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]
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
pls help pls its hard ....
Answer:
(1,5)
Step-by-step explanation:
plug in the x and y values to see if they are equal in the equation. If not, then you know the answer is wrong.
Answer: if you need help ask
Step-by-step explanation:
First you start by finding a problem
Next you ask someone to help you with the problem, simple :)
pls answer soon it's a study guide
Answer:
Step-by-step explanation:
I NEED HELP RiGHT AWAY
8−4(−x+5)
Answer:
4x-12
Step-by-step explanation:
A baseball coach purchased a total of 28 helmets and caps. Each helmet cost $21.50, and each cap cost $8.25. If the coach spent a total of $363.50, how many helmets did the coach purchase?
Answer:
5 helmets
31 caps
8.25, 16.50 24.75 33 x 10 = 330
330/2 = 165 = 20 helmets
363.50 - 165 = 198.50
5 x 21.50 = 107.50 (+ 11 x 8.25 = 16.50+24.75 +24.75+24.75 = 49.50+41.25) =£91 + 107.50 = 198.50
20+11 = 31
31 caps
5 helmets
Step-by-step explanation:
There are 10 helmets did the coach purchase.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
A baseball coach purchased a total of 28 helmets and caps.
And, Each helmet cost $21.50, and each cap cost $8.25. and the coach spent a total of $363.50.
Let number of helmets = x
And, Number of caps = y
Here, A baseball coach purchased a total of 28 helmets and caps.
Hence, We get;
⇒ x + y = 28 ..(i)
And, Each helmet cost $21.50, and each cap cost $8.25. and the coach spent a total of $363.50.
Hence, We get;
⇒ 21.50x + 8.25y = 363.50
⇒ 5 (4.30x + 1.65y) = 5 × 72.7
⇒ 4.30x + 1.65y = 72.7 .. (ii)
Multiply by 4.30 in (i) ad subtract from (ii);
⇒ 4.30x + 4.30y - 4.30x - 1.65y = 120.4 - 72.7
⇒ 2.65y = 47.7
⇒ y = 18
And, From (i);
⇒ x + y = 28
⇒ x + 18 = 28
⇒ x = 10
Hence, Number of helmets = 10
Learn more about the mathematical expression visit:
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1
1
Jump ropes are given out during gym class. A student has a chance of getting a red jump rope and a
3
chance of getting a green jump rope. Meg is given a jump rope.
2
What is the probability that Meg gets a red or green jump rope?
The probability that Meg gets a red or green jump rope is
Answer:
2/2
Step-by-step explanation:
There are only red and green jump ropes so she is for sure going to get a red or green jump rope. If she wants specifically a red or green jump rope her chances are 1/2.
HELP ASAP
Find the volume of the corner, R measures 10 feet, height measures 30 feet
Answer:
3141.59
Step-by-step explanation:
Answer:
[tex]3141.59 \: \: {ft}^{3} [/tex]
Step-by-step explanation:
[tex]V
=
π
{r}^{2}
\frac{h}{3}
\\
=
π
·
{10}^{2}
·
\frac{30}{3}
\\
≈
3141.59265
[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Find z 1 z 2 if z 1 = 3(cos37° + isin37°) and z 2 = (cos53° + isin53°
Answer:
[tex]Z_{1} Z_{2} = 3 i[/tex]
Step-by-step explanation:
Step(i):-
Given z 1 = 3(cos 37° + i sin 37°)
z 2 = (cos 53° + i sin 53°)
by using complex numbers
[tex]Z_{1} = r_{1} ( cos\alpha_{1} + isin\alpha_{1} ) = r_{1} cis\alpha _{1}[/tex]
[tex]Z_{2} = r_{2} ( cos\alpha_{2} + isin\alpha_{2} ) = r_{2} cis\alpha _{2}[/tex]
step(ii):-
now
[tex]Z_{1} Z_{2} = r_{1} r_{2} cis (\alpha _{1} + \alpha _{2})[/tex]
z ₁ = 3(cos 37° + i sin 37°) = 3 c i s 37°
z ₂ = (cos 53° + i sin 53°) = c i s 53°
we will use formula
[tex]Z_{1} Z_{2} = r_{1} r_{2} cis (\alpha _{1} + \alpha _{2})[/tex]
[tex]Z_{1} Z_{2} = 3 X 1 cis (37 + 53) = 3cis (90) = 3 cis(\frac{\pi }{2} )[/tex]
[tex]Z_{1} Z_{2} = 3(cos(\frac{\pi }{2} ) + isin(\frac{\pi }{2}))[/tex]
[tex]Z_{1} Z_{2} = 3(0 + i (1)) = 3 i[/tex]
Conclusion:-
[tex]Z_{1} Z_{2} = 3 i[/tex]
Answer:
2i
Step-by-step explanation:
z 2 = 2/3(cos53° + isin53°
I got it right on odyssey ware
What will be the distance from the center of dilation, P, to the
image S'?
2 units
4 units
6 units
8 units
Answer:
6
Step-by-step explanation:
Answer:
6 units on edge
Step-by-step explanation:
Sara says, "If you subtract 15 from my number and multiply the difference by negative 4, the result is negative 48." What is Sara's number?
Answer:
I'm not 100% sure but I believe the answer is 27
because -48/-4=12
12+15=27
Answer:
Write the equation and go backwards.
N - 15 x -4 = -48
Instead of multiply divide and add instead of subtract
-48/-4=12
12+15=27
check if 27 is correct. 27-15=12 x -4 = -48
27 is your number. Hope this helps
Step-by-step explanation:
There is a line that includes point (1,2) and has a slope of 10 what is equation in intercept form
Answer:
[tex]y=10x-8[/tex]
Step-by-step explanation:
Given: Point (1,2) lies on the line such that it's slope is 10.
To find: equation of line
Solution:
Let m be the slope of line and b be the y - intercept.
Here, slope is a number that describes the direction and the steepness of the line.
y-intercept is the y-coordinate of the point where the graph of the line intersects the y-axis.
Equation of line is [tex]y=mx+b[/tex]
Put [tex](x,y)=(1,2),m=10[/tex]
[tex]2=10(1)+b\\2=10+b\\b=2-10=-8[/tex]
So, equation of line is [tex]y=10x-8[/tex]
Which is the largest amount of liquid? A. one quart
B. one cup
c. one milliliter
D. one liter
E. one pint
Answer:
one pint
Step-by-step explanation:
This is because one pint is larger than one cup, there are two cups in a pint.
One milliliter is way smaller than one liter and there are 0.473176473 liters in a pint.
Answer:
pint
Step-by-step explanation:
1 Pint is equal to 0.47317647299 liter.
Liter and Pint are the largest on there, and pint is bigger.
Hope this helps! :)
Stephen opened a savings account with $100. He deposits $ 20 every time he mows a lawn during the summer. He wants at least $400 in his
account by the end of the summer Leten be the number of lawns Stephen mows.
which inequality can be used to determine the number of lawns Stephen needs to mow?
A 100 + 20 < 400
B 100n + 20 S 400
C 100+ 20n > 400
D. 100 + 200 2400
Answer:
c
Step-by-step explanation:
The width of a rectangle is the length minus 4 units. The area of the rectangle is 12 units. What is the width in units of the rectangle
Answer:
width = 2 units
Step-by-step explanation:
If the length of a rectangle is (x) units, then that means that the width of a rectangle is x - 4 units.
the area of a rectangle is length * width
so just substitute the values that we have now.
x (length) * (x-4) width = 12 (area of rectangle)
so that gives us
x^2 - 4x =12
subtract 12 from both sides
x^2 - 4x - 12 =0
now factor this equation
x^2 + 2x - 6x -12 = 0
x(x+2) - 6(x+2) = 0
(x-6)(x+2) = 0
x = 6, or x = -2 REMEMBER THAT VALUE OF x = LENGTH, IT CANNOT BE NEGATIVE AS YOU CANT HAVE NEGATIVE VALUE OF A SIDE
length = 6, and width = 6 -4 = 2
Answer:
W=2 units
Step-by-step explanation:
Length=L
Width=L-4
Area of a rectangle= L*W
L(L-4)=12
L^2-4L=12
L^2-4l-12=0
Now we have a quadratic equation
(L-6)(L+2)=0
L=6, L=-2
L cannot be -2 because it is negative, so L must be 6.
BUT it is asking for the width
and it is given that the width is the length minus 4 units, so
6-4= 2 units
Which scatter plot shows that the number of gallons of milk sold decreased as the price per gallon increased?
Answer:
The answer is D
Step-by-step explanation:
If P(A) = 0.25, P(B) = 0.60 and P(A and B) = 0.15, are the event A and B independent? Explain/show work.
Answer:
event A and B are independent because P(A and B) = P(A) x P(B) = 0.15
Step-by-step explanation:
When two events are independent, the probability of both occurring is the product of their separate probabilities, as expressed below;
P(A and B) = P(A) x P(B)
Given;
P(A) = 0.25
P(B) = 0.60
P(A and B) = 0.15
Now, let's check if P(A and B) will be equal to P(A) x P(B)
P(A) x P(B) = 0.25 x 0.60 = 0.15
P(A and B) = P(A) x P(B), thus event A and B are independent.
is it true that energy never moves
Answer:
False
Step-by-step explanation:
Energy is transferred from one object to another when a reaction takes place. Energy comes in many forms and can be transferred from one object to another as heat, light, or motion, to name a few.
PLEASE HELP ME YALL
What is the hourly difference in median income for a male versus female with an advanced degree?
$__ /hr
Answer:
around 3$
Step-by-step explanation:
According to US bureau of census, the average hourly income difference between male and female working fro an employer for less than 10 years is around $3.
Answer:
$11.28
Step-by-step explanation:
Assuming your referring to the chart
median usual weekly earnings of full-time wage and salary workers by educational attainment and ... 2018 annual averages
I don't know how they got that answer I just know I got it wrong
Is this angle acute right obtuse or straight
Answer:
obtuse
Step-by-step explanation:
Over 90 degrees
Answer:
Obtuse
Step-by-step explanation:
The angle is obtuse because the angle is more than 90 degrees.
Solve: x(squared) = 5x - 6
A. 3, 2 B. -3, -2 C. (x – 3)(x – 2) D. no solution
Answer:
x=-3 x=-2
Step-by-step explanation:
x^2 = 5x-6
Subtract x^2 from each side
x^2 - x^2 = -x^2 -5x-6
0 = -x^2 -5x-6
0 =-(x^2 +5x+6)
Factor
0 = (x+3)(x+2)
Using the zero product property
0=x+3 0=x+2
x=-3 x=-2
a pitcher contains 17.5 cups of iced tea. you drink 0.75 cup of tea each morning and 1.75 cups of tea each evening. when will you run out of iced tea?
Answer:
7 days
Step-by-step explanation:
Based on the amount of iced tea in the pitcher and the amount drank per day, you will run out of iced tea in 7 days.
The total number of cups drank per day is:
= 0.75 + 1.75
= 2.5 cups
With 2.5 cups being drank per day, the pitcher would last:
= Pitcher quantity / Cups per day
= 17.5/2.5
= 7 days
In conclusion, you will run out after 7 days.
Find out more at https://brainly.com/question/13426420.
Explain how to use a graph of the function f(x) to
find f(3).
Answer:
For f(3), the input is 3 and you are looking for the output. To determine the function's value when x = 3, go to the value of 3 on the x-axis and then locate the graph for that value of x. Determine the value of y from the y-axis at that location on the graph.
Step-by-step explanation:
up there
pls help will mark as brainliest
Answer:
C
Step-by-step explanation:
Answer:
D cannot be used. first 3 are correct
Step-by-step explanation:
Place the indicated product in the proper location on the grid.
(ab - 9)(ab + 8)
Answer:
(2b)
Step-by-step explanation:
2/5 of it is 22.
Pls help me I'm really stuck on this
Answer: 55
Step-by-step explanation:
2/5 * x = 22
2/5x = 22
x= 55
Which number is divisible by 9?
121
137
127
144
Answer:
144
Step-by-step explanation:
144/9=16
Answer:
The answer is 144
Explanation:
144÷9=16
Stacy uses a spinner with six equal sections numbered 2, 2, 3, 4, 5, and 6 to play a game. Stacy spins the pointer 120 times and records the results. The pointer lands 30 times on a section numbered 2, 19 times on 3, 25 times on 4, 29 times on 5, and 17 times on 6. How does the theoretical probability compare with the experimental probability of landing on an even number? Use the drop-down menus to explain your answer. The_______ probability is greater than the_____ probability of landing on an even number. The_______ probability is 72/120 and the_______ probability is 80/120.
Answer:
The theoretical probability is greater than the experimental probability of landing on an even number. The experimental probability is 72/120 and the theoretical probability is 80/120.
Step-by-step explanation:
Experimental probability of landing on an even number: (30+25+17)/120 = 72/120 = 0.6
Even outcomes: 4
Total outcomes: 6
Theoretical probability of landing on an even number: 4/6 = 0.67
After 120 spinners it is expected 4/6*120 = 80 even results
you and your friend are walking through town. there is a building making a 90 degree angle with the ground and you are standing 40ft away looking up and a 30 degree angle. how tall is the building?
Answer:
tan 30 = height of building / 40
height = 40 × 1/√3=40/√3
or = 23.1 feet
Find the value of x.
Answer:
x=51
Step-by-step explanation:
Formula: 35+16=x
Step 1: Simplify both sides of the equation.
35+16=x
(35+16)=x(Combine Like Terms)
51=x
51=x
Step 2: Flip the equation.
x=51
Hope this helps.
Choose the appropriate plan letter for each question
Plan____ has the lowest range
Plan____ has the highest y intercept
Plan___ is the plane that is the best value
c is the lowest range
a has the highest y incerpt
d is the best value
DVD players are going out of fashion in the modern era. If 400,000 DVD players were sold this year and sales are declining at a rate of 31% per year, how many will be sold 3 years from now?
130,000
131,404
128,000
399,876
Answer:
c
Step-by-step explanation:
Answer:
399,876
Step-by-step explanation:
So, 400,000 DVD sales with a 31% decline means in the first year following, there will be a decline of 124,000 DVDs sold. So we need to take 400,000-124,000 which equals a starting point for your two is 276,000 dvds. Then, add 123,876, which gives you 399,876.
