Answer:
The number 200 has two distinct prime factors. The prime factorization of 200 is as follows: 200 = 2 × 2 × 2 × 5 × 5.
Step-by-step explanation:
The index form of 200 as a product of prime factors is 2³ × 5².
The given number is 200.
What is a index form?The index form of a number is that number written as an exponential expression, or a single number raised to another number.
Prime factorization is a process of writing all numbers as a product of primes.
The prime factors of 200=2×2×2×5×5
=2³ × 5²
Therefore, the index form of 200 as a product of prime factors is 2³ × 5².
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Write an equation in point-slope form of a line that has a slope of -2 and
passes through the point (2, 3).
Answer:
y=-2x+7
Step-by-step explanation:
Please gimme brainliest!!
Answer:
y-3=-2(x-2)
Step-by-step explanation:
y-y1=m(x-x1)
y-3=-2(x-2)
If f(x) = x², then f(2 – 3i) equals
A. -5
B. -5 – 12i
C. 13 – 12i
D. 13
Answer:
A
Step-by-step explanation:
f(2 – 3i) = (2 – 3i)^2
f(2 – 3i) = (2)^2 + (-3i)^2
f(2 – 3i) = 4 + (9)(-1)
f(2 – 3i) = 4 - 9
f(2 – 3i) = -5
These are functions in another function. The result of the function f(2-3i) is -5-12i
Composite functionsThese are functions in another function. Given the function shown below;
f(x) = x²
In order to determine f(2 – 3i), you will replace as 2 - 3i to have:
f(2 - 3i) = (2 - 3i)²
Expand
f(2 - 3i) = 2² - 12i + 9i²
f(2 - 3i) =4 - 12i - 9
f(2 - 3i) = -5-12i
Hence the result of the function f(2-3i) is -5-12i
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How do I write a polynomial with nine roots? Do I just have to make sure I have x^9 or is that wrong?
Step-by-step explanation:
Yes, the degree of the of the polynomial will tell how much roots it has.
A linear equation with degree has one root so it only has 1 possible answer.
A quadratic equation with the degree of 2 has two possible roots.
So write a polynomial equationcwith the highest degree of 9.
When 0.5(20x – 50y + 36) – 0.25(–100x + 40y – 12) is simplified, what is the resulting expression?
A) 10x - 25y + 18 - 25x + 10y - 3
B) -15x - 15y + 15
C) -10x + 25y + 18 + 25x - 10y + 3
B) 35x - 35y + 21
Answer:
D. 35x-35y+21
Step-by-step explanation:
if the simple interest on $5000 for 5 years is $1500 then what is the interest rate?
Answer:
6%
Step-by-step explanation:
Simple interest: A = P(1 + rt)
Solve for r: r = (1/t)((A/P) - 1)
Given:
A = $1500 + $5000 = $6500
P = $5000
t = 5 yrs
r = (1/5)((6500/5000) - 1)
= (1/5)(0.3)
= 0.06
0.06 = 6%
Isabella flew 720 miles in 120 minutes. How many miles per minute did
she fly?
Answer:
6 miles per minute.
Step-by-step explanation:
All you need to do is, divided 720 into 120, and you will get your answer. :)
Consider the function represented by 9x+3y= 12 with x as the independent variable. How can this function be written
using function notation?
flv -v+
f(x) = - 3x + 4
f(x) = - *x+
f(V) = - 3y + 4
Answer:
b) y = f(x) = -3x+4
Step-by-step explanation:
Explanation
Given that the equation 9x+3y =12
Let 'x' be an independent variable and 'y' be the dependent variable then the function is of the form
y = f(x)
3 y = 12 - 9x
[tex]y = \frac{-9x+12}{3}[/tex]
y = -3x+4
The function represented by y = -3x+4
A rental car agency charges $160.00 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $340.00?
Answer:
720 miles
Step-by-step explanation:
let 'm' = # miles you can travel for $340
340 = 160 + .25m
180 = .25m
m = 180/.25
m = 720
To investigate water quality, the Columbus Dispatch took water specimens at 16 Ohio State Park swimming areas in central Ohio. Those specimens were taken to laboratories and tested for E. Coli, which are bacteria that can cause serious gastrointestinal problems. For reference, if a 100 100 -milliliter specimen (about 3.3 3.3 ounces) of water contains more than 130 130 E. Coli bacteria, it is considered unsafe. Here are the E. Coli levels per 100 100 milliliter found by the laboratories:
Answer:
mean=56.28ml
The mean is greater than most of the observations because of the two outliers
Step-by-step explanation:
mean=56.28ml
The mean is greater than most of the observations because of the two outliers.
Out of the 100 cells shown how many are in the process of dividing?
help me asap please!!!!
PLZ HELP ME WITH THIS QUESTION!
Answer:
C
Step-by-step explanation:
Max is selling iPhone cases online. He offers two colors red and green. The red
cases (x) cost $10 each and the green cases (y) cost $20 each. He is trying to sell at
least $500 worth of cases each week. Create an inequality and graph it below.
Please state a combination of cases that meets his goal.
(Scale suggestion 1 box = $5)
Answer:
See belowStep-by-step explanation:
Red cases x = $10 eachGreen cases y = $20 eachMinimum target is $500Required inequality:
10x + 20y ≥ 500The graph is attached
Some combinations:
50 red or 25 green or 18 of each color etc.Any combination of positive numbers in the shaded region.Howdy;)
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7x+3(-4x-2)=-6 how do i solve
Answer:
Step-by-step explanation:
7x+3 (-4x-2)=-6
remove the parenthesis
7x-12x-6=-6
-5x=0
x=0
How to solve your question- 7
Given the diagram below, find the value of x:
a
27.5
b
62
c
8.5
d
31
Answer:
x = 31
Step-by-step explanation:
The 3 angles in a triangle sum to 180°
Sum the 3 given angles and equate to 180
2x - 7 + 2x + 63 = 180, that is
4x + 56 = 180 ( subtract 56 from both sides )
4x = 124 ( divide both sides by 4 )
x = 31
Describe and correct the error in solving the following rational equation , plz help!!!!!
First of all, x cannot ever equal -1 because if it does then in the original equation you'd be dividing by 0, which is not possible. anything divided by 0 is undefined.
I think the error was in the second step: x(x+1) = 2(x+1) because they didn't need to go from the first step to there. I'm assuming they multiplied both sides of the equation with (x+1) to get rid of the fraction, but since both sides have (x+1) as the denominator the (x+1) would've cancelled out instead of multiplying with the numerator.
Correction:
[tex]\frac{x}{x+1} = \frac{2}{x+1}\\(\frac{x+1}{1}) (\frac{x}{x+1}) = (\frac{2}{x+1})(\frac{x+1}{1}) \\x = 2[/tex]
as u can see, in the second step of this correction, the (x+1)s on both sides cancel out so only the numerators remain.
Hope this helps!
PLEASE HURRY I NEED THIS ANSWERED Which expressions are equivalent?
Answer:B
Step-by-step explanation:
B because 3 is still x answers are just flipped
help me out with this pls (multiple choice)
Answer:
45 45 90 special triangle
7√2 = √98
x² + y² = 98
x = y
x² + x² = 98
2x² = 98
x² = 49
x = 7
y = 7
ANSWER: c
What is the slope????
Answer:
-6
Step-by-step explanation:
is that quizzes join lol
PLEASE HELP MEEE !!!!
Answer:
Step-by-step explanation:
Lets find out first the Area of the rectangle building
A=50*100=5000 ft^2
we have 2 circles with the radius of 42 ft, r=21ft
Acircle=3.14*(21)^2=1384.74
Area of 2 circles=2*1384.74=2769.48
What is not covered by the rings is
5,000.00-2769.48=2230.52, rounded is 2231
Choice A
Use the x-intercept method to find all real solutions of the equation.
x? - 7x2 + 4x + 12 = 0
Correct equation is;
x³ - 7x² + 4x + 12 = 0
Answer:
All the real solutions are -1, 2 and 6
Step-by-step explanation:
The x-intercept of x³ - 7x² + 4x + 12 = 0 will occur where y is zero. This is where the curve crosses the x-axis on the graph of this function.
Now, I have plotted a graph of this function and attached it.
From the attached image, the curve crosses the x - axis at the points, x = -1, x = 2, x = 6.
Therefore all the real solutions are -1, 2 and 6
NEED HELP ASAP
A car is purchased for 32,000. The value of the car depreciates by 3% per year.
A. Write an exponential function to model the value of the car after t years?
B. What is the value of the car 6 years after it is purchased?
Answer:
A) car one is linear because it decreases the same amount every year.
car two decreases by the same ratio so it's exponential.
B) for car one y = -6,000x + 38,000 (y is the value after x years, -6,000 is what it changes by every year, and 38,000 is the amount of year 0)
for car two y = (44,000) (17/20)x-1 (y is the value after x years, 44,000 is the amount on year 0, and 17/20 is the ratio)
C) after 5 years car one will be 8,000
after 5 years car two will be about 16,860
Emma receives a large box in the mail.The box is 10cm longer than it wide,and the height is 6 cm more than the width
Answer:
y³+16y²+60y
Step-by-step explanation:
Complete question
Emma receives a large box in the mail. The box is 10cm longer than it wide, and the height is 6 cm more than the width. Find the polynomial function for volume of the box
Let the length be x
Let the width be y
let the height be z
If the box is 10cm longer than it wide, then x = y + 10
Also if the height is 6 cm more than the width,
z = y + 6
Volume of the box = xyz
Substitute
Volume of the box = (y+10)(y)(y+6)
Volume of the box = (y+10)(y²+6y)
Volume of the box = y³+6y²+10y²+60y
Volume of the box = y³+16y²+60y
Hence the required polynomial function is y³+16y²+60y
Note that the question asked was assumed
Please help with this i will give brainliest
Answer:
15.5 meters of wood.
Step-by-step explanation:
Find the perimeter of the box.
2(1.50)+2(6.25)=15.5
Answer:
15.5 m of wood
Step-by-step explanation:
The perimeter of this 1.5 m by 6.25 m frame is a measure of the length of wood needed. Here P = 2(1.5 m) + 2(6.25 m) = 3 m + 12.5 m, or 15.5 m
Denzel wants to work out the density of a block of wood the block of wood is in the shape of the cuboid
Answer:
[tex]Density = 1.094g/cm^3[/tex]
Step-by-step explanation:
Given
[tex]Length = 17.7cm[/tex]
[tex]Width = 8.3cm[/tex]
[tex]Height = 13.0cm[/tex]
[tex]Mass = 2090g[/tex]
See attachment
Required
Determine the density of the wood
First, we calculate the volume of the wood.
[tex]Volume = Length * Width * Height[/tex]
Substitute values for Length, Width and Height
[tex]Volume = 17.7cm * 8.3cm * 13.0cm[/tex]
[tex]Volume = 1909.83cm^3[/tex]
The density is:
[tex]Density = \frac{Mass}{Volume}[/tex]
[tex]Density = \frac{2090g}{1909.83cm^3}[/tex]
[tex]Density = 1.094g/cm^3[/tex] --- approximated
Rosanne and Jimmy are looking to purchase a house. They found one that they like, but the inspection report showed that there was a problem. The foundation has termites. The report states that the foundation of a house has 1200 termites. The termites grow at a rate of about 2.4% each day. A. Formulate an equation in exponential form that represents the termite situation. (5 points) B. The extermination is scheduled out for one week from the date of the report. Use your equation to determine how many termites will be in the home at the time of the extermination. (5 points)
Answer:
A.P(t) = Po (1 + r)^t
P(t) = 1200( 1 + 0.024)^t
B. 1417 termites
Step-by-step explanation:
Rosanne and Jimmy are looking to purchase a house. They found one that they like, but the inspection report showed that there was a problem. The foundation has termites. The report states that the foundation of a house has 1200 termites. The termites grow at a rate of about 2.4% each day.
A. Formulate an equation in exponential form that represents the termite situation.
The formula for exponential growth or increase =
P(t) = Po (1 + r)^t
Where:
P(t) = Population growth after time t
P(o) = Initial Population = 1200 termites
r = Growth rate = 2.4% = 0.024
t = Time in days
Hence, the equation in exponential form that represents the termite situation is given as:
P(t) = 1200( 1 + 0.024)^t
B. The extermination is scheduled out for one week from the date of the report. Use your equation to determine how many termites will be in the home at the time of the extermination.
The time of extermination = 1 week
1 week = 7 days
Hence,
t = 7 days
P(t) = Po (1 + r)^t
P(7) = 1200( 1 + 0.024)⁷
P(7) = 1200(1.024)⁷
P(7) = 1416.7099449 termites
Approximately
= 1417 termites
Would the 2nd answer here be correct?
Answer:
yes (i think im not for sure)
Step-by-step explanation:
Pls help me with my homework
Answer:
NO
Step-by-step explanation:
It is a right triangle if the thee sides satisfy the following pythagorean triple rule/theorem, c² = a² + b², where,
c is the longest side = 50
a = 15
b = 49
Let's check:
50² = 15² + 49²
2500 = 2626 (this is not true).
Therefore, the triangle is not a right triangle. The answer is NO.
Slope 7; (4,-30 equation
Answer: y=7x-68
Step-by-step explanation: Ok so you would use point slope to slope so plug the points in. y+30=7(x-4) then if you need to convert it further into slope intercept form just simplify and distribute. So y+30=7x-28, subract 30 from both sides to get y=7x-68
Hence, the slope of line is [tex]y=7x-58[/tex].
What is the slope of line?
The slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] can be easily determined by finding the difference between the coordinates of the points.
The slope is usually represented by the letter ‘m’.
Here given that,
Slope is [tex]7[/tex] and the coordinates of [tex](x,y)=(4,-30)[/tex].
As we know slope of line is
[tex]y=mx+c[/tex]
where [tex]m[/tex] is the slope.
So,
[tex]y+30=7(x-4)[/tex]
Now convert it further into slope intercept form
[tex]y+30=7x-28\\\\y=7x-28-30\\\\y=7x-58[/tex]
Hence, the slope of line is [tex]y=7x-58[/tex].
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The line models the cost of renting a bike. It costs $2 per hour plus a $4 deposit. Write an equation in slope-intercept form for the line where x is the number of hours a bike is rented and y is the total cost of renting a bike. How much does it cost to rent a bike for 3 hours?
Answer:
Step-by-step explanation:
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