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
22 .Siswa dapat menganalisis persamaan menggunakan identitas trigonometri
a) cot x.cos x per cosec x
b) cos pangkat 4 x - sin pangkat 4 x
Anna runs a 5k in 20 minutes. What is her speed in kilometers per hour?
Answer:
15kmh
Step-by-step explanation:
Answer:
15k
Step-by-step explanation:
There is 60 mins in an hour. Since she runs 5k in 20 mins you would multiply 20 by 3 because it would equal 60. Also you would multiply 5k by 3 also.
i hoped that made sense ;-;
John is creating a shed in his backyard he wants to use brick for the front side with the door using the given brick how many will he need to cover the front of the shed
Answer:
180 bricks.
Step-by-step explanation:
The dimensions of the front of the shed are 30 x 12.
30 x 12 = 360
The dimensions of the brick are 2 x 1.
2 x 1 = 2.
360/2 = 180.
x=?? will give brainliest
Answer:
I think its a right angled triangle
and so x= 90°
rewrite the equation of the circle (x-2)^2+y^2=3 in general form
Step-by-step explanation:
x²+4-4x+y²=3
x²+y²-4x+1=0
Answer:
?? Bro write the question better
Step-by-step explanation:
WILL MARK BRAINLIEST:
Hello! So I need to know HOW to do this. Please don't do the work for me, I just need an explanation. thank you!
Answer:
Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8.
Answer:
as the other guy said, scientific notation in simple words is expressing large quantities in terms of being multiplied with powers of 10
hence,
11. 7.5 x 10^6
12. 2.9 x 10^5
13. 3.7 x 10^(-4)
14. 1.26 x 10^4
15. 2 x 10^(-7)
16. 4 x 10^(-3)
17.6 x 10^7
18. 4.07 x 10^7
19. 8.1 x 10^(-4)
20. 1.25 x 10^(4)
This circle is circumscribed about quadrilateral ABCD. What is the value of x?
Answer:
The value of x is 56°
Step-by-step explanation:
Given that opposite angles in a cyclic quadrilateral is add up to 180°. So in order to find x, you have to write an expression in terms of x :
[tex]97 + x + 27 = 180[/tex]
[tex]x + 124 = 180[/tex]
Next you have to solve it by substracting 124 to both sides :
[tex]x + 124 - 124 = 180 - 124[/tex]
[tex]x = 56[/tex]
Multiply
(2x + 4)(2x - 4)
Answer:
4x^2 -16
Step-by-step explanation:
(2x + 4)(2x - 4)
FOIL
first:2x*2x = 4x^2
outer: -4 *2x = -8x
inner: 4*2x = 8x
last: -4*4 = -16
Add them together
4x^2 -8x+8x =-16
4x^2 -16
The multiplication of the expression (2x + 4)(2x - 4) is 4x² - 16.
What is the simplified form of the expression?Given the expression in the question:
(2x + 4)(2x - 4)
We can multiply the expression (2x + 4)(2x - 4) using the distributive property and the FOIL method.
(2x + 4)(2x - 4)
Apply the FOIL method:
2x( 2x - 4 ) + 4( 2x - 4 )
Apply distributive property:
2x × 2x + 2x × - 4 + 4 × 2x 4 × - 4
Multiply the terms:
4x² - 8x + 8x - 16
Collect and add like terms:
4x² - 16
Therefore, the simplified form is 4x² - 16.
Learn more about the FOIL method here: https://brainly.com/question/27980306
#SPJ6
a) Which of these numbers is 6 less than -11?
A) -5
B) -17
С) 17
D) 5
b) Which of these numbers is 34 less than -7?
A) -27
B) 27
C) -41
D) 41
Answer:
For the first on it is A) 17
For the second one it is B) 41 I hope cause I haven't done these in along time
Step-by-step explanation:
For the first on it's going to 17 because if you turn the less than sign into a minus sign you're going to get 6 - -11. You turn the two signs into a plus sign you get 6 + 11 and you add them you get 17
For the second one your going to the same thing you add 34 + 7 and you get 41
PLS I MARK BRAINLIEST I ONLY HAVE 30 MINS LEFT
You notice that another cupboard door is in the shape of a square that is divided into two isosceles triangles. You measure the height of the cupboard to be 16 "2" /"3" inches. What is the area of one of the triangles shown on the face of the cupboard door? Show your work AND I NEED TO KNOW HOW YOU DID IT IT SAYS SHOWYOUR WORK
When solving a word problem why is it important to check if the final answer makes sense for the problem?
can someone helpp ??
Answer:
21.24°
Step-by-step explanation:
I hope it helps :)
Darin skateboarded to the west at 8 m/s. In 7 seconds, he slowed down to 3
m/s. What was his acceleration?
O A. -1.4 m/s2 west
B. 1.4 m/s2 west
O C. -0.71 m/s2 west
D. 0.71 m/s2 west
Answer:
C) -0.71m/s²
Step-by-step explanation:
V = V0 + at
V = final veloctiy
V0 = Initial velocity
a = acceleration
t = time
3 = 9 + a7
-5 = a7
[tex]-\frac{5}{7}[/tex] = a
a ≅ -0,71
Answer:
C. -0.71 m/s2 west
Step-by-step explanation:
14) Simplify. 6(3x - 5) + 2(3x - 5) - 8(3x - 5)
Answer:
0
Step-by-step explanation:
To simplify you need to distribute then add like terms.
6(3x-5) + 2(3x-5) - 8(3x-5)
18x - 30 + 6x - 10 - 24x + 40
0x + 0
0
Answer:
6(3x - 5) + 2(3x - 5) - 8(3x - 5) = 0
Step-by-step explanation:
The expression is,
→ 6(3x - 5) + 2(3x - 5) - 8(3x - 5)
Now we have to,
→ Simplify the given expression.
Let's simplify the expression,
→ 6(3x - 5) + 2(3x - 5) - 8(3x - 5)
Applying Distributive property:
→ 6(3x) - 6(5) + 2(3x) - 2(5) - 8(3x) - 8(-5)
→ 18x - 30 + 6x - 10 - 24x + 40
Rearranging the expression:
→ 18x + 6x - 24x - 30 - 10 + 40
→ (18 + 6 - 24)x - (30 - 10 + 40)
→ 0x - 0
→ 0 => {final answer}
Therefore, the answer is 0.
Picture attached
A 15
B 41
C 20
D 30
Step-by-step explanation:
Find the distance between the line segments XY & YZ
XY = 4 units
YZ = 5 units
Use the following equation to solve for the hypotenuse of the triangle:
Hypotenuse = √(a² + b²)
Let: a = XY
b = YZ
Hypotenuse = √(4² + 5²)
Remember to follow PEMDAS. Solve the parenthesis first, and the powers first before adding:
Hypotenuse = √(16 + 25)
Hypotenuse = √(41)
B) 41 is your answer, if you keep it as c². However, if it is not, then none of your answer choices work, as the answer would be √41.
~
Which is correct?
O A. 463 < 437
OB. 763 > 746
OC. 674 < 643
OD. 734 > 743
O E. 634 > 647
Answer:
B
Step-by-step explanation:
763 is greater 746
Answer:
if my math is right its B
Part A The dot plot shows the daily lunch money of a group of students. Each dot represents one student. What is the mean daily pocket money? A $1.50 B $2.00 C $2.15 D $2.20 Part B What is the mode of the daily pocket money? Answer:
Answer:
Mean= $ 1.96
Mode= No mode
Step-by-step explanation:
Mean is the value obtained by dividing the sum of all the observations by their numbers.
Mean is obtained by dividing the total number of the values with the number of values.
Mean= x1+ x2+ x3 + x4/ 4
Mean = $ 1.5 + $ 2.0 + $ 2.15 + $ 2.20/4= 7.85/4= 1.9625or 1.963 or $ 1.96
Mode is the most frequent occurring value in a data set. But since all the values in the given set occur only once the data does not have any mode .
There is no mode because every value has the same frequency, that is it occurs the same number of times.
PLEAS HELP
At a car dealership, the sales records of weekdays and weekends were examined. Ten of the days examined were weekdays and 10 of them were weekend days. The following statistical information was calculated from the number of sales made during weekdays and weekends.
Weekday
Sales Weekend
Sales
Mean 15 18
Median 13 19
Mode 14 21
Range 10 13
Based on these samples, what generalization can be made?
A.
Not enough information is provided to draw any of these conclusions.
B.
More cars were sold on the weekdays than on the weekends.
C.
The same number of cars were sold on the weekends as on the weekdays.
D.
Less cars were sold on the weekdays than on the weekends.
Answer:
I believe it to be D
Step-by-step explanation:
PLEASE HALP!!!!
Carlos wants to get an average of 86% in his science class. The science
teacher has given 5 tests. Carlos's scores on 4 of the tests have been 85%,
89%, 90%, and 82%. What score does Carlos need to get on the 5th test to
get a mean score of 86%?
O A) 81
OB) 84
OC) 86
OD) 92
Answer:
The answer is B
Step-by-step explanation:
Answer:
B. 84
(85+89+90+82+x)/5=86
so x=84
Evaluate without using a calculator by using ratios in a reference triangle.
cos 5pi/3
Answer:
The answer is 1 /2
Step-by-step explanation:
Cos, tan and sin are all positive in the first quadrant, but depends on the direction of the angle. Reference angle here we are looking for is the one in relation to the quadrant cos 5pi/3.
Any multiples of cos outside 2nd quadrant will give a positive value.
cos 5pi/3 is located in the 4th quadrant, while, cos pi/3 is located in the 1st quadrant, where the cos ratio has a positive value.
In terms of cosine, anytime the angle falls on the first or fourth quadrant it will always produce a positive graph.
For cos 5pi/3, cos pi/3 and cos 7pi/3 will give the same answer as "1/2" or "0.5" because, cos pi/3 will give 60 degrees which fall in the first quadrant
If "R" is a real number, for all R multiplied by pi/3, the new value gives an angle in the first or fourth quadrant, the angle will be 0.5
The exact value of cos 5 ( π /3 ) is 1 /2 .
Given the regular square pyramid with RS = 6 and PX = 4, then XY=3.
True
False
Please help
Find the unknown radius of the circle. A measures 628 sq cm find r
Answer:
14.14 cm
Step-by-step explanation:
The formula for the area of a circle is : [tex]\pi *radius^2[/tex]
In order to find the radius you would first have to divide the area of 628 by pi, this gives you 200. This is because by dividing the area by pi it will leave us with the radius squared.
The next step is to find the square root of 200, this gives us 14.14. This is because by finding the square root it will leave us with the radius. The square root is another number that when multiplied by itself equals the number.
1) Divide 628 by pi.
[tex]628/\pi =200[/tex]
2) Find the square root of 200.
[tex]\sqrt{200}=14.14[/tex]
Pi as in 3.14
Find the volume of the planets
Answer:
can you show the planets. or do you want real planets volumes?
find the area of the composite figure
Answer:
Quickly learn how to find the Area of Composite Figures in today's geometry lesson. With 19 worked examples, you'll have everything you need ...
Step-by-step explanation:
Giving Brainliest to teh right answer! Come quick!
Answer:
x=65
Step-by-step explanation:
145 and 2x+15 are vertical angles meaning that they are congruent to each other. Subtract 15 from both sides, and divide by 2 giving x=65.
Hope this helps!
Your grandmother has given you $200 for your birthday! You decide to
use that money and start saving to buy a used car. The car costs $6500,
and you know that you can save $350 each month. How many months will
you need to save so that you can buy this car? (Don't forget you already
have $200 from your grandma) *
Answer:
18
Step-by-step explanation:
6500= 200+ 350x
x=18
Answer:
id say eighteen
Step-by-step explanation:
Find the area of the sector.
Answer:
Step-by-step explanation:
Area of sector = angle/360 * pi * r^2
r is 19m
37/360 * 22/7 * 19 * 19
Area = 116.61 m^2
does anyone know thisss
Answer:
Step-by-step explanation:
area of sector = angle/360 * pi * r^2
59.4 = angle/360 * 3.142 * 17.9^2
angle = 21.24
Answer:
21.24°
Step-by-step explanation:
I hope it helps:)
Set up as equal rates and solve. The distance from Pensacola, Florida to Tallahassee, Florida on a map is 8 inches, which represents 200 miles. How many miles is it from Pensacola to Miami if the distance on the map measures 27 inches?
We have been given that the distance from Pensacola, Florida to Tallahassee, Florida on a map is 8 inches, which represents 200 miles. We are asked to find the actual distance from Pensacola to Miami if the distance on the map measures 27 inches.
We will use proportions to solve our given problem as proportion states that ratio between two proportional quantities is similar.
[tex]\frac{\text{Actual distance}}{\text{Map distance}}=\frac{200\text{ miles}}{\text{8 inches}}[/tex]
[tex]\frac{\text{Actual distance}}{\text{27 inches}}=\frac{200\text{ miles}}{\text{8 inches}}[/tex]
[tex]\frac{\text{Actual distance}}{\text{27 inches}}\times \text{27 inches}=\frac{200\text{ miles}}{\text{8 inches}}\times \text{27 inches}[/tex]
[tex]\text{Actual distance}=\frac{25\text{ miles}}{1}\times 27[/tex]
[tex]\text{Actual distance}=675\text{ miles}[/tex]
Therefore, the actual distance from Pensacola to Miami is 675 miles.
A pitcher can hold 8 times as much as a glass. The pitcher holds 64 ounces.
Which model shows this comparison?
54 ounces
Glass ?
Pitcher ??????
Glass ?| ?| ?| ?| ?| ?| ?| ?
Pitcher ?
54 ounces
3 ounces
Glass ????
Preher ????
Glass
Pitcher
54 ounces
84 ounces
Answer:
Im guessing this i might be wrong
54 ounces
3 ounces
Step-by-step explanation:
Answer:
To be honest i think 54 ounces and 3 ounces
Step-by-step explanation:
i was going to say 54 and 84 but i said to myself that didn't make any sense if it is 84 let me know plz
Hope this helpsHope this is right