Answer:
c
Step-by-step explanation:
The Greatest Common Factor [GCF] means the LEAST DEGREE TERM possible, plus finding a common factor, in this case, between 9 and 13, which is 1, but writing it is unnecessary.
I am joyous to assist you anytime.
The greatest common factor of 13c and 9c³ is "c".
To find the greatest common factor (GCF) of 13c and 9c³, we need to determine the largest term that divides evenly into both expressions.
First, let's break down each expression into its prime factors:
13c = 13 x c
9c³ = 3² x c³
Now, let's identify the common factors between the two expressions:
Common factors of 13c and 9c³: c
To find the GCF, we take the product of the common factors, considering the lowest exponent for each common factor:
GCF = c
Therefore, the greatest common factor of 13c and 9c³ is "c".
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Find the value of x.
At what value of x do the graphs of the equations below intersect?
2x – y = 6
5x + 10y = –10
Answer:
Step-by-step explanation:
The intersection is the point where two equations meet. It is calculated by substituting terms into the equations involved. For the given systems of equation, calculations are as follows:
2x - y = 6
y = 2x - 6
We substitute the equation above to the second equation.
5x + 10y = –10
5x + 10( 2x - 6 )= –10
Simplifying,
5x + 20x - 60 = -10
25x = 50
x = 2
Therefore, the intersection has the value of x equal to 2.
Answer with Step-by-step explanation:
The point of intersection of the graphs of system of equation is the solution to the system of equations.
So, we need to find the solution of the system of equations:
2x – y = 6
5x + 10y = –10
Multiplying first equation by 10 and add it to second equation.
5x+10y+10(2x-y)= -10+60
5x+10y+20x-10y=50
25x=50
⇒ x=2
Hence, value of x where the graphs of the equations
2x – y = 6
5x + 10y = –10 intersect is:
x=2
biggest to smallest 1/8 2/3 3/5
Convert the fractions to decimals:
1/8 = 0.125
2/3 = 0.666
3/5 = 0.6
Now arrange from largest to smallest
2/3, 3/5, 1/8
Answer:
2/3 biggest
3/5
1/8 smallest
Work out the total surface area of this hemisphere which has a radius of 8cm.
Give your answer to one decimal place
To calculate the total surface area of a hemisphere with a radius of 8 cm, we use the formula A = 3πr², resulting in a total surface area of approximately 602.9 cm² to one decimal place.
Explanation:The question asks us to work out the total surface area of a hemisphere with a radius of 8cm and provide the answer to one decimal place. The total surface area of a hemisphere is given by the formula A = 2πr² + πr², where π is approximately 3.14 and r is the radius of the hemisphere. The first part 2πr² represents the curved surface area, and the second part πr² represents the area of the circular base.
Substituting 8 cm for r:
A = 2π(8²) + π(8²) = 2π(64) + π(64) = 128π + 64π = 192π cm²
Converting π to 3.14:
A = 192(3.14) = 602.88 cm². Therefore, the total surface area of the hemisphere is approximately 602.9 cm² to one decimal place.
The total surface area of this hemisphere is approximately 603.2 cm².
Calculating the Total Surface Area of a Hemisphere
To find the total surface area of a hemisphere with a radius of 8 cm, we need to consider both the curved surface area and the base area.
Curved Surface Area: The formula for the curved surface area of a hemisphere is given by 2πr², where r is the radius. Substituting the given radius (8 cm), we get:
Curved Surface Area = 2π(8 cm)² = 2π(64 cm²) ≈ 2 × 3.1415927 × 64 = 402.1 cm² (rounded to one decimal place)
Base Area: The base of the hemisphere is a circle with the area given by the formula πr². Using the radius (8 cm), we get:
Base Area = π(8 cm)² = π(64 cm²) ≈ 3.1415927 × 64 = 201.1 cm² (rounded to one decimal place)
Total Surface Area: To find the total surface area, we sum the curved surface area and the base area:
Total Surface Area = 402.1 cm² + 201.1 cm² = 603.2 cm²
Therefore, the total surface area of the hemisphere is approximately 603.2 cm².
you buy a house for $130000. it appreciates 6% per year. how much is it worth in 10 years
growth or decay?
write a function that represents the situation:
initial amount=
growth/decay rate:
Final answer:
The future value of the house will be approximately $232,810.10 in 10 years, calculated by compounding the initial value of $130,000 at an annual growth rate of 6%.
Explanation:
To calculate the future value of a house appreciating at a certain rate, we can use the compound interest formula: [tex]Future\ Value = Present\ Value \* (1 + growth/decay rate)^{number of periods[/tex]
In this scenario, the house is appreciating, which means it's increasing in value over time.
We're given that the initial amount (Present Value) is $130,000 and the growth rate is 6% per year.
The function that represents the situation is:
Future Value = $130,000 × (1 + 0.06)¹⁰
To find the value of the house in 10 years, we simply plug in the values:
Future Value = $130,000 × (1 + 0.06)¹⁰
Future Value = $130,000 × (1.06)¹⁰
Future Value = $130,000 × 1.790847
Future Value = $232,810.10 approximately
Therefore, the house will be worth approximately $232,810.10 in 10 years, and this represents growth, not decay.
At Funland, all rides cost $1. Angela has $21.50. How
many rides can she take?
Answer:
21 rides, with $0.50 left.
Step-by-step explanation:
All rides cost $1. Note that you cannot take half a ride, and so the cents (0.50) is out of the question. Divide 21 with 1:
21/1 = 21
Angela can ride up to 21 rides.
~
A car is traveling at 42 mph. if its tires
have a diameter of 27 inches, how fast are
the car's tres turning? Express answer
in revolutions per minute.
Answer:
522.9 revolutions /min
Step-by-step explanation:
Given Diameter, D = 27 inches
Circumference, C = πD = 3.142 x 27 = 84.82 inches
(recall 1 mi = 63360 in)
Car speed is 42 mph = 42 mph x 63,360 inches / mile = 2,661,120 inches / hr
(recall 1 hour = 60 min)
Hence car speed becomes
= 2,661,120 inches / hr ÷ 60 min/hr
= 44,352 inches / min
Number of revolutions / min
= speed in inches/min ÷ circumference
= 44,352 ÷ 84.82 = 522.9 revolutions /min
To find out how fast a tire with a diameter of 27 inches is turning for a car moving at 42 mph, you first convert miles per hour to inches per minute, then calculate the tire's circumference in inches, and divide the car's speed by this circumference. The calculated result is approximately 523.05 revolutions per minute.
Explanation:To answer this question, we first need to convert the information about speed and tire diameter to compatible units. We'll convert the car speed from miles per hour (mph) to inches per minute since the diameter of the tire is given in inches.
Since 1 mile equals 63,360 inches, 42 mph is equal to 42*63360 = 2,661,120 inches per hour. As there are 60 minutes in an hour, that comes out to 2,661,120/60 = 44,352 inches per minute.
Next, we will find the circumference of the tire, which is its diameter multiplied by pi. Therefore, we have a circumference of 27 inches * 3.14 (pi) = 84.78 inches.
Finally, to find out how many times the tire rotates in a minute, we divide the car's speed in inches per minute by the tire's circumference in inches. This means the tires are making 44,352/ 84.78 ~= 523.05 revolutions per minute.
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Which system of equations can be used to find the roots of the equation4x^5-12x^4+6x=5x^3-2x?
Answer:
y = 4x^5 - 12x^4 + 6x and
y = 5x^3 - 2x
Step-by-step explanation:
The system of equations that can be used to find the roots of the equation 4x^5-12x^4+6x=5x^3-2x are;
y = 4x^5 - 12x^4 + 6x and
y = 5x^3 - 2x
We simply formulate two equations by splitting the left and the right hand sides of the given equation.
The next step is to graph these two system of equations on the same graph in order to determine the solution(s) to the given original equation.
The roots of the given equation will be given by the points where these two equations will intersect.
The graph of these two equations is as shown in the attachment below;
The roots are thus;
x = 0 and x = 0.813
One human year is said to be about 7 dog years. Cliff's dog is 5.5 years old in
human years. Find his dog's age in dog years. Round to the nearest tenth.
Answer:
38.5
Step-by-step explanation:
7 times 5.5
Expand the binomial (1 - 2x)^6 use Pascal’s triangle
Answer:
1 - 12x + 60x^2 - 160x^3 + 240x^4 - 192x^5 + 64x^6
Step-by-step explanation:
So we need to know the 7th line of pascals triangle so let us write it out
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1 <----- This one
Now we know we will need coefficients of x from 0 to 6, let us call this i, and for each of these the coefficient is
(-2)^i * (1)^(6-i) * number in pascals triangle
Hence
i = 0, 1 * 1 * 1 = 1
i = 1, -2 * 1 * 6 = -12
i = 2, 4 * 1 * 15 = 60
i = 3, -8 * 1 * 20 = -160
i = 4, 16 * 1 * 15 = 240
i = 5, -32 * 1 * 6 = -192
i = 6, 64 * 1 * 1 = 64
Hence (1-2x)^6 = 1 - 12x + 60x^2 - 160x^3 + 240x^4 - 192x^5 + 64x^6
solve the system of equation below by graphing them
y= 2x-3
y=-2x+5
Answer:
Step-by-step explanation:
(4x3 + 11X + 9) / (x + 3)
what is the range of g need help fast
Range is all the y values included in the graph. Look at the image below for the y values:
As you can see the highest y value this graph reaches is 6 and the lowest is -5 therefore the range is...
-5 ≤ g(t) ≤ 6
Hope this helped!
~Just a girl in love with Shawn Mendes
Find the least common multiple.
3x3, 12y7, and 15xy3
Answer:
60 x^3 y^7
Step-by-step explanation:
3x^3 = 3*xxx
12y^7 = 3*4 yyyyyyy
15xy^3 = 3*5 xyyy
We need to have the minimum of each for the least common multiply
For the numbers there is a 3 a 4 and a 5
For the x , the minimum is xxx
For the y, the minimum is yyyyyyy
Least common multiple: 3*4*5 xxx yyyyyyy
60 x^3 y^7
Factor this expression x^2+9x+8
Answer:(x+1) (x+8)
Step-by-step explanation:
Answer:
(x + 8)(x + 1)
Step-by-step explanation:
Consider the factors of the constant term (+ 8) which sum to give the coefficient of the x- term (+ 9)
The factors are + 8 and + 1, since
8 × 1 = 8 and 9 + 1 = 9, hence
x² + 9x + 8 = (x + 8)(x + 1) ← in factored form
Find the missing factor.
8x^2 - 15x + 7 = (8x - 7)( )
Answer:
Step-by-step explanation:
(8x - 7)(
The x^2 term has to come out to 8x^2.
The 8 is already there.
So your first term in the second factor is x.
(8x - 7) ( x
Now the question is what is the sign after the x. Since the question shows +7 the only way that can happen is if both signs in the factors are the same.
Since (8x - 7) has been given to you and you need 7 to come out plus, then the sign after x must minus. Both signs must be the same.
(8x - 7)(x -
Last, what comes after the minus sign? You already have a minus 7 so you need something to multiply by 7 to get seven.
That should be a one.
(8x - 7)(x - 1)
x - 1 is you answer. I leave you to check the middle term. It is - 15
How many liters of 10% alcohol solution and 5% alcohol solution must be mixed to obtain 40 liters of 8%
alcohol solution?
Answer:
x+y=40liters
10%x+5%y=8%×40
(2x+y)/20=8%×40
(2x+y)=64
x=24
y=16
A polynomial function can be written as (x - 1)(x - 4)(x + 7). What are the x-intercepts of the graph of this function?
a.(1,0). (4,0), (7,0)
b.(-1,0).(-4,0), (-7,0)
c.(1,0), (4,0), (-7,0)
d.(-1,0), (-4,0), (7,0)
X - intercepts are also known as zeros. To solve this simply take each factor of the polynomial and set it equal to zero. Solve for x then you'll have your x - value of the x intercept.
x - 1 = 0
x - 1 +1 = 0 + 1
x = 1
x - 4 = 0
x - 4 + 4 =0 +4
x = 4
x + 7 = 0
x + 7 - 7 = 0 - 7
x = -7
^^^All the above are the x values of the x - intercepts
The answer is...
C. (1 , 0) (4, 0) ( -7, 0)
Hope this helped!
~Just a girl in love with Shawn Mendes
URGENT!!!!
Which transformations could have occurred to map AABC
to AA"B"C"?
a rotation and a reflection
a translation and a dilation
a reflection and a dilation
a dilation and a rotation
Answer: a dilation and a rotation
Step-by-step explanation:
A reflection is a rigid transformation that maps every point of a figure in the plane to point of image of figure, across a line of reflection .A rotation of some degrees is a rigid transformation which rotate a figure about a fixed point known as the center of rotation.A translation is a rigid transformation of a figure that moves every point of the figure a fixed distance in a particular direction.A dilation is a transformation in which a figure is enlarged or reduced with respect to a point known as the center of dilation.From the given figure it can be seen that ΔABC is reduced to ΔA"B"C" so there must be dilation.
Also, when there is rotation about point C to create ΔA"B"C".
Therefore, the transformations could have occurred to map ΔABC to ΔA"B"C" are a dilation and a rotation.
Solve for x. x/5+ 1 = 7
x = 5 5/6
x = 30
x = 35
x = 40
Answer:
x = 30Step-by-step explanation:
[tex]\dfrac{x}{5}+1=7\qquad\text{subtract 1 from both sides}\\\\\dfrac{x}{5}+1-1=7-1\\\\\dfrac{x}{5}=6\qquad\text{multiply both sides by 5}\\\\5\!\!\!\!\diagup^1\cdot\dfrac{x}{5\!\!\!\!\diagup_1}=5\cdot6\\\\x=30[/tex]
When x=2 and y=4, what is the value of 7x-y?
Answer:
the value of 7x-y is -14.
Step-by-step explanation:
When x=2 and y=4,
To find the value of 7x - y when x =2, y = 4, this means when ever you see x, put 2 in replacement, y, put 4 respectively.
7x - y = 7(2 - 4)
14 - 28
= -14.
The value of the expression 7x - y is 10 if the values of x and y are 2 and 4 respectively.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
The expression is:
= 7x - y
The value of x and y is given:
x = 2
y = 4
Plug the above values in the expression 7x - y
= 7(2) - 4
= 14 - 4
= 10
The linear expression can be defined as the relation between two expressions, if we plot the graph of the linear expression we will get a straight line.
If in the linear expression, one variable is present, then the expression is known as the linear expression in one variable.
Thus, the value of the expression 7x - y is 10 if the values of x and y are 2 and 4 respectively.
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Find the slope of the line through the points (4, 8) and (5, 10).
A. 1/2
B. -1/2
C. 2
D. -2
Answer:
The slope is 2.
Step-by-step explanation:
Using the given function, select the correct set of ordered pairs for the following domain values.
Answer:
The set of ordered pair are { (-12,-18),(-3,-3), (0,2),(3,7),(12,22)}
Step-by-step explanation:
we have
[tex]f(x)=\frac{5}{3}x+2[/tex]
Find the values of f(x) for the domain values
For x=-12
substitute
[tex]f(-12)=\frac{5}{3}(-12)+2=-18[/tex]
The ordered pair is (-12,-18)
For x=-3
substitute
[tex]f(-3)=\frac{5}{3}(-3)+2=-3[/tex]
The ordered pair is (-3,-3)
For x=0
substitute
[tex]f(0)=\frac{5}{3}(0)+2=2[/tex]
The ordered pair is (0,2)
For x=3
substitute
[tex]f(3)=\frac{5}{3}(3)+2=7[/tex]
The ordered pair is (3,7)
For x=12
substitute
[tex]f(12)=\frac{5}{3}(12)+2=22[/tex]
The ordered pair is (12,22)
Answer with explanation:
The given function is
[tex]f(x)=\frac{5x}{3}+2\\\\x=-12,-3,0,3,12\\\\f(-12)=\frac{5\times -12}{3}+2\\\\f(-12)=-20+2\\\\f(-12)=-18\\\\f(-3)=\frac{5 \times -3}{3}+2\\\\f(-3)=-5+2\\\\f(-3)=-3\\\\f(0)=\frac{5\times 0}{3}+2\\\\f(0)=2\\\\f(3)=\frac{5\times 3}{3}+2\\\\f(3)=5+2\\\\f(3)=7\\\\f(12)=\frac{5\times 12}{3}+2\\\\f(12)=20+2\\\\f(12)=22[/tex]
So, the ordered pair will be
(-12, -18),(-3,-3),(0,2),(3,7),(12,22)
Funcions f(x) and g(x) are defined below.
Determine where f(x) = g(x) from the graph.
A: x = -2; x = 2
B: x = -2; x = 0; x = 2
C: x = 0; x = -8
D: x = 0, x = 2
The point where f(x)= g(x) is x = -2; x = 2.
The correct option is (A)
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
As, from the graph the line graph for f(x) and g(x) is coinciding at two points at 2 and -2.
At these two points the two function line overlap.
So, point where f(x)= g(x) is x=2 and x=-2.
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Lisa is a leading player on her basketball team. She has kept track of how many points she has scored over the course of the season. Her scores may be viewed in the table below. 36 20 35 13 30 14 36 11 29 19 22 40 34 17 26 21 What is the median of Lisa’s scores? Round to the nearest point, if necessary. a. 23 b. 24 c. 26 d. 30
Answer: Option b
[tex]M=24[/tex]
Step-by-step explanation:
We have the following list of data
36 20 35 13 30 14 36 11 29 19 22 40 34 17 26 21
The list contains 16 data.
The first step to calculate the median is to order the data from least to highest
11,13,14,17,19,20,21,22,26,29,30,34,35,36,36,40
Now mark the two central values of the data set
11,13,14,17,19,20,21 [22,26] 29,30,34,35,36,36,40
The median of the data is the average of the two central values
[tex]M=\frac{22+26}{2}[/tex]
[tex]M=24[/tex]
Note that the median is the central value of the ordered data set
GEOMETRY Please HELP
Answer:
x = 6.93
Step-by-step explanation:
If a tangent and a secant are drawn to a circle from the same exterior point, the square of the length of the tangent is equal to the product of the total length of the secant and the length of the external segment of the secant.
From the given diagram,
(8+4)×4=x²
12×4=x²
48=x²
x=√48
x=6.93
x=7 to the nearest whole number.
Determine the standard form of the equation of the line that passes through (-2,0) and (8,-5)
Answer:
x + 2y = - 2
Step-by-step explanation:
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
Obtain the equation in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (8, - 5)
m = [tex]\frac{-5-0}{8+2}[/tex] = [tex]\frac{-5}{10}[/tex] = - [tex]\frac{1}{2}[/tex]
y = - [tex]\frac{1}{2}[/tex] + c ← partial equation of line
To find c substitute either of the 2 points into the partial equation
Using (- 2, 0), then
0 = 1 + c ⇒ c = - 1
y = - [tex]\frac{1}{2}[/tex] x - 1 ← in slope- intercept form
Multiply through by 2
2y = - x - 2 ( add x to both sides )
x + 2y = - 2 ← in standard form
Which description can be written as the expression
N/4-13
Answer:
(A) Joel wants to find the quotient of a number and four, minus thirteen.
Step-by-step explanation:
The correct description that can be written as the expression [tex]\frac{n}{4}[/tex] - 13 is 'Joel wants to find the quotient of a number and four, minus thirteen'.
Mathematically, an expression is a combination of numbers, variables, operations, and functions that are combined according to specific rules to represent a mathematical computation or relationship. It can be thought of as a mathematical phrase or formula.
By combining numbers, variables, operators, and functions, mathematical expressions can represent a wide range of computations and relationships.
Expressions are fundamental in mathematics as they allow us to represent and manipulate mathematical concepts, solve equations, evaluate formulas, and analyze mathematical relationships. They are used in various areas of mathematics, including algebra, calculus, geometry, and more.
Hence, the expression [tex]\frac{n}{4}[/tex] - 13 can be written as 'Joel wants to find the quotient of a number and four, minus thirteen'.
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The data in the table represent the height of an object over
time.
Which model best represents the data?
Height of an Object
Time (seconds) Height (feet)
05
1
50
2
70
3
48
quadratic, because the height of the object increases or
decreases with a multiplicative rate of change
quadratic, because the height increases and then
decreases
exponential, because the height of the object increases
or decreases with a multiplicative rate of change
exponential, because the height increases and then
decreases
Answer:
The correct answer option is quadratic, because the height increases and then decreases.
Step-by-step explanation:
We are given the following data in the table which represents the height of an object over time:
Time (s) Height (ft)
0 5
1 50
2 70
3 48
We know that in situation where the values increase and then decreases, a quadratic model is used.
From the values given in the table, we can see that the values of height first increased and then decreased with the increase in time.
Therefore, the model used is quadratic, because the height increases and then decreases.
Answer:
BStep-by-step explanation:
if f(x)=x/2-3 and g(x)=4x^2+x-4, find (f+g)(x)
Answer:
[tex]\large\boxed{(f+g)(x)=4x^2+\dfrac{3}{2}x-7}[/tex]
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=\dfrac{x}{2}-3=\dfrac{1}{2}x-3,\ g(x)=4x^2+x-4\\\\\text{Substitute:}\\\\(f+g)(x)=\left(\dfrac{1}{2}x-3\right)+(4x^2+x-4)\\\\=\dfrac{1}{2}x-3+4x^2+x-4\qquad\text{combine like terms}\\\\=4x^2+\left(\dfrac{1}{2}x+x\right)+(-3-4)\\\\=4x^2+1\dfrac{1}{2}x-7\\\\=4x^2+\dfrac{3}{2}x-7[/tex]