write an equation that represents the situation in the table?
x: y:
6 122
10 170
15 230
28 336
Answers
.. y = -0.00971251x^3 +0.301088x^2 +9.08625x +58.7413
This function agrees with the table when rounded to 3 decimal places.
Related Questions
Find the zeros K(x) = -x²+ 2x + 15 EXPLAIN EVERY STEP!
Answers
k(x) = -1(x^2 - 2x - 15) Now factor what's inside the brackets. The numbers you pick must add to - 2 and multiply to -15.
When you multiply to -15 you should note that one of the numbers is plus and the other is minus.
(x - )(x + ) is the way it looks.
They differ by 2 and the "largest" one is minus. That means your answer is -5 and +3
k(x) = - (x - 5)(x + 3)
Now for the zeros.
x - 5 can be a zero
x - 5 = 0
x = 5
x + 3 = 0
x = - 3
WILL GIVE A BRAINLEST
What is the solution of x+4/2x-1<0 ?
Answers
To solve the inequality x + 4/2x - 1 < 0, first find the critical value x = 1/2. Then, test the intervals to determine the solution set x < 1/2.
To find the solution of the inequality x + 4/2x - 1 < 0, we can follow these steps:
First, find the critical values by setting the denominator, 2x - 1, equal to zero and solve for x. The critical value is x = 1/2.
Next, test the intervals created by the critical value in the original inequality x + 4/2x - 1 < 0. This helps determine the solution set which is x < 1/2.
NEED HELP PLEASE :) ONLY 100% ANSWERS
1) An Egyptian pyramid has a square base that measures 80 meters on each side. If the height of the pyramid is 30 meters, what is the slant height of the pyramid?
2) A room in a bank is shaped like the rectangular prism shown below. The room has a security system that is triggered by two laser beams which stretch from Point A to D and Point B to C. How many total feet of laser beams are there?
*A 3-D rectangle 15 ft. length the back rectangle 12 ft. width the side 35 ft. width front*
Answers
Answer:
1) the slant height of the pyramid is 50 meters.
2) there are (approximately) a total of 80 ft of laser beams.
Step-by-step explanation:
1) The height of the pyramid (30 m) and half of the length of its base (40 m) form a rectangular triangle, where the slant height is its hypotenuse (H). From Pythagorean theorem:
H^2 = 30^2 + 40^2
H = √2500
H = 50 m
2) In the figure attached the rectangular prism is shown (point E was added).
The length of the laser beams is the addition of the segments AD to segment CB (which are equal).
We can make a rectangular triangle between points ECD. From Pythagorean theorem:
ED^2 = EC^2 + CD^2
ED = √(12^2 + 35^2)
ED = 37 ft
We can make a rectangular triangle between points AED. From Pythagorean theorem:
AD^2 = EA^2 + ED^2
AD = √(15^2 + 37^2)
AD ≈ 40
Then, there are (approximately) a total of 80 ft of laser beams.
PLZ HELP!!!! 43 POINTS!!!!! Koji is installing a rectangular window in an office building. The window is 8 2/3 ft wide and 5 3/4 ft high. The formula for the area of a rectangle is A=bh. What is the area of the window?
Answers
multiply 8 and 2/3 by 5 and 3/4!
On a map, 1.5 centimeters represents a distance of 45 kilometers. If two points on the map are 0.8 centimeters apart, what is the actual distance between the two points?
Answers
centimeters / kilometers
1.5 / 45 = 0.8 / x
cross multiply
(1.5 * x ) = (45 * 0.8)
1.5x = 36
divide both sides by 1.5
x = 24
The actual distance between the two points is 24 kilometers.
Hope this helps
Find the volume of the prism. 1,728 cu. in. 864 cu. in. 288 cu. in.
Answers
you multiply 12 by 12 by 12
Volume of cube is given by the formula :
[tex] Volume = a * a * a [/tex]
Where a is edge of the cube.
We are given edge of cube as 12 inches.
Plugging the value of edge in given formula:
[tex] Volume = 12 * 12 * 12 [/tex]
Volume = 1728 cubic inches.
Answer : Volume of cube is 1728 cubic inches.
Volume of cube is given by the formula :
[tex] Volume = a * a * a [/tex]
Where a is edge of the cube.
We are given edge of cube as 12 inches.
Plugging the value of edge in given formula:
[tex] Volume = 12 * 12 * 12 [/tex]
Volume = 1728 cubic inches.
Answer : Volume of cube is 1728 cubic inches.
I need more math help, the!
Cement truck A can pour 200 cubic ft of concrete in 20 minutes. It only takes truck B 15 minutes to do the same job. If they both work together,how long will it take them to pour the 200 cubic feet?
I need help setting up the problem and solving it, thank you!
Answers
Track B takes 15 minutes
In 1 minute track be will do a fraction of 1/20, while track B will do 1/15
Both tracks in a minute = 1/20+1/15
= 35/300
Therefore the two tracks will take 300/35 minutes to fill the 200 cubic feet
That is 300/35
= 8.57 minutes
≈ 9 minutes
Kohl's sells casual shirts for $9 and polo shirts for $18.00. Total sales were $1,080, and customers bought 4 times as many casual as polo shirts. How many casual shirts did Kohl's sell?
a. 40
b. 12
c. 20
d. 60
Answers
60
please correct e if im wrong
He first three terms of a geometric sequence are as follows. 10 , 30 , 90 find the next two terms of this sequence.+
Answers
30*3=90
90*3=270
270*3=810
or
10*3^1=30
10*3^2=90
10*3^3=270
10*3^4=810
the next two terms of this sequence are 270 and 810.
The next two terms of the given geometric sequence is 810.
The first three terms of a geometric sequence are 10, 30, 90.
What is a geometric sequence?A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.
The formula to find nth term of the geometric sequence is [tex]a_n = ar^{n - 1[/tex].
Where, a = first term of the sequence, r= common ratio and n = number of terms.
Here, the common ratio is 30/10 = 90/30 = 3
Now, [tex]a_4=10\times 3^{4-1}[/tex]
= 10 × 3³
= 270
[tex]a_5=10\times 3^{5-1}[/tex]
= 810
Therefore, the next two terms of the given geometric sequence is 810.
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Nicholas used a $10 bill to pay for a granola bar that only costs p dollars. How much change did Nicholas receive from the cashier?
Answers
Nicholas would have spent $p, so he has $p less than $10!
equation that passes through the points (-1,0)(0,2)
Answers
2. Plug the slope you found in step 1, one of the given points, and plug both into the point-slope formula.
The point-slope formula is:
y - y_1 = m(x - x_1)
3. Solve the point-slope formula for y.
Your final answer must be in the form
y = mx + b
Use the diagram to complete the statement. Given JKL, sin(38) equals—
(Diagram is a right triangle. Angle K is 52 degrees and angle L is 38)
cos(38)
cos(52)
tan(38)
tan(52)
Answers
sin(38) = 0.61566......
cos(52) = 0.61566......
Answer:
Answer is b
Step-by-step explanation:
y+2=−2(x−3)
Slope from equation
Problem
What is the slope of the line?
Answers
y = -2x + 4
The slope of the line is -2.
Please find below the given equation-
y + 2 = -2 ( x - 3 )
y + 2 = -2 x - 2(- 3)
y + 2 = -2 x + 6
y = -2 x + 6 - 2
y = -2 x + 4
Let's compare this equation with the form y = mx +c
By comparing we get,
m = -2 and c = 4
We know, in y = mx + c , slope of the line is given by m
Here m = -2, as discussed above
Therefore the slope of the given line is -2
Hope it helps ..!!
Need help ASAP WILL GIVE TEN POINTS FIVE QUESTIONS-
1
What is the solution to the inequality?
6x−5>−29
A x>−4
B x<4
C x>4
D x<−4
2
What is the solution to the inequality?
−4x−8>−20
A x>3
B x>−3
C x<−3
D x<3
3Solve.
−4.2y+2.1>−2.52
Drag and drop a number or symbol into each box to show the solution.
< > 0.1 1.1 4.62 −4.62
Y.(number) (number)
4 Solve.
−12x+13>35
Drag and drop a number or symbol into each box to show the solution.
< > −8/15 −4/15 4/15 8/15
x (number) (number)
What is the solution set?
−2.8x+5.6<8.4
Enter your answer in the box.
x (answer) plz help and ty
Answers
1) x>-4
2)x<3
3)y<1.1
4)x<-11/6
5)x>-1
HOPE THIS HELP
Answer:
Part 1) Option A [tex]x>-4[/tex]
Part 2) Option D [tex]x<3[/tex]
Part 3) [tex]y < 1.1[/tex]
Part 4) [tex]x<-8/15[/tex]
Part 5) [tex]x>-1[/tex]
Step-by-step explanation:
Part 1) we have
[tex]6x-5>-29[/tex]
[tex]6x>-29+5[/tex]
[tex]x>-24/6[/tex]
[tex]x>-4[/tex]
Part 2) we have
[tex]-4x-8>-20[/tex]
[tex]-4x>-20+8[/tex]
[tex]-4x>-12[/tex] -----> Multiply by [tex]-1[/tex] both sides
[tex]4x<12[/tex]
[tex]x<12/4[/tex]
[tex]x<3[/tex]
Part 3) we have
[tex]-4.2y+2.1 >-2.52[/tex]
[tex]-4.2y >-2.52-2.1[/tex]
[tex]-4.2y >-4.62[/tex] ----> Multiply by [tex]-1[/tex] both sides
[tex]4.2y < 4.62[/tex]
[tex]y < 1.1[/tex]
Part 4) we have
[tex]-(1/2)x+(1/3)>3/5[/tex]
[tex]-1/2x>(3/5)-(1/3)[/tex]
[tex]-1/2x>4/15[/tex] ---> Multiply by [tex]-1[/tex] both sides
[tex]1/2x<-4/15[/tex]
[tex]x<-8/15[/tex]
Part 5) we have
[tex]-2.8x+5.6< 8.4[/tex]
[tex]-2.8x< 8.4-5.6[/tex]
[tex]-2.8x< 2.8[/tex] ---> Multiply by [tex]-1[/tex] both sides
[tex]2.8x>-2.8[/tex]
[tex]x>-2.8/2.8[/tex]
[tex]x>-1[/tex]
When you add two rational numbers, each number can be written as a?
Answers
When you add two rational numbers, each number can be written as a
✔ fraction .
Step-by-step explanation:
When you add two rational numbers, each number can be written as a fraction.
What is a rational number?A Rational number can be defined as any number which can be represented in the form of p/q where q ≠ 0. It can be made by dividing an integer by an integer.
For the given situation,
The sum of two rational numbers is rational.
The closure property of addition of rational number states that if we add two rational number, then the sum of these two rational number will also be a rational number.
Adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication.
Hence we can conclude that when you add two rational numbers, each number can be written as a fraction.
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help me, please............
Answers
-3/x
In the diagram a || b. Use the diagram to answer the question. (Diagram not to scale.) Name the interior angle to 7
A. 1
B. 2
C. 6
D. 4
Answers
Let f(x)=x2+14x+48. What are the zeros of the function? Enter your answers in the boxes.
Answers
[tex] x^{2} +14x+48=(x+6)(x+8)[/tex]
Since we are trying to find the zeroes of the function, we are going to set each one of our factored binomial equal to zero and solve for x:
[tex]x+6=0[/tex]
[tex]x=-6[/tex]
and
[tex]x+8=0[/tex]
[tex]x=-8[/tex]
We can conclude that the zeroes of the function [tex]f(x)= x^{2} +14x+48[/tex] are [tex]x=-6[/tex] and [tex]x=-8[/tex].
Answer:x= -6 and -8
Step-by-step explanation: I took the test
Write an algebraic expression for the verbal description. the sum of two consecutive natural numbers, the first of which is n
Answers
n + (n + 1)
hope this helps
If the first number is n and the second number is n+1, then you are writing [tex]n+(n+1)=2n+1[/tex].
the distance light travels in one second (one light-second) is about 1.86 x 10^5 miles. Saturn is about 475 light-seconds from the sun. About how many miles from the sun is saturn?
Answers
Saturn is 475 light seconds away from the sun. Using this information we are asked to find the distance saturn is away from the sun.
1 light second - 1.86 x 10^5 miles
Therefore 475 light seconds -1.86 x 10^5 miles/light second * 475 light seconds
= 8.83 x 10^7 miles
Saturn is 8.83 x 10^7 miles away from the sun
Answer:
Step-by-step explanation:
Given that the distance light travels in one light second about
[tex]1.86(10^5) miles[/tex]
Distance of Saturn from Sun = Time taken for travel x speed
Here speed = [tex]1.86 x 10^5[/tex]
Time taken = 475 light seconds
Hence distance = [tex]1.86 x 10^5x475\\=883.5x10^5\\=8.835x10^7[/tex] miles
What is the maximum number of distinct lines that can be drawn through 10 distinct points if no 3 of the points are collinear?
Answers
.. 10*9/(2*1) = 45 ways
45 distinct lines can be drawn
Jacey obtains a 30-year 6/2 ARM at 4% with a 2/6 cap structure in the amount of $224,500. What is the monthly payment during the initial period?
Answers
where
[tex]m[/tex] is the monthly payment
[tex]P[/tex] is the amount
[tex]r[/tex] is the interest rate in decimal form
[tex]t[/tex] is the number years
First we need to convert our interest rate of 4% to decimal form by dividing it by 100%:
[tex] \frac{4}{100} =0.04[/tex]
We also know from our question that [tex]P=224500[/tex] and [tex]t=30[/tex], so lets replace those values into our formula to find the monthly payment:
[tex]m= \frac{224500( \frac{0.04}{12}) }{1-(1+ \frac{0.04}{12})^{-(12)(30)} } [/tex]
[tex]m=1071.80[/tex]
We can conclude that the monthly payment during the initial period is $1071.58
Solve the following equation. Then place the correct number in the box provided. 9(x - 6) = 8(x + 6)
x=
Answers
9(x - 6) = 8(x + 6)
The first step to take here is to apply the Distributive Property, which is
a(b + c) = ab + ac.
9(x - 6) = 8(x + 6)
9x - 54 = 8x + 48
After this, you want to begin to eliminate terms to ultimately isolate x; you can subtract 8x from both sides first:
9x - 54 = 8x + 48
x - 54 = 48
Finally, add 54 to both sides to get x by itself:
x - 54 = 48
x = 102
Answer:
x = 102
9(x -6) = 8(x+6)
9x - 54= 8x +48
x- 54= 48
x= 102
22.6 is an outlier for which of the following sets of data?
1. 22.6, 21.5, 23.7, 22.6, 28.9, 22.6, 20.9
2. 2.4, 5.3, 3.5, 22.6, 1.8, 2.1, 4.6, 1.9
3. 20.5, 20.8, 21.6, 22.6, 23.7, 24.5, 25.1
4. 13.6, 31.7, 25.8, 22.6, 18.9, 21.6, 30.5
Answers
Step-by-step explanation: B
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle A?
Enter your answer in the box.
°
Answers
Remember that the angles opposite of each other equal to 180. So a+c=180 and b+d=180.
First, we solve for x. Since we know that b and d equal to 180, we subtract 148 from 180.
180-148=32. x=32.
Then we plug that in the expression for angle a.
2x+1 becomes 2(32)+1
2*32=64
64+1=65.
a=65
As cars passed a checkpoint, the following speeds were clocked and recorded. Speed (mph): 55 62 61 54 68 72 59 61 70
What are the minimum, first quartile, median, third quartile, and maximum of the data set? Show your work.
Answers
We have ---- > 55, 62, 61, 54, 68, 72, 59 ,61, 70
In total 9 numbers
step 1
order the numbers from smallest to largest
54,55,59,61,61,62,68,70,72
1) What is the minimum of the data set ?
The lowest number is the minimum------------ > 54
2) What is the median of the data set ?
Find the number that is in the middle
54,55,59,61,61,62,68,70,72
The middle number is 61. That is the median.
Find the middle of each half. Since these numbers are between 2 numbers, you average the numbers (add then divide by 2).
55+59=114/2=57 This is the first quartile.
68+70=138/2=69 This is the third quartile
3) What is the first quartile of the data set ?
the answer is 57
4) What is the third quartile of the data set ?
the answer is 69
5) What is the maximum of the data set ?
The highest is the maximum------------ > 72
Answer:
Minimum = 54
Maximum = 72
Median = 61
First quartile = 57
Third quartile = 69
Step-by-step explanation:
Data : 55 62 61 54 68 72 59 61 70
Arrange the data is ascending order
54 , 55, 59, 61,61 ,62 , 68,70 ,72
So, minimum = 54
Maximum = 72
Median is the mid value .
There are nine observations.
So, 5th observation is the median
So, Median = 61
First quartile = It is the median of data of the left side data of the median .
Left side data : 54 , 55, 59, 61
There are four observations
Median = [tex]\frac{\frac{n}{2}th+(\frac{n}{2}+1)th}{2}[/tex]
Median = [tex]\frac{\frac{4}{2}th+(\frac{4}{2}+1)th}{2}[/tex]
Median = [tex]\frac{2th+3rd}{2}[/tex]
Median = [tex]\frac{55+59}{2}[/tex]
Median = [tex]57[/tex]
First quartile = 57
Third quartile = It is the median of data of the right side data of the median .
Right side data : 62 , 68,70 ,72
There are four observations
Median = [tex]\frac{\frac{n}{2}th+(\frac{n}{2}+1)th}{2}[/tex]
Median = [tex]\frac{\frac{4}{2}th+(\frac{4}{2}+1)th}{2}[/tex]
Median = [tex]\frac{2th+3rd}{2}[/tex]
Median = [tex]\frac{68+70}{2}[/tex]
Median = [tex]69[/tex]
Third quartile = 69
Hence minimum is 54 , maximum is 72 ,median is 61 , first quartile is 57 and third quartile is 69
A toy rocket is launched from a platform 42 feet above the ground at a speed of 91 feet per second. The height of the rocket in feet is given by the polynomial −16t^2 + 91t + 42, where t is the time in seconds. How high will the rocket be after 3 seconds? HELP ASAP!!
A. 122 feetB. 218 feetC. 93 feetD. 2570 feet
Answers
height = -16t² + 91t + 42
After 3 sec means, t = 3, so we substitute t with 3
H = -16(3)² + 91(3) + 42
= -144 + 273 + 42
= 171 feet
The height of the rocket after 3 seconds is 171 feet.
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
The height = -16t² + 91t + 42
After 3 sec means, t = 3, so we substitute t with 3
In order to find the height of the rocket after t seconds we plugin t = 3 in the function.
height H = -16t² + 91t + 42
H = -16(3)² + 91(3) + 42
= -144 + 273 + 42
= 171 feet
Thus, the height of the rocket after 3 seconds = 171 feet.
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If two figures are congruent, their perimeters are equal true or false?
Answers
WILL GIVE A BRAINLEST!!!!!!!!!!
Which is true about the statements
The graph of f(x) has a vertex of (–4, 6).
The graph of f(x) is horizontally stretched.
The graph of f(x) opens upward.
The graph of f(x) has a domain of x <=–6.
Answers
hope this helps<3
Answer: B) The graph of f(x) is horizontally stretched.
Step-by-step explanation: We are given an absolute function [tex]f(x)=-\frac{2}{3} |x+4|-6[/tex].
The standard equation of an absolute function is [tex]f(x)= a|x-h|+k[/tex].
Where (h,k) is the vertex of the absolute function.
If we compare [tex]f(x)=-\frac{2}{3} |x+4|-6[/tex] and [tex]f(x)= a|x-h|+k[/tex], we can see a=[tex]-\frac{2}{3}[/tex], h= -4 and h= -6.
Therefore, vertex of the given function is (-4,-6).Because we have value of a is a negative number so it would open down.An absolute function always have domain " All real numbers".Therefore, first, third and fourth options are incorrect.
So, the second option would only be applicable.
B) The graph of f(x) is horizontally stretched.Use inductive reasoning to find the next term in the sequence 1, 2, 4, 7, 11, 16… what is the next term?
a. 18
b. 19
c. 22
d. 26
Answers
[tex]u_1=1\\ u_2=2\\ u_3=4\\ u_4=7\\ u_5=11\\ u_6=16\\ u_2-u_1=2-1=1\\ u_3-u_2=4-2=2\\ u_4-u_3=7-4=3\\ u_5-u_4=11-7=4\\ u_6-u_5=16-11=5\\ ... u_n-u_{n-1}=n-1\\ \boxed{u_n=u_{n-1}+n-1}\\ u_7=u_6+(7-1)=16+6=22\\ [/tex]
Answer C