Step-by-step explanation:
apter 5 – Finance – The first part of this review will explain the different interest and
investment equations you learned in section 5.1 through 5.4 of your textbook and go through
several examples. The second part of this review will give you various sample problems to work
on – you should know how to do all these sample problems for Exam II. The sample exam is
posted to the Math 113 webpage – please come to the Math Resource Center if you need help!
The sum of money you deposit into a savings account or borrow from a bank is called the
principal. The fee to borrow money is called interest. When you borrow money you pay back
the principal and interest to your lender. When you deposit money into a savings account or
other investment, the bank pays you back the principal and the interest earned. Interest is
calculated as a percent of the money borrowed, a percent of the principal. Depending on the type
of loan, interest can be calculated in a variety of ways.
Simple Interest Loans (Section 5.1) :
Simple Interest involves a single payment and the interest computed on the principal only. The
equation for simple interest is a linear function. If the problem refers to a simple interest rate,
then you know you need to use simple interest rate formulas.
Equation #1:
:
Pr
where
I = t
I = the amount of interest paid for borrowing the money
P= the principal or the amount of money you borrowed from the bank
r = is the simple interest rate – this is a per annum rate (i.e. yearly)
t = the amount of time the money is borrowed for – this needs to be in years if the problem gives
you t in months then you need to divide the number of months by 12 to convert t into years.
Equation #2:
A = (P+Prt)=P*(1+rt)
where:
A = the future value - the total amount the borrower owes at the end of the loan period – this is
Principal plus Interest.
I = the amount of interest paid for borrowing the money
P= the principal or the amount of money you borrowed from the bank
r = is the simple interest rate – this is a per annum rate (i.e. yearly)
t = the amount of time the money is borrowed for – this needs to be in years if the problem gives
you t in months then you need to divide the number of months by 12 to convert t into years.
Equation #3:
I = A – P
where:
A = the total amount you owe at the end of the loan period – this is Principal plus Interest.
I = the amount of interest paid for borrowing the money
Which value is the best estimate for 6√10
Answer:
18.97366596
Step-by-step explanation:
round however manu you need too
PLZ HELP PLZ PLZ ILL MARK AS BRAINLIESTT!!!
Answer: D lol-
Step-by-step explanation:
Answer: 37
Step-by-step explanation:
25 x.75 = 18 but x 2 = 37.5
Solve for x. Answer as a whole number.
Given:
In triangle ABC, AE is the angle bisector.
[tex]AB=4, BE=2, AC=x, CE=3[/tex]
To find:
The value of x.
Solution:
According to the angle bisector theorem, the angle bisector of a triangle divides the opposite side of the triangle into two parts. These two parts are proportional to the other two sides of the triangle.
Using the angle bisector theorem, we get
[tex]\dfrac{AB}{AC}=\dfrac{BE}{CE}[/tex]
[tex]\dfrac{4}{x}=\dfrac{2}{3}[/tex]
On cross multiplication, we get
[tex]4\times 3=2\times x[/tex]
[tex]12=2x[/tex]
Divide both sides by 2.
[tex]\dfrac{12}{2}=x[/tex]
[tex]6=x[/tex]
Therefore, the value of x is 6.
What is the solution of the following system of linear equations?
y = x - 7
2y + x=1
Answer:
x=5
y=-2
Step-by-step explanation:
I just took this!
Hope I helped
can someone do my math homework pls its on (quadratics)
I want to try but I am tooooo much bad in math
Why do you sometimes finish the square (ex.[tex]x^{2} + 4x=1[/tex]) and sometimes you make one side zero(ex[tex]x^{2} -12x=-35[/tex])? How should I know the difference? Any help is appreciated! TIA
Answer:
Lets say there's a quadratic equation → ax² + bx = -c
Lets make one side zero which gives → ax² + bx + c = 0
From the above equation ,
if you can split b into 'p' & 'q' (some real numbers) such that p + q = b & pq = ac ; then the quadratic equation can be easily solved by using factorisation method. Here the easiest way to guess the values of 'p' & 'q' is to find out the prime factors of 'ac' and taking any two prime numbers in random , just check whether the sum of those two primes is equal to 'b' (excluding their signs).if you can't split b into 'p' & 'q' (some real numbers) such that p + q = b & pq = ac ; then try solving quadratic equation by completing the squares method.For example :- x² - 12x = -35.
Lets make one side zero → x² - 12x + 35 = 0 . Now, lets break -12x into two real numbers 'p' & 'q' such that p + q = -12x & pq = 35. Prime factors of 35 are 1 , 5 & 7. If we take 5 & 7 as 'p' & 'q' then p + q = 5 + 7 = 12. but as we need -12 , the values of 'p' & 'q' are -5 & -7.
⇒ [tex]x^2 -5x - 7x + 35 = 0[/tex]
⇒ [tex]x(x - 5) - 7(x - 5) = 0[/tex]
⇒ [tex](x - 5)(x - 7) = 0[/tex]
⇒ [tex]x = 5 \: or \: 7[/tex]
Lets take another example :- x² + 4x = 1.
Lets make one side zero → x² + 4x - 1 = 0 . Now , lets split +4x into into two real numbers 'p' & 'q' such that p + q = +4x & pq = -1 . Prime factors of 4 are 1 & 2 only. But there's no such combination of its primes such that their sum would be equal to 4. So, the quadratic equation can't be solved by factorisation method. Now, lets bring -1 to Right Hand Side & try solving by completing squares method.
⇒ [tex]x^2 + 2 \times x \times 2 + 2^2 = 1 + 2^2[/tex]
⇒ [tex](x + 2)^2 = 1 + 4 = 5[/tex]
⇒ [tex]x + 2 = +\sqrt{5} \: \: or \: -\sqrt{5}[/tex]
⇒ [tex]x = (\sqrt{5} - 2) \: or \: (-\sqrt{5} -2)[/tex]
Conclusion:
First try making one side zero and try to solve the equation by factorisation method. If it got factorised , then you are done and if it didn't get factorised , then solve it by completing squares method.
Answer:
I'm assuming we're asking about the difference between:
[tex]ax^2 + bx + c = 0[/tex]
and
[tex]ax^2 + bx = -c[/tex]
Let's preface this by stating the obvious: there's no actual difference. Both equations are equivalent.
Now, it has a lot to do with our goal. Sometimes our goal is to write an equation concisely (then the "no-zero" way uses less characters), and sometimes we're dealing with a quadratic function of
[tex]y = ax^2 + bx + c[/tex]
in the second case, we wouldn't write
[tex]y - c = ax^2 + bx[/tex]
because it'd be confusing. That means that when we're looking for y=0 points of a quadratic equation, the way to convey that goal is that we're looking for the point where [tex]ax^2 + bx + c = 0[/tex] - so we preserve the structure of the quadratic function.
Please help me correct my answers!! im really confused
The measure of arc BC is ___ degrees.
Answer:
84°
Step-by-step explanation:
Solve |3x - 4| = 6
please help me solve
Step-by-step explanation:
|3x - 4| = 6
3x-4 = 6 or 3x-4 = -6
3x=6+4 3x=-6+4
3x=10 3x = -2
x= 10/3 x = -2/3
so, x1= 10/3 or x2 = -2/3
What is 4x/7 - 2/3
Fraction help
Answer:
2/21 * (6x-7)
Step-by-step explanation:
1/21 * (3*4x - 14)
1/21* (12x-14)
1/21* 2(6x-7)
2*1/21 * (6x-7)
2/21* (6x-7)
Which has a slope of 4 and a y-intercept of -2
Answer:
C
Step-by-step explanation:
Have a good day :)
Juliet wants to know if the chicken broth in this beaker will fit into this rectangular food storage container.
a) Explain how you would figure it out without pouring the contents in. (Remember: 1 cm3 = 1 mL.)
Answer:
Doesn't fit
Step-by-step explanation:
There are 2.4litres in the beaker if you count the lines; they increment by 0.4 litres each. The volume of the storage container is 20 x 15 x 7 = 2100 cm^3 (cm cubed). 1 cm^3 = 1 ml; the cube can hold 2100 mL which is 2.1 litres, which is less than the 2.4 litres in the beaker, therefore it will not fit.
This beaker will not fit into this rectangular food storage container.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Since, There are 2.4litres in the beaker, they increment by 0.4 liters each.
Hence, The volume of the storage container is,
⇒ 20 x 15 x 7
⇒ 2100 cm³
Since, Here we have;
1 cm³ = 1 ml
So, The cube hold 2100 mL which is 2.1 liters,
Clearly, It is less than 2.4 liters in the beaker.
Thus, This beaker will not fit into this rectangular food storage container.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ3
please answer accurately with a full explanation and please don't do short answers thank u, and if u spam this question u will be reported. please answer with a proper answer, not a short one thank u so much
Answer: 31500 cm^3
Step-by-step explanation:
Volume = Length x Width x Height
60 x 35 x 15= 31500
when we multiply three times it is known as cube /^3
answer is 31500 centimeters cube
What is the volume of the prism? The image is here. Please help.
Answer: 42
How to: Height = 7 weight = 2 length = 3
multiply all together is 42 .
Have a great day and stay safe !
last one please help will mark brainest plz helpppp urgent
Convert the following equation into slope intercept form y-6=2(x+4)
Answer:
y = 2x +14
Step-by-step explanation:
We need to convert the given equation into slope intercept form ,
=> y - 6 = 2(x+4)
=> y -6= 2x + 8
=> y = 2x +8+6
=> y = 2x + 14
• Hence the required answer is y = 2x + 14
The table models how the population of a city has changed over time. What does the y-intercept represent?
Answer:
Since it is 0 years after 1985, the y intercept means that the population was 122,000 in 1985.
Step-by-step explanation:
Find the area of the shaded region.
Round to the nearest tenth.
Answer:
The area of the shaded region is 11.606 square centimeters.
Step-by-step explanation:
The area of the shaded region is obtained by subtracting the area of the triangle from the area of the circular section. The area of the triangle ([tex]A_{t}[/tex]), in square centimeters, can be calculated by the Heron's formula:
[tex]A_{t} = \sqrt{s\cdot (s-a)\cdot (s-b)\cdot (s-c)}[/tex] (1)
[tex]s = \frac{a + b + c}{2}[/tex] (2)
Where:
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Lengths of the sides of the triangle, in centimeters.
[tex]s[/tex] - Semiperimeter, in centimeters.
If we know that [tex]a = 10.50\,cm[/tex] and [tex]b = c = 9.28\,cm[/tex], then the area of the triangle is:
[tex]s = \frac{10.50\,cm + 2\cdot (9.28\,cm)}{2}[/tex]
[tex]s = 14.53\,cm[/tex]
[tex]A_{t} = \sqrt{(14.53\,cm)\cdot (14.53\,cm - 10.50\,cm)\cdot (14.53\,cm - 9.28\,cm)^{2}}[/tex]
[tex]A_{t} \approx 40.174\,cm^{2}[/tex]
And the area of the circular section ([tex]A_{c}[/tex]), in square centimeters, is determined by the following formula:
[tex]A_{c} = \left(\frac{\theta\cdot \pi}{360} \right)\cdot r^{2}[/tex] (3)
Where:
[tex]r[/tex] - Radius of the circle, in centimeters.
[tex]\theta[/tex] - Internal angle, in sexagesimal degrees.
If we know that [tex]r = 9.28\,cm[/tex] and [tex]\theta = 68.9^{\circ}[/tex], then the area of the circular section is:
[tex]A_{c} = \left(\frac{68.9}{360}\right)\cdot \pi\cdot (9.28\,cm)^{2}[/tex]
[tex]A_{c} \approx 51.780\,cm^{2}[/tex]
Finally, the area of the shaded region ([tex]A[/tex]), in square centimeters, is:
[tex]A = A_{c} - A_{t}[/tex] (4)
[tex]A = 51.780\,cm^{2}- 40.174\,cm^{2}[/tex]
[tex]A = 11.606\,cm^{2}[/tex]
The area of the shaded region is 11.606 square centimeters.
You and your friends went to dinner and you decided to pay for everyone's meal. The total bill came to $65.00. You decided to give the waiter a 20% tip before tax. You also had to pay 6.8% sales tax. How much did you have to pay in all?
Answer:
82.236
Step-by-step explanation:
20% of 65 is 12
65+12=77 before tax
6.8% of 77=5.236
77+5.236=82.236
On a map, 1 inch equals 7.4 miles. Two houses are 1.5 inches apart on the map.
What is the actual distance between the houses?
Answer:
11.1 miles.
Step-by-step explanation:
1 inch is 7.4 miles.
1.5 inch is 7.4 times 1.5 miles.
11.1 miles.
What is the average rate of change for this quadratic function for the interval from x = 0 to x = 2?
A. 4
B. 2
C. -4
D. -2
Answer:
Option B
Step-by-step explanation:
Average rate of change of a function between x = a and x = b will be,
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
We have to calculate average rate of change of the given quadratic function between x = 0 and x = 2.
From the given graph,
f(2) = 6
f(0) = 10
Therefore, average rate of change = [tex]\frac{f(2)-f(0)}{2-0}[/tex]
= [tex]\frac{10-6}{2-0}[/tex]
= 2
Option B will be the answer.
PLEASE HELP 20 points
Answer:
2.greatest common factor is 4
3.[tex]x^{2}[/tex]-3x-10
[tex]x^{2}[/tex]-(5-2)x-10
[tex]x^{2}[/tex]-5x+2x-10
x(x-5)+2(x-5)
(x+2)(x-5)
Step-by-step explanation:
Answer:
2. 4
3. (x+2)(x−5)
Step-by-step explanation:
Question One.
Factor 8x+12
8x+12
4(2x+3)
Question Two.
Factor [tex]x^{2}[/tex]−3x−10
The middle number is -3 and the last number is -10.
Factoring means we want something like:
(x+_)(x+_)
We need to figure out which numbers go in the blanks.
You will need two numbers. They need to...
Add together to get -3.
Multiply together to get -10.
2+-5=-3
2·-5=-10
Fill in the blanks.
(x+2)(x-5)
Answer:
(x+2)(x−5)
Sam is 10 years younger than one-half the age of his aunt. Let a represent his aunt’s age. Which algebraic expression can be used to determine Sam’s age if his aunt is 40?
Find the tangent ratio of angle Θ
Answer:
4 / 3
Step-by-step explanation:
tan x = opposite / adjacent
tan x = AB / AC
tan x = 4 / 3
{ x = theta ]
9514 1404 393
Answer:
tan(θ) = 4/3
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Tan = Opposite/Adjacent
Then ...
tan(θ) = AB/AC
tan(θ) = 4/3
Work out the surface area of this solid prism
Answer:
3220 cm²
Step-by-step explanation:
Lets find the area of the two triangles
I am making a modification:
Both of the triangles are the same, so I wont divide by 2 using the area of triangle formula 1/2(b * h) because we end up multiply by 2
Area of triangles = 15 cm x 28 cm = 420 cm²
Area of front facing parallelogram = 24 cm x 4(10)cm = 100(10)cm = 1000 cm²
Area of back facing parallelogram = 17 cm x 40 cm = 680 cm²
Area of bottom parallelogram = 40 cm x 28 cm = 1120 cm²
Total Surface area = 420 cm² + 1000 cm² + 680 cm² + 1120 cm² = 1100 cm² + 2120 cm² = 3220 cm²
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Solve the equation for y. Then find the value of y for each value of x.
y + 5x = 8; x = - 2, 0,3
Solve the equation for y.
Answer:
y = 8 - 5x, y(-2) = 18, y(0) = 8, y(3) = -7
Step-by-step explanation:
y + 5x = 8
y = 8 - 5x
y(-2) = 8 - 5*(-2) = 8 + 10 = 18
y(0) = 8 - 5*(0) = 8 - 0 = 8
y(3) = 8 - 5*(3) = 8 - 15 = -7
Evaluate the expression for the given value.
3x(x−2), when x=7 .
Answer:
[tex]\huge\boxed{Answer\hookleftarrow}[/tex]
Given,
[tex]x = 7[/tex]
Substitute the value of 'x' in the equation 3x (x - 2).
One way :-
[tex]3x(x - 2) \\ = 3 \times 7(7 - 2) \\ = 21(5) \\ = 21 \times 5 \\ = 105[/tex]
Second way :-
[tex]3x(x - 2) \\ = 3x {}^{2} - 6x \\ = 3 \times (7) {}^{2} - 6(7) \\ = (3 \times 49) - (6 \times 7) \\ = 147 - 42 \\ = 105[/tex]
✐ The answer is 105.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
# ꧁❣ RainbowSalt2²2² ࿐
HELP! i only have 5 minutes to turn it in if you already did it im on 50 percent give me all answers this is 5th grade
there are 4 trucks for every 5 cars in a parking lot. how many trucks and cars could be in the parking lot? A. 64 trucks and 80 cars B. 72 trucks and 73 cars C. 84 trucks and 100 cars D. 96 trucks and 110 cars
Answer:
A.
Step-by-step explanation:
64/4=16 80/5=16 They are multiplied by the same number so it is A
Find the volume of each square pyramid given its slant height. Round to the nearest tenth. It looks like a normal pyramid with a slant height of 2.8 and a base of one of the triangles is 1.2.
Answer:
1.344 cubic units
Step-by-step explanation:
Given data
Base edge a= 1.2
Hieght= 2.8
The expression for the volume of a pyramid is
V= a^2h/3
substitute
V= 1.2^2* 2.8/3
V= 1.44*2.8/3
V= 4.032/3
V= 1.34cubic units
During a sale, a store offered 60% discount on a particular camera that was originally priced $450. After the sale, the discounted price of the camera was increased by 60%. What was the price of the camera after this increase?
Answer:
$288.00
Step-by-step explanation:
Im just going off what my calculator told me, but im 95% sure its correc
450- 60%= 180
180+60%=288