Answer:
The quotient of these numbers is 1.7 × 10⁴
Scientifically in the notion, these would be the correct numbers.
The quotient of the given numbers is 1.7×10⁴.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.
The given numbers are 7.14×10⁷ and 4.2×10³.
Here, quotient = 7.14×10⁷ ÷ 4.2×10³
= 1.7×10⁴
Therefore, the quotient of the given numbers is 1.7×10⁴.
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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)
Could the following side lengths make a right triangle?
28, 53, 45
Answer:
no. the triangle would be acute
Step-by-step explanation:
[tex]a^2 +b^2=c^2[/tex] ← formula for right triangle
↓
[tex]28^2+53^2=45^2[/tex]?
↓
[tex]28^2=784\\53^2=2809\\45^2=2025[/tex]
↓
[tex]784+2809=3,593[/tex]
↓
[tex]3,593 > 2025\\a^2 +b^2 > c^2[/tex]
which means the triangle is acute, not right.
Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day!
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−Kallmekrish
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~
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
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
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
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 WILL GIVE BRAINLIEST TO WHOEVER ANSWERS!!!
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 )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 area of a sector with a central angle of 10π7 radians and a radius of 18. 4 m? Use 3. 14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box. M².
The area of the sector of the circle will be 759.34 m². It is the amount of area enclosed inside the sector's perimeter.
What is an area of the sector?The area of a circle's sector is the amount of space encompassed inside the sector's perimeter. The origin of a sector is always the circle's center.
The region of a circle encompassed by its two radii and the arc connecting them is known as the sector of a circle.
The given data in the problem is;
[tex]\rm \theta[/tex] is the central angle=[tex]\frac{10\pi}{7}[/tex]= 4.485
r is the radius = 18.4 m
The area of a sector of a circle is found as;
[tex]\rm A= \frac{\theta}{2} \pi r^2 \\\\ \rm A= \frac{4.485}{2} \times (18.4)^2 \\\\ \rm A=759.34 \ m^2[/tex]
Hence the area of the sector of the circle will be 759.34 m².
To learn more about the area of the sector refer to the link;
https://brainly.com/question/1582027
A candy bar box is in the shape of a triangular prism. The volume of the box is 2,400 cubic centimeters.
A triangular prism is shown with base of triangle labeled 16 cm, sides of triangles labeled 17 cm, and length of the box equal to 20 cm.
Part A: What is the height of the base? Show your work. (5 points)
Part B: What is the approximate amount of cardboard used to make the candy box? Explain how you got your answer. (5 points)
Answer: the answer is 1000cm2.
The volume of a triangular prism shaped box is 2,400 cubic centimeters.
Base of the triangle = 16cm
Sides of the triangle = 17cm
Length of the box = 20cm
Triangular prismA triangular prism is a three-sided prism made of a triangular base and a corresponding side.
A. To find the height of the base = 3 x the volume divided by the base area = 15cm. B. The approximate amount of card board used to make the candy box:Using the lateral prism as the sides will be:Lateral area = Perimeter of triangle X height of the prism
Lateral area = (16 + 17 + 17) X 20
Lateral area = 50 X 20
Lateral area = 1,000 cm2
Therefore, the answer is 1000cm2.
A 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
PLS ANSWER IT I just need the answer
The y-intercept is (0,2)
you can find the y-intercept by finding the value of y when x = 0The slope is -5/2.
you can find the slope by using the equation below and any two points on the line, such as (0,2) and (2,-3)[tex]\frac{y2-y1}{x2-x1}=\frac{-3-2}{2-0} =\frac{-5}{2}[/tex]
Hope that helps!
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]
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
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:
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If the cost of a dozen pencil is ₹ 159.48, what will be the cost of 24 such pencil?
Answer:
₹ 318.96.
Step-by-step explanation:
24/12 = 2 , so twice as much;
159.48 * 2 = 318.96
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.
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.
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 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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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
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
What is 125x to the 3rd power +343y to the 3rd power
Answer: 125 to the power of 3 = 1253 = 1,953,125
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
(-∞ , +∞).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
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.