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
Find the length of arc KN.
can a genius help me??please
Answer:
Length KN = 2π/3 = 2.094
Step-by-step explanation:
Length KN = (mKN/360)2πr
Length KN = (40/360)2π3
Length KN = (1/9)6π
Length KN = 6π/9
Length KN = 2π/3 = 2.094
A square pyramid has a base with a total area of 144 m2 and the volume of 384m3, what is the slant height of the pyramid
Answer:
8mStep-by-step explanation:
Volume of a square based pyramid is expressed as [tex]V = a^{2} \frac{h}{3}[/tex] where;
a is the base edge
a² is the base area
h is the slant height
Given Volume of the pyramid V = 384m³
Base area a² = 144m²
h =?
On substituting to get the slant height;
[tex]384 = 144*\frac{h}{3}\\ 1152 = 144h\\h = \frac{1152}{144} \\h = 8m[/tex]
The slant height of the pyramid is 8m
write the equation of circle b with center B(-2,3) that passes through (1,2)
Answer:
[tex](x+2)^2 + (y-3)^2 = 10[/tex]
Step-by-step explanation:
The standard equation for circle is
[tex](x-a)^2 + (y-b)^2 = r^2[/tex]
where point (a,b) is coordinate of center of circle and r is the radius.
______________________________________________________
Given
center of circle =((-2,3)
let r be the radius of circle
Plugging in this value of center in standard equation for circle given above we have
[tex](x-a)^2 + (y-b)^2 = r^2 \ substitute (a,b) \ with (-2,3) \\=>(x-(-2))^2 + (y-3)^2 = r^2 \\=>(x+2)^2 + (y-3)^2 = r^2 (1)[/tex]
Given that point (1,2 ) passes through circle. Hence this point will satisfy the above equation of circle.
Plugging in the point (1,2 ) in equation 1 we have
[tex]\\=>(x+2)^2 + (y-3)^2 = r^2 \\=> (1+2)^2 + (2-3)^2 = r^2\\=> 3^2 + (-1)^2 = r^2\\=> 9 + 1 = r^2\\=> 10 = r^2\\=> r^2 = 10\\[/tex]
now we have value of r^2 = 10, substituting this in equation 1 we have
Thus complete equation of circle is [tex]=>(x+2)^2 + (y-3)^2 = r^2\\=>(x+2)^2 + (y-3)^2 = 10[/tex]
The polynomial f(x) is written in factored form:
f(x) = (x - 3)(x + 8)(x - 11)
What are the zeros of the polynomial function?
O x = 3, x = 8, x = 11
O x = 3, x = -8, x = 11
OX=-3, x = 8, X = -11
x = -3, x = 3, x = -8, x = 8, x= -11, x = 11
Answer:
F(x)=(x-3)(x+8)(x-11)=0
(x-3)=0, (x+8)=0, (x-11)=0
X=3
X=-8
X=11
Can someone help me with this? ;^;
Answer:
The mode would be 10
Step-by-step explanation:
Because it is there more than the others
hope this helps! =D
Answer:
10
Step-by-step explanation:
Doug is a dog, and his friend Bert is a bird. They live in Salt Lake City, where the streets are 1/16 miles apart and arranged in a
square grid (see map). They are both standing at the corner of 6th avenue and L street. Doug can run at an average speed of 30
mi/hr through the streets of Salt Lake, and Bert can fly at an average speed of 20 mi/hr. They are about to race to the corner of
10th avenue and Estreet. who would win and why?
No map given but it shouldn't matter.
E is the 5th letter, L the 12th.
Start at S(6,12). End at E(10,5)
The vector between them, E-S=(4,-7)
Each unit is 1/16 of a mile, though that probably doesn't matter that much.
Doug has to stay on the grid, so has to run |4|+|7|=11 units. At 30 mi/hr that takes (11/16)/30 = 0.022916 hours.
Bert can go diagonally, so flies √(4²+7²)=√65 ≈ 8.06 units. At 20 mi/hr that takes (8.06/16)/20 = 0.025194 hours.
Answer: Doug wins
Why? Because it's quicker to cover 4+7 at 30 mph than it is to cover √(4²+7²) at 20 mph. That is, Doug is 1.5 times faster and the 1.5 times the diagonal distance is more than the grid distance.
Answer:
Doug wins. He finishes in 1.38 minutes. Bert takes 1.51 minutes.
Step-by-step explanation:
Each city block is a square 1/16 mile by 1/16 mile.
From 6th Av and L Street to 10th Av and E Street, they need to go 4 avenues and 7 streets over. These two distances along blocks are the legs of a right triangle. The right triangle has legs of length 4 * 1/16 mile and 7 * 1/16 mile.
leg1 = 4 * 1/16 mile = 0.25 mile
leg2 = 7 * 1.16 mile = 0.4375 mile
The hypotenuse of the right triangle can be calculated by the Pythagorean theorem.
a^2 + b^2 = c^2
(0.25 mile)^2 + (0.4375 mile)^2 = c^2
c = 0.50389
The direct distance from one corner to the other is 0.50389 miles.
The bird travels this distance since the bird can fly above the streets.
The dog has to travel along the legs of right triangle by running in the streets and avenues. The dog travels 0.25 mile + 0.4375 mile = 0.6875 miles
Now we need to see what takes less time:
Bird: distance of 0.50389 miles at 20 mph, or
Dog: distance of 0.6875 miles at 30 mph
We start with the formula for speed:
speed = distance/time
s = dt
Now we solve it for time:
st = d
t = d/s
Time equals distance divided by speed.
Now we find the times for the bird and for the dog.
Bird:
t = d/s = (0.50389 mi)/(20 mi/h) = 0.02519 hours = 1.51 minutes
Dog:
t = d/s = (0.6875 mi)/(30 mi/h) = 0.0229 hours = 1.38 minutes
The bird takes 1.51 minutes, and the dog takes 1.38 minutes.
The dog takes less time to get there, so the dog wins.
What factors do 6 and 12 have in common?
Answer:
6x^2 im pretty sure thats whats its asking for
Step-by-step explanation:
NEED HELP WITH THIS ASAP
Answer:
D; y= 2.52x
Step-by-step explanation:
You half $5.04 (the cost of two lbs of cranberries) and get $2.52 then multiply by x (the lbs.) equals y the cost of all the lbs. of cranberries.
Therefore getting the equation of y= 2.52x
Answer: y=2.52x
Step-by-step explanation:
if you take any of the statements you can calculate it.
Let "x" be pounds, and "y" the total cost of x pounds.
2x=5.04
Divide by 2
x=5.04/2
x=2.52
4) The diameter of a circle is 32m. The radius is represented by 4(x + 2).
Part A: Write an equation you can use to find the value of x.
Part B: What is the value of x?
Answer:
The value of x is 2
Step-by-step explanation:
Diameter = 2r -------------------------------------------------------------------(1)
where r is the radius
The value of the diameter = 32 m and radius is given to be 4(x+2)
substitute the above into equation (1) and then solve for x
32 = 2 [ 4(x + 2)]
first open the inner bracket
32 = 2[4x + 8}
then open the outer bracket
32 = 8x + 16
subtract 16 from both-side of the equation
32 - 16 = 8x +16 - 16
16 = 8x
Divide both-side of the equation by 8
16/8 = 8x/8
2 = x
x = 2
Therefore, the value of x is 2
find x and y i will give brainliest
Answer: N= 135, M=45.
Step-by-step explanation:The formula to find the degree inside of a shape is: (n-2)180. This is an octagon, so it has 8 sides, plug this in for n.
8-2 * 180
1080 divide by 8 to get the value of n
n=135
The formula for an angle outside of the shape is:
360/n n is still eight, so plug this in for n
360/8
m=45
Answer:
n = 135 degrees ( ° ) ,
m = 45 degrees ( ° )
Step-by-step explanation:
* Sorry I didn't answer this before *
1. In this figure we can see that this visual is a representation of an octagon, provided it's 8 sides.
2. Knowing this, let us split this figure into triangle 180 degrees each ⇒ compute the total interior angles in degrees.
3. If you were to draw lines from one vertex to any other non-adjacent vertices, it would be that 6 triangles are formed.
4. One triangle ⇒ 180 degrees ( ° ) so that this octagon ⇒ 180° * number of triangles, or ⇒ 180 * 6 = 1080°
5. Knowing that this shape is a regular polygon, all angles are congruent such that if x represents one interior angle ⇒ 8x = 1080, ⇒ x = 135°. As n acts as one of the interior angles in this figure ⇒ n = 135 degrees ( ° )
6. Now through supplementary angles, the interior angle adjacent to angle m would form a linear pair, adding to 180°.
7. This would mean that m + interior angle = 180, and as all interior angles were found to be 135 degrees ⇒ m + 132 = 180 ⇒ m = 45 degrees ( ° )
What type of graph does not show the mean?
The misleading one or the one that miss out information.
"Mean" Means the middle number of the total number. Like add all the number in the graph and divide by 2
Answer:
A bar graph.
Step-by-step explanation:
Because a bar graph is a chart used to represent data visually using bars of different heights or lengths.
What is the solution to the equation ^3sqrtX+4+ ^3sqrt2X+8=0?
x = –12
x = –4
x = 4
x = 12
Answer:
Cover 2
Step-by-step explanation:
Answer:
Uhh x is like -4 bruh
Step-by-step explanation:
So b on edge ye
Find the hypotenuse of each Isosceles right triangle when the legs are of the given measure.
Given = 6squareroot2
Answer:
12
Step-by-step explanation:
We can use the pythagorean theorem giving us:
a^2+b^2=c^2
(6sqr2)^2 + (6sqr2)^2 = c^2
72+72=c^2
144=c^2
12=c
Simplify 5(x – 7) + 6x.
Answer:
11x -35
Step-by-step explanation:
5(x – 7) + 6x.
Distribute
5x - 35 +6x
Combine like terms
11x -35
Answer:
11x-35
is the answer
What is the volume of the pyramid h=9.6 l=8.5 w=8.5
Answer:
V = 231.2
Step-by-step explanation:
v = (l * w * h )/3
Answer:
V ≈ 231.2
Step-by-step explanation:
Using the formula: V = 1/3 x L x W x H
What number should both sides of the following equation be multiplied by to solve for x?
x/7.25 = 4
4
7.25
7
29
Answer:
[tex] \frac{x}{7.25} = 4 \\ x = 4 \times 7.25 \\ x = 29[/tex]
Brett is comparing the graphs of y = 2X and y = 5x. Which statement is true?
The correct question is:
Brett is comparing the graphs of y = 2^x and y = 5^x. Which statement is true?
(1) The y-intercept of y = 2^x is (0,2), and the y-intercept of y = 5^x
is (0,5). [
(2) Both graphs have a y-intercept of (0,1), and y = 2^x is steeper.
(3) Both graphs have a y-intercept of (0,1), and y = 5^x is steeper.
(4) Neither graph has a y-intercept.
Answer:
(2) and (3) are true.
Step-by-step explanation:
The correct options are:
(2) Both graphs have a y-intercept of (0,1), and y = 2^x is steeper. Since X < 0
(3) Both graphs have a y-intercept of (0,1), and y = 5^x is steeper. Since X > 0
A person purchases items marked $2.95, $12.99, $6.97, and $4.19. What is the total cost of these purchases including 6% sales tax
The cost of a shirt is $56. There is a markup of 18%
for the store. Wha t will be the cost of the shirt in the
store?
Answer:
66.08
Step-by-step explanation:
First find the markup
56 * 18%
56*.18 =10.08
Add this to the original price
56+10.08
66.08
This is the cost in the store
Answer:
$66.08
Step-by-step explanation:
18% of 56= 10.08
56+10.08=66.08
hope this helps :)
Which ordered par Woud form a proportional relationship with the point graphed Below?
A (10,10)
B (25,35)
C (70,50)
D (90,60)
pls help will mark as brainliest
Answer:
1/3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
It would have to be 3, because it says that 1/3 is wrong.
A painter pays $15 per can of paint. How many cans of paint can she buy with $1052
Answer:
70 cans
Step-by-step explanation:
1052/15=70.1333333
but you have to round down to 70
ANSWER: 70
EXPLANATION:
many organize a classroom party. there are 20 of cold drinks at the party, 13 of which contain diet Pepsi, what is the probability that randomly selected drink will be a diet Pepsi? answer key
Answer:
so its either 13/20
Step-by-step explanation:
if you get this wrong sorry:(
Help help help me me me
Step-by-step explanation:
...
the answer is 49/40
A rectangle has a height of 7a^2 and a width of a^4+5a^2+4.
Express the area of the entire rectangle.
Can someone helpppppppppp
Answer:
A
Step-by-step explanation:
The reason it is A is because
It goes in biggest to lowest A B C D
C and B don't follow that so we are left with A and D
In answer D C and B are too close in percentage therefore it cannot be D
Therefore your answer is A
Hope this helped!
Find the area to the nearest hundredth
Answer:
9.0586 OR
9.06
Step-by-step explanation:
IDK, used fusion 360
Does the function model exponential growth or decay?
h(t) = 0.25 - 1.5t
A.) growth
B.) decay
Answer: it’s growth
Step-by-step explanation:
Sal is tiling his entryway. The floor plan is drawn on a unit grid. Each unit length represents 1 foot. Tile costs $1.85 per square foot. How much will Sal pay to tile his entryway? Round your answer to the nearest cent.
Answer:
$80.48
Attached is the image of the entry way
Step-by-step explanation:
Given that each unit length represents 1 foot.
To find the area of the shape shown in the attached image, we need to divide the shape into two parts at about 4 ft from the bottom.
The top shape is a trapezoid of base length 4 ft, top length 7 ftand height 5 ft, while the bottom shape is a parallelogram with one side equal to 4 ft and height 4 ft
Area of a Trapezium = 1/2 × (a+b)h
a = 4ft, b= 7ft, h = 5ft
Substituting the values;
Area of trapezoid = 1/2 × (7 + 4)x 5
Area of trapezoid = 27.5 ft^2
Area of a parallelogram = length × height
Length = 4 ft, height = 4 ft
Substituting the values;
Area of parallelogram = 4 x 4
Area of parallelogram = 16 ft^2
Total area = area of trapezium + parallelogram
Total area = 27.5 + 16 = 43.5 ft^2
Cost per square foot = $ 1.85
Total cost = cost per square foot × area
Total cost = $1.85 per square foot × 43.5ft^2
Total Cost = $80.48
Answer:
Sal will pay $ 80.48 to tile his entryway.
Step-by-step explanation:
Separate the entryway into simpler shapes: a trapezoid and a parallelogram.
Find the area of the simpler figures. Count units to find the dimensions.
Trapezoid
A = 1/ 2
h(b₁ + b₂)
A = 1/ 2
(5)(4 + 7)
A = 1/ 2
(5)(11)
A = 27.5
The area of the trapezoid is 27.5 ft
2 .
Parallelogram
A = bh
A = 4 · 4
A = 16
The area of the parallelogram is 16 ft
2 .
Find the area of the entryway.
A = 27.5 + 16
A = 43.5
The area of the entryway is 43.5 ft
2 .
Calculate how much Sal will pay to tile his entryway.
Area · Cost per foot = Total Cost
43.5 · $1.95 = $84.83
Sal will pay $84.83 to tile his entryway.
Find the interquartile range (IQR) of the data in the box plot below.
Asap ASAP Please PLZ
Answer:
3
Step-by-step explanation:
IQR is the difference between the upper and lower medians so the IQR = 7 - 4 = 3
The interquartile range (IQR) of the data in the given box plot is: 3.
What is the Interquartile Range (IQR) of a Data?In a box plot, the interquartile range (IQR) is the difference between the upper quartile and the lower quartile which are represented as each edge of the rectangular box.
Upper quartile = 7Lower quartile = 4Interquartile range (IQR) = 7 - 4
Interquartile range (IQR) = 3
Learn more about Interquartile range (IQR) on:
https://brainly.com/question/17083142
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