the third term (5) and the second term (2) is 3.
- The difference between the fourth term (10) and the third term (5) is 5.
- The difference between the fifth term (17) and the fourth term (10) is 7.
We can see that the differences between consecutive terms are increasing by 2 each time. This suggests that the sequence is generated by adding consecutive odd numbers to the previous term. To find the next terms, we continue this pattern:
- The sixth term will be the fifth term (17) plus the next odd number (9), which is 17 + 9 = 26.
- The seventh term will be the sixth term (26) plus the next odd number (11), which is 26 + 11 = 37.
- The eighth term will be the seventh term (37) plus the next odd number (13), which is 37 + 13 = 50.
Therefore, the next three terms of the sequence are 26, 37, and 50, confirming option a as the correct answer.
Which of these is the algebraic expression for "3 times the sum of 2 and y?" (1 point) 3(2 + y) 3 ⋅ 2 + y 2 + 3 ⋅ y 2(3 + y)
The algebraic expression of "3 times the sum of 2 and y" is 3(2 + y) ⇒ 1st answer
Step-by-step explanation:
Let us revise some words in the operations of mathematics problems
Sum ⇒ answer of addDifference ⇒ answer of subtractProduct ⇒ answer of multiplyQuotient ⇒ answer of divideTimes ⇒ multiply∵ The algebraic expression is " 3 times the sum of 2 and y "
∵ Sum is the answer of add
∴ add 2 and y
∴ The sum of 2 and y = 2 + y
∵ 3 times means multiply by 3
∴ 3 times the sum
∴ Multiply the sum by 3
∵ The sum = 2 + y
∴ Multiply (2 + y ) by 3
∴ 3(2 + y)
∴ 3 times the sum of 2 and y = 3(2 + y)
The algebraic expression of "3 times the sum of 2 and y" is 3(2 + y)
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Answer:
a
=
Step-by-step explanation:
uo[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[
If 6 + 2 = 8, does 6+2 +3= 8+3? Why or
why not?
Answer:
yes
Step-by-step explanation:
Because 6+ 2 equals 8 then plus 3 equals 11 and 11 equals 8+3
What is the exact volume of the cone?
108π cm3
162π cm3
18π cm3
486π cm3
V = π·r²·h/3 = π·81·6/3 = 2·81·π = 162π cm³
need help please and thanks
Answer:
2. n = 11
4. g = -2
6. t = 21
8. n = 4
10. y = -1
Step-by-step explanation:
2. 63 = -3(1 - 2n)
Dividing both the side by negative 3 we get
[tex]-21=1-2n\\2n=1+21\\2n=22\\n=\frac{22}{2} \\\therefore n=11[/tex]
4. -g + 2(3 + g) = -4(g + 1)
First we will open the bracket by distributive property A( B +C) = AB + AC
[tex]-g+2\times 3 + 2\times g = -4\times g + -4\times 1\\-g+6+ 2g=-4g-4\\\textrm{we will take all the g term the left side and the constant to the right side}\\4g-g+2g=-6-4\\5g=-10\\g=\frac{-10}{5}\\\therefore g=-2[/tex]
6.-3(t +5 ) + (4t + 2) = 8
Using distributive property A( B +C) = AB + AC we get
[tex]-3\times t + -3\times 5 + 4t + 2=8\\-3t-15+ 4t + 2=8\\t=8+15-2\\t=21\\\therefore t=21\\[/tex]
8. -8 - n = -3(2n -4)
Using distributive property A( B +C) = AB + AC we get
[tex]-8 - n = -3\times 2n - -3\times4\\-8-n=-6n+12\\\textrm{all the n terms to the left inside and the constant of the right-hand side}\\6n-n=8+12\\5n=20\\n=\frac{20}{5}\\ \therefore n= 4[/tex]
10. -4( 2 - y) + 3y = 3(y - 4)
Using distributive property A( B +C) = AB + AC we get
[tex]-4\times 2 --4\times y + 3y = 3\times y -3\times 4\\-8+4y+3y =3y-12\\\textrm{all the y terms to the left side and the constant to the right side}\\4y+3y-3y=-12+8\\4y=-4\\y=\frac{-4}{4}\\ \therefore y=-1[/tex]
This year, a small business had a total revenue of 33,500. If this is 34% more than their total revenue the previous year, what was their total revenue the previous year?
Final answer:
To find the previous year's total revenue, divide the current year's revenue by 1.34 since the current revenue is 34% higher than the previous year. The calculation shows that the previous year's revenue was $25,000.
Explanation:
The question asks us to find the total revenue of a small business for the previous year, given that the current year's revenue is 34% higher. To do this, we let x represent the revenue from the previous year. Since this year's revenue is 34% more than last year's, we have the equation:
1.34x = 33,500
To find the value of x, we divide both sides of the equation by 1.34:
x = 33,500 / 1.34
x = 25,000
Therefore, the total revenue for the previous year was $25,000.
For apples 2 lb for $3.38 unite rate___ cost___
Answer:
1.69
Step-by-step explanation:
well to find out the unit rate that would be a pound now we need to find out how much it would cost for 1 lb which would be 3.38 / 2 which would be 1.69 as your answer
Answer:
$1.69 per pound
Step-by-step explanation:
3.38/2=1.69
RS = 3y + 41, ST = 18y - 76 and RT = 91.
2) Find y.
Answer:
The answer is y = 6.
Step-by-step explanation:
Given:
RS = [tex]3y+41[/tex], ST = [tex]18y-76[/tex] and RT = 91.
Now, to find the [tex]y[/tex].
According to question add the equations:
RS + ST = RT
[tex]3y+41+18y-76=91[/tex]
Adding the numbers and variables in L.H.S.
[tex]3y+18y-76+41=91[/tex]
[tex]21y-35=91[/tex]
Adding 35 on both sides:
[tex]21y-35+35=91+35[/tex]
[tex]21y=126[/tex]
Dividing both sides by 21:
[tex]21y\div 21=126\div 21[/tex]
[tex]y=6[/tex]
Therefore, the answer is y = 6.
what is integers?
what is natural number?
1 An integer is a number that has no fractional part, and no digists after the decimal point. An integer can be positive, negative or zero. example 12, 34,-4,0 etc.
2. A natural number is a number that occurs commonly and obviously in nature. As such it is a whole, non -negative number. The set of natural numbers, denoted N, can be defined in either of two ways : N = (0,1,2,3,.......)
Natural numbers include 1, 2, 3, 4...; they are numbers you normally count and will go onto infinity and beyond. ZERO IS NOT A NATURAL NUMBER BECAUSE IT IS NEUTRAL.
Integers are all negative and positive counterparted whole numbers; e.g.... −4, −3, −2, −1, 0, 1, 2, 3, 4,...
I am joyous to assist you anytime.
The first three terms of a geometric sequence are as follows.
-4, -12, -36
Find the next two terms of this sequence.
Give exact values (not decimal approximations).
-4, -12, -36, 1:0
:
:
x
5
Answer:
The next two terms for the geometric sequence are - 108 and - 324.
Step-by-step explanation:
1. Let's find the next two terms for the geometric sequence which first three terms are as follows:
- 4, 12, - 36.....
Aₓ = Aₓ₋₁ * 3 ; A₁ = - 4
A₁ = - 4
A₂ = A₁ * 3 = - 4 * 3 = - 12
A₃ = A₂ * 3 = - 12 * 3 = - 36
A₄ = A₃ * 3 = - 36 * 3 = - 108
A₅ = A₄ * 3 = - 108 * 3 = - 324
The next two terms for the geometric sequence are - 108 and - 324.
A restaurant manager can spend at most $400 a day for operating costs and payroll. It costs $100 each day to operate the bank and $50 dollars a day for each employee. Use the following inequality to determine how many employees the manager can afford for the day, at most: 50x + 100 ≤ 600
Answer:
The restaurant Manager can afford 6 employees for the day.
Step-by-step explanation:
Manager can spend at most of $400.
Total Money ≤ $400
Cost to operate bank = $100
Cost for each employee = $50
Let number of employees for the day be[tex]x[/tex]
Hence the equation will become;
[tex]50x + 100 \leq 400[/tex]
Solving this equation we get;
[tex]50x + 100 \leq 400\\50x \leq 400-100\\50x \leq 300\\x\leq \frac{300}{50}\\\\x\leq 6[/tex]
Hence, The restaurant Manager can afford 6 employees for the day.
Answer:
x < = 10
Step-by-step explanation:
i did it on photo math so yah
how do you make 1 1-2/1-6-7/8 a mixed number
Answer:
17/8
Step-by-step explanation:
2/1=2
11-2-6-7/8
9-6-7/8
3-7/8
24/8-7/8
17/8
Find the value of each expression.
10. |-41|
12. -|1.5|
Step-by-step explanation:
10. |-41|= 41
12. -|1.5|= -1.5
Answer:
A.) 41
B.) -1.5
Step-by-step explanation:
Absolute value means to make whatever that is inside positive
10.) The absolute value of negative 41 would simply be positive 41
11.) Since the negative sign is on the outside of the absolute value, you do the absolute value of everything inside then apply a negative sign. Absolute value of 1.5 is just 1.5 because it's already positive. Then apply the negative sign, which would make it -1.5
A park ranger at the top of a 700-meter station sees a fair that is 1800 meters from the base of the tower.
What is the angle of elevation in degrees?
Final answer:
To find the angle of elevation, we can use the concept of tangent. The angle of elevation is approximately 67.7 degrees.
Explanation:
To find the angle of elevation, we can use the concept of tangent.
Tan(Angel of Elevation) = Opposite/Adjacent
Here, the opposite side is the height of the fair, which is 1800 meters, and the adjacent side is the height of the station, which is 700 meters.
Tan(Angel of Elevation) = 1800/700
Angel of Elevation = tan-1(1800/700)
Using a calculator, the angle of elevation is approximately 67.7 degrees.
What is the value of this expression (3/7)^0
Answer:
1
Step-by-step explanation:
Using the rule of exponents
[tex]a^{0}[/tex] = 1
Any expression raised to the power of zero will equal 1
Given
[tex](3/7)^{0}[/tex] = 1
8/11 divide by 3/5
find the quotient
Answer:
=40/33
8/11 divide 3/5 -> 8/11 x 5/3 and multiply 8x5 then 11x3 then u got your answer! :)
Hope this worked :D
Answer:
Your answer is 40/33
Step-by-step explanation:
8/11 * 3/5
flip the fraction
8/11* 5/3
Multiply
It is known that homing pigeons fly faster over land than over water. Assume that they fly 10 meters per second over land but only 8 meters per second over water. if a pigeon is located at the edge of a straight river 500 meters wide and must fly to its nest located 1300 meters away on the opposite side of the river, what path would minimize its flying time?
The homing pigeon will minimize its flying time by flying straight across the river, then directly to its nest. The time to fly this route would be 142.5 seconds.
Explanation:The homing pigeon's path that will minimize its flying time would-be one where it flies straight across the river and then flies directly to its nest. The total time can be calculated by adding the time it flies over water and the time it flies over land. Initially, calculating the flying time over water, if the river is 500 meters wide, the time will be the distance divided by speed which equals 500m/8m/s = 62.5s . Now the land distance is the total distance minus the width of the river, so it would be 1300m – 500m = 800m. The time to cross this distance will be 800m/10m/s = 80s. Hence, adding both times, total flying time will be 62.5s + 80s = 142.5s. Therefore, the shortest path is firstly, flying straight across the river, and then straight towards its nest.
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If lines m and n are parallel, and the measure of
angle 1 is 130°, what is the measure of angle 8?
Answer:
18.55, lines m and n are parallel and t is the transversal. If ∠1 = 130o, find the measures of the other angles and give reasons.
Step-by-step explanation:
The measure of angle 8 will be 130° since it corresponds to angle 1, and their measures are equal because lines m and n are parallel.
Explanation:To find the measure of angle 8 when lines m and n are parallel, and the measure of angle 1 is 130°, it's important to understand the concept of corresponding angles in the context of parallel lines. Corresponding angles are equal when two lines are parallel. Given that angle 1 is 130°, and assuming that angle 1 and angle 8 are corresponding angles (since the question does not specify their positions), the measure of angle 8 is also 130°.
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14) What is the graph of the function rule ?
y= |2x|-1
Because the equation contains an absolute value, the shape of the graph would be a V,.
The Y intercept is -1, so this would be the lowest point on the graph.
Replace X with 1 and solve:
y = 2(1) -1 = 2-1 = 1, so another point would be (1,1) and another point would be (-1,1) ( Absolute value would use both -1 and 1 as the same).
Make 3 points on the graph:
(-1,1) (1,1) ans (0,-1) and draw lines through them.
See attached picture:
-2+4(-x+4)=10 using distributive property and collecting like terms
Answer:
x = 1Step-by-step explanation:
[tex]-2+4(-x+4)=10\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\-2+(4)(-x)+(4)(4)=10\\\\-2-4x+16=10\qquad\text{combine like terms}\\\\-4x+(-2+16)=10\\\\-4x+14=10\qquad\text{subtract 14 from both sides}\\\\-4x+14-14=10-14\\\\-4x=-4\qquad\text{divide both sides by (-4)}\\\\\dfrac{-4x}{-4}=\dfrac{-4}{-4}\\\\x=1[/tex]
Quadrilaterals A and B are both squares. Are A and B necessarily scale copies
of one another? Explain.
Answer:
No
Step-by-step explanation:
because one can be 5 by 5 and the other can be 7 by 7.
Hope this helps!!!I know it's to short but this is what I got.
Answer:
5 by 5 and 7 by 7. Really hope this helped :)
Step-by-step explanation:
The black graph is the graph of y=f(x). Choose the equation for the red graph.
Please help!!!
Answer:
C
Step-by-step explanation:
Given f(x) then f(x) + c is a vertical translation of f(x) by c units
• If c > 0 then shift c units up
• If c < 0 then shift c units down
The red graph is a vertical translation f(x) of 3 units down
Thus
y = f(x) - 3 ( add 3 to both sides )
y + 3 = f(x) ← equation of red graph
What is the final step in solving the inequality -2(5 - 4x)
Step 1: -10 + 8x < 6x - 4
Step 2: -10 <-2x - 4
Step 3: -6<-2x
Step 4
AVA
Step-by-step explanation:
[tex]-2(5-4x)<6x-4\qquad\text{use the distributive property}\\\\(-2)(5)+(-2)(-4x)<6x-4\\\\-10+8x<6x-4\qquad\text{subtract}\ 8x\ \text{from both sides}\\\\-10+8x-8x<6x-8x-4\\\\-10<-2x-4\qquad\text{add 4 to both sides}\\\\-10+4<-2x-4+4\\\\-6<-2x\qquad\text{divide both sides by (-2)}\\_{\text{by dividing by a negative number, flip the inequality sign}}\\\\3>x[/tex]