The area of square flake of gold is [tex]53.29 \times 10^{-8} \mathrm{mm}[/tex]
Solution:Given that width of square flake of gold is [tex]7.3 \times 10^{-4}[/tex] millimeter
To find : Area of square flake
Since gold flake is in shape of square, we can use area of square formula
The formula for area of square is given as:
[tex]area = s^2[/tex]
where "s" is the length of one side
[tex]\begin{array}{l}{\text { Area of a square flake }=\left(7.3 \times 10^{-4}\right) \times\left(7.3 \times 10^{-4}\right)} \\\\ {\text { Area of a square flake }=53.29 \times 10^{8}}\end{array}[/tex]
Hence , the calculated area of flake is [tex]53.29 \times 10^{-8} \mathrm{mm}[/tex]
y + 7 = - 2/5 * (x - 10) . What is theThe point-slope of the equation of the line that passes through (- 5, - 1) and (10, - 7) is standard form of the equation for this line? 2x - 5y = - 15 2x - 5y = - 17 2x + 5y = - 15 2x + 5y = - 17
Answer:
The Standard Form of the Equation is A. 2x - 5y = -15
Step-by-step explanation:
Given points: (-5, -1) and (10, -7).
Find the slope:
m = (y - y1)/(x - x1)
= -1 - (-7)/-5 - 10
= -1 + 7/-15
= 6/-15
m = -2/5
You already had the point slope form:
y - y1 = m(x - x1)
y - (-7) = -2/5(x - 10)
y + 7 = -2/5(x - 10)
The rest of the question is looking for the standard form of the equation:
Ax + By = C
Begin by solving the point slope form for y:
y + 7 = -2/5x + 20/5
y + 7 = -2/5x + 4
y = -2/5x - 3
Now, put the equation into the standard form:
y + 2/5x = -3
Multiply by 5, and place x first:
2x + 5y = -15, the Standard form of the Equation
Prove by setting x = 0 and finding the y intercept:
5y + 2(0) = -15
5y = -15
y = -3, giving the y intercept, when x = 0 as -3 or (0, -3)
Hope this helps!! Have an Awesome Day!! :-)
Gail bought 80 buttons to put on the shirts she makes. She uses 5 buttons for each shirt. How many shirts can Gail make with the buttons she bought?
hellppp
step for step please
Answer:
[tex]\left\{\begin{array}{l}x\ge 0\\ \\y\ge 0\\ \\x+y\ge 20\\ \\3.5x+5y\le 80\end{array}\right.[/tex]
Step-by-step explanation:
Let x be the number of small candles and y be the number of large candles.
Santhi needs to buy at least 20 candles, so
[tex]x+y\ge 20[/tex]
Small candles:
Cost of 1 small candle = $3.50
Cost of x small candles = $3.50x
Large candles:
Cost of 1 large candle = $5.00
Cost of y large candles = $5.00y
Total cost of all candles:
$3.50x + $5.00y
Thus,
[tex]3.5x+5y\le 80[/tex]
Using Desmos, plot the system of two inequalities:
[tex]\left\{\begin{array}{l}x+y\ge 20\\ \\3.5x+5y\le 80\end{array}\right.[/tex]
Last year, Ariq made a 6-1 cup servings of soup for a party this year he will make 8 times the amount of soup that he made last year how many gallons of soup will he make this year?
Answer:
3 gallons
Step-by-step explanation:
Last year, Ariq made a 6 1-cup servings of soup for a party.
This year he will make 8 times the amount of soup that he made last year, so he will make
[tex]8\cdot 6=48[/tex] 1-cup servings of soup.
In total, 48 cups of soup.
Note that
1 gallon = 16 cups,
then
48 cups is equal to
[tex]48 :16=3[/tex] gallons
Answer:
The number of gallons of soup will he make this year is 3 gallons
Explanation:
No of 1 cup servings made by Ariq last year = 6
Suppose last year he made x 1 cup servings
Hence this year he will make 8x, 1 cup servings
Since last year he made 6, 1 cup serving
Therefore
This year 8x, 1 cup servings
= 8×6
=48, 1 cup servings
Now
1 gallon of soup=16 cups
Therefore
48 cup servings will be
=[tex]\frac{48}{16}[/tex]= 3 gallons
The number of gallons of soup will he make this year is 3 gallons
use inverse operations to solve equation 15=x/6-1
Answer:
x=90.
Step by step explanation:
To solve the expression [tex]15=\frac{x}{6}-1[/tex], and obtaining a value for x we can do the following:
Add 1 both sides of the equation. This will result in [tex]15+1=\frac{x}{6}-1+1[/tex]⇒[tex]16=\frac{x}{6}[/tex].Multiply both sides by 6, which yields [tex]15\times6=\frac{x}{6}\times6[/tex]. This results in [tex]90=x[/tex].I really need help with this answer
Answer:
The given two triangles are not congruent.
Step-by-step explanation:
See the diagram of the two triangles attached to this question.
The third angle of the second triangle is [180° - (31° + 124°)] = 180° - 155° = 25°.{Since the other two angles of the triangle are 31° and 124°}
Now, for the first triangle, the values of the adjacent angles of the side with length 6 are 45° and 31°, but for the second triangle, the values of the adjacent angles of the side with length 6 are 25° and 31°.
Therefore, two triangles do not satisfy the Angle=Side-Angle i.e. ASA criteria to become congruent.
So, the given two triangles are not congruent. (Answer)
graph the equation y= -2x+3
Pedro created a scatterplot and a trend line for data that he collected by comparing the number of minutes playing a game and the number of levels passed. Video Game Y=0.49x-0.88 Based on the information shown, which is the best prediction for the number of levels passed after playing for 20 minutes? 9 10 40 42
Answer:
9 on edge
Step-by-step explanation:
on a number line, what is x-4<-3?
Add 4 to both sides
x - 4 < -3
x-4+4 < -3+4
x < 1
To graph this on a number line, plot an open circle at 1 on the number line. Do not fill in the open circle. Shade to the left of the open circle. The shaded region represents all x values smaller than 1.
The graph is shown below.
Mother is m years old, and she is four times as old as her daughter. How much older is the mother than her daughter?
To find out how much older the mother is than her daughter, we subtract the daughter's age (m/4) from the mother's age (m), resulting in the mother being three-fourths of her own age older than her daughter, which is 3m/4.
Explanation:The question relates to a linear equation in the context of ages. If the mother is m years old, and she is four times as old as her daughter, then the daughter's age would be m/4 years old. To find out how much older the mother is than her daughter, we subtract the daughter's age from the mother's age, which gives us m - (m/4). Simplifying this, we get 3m/4, which means the mother is three-fourths of her own age older than her daughter.
A store sells packages of comic books with a poster. A poster and 2 comics cost $7.99. A poster and 11 comics cost $16.99. Write a linear function rule that models the cost y of a package containing any number x of comic books.
Answer:
[tex]y=x+5.99[/tex]
Step-by-step explanation:
A poster and 2 comics cost $7.99
(2,7.99)
A poster and 11 comics cost $16.99.
(11,16.99)
Let y be the cost of package and x be the no. of comics
We will use two point slope form :
[tex](x_1,y_1)=(2,7.99)[/tex]
[tex](x_2,y_2)=(11,16.99)[/tex]
Formula : [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Substitute the values:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-7.99=\frac{16.99-7.99}{11-2}(x-2)[/tex]
[tex]y-7.99=1(x-2)[/tex]
[tex]y-7.99=x-2[/tex]
[tex]y=x-2+7.99[/tex]
[tex]y=x+5.99[/tex]
Hence a linear function rule that models the cost y of a package containing any number x of comic books is [tex]y=x+5.99[/tex]
The linear function that models the cost 'y' of a package containing 'x' number of comics is y = $5.99 + $1*x. This was determined by equating the differences in costs and numbers of comics to find the price per comic, and then solving one of the original equations for the price of the poster.
Explanation:To solve this problem, let's consider the cost difference between buying a package with 2 comics and a package with 11 comics. The difference between $16.99 and $7.99 is $9, and the difference between 11 comics and 2 comics is 9 comics. This gives us a cost of $1 per comic book. Let's denote the cost of a comic book as 'c' and the cost of the poster as 'p'. It can be represented by the equation c = $1. We can use one of the original equations to find the cost of the poster.
Let's use the first one 'p' + 2*c = $7.99. We substitute the cost of a comic book ('c' = $1) into that equation, resulting in a price for 'p' (the poster) of $5.99. So, the linear function which represents the cost 'y' of a package containing any number 'x' of comics is y = p + c*x, or y = $5.99 + $1*x, with 'y' being the total cost and 'x' being the number of comic books.
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[(5.5+3)×7]+[(12÷3)×2]-4.5
Answer:
63
Step-by-step explanation:
[(5.5+3)*7]+[(12/3)*2]-4.5
[8.5*7]+[4*2]-4.5
59.5+8-4.5
67.5-4.5
63
The temperature in Greenland is -8.3°C. The temperature in Jamaica is 30°C. What is the difference between the temperatures in the two countries?
A.21.7°C
C.25°C
B.-21°C
D.38.3°C
Answer:
The difference between the temperatures in the two countries is 38.3°C.
Step-by-step explanation:
Given:
Temperature in Greenland = - 8.3°C
Temperature in Jamaica = 30°C
To find :
The difference between the temperature in the two countries = ?
[tex]\textrm{difference between the temperature in the two countries} =\textrm{temperature in Jamaica} - \textrm{temperature in Greenland}\\= 30 - (-8.3)\\= 30 +8.3\\= 38.3\°C[/tex]
Therefore,the difference between the temperatures in the two countries is 38.3°C
some investments in the stock market have earned 10% annualy. At this rate, earnings can be found using the formula a = p (1.10)^n where A is the total value of the investment, P is the initail value of the investment, and N is the number of years the money is invested if $1,500 is invested in the stock market at this annual rate of return, what is the expected value after 18 years
Answer:
Calculate it
Step-by-step explanation:
1,500 = 1,500/10% x 1.1^18
If A={2,4,6,8,10,12} and B={3,6,9,12,15} then A n B is
A. (A n B) = {2. 3. 4. 6. 8. 9. 10. 12}
B.(A n B) = {2,3,4,8,9,10}
C. (A n B) = {2,3,10,12}
D. (A n B) = {6,12}
Answer: Choice D) {6, 12}
============================================
Explanation:
The upside down U symbol means "set intersection". The intersection of two sets is the collection of all items that are in both sets at the same time.
In this case, only 6 and 12 are in both set A and set B at the same time, which is why choice D is the answer.
We can rule out choices A through C because 3 is not in set A (its only in set B).
Visually on a Venn Diagram, the intersection of the two sets will be shown as the overlapping region between the two circles A and B. So we'll have 6 and 12 in this overlapped region. The other values will go in their respective circles but not be in the overlapped region.
The intersection of sets A and B, denoted as A n B, includes only the elements that are present in both sets, which are 6 and 12. Therefore, A n B = {6,12}, which corresponds to option D of the provided choices.
The question asks for the intersection of sets A and B, which is denoted as A n B. Intersection means we look for elements that are common to both sets. In set A, we have {2,4,6,8,10,12}, and in set B, we have {3,6,9,12,15}. Therefore, the elements that are present in both sets are 6 and 12. Hence, A n B = {6,12}.
When comparing the answer choices provided, option D (A n B) = {6,12} is the correct answer because it lists exactly those numbers that are present in both set A and set B.
how do i put this in slope-intercept form. passes through 2,-2 and 4,-1
Answer:
[tex]\large\boxed{y=\dfrac{1}{2}x-3}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation 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 two points (2, -2) and (4, -1).
Substitute:
[tex]m=\dfrac{-1-(-2)}{4-2}=\dfrac{-1+2}{2}=\dfrac{1}{2}[/tex]
Put the value of a slope and the coordinates of the point (2, -2) to the equation of a line:
[tex]-2=\dfrac{1}{2}(2)+b[/tex]
[tex]-2=1+b[/tex] subtract 1 from both sides
[tex]-3=b\to b=-3[/tex]
Finally:
[tex]y=\dfrac{1}{2}x-3[/tex]
10) 5x – 8y= 1
y=-2
What are the answer
Answer:
x=-3
Step-by-step explanation:
5x-8y=1
5x-8(-2)=1
5x+16=1
5x=1-16
5x=-15
x=-15/5
x=-3
A conviniénce store sells two brands of orange juice .brand a contains 11 fluid ounces and costs 2.31 brand b contains 15 fluid ounces and costs 2.70
Answer:
Brand has less mass or fluids than b does and since b has greater fluid it will cost more then the smaller brand
Answer:
Brand has less mass
Step-by-step explanation:
if r=8 and s=3, find the value of rs+2s.
Answer: 30
Step-by-step explanation:
rs + 2s when r = 8 and s = 3
8(3) + 2(3)
8 * 3 = 24
2 * 3 = 6
24 + 6 = 30
Answer:
30
Step-by-step explanation:
You first plug in the value of s and r into the equation.
(8)(3)+2(3)
Then you solve it.
24+6
30
So, the answer is 30.
Brass costs $0.90 per pound, copper costs $2.15 per pound, and aluminium costs $0.75 per pound. Which medal would you recommend be for, for use as a heat sink in the tablet?
Can you find the solution to the following system of linear equations. −4x+14y=−16 x−7/2y=4
Answer:
Infinitely many solutions.
Step-by-step explanation:
-4x+14y=-16
x-7/2y=4
------------------
-4x+14y=-16
4(x-7/2y)=4(4)
----------------------
-4x+14y=-16
4x-14y=16
---------------------
Infinitely many solutions
The denominator of a fraction is five more than twice the numerator. If both the numerator and denominator are decreased by seven, the simplified result is 1/3. Find the original fraction.
THe fraction is:
X
----------
2X + 5
Decreases the numerator and denominator by 1, the fraction becomes 3/8.
So now the fraction looks like this:
X-1 3
--------- = -----------
2x +5-1 8
Cross multiplies:
8(x-1) = 3 ( 2x +5 -1)
8x - 8 = 3( 2x + 4)
8x - 8 = 6x + 12 <--- distributive right side
8x - 8 - 6x - 12 = 0 <--- everybody moves left,changing signs, to keep leading coefficient of x term positive
2x - 20 = 0 <-- combines like terms
2x = 20 <--- solves for x
x=10
So the fraction 10/25.
(10-1)/(25-1) = 9/24 = 3/8
The original equivalent value of the fraction is A = 19/43
What is a Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given data ,
Let's start by assigning variables to the numerator and denominator of the original fraction. Let x be the numerator and y be the denominator.
Then we can write:
y = 2x + 5 (since the denominator is five more than twice the numerator)
If both the numerator and denominator are decreased by 7, the new fraction can be written as (x-7)/(y-7), and we know that this is equal to 1/3:
(x-7)/(y-7) = 1/3
To solve for x and y, we can start by cross-multiplying to get:
3(x-7) = y-7
Next, we can substitute the expression for y that we derived earlier:
3(x-7) = 2x + 5 - 7
Simplifying this equation gives:
3x - 21 = 2x - 2
Bringing all the x terms to one side and all the constant terms to the other gives:
x = 19
Now that we know the value of x, we can substitute it back into our expression for y:
y = 2x + 5 = 43
Hence , the original fraction is x/y = 19/43
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PLEASE HURRY!!
Which scenario could be represented by this graph?
O
A. Jane lights a candle. The x-axis represents time; the y-axis
represents the height of the candle.
O
B. Jane lights a candle. After 15 minutes, she puts it out. Half an
hour later, she lights it again. The x-axis represents time; the yaxis
represents the height of the candle.
O
C. Jane steadily fills a cup of water, stopping when it is almost full.
The x-axis represents time; the yaxis represents the amount of
water.
O
D. Jane steadily fills a cup of water. After 15 minutes, she dumps it
out. The x-axis represents time; the yaxis represents the amount
of water.
Without the actual graph, it's difficult to precisely match it to the given scenarios. If the graph shows a continuous increase or decrease, it could correspond to options A or C. If the graph displays changes with distinct intervals, it might match with options B or D.
Explanation:To answer your question about which scenario could be represented by the graph, we need more specific information about the graph. Without the visual graph and only with the given information, it's somewhat complicated to identify an exact match. However, some general presumptions can be made.
If the graph shows a continuous decrease or increase, it could be option A or C. These scenarios talk about a steady decrease (candle-burning) or increase (filling a cup), suggested by the x-axis representing time and y-axis representing a value that changes consistently (height of the candle or amount of water).
However, if the graph shows changes with significant intervals, it could be option B or D. These scenarios show an event that takes place, stops for a while (represented by a straight line on the graph), and then resumes or has an opposite effect ( candle being lighted again, or water being dumped). In all scenarios, the x-axis represents time, while the y-axis represents the scenario's varying condition, whether it's the height of a candle or amount of water.
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There are 12 girls and 8 boys in a class.
What is the ratio of girls to the total students
in the class?
a. 2:3
b. 3:2
C. 2:5
d. 3:5
Students, drew anywhere on this sider
I am pretty positive that it is b...
How to I solve this by graphing?5x2 + 8x – 13 = 0
To solve the equation by graphing, plot the quadratic function on a graph and determine the x-values where it intersects the x-axis.
Explanation:To solve the equation 5x² + 8x - 13 = 0 by graphing, you can plot the quadratic function on a graph and determine where it intersects the x-axis. The x-values at the points of intersection will be the solutions to the equation.
Write the equation in the form y = 5x² + 8x - 13.Plot the graph of the equation by selecting different values of x and calculating corresponding y-values.Find the x-values where the graph intersects the x-axis. These are the solutions to the equation.The solutions to the equation 5x² + 8x - 13 = 0 can be found by graphing.
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Find the missing side of the right triangle
Answer:
1Step-by-step explanation:
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have
[tex]leg=3,\ leg=x,\ hypotenuse=\sqrt{10}[/tex]
Substitute:
[tex]3^2+x^2=(\sqrt{10})^2[/tex]
[tex]9+x^2=10[/tex] subtract 9 from both sides
[tex]9-9+x^2=10-9[/tex]
[tex]x^2=1\to x=\sqrt1\\\\x=1[/tex]
23128
Which expression is equivalent to 4V32xV2 ?
412
• 1682
HER
Answer:
16
Step-by-step explanation:
The equation of the line with slope – 4 that goes through the point (6,-4) can be written in
the form y = mx + b where m is:
and b is:
Answer:
m is= -4
and b is also -4 bc it croses through -4 at at the y axis and -4 is the slope
Step-by-step explanation:
what is the volume of a brick that is 20.3 cm long, 8.9 cm wide, and 5.7 cm high?
Answer:
1029.819
Step-by-step explanation:
20.3 * 8.9 * 5.7 = 1029.819
Answer: 1,029.819 cm³
Step-by-step explanation: In this problem, we're asked to find the volume of a brick. To find the volume of a brick, we use the formula for the volume of a rectangular prism.
To find the volume of a rectangular prism or a prism whose base is a rectangle, we use the following formula.
Volume = length × width × height
Since the brick has a length of 20.3 centimeters, a width of 8.9 centimeters, and a height of 5.7 centimeters, we can plug this information into the formula.
Volume = (20.3 cm) (8.9 cm) (5.7 cm)
Volume = 1,029.819
Therefore, the volume of the brick is 1,029.819 cm³.
Also, it's important to understand that we can plug any number in for the length width or height as long as it's one of the numbers given and it's not used more than once.
This is because the commutative property of multiplication tells us that changing the order of the factors doesn't change the product.
What is an equation of a line, in point-slope form, that passes through (1, −7) and has a slope of −23 ?
y+7=23(x+1)?
y−7=−23(x+1)?
y−7=23(x−1)?
y+7=−23(x−1)
IN SLOPE FORM
point slope form: y-y1=m(x-x1)
coordinate (1,-7):
point y1--7
point x1=1
slope (m)=-23
input into equation:
y-(-7)=-23(x-1)
convert to slope intercept form:
-*-=+ so 7 becomes +7
y+7
distribute -23 in -23(x-1) using the rule: a(b+c)=ab+ac
-23x+23
refine
y+7=-23x+23
perform some inverse operations:
y+7=-23x+23
y+7=-23x+23-7
y=-23x+16
therefore, D. y+7=−23(x−1) equals y=-23x+16 in slope-intercept form
Required equation of the line is y+7 = −23(x−1).
So, Option four is the correct answer.
What is slope?
In mathematics, the slope of a line is the change in the y-coordinate relative to the change in the x-coordinate.
The net change in the y-coordinate is denoted by Δy and the net change in the x-coordinate by Δx.
Thus, the change in the y-coordinate with respect to the change in the x-coordinate is obtained as follows:
m = change in y/change in x = Δy/Δx
Where "m" is the slope of the line.
You can also specify the slope of the line
tan θ = Δy/Δx
So, tan θ is the slope of the line.
In general, the slope of a line gives its steepness and direction. The slope of a line between two points (x1,y1) and (x2,y2) is easily determined by finding the difference in the coordinates of the points. The slope is usually denoted by the letter "m".
Here given,a line, in point-slope form, that passes through (1, −7) and has a slope of −23.
We want to find what is an equation of a line which passes through (1, −7) and has a slope of −23 ?
We know, if a line passes through the point (a,b) and has slope m then equation of the line,
[tex](y - b) = m(x - a)[/tex]
Here,
[tex]a = 1 \\ b = - 7 \\ m = - 23[/tex]
So, required equation is
[tex](y -( - 7)) = ( - 23)(x - 1) \\ (y + 7) = ( - 23)(x - 1)[/tex]
Therefore,required equation of the line is y+7 = −23(x−1).
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