E Homework: 3.1 Homework
Evaluate the function f(z) = 3z-8 at the indicated values.
a) Find f(-4).
1
b) Find f
2
c) Find f(z-7).
a) f(-4)=
(Simplify your answer. Type an integer or a simplified fraction.)
THINGS
Answers
The given function is f(z)=3z-8 for the values f(-4), f(2) and f(z-7) respectively -20, -2 and 3z-29 respectively.
The given function is f(z)=3z-8.
We need to find the value of f(-4), f(2), f(z-7).
What is a function?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
Now to find f(-4), replace z from -4.
f(-4)=3(-4)-8=-12-8=-20
Now to find f(2), replace z from 2.
f(2)=3(2)-8=6-8=-2
Now to find f(z-7), replace z from z-7.
f(z-7)=3(z-7)-8=3z-21-8=3z-29.
Therefore, the given function is f(z)=3z-8 for the values f(-4), f(2) and f(z-7) respectively -20, -2 and 3z-29 respectively.
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Related Questions
Use the spinner shown to answer the question. Assume that it is equally probable that the pointer will land on any one of the colored regions. If the pointer lands on a borderline, spin again
If the spinner is spun once, find the probability that the pointer lands in a region that is red or blue.
D
The probability that the pointer lands in a region that is red or blue is
(Type an integer or a simplified fraction.)
Answers
The probability that the pointer lands in a region that is red or blue is 1/2
How to determine the probability?The spinner that completes the question is added as an attachment
From the attached spinner, we have:
Total section = 8Red or blue = 4The probability is then calcuated as:
P =Red or blue/Total section
This gives
P =4/8
Evaluate
P= 1/2
Hence, the probability that the pointer lands in a region that is red or blue is 1/2
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how to solve 52 divided by 4!
Answers
Find the value of x.
Answers
[tex]3(x+4)=90\\x+4=30\\x=26[/tex]
Deion has 62 m of fencing to build a four-sided fence around a rectangular plot of
land. The area of the land is 228 square meters. Solve for the dimensions (length and
width) of the field?
Answers
The dimensions of the the plot of land is a length of 19 meters and width of 12 meters.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the length of the field and y represent the width of the field, hence:
Deion has 62 m of fencing:
2(x + y) = 62
x + y = 31
y = 31 - x (1)
The area of the land is 228 square meters. hence:
xy = 228
x(31 - x) = 228
x² - 31x + 228 = 0
x = 12 or x = 19
when x = 12; y = 31 - 12 = 19
when x = 19; y = 31 - 19 = 12
The dimensions of the the plot of land is a length of 19 meters and width of 12 meters.
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Which statement is true about the polynomial
5s6t2 + 6st9 – 8s6t2 – 6t7 after it has been fully simplified?
It has 3 terms and a degree of 9.
It has 3 terms and a degree of 10.
It has 4 terms and a degree of 9.
It has 4 terms and a degree of 10.
Answers
The polynomial 6st⁹ – 3s⁶t² – 6t⁷ has 3 terms and the degree of the polynomial is 10. Then the correct option is B.
What is polynomial?A polynomial expression is an algebraic expression with variables and coefficients.
The polynomial is given below.
5s⁶t² + 6st⁹ – 8s⁶t² – 6t⁷
Then polynomial can be arranged as
⇒ 6st⁹ + 5s⁶t² – 8s⁶t² – 6t⁷
⇒ 6st⁹ – 3s⁶t² – 6t⁷
The polynomial 6st⁹ – 3s⁶t² – 6t⁷ has 3 terms and the degree of the polynomial is 10.
Then the correct option is B.
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Mr. Apollo’s art class is designing tiles for a mosaic.
The class worked in groups, and each group selected a color and a set of shapes to use.
Match the shape names of all of the shapes in each group by dragging them to the correct color in the table.
Names may be used once, more than once, or not at all.
Set 1 has 4 blue rectangles, Set 2 has 4 red triangles, Set 3 has 4 green kites and Set 4 has 3 yellow trapezoids.
Rectangle returned to the choices list. Parallelogram
Rhombus
Square
Trapezoid
Rectangle
Triangle
Right Triangle
Isosceles Trapezoid
Obtuse Triangle
Blue
Red
Green
Yellow
Answers
To complete this task classify the shapes by considering both the color and the features of the shape.
How to classify a shape?Identify the shape. For example, a triangle has 3 sides and if one of the sides has a 90° angle, the triangle is a right triangle.Assign the name to the shape.Identify the color.Match the shape to set 1, 2 or 3. For example if the right triangle is red, this will belong to set 2.Note: This question is incomplete because the shapes are not given; due to this, the answer is based on general knowledge.
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What is the greatest common factor of 20 and 10?
Answers
Answer:
Step-by-step explanation:
The factors common to 20 and 10 are 1, 5 and 10. The largest of these is 10. That's the GCF of 20 and 10.
A square vegetable garden has side lengths of 8 feet. You plant flowers in the center portion of the garden, a square that has side lengths of 2 feet. You divide the remaining space into 4 equal sections and plant tomatoes, onions, zucchini, and peppers. What is the area of the zucchini section?
Answers
Base on the total area of the square garden and the number of plants planted on it, the area of the zucchini section is 15 feet²
How to find area of zucchini section?Side Length of the square garden = 8 feet
Area of the garden = side length ²
= 8 feet × 8 feet
= 64 feet²
Flower portion:
Side Length = 2 feet
Area of flower portion = side length ²
= 2 feet × 2 feet
= 4 feet²
Remaining space = Area of the garden - Area of flower portion
= 64 feet² - 4 feet²
= 60 feet²
Remaining space is divided into 4 equal sections
= 60 feet² / 4
= 15 feet²
Therefore,
Tomatoes section = 15 feet²
Onions section = 15 feet²
Zucchini section = 15 feet²
Pepper section = 15 feet²
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Jessica works at a restaurant. She earns $5 an hour and received $100 in tips on Saturday night. If she earned $140 total, how many hours did she work?
Answers
$140 total - $100 tips = $40
$40 / $5 per hour = 8 hours
She worked 8 hours
The diameter of a semicircle is 8 millimetres. What is the semicircle's radius?
Answers
Answer:
The radius is 4.
Step-by-step explanation:
Concepts:
Diameter is usually defined as a straight line passing through the center of a circle or sphere and meeting the circumference or circle at each end.Radius is usually defined as a straight line extending from the center of a circle or sphere to the circumference of surface. (Half of diameter).To figure this out:
R = 1/2 d
R = 1/2 8
R = 4
he graph of the function f(x) = –(x + 3)(x – 1) is shown below. On a coordinate plane, a parabola opens down. It goes through (negative 3, 0), has a vertex at (negative 1, 4), and goes through (1, 0). What is true about the domain and range of the function? The domain is all real numbers less than or equal to 4, and the range is all real numbers such that –3 ≤ x ≤ 1. The domain is all real numbers such that –3 ≤ x ≤ 1, and the range is all real numbers less than or equal to 4. The domain is all real numbers, and the range is all real numbers less than or equal to 4. The domain is all real numbers less than or equal to 4, and the range is all real numbers.+
Answers
What is true about the domain and range of the function is; The domain is all real numbers, and the range is all real numbers less than or equal to 4.
How to find the domain of a graph function?Let us first find the roots of the function f(x):
0 = (x - 3)(x + 1)
(x - 3) = 0
x = 3
and (x + 1) = 0
x = -1
Therefore, the roots of the function are x = 3 and x = -1.
Now, the vertex is between the roots (x = 1) and has a negative value of y (y = -4), therefore, we can say that the concavity of the parabola is upwards.
This means that the graph is decreasing until it reaches the vertex, then the graph is increasing.
Therefore, we can conclude that the graph is positive and decreasing for all real values of x where x < -1.
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Answer:
The domain is all real numbers, and the range is all real numbers less than or equal to 4.
Step-by-step explanation:
Nick walked 5 miles to reach his aunt's house. From there he traveled 8 miles to the shopping mall on a bicycle. He traveled 80% faster on the bicycle than on foot. Let r represent his rate of walking in miles per hour. Identify the expression that represents the number of hours Nick took to reach the shopping mall in terms of r. Then find the time taken by Nick to reach the shopping mall if he walked at an average speed of 3 miles per hour
Answers
The number of hours Nick took to reach the shopping mall in terms of r is ; 3.14 hours.
What is rate?Rate is a measure of a quantity using another quantity as the basis.
Analysis:
speed travelling on foot = r
distance travelled on foot = 5 miles
time taken = 5/r
speed travelling on bicycle 80 percent faster than on foot is 1.8r
distance travelled on bicycle = 8 miles
time taken = 8/1.8r = 40/9r
total time taken to get to the mall = 5/r + 40/9r = 85/9r
speed while walking = 3 miles per hour = r
time taken = 85/9 x 3 = 3.14 hours
In conclusion, number of hours Nick took to reach the shopping mall in terms of r is 85/9r is 3.14 hours.
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Answer:
3 hours 9 minutes
A number is divided in the ratio 3:4. If the first part is 24, find the number.
Answers
Answer:
31Step-by-step explanation:
Let the other part be x.Now,24:x=3:43x=96X = 96/3 = 321Other part = 32mark me brainlist!Suppose that the function f is defined, for all real numbers, as follows.
-x-1 if x #-2
f(x)=
3
if x = -2
Find f(-4), f(-2), and ƒ(0).
S(-4)= 0
X
ƒ(-2) - D
ƒ(o) - D
S
?
Answers
The solutions of the function are:
When f(x) = -4, the solution is -4When f(x) = -2, the solution is -5/2When f(x) = 0, the solution is -1How to solve for the equationThe equation is given as
[tex]\frac{3}{4} x-1\\\\[/tex]
When x = -4
3/4 * -4 -1
= -12/4 - 1
= -4
When x = -2
3/4*(-4) - 1
= -6/4 - 1/1
Take the lcm
-10/4
= -5/2
When x = 0
3/4(0) - 1
= -1
When f(x) = -4, the solution is -4
When f(x) = -2, the solution is -5/2
When f(x) = 0, the solution is -1
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What does negative 3 over 5 > −2 indicate about the position of negative 3 over 5 and −2 on the number line?
A. negative 3 over 5 is located on the right of −2
B.negative 3 over 5 is located on the left of −2
C.negative 3 over 5 is located on the right of 0 and −2 is located on the left of 0 D.negative 3 over 5 is located on the left of 0 and −2 is located on the right of 0
Will mark Brainliest!
Answers
Answer: A. negative 3 over 5 is located on the right of −2
Step-by-step explanation:
On a number line, the greater numbers are to the right and the smaller numbers are to the left.
Math work math rr rrr
Answers
Answer:
The correct answer is infinite. The equation is always true.
Simplify the expression.
3.2a + 3.5b – 2.1a
Answers
Answer:
1.1a+3.5b
Step-by-step explanation:
A. 10
B. 11
C. 12
D. 13
Answers
Answer:
D. 13
Step-by-step explanation:
13 is the answer I guess I hope it will be the right answer
Minh is packing books into
boxes. The mass of one of the boxes is 20 kilograms. If the box
holds 10 books that each have the same mass, what is the mass of
each book in grams?
Answers
The mass of each book in grams if each box weighs 20 kilograms is 2000 grams
Mass of each box = 20 kilogramsTotal books in the box = 10 booksConverting kilograms to grams1 kilograms = 1000 grams
20 kilograms = 20,000 grams
Mass of each book in grams = 20,000 grams / 10
= 2000 grams
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Can someone explain me this please
Consider a space shuttle which has a mass of about 1.0 x 105 kg and circles the Earth at an altitude of about 200.0 km. Calculate the force of gravity that the space shuttle experiences
uhm i don't understand wut to put below the formula please make it clear thank you alot
Answers
Answer:
The force of gravity experienced by the shuttle would be 1.6675×10^N
Write the standard equation of the circle with center (-4,-4) and radius 6.8
Answers
Answer: [tex](x+4)^{2}+(y+4)^{2}=46.24[/tex]
Step-by-step explanation:
[tex](x+4)^{2}+(y+4)^{2}=6.8^{2} \\(x+4)^{2}+(y+4)^{2}=46.24[/tex]
Which ones are variable expenses? (Check all that apply)
1. loans
2. food bill
3. rent
4. electric bill
Answers
Answer:
food bill, electric bill
Step-by-step explanation:
Variable expenses change every money
Loan payments are usually fixed, the same every month
food bill - variable expense since you buy different food each month and they will cost different amounts
rent is a fixed expense
the electric bill is different every month because some months you use more electricity than others
Mitosis is a process of cell reproduction in which one cell divides into two identical cells. A bacterium called E. coli often causes serious food poisoning. It can reproduce itself in 15 min.
a) Starting with one bacterium, make a table with time in
1/4-h blocks and the corresponding number of E. coli
bacteria up to 2 h of bacteria growth.
b) About how long will it take before there are 10 000 bacteria?
Answers
Answer:
I'm just a kid
Step-by-step explanation:
plssss give me brainkest
Sasha is playing a game where she tosses a coin, then rolls a die. She wins if she gets heads on the coin and a 5 on the die. What is the probability she wins?
A) `1/3`,`P(H and 5) = P(H) - P(5) = 1/2-1/6=3/6-1/6=2/6` or `1/3`. That makes sense since tossing a coin and rolling a die are independent events.
B) `2/3`,`P(H and 5) = P(H) + P(5) = 1/2+1/6=3/6+1/6=4/6` or `2/3`.That makes sense since tossing a coin and rolling a die are independent events.
C) `1/12`. That makes sense since tossing a coin and rolling a die are independent events. `P(H and 5) = P(H) × P(5) = 1/2 × 1/6=1/12`
D) `12/12` or `1`. That makes sense, because she should win every time she plays.
Answers
Answer:
i hope the answer is clear to you
Step-by-step explanation:
i don’t know if I explained well but yeah here are the answers
Hope this helped!
7. A man leaves ⅓of his property to his son, two fifths to his wife and the remainder to his daughter. If the daughter received sh. 24,000, what was the total amount left?
Answers
Answer:
sh 90,000
Step-by-step explanation:
let x be the total amount left , then
x = [tex]\frac{1}{3}[/tex] x + [tex]\frac{2}{5}[/tex] x + 24,000
multiply through by 15 ( the LCM of 3 and 5 ) to clear the fractions
15x = 5x + 6x + 360,000
15x = 11x + 360,000 ( subtract 11x from both sides )
4x = 360,000 ( divide both sides by 4 )
x = 90,000
the total amount left was sh 90,000
Which expressions below equal a rational number? Choose all that apply. 4/5 + 3/8; sqrt(100) + sqrt(5); 7sqrt(5) - sqrt(245); (4sqrt(7))(2sqrt(7)); pi * sqrt(36)
Answers
Answer:
Step-by-step explanation:
Rational number[tex]1) \dfrac{4}{5}+\dfrac{3}{8}\\\\\dfrac{4}{5} \ \text{is a rational number} \ and \ \dfrac{3}{8} \ \text{is a rational number}\\\\\dfrac{4}{5}+\dfrac{3}{8} \ \text{is also a rational number}[/tex]
[tex]b) \sqrt{100}+\sqrt{5} = 10+\sqrt{5}\\\\\sqrt{5} \ \text{is a irrational number}. \\\\ \text{Rational number added to irrational number will result in an irrational number}\\\\10 + \sqrt{5} \ is \ not \ a \ rational \ number.[/tex]
c)
[tex]7\sqrt{5}-\sqrt{245}=7\sqrt{5}-\sqrt{7*7*5}[/tex]
[tex]= 7\sqrt{5}-7\sqrt{5}\\\\=0\\\\\text{\bf $ 7\sqrt{5}-\sqrt{245}$ ia a rational number}[/tex]
d)
[tex](4\sqrt{7})*(2\sqrt{7})=4*2*\sqrt{7*7}\\[/tex]
= 4*2*7
= 56
[tex]4\sqrt{7}*2\sqrt{7} \ \text{\bf is a rational number}[/tex]
A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 3 hours, while the outlet pipe can empty it in 10 hours. How long will it take to fill the vat if both pipes are left open?
Answers
The time it will take to fill the vat if both pipes are left open is = 4.3 hours
Calculation of time taken to fill vatThe number of pipes a vat has = 2
The time it takes the inlet pipe to fill the vat = 3hrs
The time it takes the outlet pipe to empty the vat= 10hrs
Therefore, the time it will take to fill the vat if both pipes are left open is;
1/t = 1/3-1/10
1/t = 7/30
Make t the subject of formula,
t = 30/7
t= 4.3 hours
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What does the expression n + 3 represent?
Answers
Answer:
Step-by-step explanation:
BASICALLY ANYTHING WITH 3
In which scenario can you reverse the dependent and independent variables while keeping the interpretation of the slope meaningful?
A.
As the amount of snowfall increases, the number of shovels sold increases.
B.
As number of hours spent watching TV increases, the amount spent on electricity increases.
C.
As the radius of a circle increases, circumference of the circle increases.
D.
As foot size increases, sock size increases.
Answers
Answer:
C. As the radius of a circle increases, circumference of the circle increases.
Draw and simplify the karnaugh maps of x,y,Z for (a)m0 +m1+ m5+m7. (b)F(1,3,5,4,7). (c)m0+m2+m4+m6. (d)F(0,2,4,6)
Answers
The simplified Karnaugh maps are F(A, B, C) = A’B’ + AC , F(A, B, C) = C + AB’, F(A, B, C) = C’.
What are Karnaugh Maps ?A Karnaugh map can be compared to a more advanced version of a truth table
In a K-map there are all the possible input variables and outcomes stored in cells.
It is a method to simplify and optimize Boolean expressions.
(a) m0 +m1+ m5+m7
Mapping the given function in a Karnaugh map,
The image is attached with the answer.
we can see two pairs
Pair-1 is m0 + m1
and Pair-2 is m5 + m7
= A’B’C’ + A’B’C + AB’C + ABC
= A’B’(C’ + C) + AC(B’ + B)
= A’B’ + AC
Therefore the simplified Boolean expression for the given data is
F(A, B, C) = A’B’ + AC.
(b) F(1,3,5,4,7)
On Mapping the given function in a Karnaugh map, we will see
1 Pair and 1 Quad
Pair is m4 + m5
Quad is m1 + m3 + m5 + m7
= A’B’C + A’BC + AB’C + ABC + AB’C’ + AB’C
= A’C(B’ + B) + AC(B’ + B) + AB’(C’ + C)
(B +B' ) = 1 , (C’ + C) = 1
= A’C + AC + AB’
= C(A’ + A) + AB’
= C + AB’
Therefore the simplified Boolean expression for the given data is
F(A, B, C) = C + AB’.
(c) m0+m2+m4+m6.
On Mapping the given function in a Karnaugh map, we will see
2 Pairs
Pair-1 is m0 + m4
Pair-2 is m2 + m6
= A’B’C’ + AB’C’ + A’BC’ + ABC’ = B’C’(A’ + A) + BC’(A’ + A)
= B’C’ + BC’
= C’(B’ + B)
= C’
Therefore the simplified Boolean expression for the given data is
F(A, B, C) = C’.
(d) (0,2,4,6)
It will have the same expression as that of Option (c)
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