Answers
The equation is solved to give 16z² - z - 4 = 0
How to determine the valueNote that algebraic expressions are defined as expressions that are composed of terms, variables, coefficients, constants and also factors.
The expressions are also identified with mathematical operations, such as;
BracketParenthesesAdditionSubtractionMultiplicationDivisionFrom the information given, we have that;
√z= -4z - 2
Find the square of both sides, we get;
z = 16z² - 4
collect the like terms
16z² - z - 4
Equate to zero
16z² - z - 4 = 0
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Related Questions
In school please help me
Answers
Answer:
Step-by-step explanation:
4992223553535
your in school ask a teacher
[Two home-improvement stores (Great Home and Super Home) in a growing urban area are interested in expanding their market share. Both are interested in expanding the size of their store and parking lot to accommodate potential growth in their customer base. Two possible actions for both the firms are: ‘increase the size of the store and parking lot’ and ‘do not increase the size of the store and parking lot’. Payoffs are defined in terms of increase in annual profits in $million. The following table describes the payoffs for both the firms to alternative actions taken by each of them. Note, Great Home’s payoffs are given first and Super Home’s payoff are given second.]
Super Home
Increase
Do not increase
Great Home Increase
($1.5 million, $1m) ($3.4m, $0.4m)
Do not increase
($0.6m $3.2m) ($2.5m, $2m)
“You can delete this table as well from your submitted file”.
a) [Let’s say, each store is pursuing its own best interest. What will be a rational (or dominant) strategy for Super Home to follow? Explain in 3-4 sentences. What will be a rational (or dominant) strategy for Great Home to follow? Explain in 3-4 sentences. (4 marks)]
b) [What will be the annual profit growth for each store, if they both follow their dominant strategy? Define Nash Equilibrium and identify the Nash Equilibrium in the table above. (4 marks)]
c) [Suppose the owners of Super Home and Great Home meet for a friendly game of golf one afternoon and happen to discuss a strategy to optimize profit. What should the joint strategy be they should both agree to? What will annual profit growth be for each store under this agreement? (2 marks)]
Answers
a) For Super Home, the superior (or dominant) tactic is to magnify the size of the store and parking lot. This is, regardless of what Great Home does, Super Home's payoff is amplified when it expands its size ($1m vs $0.4m if Great Home amplifies; $3.2m vs $2m if Great Home passes).
What is the best strategy for Great Home?Similarly, for Great Home, the logical (or dominant) strategy is also to expand the size of the store and parking lot. This is because, although unrelated to Super Home's decision, Great Home's payoff is augmented when it enlarges its size ($1.5m vs $0.6m if Super Home magnifies; $3.4m vs $2.5m if Super Home disallows).
b) If both stores implement their authoritative plan, Great Home will witness an annual profit growth of $1.5 million, and Super Home will observe an annual profit growth of $1 million.
A Nash Equilibrium comprehends a state wherein each player chooses their finest ploy given the stratagems selected by the other participant(s), and no player can modify their consequence through exclusively adapting their strategy. In this case, the Nash Equilibrium exists in (Increase, Increase), which spans over the payoffs ($1.5m, $1m).
c) The conjunctive approach both stores should commit to would be for Great Home to amplify the size of its store and parking lot, and Super Home to renounce increasing its size.
Under this harmonized approval, the annual profit growth for Great Home will come out at $3.4 million, and for Super Home, it will arrive at $0.4 million. This system gives rise to a higher collective gain compared to the Nash Equilibrium.
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For each relation, decide whether or not it is a function.
Answers
Answer:
relation 1-function
relation 2-not a function
relation 3-function
relation 4-funtion
A fair, 6-sided die is rolled 60 times. Predict how many times it will land on a number greater than 2. 60 40 20 two thirds
Answers
To predict how many times a number greater than 2 will be rolled in 60 rolls, we can use the following formula:
Number of times = Probability x Total number of rolls
So, using the probability of 2/3, we can calculate:
Number of times = 2/3 x 60
Number of times = 40
Therefore, we can predict that a number greater than 2 will be rolled approximately 40 times out of 60 rolls.
Q14 20 students take a maths test. Their tutor records the scores. The list below shows
their scores:
15, 24, 6, 8, 29, 6, 12, 17, 24, 22, 25, 30, 18, 3, 11, 7, 18, 27, 28, 27
Present these scores in three suitable groups
Answers
The scores of the maths students recorded by their tutor presented in three suitable groups are 1 - 10, 11 - 20, 21 - 30.
How to present scores in groups?Math test scores: 15, 24, 6, 8, 29, 6, 12, 17, 24, 22, 25, 30, 18, 3, 11, 7, 18, 27, 28, 27
The group of scores when divided into 3;
Group frequency
1 - 10 5
11 - 20 6
21 - 30 9
Therefore, the groups 1 - 10, 11 - 20, 21 - 30 have the frequency 5, 6 and 9 respectively.
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pleas
HELP IMMEDIATELY
Answers
Answer:
144ft^3
Step-by-step explanation:
To start, we have your formula: [tex]V=\frac{1}{2} (bh) (l)[/tex]
b = base length of the triangle.
h = height of the triangle.
l = length of the prism
Fill in for each of those values:
[tex]V = \frac{1}{2} (6x6)(8)[/tex]
[tex]V=\frac{1}{2} (36)(8)[/tex]
[tex]V=(18)(8)[/tex]
[tex]V=144[/tex]
Your answer, because it is a 3D shape, should be cubed, so:
[tex]V=144ft^{3}[/tex]
Help
Applying the Solution to a 3X3 System
At a family reunion, there only blood relatives, consisting of children, parents, and grandparents, in attendance. There were 400 people total. There were twice as many parents as grandparents, and 50 more children than parents. How many children, parents, and Grandparents were in attendance?
Show up all steps please
Answers
Solving the system of equations, the number of children, parents, and Grandparents who were in attendance are 190, 140 and 70 respectively.
Let C, P and G denotes the number of children, parents and the grandparents in the function.
We get the system of equations,
C + P + G = 400 [equation 1]
P = 2G ⇒ G = P/2 [equation 2]
C = P + 50 [equation 3]
Substituting 2 and 3 in 1,
(P + 50) + P + (P/2) = 400
2P + P/2 = 350
5/2 P = 350
P = 140
C = P + 50 = 140 + 50 = 190
G = P/2 = 140/2 = 70
Hence the number of parents = 140, grandparents = 70 and children = 190.
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On January 1, a company issued a $500,000, 10%, 8-year bond payable, and received proceeds of $487,000. Interest is payable each June 30 and December 31. The total interest expense on the bond over its eight-year life is $400,000. True or False?
Show working
Answers
True. The total interest expense on the bond over its eight-year life is $400,000.
What is the total interest?The total interest expense on the bond is calculated as follows;
Annual interest payment = face value of bond x annual interest rate
= $500,000 x 10%
= $50,000
Semi-annual interest payment = Annual interest payment / 2
= $50,000 / 2
= $25,000
The total interest expense over the bond's life is then calculated as:
Total interest expense = Semi-annual interest payment x Number of semi-annual periods
= $25,000 x 16
= $400,000
Therefore, the statement is true.
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PLEASE HELP. The steps to derive the quadratic formula are shown below:
Step 1 ax2 + bx + c = 0
Step 2 ax2 + bx = − c
Step 3
Provide the next step to derive the quadratic formula.
a times the quantity x squared plus b over a times x end quantity equals negative c
x(ax + b) = −c
x squared over a plus b over a times x equals negative c over a
x squared over a plus b over a equals negative c over a
Answers
Answer:
Step 3: Divide both sides of the equation in Step 2 by a to get x² + (b/a)x = -c/a.
Elijah wrote two numbers that follow the rules in box below. Both numbers are less than 10. Both numbers are whole numbers. The least common multiple of th numbers is 18. The greatest common factor of the number is 3.
Answers
Answer:
2,3,6 is answer for this question
The base of a box is 8 Square centimetres and its height is 10cm. Find its volume
Answers
Answer:
80 cm³
Step-by-step explanation:
Volume = w x l x h = width x length x height
You already know the area of the base: w x l = 8 cm², so the volume is:
V = 8 cm² x 10 cm = 80 cm³
Problem
Look at the image below.
Find the area of the parallelogram.
square units
Answers
The area of the parallelogram is A = 72 units²
Given data ,
Let the parallelogram be represented as ABCD
Now , the height of the parallelogram is = 12 units
The base of the parallelogram = 6 units
And , area of parallelogram A = base x height
On simplifying , we get
A = 12 x 6
A = 72 units²
Hence , the area is A = units²
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Identify a fraction that is greater. than five-eighths and less than thirteen-eighths. Write the fraction using three different forms.
Answers
One of the fractions is 7/8 and can be written as
decimal notation of 0.875, percent representation at 87.5%, and fraction form = 7/8 How to find the fractionInformation made available in the question includes
a fraction that is greater. than five-eighths and less than thirteen-eighthsMathematically this is written as
assuming the number is x
five-eighth = 5/8thirteen-eighths = 13/85/5 < x < 13/8
For fractions greater than five eighths but lesser than thirteen eighths is seven eighths (7/8) within the two.
This fraction can be expressed in three unique forms which include:
decimal notation of 0.875,
percent representation at 87.5%, and
fraction form = 7/8
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Trigonometry. Can someone help? (Do as many as you can please)
Answers
Answer:
1) Let x be the distance from Alberto to the base of the building. Using trigonometry, we have:
tan(70) = 40 / (x + 6)
x + 6 = 40 / tan(70)
x = 40 / tan(70) - 6
x ≈ 11.1 feet
Therefore, Alberto is about 11.1 feet away from the base of the building.
2) Let h be the height of the building. Using trigonometry, we have:
tan(θ) = h / (100 + 1.55)
h = (100 + 1.55) tan(23)
h ≈ 42.9 feet
Therefore, the height of the building is about 42.9 feet.
3) Let θ be the angle of elevation for each ramp. Using trigonometry, we have:
sin(θ) = 22 / 122
θ = sin⁻¹(22/122)
θ ≈ 10.3 degrees
Therefore, the measure of the angle of elevation for each ramp is about 10.3 degrees.
4) Let d be the distance from the boat to the base of the lighthouse. Using trigonometry, we have:
tan(28) = 40 / d
d = 40 / tan(28)
d ≈ 78.5 feet
Therefore, the distance from the base of the lighthouse to the boat is about 78.5 feet.
5) Let x be the distance from General Han Xin's position to the palace. Using trigonometry, we have:
tan(35) = x / 800
x = 800 tan(35)
x ≈ 595.4 meters
Therefore, the palace is about 595.4 meters away from General Han Xin's position.
6) Let h be the height of the clouds. Using trigonometry, we have:
tan(80) = h / 165
h = 165 tan(80)
h ≈ 702.4 meters
Therefore, the clouds are about 702.4 meters high.
Step-by-step explanation:
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 15(0.94)
Answers
The exponential function in this problem represents a decay, with a percentage rate of 6%.
How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The function is classified as growth or decay as follows:
Growth: |b| > 1.Decay: |b| < 1.The function in this problem is defined as follows:
y = 15(0.94)^x.
As |b| = 0.94 < 1, the function is a decay function, and the rate is obtained as follows:
1 - r = 0.94
r = 1 - 0.94
r = 0.06
r = 6%.
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I seQuestion 10nd you a picture in few minutes
Answers
8.) The inequality that describes the possible number of calories X, you can eat during the rest of the day would be < 1200. That is option A.
9.) The value of X would be = 3.
How to determine the quantity of calories you will eat for the day?For question 8.)
The quantity of calories for each day < 2200. That is;
1 day < 2200
The calories consumed for breakfast = 350
The calories consumed for lunch = 650
The total calories consumed = 350+650 = 1000 calories.
The amount of calories needed to be consumed the more = 2200-1000 = 1200
Therefore the quantity of calories needed more < 1200 calories.
For question 9.)
t(X) = 3x - 5
where;
t(X) = 4
That is;
4 = 3x - 5
3x=4+5
3x = 9
X = 9/3 = 3
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please i need
thank you so much
Answers
Step-by-step explanation:
Similar triangle ratio:
15 is to 10 as AB is to 6
15/10 = AB / 6
6 * 15/10 = AB = 9 units
The data shows the weight of the potting soil brought by each student. Draw a line plot and answer the questions below. 1 1/2 kg 3/4 kg 1 1/2 kg Title: 1 kg 1 1/2 kg 2 kg 3/4 kg 2 kg 3/4 kg Roading and Math for K-5 2 kg 2 kg 2 kg 2 1/2 kg 3/4 kg 1 kg 1. How many students brought 3/4 kg of soil? 2. How many students brought less than 1 1/2 kg? 3. How many students brought 1 kg or more? 4. How many fewer students brought 1 kg than 2 kg? 5. How many students brought more than 1 1/2 kg but less than 2 1/2 kg? 6. How much soil was brought by all the students together?
Answers
Answer:
|
| 3/4 kg
| x
|
| x
| x
| x
| x
| x
| x
|_________
1 kg 1 1/2 kg 2 kg 2 1/2 kg
Two students brought 3/4 kg of soil.
Four students brought less than 1 1/2 kg of soil (the ones who brought 3/4 kg and the one who brought 1 kg).
Eight students brought 1 kg or more of soil.
Two fewer students brought 1 kg than 2 kg (two students brought 1 kg and four students brought 2 kg).
Two students brought more than 1 1/2 kg but less than 2 1/2 kg (the ones who brought 2 kg).
The total amount of soil brought by all the students is:
Copy code
1 1/2 kg + 3/4 kg + 1 1/2 kg + 1 kg + 2 kg + 3/4 kg + 2 kg + 2 kg + 2 kg + 2 1/2 kg + 3/4 kg
= 19 3/4 kg
Step-by-step explanation:
Answer:
Step-by-step explanation:
it is timed by 1 1/2kg
The equation y = 2x2 – 4x – 3 models the cross-section of a sculpture that sits in the water, where x is horizontal distance, and y is height above sea level. At what two x-values is the sculpture at sea-level?
Answers
The two x-values where the sculpture at sea-level are x = 2.581 and x = -0.581
At what two x-values is the sculpture at sea-level?From the question, we have the following parameters that can be used in our computation:
y = 2x^2 - 4x - 3
When the sculpture at sea-level, the value of y is 0
So, we have
2x^2 - 4x - 3 = 0
When solved graphically, we have
x = 2.581 and x = -0.581
Hence, the x values are x = 2.581 and x = -0.581
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Need answer ASAP please!
What is the total perimeter
Answers
Answer:
12 + 3 + 12 + (1/2)π(3) = 27 + (3/2)π ft
= 31.71 ft
can someone help me with number 1 through 4
Answers
1. 13 cm
2. 27.2 in
3.24x
4. 7 m
radius is half of the diameter
diameter is twice of the radius so
radius=diameter/2,diameter =2x radius
In a football tournament, each team plays exactly 19 games. Teams get 3 points for every win and 1 point for every tie. At the end ot the tournament, Team Olympus got a total of 28 points. From the following options, how many times could Team Olympus have tied? 3, 4, 2, 5, 0?
Answers
The number of times the Team Olympus could have tied is not given in the below options
Given data ,
Let's use "W" for the number of victories and "T" for the number of ties. The information available indicates that Team Olympus played 19 games and earned a total of 28 points.
Team Olympus receives three points for each victory, so three victories would result in a total of nine points.
Team Olympus receives one point for each tie, making the sum of the tie-related points (T) equal to one times the number of ties.
We may construct the following equation using the information provided:
3W + 1T = 28 be equation (1)
Now , Since Team Olympus played 19 games in total, the total number of games (W + T) should be equal to 19.
W + T = 19 be equation (2)
Subtracting equation (2) from equation (1) , we get
2W = 9
Divide by 2 on both sides , we get
W = 4.5 wins
And , the supplied possibilities (3, 4, 2, 5, 0) do not add up to a total of 28 points, hence none of them are acceptable answers for Team Olympus.
Hence , in this situation, Team Olympus could not have tied many times
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A bag of apples weighs 8 7 8 pounds. A crate of bananas is 6 times as heavy as the apples. How much heavier are the bananas than the apples?
Answers
The crate of bananas is heavier than the bag of apples by 53 1/4 pounds.
How much heavier are the bananas than the apples?An apple and a banana are both kinds of fruits. They both weigh differently.
Weight of a bag of apple = 8 7/8 pounds
Weight of a crate of bananas = 6 times as heavy as the apples
= 6 × 8 7/8
= 6 × 71 /8
= 426 / 8
= 53 1/4 pounds
Therefore, the weight of a crate of bananas is 53 1/4 pounds
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Need help with these math problems , I know #2 is on the arrow looking on is original is A = 36 units^2 and scale drawing is A = 9 units^2, just don’t know how I got it.
Answers
The areas of the figures are 36 square units & 9 square units and the scale factor of dilation is 1/2
Estimating the areas of the figuresFrom the question, we have the following parameters that can be used in our computation:
The composite figures
The areas of the figure is calculated using the sum of the individual areas
So, we have
Figure 1 = Rectangle + Triangle
Using the area formulas, we have
Figure 1 = 5 * 4 + 1/2 * 8 * 4
Evaluate
Figure 1 = 36
The second figure is not clear
However, from the question text we have the area to be
Figure 2 = 9
So, the scale factor from figure 1 to 2 is
Scale factor = √[Figure 2/Figure 1]
This gives
Scale factor = √[9/36]
Evaluate
Scale factor = 1/2
Hence, the scale factor is 1/2
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Express each of the following as a function or 15°:
1. sin195°
2. cos75°
3. tan345°
4. sin105°
5. sin225°
Answers
You can express sin195° as -sin15° by using the trig identities.
Here is how to simplify trigWe will be applying trig identities to solve this question
sin195°:
Recall that:
sin(x + 180°) = -sin(x)
then:
sin(195°) = sin(15° + 180°) = -sin(15°)
Therefore,
sin(195°) = -sin(15°).
cos75°:
Recall that:
cos(x) = sin(90° - x)
then:
cos(75°) = sin(90° - 75°) = sin(15°)
Therefore,
cos(75°) = sin(15°)
tan345°:
Recall that:
tan(x + 180°) = tan(x)
then:
tan(345°) = tan(15° + 330°) = tan(15°)
Therefore,
tan(345°) = tan(15°)
sin105°:
Recall that:
sin(x + 90°) = cos(x)
then:
sin(105°) = cos(15°)
Therefore,
sin(105°) = cos(15°).
sin225°:
Recall that:
sin(x + 180°) = -sin(x)
then:
sin(225°) = sin(45° + 180°) = -sin(45°)
Therefore,
sin(195°) = -sin(15°).
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Dmitry Mendeleyev and his wife obtained a 30-year, $210,000 mortgage loan from
Community Bank. The interest rate is 6.5%. Their monthly payment is $1,362.06. For the first payment, what is the amount of the interest, payment to principal, and new principal?
Answers
The amount of the interest, payment to principal, and new principal for the first payment is solved
Given data ,
Let the loan amount = $ 210,000
Let the interest rate r = 6.5 %
Let the monthly payment be = $ 1,362.06
Now , On calculating the monthly interest rate
Monthly interest rate = 0.065 / 12 = 0.00542 or 0.542%
Calculate the interest amount
Interest amount = 0.00542 x $210,000 = $1,138.20
Calculate the payment to principal
Payment to principal = $1,362.06 - $1,138.20 = $223.86
Calculate the new principal balance
New principal balance = $210,000 - $223.86 = $209,776.14
Hence , for the first payment, the amount of interest is $1,138.20, the payment to principal is $223.86, and the new principal balance is $209,776.14
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If the area of triangle abc is 21 square units, find sinA if b=14 and c=9
Answers
Applying the formula for the area of triangle using sine, we have:
sin A = 1/3 (A ≈ 19.5°).
How to Find the Area of a Triangle Using Sine Rule?Given that a triangle has the following parameters:
Area of triangle ABC = 21 square units
Side b = 14 units
Side c = 9 units
Thus, applying the area of a triangle using the sine rule, we have the following formula:
Area = 1/2 * b * c * sin A
Plug in the values:
21 = 1/2 * 14 * 9 * sin A
2 * 21 = 126 * sin A
42 = 126 * sin A
42/126 = sin A
sin A = 1/3
A = sin^(-1)(1/3)
A ≈ 19.5°
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HELP ME PLEASE ITS DUE TODAY!!! The following data shows the number of times a class of 7th graders ate breakfast over a 30-day period.
{4, 18, 22, 25, 15, 12, 22, 14, 19, 30, 24, 20, 21, 24, 29, 16, 20, 27, 24, 25}
Part A: Determine the best graphical representation to display the data. Explain why the type of graph you chose is an appropriate display for the data. (2 points)
Part B: Explain, in words, how to create the graphical display you chose in Part A. Be sure to include a title, axis label(s), scale for axis if needed, and a clear process of how to graph the data. (2 points)
Answers
The best graphical representation to display the data would be a Histogram. This is appropriate because it will display the distribution and frequency of the grades, thus making it easy to compare the classes. To create the graph, you will use bars to depict the range of figures. This is on the x-axis while the y-axis will contain the frequency of occurrence.
How to design a histogramDesigning a histogram requires an understanding of the range of values, the frequency of occurrence, and the general picture that the graph is meant to paint in the mind of the reader.
So, for the histogram above, you can have a title like The distribution of 7th graders' breakfast over a 30-day period. Next, you label the x and y axis and plot the figures based on the information provided.
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Graph the system below and write its solution.
x+3y=-6
Note that you can also answer "No solution" or "Infinitely many" solutions.
Solution:
0
solution
Answers
The number of solutions of the system of equations in this problem is given as follows:
Infinitely many solutions.
How to obtain the solution of the system of equations?The system of equations for this problem is defined as follows:
x + 3y = -6.y = -x/3 - 2.Writing the second equation in standard format like the second, we have that:
x/3 + y = -2.
Multiplying by 3:
x + 3y = -6.
The two equations are equal, meaning that the system has an infinite number of solutions, and the two equations are the same on the graph.
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The height of an arch x meters to the right of the center is 1/10(x^2-36). What is the height of 3 meters to the left of the center when x=-3
Answers
The height of 3 meter to the left of the center of arch is -2.7 meters which is found by the evaluation of the given equation when x = -3.
We can solve it through
The Height at x = -3 meters on the left of the center = [tex](1/10)(-3^2 - 36) [by Substituting x = -3]= (1/10)(9 - 36)= (1/10)(-27)= -2.7 meters[/tex]
At the end height of the arch at 3 meters to the left of the center when x = -3 is -2.7 meters. This negative value means the point is actually below the ground level at that position. So the height is -2.7 meters where - insists negative value.
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