Step-by-step explanation:
a)
[tex]f(x+h) = 4(x+h)+4[/tex]
[tex]f(x+h)=4x+4h+4[/tex]
b)
[tex]f(x+h)-f(x)=4x+4h+4-(4x+4)[/tex]
[tex]f(x+h)-f(x)=4x+4h+4-4x-4[/tex]
[tex]f(x+h)-f(x)=4h[/tex]
c)
[tex]f(x+h)-f(x)h=4x+4h+4-h(4x+4)[/tex]
[tex]f(x+h)-f(x)h=4x+4h+4-4hx+4h[/tex]
[tex]f(x+h)-f(x)h=-4hx+8h+4x+4[/tex]
Use the sequence below to complete each task. -5, 15, -45, ... a. Identify the common ratio (r). b. Write an equation to represent the sequence. C. Find the 12th term (22)
you get he common ratio by dividing a term by the previous term
so,
15/-5 = -3
common ratio = -3
Geometric seuqence has a general term of:
[tex]a_n=ar^{n-1}[/tex]Wher
r is common ratio
a is first term
Given,
a = -5
r = -3
We have:
[tex]\begin{gathered} a_n=ar^{n-1} \\ a_n=-5(-3)^{n-1} \\ a_n=-5\times-3^n\times-3^{-1} \\ a_n=-5\cdot-3^n\times-\frac{1}{3} \\ a_n=-\frac{5}{3}(3)^n \end{gathered}[/tex]12th term is basically n = 12
So, we have:
[tex]\begin{gathered} a_n=-\frac{5}{3}(3)^n \\ a_{12}=-\frac{5}{3}(3)^{12} \\ a_{12}=-885735_{} \end{gathered}[/tex]A paralegal bills a law firm for 15.5 hours of work at a rate of $120 per hour. How much money has the paralegal earned from this job? Include units in your answer.
b) The paralegal splits her earnings between utilities and savings in a ratio of 2 ∶ 3. How much money will be allocated to her savings?
The amount paralegal earned from the job is 1860 dollars.
The amount allocated for savings is 1116 dollars.
How to find the earnings of paralegal?Paralegal bills the law firm for 15.5 hours of work at a rate of $120 per hour.
Therefore, the law firm have to pay paralegal 120 dollars for every hour worked.
Therefore,
the amount earned by paralegal = 15.5 × 120
the amount earned by paralegal = 1860 dollars
Paralegal splits her earnings between utilities and savings in a ratio of 2 ∶ 3.
Therefore, let's find the amount of money allocated for her savings.
amount allocated for savings = 3 / 5 × 1860
amount allocated for savings = 5580 / 5
Therefore,
amount allocated for savings = 1116 dollars
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The sum of three numbers is 135. The second number is 4 times the third. The first number is 9 less than the third. What are the numbers?
First number:
Second number:
Third number:
Answer:
First number: 21
Second number: 84
Third number: 30
21 times 4 = 84 which checks out.
30 - 21 = 9 which also checks out
21 + 84 + 30 = 135 so they are correct!
Step-by-step explanation:
Hope it helps! =D
The longest side of a triangle must be less than the sum of the other two sides.
Suppose a triangle is made up of lengths 2 inches, 5 inches and L. inches, where L is the longest side.
Describe the solution set for all possible side lengths for L verbally and graphically.
The solution set for all possible side lengths for side L is;
⇒ L < 7
What is Triangle?
A triangle is a three sided polygon , which has three vertices and three angles.
Given that;
The longest side of a triangle must be less than the sum of the other two sides.
Suppose a triangle is made up of lengths 2 inches, 5 inches and L. inches, where, L is the longest side.
Now, By the given condition;
''The longest side of a triangle must be less than the sum of the other two sides.''
We can formulate;
L < 2 + 5
L < 7
So, The solution set for all possible side lengths for side L is;
⇒ L < 7
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You've learned about linear, quadratic, and exponential functions.
How can you tell the difference between each type of function just by looking at the equation?
Describe a real world situation that can be represented by each type of function.
We can tell the difference among linear, quadratic, and exponential functions just by looking at equation as Exponent functions are rapidly increasing or decreasing, and the highest power of variable for a linear function is 1. The highest power of variable for a quadratic function is 2.
Linear functions are functions that are used to model phenomena that increase or decrease at a constant rate. These types of functions are polynomial functions with a highest exponent of one on the variable. The graphs of these functions are in the shape of a straight line.
Exponential functions are functions that have the variable in the exponent. They increase or decrease slowly then quickly or quickly then slowly.
Quadratic functions are the functions that have the highest power of variables equal to 2.
For example,
Linear Equation : The population of a family of rabbits starts with 2 rabbits and doubles every month.
Expoential Equation : Compound interest is example of exponential function.
Quadratic Equation : When you throw a ball (or shoot an arrow, fire a missile or throw a stone) it goes up into the air, slowing as it travels, then comes down again faster and faster and a Quadratic Equation tells you its position at all times!
Therefore, we can conclude that linear function have highest power of variable as 1 , exponent functions are quickly increasing or decreasing, Quadratic functions have the power of variables equal to 2.
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7. Find the perimeter of an isosceles triangle whose base is 6 cm and two equal sides are 7.5 cm.
8. Perimeter of a regular nonagon is 99 cm, its side will be
9. Find the cost of fencing a square park with 4 rows of wires at the rate of Rs. 15.75 per metre, if
the side is 350 m long.
10. What is the length of wooden strip required to frame a photograph of length 33 cm and breadth
19 cm.
11. A wire 1m 68 cm long is cut into two pieces. One piece is used to make a regular hexagon and
the other is used to make a regular pentagon. Find the difference in the length of the pentagon and
hexagon formed.
12. The perimeter of a rectangular garden is 190 m and breadth is 10.5 m. Find the length and area
of the garden.
13. Compare the areas of: a) square of 25.4 cm b) rectangle of 15 cm and 12.5 cm
Also study Solved examples 3, 4 from page 67,
Examples 2, 3, 4 from page 62
The perimeter of the isosceles triangle whose base is 6 cm and two equal sides are 7.5 cm is 21 centi-meters.
What is isosceles triangle?
An isosceles triangle in geometry is one with at least two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception. The isosceles right triangle, the golden triangle, the faces of bipyramids, and some Catalan solids are all examples of isosceles triangles.
To calculate the perimeter of isosceles triangle, we use equation:
Perimeter = Base + 2(Two equal side)
Perimeter = 6 + 2(7.5)
Perimeter = 21 cm
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I need help answering this question
If this is an arithmetic sequence, each of the terms will have a common difference. Let's check.
[tex]\begin{gathered} 3-21=-18 \\ 21-147=-126 \end{gathered}[/tex]As we can see, each of the terms does not have a common difference. The first one is -18 while the other one is -126. Therefore, this is not an arithmetic sequence.
Now, let's check if this is a geometric sequence. If it is, each of the terms will have a common ratio.
[tex]\begin{gathered} 3\div21=\frac{1}{7} \\ 21\div147=\frac{1}{7} \end{gathered}[/tex]As we can see, each of the terms has a common ratio which is 1/7. Therefore, 147, 21, 3 is a geometric sequence and the common ratio is equal to 7.
ben bowled 157 and 193 in his first two games. what must he bowl in his third game to have an average of at least 160?
Ben must bowl 130 in his third game so that the average will be of at least 160.
Given that, Ben bowled 157 and 193 in his first two games. So, we have to calculate the average of his third bowl to have an average of at least 160.
Let the average of third bowl be x.
The average is known as the arithmetic mean which is the sum of all numbers in a collection, divided by the count of the numbers present in the collection. In other words, the average is the ratio of the sum of all given observations to the total number of observations. Hence, the average formula is:
Average = Sum of the Observations/Number of Observations
160 = 157+193+x/3
⇒ 160×3 = 157+193+x
⇒ 480 = 350+x
⇒ 480-350 = x
⇒ 130 = x
Therefore, Ben must bowl 130 in his third game so that the average will be of at least 160.
Hence, 130 is the required answer.
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The line below is the function y=2x-1. Identify the equation of a parallel line
The equation of parallel line is y = 2x + 3
Given,
The line below is the function y=2x-1.
From the figure,
Identify the equation of a parallel line.
Now, According to the question:
We are given that line a represented by the equation
y = 2x -1
and, We know that
Slope- intercept form of line is given by
y = mx + c
Where m=Slope of line a
c = y- intercept
Comparing it with the given equation then, we get
Slope of line a = 2
We know that
When two lines are parallel then their slopes are equal.
Hence, Option (b) slope is equal to the given function
It means, y = 2x - 1 and y = 2x +3
Value of slope m = 2 = 2
Hence, The equation of parallel line is y = 2x + 3
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please show all work
the probability of the event that 0
Answer:
basically the even twill not happen as the probability of that is 0
Zevel overheard Bradley say he got a 66% on the last test. If Zevel only got one-third whatBradley got, what is Zevel's score?
Let the total marks are 100.
And Bradely got 66% marks.
So the marks of Bradely are:
[tex]\begin{gathered} M_B=\frac{66}{100}\times100 \\ M_B=66 \end{gathered}[/tex]And Zevel got one third of Bradely's marks so:
[tex]\begin{gathered} M_Z=\frac{1}{3}M_B \\ M_Z=\frac{1}{3}\times66 \\ M_Z=22 \end{gathered}[/tex]my dog has a 30%chance of tearing up the trash on a given day and there's a 10% chance of rain tomorrow. What is the chance that my dog tears up the trash and it rains tomorrow
The probability that that my dog tears up the trash and it rains tomorrow is 0.03.
How to illustrate the information?From the information, the dog has a 30% chance of tearing up the trash on a given day and there's a 10% chance of rain tomorrow.
Therefore, the that my dog tears up the trash and it rains will be:
= Probability of tearing up × Probability of rain
= 30% × 10%
= 0.3 × 0.1
= 0.03
The probability is 0.03.
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A biased dice is rolled and the results are recorded in a table. The dice is rolled once more. a) Use the table to estimate the probability that a 3 will be rolled. b) If the dice is rolled another 500 times, how many sixes would you expect to roll? Score 1 2 3 4 5 6 Frequency 12 35 11 23 7 12
The probability that a 3 will be rolled would be 0.125 and the expected number of 6's roll would be 68.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
The events' estimated probabilities are as follows, according to the exponential probability theory:
P(3) = 0. 125
P(6 in 500 rolls) = 68 rolls
Number of times event occurs / number of trials
A number of attempts = sum of frequency:
(12+35+11+23+7+12) = 88
So the probability that a 3 will be rolled as
⇒ number of 3's / number of attempts
⇒ 11/88 = 0.125
The number of 6's probable in 500 rolls
⇒ (12 /88) × 500
⇒ 68.18 = 68
Therefore, the expected number of 6's roll would be 68.
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100 POINTS!
You want to buy a newest gaming system, which costs $500. In addition, you want to be able to buy the accessories that go with it (e.g., controllers, games, headset, etc.). You already have $150 saved up from your birthday but decide to ask your neighbors if you could wash their dogs to earn more money. You charge $10 per dog.
How many dogs must you wash before you have enough money to buy the gaming system and additional accessories?
Write an equation or inequality to represent the situation. Then solve for your variable [show all steps].
Write a mathematical expression to represent the sentence: “You charge $10 per dog.”
Write a complete sentence that explains what your solution means in terms of the video game system situation.
Assuming the system costs exactly $500 (ignoring taxes), how much extra money would you be able to spend on accessories if you washed 60 dogs? Explain and show your work to justify your answer.
The inequality that represents having enough money to buy the gaming system is x ≥ 35.
The mathematical expression that represents the sentence " you charge $10 per dog" is x = 10 where x is the number of dogs.
x ≥ 35 means that the minimum number of dogs to wash is 35 to make $500.
What is inequality?It is a statement of an ordered relationship
- greater than,
- greater than or equal to,
- less than,
- less than or equal to between two numbers or algebraic expressions.
We have,
The cost of the gaming system = $500
Amount already saved = $150
Charges per dog = $10
The inequality that represents having enough money to buy the gaming system:
150 + 10x ≥ 500
10x ≥ 500 - 150
10x ≥ 350
x ≥ 35 where x is the number of dogs.
The mathematical expression that represents the sentence " you charge $10 per dog ":
x = 10 where x is the number of dogs.
x ≥ 35 means that the minimum number of dogs to wash is 35 to make $500.
Thus,
The inequality that represents having enough money to buy the gaming system is x ≥ 35.
The mathematical expression that represents the sentence " you charge $10 per dog" is x = 10 where x is the number of dogs.
x ≥ 35 means that the minimum number of dogs to wash is 35 to make $500.
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What is a separate-variance t-test
Answer:
it is often known as the unequal variance t test. It assumes that both groups of data are drawn from Gaussian populations, but does not assume that their standard deviations are the same.
Find an equation for the perpendicular bisector of the line segment whose endpoints
are (-2, 4) and (-8,-6).
The equation for the perpendicular bisector of the line segment whose endpoints are (-2, 4) and (-8,-6) is 3x + 5y + 20 = 0.
What is a perpendicular bisector?A line segment known as a perpendicular bisector is at a right angle (90°) to another line segment and divides the line segment that was intersected into two equal pieces.The midpoint of a line segment is the location where the perpendicular bisector intersects it.Given:
Endpoints of the line segment are (-2, 4) and (-8,-6).
Midpoint of the line segment = ( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )
= [tex]\frac{-2 +(-8) }{2}[/tex] , [tex]\frac{4 +(-6) }{2}[/tex]
=( [tex]\frac{-10}{2}[/tex] , [tex]\frac{-2}{2}[/tex] ) = (-5, -1)
Slope of the line segment = [tex]\frac{y_{2} - y_{1} }{x_{2} -x_{1} }[/tex]
= [tex]\frac{(-6) - 4 }{(-8) - (-2) }[/tex]
= [tex]\frac{-10}{-6}[/tex] = [tex]\frac{5}{3}[/tex]
The line perpendicular to the line segment will have a slope of the negative reciprocal of the line segment which is -3/5.
Therefore, the perpendicular bisector passes through (-5,-1) and has a slope of -3/5.
Equation of the line will be,
y - y₁ = m(x - x₁)
⇒ y - (-1) = -3/5(x -(-5))
⇒ 5( y + 1) = -3(x + 5)
⇒ 5y + 5 = -3x - 15
⇒ 3x + 5y + 20 = 0
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Carlos drives 161 kilometers at a speed of 70 kilometers per hour. For how many hours does he drive?
He drove for 2.3 hours.
What is speed?The speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
A body's speed is the amount of distance it travels in one unit of time.
Therefore, the SI Unit for speed is the meter per second, abbreviated as m/s
Formula
Speed = [tex]\frac{distance}{time }[/tex]
Time = [tex]\frac{distance}{speed}[/tex]
Given Data
Distance = 161km
Speed = 70km
Putting values in the formula
Time = [tex]\frac{161}{70}[/tex]
Time = 2.3
He drove for 2.3 hours.
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7 over 8 subtracted by 1 over 12
The table shown gives values of the function y=g(x) for selected values of x. Which represents g(x)
Given:
A table with the given values of the function y=g(x).
To find the function that represents g(x), we substitute a value of x into the given options.
For:
g(x =3+2x:,:
Let x=3
[tex]\begin{gathered} g(x)=3+2x \\ =3+2(3) \\ =9 \end{gathered}[/tex]Based on the given table, the value g(x) is 24 when x=3. So g(x)=3+2x is not the function that represents g(x).
For
[tex]\begin{gathered} g(x)=3\cdot2x \\ =3\cdot2(3) \\ =18 \end{gathered}[/tex]The value of g(x) =18 when x=3, so this is not the function.
For g(x)=3x^2:
[tex]\begin{gathered} g(x)=3x^2 \\ =3(3)^2 \\ =27 \end{gathered}[/tex]Hence, this is not the function as well.
For g(x)=3(2)^x:
[tex]\begin{gathered} g(x)=3\cdot2^x \\ =3\cdot2^3 \\ =3(8) \\ g(x)=24 \end{gathered}[/tex]We can notice that when x=3, the value of g(x) =24 which is the same as the value of g(x) in the given table.
To double check this, we plug in the other values of x.
Therefore, the answer is:
[tex]g(x)=3\cdot2^x[/tex]It's possible to build a triangle with side lengths of 3, 3, and 9.
A. True
B. False
Answer:
true
Step-by-step explanation:
Solve the quadratic equation by factoring Write the answer in reduced fraction form, if necessary.
Given:
The quadratic equation ,
[tex]42x^2-29x-5=0[/tex]The solution of the given quadratic equation can be obtained as,
[tex]\begin{gathered} x=\frac{-(-29)\pm\sqrt[]{(-29)^2-4(42)(-5)}}{2\times42} \\ \text{ =}\frac{29\pm41}{84} \\ x=\frac{29+41}{84}\text{ or x=}\frac{29-41}{84} \\ x=\frac{70}{84}\text{ or x=}\frac{-12}{84} \\ x=\frac{10}{12}\text{ or x=}\frac{-3}{21} \\ x=\frac{5}{6}\text{ or x=}\frac{-1}{7} \end{gathered}[/tex]Hence, the solutions are,
[tex]x=\frac{5}{6},\text{ }\frac{-1}{7}[/tex]What is the mixed number and improper fraction represented in the picture shown below?
? ?
? --------- and ---------
? ?
Answer:
mixed: 2 and 1/4
improper: 9/4
Step-by-step explanation:
The mixed number in picture is [tex]2\frac{1}{4}[/tex] and improper fraction represented in the picture 9/4.
What are fractions?Fractions are the components of a collection or whole. Two parts make up a fraction. The numerator is the number at the top of the line. It indicates the number of equal portions taken from the collection or whole. The number beneath the line is known as the denominator. It indicates the total number of identical parts that make up a collection or the total number of parts that make up the whole.
Given picture shows three circles each are divided in 4 equal parts,
circle 1 and 2 are completely filled it can be counted 1 for each,
1 + 1 = 2
but for third circle only one part is filled out of 4,
it is represented by 1/4
total value of 3 figures is 1 + 1 + 1/4 = 2 + 1/4 = 9/8
and of mixed fraction [tex]2\frac{1}{4}[/tex] .
Hence the mixed fraction [tex]2\frac{1}{4}[/tex] and improper fraction 9/8.
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The coordinates of the vertices of the triangle shown are P(2, 13), Q(7, 1) and R(2, 1).
What is the length of segment PQin units?
Answer:
13
Step-by-step explanation:
Algebraic expression
2(x-7) + 10
Answer:
2(x-2)
Step-by-step explanation: distribute, add the numbers, common factor
What is an equation of the line that passes through the point (-1, 4) and is
parallel to the line x + y = 4?
The equation of the line is y = -1x + 3.
what is parallel lines?Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. In this essay, let's study more about parallel lines. No matter how far we extend a parallel line, it will never meet another parallel line.
The slope so rewrite the equation for the line as y = -x + 1.
The equation in “y = mx + b” form, the slope is always the number m in front of x.
The slope is -1.
First, by using “y = mx + b” form,
we know m is -1 so only need b.
To get b, plug in the (x, y) coordinates for the point (-1, 4)
(4) = -1×(-1) + b.
The y-coordinate 4 on the left side, and the x number -1 on the right.
b = 3.
Therefore, the equation of the line is y = -1x + 3.
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Apple has created a new i-Pad. There are 4 choices for memory size (M), 8 choices for color (C) and 3 apps (A) to select when you purchase the product. From the options below what is the ONLY option the customer can select?
It is to be noted that the ONLY option that the customer can select from when purchasing the product is "(M2, C2, A3)" Option C.
The above exercise is a test of logic, as it is with a simple calculation.
What is logic in Maths?The study of formal logic within mathematics is known as mathematical logic. Mathematical logic research frequently focuses on the mathematical aspects of formal logic systems, such as their expressive or deductive capability.
Hence, from the above, we can see that:
Option (a) contains four App alternatives, which is not feasible. Option (b) contains nine color options, however, only eight are available. This is also not feasible.Option (d) contains eight App options, but only three are available. Hence this is not possible.Learn more about logic:
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Full Question:
Apple has created a new i-Pad. There are 4 choices for memory size (M), 8 choices for color (C) and 3 apps (A) to select when you purchase the product. From the options below what is the ONLY option the customer can select?
(M1, C2, A4)
(M1, C9, A3)
(M2, C2, A3)
(M4, C2, A8)
find the value of y 18y+5
Answer:
y=13
Step-by-step explanation:
list 6 geometric principles represented in the picture.
We will have that some of the principles that geometry works with, that are present in the image are:
Length, Area, Volume, Surfaces, Angles & Curves.
Find area of the figure. Round your answer to nearest hundredth and use 3.14
Answer
Area of the figure = 105.12 ft²
Explanation
The figure shown is a combination of a rectangle with length 10 ft. and width 8 ft., with a semicircle that has diameter 8 ft., which translates to a radius of 4 ft.
The area of the figure = (Area of the rectangle) + (Area of the semicircle)
Area of rectangle = L × W
L = Length = 10 ft.
W = Width = 8 ft.
Area of the rectangle = 10 × 8 = 80 ft²
Area of semicircle = Half of the area of a circle = ½ × πR²
π = pi = 3.14 (According to the question)
R = Radius of the semicircle = 4 ft.
Area of semicircle = ½ × 3.14 × 4² = 25.12 ft²
Area of the figure = 80 + 25.12 = 105.12 ft²
Hope this Helps!!!