Step-by-step explanation:
Use grouping.
f(x) = x⁴ + 2x³ − 9x² + 18x
f(x) = x³ (x + 2) − 9x (x + 2)
f(x) = (x³ − 9x) (x + 2)
f(x) = x (x² − 9) (x + 2)
f(x) = x (x − 3) (x + 3) (x + 2)
Write an exponential model, y=a(b)^x, given the two points (9,171) and (10,190)
Please hurry!
Answer:
[tex]y = 66.25(1.11)^x[/tex]
Step-by-step explanation:
Let's plug in 9 for x and 171 for y into the given exponential equation:
y = [tex]ab^x[/tex]
171 = [tex]ab^9[/tex]
Now do the same with (10, 190):
190 = [tex]ab^{10}[/tex]
Write them both in terms of a and set them equal:
a = 171/[tex]b^9[/tex]
a = 190/[tex]b^{10}[/tex]
171/[tex]b^9[/tex] = 190/[tex]b^{10}[/tex]
Multiply both sides by [tex]b^{10}[/tex]:
171b = 190
b = 190/171 = 10/9 ≈ 1.11
Plug this in to find a:
a = 171 / (10/9)^9 ≈ 66.25
So, the exponential model is:
[tex]y = 66.25(1.11)^x[/tex]
Answer:
y = 66.25[(10/9)^x]
Step-by-step explanation:
171 = a(b⁹)
b⁹ = 171/a
190 = a(b¹⁰)
190 = a(171/a) × b
b = 190/171
b = 10/9
(10/9)⁹ = 171/a
a = 66.24890362
You might need:
A circle has a circumference of 1,133.54 units.
What is the diameter of the circle?
units
Answer 360.81 units
Answer:
360.82 units
Step-by-step explanation:
The circle has a circumference of 1,133.54 units.
The circumference of a circle is given as:
C = πD
where D = diameter
This implies that:
1133.54 = πD
=> D = 1133.54 / π
D = 360.82 units
Its diameter is 360.82 units
Easy question
Topic: Volume
Use the other attachment to help u what formula is it
Answer:
see below
Step-by-step explanation:
V = l*w*h for the rectangular tank
V = 70* 40*40
=112000 cm^3 = 1mL
The water is 84000
Make this a fraction
84000/112000 = 3/4
The water fills 3/4 of the tank
1-3/4 = 1/4
It is 1/4 from the top
Find the volume of the treasure chest
V = 12*10*8 =960
Tower
V = pi r^2
3.14 * 10^2 *10
=3140
Water + chest + tower
84000+960+3140 =88100
This is less than 112000 so the water will not overflow
Answer:
a) 10 cm
b) Will not overflow
Step-by-step explanation:
8400 = base area × height
84000 = 70 × 40 × h
h = 30
From the top: 40 - 30 = 10cm
b) Capacity of the tank:
70 × 40 × 40
112,000 cm³
Combined volume of the two vessels:
(12 × 10 × 8) + (3.14 × 10² × 10)
960 + 3140
4,100 cm³
4100 = 70 × 40 × rise
rise = 1.464285715 cm
Since 1.464285715 < 10
It will not overflow
Can you please help me with this?
Answer:
30 ,345,986
Step-by-step explanation:
Kayla hit 4 homeruns at batting practice
out of 12 pitches thrown. What is the
experimental probability that Kayla will hit a
homerun at batting practice?
Answer:
[tex]\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given,
Total number of trial = 12
Total number of favorable event = 4
Experimental probability of hitting home run is
[tex]P(home\ run)=\dfrac{Favorable\ event}{Total\ trial}[/tex]
[tex]P(home\ run)=\dfrac{4}{12}[/tex]
[tex]P(home\ run)=\dfrac{1}{3}[/tex]
Answer:1/3
Step-by-step explanation:Answer:
Step-by-step explanation:
Given,
Total number of trial = 12
Total number of favorable event = 4
Experimental probability of hitting home run is
A machine can scan 12 pages in 3/5 minute. How many pages can be scanned in 1 minute?
Answer:
20 pages
Step-by-step explanation:
Answer:
20 pages
Step-by-step explanation:
3/5 minute =36sec
if 36=12
.·.60= 60×12÷36=20
Help me with this problem plzzzzzz
Answer:
B. Opposite angles add up to 180 degrees.
Step-by-step explanation:
Answer Choice B is incorrect because opposite angles are actually congruent. However, adjacent angles of a parallelogram do add up to 180 degrees.
houses cost £100000 one year ago
now they cost £________
this is a 25% increase
Final answer:
The new cost of houses after a 25% increase from the original price of £100,000 is £125,000. You calculate this by finding 25% of £100,000, which is £25,000, and then add it to the original price.
Explanation:
The student is asking how to calculate the new cost of houses after a 25% price increase from the previous year when the houses cost
£100,000. To find the new price, we need to calculate 25% of £100,000 and then add that to the original price.
First, find 25% of £100,000:
0.25
(multiplier for 25%)
× £100,000
(original cost)
= £25,000
(the increase).
Next, add the increase to the original cost:
£100,000
+ £25,000
= £125,000.
Therefore, the new cost of the houses after a 25% increase is £125,000.
f(x)=4x2−16
find the zeros of the function
Answer:
x=2 x=-2
Step-by-step explanation:
f(x)=4x^2−16
f(x)=4(x^2-4)
f(x)=4(x-2)(x+2)
x=2 x=-2
Hope this helps! Please mark brainliest :)
The zeros of the function f(x) = 4x2 − 16 are found by factoring the quadratic equation, which results in two solutions x = -2 and x = 2.
Explanation:To find the zeros of the function f(x) = 4x2 − 16, we need to set the function equal to zero and solve for x:
0 = 4x2 - 16
To solve this quadratic equation, you can factor out the common factor of 4:
0 = 4(x2 - 4)
We now have a difference of squares, which can be factored further:
0 = 4(x + 2)(x - 2)
Set each factor in the parentheses equal to zero:
x + 2 = 0 → x = -2x - 2 = 0 → x = 2So the zeros of the function are x = -2 and x = 2.
PLEASE HELP ME
Find the surface area of the sphere. *
We have been given a sphere with radius 8.6 ft. We are asked to find the surface area of the given sphere.
We know that surface area of a sphere is equal to [tex]4\pi r^2[/tex].
[tex]A=4\pi r^2[/tex]
Upon substituting [tex]r=8.6\text{ ft}[/tex] in surface area formula, we will get:
[tex]A=4\pi (8.6\text{ ft})^2[/tex]
[tex]A=4\pi \cdot 73.96\text{ ft}^2[/tex]
[tex]A=295.84\pi\text{ ft}^2[/tex]
[tex]A=929.4087706\text{ ft}^2[/tex]
Upon rounding to nearest hundredth, we will get:
[tex]A\approx 929.41\text{ ft}^2[/tex]
Therefore, the surface of the given sphere would be approximately [tex]929.41\text{ ft}^2[/tex].
What are the solutions to the equation x2 - 4x = -1?
Answer:
x= [tex]2-\sqrt{3}[/tex] and x=[tex]2+\sqrt{3}[/tex]
Step-by-step explanation:
- transfer the -1 to the other side so that the equation reads as [tex]x^{2} -4x+1[/tex]
- factor! think about what numbers add -4 but also multiply to be 1
- you may then realize that there are no numbers with those characteristics
- since that is the case, we have to use the quadratic formula, which is:
[tex]\frac{-b+\sqrt{b^{2}-4ac }}{y}[/tex] and [tex]\frac{-b-\sqrt{b^{2}-4ac }}{y}[/tex]
- the equation is shown as [tex]a^{2}+b^{2}=c^{2}[/tex]
- using the numbers that correspond with those lettered values, plug it in the quadratic formulas
the solutions to the equation [tex]\( x^2 - 4x = -1 \) are \( x = 2 + \sqrt{3} \) and \( x = 2 - \sqrt{3} \)[/tex].
To find the solutions to the equation [tex]\( x^2 - 4x = -1 \)[/tex], we can follow these steps:
1. Move all terms to one side of the equation to set it equal to zero:
[tex]\[ x^2 - 4x + 1 = 0 \][/tex]
2. We can solve this quadratic equation using the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
where [tex]\( a = 1 \), \( b = -4 \), and \( c = 1 \).[/tex]
3. Plug in the values and simplify:
[tex]\[ x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(1)}}{2(1)} \] \[ x = \frac{4 \pm \sqrt{16 - 4}}{2} \] \[ x = \frac{4 \pm \sqrt{12}}{2} \] \[ x = \frac{4 \pm 2\sqrt{3}}{2} \] \[ x = 2 \pm \sqrt{3} \][/tex]
So, the solutions to the equation [tex]\( x^2 - 4x = -1 \) are \( x = 2 + \sqrt{3} \) and \( x = 2 - \sqrt{3} \)[/tex].
Which rule describes the relationship between the x- and y- coordinates on following graph?
A: y = 3x B: y = 2x + 2
Use the multiplier method to increase £258 by 43%
You must show your working.
To increase £258 by 43%, convert the percentage to a decimal, calculate the increased amount, and add it to the original amount. The increased amount to the original amount is £368.94
To increase £258 by 43% using the multiplier method:
Convert the percentage to a decimal: 43% = 0.43
Calculate the increased amount: £258 x 0.43 = £110.94
Add the increased amount to the original amount: £258 + £110.94 = £368.94
Evaluate e – 2 when e=7.
Answer:
5
Step-by-step explanation:
If e = 7, you would replace e in the expression e - 2 with 7 so that the expression becomes 7 - 2 which results in 5.
Does that help?
What is the solution to the inequality -4x < 8?
x < -2
x > -2
x < -24
x > -24
Answer:
x > -2
Step-by-step explanation:
-4x < 8
-8 < 4x
-2 < x
x > -2
−11x 5 (−9x 3 y 4 ) fully simplify
Answer:
5940 y
Step-by-step explanation:
Simplify the following:
-11 (-9)×5×3×4 y
-9×3 = -27:
-11×5×-27×4 y
-27×4 = -108:
-11×5×-108 y
-11×5 = -55:
-108-55 y
-55 (-108) = 5940:
Answer: 5940 y
Two sides of a rectangular fence are 5 5/8 feet long.The other two sides are 6 1/4 feet long.What is the perimeter?
Answer:
im not sure
Step-by-step explanation:
so sorry i didnt know the answer.
Answer:
the perimeter of the rectangle is 23.75 feet.
Step-by-step explanation:
5 5/8 × 2 = 11 1/4.
6 1/4 × 2 = 12 1/2
11 1/4 + 12 1/2 = 23 3/4 or 23.75
Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 17 feet by 17 feet by 2 inches for a patio if the concrete costs $64.00 per cubic yard?
Answer:
$114.17
Step-by-step explanation:
First we need to convert cubic yard to cubic feet.
One yard is equivalent to three feet, so one cubic yard is 3^3 = 27 cubic feet.
So the cost of one cubic feet is 64/27 = $2.3704
We also need to convert from inches to feet.
One inch is 1/12 feet, so 2 inches is 2/12 = 1/6 feet
Now we need to find the volume of the slab:
Volume = 17 * 17 * (1/6) = 48.1667 ft3
Now, to find the cost, we can use a rule of three:
1 cubic feet -> $2.3704
48.1667 cubic feet -> X
X = 48.1667 * 2.3704 = $114.1743
what is (a^4/-7b^3)^2 simplified?
Answer:
Step-by-step explanation:
[tex](\frac{a^{4}}{-7b^{3}})^{2}=\frac{(a^{4})^{2}}{(-7b^{3})^[2}}\\\\=\frac{a^{4*2}}{(-7)^{2}b^{3*2}}\\\\=\frac{a^{8}}{49b^{6}}[/tex]
Subtract 55 from the sum of 9g and 4 when g=8
Answer:
21
Step-by-step explanation:
(9g+4)-55=
(72+4)-55=
76-55=
21
Final answer:
To find the answer, first multiply 9 by 8, then add 4, resulting in 76. Finally, subtract 55 to get the answer, which is 21.
Explanation:
To solve the problem, we need to first calculate the sum of 9g and 4 when g=8. This will be 9 × 8 + 4.
After calculating the sum, we will subtract 55 from this amount to get the final answer.
Following the steps:
Substitute the value of g: We are given that g = 8. So, we need to find the sum of 9 * 8 and 4.Calculate the sum: The sum of 9 × 8 and 4 is 72 + 4 = 76.Subtract 55:Finally, we subtract 55 from the calculated sum: 76 - 55 = 21.Therefore, when g = 8, subtracting 55 from the sum of 9g and 4 results in 21.
3m + 9 - 9m = 2m + 25 whats m
Answer:
8
Step-by-step explanation:
3m + 9 -9m = 2m + 25
3m + 9 = 11m + 25
9 = 8m + 25
16/2 = 8m/2
M = 8
Examine the number line and select all the statements that are true.
The sum of B and C is negative.
the product of A and B > the product of A and D
|A| < |D|
A - B = -2 2/3
A + D = B
The quotient of C and B is equivalent to -2/3
Answer:
the sum of B and C is negative
A + D = B
The quotient of C and B is equivelent to -2/3
Step-by-step explanation:
The quotient of C and B is equivalent to -2/3. Therefore, the correct option is option D among all the given options.
What is number line?A picture of numbers along a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it. Just to refresh your memory, a whole number is a collection of numbers that contains all counting numbers.
Comparing numbers is made simpler by writing them on a number line. As seen in the aforementioned graphic, the integers to the left are smaller compared to the integers for the right. As an illustration, the numbers 0 and 1 are less than each other, as are the numbers -1 and -2. The sum of B and C is negative.
Therefore, the correct option is option D.
To know more about number line, here:
https://brainly.com/question/16191404
#SPJ3
Please help for both of them
Answer:
18 is for the top
6 is for the bottom
Answer:
1. C
2. D
Step-by-step explanation:
The music teacher asked his class to vote for their favorite instrument and created a pie chart to display the results. There are
20 students in his class. Which statements are true? Check all that apply.
Popularity of Musical
Instruments
Horns
15%
Guitar
35%
Flute
20%
Piano
30%
Exactly half of the students voted for flute or guitar.
Three students voted for horns.
Less than one-third of the class voted for guitar.
Answer:
Three students voted for horns.true
Step-by-step explanation:thats all i know
Answer:
B, D, E, F
Step-by-step explanation:
Three students voted for horns.
Thirteen students voted for piano or guitar.
Twice as many students voted for piano as horns.
Eleven students voted for flute or guitar.
A pilot flies 416 miles from Tampa to Atlanta 5 times in one week. She flies 721 miles from Atlanta to Dallas 8 times. What is the total number of miles she flies? ANSWERS!!!!
Answer:
416 x 5 = 2080
721 x 8 = 5768
5768 + 2080 = 7848. Have a great day.
When finding the volume of a soup can, Tommy needs to calculate the area of the base. Describe what type of base Tommy’s soup can has and what formula he should use to find its area.
Answer: The base is a circle and you can use the formula (pi)r^2 the find the area of the base
Step-by-step explanation:
a soup can is a cylinder and the base of a cylinder is a circle. you can google "area of a circle calculator" on google to show you the formula
Answer:
Sample response: The soup can has a circular base. The radius measure is needed. If the diameter is given, find the radius, which is half the diameter. Square the radius and multiply that answer by pi for the base area.
Step-by-step explanation:
I just did it on edge
In one year the perseid metor shower had a metor appear every 1/5 5 minutes on average That same year the Leonid metor shower had a metor appear every 4/2 3 minutes on average.
In one year, the Perseid meteor shower had a meteor appear every 1 1/5 minutes on average. That same year, the Leonid meteor shower had a meteor appear every 4 2/3 minutes on average. How many more meteors fell during the Perseid meteor shower?
Answer:
325,452 meteors
Step-by-step explanation:
We all know that :
We have 365 days in a year and in each day there are 24 hours, Likewise an hour has 60 minutes
SO, the total number of minutes in a year is :
365 × 24 × 60 = 525600 minutes
For Perseid meteor:
[tex]1 + \frac{1}{5} \\ \\ = 1 + 0.2 \\ \\ = 1.2[/tex]
So one meteor fall at 1.2 minutes interval Thus, in a year, we will have :
1 meteor - 1.2 minutes.
x meteor - 525600 minutes.
1.2x = 525600
[tex]x = \frac{525600}{1.2}[/tex]
x = 438000
∴ 438,000 meteors fell during the Perseid shower.
For Leonid meteor shower:
[tex]4 + \frac{2}{3} = 4.67[/tex]
So one meteor fall at 4.67 minutes interval Thus, in a year, we will have :
1 meteor - 4.67 minutes.
x meteors - 525600 minutes.
[tex]4.67x = 525600[/tex]
[tex]x = \frac{525600}{4.67}[/tex]
x = 112548
112,548 meteors fell during the Leonid Shower.
Finally , the numbers of more meteors that fell during the Perseid meteor shower is calculated by the difference in the number of Perseid meteor shower and Lenoid meteor shower. i.e
438,000 - 112,548 = 325,452
325,452 more meteors fell during the Perseid meteor shower
Answer:
For Leonid meteor shower: So one meteor fall at 4.67 minutes interval Thus, in a year, we will have : 1 meteor - 4.67 minutes. x meteors - 525600 minutes
Step-by-step explanation:
how much space do all three of the soccer balls take up ?
Answer: 2713 cubic centimeter
Step-by-step explanation:
Answer:
339 cubic centimeters
Step-by-step explanation:
The formula for the volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex]. In this case, a ball with the radius of 3 centimeters would have a volume of [tex]\frac{4}{3}\pi \cdot 3^3=113.04[/tex] cubic centimeters. Multiplying this by the three soccer balls, you get about 339 cubic centimeters, or the third option. Hope this helps!
The height of a right circular cylinder is 1.5 times the radius of the base. What is the ratio of the total surface area to the lateral (curved) surface area of the cylinder?
Let r represent the radius of cylinder.
We have been given that the height of a right circular cylinder is 1.5 times the radius of the base. So the height of the cylinder would be [tex]1.5r[/tex].
We will use lateral surface area of pyramid to solve our given problem.
[tex]LSA=2\pi r h[/tex], where,
LSA = Lateral surface area of pyramid,
r = Radius,
h = height.
Upon substituting our given values in above formula, we will get:
[tex]LSA=2\pi r\cdot (1.5)r[/tex]
Now we will find the total surface area of cylinder.
[tex]TSA=2\pi r(r+h)[/tex]
[tex]TSA=2\pi r(r+1.5r)[/tex]
[tex]TSA=2\pi r(2.5r)[/tex]
[tex]\frac{TSA}{LSA}=\frac{2\pi r(2.5r)}{2\pi r(1.5r)}[/tex]
[tex]\frac{TSA}{LSA}=\frac{2.5r}{1.5r}[/tex]
[tex]\frac{TSA}{LSA}=\frac{25}{15}[/tex]
[tex]\frac{TSA}{LSA}=\frac{5}{3}[/tex]
Therefore, the ratio of total surface area to lateral surface area is [tex]5:3[/tex].
What is the center of the data?
Answer:
The center of data is a single number that summarizes the entire data set.
Step-by-step explanation: