Answer:
6ft
Step-by-step explanation:
simon will deposit $250 into two savings accounts. account 1 earns 1.6% interest compounded annually. account 2 earns 1.6% simple annual interest. if simon makes no additional deposit or withdrawals, which account is closest to the difference in the interest that the account will have earned at the end of 10 years. A. $253.01 B.$43.01 C.$83.01 D.$3.01
The difference in the interest that the account will have earned at the end of 10 years is of:
D. $3.01.
What is the account 1 interest earned?The amount of interest earned, in compound interest, after t years, is given by:
[tex]I(t) = P\left(1 + \frac{r}{n}\right)^{nt} - P[/tex]
In which the variables are listed as follows:
P is the principal.r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.In the context of this problem, these parameters are given as follows:
P = 250, r = 0.016, n = 12, t = 10.
Hence the interest earned by account 1 is:
[tex]I(10) = 250\left(1 + \frac{0.016}{12}\right)^{12 \times 10} - 250 = 43.35[/tex]
What is the account 2 interest earned?For simple interest, the amount of interest earned is:
I(t) = Prt.
Hence:
I(10) = 250 x 0.016 x 10 = 40.
Hence the difference is:
43.35 - 40 = $3.35.
Which is closest to option D.
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The total mass of cells in a petri dish is 3 × 10–2 gram. The mass of each cell is 4 × 10–5 gram.
How many cells are in the dish?
A. 7.5
B. 7,500
C. 75
D. 750
Solve the solution by substitution.
Y= —5x + 13
-6x + 6y = 6
Show/ explain your work
Answer:
the solution is (2, 3)
Step-by-step explanation:
Make this work easier by reducing the second equation:
-x + y = 1, or y = x + 1
Substititing x + 1 for y in the first equation, we get:
x + 1 = -5x + 13, or (after combining like terms):
6x = 12
Then x = 2, and bercause y = x + 1 (see above), y = 2 + 1 = 3
Then the solution is (2, 3)
ASAP!!!!!!!!!!!!!!!!!!
Answer:
d $258.50
Step-by-step explanation:
hope it helps
Which is greater 52.708 or 52.078
Answer:
52.708
Explanation:
It's 708 instead of 78 even rounded 52.708 would be more.
Answer:
52.708 is greater then 52.078
Step-by-step explanation:
Thats the answer!! Hope I could help u!! :)
Find the missing side or angle
Round to the nearest tenth.
C=95°
a=5
C=6
A=[ ? ]
Step-by-step explanation:
but you have to add or divide
Answer:
56.1
Step-by-step explanation:
may someone please help me out
C. 700 units.
The formula for the surface area of a rectangular prism is: 2 ((Width × Length) + (Height × Length) + (Height × Width))
(14 × 12) + (7 × 12) + (7 × 14)
168 + 84 + 98 = 350
Now do 350 × 2 = 700
700 units squared.
determine algebraically the zeros of f(x)=4x^3+32^2-36x
Answer:
x = 8
x = 1
Step-by-step explanation:
STEP 1:
Equation at the end of step 1
(22x2 - 36x) + 32 = 0
STEP 2:
STEP 3: Pulling out like terms
3.1 Pull out like factors :
4x2 - 36x + 32 = 4 • (x2 - 9x + 8)
Trying to factor by splitting the middle term
3.2 Factoring x2 - 9x + 8
The first term is, x2 its coefficient is 1 .
The middle term is, -9x its coefficient is -9 .
The last term, "the constant", is +8
Step-1 : Multiply the coefficient of the first term by the constant 1 • 8 = 8
Step-2 : Find two factors of 8 whose sum equals the coefficient of the middle term, which is -9 .
-8 + -1 = -9 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and -1
x2 - 8x - 1x - 8
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-8)
Add up the last 2 terms, pulling out common factors :
1 • (x-8)
Step-5 : Add up the four terms of step 4 :
(x-1) • (x-8)
Which is the desired factorization
Equation at the end of step
3
:
4 • (x - 1) • (x - 8) = 0
STEP
4
:
Theory - Roots of a product
4.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Equations which are never true:
4.2 Solve : 4 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
4.3 Solve : x-1 = 0
Add 1 to both sides of the equation :
x = 1
Solving a Single Variable Equation:
4.4 Solve : x-8 = 0
Add 8 to both sides of the equation :
x = 8
Supplement : Solving Quadratic Equation Directly
Solving x2-9x+8 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex:
5.1 Find the Vertex of y = x2-9x+8
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 4.5000
Plugging into the parabola formula 4.5000 for x we can calculate the y -coordinate :
y = 1.0 * 4.50 * 4.50 - 9.0 * 4.50 + 8.0
or y = -12.250
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-9x+8
Axis of Symmetry (dashed) {x}={ 4.50}
Vertex at {x,y} = { 4.50,-12.25}
x -Intercepts (Roots) :
Root 1 at {x,y} = { 1.00, 0.00}
Root 2 at {x,y} = { 8.00, 0.00}
Solve Quadratic Equation by Completing The Square
5.2 Solving x2-9x+8 = 0 by Completing The Square .
Subtract 8 from both side of the equation :
x2-9x = -8
Now the clever bit: Take the coefficient of x , which is 9 , divide by two, giving 9/2 , and finally square it giving 81/4
Add 81/4 to both sides of the equation :
On the right hand side we have :
-8 + 81/4 or, (-8/1)+(81/4)
The common denominator of the two fractions is 4 Adding (-32/4)+(81/4) gives 49/4
So adding to both sides we finally get :
x2-9x+(81/4) = 49/4
Adding 81/4 has completed the left hand side into a perfect square :
x2-9x+(81/4) =
(x-(9/2)) • (x-(9/2)) =
(x-(9/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-9x+(81/4) = 49/4 and
x2-9x+(81/4) = (x-(9/2))2
then, according to the law of transitivity,
(x-(9/2))2 = 49/4
We'll refer to this Equation as Eq. #5.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(9/2))2 is
(x-(9/2))2/2 =
(x-(9/2))1 =
x-(9/2)
Now, applying the Square Root Principle to Eq. #5.2.1 we get:
x-(9/2) = √ 49/4
Add 9/2 to both sides to obtain:
x = 9/2 + √ 49/4
Since a square root has two values, one positive and the other negative
x2 - 9x + 8 = 0
has two solutions:
x = 9/2 + √ 49/4
or
x = 9/2 - √ 49/4
Note that √ 49/4 can be written as
√ 49 / √ 4 which is 7 / 2
Solve Quadratic Equation using the Quadratic Formula
5.3 Solving x2-9x+8 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -9
C = 8
Accordingly, B2 - 4AC =
81 - 32 =
49
Applying the quadratic formula :
9 ± √ 49
x = —————
2
Can √ 49 be simplified ?
Yes! The prime factorization of 49 is
7•7
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 49 = √ 7•7 =
± 7 • √ 1 =
± 7
So now we are looking at:
x = ( 9 ± 7) / 2
Two real solutions:
x =(9+√49)/2=(9+7)/2= 8.000
or:
x =(9-√49)/2=(9-7)/2= 1.000
Two solutions were found :
x = 8
x = 1
On a coordinate grid the x axis represents the age of a plant in weeks, and the y axis represents the height of the plant in inches. After 2 weeks, the plant was 4 inches tall. Write the coordinates.
Answer: (2,4)
Step-by-step explanation: The coordinates are 2,4
HELPP ASAP IS PLEASEEE DONT SEND A FILE AT ALL STEP BY STEP EXPLANATION
Answer:
x + 6 y - 4
Step-by-step explanation:
A moved 6 units to the right so plus 6 then moved 4 units down so minus 4
Find the value of x explain how you got your answer
Answer:
step 1: x+50+4x=90
the angle of a right-angled triangle is 90 degrees, therefore if we add everything together ,we could work out what x is.
step 2: x+50+4x=90
x+4x=50
5x=50
x=10
then you solve the equation, x is 10
Sam is going to put wooden baseboard around a rectangular bedroom.
The length of the bedroom is 26 feet. The width is 1/2 of the length.
How many feet of baseboard does Sam need?
Answer: 338 Sq. Ft.
Step-by-step explanation:
26 is the identified length, half of 26 is 13 therefor 13 is the width. Length x Width gives you the area, 26 x 13 gives you 338 Sq. Ft.
Rewrite in radical form 1/-3/6^x
Answer:
[tex] \frac{1}{ \frac{ - 3}{ {6}^{x} } } \\ = 1 \times \frac{ {6}^{x} }{ - 3} \\ = - \frac{ {6}^{x} }{3} [/tex]
What value is a discontinuity of
(x2 + 3x -4)/(x2 + x -12)?
Answer:
x=-4 , x=3
Step-by-step explanation:
just did it on math-ways
Which table represents a linear function?
Rafael drove 819 miles in 13 hours. At the same rate how many miles would he drive in 5 hours
Answer:
315
Step-by-step explanation:
819 miles/13 hours = 63 miles per hour
63 x 5 = 315
Please help me last time I asked 2 days ago! No one answered. :(
Answer: The answer is number 4
Step-by-step explanation:
The answer is the one in the right up, the first one.
What transformations are applied to the graph of the function f(x)=10^x to produce the function g(x)=3(10)^x-2
A.) a vertical dilation by a factor of 3 and a horizontal shift to the right 2 units
B.) a vertical dilation by a factor of 1/3 and a horizontal shift to the right 2 units
C.) a vertical dilation by a factor of 1/3 and a vertical shift down 2 units
D.) a vertical dilation by a factor of 3 and a vertical shift down 2 units
Answer:
D) A vertical dilation by a factor of 3 and a vertical shift down 2 unitsStep-by-step explanation:
Given
f(x)=10^xg(x)=3(10)^x - 2We see that:
g(x) = 3f(x) - 2This is a vertical stretch by a factor of 3 and translation down 2 units
Correct choice is D
The distance be
Find the distance between P and Q
9514 1404 393
Answer:
10
Step-by-step explanation:
The distance formula is useful.
d = √((x2 -x1)^2 +(y2 -y1)^2)
d = √((7 -1)^2 +(12 -4)^2) = √(6^2 +8^2) = √(36 +64) = √100
d = 10
The distance between P and Q is 10.
_____
Additional comment
You may recognize the run : rise ratio of 6 : 8 = 3 : 4. This suggests a 3-4-5 right triangle with a scale factor of 2. If you're familiar with that Pythagorean triple, you can write down the answer as soon as you see the rise and run numbers.
Find the areas of a circle whose diameter is 21 cm
Answer:
Your answer is 346.36059
Step-by-step explanation:
A = pi*r²
A = pi * 10.5²
A = pi * 110.25
A = 346.36059
We can write the the area of the circle as 110.25π square centimeter.
What is Area?Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -
V = ∫∫F(x, y) dx dy
Given is a circle whose diameter is 21 cm.
It is asked to find the area of a circle whose diameter is 21 cm.
It is given that the diameter of the circle is -
d = 21 cm
r = d/2 = 21/2
r = 10.5 cm
We know that the area of the circle as -
Area = πr²
Area = π x 10.5 x 10.5
Area = 110.25π
So, it can be concluded that the area of the circle is 110.25π square centimeter.
Therefore, we can write the the area of the circle as 110.25π square centimeter.
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A spinner with five equal-sized sections numbered 1 through 5 is shown. The spinner is spun twice and the product of the numbers in the sections where the arrow lands is calculated. What is the probability that the product of the numbers is even?
A.)1/16
B.)4/25
C.)1/2
D.)16/25
Answer: The Answer is D.) 16/25
Step-by-step explanation: I got it correct on Study Island
Amelia received $4.15 in tips from one table. All of her tips were in quarters, dimes and nickels. There were five less dimes than quarters and three more nickels than twice the number of quarters. How many dimes did she have?
Answer:
the answer is 23.........
a truck has 36 inch diameter. how far does the truck roll if the wheels rotate 5 complete revolutions. round answer to the nearest tenth of an inch
Resposta:
180
Espero ter ajudado
"People should not be afraid of their governments.
Governments should be afraid of their people." [V]
DO YOU AGREE????
YES OR NO
Answer:
YESSSSSSSSSSSSSSSSSS
i mean theres a ton of us we can over power them anytime!
through: (2,-2) slope = -2
y=mx+b
-2=-2(2)+b what ur answer
Answer:
b= 2
Step-by-step explanation:
x=2
y=-2
slope= -2
y=mx+b
-2= -2(2) + b
-2= -4 +b
-2+4= b
2= b
Answer:
2=b through the slope -2=-2(2)+b
-2/7 + 1/3 , what would this be?
Answer:
1/21Step-by-step explanation:
-2/7 + 1/3 = 3(-2) / 3(7) + 7(1) / 7(3) = -6/21 + 7/21 = (-6 + 7) / 21 = 1/21Answer:
[tex]\sf \dfrac{1}{21}[/tex]
Step-by-step explanation:
[tex]\textsf{To calculate}-\dfrac{2}{7}+\dfrac{1}{3}, \: \textsf{ first make the denominators the same}.[/tex]
[tex]\textsf{Adjust the fractions based on their lowest common multiplier}:[/tex]
[tex]\implies -\dfrac{2}{7} \cdot \dfrac{3}{3} + \dfrac{1}{3} \cdot \dfrac{7}{7}[/tex]
[tex]\implies -\dfrac{2 \cdot 3}{7 \cdot 3} + \dfrac{1 \cdot 7}{3 \cdot 7}[/tex]
[tex]\implies -\dfrac{6}{21}+\dfrac{7}{21}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \dfrac{-6+7}{21}[/tex]
[tex]\textsf{Add the numbers of the numerator}:[/tex]
[tex]\implies \dfrac{1}{21}[/tex]
Learn more about fractions here:
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The ratio of cups of sugar to cups of flour needed to bake cookies is 1:5.
If Myesha uses 25 cups of flour, how much sugar is needed? *
what is the solution to 1< 25-4x<19?
Can someone please help me!! Ive been asking for help and I not getting any.. please help
HELP!!!!
What is the surface area of the figure below?
surface area= perimeter x height + 2b
s= pxh+2b
example: 18(8)+2(12)
explain: 18 is the perimeter and 8 is the height then you have to add the base times 2