Answer:
a = 3
b = 2
c = 0
d = -4
Step-by-step explanation:
Form 4 equations and solve simultaneously
28 = a(2)³ + b(2)² + c(2) + d
28 = 8a + 4b + 2c + d (1)
-5 = -a + b - c + d (2)
220 = 64a + 16b + 4c + d (3)
-20 = -8a + 4b - 2c + d (4)
(1) + (4)
28 = 8a + 4b + 2c + d
-20 = -8a + 4b - 2c + d
8 = 8b + 2d
d = 4 - 4b
Equation (2)
c = -a + b + d + 5
c = -a + b + 4 - 4b+ 5
c = -a - 3b + 9
28 = 8a + 4b + 2c + d (1)
28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b
28 = 6a - 6b + 22
6a - 6b = 6
a - b = 1
a = b + 1
220 = 64a + 16b + 4c + d (3)
220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b
220 = 60b + 100
60b = 120
b = 2
a = 2 + 1
a = 3
c = -3 - 3(2) + 9
c = 0
d = 4 - 4(2)
d = -4
Step-by-step explanation:
Step 1: Solve using the first point
(2, 28)
[tex]28 = a(2)^3 + b(2)^2 + c(2) + d[/tex]
[tex]28 = 8a + 4b + 2c + d[/tex]
Step 2: Solve using the second point
(-1, -5)
[tex]-5 = a(-1)^3 + b(-1)^2 + c(-1) + d[/tex]
[tex]-5 = -a + b - c + d[/tex]
Step 3: Solve using the third point
(4, 220)
[tex]220 = a(4)^3 + b(4)^2 + c(4) + d[/tex]
[tex]220 = 64a + 16b + 4c + d[/tex]
Step 4: Solve using the fourth point
(-2, -20)
[tex]-20 = a(-2)^3 + b(-2)^2 + c(-2) + d[/tex]
[tex]-20 = -8a + 4b - 2c + d[/tex]
Step 5: Combine the first and fourth equations
[tex]28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d[/tex]
[tex]8 = 8b + 2d[/tex]
[tex]8 - 8b = 8b - 8b + 2d[/tex]
[tex](8 -8b)/2 = 2d/2[/tex]
[tex]4 - 4b = d[/tex]
Step 6: Solve for c in the second equation
[tex]-5 + 5 = -a + b - c + d + 5[/tex]
[tex]0 + c = -a + b - c + c + d + 5[/tex]
[tex]c = -a + b + d + 5[/tex]
Step 7: Substitute d with the stuff we got in step 5
[tex]c = -a + b + (4 - 4b) + 5[/tex]
[tex]c = -a + b + 4 - 4b + 5[/tex]
[tex]c = -a - 3b + 9[/tex]
Step 8: Substitute d and c into the first equation
[tex]28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)[/tex]
[tex]28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b[/tex]
[tex]28 - 22 = 6a - 6b + 22 - 22[/tex]
[tex]6 / 6 = (6a - 6b) / 6[/tex]
[tex]1 + b = a - b + b[/tex]
[tex]1 + b = a[/tex]
Step 9: Substitute a, b, and c into the third equation
[tex]220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)[/tex]
[tex]220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b[/tex]
[tex]220 - 100 = 60b + 100 - 100[/tex]
[tex]120 / 60 = 60b / 60[/tex]
[tex]2 = b[/tex]
Step 10: Find a using b = 2
[tex]a = b + 1[/tex]
[tex]a = (2) + 1[/tex]
[tex]a = 3[/tex]
Step 11: Find c using a = 3 and b = 2
[tex]c = -a - 3b + 9[/tex]
[tex]c = -(3) - 3(2) + 9[/tex]
[tex]c = -3 - 6 + 9[/tex]
[tex]c = 0[/tex]
Step 12: Find d using b = 2
[tex]d = 4 - 4b[/tex]
[tex]d = 4 - 4(2)[/tex]
[tex]d = 4 - 8[/tex]
[tex]d = -4[/tex]
Answer: [tex]a = 3, b = 2, c = 0,d = -4[/tex]
If you save $3,000 at an interest rate of 14 percent per year, how much will you have at the end of six years? The interest should be compounded. A. $5,805.96 B. $6,502.34 C. $6,584.91
Answer:
C.) $6,584.91
Step-by-step explanation:
Amount earned in compound interest = P(1 + r)^n;
where P is the principal,
r is the rate and n is the number of periods.
Amount = 3,000(1 + 14%)^6 = 3,000(1 + 0.14)^6 = 3,000(1.14)^6 = $6,584.91
Answer:
C) 6584.91
Step-by-step explanation:
plato
A biased coin is tossed 40 times. Out of those 40 tosses, the coin landed on heads 12 times.
Find the probability of the coin landing on tails.
Answer:
Step-by-step explanation:The probability of picking the biased coin: P(biased coin)=1/100. The probability of all three tosses is heads: P(three heads)=1×1+99×18100. The probability of three heads given the biased coin is trivial: P(three heads|biased coin)=1.
A triangle has sides with lengths of 6 yards, 8 yards, and 10 yards. Is it a right triangle?
Answer:
Step-by-step explanation:
so, by the Pythagorean theorem
If it is a right triangle:
a^2 + b^2 = c^2
so,
6^2 = 36
8^2 = 64
10^2 = 100
okay, now we plug these into the equation
36 + 64 = 100
so yes, it is a right triangle.
Hope this helped!
Answer:
No, it's not a right triangle.
Explanation:
If you think about it a right triangle has 2 equal sides. So no this isn't a right traingle.
Pleaseeeeee helpppp meeeeeeeeeeeeeeeeeee!!!! Reallyyy need it
Answer:
I cant see the whole question...
Find the surface area of a cube is 150 cm2. What is the length an edge of
the cube? (all of the sides are squares)
Answer:
5
Step-by-step explanation:
The formula is 6x^2
If you set it equal to 150
Answer:
5 x 5 + 5 x 5 + 5 x 5 + 5 x 5 + 5 x 5 + 5 x 5 = 25 + 25 + 25 + 25 + 25 + 25 = 50 + 50 + 50 = 150
5 would be the missing side because it fits the formula
(A x A) + (A x A) + (A x A) + (A x A) + (A x A) + (A x A) = Surface area
Step-by-step explanation:
Can you answer the questions
Below please and thank you
Answer:
1. 60
2. 90
Step-by-step explanation:
Answer:
1.
1/5
2.
1/15
Step-by-step explanation:
UPS charges $6.00 for the first pound, $1.00 for the second pound, and $0.15 for each additional pound. FedEx charges $4.00 for the first pound, $2.00
for second pound, and $0.25 for each additional pound. How many pounds, p. will it take for UPS and FedEx to cost the same?
Complete the equation that represents this situation.
Answer:
12 pounds
Step-by-step explanation:
It takes 12 pounds for the UPS and FedEx packages to cost the same amount to ship.
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, UPS charges $6.00 for the first pound, $1.00 for the second pound, and $0.15 for each additional pound. FedEx charges $4.00 for the first pound, $2.00 for the second pound, and $0.25 for each additional pound.
Equations to represent the situation in this problem.
x=weight of package
UPS cost=6+1+0.15(x-2)
UPS cost=6+1+0.15x-0.3
UPS cost=6.7+0.15x
FedEx cost=4+2+.25(x-2)
FedEx cost=4+2+0.25x-0.5
FedEx cost=5.5+0.25x
Next, we can set the two equations equal to each other to solve for x.
6.7+0.15x=5.5+0.25x
6.7+0.15x-5.5=5.5+0.25x-5.5
1.2+0.15x-0.15x=0.25x-0.15x
1.2/0.1=0.1x/0.1
x=12
Hence, It takes 12 pounds for the UPS and FedEx packages to cost the same amount to ship.
For more references on equations, click;
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1. A jet leaves the Charlotte, North Carolina, airport traveling at an average rate of
564 km/h. Another jet leaves the airport one half hour later traveling at 744
km/h in the same direction. Use an equation to find how long the second jet will
take to overtake the first.
A
17
30
h
17
h
30
1
15
h
Answer:
The time needs for second plane to catch up with first plane is t.
We have, 564(t + 0.5) = 744t
=> 180t = 282
=> t= 282/180 = 1.57 hour
Hope this helps!
:)
Solve for x
8+10x-3x^2=0
Answer: x = 4
or x= -2/3 = -0.667
Step-by-step explanation:
Sarah claims that when you divide, the number you are dividing always gets smaller. John says this is not true. Who is correct? If John is correct, give a counterexample.
A) Sarah is correct.
B) John is correct. A counterexample is 4 ÷ 5.
C) John is correct. A counterexample is 4 ÷ 1.25.
D) John is correct. A counterexample is 4 ÷ 1/2
Answer:
D
Step-by-step explanation:
John is correct as Dividing does not always gets the quantity smaller for example if we divide 4 by 0.5
We get
4/0.5= 8
How would you factor 6a - 15
What are the solution(s) of the quadratic equation 98 - x2 = 0?
x = +27
x= 163
x = 17/2
no real solution
Answer: it’s c
Step-by-step explanation:
can someone plz help me with i don't understand it at allll
Calculating Vacation Costs
Situation:
Imagine that you’ve just won the coveted “Most Likely to Succeed in Math” award! Your prize is $4,500.00, which must be applied to a vacation. You will be provided a list of choices. You, a parent/guardian, and two others will be traveling by car, and you must plan all the expenses for your trip without exceeding $4,500.00.
Special Considerations:
• Do not include costs for souvenirs or extras. These items do not get deducted from the prize money.
• Travel and lodging must be calculated for a round trip.
• You may need two hotel rooms, such as one for girls and one for boys, so make sure to consider who is in the group. All boys or all girls can stay in one room.
• You have various choices and options. Choose what will give you an outstanding vacation.
• You may remain on vacation as long as the prize money is available.
• You must pay all expenses of the group of 4.
• Calculate costs on this sheet.
• Be sure to total costs.
Answer:
i don't understand
Step-by-step explanation:
Write the vector u as a sum of two orthogonal vectors, one of which is the vector projection of u onto v, projvu. u = <-8, -8> and v = <-1,2>
a.) <-0.5, 1> + <-7.5, -9>
b.) <-1, 2> + <-7, -10>
c.) <-1, 2> + <-2, -1>
d.) <1.6, -3.2> + <-9.6, -4.8>
Answer:
c.) <-1, 2> + <-2, -1>
Step-by-step explanation:
hope i helped
Please help! Surface Area
Answer: The surface area is 219.8 ft
Step-by-step explanation: the radius= 7 and the height=4
2(3.14 x 7) + (2 x 3.14 x 7) 4
43.96 + 175.84
219.8
3. After completing a statistical analysis of a survey of 40 students, the principal
of North High School made the following conclusion: reject the null hypothesis;
there is convincing evidence that more than 50% of students support a schedule
change to have lunch occur earlier in the day. Which error could have been
committed?
(A) Type I error: Conclude that more than 50% of students want earlier lunch, when
50% or less want earlier lunch.
(B) Type l error: Conclude that more than 50% of students want earlier lunch, when
more than 50% want earlier lunch.
(0) Type Il error: Fail to reject that 50% of students want earlier lunch, when more than
50% want earlier lunch.
(D) Type Il error: Fail to reject that 50% of students want earlier lunch, when 50% or less
want earlier lunch.
(E) Type Il error: Fail to reject that more than 50% of students want earlier lunch, when
50% or less want earlier lunch.
Answer:
Option A
Step-by-step explanation:
A type I error is committed when a researcher rejects the null hypothesis when it is actually true.
The null hypothesis is: U <= 50%
The alternative is: U > 50%
Thus, the principal could have committed an error by rejecting null hypothesis and concluding that more than 50% of students want earlier lunch, when in actuality 50% or less want earlier lunch.
4.9.21
Solve the system of equations.
y=x² + 6x-2
y= - x2 + 4x + 22
Select the correct choice below and, if necessary, fill in box
- the solution(s) are:
- there is no solution
Answer:
x = -4 or 3
Step-by-step explanation:
[tex]x^{2}[/tex] + 6x - 2 = -[tex]x^{2}[/tex] + 4x + 22
2[tex]x^{2}[/tex] + 2x - 24 = 0
[tex]x^{2}[/tex] + x - 12 = 0
(x + 4)(x - 3)=0
x = -4 or 3
graph the circle (x-7)^2 + (y-5)^2 = 4
Answer:
I graphed the circle below.
Step-by-step explanation:
If this answer is correct, please make me Brainliest!
The graph of the circle is attached.
What is a circle?A circle is a shape or a curve in a plane that has a fixed distance, called the radius, from a given point, called the centre.
A circle is also the set of all points that are equidistant from the centre.
A circle is a special case of an ellipse with zero eccentricity and coincident foci.
Given is an equation of a circle, we need to graph, it,
The equation =
(x-7)² + (y-5)² = 4
Here, the center of the circle is (7, 5) and the radius is 2.
Hence, the graph of the circle is attached.
Learn more about circle, click;
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Find the missing angle.
Which equation represents the relationship between the angles in the figure?
A. 88 + b = 90
889
B. 88 + b = 180
a. 2b + 88 = 90
D. 2b + 88 = 180
Solution:
What is the height of the pole?
top
O 12 ft
O 125 ft
O 18 ft
O 182 ft
the ratio of the corresponding edge lengths of two similar solids is 4:5. What is the ratio of their volumes?
Answer: i think its b
Step-by-step explanation:
must read!!1
because the other ones for ex: A when 4 times 4 =16 but 5 times 5=25 not same numbers being multiplied this I my hypothesis
Hunter decides to invest $840,000 in a period annuity that earns a 4.2% APR,
compounded monthly, for a period of 30 years. How much money will Hunter
be paid each month?
Answer: $4107.74
Step-by-step explanation:
Below is the data of ages at the local amusement park on a certain day.
17, 18, 17, 17, 20, 22, 17, 18, 13, 14, 19, 14, 13, 33, 31, 8, 9, 10, 8, 8, 16, 17, 19, 35, 29, 8, 10, 15, 17, 30, 29, 5, 9, 10, 15, 14
Provide the intervals and frequencies you would use to construct the histogram for this data set.
Answer:
39
Step-by-step explanation:
To find the intervals you will need to find the lowest and highest numbers, in this case, it would be 1 and 35. A general rule would be 5-7 intervals, I will use 5.
Here are the intervals with the number of people that were in each:
1-7 (9)
8-14 (14)
15-21 (8)
22-28 (3)
29-35 (5)
14+9+8+3+5=39
Problem PageQuestion
Pamela's age is two times Jiri's age. The sum of their ages is 66. What is Jiri's age?
Answer:
Jiri is 22
Pamela is 44
Step-by-step explanation:
Look at the attachment
Answer:
Jiri is 22 years old.
Step-by-step explanation:
P=2J
P+J=66
2J+J=66
3J=66
J=22
The ratio of pens to pencils in the box is 84 to 112. Which statement describes this relationship?
A)
There are 3 pens for every 4 pencils in the box.
B)
There are 4 pens for every 6 pencils in the box.
There are 4 pens for every 3 pencils in the box.
D)
There are 6 pens for every 4 pencils in the box.
Answer:
A) There are 3 pens for every 4 pencils in the box
Hope this helps!
Please help with this question!!
5/8
A. Real number. True, all rational numbers are real; SELECT ME
B. Non-real; nope, it's real, so not non-real
C. Irrational; nope, it's a rational number, the ratio of integers
D. Rational. Natural numbers on top and bottom, bottom not zero. SELECT ME.
E. Integer; no, it's a fraction.
F. Whole; that's a non-negative integer, nope.
G. Natural, that's a non-zero whole number, nope.
Answer: A D
A company is trying to calculate the amount of
concrete that will be needed to create one concrete
block that is in the form below.
The concrete block is a rectangular prism with two
cubes cut out. The cubes have a side length of 6
inches.
What is the total volume, cubic feet, of concrete
needed to make this block?
Answer:
[tex]0.19\,\,cubic\,\,feet[/tex]
Step-by-step explanation:
Given:
The concrete block is a rectangular prism with two cubes cut out. The cubes have a side length of 6 inches.
To find: total volume, cubic feet, of concrete needed to make this block
Solution:
Side of cube = 6 inches
Volume of cube = [tex](side)^3=6^3=216\,\,cubic\,\,inches[/tex]
So, volume of two cubes = 2(216) = 432 cubic inches
Length of rectangular prism = 12 inches
Breadth of rectangular prism = 8 inches
Height of rectangular prism = 8 inches
Volume of rectangular prism = length × breadth × height = [tex]12(8)(8)=768 \,\,cubic\,\, inches[/tex]
Total volume of concrete needed to make this block = Volume of rectangular prism - Volume of two cubes = 768 - 432 = 336 cubic inches = [tex]\frac{336}{1728} =0.19\,\,cubic\,\,feet[/tex]
( use 1 cubic inch = [tex]\frac{1}{1728} \,\,feet[/tex])
okay who knows there stuff good ? i failed geometry last year and were back at it plz helppp
In regular polygons, if the number of sides, n, is off, the lines of symmetry will pass through a __________ and the __________ of the opposite side.
Answer:
In regular polygons, if the number of sides, n, is odd, the lines of symmetry will pass through a vertex and the half of the opposite side.
Step-by-step explanation:
This is equivalent to say that a perpendicular bisector of a side of the regular polygon bisects the angle of the opposite vertex to the side, and divide the polygon into two symmetrical parts.
What creatures terrify Aeneas as he enters the realm of the dead?
Answer:
The sibyl tells Aeneas that he must find and pluck a golden bough from a tree in an ... First, however, he must find and bury the body of a dead comrade. ... spirits and monsters and eventually reach Acheron, one of the underworld's rivers. Here ... Also punished in Tartarus's realm are mortals who have sinned abhorrently
Step-by-step explanation:
