Step-by-step explanation:
[tex]12y^{2} + 4y \\4y( \frac{12y^{2} }{4y} + \frac{4y}{4y} ) \\ 4y(3y + 1)[/tex]
Step-by-step explanation:
12y²+4y
divide both sides by 4
therefore,
3y²+y
y(3y+1)
Type the correct answer in the box. Use numerals Instead of words. If necessary, use / for the fraction bar.
David invested $230 in a savings account that offers a 3% return on the Investment. The value of David's Investment will be at least $415 after a
period of
years.
Hint: Use the formula A= P1+, where A is the amount after tyears, Pls the amount Invested, r is the rate of interest, and t is the time period.
Use a calculator to compute the answer, and round It off to the nearest year.
Reset
Next
Using an exponential function, it is found that the value of David's Investment will be at least $415 after a period of 20 years.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, the initial value and the growth rate for his investment are given by:
A(0) = 230, r = 0.03.
Hence, the value after t years is given by:
[tex]A(t) = 230(1.03)^t[/tex]
Then, the value will be of at least $415 when:
[tex]A(t) \geq 415[/tex]
[tex]230(1.03)^t \geq 415[/tex]
[tex](1.03)^t \geq \frac{415}{230}[/tex]
[tex]\log{(1.03)^t} \geq \log{\frac{415}{230}}[/tex]
[tex]t\log{1.03} \geq \log{\frac{415}{230}}[/tex]
[tex]t \geq \frac{\log{\frac{415}{230}}}{\log{1.03}}[/tex]
[tex]t \geq 20[/tex]
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a line contains the point (2,3) and has a slope of 1/2 What is the point-slope form of the equation for the line
The point-slope form of the equation for the line is y - 3 =1/2(x - 2)
Point-slope formFrom the question, we are to determine the point-slope form of the equation for the line
The point-slope form of the equation of a line is given by
y - y₁ = m(x - x₁)
Where (x₁, y₁) is a point on the line
and m is the slope of the line
From the given information,
Slope, m = 1/2
and we have the point (2,3)
∴ The point-slope form of the equation for the line is
y - 3 =1/2(x - 2)
Hence, the point-slope form of the equation for the line is y - 3 =1/2(x - 2)
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Help please this is due today
The experimental probability that in a group of 4 students, at least one of them has brown eyes is 95%.
What is Experimental Probability?
Experimental probability is a probability that is determined on the basis of a series of experiments. A random experiment is done and is repeated many times to determine their likelihood and each repetition is known as a trial. The experiment is conducted to find the chance of an event to occur or not to occur.
Here , Favorable Outcome = 19
Total outcomes = 20
Probability = Favorable Outcome/ Total Outcome
= 19 / 20
= 95%
Thus, the experimental probability that in a group of 4 students, at least one of them has brown eyes is 95%.
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what is the value of x
Answer:
Should be 60°
Step-by-step explanation:
Since each interior angle in an octagon is 120°, you would subtract 120° from 180° (which is the angle of a line). This would get you 60 °.
20 points, please explain your answer :)
Answer:
Angle 3 = 70
Step-by-step explanation:
This is a geometry property
"opposite angle theorem"
It's pretty easy to prove it as well
180-70 = 110
180-110 = 70
Find the volume of rectangular pyramid 5in 5 in 2 in
Answer:
16.67
Step-by-step explanation:
formula for a rectangular pyramid =
lengthxwidth= base area x height/3
2x5=10x5=50
50/3=16.67
H
Which line is parallel to line r?
Oline p
O line q
O line s
Oline t
Answer:
Line s
Step-by-step explanation:
They are the same distance apart, so this makes them parallel.
By the definition of parallel lines, the line r is parallel to line s.
What is Coordinate System?Arrangement of reference lines or curves used to identify the location of points in space is called as Coordinate System.
We have to find the line which is parallel to line r.
Parallel lines are the lines that do not intersect or meet each other at any point in a plane.
They are always parallel and are at equidistant from each other.
Parallel lines are non-intersecting lines.
We can also say Parallel lines meet at infinity.
As we observe the figure line s is parallel to line r and it is equidistant from r.
Hence, line s is parallel to line r.
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Find a polynomial f(x) of degree 3 with real coefficents and following zeros. -4,4i
Answer:
[tex]f(x)=x^3 +4x^2 +16x +64[/tex]
Step by step explanation:
[tex]\text{Given that, two roots are}~ -4~ \text{and}~ 4i.\\\\\text{Let,}\\\\~~~~~~~x = 4i\\\\\implies x^2 = 16i^2~~~~~~~;[\text{Square on both sides}]\\\\\implies x^2 = -16~~~~~~~~;[i^2 = -1]\\\\\implies x^2 +16 = 0\\\\\text{So,}~ x^2 +16~ \text{ is a factor of the 3 degree polynomial}.\\ \\ \text{The polynomial is ,}\\\\ f(x) = (x+4)(x^2 +16)\\\\~~~~~~~=x^3 +16x +4x^2 +64\\\\~~~~~~~=x^3 +4x^2 +16x +64[/tex]
Find the center and radius of the circle whose equation is x2 + y2 + 8x - 2y + 15 = 0
(4, 1) r = 2
(-16, 1), r = 4
(-4, 1),
(-4, -1),
The equation represents a circle whose center is (-4, 1) and has a radius r = √2
How to find the center and radius of the circle?We have the equation:
[tex]x^2 + y^2 + 8x - 2y + 15 = 0[/tex]
We can rewrite this as:
[tex](x^2 + 8x ) + (y^2 - 2y ) + 15 = 0\\\\\\\\(x^2 + 8x + 16) - 16 + (y^2 - 2y + 1) - 1 + 15 = 0\\\\(x + 4)^2 + (y - 1)^2 - 16 - 1 + 15 = 0\\\\(x + 4)^2 + (y - 1)^2 = 2[/tex]
Where we just completed squares.
Comparing this with the general circle equation, we can see that the center is the point (-4, 1) and the radius is √2.
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a machine makes 1 gadgets every 20 seconds .how many gadgets does it makes in 5 minutes
Answer:
it makes 15 gadgets in 5 minutes
Step-by-step explanation:
you take thw 1 gadget every 20 seconds there are 60 seconds in 1 minutes so 60 ÷ 20 is 3 so it makes 3 gadgets every minute so 3 x 5 is 15 so it makes 15 gadgets every 5 mins
Answer:
15 gadgets
Step-by-step explanation:
look above
hope ot helps
(04.02 mc)
segment ab falls on line 6x + 3y = 9. segment cd falls on line 4x + 2y = 8. what is true about segments ab and cd?
You can see that both lines have the same slope showing that they are both parallel
Linear equationsThese are equations that has a degree of 1. Given the equation of the lines
ab = 6x + 3y = 9
cd: 4x + 2y = 8
Write then in slope-intercept form
ab: y = -2x + 3
cd = y = -2x +8
You can see that both lines have the same slope showing that they are both parallel
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Answer:
They are parallel because they have the same slope of −2.
Step-by-step explanation:
Question 15 of 26
AABC has side lengths that measure 10 centimeters, 10 centimeters, and 15
centimeters. Which of the following best describes this type of triangle?
Answer:
isosceles
Step-by-step explanation:
▪︎ Isosceles triangle is a triangle that has two sides of equal length.
The compound interest formula can be rewritten as
P = A/(1 + r/n)nt.
Find the principal P that you need to invest on the day your child is born at 4.2% annual interest compounded quarterly to make your child a millionaire on his or her 21st birthday. (Round your answer to the nearest cent.)
Answer:
Compound interest, or 'interest on interest', is calculated using the compound interest formula.
The formula for compound interest is A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded per time period and t is the number of time periods.
Step-by-step explanation:
Solve for x: 3(x + 1) = −2(x − 1) − 4
1
−1
−5
−25
Answer:
x = - 1
Step-by-step explanation:
3(x + 1) = - 2(x - 1) - 4 ← distribute parenthesis on both sides
3x + 3 = - 2x + 2 - 4
3x + 3 = - 2x - 2 ( add 2x to both sides )
5x + 3 = - 2 ( subtract 3 from both sides )
5x = - 5 ( divide both sides by 5 )
x = - 1
a rectangle has an area of 7.5m2. one of the sides is 0.3m in length. what is the perimeter of the rectangle?
Step-by-step explanation:
the area of a rectangular is
length × width
we know the area and one side, let's say it's the width (it does not matter, as multiplication are commutative, and a×b = b×a).
so,
7.5 = length × 0.3
length = 7.5 / 0.3 = 25 m
the perimeter of a rectangle is
2×length + 2×width = 2×25 + 2×0.3 = 50 + 0.6 = 50.6 m
Imagine buying a brand new Ford Fusion hybrid. If x represents the number of miles a car is driven, and y represents the total amount of money spent on the car, write an equation that relates x and y for the Fusion hybrid.
The equation that relates x and y for the Fusion hybrid is y = k + x
How to write and solve equation?Total amount of money spent on the car = yNumber of miles a car is driven = xAssume, other money spent on the car = kSo,
y = k + x
Therefore, the equation that relates x and y for the Fusion hybrid is y = k + x
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I want to know the answer of these questions and the questions are
2 + 7
6 + 4
2 + - 7
- 2 + 7
- 2 + - 7
6 + - 4
- 6 + 4
- 6 + -4
2 + 7 = 9
6 + 4 = 10
2 + - 7 = -5
- 2 + 7 = 5
- 2 + - 7 = -9
6 + - 4 = 2
- 6 + 4 = - 2
- 6 + - 4 = -10
what is nine minus one third?
Answer:
[tex]\frac{26}{3}[/tex]=[tex]8.6...[/tex]=[tex]8\frac{2}{3}[/tex]
Step-by-step explanation:
You multiply 9 x 3=27
(leave 1/3 alone, it's already good)
you have a 27/3-1/3
(subtract those)
your answer is 26/3
(see answer above for decimal form and mixed fraction form)
Pls help asap !!! Show all work and I’ll give brainliest
Implementing the LSA from your other question
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LSA=3360ft²One can can paint 400ft²
Total cans
3360/4008.4cans9cans you need
What is the approximate solution to this equation? 15(3)^2x=90
Answer:
x ≈ 0.67
Step-by-step explanation:
[tex]15(3)^2x = 90\\\\15(9)x = 90\\\\135x = 90\\\\x = 90/135\\\\ x = 2/3\\\\x = 0.666...\\\\x = 0.67 \ (rounded \ to \ nearest \ hundredth )[/tex]
Part A: In your own words, describe the steps that are necessary to determine whether angles are coterminal.
Part B: Explain why coterminal angles have a difference that is a multiple of 360° degrees, such as 720° or 1080°.
Part C: Find three angles that are coterminal with an angle measuring 75°. Show all work.
Answer:
Part A:
In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.
Part B:Simply put, coterminal angles start at 0° and end at the same place, though in different directions and multiple times around (you're probably going to want to make that sound a little more formal). Since each time around is 360°, boom
Part C: 75° is in Quadrant II, right? If I go one more time around, 75 + 360 = 435°. I can also go "backward. Starting at 0 and going clockwise, I'm going 75 fewer degrees than all the way around, so 360-75 = 285° but since I'm going "backward" 75 - 360 = -285°. One more is on you.
Step-by-step explanation:
Stacy uses 4 cups of milk to make a batch of rice pudding. How many batches of rice pudding
can she make with 3 gallons of milk?
Hint: There are 16 cups in 1 gallon.
Answer:
12
Step-by-step explanation:
There are
16 cups = 1 gallon
3 gallons = 48 cups
48 divided by 4 = 12 batches of rice pudding
Answer
12
Step-by-step explanation:
4 cup of milk = 1 batch of rice pudding
1 gallon of milk= 16 cups of milk
3 gallon of milk = 3x 16
=48 answer
then, 48 cup of milk = 48 ÷ 4
= 12 answer
Hence, stacy can make 12 batch of pudding with 3 gallon of milk.
Convert 0.0150 km to meters and express the answer to the correct number of significant digits. a. 150 m b. 15 m c. 15.0 m d. 150.0 m
The correct answer is option C which is 15 meters.
What is unit conversion?
Unit conversion is a multi-step process that entails multiplying or dividing by a numerical factor, selecting the correct number of significant digits, and then multiplying or dividing by another numerical factor.
The unit conversion will be done as:-
1 km = 1000 meters
0.0150 Km = 0.0150 x 1000 meters
0.0150 Km = 15 meters
Therefore the correct answer is option C which is 15 meters.
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STATISTICS!!!! PLEASE HELP ASAP
Answer: they can conclude the distributions are different at the 95% confidence interval. Compute the z test statistic to solve this.
Step-by-step explanation: to get the 95% confidence interval on the mean take the mean value (984) +/- (2*standard deviation divided by the square root of the number of samples) (I.e. 984 +/- (2*267/sqrt(501)))
How much is 55 as a percentage of 50?
Answer:
50 27.5
50.01 27.5055
50.02 27.511
50.03 27.5165
Step-by-step explanation:
Answer:
55 is 110% of 50
Step-by-step explanation:
A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 16% are pennies and 34% are dimes. There are 3 more nickels than pennies. How much money does the bag contain?
see the attachment for solution
hope it helps...!!!
Answer:
$5.83
Step-by-step explanation:
The total amount of money is the sum of the values of the various denomination coins.
__
setupLet p, n, d, q represent the numbers of pennies, nickels, dimes, and quarters, respectively.
p + n + d + q = 50 . . . . . . there are 50 coins in all
16% × 50 = p . . . . . . . . . . 16% are pennies
34% × 50 = d . . . . . . . . . . 34% are dimes
n = p +3 . . . . . . . . . . . . . . there are 3 more nickels than dimes
The total value is ...
v = 0.01p +0.05n +0.10d + 0.25q
__
solutionThe numbers of pennies and dimes are found easily:
0.16 × 50 = p = 8
0.34 × 50 = d = 17
Then the number of nickels can be found:
n = p +3 = 8 +3 = 11
Finally, the number of quarters is found from the total number of coins:
p + n + d + q = 50
8 + 11 + 17 + q = 50 . . . substitute known values
q = 14 . . . . . . . . . . . . . subtract 36 from both sides
The total value is then ...
v = 0.01(8) +0.05(11) +0.10(17) +0.25(14) = 0.08 +0.55 +1.70 +3.50
v = 5.83
The bag contains $5.83.
If you know that the product of two powers is 5 to the power of 3, and that the quotient is 5 to the power of 17, what could the two powers be? Explain how you know this answer is correct.
Answer:
[tex]5^{10} \cdot 5^{-7} = 5^3[/tex]
[tex]\frac{5^{10}}{5^{-7}} = 5^{17}[/tex]
Step-by-step explanation:
You have two equations:
[tex]5^a \cdot 5^b = 5^3[/tex]
[tex]\frac{5^a}{5^b} = 5^{17}[/tex]
But since
[tex]x^a \cdot x^b = x^{a+b}[/tex]
you only need to solve a+b = 3 and a-b=17
Rewrite the second as a = 17+b and plug it into the first:
17+b + b = 3, then you find, 2b = -14, so b = -7.
Then a=3-b, so a = 10.
The bases of the prism below are right triangles. If the prism's height measures 8 units and its volume is 60 units³, solve for x.
Answer:
3
Step-by-step explanation:
Volume of prism = 0.5 times height times length times width
60 = (0.5)(8)(5)(x)
120 = 8(5)(x)
120 = 40x
x = 3
Let me know if its right
Length of another side of base x = 3 unit
What is prism?A prism has a solid shape consisting of two identical ends (such as triangle, square, rectangle, etc.), flat faces or surfaces and uniform cross-section across its length. The cross-section looks like a triangle hence called triangular prism. The shape of the prism does not have any curve. Therefore, a prism can have square, rectangular, pentagonal and other polygon shapes but not the circular shape.
Height of the prism = 8units
Length of one side of base = 5 units
Length of another side of Base = x
Base is a right angle
Base Area = 5x/2
Volume of prism = 60 unit³
Volume of Prism = Base Area × Height
60 = (5x/2) × 8
60/8 = 5x/2
x = 120/40
x = 3 unit.
Hence, x = 3 unit which is length of another side of base.
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i need help on this hegarty question i have been stuck on for hours
The difference of the two numbers in scientific form is:
[tex]493*10^{-9} = 0.00000493[/tex]
How to solve the difference?
Here we want to solve:
[tex](5*10^{-7}}) - (7*10^{-9})[/tex]
To solve this, we should have the same exponent in both sides, to get that, we can rewrite the first number as:
[tex]5*10^{-7} = 500*10^{-9}[/tex]
Replacing that, we will get:
[tex](500*10^{-9}) - (7*10^{-9}}) = 493*10^{-9}[/tex]
To write it in standard form, we need to move the decimal point 9 times to the left, so we get:
[tex]493*10^{-9} = 0.00000493[/tex]
The difference is equal to 0.00000493.
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the lenth of a rectangle is twice the width if the permeter is 20 cm find the width
L = 2W
perimeter = 2( L + W ) = 20 .
2 ( 2W + W ) = 20
6 W = 20
W = 20/6
= 10/3
L = 20/3
Answer:
10/3
Step-by-step explanation:
Given properties of the rectangle:
The length is twice the width ( So we can say l = 2w ) The perimeter is 20cmGiven this we want to find the width of the perimeter.
Creating a system of equation:
First off we know that perimeter = 2L + 2W
We also know that the perimeter of this rectangle is 20 cm
So we can say that 20 = 2L + 2W
We also know that the length of this rectangle is twice the width or in other words l = 2w
So we have the two equations, 20 = 2l + 2w and l = 2w
Solving the system:
We are going to use the substitution method to solve this system.
The substitution method works when you have two equations, one can be just a plain equation but the other must have one of the variables defined ( by itself on either side of the equal sign )
If you have one of the variables defined, you can plug it in ( substitute ) into the other equation and solve for the other variable.
Plugging in the defined variable into the other equation
Equation : 20 = 2l + 2w
Defined variable : l = 2w
==> plug in l = 2w
20 = 2(2w) + 2w ( now we solve )
==> multiply 2 and 2w
20 = 4w + 2w
==> combine like terms
20 = 6w
==> divide both sides by 6
20/6 = w
==> simplify fraction
10/3 = w
The width = 10/3
Checking our work:
First we must solve for length as well
Solving for length by plugging in width into either equation
l = 2w
==> plug in w = 10/3
l = 2(10/3)
==> multiply 2 and 10/3
l = 20/3
Now to check our we we plug in the length and width into both equations, if both are true then our answer is correct
Equation 1 : 2l + 2w = 20
==> plug in l = 20/3 and w = 10/3
2(20/3) + 2(10/3) = 20
==> simplify multiplication
40/3 + 20/3 = 20
==> add fractions
20 = 20
Equation 2 : l = 2w
==> plug in l = 20/3 and w = 10/3
20/3 = 2(10/3)
==> multiply 2 and 10/3
20/3 = 20/3
Both are correct so our final answer is correct as well! :)