Setting up a system of equation, the number of small boxes shipped is 13 and large box shipped is 6
System of EquationSystem of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.
Let;
x = small boxy = large boxWe can represent this using equations;
35x + 60y = 815 ...eq(i)
x = 7 + y ... eq(ii)
Solving equation (i) and (ii)
x = 13, y = 6
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Let y = tan(3x + 8). Find the differential dy when x = 4 and dx = 0.1 cbc homepage Find the differential dy when x = 4 and dx = 0.2
The value of differential dy when x = 4 and dx = 0.2 is 0.68 .
In the question ,
it is given that ,
the equation is y = tan(3x + 8) ,
we need to find the differential dy , when x = 4 and dx = 0.2
So , differentiating y = tan(3x + 8) with respect to "x" ,
we get
dy/dx = sec²(3x + 8) *3
dy/dx = 3*sec²(3x + 8)
Substituting the values of x = 4 and dx = 0.2 ,
we get ,
dy/(0.2) = 3*sec²(3(4) + 8)
dy/0.2 = 3*sec²(20)
dy/0.2 = 3*1.1324
dy/0.2 = 3.3972
dy = 0.2 * 3.3972
dy = 0.67944
dy ≈ 0.68
Therefore , The value of differential dy when x = 4 and dx = 0.2 is 0.68 .
The given question is incomplete , the complete question is
Let y = tan(3x + 8). Find the differential dy when x = 4 and dx = 0.2 ?
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A line goes through the points (−8,−5) and (−10,−6). Find its slope. Enter your answer as a simplified improper fraction, if necessary. Do not include "m=" in your answer.
Answer:
4/3 i think
Step-by-step explanation:
C Apply Your Knowledge (See Ex. 7)
10 A factory produces lemon-scented widgets. Each widget is
cheaper, the more that are produced, but costs will go up if
too many widgets are produced, due to storage requirements.
The accountant for the factory says that the costs for
producing x thousands of units a day can be approximated by
the formula C = 0.04x² -8.504x + 25302. Find the daily
production level that will minimize the costs. Be sure to
show your work and include units of measurement.
The daily production level that will minimize the costs is 106300 units.
Given,
In the question:
The accountant for the factory says that the costs for producing x thousands of units a day can be approximated by the formula
C = 0.04x² -8.504x + 25302.
To find the daily production level that will minimize the costs.
Now, According to the question:
From the information, the function is given as
C = 0.04x² - 8.504x + 25302.
C = cost
From the function, the following can be deduced:
a = 0.04
b = 8.504
c = 25302
Then, -b/(2a) will be:
= -8.504 / (2 × 0.04)
= 106.300
Note that production level will minimize the cost in thousands.
The production level will now be:
= 106.300 × 1000
= 106300 units
Hence, The daily production level that will minimize the costs is 106300 units.
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Use matrices A and B. compute B-a, if you can. A=[-5 4 -8 -2] B=[-2 7 -3 1 -6 0]
The subtraction of matrices B and A cannot be computed, as the matrices have different dimensions, hence we cannot calculate the matrix B - A.
How to subtract matrices?Matrices are subtracted subtracting the terms at the same position in each matrix.
Hence, two matrices can only be subtracted if they have the same dimensions.
Matrix A in this problem is defined as follows:
A = [-5 4]
[-8 -2]
Hence it's dimensions are 2 x 2, as it has 2 rows and 2 columns.
Matrix B in this problem is defined as follows:
B = [-2 7 -3]
[1 -6 0]
Hence it's dimensions are 2 x 3, as it has 2 rows and 3 columns.
The matrices A and B have different dimensions, a different number of columns in this case, and hence their subtraction cannot be computed.
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A producer wishes to determine the equilibrium price and quantity of his good in the market. He estimated the market demand and supply function as follows demand :P=q^2+13/2q+64 and supply: P= 10q^2-45/2q-164
The equilibium price is 163.39 and the supply quantity is 150
He estimated the market demand and supply function as follows demand :P=q²+13/2q+64 and supply: P= 10q²-45/2q-164
We need to find the equilibium price
The equilibrium price (EP) is the price where the demand for a product or service balances its supply. .
At equilibium price
Demand function = supply function
q²+13/2q+64 = 10q²-45/2q-164
(10 - 1)q² - (45/2 + 13/2)q - (164 + 64) = 0
9q² - 29q - 228
q = 6.895 = 6.9
The equilibium price = 6.9² + (13/2)6.9 + 64
= 163.36
similarly putting the value of q in supply function we get supply quantity ie 149.95 = 150
Therefore, the equilibium price is 163.39 and the supply quantity is 149.95 = 150
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find m help pls worth alot of points :)
Answer:
m∠C = 50 degrees
Step-by-step explanation:
∠CAQ is a straight angle (180) so ∠CAB is supplementary to ∠QAB
∠CAQ = ∠QAB + ∠CAB
180 = 110 + ∠CAB
180 - 110 = ∠CAB
70 = ∠CAB
The total angle measurement in all triangles is 180 degrees, knowing this, we can set up the equation:
180 = ∠CBA + ∠BCA + ∠CAB
180 = 2 + 29x + 24x + 2 + 70
180 = 74 + 53x
180 - 74 = 53x
106 = 53x
2 = x
Knowing x = 2, we can solve for m∠C
24(2) + 2 = ∠C
48 + 2 = ∠C
50 = ∠C
Use the Distributive property to express 18+24
The distributive property allows the expression 18 + 24 to be expressed as 6(3 + 4).
What is a distributive property?Most algebraic structures that include two operations, addition and multiplication, such as complex numbers, polynomials, matrices, rings, and fields, are defined in terms of this fundamental feature of numbers. The distributive property of binary operations generalizes the equality-proclaiming distributive law in mathematics. One of the axioms for rings and fields is that of the distributive laws. Boolean algebras like the algebra of sets or the switching algebra are examples of structures with two operations that are each distributive over the other.
We do the following to express using the distributive property:
Find the biggest common factor between the numbers 18 and 24.
18 = 1, 2, 3, 6, 9, 18
24 = 1, 2, 3, 4, 6, 8, 12, 24
6 is the most common value between the numbers 18 and 24, making it the most common factor
The values should be divided by 6 and expressed in the form a(b + c):
b = 18 /6 = 3
c = 24 / 6 = 4
6(3 + 4)
Consequently, the necessary expression is 6(3 + 4).
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Assuming the assumptions of Analysis of Variance are satisfied, a higher F value means... (select all that apply)
a.
...a greater chance of rejecting the null hypothesis.
b.
...higher between-group variability relative to within-group variability.
c.
...a higher p value.
The higher F value means higher between-group variability relative to within-group variability. Option(b) is correct.
Analysis of variance (ANOVA) is a statistical formula used to compare variances between means (or averages) of different groups. It is used in a variety of scenarios to determine whether there is any difference in the means of different groups.
The F-value is the ratio of between-group and within-group variation. A high F-value indicates that the between-group variation is greater than the within-group variation. This can be interpreted as a statistically significant difference in the means of your groups.
A large f value (one greater than the F critical value found in a table) indicates that something is significant, whereas a small p-value indicates that all of your results are significant.
Therefore a higher F value the higher between-group variability relative to within-group variability.
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Crane Company owns equipment that cost $78,000 when purchased on
January 1, 2019. It has been depreciated using the straight-line method
based on an estimated salvage value of $18,000 and an estimated useful lifeof 5 years.
Prepare Crane Company's journal entries to record the sale of the
equipment in these four independent situations. (Credit account titles areautomatically indented when amount is entered. Do not indent
manually. If no entry is required, select "No Entry" for the account
titles and enter O for the amounts.)
(a.) Sold for $44,000 on January 1, 2022.
(b.) Sold for $44,000 on May 1, 2022.
(c.) Sold for $20,000 on January 1, 2022.
(d.) Sold for $20.000 on October 1. 2022.
The journal entries to record the sale of the equipment by Crane Company are as follows:
a) Sold for $44,000 on January 1, 2022:
Debit Cash $44,000
Credit Sales of Equipment $44,000
Debit Sale of Equipment $78,000
Credit Equipment $78,000
Debit Accumulated Depreciation $36,000
Credit Sale of Equipment $36,000
Debit Sale of Equipment $2,000
Credit Profit from Sale of Equipment $2,000
b) Sold for $44,000 on May 1, 2022:
Debit Cash $44,000
Credit Sales of Equipment $44,000
Debit Sale of Equipment $78,000
Credit Equipment $78,000
Debit Accumulated Depreciation $40,000
Credit Sale of Equipment $40,000
Debit Sale of Equipment $6,000
Credit Profit from Sale of Equipment $6,000
c) Sold for $20,000 on January 1, 2022:
Debit Cash $20,000
Credit Sales of Equipment $20,000
Debit Sale of Equipment $78,000
Credit Equipment $78,000
Debit Accumulated Depreciation $36,000
Credit Sale of Equipment $36,000
Debit Loss from Sale of Equipment $22,000
Credit Sale of Equipment $22,000
d) Sold for $20.000 on October 1. 2022:
Debit Cash $20,000
Credit Sales of Equipment $20,000
Debit Sale of Equipment $78,000
Credit Equipment $78,000
Debit Accumulated Depreciation $45,000
Credit Sale of Equipment $45,000
Debit Loss from Sale of Equipment $13,000
Credit Sale of Equipment $13,000
Cost of equipment = $78,000
Salvage value = $18,000
Depreciable amount = $60,000 ($78,000 - $18,000)
Purchase date = January 1, 2019
Estimated useful life = 5 years
Annual depreciation expense = $12,000 ($60,000/5)
Sales Situations:a) Accumulated Depreciation to January 1, 2022 = $36,000 ($12,000 x 3)
Book value of equipment = $42,000 ($78,000 - $36,000)
Transaction Analysis:Cash $44,000 Sales of Equipment $44,000
Sale of Equipment $78,000 Equipment $78,000
Accumulated Depreciation $36,000 Sale of Equipment $36,000
Sale of Equipment $2,000 Profit from Sale of Equipment $2,000
b) Accumulated Depreciation to May 1, 2022 = $40,000 ($12,000 x 3.333)
Book value of equipment = $38,000 ($78,000 - $40,000)
Transaction Analysis:Cash $44,000 Sales of Equipment $44,000
Sale of Equipment $78,000 Equipment $78,000
Accumulated Depreciation $40,000 Sale of Equipment $40,000
Sale of Equipment $6,000 Profit from Sale of Equipment $6,000
c) Accumulated Depreciation to January 1, 2022 = $36,000 ($12,000 x 3)
Book value of equipment = $42,000 ($78,000 - $36,000)
Transaction Analysis:Cash $20,000 Sales of Equipment $20,000
Sale of Equipment $78,000 Equipment $78,000
Accumulated Depreciation $36,000 Sale of Equipment $36,000
Loss from Sale of Equipment $22,000 Sale of Equipment $22,000
d) Accumulated Depreciation to January 1, 2022 = $45,000 ($12,000 x 3.75)
Book value of equipment = $33,000 ($78,000 - $45,000)
Transaction Analysis:Cash $20,000 Sales of Equipment $20,000
Sale of Equipment $78,000 Equipment $78,000
Accumulated Depreciation $45,000 Sale of Equipment $45,000
Loss from Sale of Equipment $13,000 Sale of Equipment $13,000
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Pleaseeee help me. I'm stuck on a math question.
The slope of the function for pronghorn antelope is 60.78 which infers that the rate of speed of the pronghorn is 60.78 miles per hour.
7) The given function that represents the speed of the pronghorn is
y = 60.78x - 5.4
Comparing this function with the general equation of a straight line
y = mx + c we can conclude that the slope of the function is 60.78 .
So the Pronghorn's rate of speed is 60.78 miles per hour.
8) Now the speed of the cheetah is given in the form of a table.
Let us take any two points on the graph
(0.5,21.85) and (2,118.60)
Slope of the line passing through these two points
= (118.6-21.85)/(2-0.5)
=64.5
So the slope of the graph is 64.5 and the average rate of speed of the Cheetah is 64.5 miles per hour.
9) From the above two slopes and the rate of speed we can conclude that the speed of the cheetah is 64.5 mph which is greater than that of the pronghorn 's speed of 60.78 miles per hour.
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A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.M. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 8.8 gallons. What is the average rate of flow of the gasoline into the gas tank?
The average rate of flow of gasoline into the gas tank is 2.2 gallons per minute.
What is the average?The average is the mean value of the data set values.
The mean is computed by dividing the total value by the number of items.
For the average rate of flow, divide the total gallons of gasoline filled by the driver, 8.8 gallons, by the number of minutes used in filling the tank.
In this case, the average rate of flow shows the speed that the driver used to fill the car with gasoline.
Starting time = 3:40 P.M.
Ending time = 3:44 P.M.
The difference in filling time = 4 minutes (3:44 - 3:40)
Total number of gallons of gasoline filled = 8.8 gallons
Average rate of flow of the gasoline = 2.2 gallons per minute (8.8/4)
Thus, at an average rate of 2.2 gallons per minute, the driver was able to fill his gas tank in 4 minutes.
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A city administrator with a $100,000 annual budget is trying to decide between fixing potholes or directing traffic at several busy intersections after school. Studies have shown that 15 cars hit potholes every week, causing average damages of $200. Collisions at the intersections are less frequent, averaging one per month at an average cost of $6,000, although none have ever caused injuries or deaths. Use this information to answer the following questions.
1. What are the annual costs from the pothole damage?
2. What are the annual costs due to damage from
collisions?
3. Given the size of the annual budget, make your
recommendation as to which project should be
undertaken. Explain you answer in terms of dollar
benefits per dollar spent.
1. The annual costs from the pothole damage is $156428.
2. The annual costs due to damage from
collisions is $72000 per year.
3. The project should be undertaken
How to calculate the value?1. The budget is given as $100,000
The number of cars hit potholes per week = 15
Number of cars hit potholes per year = 15*52.148
= 782.14 cars
Total amount of damage per year will be:
= 782.14 * 200 = $156428
2. Number of collusion at intersection per month = 1
Number of collusion at intersection per year = 1 * 12 = 12
Total cost of collusion at intersection per year = 12*6000
= $72000 per year
3. Saving on potholes = 156248 / 100000 = $ 1.56
Saving on collusion at intersection:
= 72000 / 100000
= $0.72
So from above, it is clear that if the budget is spent on potholes, more savings will be done. Thus the budget should be invested in potholes.
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What is the best search engine for Musical Instrument and Sound Effects in MP3 Audio Online?
The best search engine for Musical Instrument and Sound Effects in MP3 Audio Online is MP3 realm.
What is MP3?MP3 is a digital audio coding format developed primarily by the Fraunhofer Society in Germany, with assistance from other digital scientists in the United States and elsewhere.
MP3 (MPEG-1 Audio Layer-3) is a standard technology and format for compressing a sound sequence into a small file (about one-twelfth the size of the original file) while maintaining the original level of sound quality when played. MP3 files, which take up very little hard drive space, are commonly used to store a song or an entire CD.
MP3 Realm is a music search engine that allows you to find MP3 tracks from all over the Internet.
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NO LINKS!! Use the diagram below to answer the following questions Part 5
Answer:
1a. BF, CG, DH.
1b. (1) ABF and DCG.
(2) ADH and BCG.
1c. AD, AE, BC, BF, CE, DF.
2a. OP.
2b. JO, KP, LQ, MR.
2c. OPQ.
2d. JK, JN, KL, MN.
Step-by-step explanation:
A prism is a polyhedron that has:
Two bases that are congruent and parallel to each other.Lateral sides that are parallelograms and link the two bases.Height that is the distance between the two bases.Lines
Parallel lines are lines on a plane that never meet and are the same distance apart.Intersecting lines cross each other in a plane and share a common point called the point of intersection.Skew lines are a pair of non-coplanar lines that do not intersect, and are not parallel to each other.Planes
A plane is a flat, two-dimensional surface that extends into infinity.
A plane can be named by the letters naming three non-collinear points in the plane.
Parallel planes are planes that never intersect. Intersecting planes are not parallel and always intersect along a line. Question 1From inspection of the give diagram, the figure appears to be a rectangular prism with bases ABCD and EFGH.
1a. All segments that are parallel to AE are:
BF, CG and DH.1b. Two examples of parallel planes:
(1) ABC and EFG.(2) ADH and BCG.1c. All segments that are skew to GH:
AD, AE, BC, BF, CE and DF.Question 2From inspection of the give diagram, the figure appears to be a pentagonal prism with bases JKLMN and OPQRS.
2a. All segments that are parallel to JK:
OP.2b. All segments that are parallel to NS:
JO, KP, LQ and MR.2c. A plane that is parallel to plane JKL:
OPQ.2d. Four segments that are skew to RQ:
JK, JN, KL and MN.Complete the statements below with the process used to achieve steps 1-4. Select the correct answer from each drop-down menu. Consider the equation below. -2(5x+8)=14+6x The equation was solved using the following steps.
The complete statements for solving the equation in the steps are:
1. Distribute -2 to 5x and 8
2. Subtract both sides by 6x
3. Add both sides by 16
4. Divide both sides by -16
How to Solve an Equation?Solving an equation involves finding the value of the variable in the equation that would make the it true. This is done by isolating the variable to one side of the expression to determine its value.
Given the equation, -2(5x + 8) = 14 + 6x, the following steps are taken to find the value of x in the expression:
Step 1: Distribute -2 to 5x and 8
10x + 16 = 14 + 6x
Step 2: Subtract both sides by 6x
-16x + 16 = 14
Step 3: Add both sides by 16
-16x = 30
Step 4: Divide both sides by -16
x = 30/-16
Simplify
x = -15/8
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$
Amount Due at Maturity
6,000.00
Discount Rate
3.50%
1. Calculate the bank discount:
2. Calculate the proceeds:
Time
160
Ordinary Interest
360
Required:
Using the information above please answer the following:
Note: Use cells A2 to D3 from the given information to complete this question.
The bank discount is $93.33 and the proceeds are $5,906.67.
What is the discount?
Discount causes the product's selling price to drop, which increases its allure for the consumer. A price reduction has a psychological effect on the buyer, influencing them to make the purchase. The two types of discounts offered are trade discounts and cash discounts.
We have,
Amount Due at Maturity = $6,000
Discount rate = 3.5%
Time = 160 days
Bank Discount = $6,000*3.5%*160/360=$93.33
Proceeds = Maturity value - Bank Discount
= $6,000 - $93.33
= $5,906.67
Therefore, the bank discount is $93.33 and the proceeds are $5,906.67.
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29. According to the weather reports, the probability of rain on a certain day is
70% in Yellow Falls and 50% in Copper Creek. What is the probability that it
will rain in both cities? State if Dependent or Independent
The probability that it will rain in both cities is 0.35. It is independent.
What is probability?Probability is the likelihood that a particular event will occur.
In this case, the probability of rain on a certain day is 70% in Yellow Falls and 50% in Copper Creek.
The probability that it will rain will be:
= P(Yellow Falls) × P(Copper Creek)
= 0.7 × 0.5
= 0.35
This is independent.
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Nakeisha is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Nakeisha will earn $30 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Nakeisha's songs were played on 2 more commercials than movies, and her total earnings on the royalties from all commercials and movies was $760. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Nakeisha's songs were played. Define the variables that you use to write the system. Please help this is due tonight!!!
Solving a system of equations we will see that the song was used on 5 movies and 7 commercials
How to determine the numbers of commercials and movies?The variables we will use are:
x = number of commercial.y = number of movies.We know that:
x = y + 2
and:
x*$30 + y*$110 = $760
So the system of equations is:
x = y + 2
x*$30 + y*$110 = $760
Replacing the first equation in the second one:
(y + 2)*$30 + y*$110 = $760
$60 + y*$30 + y*$110 = $760
y*$140 = $760 - $60
y*$140 = $700
y = $700/$140 = 5
Then the value of x is:
x = y + 2 = 5 + 2 = 7
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h(x) = -4x + 2 x+7 3x - 5 x < -5 −5 < x < 5 x>5 Given the piecewise function shown, find the value of h(-6).
Answer:
answer in image
Step-by-step explanation:
determine if each ordered pair is a solution to the given system of linear inequalities in two variables.
Answer:
A. yes, B. yes,C. yes
Step-by-step explanation:
A. (3,0) yes
b. (4,-2) yes
c. (5,-4)yes
Find the area of the shaded region in the figure below, if the diameter of the circle is 12 and the height of the rectangle is 11. Use 3.14 for pi and round to the nearest hundredth.
The area of the shaded region is 75.48 rounded to the nearest hundredth, considering the areas of the circle and rectangle
How to calculate for the area of the shaded regionWe have to first calculate for the area of the rectangle, and then calculate for the area of half the circle and then subtract it from the area of the rectangle to get the area of the shaded region.
Area of rectangle = Length × breadth
Area of rectangle = 12 × 11(diameter of the circle is also the length of the rectangle)
Area of rectangle = 132.
Area of circle = πr²
Area of the circle = 3.14 × 6² (6 is the radius given that the diameter = 12)
Area of the circle = 3.14 × 36
Area of the circle = 113.04
Half the area of the circle = 113.04/2
Half the area of the circle = 56.52
Area of the shaded region = 132 - 56.52
Area of the shaded region = 75.48
Therefore, by calculating for areas of the circle and rectangle, we are able to derive the area of the shaded region to be 75.48
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Catherine needs to sell boxes of cookies as a fundraiser for a team. She starts with 135 boxes and begins selling at constant rate of
15 boxes each day.
Use the Segment tool to plot a graph representing the number of boxes of cookies Catherine has left to sell from the time she begins
selling until the cookies are gone.
Answer: The equation that represents this situation is y = -15x + 135
A linear equation is given by:
y = mx + b;
where y, x are variables, m is the rate of change and b is the y intercept.
Let y represent the amount of boxes remaining after x days.
She starts with 135 boxes, hence b = 135. She sells at a constant rate of 15 boxes each day, hence m = -15. The equation becomes:
y = -15x + 135
The first point should be plotted at (9,0) then the next at (0,135). Just plot multiples of 15 on the chart until you get to the 9th multiple
Step-by-step explanation:
[tex]\sqrt{2x+3} = 5\\[/tex]
x= 11.
Step-by-step explanation:1. Write the expression.[tex]\sqrt{2x+3}=5[/tex]
2. Square both sides of the equation.[tex]\sqrt{2x+3} ^{2} =5^{2} \\ \\2x+3=25[/tex]
3. Subtract 3 from both sides of the equation.[tex]2x+3-3=25-3\\ \\2x=22[/tex]
4. Divide both sides by 2.[tex]\frac{2x}{2} =\frac{22}{2} \\ \\x=11[/tex]
5. Verify your answer.[tex]\sqrt{2(11)+3}=5\\ \\\sqrt{22+3}=5\\ \\\sqrt{25}=5\\ \\5=5.[/tex]
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Graph the absolute value equation that represents the given situation, d = 1/5|8-250| - 50.
-
Then mark the points that represent the horizontal distance from the left shore where the
river bottom is 20 feet below the surface.
For the given graph of absolute value equation d = (1/5)|s-250| -50 , the point that represents the horizontal distance from the given left shore when river bottom is 20 feet below the given surface is equal to 400 feet or 100 feet.
As given in the question,
Given absolute value equation is:
d = (1/5)|s-250| -50
Simplify it for the river bottom d =-20 feet below the given surface
-20 = (1/5)|s-250| -50
⇒-20(5) = | s- 250| - 250
⇒ 250 -100 = |s-250|
⇒ 150 = | s- 250|
⇒ s - 250 = 150 or s -250 = -150
⇒ s= 400 feet or s = 100 feet
Graph of the equation is attached.
Therefore, for the given graph of absolute value equation d = (1/5)|s-250| -50 , the point that represents the horizontal distance from the given left shore when river bottom is 20 feet below the given surface is equal to 400 feet or 100 feet.
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Give the reciprocal 1/9
Which of the following statements is true for the quadratic equation x² – 16x + 64 = 0?
It's impossible to determine how many solutions the equation has.
The equation has no solutions.
The equation has two solutions.
The equation has one solution.
Since the discriminant of the quadratic equation Δ is equals to 0, the given quadratic equation has one solution. Thus, the fourth option is correct.
We know that for a quadratic equation [tex]ax^{2} +bx+c =0[/tex], there exists a discriminant, Δ = [tex]b^{2}-4ac[/tex]. This discriminant gives us the nature of roots that a quadratic equation can have.
If Δ > 0, the quadratic equation has two real rootsIf Δ = 0, the quadratic equation has single solution as two double rootsIf Δ < 0, the quadratic equation has no real rootsHere, we have the given quadratic equation as -
[tex]x^{2} -16x+64=0[/tex]
Comparing this to the general expression of a quadratic equation, we have
a = 1
b = -16
c = 64
So, now we have to find the discriminant of the given quadratic equation.
Δ = [tex]b^{2}-4ac[/tex]
[tex]= (-16)^{2} -4*1*64\\= 256-256 = 0[/tex]
We see that the discriminant, Δ = 0. This implies that the given quadratic equation has one solution. Thus, the fourth option is correct.
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Find the equation of a line that passes through the point (5,3) and has a gradient of 2. Leave your answer in the form y = m x + c
The equation of the line in slope intercept form is y = 2x - 7..
How to find the equation of a line?The equation of a line can be represented in slope intercept form as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line that passes through (5,3) and has a gradient of 2 can be found as follows;
m = 2
let's find the y-intercept using (5, 3)
3 = 2(5) + b
b = 3 - 10
b = -7
Therefore, the equation of the line is y = 2x - 7.
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A decagon has 10 sides. One angle of a regular decagon measures (8w + 17)°. Determine the value of w. Round to the nearest whole number. w = 144 w = 23 w = 16 w = 8
Answer:
I think the answer is 144
The value of w to the nearest whole number is 16°
What a regular polygon?If a polygon has equal sides and angles, it is said to be regular. As a result, an equilateral triangle is a regular triangle, and a square is a regular quadrilateral.
Given:
Decagon has 10 sides.
As, sum of interior angles of a polygon = ( n - 2) x 180
where n = number of sides of polygon
Here n = 10
sum of interior angle = ( 10 - 2) x 180 which is 1440°
If a regular polygon has equal angles and each angle is (8w + 17)
10( 8w + 17) = 1440
8w + 17 = 144
8w = 144 - 17
8w = 127
w = 127/8
w = 15.875
Thus, the value of w = 16°
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U = 2, 3, 4, 5, 7
C= 2, 4
D= 2, 7
(a) (CnD)’=
(b) C’uD=
Answer:
U={2,3,4,5,7}
C={2,4}
D={2,7}
Now,
a.) CUD
= {2,4}U{2,7}
= {2,4,7}.
again,
b.) CnD
= {2,4}n{2,7}
= {2}.ans
Step-by-step explanation:
U(union) means all of the numbers but not similar one…
n(intersection) means common factors.
Hope it really helps you
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Alisha and Emily are making t-shirts for the Math team. they need a total of 21 shirts. Alisha has made 13 shirts and Emily made p shirts . Write a formula to model this
The formula to model the given situation is 13 + p = 21 .
In the question ,
it is given that ,
Alisha and Emily are making T- Shirts for the Math's team .
total number of T- Shirts required = 21 shirts .
number of shirts made by Alisha = 13 shirts
number of shirts made by Emily = p shirts
So , the equation that represents the given situation is
13 + p = 21
Solving further , we get
p = 21 - 13
p = 8
So , Emily made 8 T - Shirts .
Therefore , The formula to model the given situation is 13 + p = 21 .
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