The area of the convex polygon is 43/2 square units
How to determine the area of the convex polygon?The vertices are given as:
(0,5), (-1,2), (4,4), (-3,-4) and (2,0)
The area is then calculated as:
[tex]A = \frac 12(\left[\begin{array}{cc}x_1&x_2\\y_1&y_2\end{array}\right] + \left[\begin{array}{cc}x_2&x_3\\y_2&y_3\end{array}\right] + ....+\left[\begin{array}{cc}x_n&x\\y_n&y\end{array}\right] )[/tex]
So, we have:
[tex]A = \frac12 * (|-1 * 5 - 2 * 0 + 0 * 4 - 5 * 4 + 4 * 0 - 4 * 2 + 2 * -4 - 0 * -3 -3 * 2 + 4 * 1|)[/tex]
Evaluate
[tex]A = \frac12 * (|-43|)[/tex]
Remove the absolute bracket
[tex]A = \frac12 * 43[/tex]
This gives
[tex]A = \frac{43}2[/tex]
Hence, the area of the convex polygon is 43/2 square units
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a cone has a height of 16 centimeters and a radius of 12 centimeters. what is the exact lateral and surface area of the cone? type the correct answer in each box. use numerals instead of words.
The lateral and total surface areas of the given cone are 753.98 cm² and 1206.31 cm² respectively.
What are the formulae for lateral and total surface areas of a cone?A cone has a height 'h', radius 'r', and slant height 'l'.
The slant height of the cone is obtained by the Pythagorean theorem. I.e.,
l² = h² + r²
Then,
Its lateral surface area(LSA) = πr([tex]\sqrt{h^2+r^2}[/tex]) square units and
Its total surface area(TSA) = πr(r + l) square units
Calculation:It is given that,
A cone has a height h = 16 cm and radius r = 12 cm
Then, the slant height is calculated by
l² = h² + r²
l = [tex]\sqrt{h^2+r^2}[/tex]
On substituting,
l = [tex]\sqrt{16^2+12^2}[/tex]
= [tex]\sqrt{400}[/tex]
= 20 cm
So,
LSA = πr([tex]\sqrt{h^2+r^2}[/tex])
= π × 12 × ([tex]\sqrt{16^2+12^2}[/tex])
= π × 12 × 20
= 753.98 cm²
and
TSA = πr(r + l)
= π × 12 × (12 + 20)
= π × 12 × 32
= 1206.37 cm²
Therefore, the lateral and total surface areas of the cone with a height of 16 cm and a radius of 12 cm are 753.98 cm² and 1206.37 cm².
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Answer: The lateral area is 240π square centimeters. The total surface area is 384π square centimeters.
Step-by-step explanation:
f(x) = 2x – 4
g(x) = 3x + 1
what is is h(x) = f(x)g(x)?
Answer:
h(x) = 6x² - 10x - 4
Step-by-step explanation:
h(x) = f(x) g(x)
= (2x - 4)(3x + 1)
each term in the second factor is multiplied by each term in the first factor, that is
2x(3x + 1) - 4(3x + 1) ← distribute parenthesis
= 6x² + 2x - 12x - 4 ← collect like terms
= 6x² - 10x - 4
that is h(x) = 6x² - 10x - 4
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equations which gave the same solution as; 2.3p – 10.1 = 6.5p – 4 – 0.01p are;
2.3p – 10.1 = 6.49p – 4 and230p – 1010 = 650p – 400 – pWhich equations have the same solution as the given equation?It follows from the answer choices that the equation; 2.3p – 10.1 = 6.49p – 4 is equivalent to the given equation as the algebraic sum of p variables is evaluated on the right hand side.
The second equation; 230p – 1010 = 650p – 400 – p also is equivalent to the given equation, when multiplied through by 100.
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The variability around a regression line, which determines the fit of a regression line, can be calculated in Excel. Which function does Excel use for this residual variance?
Excel uses VAR function for determining the residual variance.
What is residual variance?The variation of any error is known as residual variance, also known as unexplained variance or error variance.
Depending on the type of analysis you're doing, the precise definition will vary. For instance, random fluctuations in regression analysis produce volatility around the "actual" regression line.There are two components to a regression line's total variance: variation that can be explained and variance that cannot. Simply put, the residual variance after deducting the variation resulting from the regression from the total variance of the dependent variable is the residual variance.
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What is the equation in vertex form of a
parabola with vertex (2, 4) that opens
downward and is stretched by a factor of
3?
Answer:
B.
Step-by-step explanation:
Vertex with (2,4) means that the equation will have:
y=a(x-2)^2 + 4
Open downwards means that the a will be negative:
so: y = -a (x-2)^2 + 4
Stretched by a factor of 3 means that the a=3
So if we combine all of these, we will get the equation:
y = -3 (x-2)^2 + 4
The solution to the system of equations shown is (2, 0).
3x − 2y = 6
x + 4y = 2
When the first equation is multiplied by 2, the sum of the two equations is equivalent to 7x = 14
.
Which system of equations will also have a solution of (2, 0)?
Answer:
7x = 14
x + 4y = 2
Step-by-step explanation:
3x − 2y = 6
x + 4y = 2
6x - 4y = 12
x + 4y = 2
-----------------------
7x = 14 Replace the first equation with this one.
1. when y=7 , what is the value of x?
2. what is the y-intercept of the graph?
1) Correct.
2) The y-intercept is when x=0, so it is (0,5).
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. On a number line, point D is at -3, and point E is at 6. The point F lies on . The ratio of to is 2 : 3. Where does point F lie on the number line
On the number line the position of point F is at point 4.
According to the statement
We have a given that the on a number line , point D is at -3, and point E is at 6. The point F lies on the ratio of to is 2 : 3.
and we have to find the F point on the number line.
Firstly,
Number line is a line on which numbers are marked at intervals, used to illustrate simple numerical operations.
So, According to given information,
Point D is at -3, and point E is at 6.
Ratio of point E to F = 6*2/3
Then
Ratio of point E to F = 6*2/3
After solving it
The point F = 2*2
The point F = 4.
So, On the number line the position of point F is at point 4.
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Graph the line with the slope 1/3 and x-intercept 3
Step-by-step explanation:
Use the slope-intercept form to find the slope and y-intercept.
Slope:
−
1
3
y-intercept:
(0 , 3)
Any line can be graphed using two points. Select two
x
values, and plug them into the equation to find the corresponding
y
values
Graph the line using the slope and the y-intercept, or the points.
Slope:
−
1
3
y-intercept:
(0 , 3)
Concrete blocks are 8in. high. if a 3/8-in. mortar joint is used, how high will a wal of 12 courses of concrete blocks be?
Answer:
100.5 inches
Step-by-step explanation:
If each course has 3/8 inch of concrete below it (including the bottom one)
8 in * 12 + 3/8 in * 12 = 100 1/2 inches
Given the parent cosine function f(x) = cos x , find the function g(x) after the parent function undergoes a horizontal shift right 7 units, and up 4 units.
By applying the transformation rules for horizontal and vertical translation, we find that the resulting function is g(x) = cos (x - 7) + 4.
How to find the resulting function by transformation rules
Transformation rules are rules that makes changes on charateristics and behavior of a function to create a new one. Rigid transformations like horizontal and vertical translations are examples of transformation rules. In this question we must apply the following transformation rules to the parent cosine function f(x) = cos x:
Horizontal translation: f'(x) = f(x - 7) (1)Vertical translation: g(x) = f'(x) + 4 (2)Now we proceed to derive the resulting function by applying the rules defined above:
Horizontal translation
f'(x) = cos (x - 7) (3)
Vertical translation
g(x) = cos (x - 7) + 4 (4)
By applying the transformation rules for horizontal and vertical translation, we find that the resulting function is g(x) = cos (x - 7) + 4.
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A right rectangular pyramid is sliced vertically (down) at the red line by a plane not passing through the vertex of the pyramid m. what is the shape of the cross section?
The cross-section of a right rectangular pyramid will be shaped similar to the base, that is, a rectangle. Hence, 4th option is the right choice.
If the peak of the rectangular pyramid is directly above the center of the base, it creates a perpendicular to the base, indicating the height of the pyramid. This type of rectangular pyramid is known as the right rectangular pyramid.
A rectangle is a quadrilateral, that is a closed figure with 4 line segments, with all four interior angles at 90°.
When we slice a right rectangular pyramid vertically down at the red line by a plane, not passing through the vertex, of the pyramid will be a dilated image of its base.
A dilated image is an enlarged or diminished image of the preimage, similar with all angles.
Thus, the cross-section of a right rectangular pyramid will be shaped similar to the base, that is, a rectangle. Hence, 4th option is the right choice.
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For complete question, refer to the attachment.
Answer:trapozoid
Step-by-step explanation:
please help me im in a rush
(a) The city with a larger median room temperature is city B.
(b) The city having the highest noon temperature is city B.
(c) The city having the noon temperatures with a higher interquartile range is city A.
(d) The city having more noon temperatures that 81°F is city B.
In the given question, the noon temperatures for two cities, A and B, recorded over a month are shown via the box-and-whisker plots.
We are asked to use it and answer the questions:
(a) The median of data is represented by the line in the box of the box-and-whisker plot. Thus,
The median noon temperature for city A is 73°F.
The median noon temperature for city B is 76°F.
Thus, the city with a larger median room temperature is city B.
(b) The highest temperature is seen as the end point of the whiskers. Thus,
The highest temperature for city A is 85°F.
The highest temperature for city B is 92°F.
Thus, the city having the highest noon temperature is city B.
(c) The interquartile range is the difference between the end line of the box and its start line. Thus,
The interquartile range for city A is (81 - 64)°F or 17°F.
The interquartile range for city B is (81 - 68)°F or 13°F.
Thus, the city having the noon temperatures with a higher interquartile range is city A.
(d) From the given box-and-whisker plots, we can see that after 81°F, city B has a long whisker, showing more outliers.
Thus, the city having more noon temperatures that 81°F is city B.
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Drag each number to the correct location on the table. classify the real numbers as rational or irrational numbers.
The rational numbers are -5/250, [tex]\sqrt{400}[/tex] ,and irrational numbers are 5.012121212......., [tex]\sqrt[3]{30}[/tex] , 0.01562138411........,[tex]\sqrt{1000}[/tex]
Given six numbers:5.012121212..,[tex]\sqrt{1000}[/tex],[tex]\sqrt[3]{30}[/tex], -5/250, 0.01562138411.....,[tex]\sqrt{400}[/tex].
We have to identify which numbers are rational and which are irrational numbers.
Rational numbers are those numbers which can be written in p/q form where q cannot be equal to zero because if q is zeo then the value of p/q will be infinity.
Irrational numbers are those numbers which cannot be written in p/q form.
First number :5.0121212121....
In the above numbers 12 is repeating next to the decimals. So it is a irrational numbers.
Second number:[tex]\sqrt{1000}[/tex]
If we solve the above number we will find it 31.6227766017 . It is cannot be expressed in p/q form, so it is irrational number.
Third number:[tex]\sqrt[3]{30}[/tex]
The abov number is irrational number as we cannot express it in p/q form.
Fourth number:-5/250
The value of above number is -0.02.It can be in the form of -2/100. so it is rational number.
Fifth number:0.01562138411........
Because the digits are repeating after decimals so it is irrational number.
Sixth number:[tex]\sqrt{400}[/tex]
The value of above number is 20, so it is rational number.
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Question is incomplete as it should include figure.
A motorcycle travels 20 miles west and then turns and goes 52° north of west another 38 miles. How far is the motorcycle from its starting point?? Round your answer to the nearest tenth
__ miles
Answer:
52.7 miles
Step-by-step explanation:
Please refer to attached photo. (Apologies for the terrible drawing).
We can deduce from A to B the distance is 20 miles, therefore no calculations is required.
However, from B to C, we will have to find the horizontal and vertical distances.
Horizontal Distance B > C = = hBC = [tex]BCcos(52)[/tex] = [tex]38cos(52) miles[/tex]
Vertical Distance B > C = vBC = [tex]BCsin(52)[/tex] = [tex]38sin(52)miles[/tex]
Here you can see the whole diagram is a right angle triangle. Which means, we can use Pythagoras' Theorem to find AC.
By Pythagoras Theorem,
[tex]c^{2} =a^{2}+b^{2}[/tex]
[tex]AC^{2} = (AB + hBC)^{2} + vBC^{2} \\AC^{2} = (20+38cos(52))^{2} +(38sin(52))^{2} \\AC = \sqrt{(20+38cos(52))^{2} +(38sin(52))^{2} } \\AC = 52.7 miles[/tex](nearest tenth)
Write an equation of the line that passes through $\left(-1,\ 7\right)$ and is perpendicular to the line $y=-\frac{1}{8}x-1$ .
Equation of the line which is passing through the points [tex](-1,7)[/tex] and perpendicular to the line [tex]$y=-\frac{1}{8}x-1$[/tex]
is [tex]y=8x+15[/tex]
How to find the equation which passing through one point [tex](-1,7)[/tex]and perpendicular to the equation [tex]$y=-\frac{1}{8}x-1$[/tex] ?
We know that the equation of line in form of slope and point is
[tex]y-y_{1} =m(x-x_{1} )[/tex]
So first equation of line which is passing through point [tex](-1,7)[/tex] is
[tex]y-7=m_{1} (x-(-1))\\y-7=m_{1}(x+1)[/tex].....(a)
Line [tex]$y=-\frac{1}{8}x-1$[/tex] perpendicular to the line (a)
And we know when two lines are perpendicular then
[tex]m_{1} m_{2} =-1[/tex]
So [tex]m_{1} =-1/m_{2}[/tex]
and we know [tex]m_{2} =-1/8[/tex]
So
[tex]m_{1} =-1/\frac{-1}{8} \\=-1*8/-1\\=8[/tex]
The equation of the line is
[tex]y-7=8(x+1)\\y-7=8x+8\\y=8x+8+7\\y=8x+15[/tex]
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How are the coordinates of the extreme value and the equation from part B in the form y=(x-h)^2-c related.
The extreme value of y = (x - h)² - c is the vertex of the equation.
What are extreme values of a function?The extreme values of a function are either the maximum or minimum values of the function.
The equation of a parabola in vertex formThe equation of a parabola in vertex form with vertex (h', k) is given by
y = a(x - h')² + k and its extreme values are
if a > 0 (h', k) is a minimum point and if a < 0 (h', k) is a maximum point.Since y = (x - h)² - c is the equation of a parabola in vertex form, comparing with y = a(x - h')² + k,
h = h' -c = k and a = 1.So, the cooordinates of the vertex of y = (x - h)² - c is (h, -c).
Now, since a = 1 > 0, (h, -c) is a minimum point.
So, the extreme value of y = (x - h)² - c is the vertex of the equation.
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Answer:
The lowest value is at (1, -8). H and C are equal to 1 and 8 in the equation y = (x - 1)2 - 8. Therefore, the minimum's x-coordinate corresponds to the equation's h-value, and its y-value is the opposite of the c-value.
Step-by-step explanation:
i re wrote it
Point A is located in which quadrant?
IV
III
I
II
Answer:
Quadrant II
Step-by-step explanation:
This is because the top right is I, the top left
is II, the bottom left is III, and the bottom right is IV.
A summer camp has 32 campers. 22 of them swim, 20 play softball, and 5 do not play softball or swim. which values correctly complete the table? a) a = 15, b = 10, c = 7, d = 5, e = 12 b) a = 15, b = 7, c = 5, d = 10, e = 12 c) a = 14, b = 7, c = 5, d = 12, e = 10 d) a = 14, b = 12, c = 7, d = 5, e = 10
The values which completes the table regarding summer camp is option b which is a=15,b=7, c=5, d=10, e=12.
Given that there are 32 campers, 22 of them can swim, 20 play softball and 5 do not play softball or swim.
We have to find the values of a,b,c,d,e so that we can complete the table.
Table is a combination of rows and columns. In our case the third row and third column shows the total.
from the table we can write that 22+d=32-----------1
so d=32-22
=10
d=10
c+5=d-----------2
c=10-5=5
c=5
a+c=20------------------3
a+5=20
a=20-5
a=15
a+b=22--------------3
15+b=22
b=7
20+e=32----------4
e=32-22
e=10.
Hence the values which completes the table is a=15,b=7, c=5, d=10, e=12.
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Question is incomplete as it should include figure showing table of values.
The following uses a 4-step proof, starting with the given statement. Complete the following proof
Given: JK | MN
Prove: 1, 2 are complementary
1) [tex]\overline{JK} \perp \overline{MN}[/tex]
2) [tex]\angle JKM[/tex] is a right angle (perpendicular lines form right angles)
3) [tex]\triangle JKM[/tex] is a right triangle (definition of a right triangle)
4) [tex]\angle 1[/tex] and [tex]\angle 2[/tex] are complementary (the acute angles of a right triangle are complementary)
A cylinder with a base diameter of x units has a volume of πx3 cubic units. a cylinder with a base diameter of x units has a volume of pi x cubed cubic units. which statements about the cylinder are true? select two options.
The height of the cylinder is 4 x units.
The area of the cylinder’s base is One-fourthπx2 square units .
What is the volume of cylinder?
We know the volume of a cylinder is given by the formula π r2 h, where r is the radius of the cylinder and h is the height.
Formula for volume of the cylinder
V = r² π h
Volume of the cylinder= πx³
Diameter=x
Radius (r)=diameter/2
r = x/2
V = r² π h
πx³=(x/2)² πh
πx³= (x²/4)πh
Divide both sides by π
x³ =(x²/4)h
Make h the subject of the formula
h = x³ ÷ x²/4
=x³ ×4 / x²
=4x³ / x²
=4 * x * x * x / x * x
h=4x
Area of the base:
B = r² π
r=x/2
B=(x/2)² * π
=(x²/4)π
=πx²/4
=1/4(πx²)
Therefore, The area of the cylinder’s base is One-fourthπx2 square units.
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The complete question is -
A cylinder with a base diameter of x units has a volume of πx3 cubic units. A cylinder with a base diameter of x units has a volume of pi x cubed cubic units. Which statements about the cylinder are true? Select two options. The radius of the cylinder is 2x units. The area of the cylinder’s base is One-fourthπx2 square units. The area of the cylinder’s base is One-halfπx2 square units. The height of the cylinder is 2x units. The height of the cylinder is 4x units.
Which function is undefined for x=0
Answer:
of course 0
Step-by-step explanation:
because it doesn't have any value in its first equation
PLEASE HELP (the picture has the problem)
2 parallelograms. The pre-image is smaller than the image.
How can you tell that this transformation is a dilation?
The figure flipped upside down.
The figure changed size.
The figure completed a half turn.
The figure did not change.
Answer: The figure changed size.
Step-by-step explanation: Dilations change the sizes of shapes. They can either make them bigger or make them smaller.
: Nicole and Ian generate two patterns. Nicole uses the rule multiply by 3 then add 2 starting with 1.
Ian uses the rule add 1/2 then multiply by 2 starting from 0. Complete the table to show the
numbers in each pattern. Then create the ordered pairs.
help
The ordered pairs of Nicole and Ian's sequence pattern are:(5,1),(17,3),(53,5),(161,10),(485,20).
Given that Nicole uses the rule multiply by 3 then add 2 starting with it and Ian uses the rule add 1/2 then multiply by 2 starting from 0,
We ar rquired to find the ordered pairs of Nicole's and Ian's rules.
We are told that Nicole's pattern is multiply by 3 then add 2 starting with 1.
Thus Nicole's pattern is :5,17,53,161,485.
Ian's pattern is add 1/2 then multiply by 2 and starting with 0.Thus the numbers are :1,3,5,10,20.
If we combine the numbers of both the person'rule then we will get the ordered pairs which can be written as under:
The ordered pairs are (5,1),(17,3),(53,5),(161,10),(485,20).
Hence the ordered pairs are (5,1),(17,3),(53,5),(161,10),(485,20).
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Help fast!!!
each shelf holds a total of 64 deciliters of apple juice. the bottles have three different sizes: large medium, and small. how many deciliters of apple juice does a medium bottle contain?
do a quick explanation!
dont just take the points or i will report you!
less than a minute!!!
The quantity of deciliters of apple juice a medium bottle contain is 10 deciliters
EquationLarge bottles = lMedium bottles = mSmall bottles = sTotal bottles in each shelf = 644s + 3l = 64
3s + 2l + 2m = 64
6s + 4m = 64
If
m = 10
s = 4
l = 16
Check:
3s + 2l + 2m = 64
3(4) + 2(16) + 2(10)
= 12 + 32 + 20
= 64
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Help, please. I just need an answer, so if anyone is bored, for the love of god please...
Answer:B & E
Step-by-step explanation:
We can first rearrange the function to isolate y. Then, we can find the slope as the function is in the form y=mx+b.
[tex]3x-4y=7\\-4y=-3x+7\\y=\frac{3}{4}x-\frac{7}{4}[/tex]
Since parallel lines have the same slope, we can put the slope of 3/4 into the point slope form to get the answer.
For reference, the point-slope form is [tex]y-y_1=m(x-x_1)[/tex]
[tex]y+2=\frac{3}{4}(x+4)\\y+2=\frac{3}{4}x+3\\y=\frac{3}{4}x+1[/tex]
The first line is found in option E, so option E is one of the correct options.
We can also move the x to the other side, as two of the 5 options have both variables on the left (B and C).
[tex]-\frac{3}{4}x+y=1[/tex]
If we multiply the whole equation by -4, we can get rid of the fraction.
[tex]-4(-\frac{3}{4}x+y)=-4(1)\\3x-4y=-4[/tex]
Hence, option B is also correct.
d) Arrange 8/9,7/18,10/16 in ascending order of magnitude
8/9 = 0.888888....
7/18 = 0.388888888889
10/16 = 0.625
Ascending order - means going up, smallest to largest. (Imagine climbing a ladder, where you start of low, then, go higher up the ladder.)
Thus, answer is 7/18, 10/16, 8/9
Hope this helps!
Which is the graph of the function f(x) = x3 + x2 + x + 1?
Answer:
Step-by-step explanation:
the answer is on the graph
PLEASE HELP IM STUCK PLEASE HELP
Answer:
y = 3x + 5
Step-by-step explanation:
x = number of years
• bush grows 3cm per year
• the initial height is 5cm
3cm per year times x number of years: y = 3x
Add the initial height of 5cm: y = 3x + 5