Answer:
59
Step-by-step explanation:
[tex](-6)^2-5(-6)-7[/tex]
[tex]36+30-7[/tex]
[tex]59[/tex]
You invest $600 in an account that has a annual interest rate of 7%, compounded quarterly for four years. What is the equivalent interest rate, and how many times will the money be compounded?
1.75% and 1 time
5.7% and 4 times
1.75% and 16 times
5.7% and 16 times
Answer:
1.75% and 16 times
Step-by-step explanation:
Compound interest formula:
[tex]\sf A=P(1+\frac{r}{n})^{nt}[/tex]
where:
A = final amountP = initial principal balancer = annual interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periodsGiven:
P = $600r = 7% = 0.07n = 4t = 4Substituting given values into the formula:
[tex]\sf \implies A=600(1+\frac{0.07}{4})^{4 \times4}[/tex]
[tex]\sf =791.9576107...[/tex]
Equivalent interest rate:
[tex]\sf \implies \dfrac{r}{n}= \dfrac{0.07}{4}=0.0175=1.75 \%[/tex]
Number of times compounded:
[tex]\sf \implies nt=4 \times 4=16[/tex]
I need some help with these math questions.
Answer:
For the first question, D is the correct answer.
For the second question, B is the correct answer.
Step-by-step explanation:
First question:
[tex]5.89 + .61(30) = 24.19[/tex]
[tex]5.89 + .61(35) = 27.24[/tex]
So D is the correct answer.
Second question:
A function is a relation in which each element in the domain corresponds to one and only one element in the range. That said, relations A, C, and D are not functions since in each of these relations, one element in the domain corresponds to two elements in the range. Only relation B is a function.
A philanthropist pledges to donate 13% of a fund each year. If the fund initially has $761,000.00, how much will the fund have after 16 years?
Please type answers with no commas and round to 2 decimal places.
If the philanthropist pledges to donate 13% of a fund each year, at the end of 16 years, the fund will have $35,517,190.20.
How much would the fund have after 16 years?The formula that can be used to determine the value of the fund after 16 years is:
Initial value of the fund x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
(1.13^16 - 1) / 0.13 = 46.671735
46.671735 x $761,000.00 = $35,517,190.20
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bellamy is building a gate to put on a fence. the gates measurements are 7 feet by 7 feet a diagonal wooden brace is going to be attached to keep the gate rigid what is the length of wood bellany needs to cut for the brace leave your answer in simplified radical form
The length of the diagonal is the hypotenuse of the fence
The length of the wood is [tex]7\sqrt{ 2[/tex] yards
How to determine the length of the wood?The dimensions of the fence are:
7 ft by 7 ft
The length (L) of the diagonal is calculated using:
[tex]L = \sqrt{a^2 + b^2[/tex]
This gives
[tex]L = \sqrt{7^2 + 7^2[/tex]
Express as products
[tex]L = \sqrt{7^2 * 2[/tex]
Express as radical
[tex]L = 7\sqrt{ 2[/tex]
Hence, the length of the wood is [tex]7\sqrt{ 2[/tex] yards
Read more about diagonals at:
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Use the spinner to answer the question. It is divided into 8 congruent sections. Orange, Blue, Pink, Brown, Purple, Red, Bronze, Black. Determine whether the statement is true or false. After 96 spins, Tiffany would expect the spinner to land on a color section beginning with the letter "B" roughly 48 times.
Using proportions, it is found that the statement that Tiffany would expect the spinner to land on a color section beginning with the letter "B" roughly 48 times is True.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, out of 8 sections, 4(Blue, Brown, Bronze and Black) begin with letter "B". We want to find the equivalent amount out of 98 trials. Hence, the rule of three is:
8 trials - 4 start with "B".
96 trials - n start with "B".
Applying cross multiplication:
8n = 4 x 96
n = 0.5 x 96
n = 48.
Hence, the statement is True.
More can be learned about proportions at https://brainly.com/question/24372153
Find the solution of the system of equations.
-
5x – 4y = -9
10x– 7y = -22
Answer:
x = -5
y = -4
Step-by-step explanation:
5x - 4y = -9
10x - 8y = -18
10x - 7y = -22
-y = 4
y = -4
Substitue y into any equation
5x - (-16) = -9
5x = -25
x = -5
Please assist. No links or your account is getting banned
9⁻³ / 9¹² = 9⁻³⁻¹² = 9⁻¹⁵
Answer:
[tex]9^-^1^5[/tex]
Step-by-step explanation:
[tex]\frac{9^{-3}}{9^{12}}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}[/tex]
[tex]=9^{-3-12}[/tex]
[tex]\mathrm{Subtract\:the\:numbers:}\:-3-12=-15[/tex]
[tex]=9^{-15}[/tex]
Answer [tex]=9^{-15}[/tex]
~Learn with Lenvy~
What is the best first step in solving the equation 3 +[tex]3\sqrt[6]{x}[/tex] = 5?
[tex]3+3\sqrt[6]{x}~~ = ~~5\implies \stackrel{\textit{1st step,-3 to both sides}}{3\sqrt[6]{x}~~ = ~~2}\implies \sqrt[6]{x}=\cfrac{2}{3} \\\\\\ (\sqrt[6]{x})^6=\left( \cfrac{2}{3} \right)^6\implies x=\cfrac{2^6}{3^6}\implies x=\cfrac{64}{729}[/tex]
does anyone know the answer to this question?
Answer:
c = 2.5 , d = - 3
Step-by-step explanation:
f(x) = cx + d
f(4) = 7 ( substitute x = 4 into the equation and equate to 7 )
f(10) = 22 ( substitute x = 10 into the equation and equate to 22 )
4c + d = 7 → (1)
10c + d = 22 → (2)
subtract (1) from (2) term by term to eliminate d
(10c - 4c) + (d - d) = 22 - 7 , that is
6c = 15 ( divide both sides by 6 )
c = 2.5
substitute c = 2.5 into (1) and solve for d
4(2.5) + d = 7
10 + d = 7 ( subtract 10 from both sides )
d = - 3
Answer:
c = 2.5
d = - 3
Step-by-step explanation:
f(x) = cx + d
f(4) = 7
f(10) = 22
4c + d = 7
10c + d = 22
(10c - 4c) + (d - d) = 22 - 7
6c = 15
--- ----
6 6
c = 2.5
4(2.5) + d = 7
10 + d = 7
-10 -10
d = - 3
State the domain and range and determine if it's a function?
if we do a vertical line test on that graph, we'll find that a vertical line will pass by and hit the line only once on its way down, only once meaning the graph is the graph of a function.
Rangewell, is really how high and low it goes or namely over the y-axis.
well, it goes up up up to 3 then U-turns and back down it goes, now the graph has arrowheads, meaning the graph keeps on going towards infinity, vertically as well as horizontally since it's a parabola, so the range will be
[3 , +∞)Domainwell, is simply how left and right it goes or namely over the x-axis.
judging from the arrowheads it moves from infinity to infinity, so
(-∞ , +∞).Solve these pair of simultaneous equations.In each case the first step is to subtract the two equations.Give both solutions;x and y.
x-6y=32
x-4y =24
2x-3y =2
2x + 4y = 44
Please work it out
HELP HELP HELP HELO HELP HELP HELP
This function is Exponential
Reason: Exponential graphs tend to get very big quickly, and though they start out smaller than polynomial functions or vice versa
Hope that helps!
What is the distance between B and C? The Graph Below.
Answer:
250cm
Step-by-step explanation:
Answer:
433.01m.
Step-by-step explanation:
SOHCAHTOA
cos60= a/500
500cos60=a
433.01m
This year Heather watched 20 movies. She thought that 9 of them were very good. Of the movies she watched, what percentage did she rate as very good?
Answer:
45%
Step-by-step explanation:
PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP
i need help with this hard question
Answer:
Bottom left = 8
Top right = 15
Middle right = 25
Step-by-step explanation:
Total = 40
3 + 5 = 8
40 / 8 = 5
1 part = 5
5 x 3 = 15
5² = 25
A 15-meter by 23-meter garden is divided into two sections. Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section. A rectangle is shown. The length of the top and bottom sides is 23 meters. The length of the left and right sides is 15 meters. A vertical line is drawn from the top to bottom side to split the shape into a square and a rectangle. Lines are drawn from the bottom left point to the top of the vertical line and from the bottom right point to the top of the vertical line. What is the approximate sum of the lengths of the two sidewalks, shown as dotted lines? 21. 2 m 27. 5 m 32. 5 m 38. 2 m.
Approximate sum of the lengths of the two sidewalks, shown as dotted lines in the figure of rectangle garden is 38.2 meters.
What is Pythagoras theorem?Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.
A 15-meter by 23-meter garden is divided into two sections. In this rectangle,
Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section. The length of the top and bottom sides is 23 meters. The length of the left and right sides is 15 meters.Here, a vertical line is drawn from the top to bottom side to split the shape into a square and a rectangle. The length of the left side of the square will be 15 long. Thus, the lenght of its diagonal is,
[tex]d_1=15\sqrt{2}\\d_1=21.213\rm\; m[/tex]
The length of the sidewalk in smaller rectangle in the right side of figure is,
[tex]d_2=\sqrt{15^2+8^2}\\d_2=17\rm\; m[/tex]
Sum of the lengths of the two sidewalks using the pythagoras theorem is,
[tex]S=21.2+17\\S=38.2\rm\;m[/tex]
Thus, approximate sum of the lengths of the two sidewalks, shown as dotted lines in the figure of rectangle garden is 38.2 meters.
Learn more about the Pythagoras theorem here;
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Answer:
D 38.2
Step-by-step explanation:
E2020
Swimming Pool On a certain hot summer's day, 163 people used
the public swimming pool. The daily prices are $1.25 for children
and $2.00 for adults. The receipts for admission totaled $257.00.
How many children and how many adults swam at the public pool
that day?
There were
children at the public pool.
Find the simple interest earned to the nearest cent for each principal, interest rate, and time 1,050, 4.6%, two years
Answer:
The interest earned is $96.60
Step-by-step explanation:
Since we are working the a simple interest problem, we will use the formula
[tex]I=Prt[/tex],
Where P represents the principal, r represents the rate as a decimal, and t represents the time in years. First, we need to change the 4.6% into a decimal by dividing by 100:
[tex]4.6\div 100 = 0.046[/tex]
From our given information and our decimal rate, we have:
[tex]P=1050\\r=0.046\\t=2[/tex]
Substituting these into our equation, we get:
[tex]I=1050(0.046)(2)\\I=96.6[/tex]
We write that as $96.60 in context of the problem.
Answer:
principle (p)=RS 1,050
Rate(R)=4.6
time(T)=2years
we know that
I=P×R×I/100
=1050×4.6×2/100
=9660/100
=96.6
therefore the earned simple interest is RS.96.6
Jill always buys the same kind of shampoo in an 11.5-ounce bottle. She is at the store buying more and sees that the bottle is now bigger and has 20% more for the same price. How many ounces of shampoo are in the new bottle.
Step-by-step explanation:
100% = 11.5
20% more means 120%
120% = 100%×1.2 = 11.5×1.2 = 13.8 ounces
Which point on this number line has a coordinate of 7.47?
Number line from 7.0 to 8.0 with tick marks every 1 one hundredth unit. Tick marks are numbered every tenth unit. Point A is 3 tick marks to the right of 7.3. Point B is 3 tick marks to the right of 7.4. Point C is 7 tick marks to the right of 7.4. Point D is 4 tick marks to the right of 7.7.
Point A
Point B
Point C
Point D
Answer:
I think it is point D
Step-by-step explanation:
hope this helps if it is wrong please let me now
Kim says that 1/4 x 12 is the same as dividing 12 by 4 do you agree with Kim? explain your answer.
Answer:
yes i do
Step-by-step explanation:
1/4 x 12= 3
12 divided by 4 = 3
Write the equation in standard form for the circle with center (0, -5) and radius 2
The standard equation for a circle is '[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h,k): coordinate for the center of the circle --> (0,-5)r: radius --> 2--> Standard form:
[tex](x - )^2 +(y-(-5))^2=2^2\\x^2+(y+5)^2=4[/tex]
Hope that helps!
Answer:
x^2 + (y + 5)^2 = 4.
Step-by-step explanation:
Standard form is (x - a)^2 + (y - b)^2 = r^2
- where (a, b) is the center and radius = r.
So our equation is:
(x - 0)^2 + (y - (-5))^2 = 2^2
x^2 + (y + 5)^2 = 4.
A pool company offers a pool with dimensions x and 2x. They also include a 3 foot deck around the entire pool.
1. Write an equation to represent the area of the pool and deck combined.
2. If someone wants a 10ft wide pool (x = 10) how many square feet must they have available in their back yard?
Answer:
1) area = (x + 3)(2x + 3) ft²
2) 299 ft²
Step-by-step explanation:
Question 1
Area of a rectangle = width x length
Given:
width = x + 3length = 2x + 3⇒ area = (x + 3)(2x + 3) ft²
Question 2
If x = 10:
⇒ area = (10 + 3)(2(10) + 3)
= 13 · 23
= 299 ft²
#1
New dimensions=x+3 and 2x+3ftSo
Area:-
Length ×Breadth(x+3)(2x+3)x(2x+3)+3(2x+3)2x^2+3x+6x+92x^2+9x+9ft^2#2
Put x=10
2(10)^2+9(10)+92(100)+90+9200+99299ft^2Find the area of a right triangle with side lengths 12 cm, 35 cm, and 37cm
Answer:
210 cm sq
Step-by-step explanation:
Area of a triangle is 1/2bh.
12 cm and 35 cm would be both sides of the triangle, not 37 cm because it is the hypotenuse (largest side).
1/2*12*35=210 cm sq
4) What is the slope of the line joining (7, 8) and (17, 13)
slope is = (13 - 8) / (17 - 7) = 5/10 = 1/2 or 0,5
slope for A (xa ; ya) and B (xb ; yb) = (yb - ya) / (xb - xa)
What is 125x to the 3rd power +343y to the 3rd power
Answer: 125 to the power of 3 = 1253 = 1,953,125
What is the value of x?
Answer:
x = 9 cm
create proportional equation:
[tex]\sf \dfrac{9}{3x-20} = \dfrac{72+9}{3x-20+56}[/tex]
[tex]\sf \dfrac{9}{3x-20} = \dfrac{81}{3x+36}[/tex]
[tex]\sf 9(3x+36) = 81(3x-20)[/tex]
[tex]\sf 27x+324 = 243x-1620[/tex]
[tex]\sf 27x-243x=-1620-324[/tex]
[tex]\sf -216x=-1944[/tex]
[tex]\sf x = 9[/tex]
Answer:
x = 9Step-by-step explanation:
Since parallel lines cut the transversals proportionally, we can set the following equation and solve for x;
72/9 = 56/(3x - 20)8 = 56/(3x - 20)3x - 20 = 56/83x - 20 = 73x = 27x = 9A bag contains 40 red and green marbles. The number of green marbles, g, is 9 times the number of red marbles, r.
How many red marbles are in the bag?
Answer:
4 red marbles
Step-by-step explanation:
r is the number of red marbles then green marbles is 9r , so
r + 9r = 40
10r = 40 ( divide both sides by 10 )
r = 4
there are 4 red marbles
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SOLVE THIS SYSTEM OF EQUATIONS BY USING THE ELIMINATION METHOD.
3x + 2y = 6
-3x + y + 12
the ordered pair of solutions is written in the format (x, y)
([x], [y])
[tex]3x + 2y = 6[/tex]
[tex] - 3x + y = 12[/tex]
Add the systems:[tex]3x - 3x + 2y + y = 6 + 12[/tex]
[tex]3y = 18[/tex]
[tex]y = \frac{18}{3} = 6[/tex]
Replace y=6 in any equation:[tex]3x + 2y = 6[/tex]
[tex]3x + 2(6) = 6[/tex]
[tex]3x + 12 = 6[/tex]
[tex]3x = 6 - 12[/tex]
[tex]3x = - 6[/tex]
[tex]x = \frac{ - 6}{3} = - 2[/tex]
Pair: ( -2 , 6 )Write the log equation as an exponential equation. You do not need to solve for x.
In (3x + 2) = 3x
[tex]\ln(3x+2) = 3x\\\\\implies \log_e (3x+2) = 3x\\\\\implies e^{3x} = 3x+2[/tex]