To determine the first five terms of the given recursive sequence, we begin with the first term, a1 = -10, and use the provided recurrence relation to calculate each subsequent term. The first five terms of the sequence are -10, -33, -125, -493, and -1965.
Explanation:The student has presented a recursive sequence with the first term stated as – 10 and a recursive formula to find any subsequent term, an, defined as an = 4an-1 + 7 for n ≥ 2.
To find the first five terms of the sequence, we'll apply the formula starting with a1 and proceed to each next term.
First term, a1: – 10
Second term, a2: 4(– 10) + 7 = – 40 + 7 = – 33
Third term, a3: 4(– 33) + 7 = – 132 + 7 = – 125
Fourth term, a4: 4(– 125) + 7 = – 500 + 7 = – 493
Fifth term, a5: 4(– 493) + 7 = – 1972 + 7 = – 1965
Therefore, the first five terms of the sequence are – 10, – 33, – 125, – 493, and – 1965.
How many square inches are in 60 square feet?
Answer:
8640 in ^2
Step-by-step explanation:
1 ft = 12 in
60ft^2 * 12 inches * 12 inches
-------------- -------------- = 8640 in ^2
1 ft 1 ft
Answer:8640
Step-by-step explanation:
Which expression is equivalent to log5^(x/4)^2?
2log5(x) + log5(4)
2log5(x) + log5(16)
2log5(x) - 2log5(4)
2log5(x) - log5(4)
Answer:
2log5(x) - 2log5(4)
Step-by-step explanation:
An expression is defined as a set of numbers, variables, and mathematical operations. The expression that is equivalent to log₅(x/4)² is 5log(x) - 5log(4).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression log₅(x/4)² can be expressed as,
log₅(x/4)²
= 5log(x/4) {∵ log(aᵇ) = b log(a) }
=5[log(x) - log(4)]
= 5log(x) - 5log(4)
Hence, the expression that is equivalent to log₅(x/4)² is 5log(x) - 5log(4).
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A number is 5 more than 3 times another number. The sum of the two numbers is 33. As an equation, this is written x + 3x + 5 = 33, where x represents the smaller number. Plug in the numbers from the set {3, 5, 7, 9} to find the value of x.
The value of x that holds true for the equation is blank . So, the smaller number is blank and the larger number is blank .
Answer:
x=7
Step-by-step explanation:
Solve for x:
3 x + x + 5 = 33
x + 3 x = 4 x:
4 x + 5 = 33
Subtract 5 from both sides:
4 x + (5 - 5) = 33 - 5
5 - 5 = 0:
4 x = 33 - 5
33 - 5 = 28:
4 x = 28
Divide both sides of 4 x = 28 by 4:
(4 x)/4 = 28/4
4/4 = 1:
x = 28/4
The gcd of 28 and 4 is 4, so 28/4 = (4×7)/(4×1) = 4/4×7 = 7:
Answer: x = 7
The larger number is 26 and the smaller number is 7.
What are the numbers?To determine the solution, take the following steps:
The given equation is x + 3x + 5 = 33
Combine similar terms: x + 3x =33 - 5
Add similar terms: 4x = 28
Divide both sides by 4 : 7
The larger number = 33 - 7 = 26
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Hi my sister needs help with this
Answer:
Step-by-step explanation:
Book A: Mass is 1000 g + 700g + 10 g, or 1720 g.
Book B: Mass is 1500 g + 100 + 80, or 1680 g.
Book A has the greater mass: 1720 g versus 1680 g.
The difference in mass is 1720 g - 1680 g, or 40 g
Answer:
Book A has the greater mass: 1720 g versus 1680 g.
The difference in mass is 1720 g - 1680 g, or 40 g
Step-by-step explanation:
Book A: Mass is 1000 g + 700g + 10 g, or 1720 g.
Book B: Mass is 1500 g + 100 + 80, or 1680 g.
A. 8pi
B. pi
C. 2pi
D. 4pi
Answer: Option C
[tex]AC = 2\pi[/tex]
Step-by-step explanation:
The arc length is calculated as
[tex]L = \theta * R[/tex]
Then
[tex]AC = \theta * R[/tex]
We know that
[tex]BC = 24\ ft[/tex]
If BC is the diameter of the circumference then the radius R is:
[tex]R = \frac{BC}{2}[/tex]
[tex]R = \frac{24}{2}[/tex]
[tex]R = 12\ ft[/tex]
Now we convert the anglo from degrees to radians[tex]\theta= 30\° * \frac{\pi}{180\°}\\\\\theta=\frac{1}{6}\pi[/tex]
Finally
[tex]AC = \frac{1}{6}\pi * 12[/tex]
[tex]AC = 2\pi[/tex]
Answer:
The length of the arc AC is 2π ⇒ answer C
Step-by-step explanation:
* Lets revise some facts in the circle
- The length of the arc is depends on the measure of the arc and the
radius of the circle
- The length of the arc is a part of the length of the circle
- The length of the circle is 2πr
- The rule of the length of the arc = [tex]\frac{\alpha }{360}*2\pi r[/tex],
where α is the measure of the arc
* Now lets solve the problem
- In circle P
∵ BC is a diameter
∵ BC = 24 ft
∵ The length of the radius of the circle is 1/2 the length of the diameter
∴ The length of the radius = 1/2 × 24 = 12 ft
- Ac is an arc in the circle
∵ The measure of the arc = 30°
∵ The length of the arc = [tex]\frac{\alpha }{360}*2\pi r[/tex] ,
where α is the measure of the arc
∴ α = 30°
∵ r = 12 ft
∴ The length of the arc = [tex]\frac{30}{360}*2(12)\pi=\frac{1}{12}*(24)\pi=2\pi[/tex]
∴ The length of the arc AC is 2π
Find the difference.
(-5ab+a+3) - (ab+2)
Enter the correct answer.
Need help ASAP !!!!
Answer:
-6ab+a+1
Step-by-step explanation:
add or subtract like terms.
The difference between (-5ab+a+3) and (ab+2) is calculated by combining like terms and performing the subtraction, resulting in -6ab + a + 1.
To find the difference between the two expressions (-5ab+a+3) and (ab+2), we need to subtract the second expression from the first. Applying the distributive property of subtraction over addition (i.e., a - (b + c) = a - b - c), we get:
-5ab - ab: Combine like terms by subtracting ab from -5ab which gives us -6ab.+ a: There's no like term to combine with a in the second expression, so it remains as is.+ 3 - 2: Subtract 2 from 3 which gives us +1.Putting it all together, the difference of the two expressions is -6ab + a + 1.
if f(x)=4x^2+1 and g(x)=x^2-5 find(f+g)(x)
Answer:
answer
Step-by-step explanation:
f(x) = 4x² + 1
g(x) = x² - 5
Then
(f + g)(x) = 4x² + 1 + x² - 5
= 5x² - 4
Answer: 5x² - 4
Simplify 24÷(-2)(3)+7
a. -29
b. 3
c. 11
Answer:
a. -29
Step-by-step explanation:
The expression is:
24÷(-2)(3)+7
We can see that there is division, multiplication and addition involved. We will use the mathematical DMAS rule to solve the problem. So, division will be done first,
Division will give us:
24÷(-2)*(3)+7
= -12 * 3 + 7
After division, multiplication will be done:
Multiplication will give us:
= -36 +7
which equals to -29
So, option a is the correct answer ..
Adam has some candy to give to his three children. He first took seven pieces for himself and then evenly divided the rest among his children. If Adam started with 13 pieces, how many did each child receive
What is the smallest angle of rotational symmetry for a square
Answer:
90°
Step-by-step explanation:
a full rotation is 360° but since there are 4 angles, then divide the 360 by 4 and you'll get 90°
fully factor 9a2 + 24ab + 16b2
ANSWER
[tex]{(3a + 4b)}^{2} [/tex]
EXPLANATION
The given function is:
[tex] 9{a}^{2} + 24ab + 16 {b}^{2} [/tex]
This can be rewritten as
[tex]{(3a)}^{2} + 2(3 \times 4)ab + {(4b)}^{2} [/tex]
Recall that:
[tex] {x}^{2} + 2xy + {y}^{2} = {(x + y)}^{2} [/tex]
Let x=3a and y=4b,
Then,
[tex]{(3a)}^{2} + 2(3 \times 4)ab + {(4b)}^{2} = {(3a + 4b)}^{2} [/tex]
Hence the fully factored form is:
[tex]{(3a + 4b)}^{2} [/tex]
Answer:
The correct answer is (3a + 4b)^2
Step-by-step explanation:
The quotient of the difference of 5 times x cubed and 4 and x
Answer:
a system of equations has 1 solution. if 4x-y=5 is a new of the equations which could be the other equation
The question asks for an algebraic expression. Based on the phrases used, the expression can be written as (5x³ - 4)/x.
Explanation:The subject of your question involves algebra, which is a branch of mathematics. When the question asks for the 'quotient of the difference of 5 times x cubed and 4 and x', it is asking for an algebraic expression. This expression can be written as (5x³ - 4)/x. This expression cannot be simplified further as the terms in the numerator are not like terms.
Remember that the 'difference' refers to subtraction, 'quotient' refers to division, and 'times' refers to multiplication in algebra. Also, 'x cubed' means x is being raised to the power of 3.
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HELP PLEASE! Thank youuuuu
Answer:
A
Step-by-step explanation:
note that the exact value of
sin ( [tex]\frac{\pi }{4}[/tex] ) = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ← the value of the x- coordinate
What is the order of magnitude for
the total weight of 5 cars that weigh
3,000 pounds each?
An expression is defined as a set of numbers, variables, and mathematical operations. The order of magnitude for the total weight of 5 cars that weigh 3,000 pounds each is 4.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The total weight of the five cars each weighing 3,000 pounds is,
Total weight = Number of cars × Weight of each car
= 5 × 3,000 pounds
= 15,000 pounds.
= 1.5 × 10⁴ pounds
Hence, the order of magnitude for the total weight of 5 cars that weigh 3,000 pounds each is 4.
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Evaluate e1/2 to one decimal place.
1.6
13.6
3.7
7.4
I believe its 1.6
For this case we have the following expression:
[tex]e ^ {\frac {1} {2}}[/tex]
We must evaluate the expression, then:
[tex]e ^ {0.5} =[/tex]
If we enter the expression in a calculator we have that the decimal form is given by:
[tex]1.64872127[/tex]
If we round the expression we have to:
[tex]e ^ {\frac {1} {2}} = 1.7[/tex]
The option that is closest is option A.
Answer:
Option A
Convert 15/9 to a decimal
Answer:
15/9 =1.7
if u divide 3 by both of them you will have 5/3 .5/ 3 with give you 1.666666667 aproximately to 1.7 that is in one decimal plave
Step-by-step explanation:
A taxi cab costs $1.50 for the first mile and $0.75 for each additional mile. Which equation could be solved to find how many miles you can travel in a taxi for $10 given that x is the number of additional miles?
A. 1.5x - 0.75= 10
B.0.75x + 1.5= 10
C. 0.75x - 1.5=10
D. 1.5x + 0.75=10
Answer:
B.0.75x + 1.5= 10
Step-by-step explanation:
Answer:
B. 0.75(x)+1.50 = 10
and 11.333333333....
Step-by-step explanation:
What is 2y^4 x 5y^3 simplified?
Answer:
10y^7
Step-by-step explanation:
Do 2(5) and do y^4 times y^3!
2(5)=10
if you have to write out what y^4 means and y^3...
How many factors of y do you have 7... so y^4*y^3=y^7
The answer is 10y^7
Factor completely 2x5 + 10x4 - 22x3.
Answer: 2x³(x² + 5x - 11)
Step-by-step explanation:
2x⁵ + 10x⁴ - 22x³
Factor out the GCF (2x³)
2x³(x² + 5x - 11)
Since there are no values whose product is -11 and sum is +5, this cannot be factored further.
Consider the expression below.
9 + 4(x + 2) – 3.1
Select the term that best describes "3" in the given expression.
O A.
coefficient
variable
exponent
constant
Which expression best estima
18-3
0 -18-3
-18+(-3)
18+(-3)
Answer:
18 + -3
Step-by-step explanation:
It is not really an estimate because it is obviously seen that +- = -.
The population (in millions) of a certain country can be approximated by the
function:
P(x) = (100)1.02^x
where x is the number of years after 2000. Which of the following calculations will tell in what year the population can be expected to reach 300 million?
To calculate the year in which the population of the country is expected to reach 300 million, set up and solve the provided equation involving the population function. By following the steps of solving for x, you can identify the specific year when the population is estimated to reach 300 million.
To find in what year the population can be expected to reach 300 million, we can set up the equation:
P(x) = 100 * 1.02^x = 300
Now, solve for x:
1.02^x = 3x = log1.02(3)Calculate x to get the number of years after 2000, which will give you the year the population is expected to reach 300 million.What is the name of a pattern of two-dimensional shapes that can be folded to make a model of a solid figure?
A)prism
B)net
C)surface area
D)face
Answer:
The correct option is B.
Step-by-step explanation:
The correct option is net.
A geometric net is a 2-dimensional shape that can be folded to form a 3-dimensional shape or a solid. Or you can say that a net is a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure. A solid may have different nets.
The basic steps to determine whether a net forms a solid: are:
1. Make sure that the solid and the net have the same number of faces and that the shapes of the faces of the solid match the shapes of the corresponding faces in the net.
2. Visualize how the net is to be folded to form the solid and make sure that all the sides are properly fit together.
Nets are helpful when we need to find the surface area of the solids....
The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −5
0 −1
1 3
g(x)
g(x) = 2x − 7
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
Part B: Which function has a greater y-intercept? Justify your answer.
Answer:
Part A:The function f(x) has a greater slope than function g(x).Part B:The function f(x) has a greater y-intercept than function g(x).Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\to(0,\ b)\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\=============================[/tex]
[tex]f(x):\\\\given:\ (-1,\ -5),\ (0,\ -1),\ (1,\ 3)\\\\m=\dfrac{3-(-5)}{1-(-1)}=\dfrac{8}{2}=4\\\\(0,\ -1)\to b=-1\\\\f(x)=4x-1\\\\---------------------------\\\\g(x)=2x-7\to m=2,\ b=-7[/tex]
Answer:
Part A: The slope of F(x) is greater than the slope of g(x)
Part B: The Y-intercept of f(x) is greater than that of g(x)
Step-by-step explanation:
To calculate the slope on f(x) we just have to take two points from the table and use the formula for slope:
[tex]m=\frac{y^{2} -y^{1} }{x^{2}- x^{1} }[/tex]
Now the points to use will be:
P1:(0,-1)
P2:(1,3)
Now we just put this values into the formula:
[tex]m=\frac{y^{2} -y^{1} }{x^{2}- x^{1} }[/tex]
[tex]m=\frac{3-(-1) }{1- (0)} }[/tex]
[tex]m=\frac{4}{1}\\ m=4[/tex]
Now to know the slope of g(x) we just have to remember that in the function form y=mx+c the "m" represents the slope, so if g(x)=2x-7 the slope would be "2".
Now we know that f(x) has a greater slope.
To know the greater Y intercept we just take the point in the table where x is "0" since it´s where the Y intercepts with the Y axis, and in f(x) that point is (0,-1), now in g(x) we just evaluate the function to x=0.
[tex]g(x)=2x-7\\g(x)=2(0)-7\\g(x)=-7[/tex]
The Y intercept in g(x) would be in (0,-7), since -1 is greater than -7, we can say that f(x) has the greatest Y-intercept.
-2(7a+4b)-6c=
Simplify
Answer:
Because of the minus sign
2 becomes - 2
The answer is -2
Multiply a and 7
Multiply a and 1
The a just gets copied along.
The answer is a
a
7*a evaluates to 7a
Multiply b and 4
Multiply b and 1
The b just gets copied along.
The answer is b
b
4*b evaluates to 4b
7*a+4*b evaluates to 7a+4b
Multiply -2 by 7a+4b
we multiply -2 by each term in 7a+4b term by term.
This is the distributive property of multiplication.
Multiply -2 and 7a
Multiply 1 and a
The a just gets copied along.
a
-2 × 7a = -14a
Multiply -2 and 4b
Multiply 1 and b
The b just gets copied along.
b
-2 × 4b = -8b
-2*(7*a+4*b) evaluates to -14a-8b
Multiply c and 6
Multiply c and 1
The c just gets copied along.
The answer is c
c
6*c evaluates to 6c
The answer is -14a-8b-6c
-2*(7*a+4*b)-6*c evaluates to -14a-8b-6c
The final answer is
-14a-8b-6c
Step-by-step explanation:
Please mark brainliest and have a great day!
What is the slope of the line that passing through (-2, 4) and the origin.
Answer:
slope= -2
Step-by-step explanation:
using [tex]\frac{y2-y1}{x2-x1}[/tex] you plug in the values of (-2,4) and (0,0)
=[tex]\frac{0-4}{0-(-2)}[/tex]
=[tex]\frac{-4}{2}[/tex]
= -2
Answer:
The slope is -2
Step-by-step explanation:
(4 - 0)/(-2 - 0) = 4/(-2) = -2
What is the solution to the equation 7/8=m/32.
14
24
28
30
Answer: 28
Step-by-step explanation:
7/8 = m/32
cross multiply the expression
8m = 224
m = 224/8 = 28
Hope it helped!
[tex]\huge{\boxed{m=28}}[/tex]
[tex]\frac{7}{8}=\frac{m}{32}[/tex]
Since [tex]8[/tex] is multiplied by [tex]4[/tex] to get 32, you also multiply [tex]7[/tex] by [tex]4[/tex] to get [tex]m[/tex].
[tex]7*4=28[/tex]
-2(5x+8)=14+6x complete the statements below with the process used to achieve steps 1-4
Expand -2(5x+8), simplify, isolate x by moving terms, and solve to get x = -15/8.
To solve the equation -2(5x + 8) = 14 + 6x step by step, here's what was done:
Step 1: Expand the left side of the equation by distributing -2 across the terms inside the parentheses:
-2(5x + 8) = -2 * 5x - 2 * 8 = -10x - 16
So, the equation becomes: -10x - 16 = 14 + 6x
Step 2: Group like terms together. Subtract 6x from both sides to get all the x terms on one side of the equation:
-10x - 6x = 14 + 16
This simplifies to: -16x = 30
Step 3: Now, isolate the variable by dividing both sides by -16:
(-16x)/(-16) = 30/(-16)
This simplifies to: x = -30/16 or x = -15/8
So, the solution for x is x = -15/8.
The complete question is here:
-2(5x+8)=14+6x The equation was solved using the following steps Step 1: -10z-16=14+6z Step 2: -16x-16=14 Step 3: -16x=30 Step 4: z= 21/-16 Step 5: z=- 15/8 Complete the statements below with the process used to achieve steps 1-4 Stop 12 to 5x and 8. Step 26x Step 3 : 16. Step 4: 16.
According to the synthetic division below, which of the following statements are true
Answer:
B and D
Step-by-step explanation:
The polynomial x² + 6x - 8 ( from values in first row )
is being evaluated at x = - 5 thus the factor is (x + 5)
If (x + 5) is a factor the remainder = 0
Hence (x + 5) is not a factor since remainder = 12 ≠ 0
When the polynomial is evaluated at x = 5 it's value is 12
The remainder theorem states that f(h) = remainder, hence
f(- 5) = 12 ← remainder
Miles paid $5824, including 4% sales tax, for an out-of-state purchase of a car. In order to calculate the amount of sales tax he owes in his state, he must first determine the price of the car without sales tax. How much did the car cost before sales tax?
Answer: $5,591
Step-by-step explanation:
4% = .04
5824 x .04 = 232.96
5824 - 232.96 = 5591
Before sales tax, the car cost $5591