the question is on the sheet .The shaded region is the area within the figure but not the corner squares
Answers
Based on the information given in the exercise, you know that the shaded region has this area:
[tex]6x^2-2xy+3y^2[/tex]And the area of each square region in the corners is:
[tex]4x^2[/tex]Since there are four square regions, you can multiply that the area of any of them by 4, in order to find the total area of them:
[tex]4(4x^2)=16x^2[/tex]Then, in order to find the total area of the figure, you must add the area of the shaded region and the total area of the square regions:
[tex](6x^2-2xy+3y^2)+(16x^2)=22x^2^{}-2xy+3y^2[/tex]Therefore, the total of the figure is:
[tex]22x^2-2xy+3y^2[/tex]Related Questions
Find the product. Write your answer in scientific notation. (6.5 X 10^8) X (1.4 x 10^-5) =
Answers
Evaluate the product of the expression.
[tex]\begin{gathered} (6.5\times10^8)\cdot(1.4\times10^{-5})=6.5\cdot1.4\times10^{8-5} \\ =9.1\times10^3 \end{gathered}[/tex]So answer is 9.1X10^3.
What is the area of a triangle that has a height of 10 feet and a base of 6 feet?A. 16 feet squaredO B. 30 feet squaredO C.35 feet squaredD. 60 feet squared
Answers
Th formula for the area of the triangle is as follows.
[tex]A=\frac{bh}{2}[/tex]where b is the base of the triangle and h is its height.
Substitute the given values into the formula and then simplify.
[tex]\begin{gathered} A=\frac{(6)(10)}{2} \\ =\frac{60}{2} \\ =30 \end{gathered}[/tex]Therefore, the area of the triangle is 30 square feet, which is option B.
See photo for problem
Answers
a. the amount of liquid in the tank: 5580 liters
b. The amount of liquid should be added to fill the tank 100% capacity : 450 liters
We have been given a right circular conical tank.
h = 4 m and r = 1.20 m
We know that the formula for the volume of cone is,
V = πr²h/3
The volume of the tank would be,
V = (π × r² × h)/3
V = (π × 1.20² × 4)/3
V = 18.09/3
V = 6.03 m³
Let h1 be the height of liquid level in the tank and V1 be the volume of the liquid in the tank.
h1 = 3.70 m
V1 = (π × r² × h1)/3
V1 = (π × 1.20² × 3.70)/3
V1 = 16.74 / 3
V1 = 5.58 m³
V1 = 5580 liters
The amount of liquid need to added to fill the tank 100% of capacity.
V2 = V - V1
V2 = 6.03 m³ - 5.58 m³
V2 = 0.45 m³
V2 = 450 liters
Therefore, a. the amount of liquid in the tank: 5580 liters
b. The amount of liquid should be added to fill the tank 100% capacity : 450 liters
Learn more about the volume of cone here:
https://brainly.com/question/1984638
#SPJ1
divide and Simplify 7/5 ÷7/9
Answers
What we have is a fractional division, this is following expression
[tex]\frac{(\frac{7}{5})}{(\frac{7}{9})}[/tex]For this procedure, it says to multiply the top and bottom ends to get the numerator, and the middle numbers to get the denominator
[tex]\frac{7\cdot9}{7\cdot5}=\frac{9}{5}[/tex]In conclusion after splitting and simplifying this, the answer is 9/5
Answer the following.(a) An astronomer's infrared telescope is able to detect radiation with a wavelength of 1.96 x 10^-5 meters. Write this number in standardnotation(b) The diameter of Venus at its equator is approximately 12,100 kilometers. Write this number in scientific notation.(a) Imeters(b) kilometers
Answers
a)
We need to convert 1.96 x 10^-5 meters. into standard notation.
Now, on the scientific notation, the power of ten shows how many places the decimal point has been moved.
- If the exponent is positive then the decimal point has been moved to the left.
- If the exponent is negative, then the decimal point has been moved to the right.
In this case, the power is negative 5 . So, the decimal point has been moved 5 places to the right.
Hence:
1.96 x 10^-5 = 0.0000196
b)
a. Meters
First, we need to convert kilometers into meters using the rule of three:
If 1k = 1000 meters
Then 12,100k = x
Where x = (12,100k*1000m)/ 1k
x =12000000 meters
We need to convert from standard notation to scientific notation:
12000000.0 = 1.2x10^7 meters
The decimal point has been moved 7 places to the left, so the power of then is positive 7.
b) We need to convert 12,100 kilometers into scientific notation:
12,100 = 12,100.0
Converting into scientific notation
1.21x10^4 kilometers
The decimal point has been moved 4 places to the left. Hence, the power of the is positive 4.
The longest side of a triangle is 5in longer than the shortest side. The medium side is 4 inches longer than the shortest side. If the perimeter of the triangle is 21 inches, what are the lengths of the three sides?
Answers
The perimeter of a triangle is given by the sum of all it is sides.
Now, we have the next measures:
- The longest side of a triangle is 5in longer than the shortest side.
- The medium side is 4 inches longer than the shortest side
Then, the perimeter is given by:
P = (s+5)+(s+4)+s
If the perimeter is P=21 inches:
21 = (s+5)+(s+4)+s
Solve for s:
21 = s+5+s+4+s
21 = 3s + 9
21-9 = 3s
12 = 3s
s = 12/3
s= 4
Therefore,
The shortest side of the triangle is 4 inches.
The medium side is s+ 4 = 4+ 4 = 8 inches
The longest side is s+5 = 4+5 = 9 inches
Question 5 of 8
What is the largest proper fraction less than 1 that can be made by using these
numbers only once: 1, 3, 6, 11 and 12?
Answers
The largest proper fraction that can be formed is 16/17
What is a fraction?
A fraction (from the Latin fractus, "broken") is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction has a numerator above a line (or before a slash like 12) and a non-zero denominator below (or after) that line. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.
The largest proper fraction that can be formed is
= 1+3+12/11+6 = 16/17
To know more about fractions, click on the link
https://brainly.com/question/1622425
#SPJ9
hey can anyone help me on this im failing school xd
Answers
slope of line is -3 for points (1,0) and (0,3)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
From graph let us take two points (1, 0) and (0, 3)
x₁=1, x₂=0, y₁=0,y₂=3
Substitute these values in slope formula
m=3-0/0-1
m=3/-1
m=-3
Hence slope of line is -3.
To learn more on slope of line click:
https://brainly.com/question/14511992
#SPJ1
3) An experiment is designed to compare the average salaries in a particular Position in two competing companies. The null hypothesis is assumed to be that there is no difference in the average salaries of empoty employees in a particular position in the two companies. What is the alternative hypothesis?
Answers
Given:
There are two competing companies.
Required:
We need to find the alternative hypothesis
Explanation:
If the null hypothesis assumes equal average salaries (i.e. no difference), then the alternative can take on three cases:
A)
One mean is greater than the other
B)
One mean smaller than the other
C)
The means are not equal
Now here A and B sound the same, so I shoukd be more precise,
Michael studied the feather lengths of some adult fox sparrows.How long is the shortest feather in the data set?
Answers
From the data set given, 3/4 is the length of the shortest feather of fox sparrow.
Given,
The image is attached with this.
The length of fox sparrow feathers studied by Michael.
1 sparrow with 3/4 inches of feather4 sparrows with 2 inches of feather7 sparrows with 2 1/4 inches of feather5 sparrows with 2 1/2 inches of feather3 sparrows with 2 3/4 inches of feather.We have to find the shortest feather in the data set.
Here,
3/4 inches is the shortest feather and only 1 sparrow has the shortest feather.
2 3/4 inches is the longest feather and 3 sparrows have the longest feather.
That is,
From the data set given, 3/4 is the length of the shortest feather of fox sparrow.
Learn more about length of feather here;
https://brainly.com/question/23986067
#SPJ1
Check picture pls this is geometry work
Answers
Answer:
45
scalene
acute
Step-by-step explanation:
Answer: The triangle classified by the sides is 59 degrees. The triangle is classified by the angel is 1
Step-by-step explanation:
Just the number 2 please a ball is tossed in the air in such a way that …..
Answers
Note that a quadratic function is increasing and decreasing at exactly half between the roots.
The roots are the point on the ground when tossing the ball into the air.
So we need to get the roots of the given equation.
Roots are the values of x when y = 0
[tex]\begin{gathered} y=-x^2+6x \\ 0=-x^2+6x \\ 0=-x(x-6) \\ -x=0\Rightarrow x=0 \\ (x-6)=0\Rightarrow x=6 \end{gathered}[/tex]So the roots are 0 and 6, this will be the x coordinate or the point on the ground.
Since the equation is increasing halfway and decreasing up to the ground, the halfway point is the midpoint between the roots.
Midpoint = (0 + 6)/2 = 3
Therefore, the ball's height is always decreasing at 3 < x < 6
The answer is 3 < x < 6
Help solving rational equations by cancelling denominator
Answers
two seventh of a number is 30 less than the number . find the number
Answers
Let x = the number
So, the given situation can be expressed as:
[tex]\frac{2}{7}x=30-x[/tex]Then, solve for x:
[tex]\begin{gathered} \frac{2}{7}x+x=30-x+x \\ \frac{9}{7}x=30 \\ \frac{7}{9}\cdot\frac{9}{7}x=30\cdot\frac{7}{9} \\ x=\frac{210}{9}=\frac{70}{3} \end{gathered}[/tex]Answer: the number is 70/3
Write the equation of the line with x-intercept -2 and y-intercept -1 in slope-intercept form
Answers
The x-intercept of -2 gives us an idea that point (-2,0) if found along the line. The y-intercept of -1, tells us that point (0,-1), this also tells us that b = -1.
Now that we have two points, we can solve for slope m
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{Given two points} \\ (-2,0)\rightarrow(x_1,y_1) \\ (0,-1)\rightarrow(x_2,y_2) \\ \\ \text{Substitute} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1-0}{0-(-2)} \\ m=-\frac{1}{2} \end{gathered}[/tex]Now that we have both m and b. Substitute these values to the slope intercept form
[tex]\begin{gathered} \text{Slope intercept form is} \\ y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \\ \\ \text{Substitute the values from before and we get} \\ y=-\frac{1}{2}x-1 \end{gathered}[/tex]i need help with this pls
Answers
Mathematically speaking, the linear pair postulate and linear pair theorem both express the same thing.
A linear pair is made up of two angles, and the sum of their measures is 180°.What is the formula for linear pairs?A two-variable linear equation of the form axe + by + c, with a, b, and c all being real numbers and not equal to zero.The Transitive Property states that if all real numbers x, y, and z are equal, then x=z. Substituting characteristics. If x=y, then x can be swapped to y in any equation or formula.Mathematically speaking, the linear pair postulate and linear pair theorem both express the same thing. A linear pair is made up of two angles, and the sum of their measures is 180°.Line pairs can be congruent. Adjacent angles are joined by a vertex. Angles that are similar cross across. A linear pairing is unnecessary.
Therefore, mathematically speaking, the linear pair postulate and linear pair theorem both express the same thing.
A linear pair is made up of two angles, and the sum of their measures is 180°.To learn more about the Linear pair theorem refer to:
brainly.com/question/5598970
#SPJ13
10 ptsQuestion 3Find the measure of each interior angle. Round to the nearest hundredth.4x(6x - 90)(3x + 31)(7x+19)X=(4x)" =(6x - 90)(7x + 19)° =(3x + 31)º =
Answers
Alexandre, this is the solution:
Let's recall that the interior angles of a rhombus add up to 360 degrees.
Upon saying that, we have:
4x + 3x + 31 + 6x - 90 + 7x + 19 = 360
20x - 40 = 360
Adding 40 at both sides:
20x - 40 + 40 = 360 + 40
20x = 400
Dividing by 20 at both sides:
20x/20 = 400/20
x = 20
Now, we can calculate each of the angles and prove they add up to 360 degrees, as follows:
• 4x = 4 * 20 =, 80
,• 3x + 31 = 3 * 20 + 31 = 60 + 31 =, 91
,• 7x + 19 = 7 * 20 + 19 = 140 + 19 = ,159
,• 6x - 90 = 6 * 20 - 90 = 120 - 90 = ,30
80 + 91 + 159 + 30 = 360
The table shows the cost for a clothing store to buy jeans and khakis. The total cost for Saturday's shipment, $1,800, is represented by the equation 15x + 20y = 1,800. Use the x- and y-intercepts to graph the equation. Then interpret the x- and y-intercepts.
Answers
The graph of the given function is attached below.
x intercept means if there will be no khakis shipped, then there will be 120 jeans shipped.
Also, y -intercept means if there will be no jeans shipped, then there will be 90 khakis shipped.
Given equation:-
15x + 20y = 1800
Where,
x represents the number of jeans shipped and,
y represents the number of khakis shipped
We have to use the x and y-intercepts to graph the equation.
Putting x = 0 to find the y -intercept, we get,
15(0) + 20y =1800
0 + 20y = 1800
y = 1800/20
y = 90
The coordinates of the point will be (0,90).
Putting y = 0 to find the x -intercept, we get,
15x + 20(0) =1800
15x + 0 = 1800
x = 1800/15
x = 120
The coordinates of the point will be (120,0).
Using the coordinates, we have graphed the graph attached.
Here, x intercept means if there will be no khakis shipped, then there will be 120 jeans shipped.
Also, y -intercept means if there will be no jeans shipped, then there will be 90 khakis shipped.
To learn more about equation, here:-
https://brainly.com/question/10413253
#SPj1
There is a 50% chance of rain here and a 10% chance of rain on Mars. Therefore, there is a 45% chance that it will rain in neither place.
Answers
The given statement is true.
This is a question of probability.
It is given in the question that:-
Chance of raining here = 50 %
Chance of raining on Mars = 10 %
The given statement is :-
There is a 45 % chance that it will rain in neither place.
Chance of not raining here = 100 - 50 % = 50 % = 1/2
Chance of not raining on Mars = 100 - 10% = 90 % = 9/10
Hence, chance of raining in neither place = (1/2)*(9/10) = 9/20
9/20 = (9/20)*100 = 45 %.
Hence, the given statement "There is a 45% chance that it will rain in neither place" is true.
To learn more about probability, here:-
https://brainly.com/question/11234923
#SPJ1
Joe earned 2,100$. He spent 1/5 on rent and 1/4 on food. How much money did he have left?
Answers
The amount of money that Joe has left is $1155
How to calculate the amount of money left ?
Joe earned $2100
He spent 1/5 of the money on rent
1/5 × 2100
= 420
$420 was spent on rent
He spent 1/4 of the money on food
= 1/4 × 2100
= 525
$525 was spent on food
The amount of money left can be calculated as follows
Total amount spent = 525 + 420
= 945
Amount left= 2100 - 945
= 1155
Hence Joe has $1155 left
Read more on amount here
https://brainly.com/question/13576984
#SPJ1
Solving Equations ** Reminder need to show ALL work **
Answers
solution
For this case we have the following equation:
[tex]\frac{3}{4}x-5=4[/tex]Then we can add 5 in both sides and we got:
[tex]\frac{3}{4}x=9[/tex]Then we can multiply both sides by 4/3 and we got:
[tex]x=9\cdot\frac{4}{3}=12[/tex]And the final solution for this case is x= 12
the top ten medal winning nations in a in a particular year are shown in the table. use the given information and calculate the median number of bronze medals for all nations round to the nearest tenth as needed
Answers
We have the following:
We know that to calculate the average we must add the corresponding values of bronze medals of each nation and then divide by the number of nations like this
[tex]\begin{gathered} m=\frac{11+7+9+5+5+3+8+4+6+0}{10} \\ m=\frac{58}{10} \\ m=5.8 \end{gathered}[/tex]the median number of bronze medals for all nations is 5.8
Ary is writing thank you cards to everyone who came to her wedding. It takes her of an hour to write one thank you card. If it took her 8 hours to finish writing all of the cards, how many thank you cards did she write?
Answers
From the question, It takes Ary an hour to write one thank you card.
So, the rate at which she writes the thank you card is;
[tex]\text{Rate R}=1\text{ card/hour}[/tex]To determine the number N of thank you card she would write in 8 hours.
[tex]N=R\times T[/tex]Where;
R is the rate = 1 card/hour
T is the time taken = 8 hours
Substituting the values we have;
[tex]\begin{gathered} N=1\text{ card/hour}\times8\text{ hours} \\ N=8\text{ cards} \end{gathered}[/tex]The number of thank you cards she write is 8 cards
Solve this equation 3n+8=20
Answers
Given the equation below
[tex]3n\text{ + 8 = 20}[/tex]Step 1
Collect like terms.
[tex]\begin{gathered} 3n=20-8 \\ 3n=12 \end{gathered}[/tex]Step 2
Divide both sides of the equation obtained, by the coefficient of the unknown.
[tex]\begin{gathered} \text{The unknown is n.} \\ \text{The co}efficient\text{ of n is 3.} \\ \text{Thus,} \\ \frac{3n}{3}=\frac{12}{3} \\ \Rightarrow n=4 \end{gathered}[/tex]Hence, the value of n in the equation is 4
у = -3х5х + y = 14i need help finding the matrix of this
Answers
3x + y = 0
5x + y = 14
[tex]\Delta\text{ = }\begin{bmatrix}{3} & 1{} & \\ {5} & 1{} & {} \\ {} & {} & {}\end{bmatrix}\text{ = (3 x 1) - (5 x 1) = 3 - 5 = -2}[/tex][tex]undefined[/tex]
HElP
pls pretty pls its due today
z
Answers
The equation of the line in slope intercept form is y = -2x - 70
How to find the equation of a line?The equation of a line can be represented in different form such as slope intercept form, point slope form and standard form.
The equation of the line can be written is slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, using the coordinates (0, - 70)(-20, -30)
Let's find the slope,
m = slope = -30 + 70 / -20 - 0
m = 40 / - 20
m = - 2
Let's find the y-intercept using (0, -70)
-70 = -2(0) + b
b = - 70
Therefore, the equation of the line is y = -2x - 70
learn more on equation of a line here: https://brainly.com/question/12952118
#SPJ1
Let x(t) = t - sin(t) and y(t) = 1 - cos(t)
Answers
Explanation:
The functions are given below as
[tex]\begin{gathered} x(t)=t-sin(t) \\ y(t)=1-cos(t) \end{gathered}[/tex]Part 1:
To find the value of x(t), we will put t=2
[tex][/tex]Triangle A has a 18.3cm side and a 3cm base. Find the hypotenuse.
Answers
Given:
The length of the sides is a=18.3 cm,
The base of the triangle is b =3 cm.
Required:
We need to find the hypotenuse.
Explanation:
Use the Pythagorean theorem.
[tex]c^2=a^2+b^2[/tex]Substitute a =18.3 and b=3 in the equation.
[tex]c^2=18.3^2+3^2[/tex][tex]c^2=343.89[/tex]Take square root on both sides.
[tex]\sqrt{c^2}=\sqrt{343.89}[/tex][tex]c=\pm18.5442[/tex]Length is always positive.
[tex]c=18.54[/tex]Final answer:
The hypotenuse is 18.54cm.
determine the interview on which the function is concave upward and concave downward
Answers
We have to identify the intervals where the function is concave upwards and where is concave downward.
We can differentiate them in a graph as:
We then have only one interval where the function is concave upwards: between x = -1 and x = 4. We can identify other intervals where the function is concave downwards and interrupted by discontinuities.
Then, we can write all the intervals as:
[tex]\begin{gathered} (-\infty,-5)\longrightarrow\text{Concave downward.} \\ (-5,-1)\longrightarrow\text{Concave downward.} \\ (-1,4)\longrightarrow\text{Concave upward}. \\ (4,\infty)\longrightarrow\text{Concave downward.} \end{gathered}[/tex]Can you please help me out with a question
Answers
The formula for the area of a sector of a circle is:
[tex]A=\frac{\theta}{360}\cdot\pi r^2[/tex]Where
θ is the angle
r is the radius
Given,
θ = 100
r = 7
We substitute into the formula and figure the answer out [remembering to use 3.14159 as π]:
[tex]\begin{gathered} A=\frac{\theta}{360}\cdot\pi r^2 \\ A=\frac{100}{360}\cdot(3.14159)(7)^2 \\ A=\frac{5}{18}\cdot(3.14159)(49) \\ A\approx42.76053 \end{gathered}[/tex]Rounding to the nearest thousandth [3 decimal places], we have:
Area = 42.761 square centimeters