Answer:
Proportion states that the two ratio or fractions are equal.
Given the statement: One grain of sand approximately weighs 7 * 10^{-5} g.
To find how many grains of sand are there in 6300 kg of sand.
Let x be the number of grains of sand in 6300 kg of sand.
Using conversion :
1 kg = 1000 g
6300 kg = 6300000 g
Then, by using proportion method, we have;
[tex]\frac{1}{7\times 10^{-5}}= \frac{x}{6300000}[/tex]
[tex]\frac{10^5}{7} = \frac{x}{6300000}[/tex]
By cross multiply we get;
[tex]6300000 \times 10^5 = 7x[/tex]
or
[tex]63 \times 10^5 \times 10^5 = 7x[/tex]
[tex]63 \times 10^{5+5} = 7x[/tex] [using [tex]x^a \cdot x^b = x^{a+b}[/tex]]
[tex]63 \times 10^{10} = 7x[/tex]
Divide both sides by 7 we get;
[tex]x = \frac{63 \times 10^{10}}{7} = 9 \times 10^{10}[/tex]
Standard form is a way of of writing down very large or very small numbers easily.
Therefore, [tex]9 \times 10^{10}[/tex] grains of sand are there in 6300 kg of sand.
Write the coordinates for the given dilation
Answer:
D[tex]_o[/tex] of Y = (-3/2, -1)
Step-by-step explanation:
We are given three points on the graph:
X (4, 0)
Y (3, 2)
Z (2, 2)
and the scale factor of dilation which is [tex]-\frac{1}{2}[/tex].
Given that, we are to find the coordinates of Y after dilation. To find that, we will multiply the coordinates of the point Y with the scale factor.
Y = [tex](-\frac{1}{2}[/tex] × [tex]3[/tex] , (-\frac{1}{2}[/tex] × [tex]2)[/tex]
Y = [tex](-\frac{3}{2} , -1)[/tex]
Quincy is trying to estimate the height of a tree in his backyard. He measures the tree’s shadow as 12 ft. He stands near the tree and measures his own shadow as 3 ft. Quincy knows that he is about 5 ft tall. He estimates the height of the tree by following these steps
Answer:
The tree is 20 ft tall.
Step-by-step explanation:
We can use ratio's to solve this problem. Take the height of the object over the shadow length.
5 ft x ft
----------- = ----------------
3ft 12 ft
Using cross products
5*12 = 3*x
60 = 3x
Divide by 3 on each side
60/3 = 3x/3
20 =x
The tree is 20 ft tall.
is y=19x-5 proportional?
If x and y are proportional, then y : a = constant.
[tex]\dfrac{y}{x}=a\to y=ax[/tex] ← the equation
We have y = 19x - 5. It's not a proportional.
makito answered 70 pecent of 30 test quedtions correctly how many questions did he answer correctly
Answer:
21
Step-by-step explanation:
What is the distance between the points (12,-8) and (-14,20)
Answer:
The approximate distance between the points is 38.2
Step-by-step explanation:
The distance between these two points is a diagonal line. In order to solve this problem, you need to plot your points and form a right triangle. The overall distance from one point to another on the x-axis is 26 (12-(-14)), and the overall distance from one point to another on the y-axis is 28 (20-(-8)). These two distances will form a right angle at (-14,-8). The distances on the x and y axis are the 'legs' of the triangle and the distance between the given points in the problem represents the hypotenuse. Using the pythagorean theorem (a^2 +b^2 = c^2), we can substitute in our values of 'a' and 'b' to get 28^2 + 26^2 = c^2, or 784 + 676= 1460, therefor the square root of 1460 is approximately 38.2.
So to find the distance between these two points, we are going to be plugging them into the Distance Formula and solving as such:
[tex]D=\sqrt{(12-(-14))^2+(-8-20)^2}\\D=\sqrt{(26)^2+(-28)^2}\\D=\sqrt{676+784}\\D=\sqrt{1460}[/tex]
Now, with this radical we can simplify it using the product rule of radicals (√ab = √a × √b) as such:
[tex]\sqrt{1460}=\sqrt{10*146}=\sqrt{5*2*2*73}=2*\sqrt{73*5}=2\sqrt{365}[/tex]
Answer:In short:
Exact distance: √1460 or 2√365 unitsApproximate Distance (rounded to the hundreths): 38.21 unitsPlease help, ASAP:
Five liters of a20% salt solution was mixed with five liters of a70% salt solution. Find the concentration of salt in the mixed solution?
Answer: 45%
Step-by-step explanation:
[tex]\underline{\qquad \qquad\quad|\text{Quantity}|\quad\%\quad|\text\quad{Qty } \times\text{\%}\qquad}\\\underline{\text{Solution A }|\text{5 liters}\quad|\text{0.20}\quad|5\times0.20=1.00}\\\underline{\text{Solution B }|\text{5 liters}\quad|\text{0.70}\quad|5\times0.70=3.50}\\\text{Mixture }\quad|\text{ 10 liters }|\quad\text{x}\quad|\qquad\text{4.50}[/tex]
10x = 4.50
x = .45
= 45%
Solve for y.
50/90-y=5/18
Answer:
y = 5/18
Step-by-step explanation:
50/90-y=5/18
Lets simplify our fractions
50/90 = 5/9 (divide top and bottom by 10)
5/9 - y = 5/18
Subtract 5/9 from each side
5/9 -5/9 -y = 5/18 - 5/9
-y = 5/18 - 5/9
We need to get a common denominator of 18
-y = 5/18 - 5/9 *2/2
-y = 5/18 -10/18
-y = -5/18
Multiply each side by -1
-1*-y = -5/18 * -1
y = 5/18
3/4 is considered a real and rational number
Answer:
It is a rational number and real number
Explanation:
it is a real number because it can become .75 and that is a real number.
it is a rational number because assume that 3/4 is a rational number. Since every rational number can be expressed as a/b form which do not have any common factor so we can say that a/b = 3/4 Squaring both side we get: a2/b2 = 9/16 a2 = (9/16) b2 Or we can say b2 = a2(16/9) a2 is divided by 9. So we can say that a is divided by 9. It implies that there exist some number c such that a/9 = c a = 9c By squaring both side we get a2 = 81 c2 Put the value of a2 from the equation a2 = (9/16) b2 we get: (9/16)b2 = 81c2 this tends to b2/ 9 = 16 c2 It implies that b2 is divided by 9. So we can say that b is divided by 9. This implies that a and b have a common factor 9. Since a and b have common factor therefore 3/4 is not a irrational number. Hence 3/4 is a rational number.
Good luck
Please mark me brainliest
Answer:
3/4 is a rational number and also a real number
Step-by-step explanation:
to prove 3/4 is real
3/4 is a fraction. It is a proper fraction since denominator is grater than numerator.
3/4 can be written as 0.75 which is terminating decimal.
Therefore 3/4 is a real number
To prove 3/4 is a rational number
3/4 is the form of p/q.
Therefore 3/4 is a rational number.
find the equation of the line passing through the points (-1,-2) (-2,7)
The slope-intercept form of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-1, -2) and (-2, 7). Substitute:
[tex]m=\dfrac{7-(-2)}{-2-(-1)}=\dfrac{9}{-1}=-9[/tex]
Therefore we have [tex]y=-9x+b[/tex].
Put the coordinates of the point (-1, -2) to the equation of a line:
[tex]-2=(-9)(-1)+b[/tex]
[tex]-2=9+b[/tex] subtract 9 from both sides
[tex]-11=b\to b=-11[/tex]
Answer: y = -9x - 11A rectangle with vertices A(6, 0), K(0,0), L(0,9), and M(6, 9) is rotated around the x-axis. To the nearest tenth of a cubic unit, what is the volume of the resulting three-dimensional figure? Approximate as 3.14.
Answer:
1526.0 cubic units
Step-by-step explanation:
Rotating rectangle AKLM you will get cylinder with height KA and base radius KL. From the given data
[tex]KA=\sqrt{(6-0)^2+(0-0)^2}=6,\\ \\KL=\sqrt{(0-0)^2+(9-0)^2}=9.[/tex]
The volume of the cylinder is
[tex]V_{cylinder}=\pi r^2\cdot H.[/tex]
Then
[tex]V_{cylinder}=\pi \cdot 9^2\cdot 6=486\pi \approx 1526.0\ un^3.[/tex]
Which table shows a proportional relationship?
Answer:
the answer is the last one
Step-by-step explanation:
i drew all the example and i would say that the last one came out having a proportional relationship.
tell me if i got it right!
kristin spent &131 on shirts. Fancy shorts cost $28 and plain shorts cost $15. if she bought a total of 7 then how many of each kind did she buy?
Answer:
3 fancy shorts
4 plain
Step-by-step explanation:
By setting up equations for the total cost and the number of shorts purchased, we find that Kristin bought 2 fancy shorts at $28 each and 5 plain shorts at $15 each.
To solve the problem, let's denote the number of fancy shorts Kristin bought as F and the number of plain shorts as P. The problem gives us two conditions: Kristin spent a total of $131 on shorts, and she bought a total of 7 shorts. Fancy shorts cost $28 each, and plain shorts cost $15 each.
Now, we can set up two equations based on this information:
For the total cost: 28F + 15P = 131 (1)For the total number of shorts: F + P = 7 (2)Using equation (2), we can express P as P = 7 - F and substitute this into equation (1) to solve for F:
28F + 15(7 - F) = 131
Simplify the equation:
28F + 105 - 15F = 131
13F = 26
F = 2
Now that we have the value for F, we can use it to find P:
P = 7 - F
P = 7 - 2
P = 5
Kristin bought 2 fancy shorts and 5 plain shorts.
You can buy 5 stickers for 3$. Write a proportion that gives you the cost of c if you buy 12 stickers.
Answer:
$7.20
Step-by-step explanation:
I got u bro, Divide the price of the stickers by the number of stickers ($3/5=$.60) multiply the price of one sticker by the number of stickers ($.60x12=) :)
Final answer:
The cost of 12 stickers can be found by writing the proportion 5 stickers/3 dollars = 12 stickers/c dollars and solving for c, which yields c = 7.2. Thus, 12 stickers cost $7.20.
Explanation:
The student is asked to write a proportion to determine the cost c if they buy 12 stickers when the known price is 5 stickers for $3. To set up the proportion, we can compare the number of stickers to the cost. We have one ratio of 5 stickers to $3, and we need to find the equivalent ratio for 12 stickers to $c. The proportion can be represented as:
5 stickers / 3 dollars = 12 stickers / c dollars
Now we cross-multiply to solve for c:
5 * c = 3 * 12
c = (3 * 12) / 5
c = 36 / 5
c = 7.2
Therefore, the cost c of 12 stickers is $7.20.
6(3c - 5d +6) using distributive property
Expanding, you get 6(3c) - 6(5d) + 6(6) = 18c - 30d +36
Answer:
18c - 30d +36
Step-by-step explanation:
6(3c - 5d +6)
When we use the distributive property, we distribute the 6 to all the terms inside the parentheses
6*3c - 6*5d +6*6
18c - 30d +36
Which of the following is a solution to the inequality 7-1/5x>0?
[tex]7-\dfrac{1}{5}x>0\qquad\text{subtract 7 from both sides}\\\\-\dfrac{1}{5}x>-7\qquad\text{change the signs}\\\\\dfrac{1}{5}x<7\qquad\text{multiply both sides by 5}\\\\\boxed{x<35}[/tex]
Millie needs the average height of the plants she is buying to be at least 73 inches.She has selected three plants that are 70,71,and 72 inches tall. Write and solve an inequality that Millie could use to determine the possible heights of her fourth plant
Please help me!!!!! PLeASe Also I will be giving Brailiest
Answer:
x = 75
y = 105
Step-by-step explanation:
Remark
You can find y in two different ways.
One
You can recall that y is the sum of the 2 interior angles not connected to it. Those angles are called the remote interior angles. Or
Two
You can add the three angles to 180 and solve for x. Then since x and y are supplementary, you can find y.
Solution
One
y = 60 + 45
y = 105 Answer
Two
x + 60 + 45 = 180 All triangles have 180 degrees. Solve for x.
x + 105 = 180 Subtract 105 from both sides
x = 180 - 105 Combine
x = 75 Find an equation that relates x and y
x + y = 180 x and y are supplementary they add to 180
75 + y = 180 Subtract 75 from both sides.
y = 180 - 75 Combine
y = 105
Factor the expression over the complex numbers.
x2+25
[tex]Use\\\\a^2-b^2=(a-b)(a+b)\\\\i=\sqrt{-1}\to i^2=-1\\------------------------\\\\x^2+25=x^2+5^2=x^2-(-5^2)=x^2-(5i)^2\\\\\boxed{x^2+25=(x-5i)(x+5i)}[/tex]
what is the value of x
enter your answer in the box
Answer:
x = 19
Step-by-step explanation:
3x - 3 = 6(x - 10)
3x - 3 = 6x - 60
+3 +3
3x = 6x - 57
- 6x
- 3x = -57
= 19
Answer:
x = 19Step-by-step explanation:
[tex](3x-3)^{0} =\left[6(x-10)] ^{0}\\[/tex] (opposite angle)
[tex]3x-3=6(x-10)\\ 3x-3=6x-60\\ 60-3=6x-3x\\ 57=3x\\ \frac{57}{3} =x\\ 19=x[/tex]
What is the solution to the system of equations?
y = x – 10
2x + y = 4
(–8, 6)
(–6, 16)
(6, –8)
(16, –6)
Answer:
The solution is the point (6,-8)
Step-by-step explanation:
we have that
The first equation is [tex]y=(1/3)x-10[/tex] instead [tex]y=x-10[/tex]
[tex]y=(1/3)x-10[/tex] -----> equation A
[tex]2x+y=4[/tex] -----> equation B
Solve the system of equations by substitution
Substitute equation A in equation B and solve for x
[tex]2x+[(1/3)x-10]=4[/tex]
[tex](7/3)x=14[/tex]
[tex]x=6[/tex]
Find the value of y
[tex]y=(1/3)(6)-10=-8[/tex]
therefore
The solution is the point (6,-8)
What is the value of x?
Answer:
The value of x is 68 degrees!
Step-by-step explanation:
In this question, we have an isosceles triangle because of Base Angles Theorem. The 2 sides are congruent, which means its an isosceles and that the Base angles are congruent. So far, we know that 2 angles are equal to 112 degrees. Due to Sum Angles Theorem, we can go 180-112 to get 68 degrees!
Answer:
x=68
Step-by-step explanation:
Since this is an isosceles triangle, the bottom two angles are the same value, 56 degrees. The three angles of a triangle add to 180 degrees.
56+56+ x = 180
Combine like terms
112 +x = 180
Subtract 112 from each side
112-122 +x = 180 -112
x =68
sasha is reading a novel wth 427 pages. she has read 276 pages. what percentage has she read?
Final answer:
Sasha has read approximately 64.66% of the novel by dividing the number of pages she read (276) by the total number of pages (427), and then multiplying the result by 100.
Explanation:
To find out what percentage of the novel Sasha has read, we need to use the formula for percentage:
Percentage = (Part / Whole) × 100
Sasha has read 276 pages of a 427-page novel. So, in this case, the part is 276, and the whole is 427.
Now we calculate:
Divide the number of pages read by the total number of pages: 276 / 427.Multiply the result by 100 to get the percentage: (276 / 427) × 100.Let's do the math:
276 divided by 427 is approximately 0.6466.Multiplying 0.6466 by 100 gives us approximately 64.66%.Therefore, Sasha has read about 64.66% of the novel.
Which values make this equation true?
(5x^7 y^2)(-4x^4 y^5)=-20x^a y^b
A.) a=11, b=7
B.) a=11, b=10
C.) a=28, b=7
D.) a=28, b=10
When multiplying terms with exponents, just add the exponents together.
You have x^7 and x^4, so 7 +4 = 11
Y^2 and Y^5 = 2+5 = 7
so it would be -20x^11 y^7
The answer is A.) a=11, b=7
The expression 50w+400 represents the amount of money Jenny has in her savings account after an unknown number of weeks. How much money does Jenny originally have in her savings account? Which part of the equation represents the amount of money she will put away each week? Explain your answers.
Answer:
400 originally, and 50 dollars a week from there!!
Step-by-step explanation:
Since the 50 is followed by the variable "w", and the w stands for week, we can believe that Jenny makes 50 dollars a week.
Because the 400 was in the her account to begin with, we know this is the amount she originally had!
What is the solution to the system of equations?
3x-2y=19
Y=x-7
Answer:
x = 5 and y = -2
Step-by-step explanation:
Here you have given what y is equal to, this means you can sub this into the first equation:
3x - 2(x - 7) = 19
Expand the brackets:
-2 * x = -2x
-2 * -7 = 14
3x -2x +14 = 19
Move the +14 over to the other side making it a -14:
3x - 2x = 19 - 14
3x - 2x = 5
3x - 2x = x
So x = 5
Now sub this into the first equation:
3(5) - 2y = 19
15 - 2y = 19
Move the -2y over to the other side making it a +2y, and move the +19 over to the other side making it a -19:
15 - 19 = 2y
-4 = 2y
Divide both sides by two:
y = -2
So x = 5 and y = -2
Can someone help me with this sat question
Answer:
2,-2
Step-by-step explanation:
What’s the area of this rounded to the nearest one’s place?
Answer:
I think I might be terribly wrong but 160,728 ft
Step-by-step explanation:
Answer:
503
Step-by-step explanation:
To find the area of a cirlce it is pi x 2 x the radius squared.
Since,this is a semi-circle you dived by 2 afterwards.
So [tex]\pi x 160 x 2 /2[/tex] is 502.857142857
Round that to the nearest one that is 503 ft squared.
which number, when placed in the box, will make the equation true?
[tex] {?}^{2} = \sqrt{64} [/tex]
A.
[tex] \sqrt{8} [/tex]
B.
[tex] \sqrt{32} [/tex]
C. 16
D. 32
[tex]\mathsf{\heartsuit\;\; (\sqrt{8})^2 = \sqrt{64}}\\\\\mathsf{\heartsuit\;\; [(8)^\frac{1}{2}]^2 = \sqrt{(8)^2}}\\\\\mathsf{\heartsuit\;\; (8)^\frac{2}{2} = [(8)^2]^\frac{1}{2}}\\\\\mathsf{\heartsuit\;\; 8 = [8]^\frac{2}{2}}\\\\\mathsf{\heartsuit\;\; 8 = 8}\\\\\mathsf{\heartsuit\;\; Option\;(A)\;is\;the\;Answer}[/tex]
The number which will make the equation true, when placed in the box is: A. √8.
How to solve for the unknown number?In order to determine the unknown number, we would assign a variable (x) to the unknown number and then evaluate the resulting algebraic equation as follows:
x² = √64
x² = 8
Taking the square root of both sides, we have:
x = √8.
Read more on algebraic equation here: brainly.com/question/13170908
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i need help thank you
Answer:
Step-by-step explanation:
The key and the most critical step is to draw the line first. Don't do anything else before that.
(2,-8) (-2,-8)
What you find out is that the y value is always - 8.
So the line has no slope and any x value
y = 0*x + b
y = - 8 is the equation of the line.
The coordinates of point b
Answer:
(3, -1) PLEASE GIVE BRAINLIEST
Step-by-step explanation: