We expect the cube to show a two 8 times out of 48 rolls.
Six faces, numbered from 1 to 6, make up a typical number cube. When the cube is rolled, there is an equal chance that every face will show up. As a result, there is a 1/6 chance that the cube will roll a two on any given roll.
We can use the calculation for the anticipated value of a discrete random variable to get the expected number of times the cube will reveal a two in 48 rolls:
E(X) = np
where n is the number of trials (in this example, 48 rolls), p is the probability of success on each trial (in this case, 1/6), and X is the random variable (in this case, the number of times the cube reveals a two).
When we change the values, we obtain:
E(X) = 48 * (1/6) = 8
Hence, we anticipate that the cube will display a two 8 times out of every 48 rolls.
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i need to graph y=-1/4x+6
Answer:y intercept is 6 slope is -1/4
Step-by-step explanation:
to graph it in y=mx+b form b is the y intercpt and where you start the graph and m is the slope is [tex]-\frac{1}{4}[/tex] the you go to the right 4 and up one to graph the line
Need help with this problem 1
By the given definition of matrix A, the value of the matrix A⁻¹ is [tex]\left[\begin{array}{ccc}-1&0&1&2&-1&-2&0&0&-1\end{array}\right][/tex] and it is true that AA⁻¹ = I₃.
Calcuting the matrix A⁻¹Given that
[tex]A = \left[\begin{array}{ccc}1&0&2\\1&1&0\\1&0&1\end{array}\right][/tex]
To find the inverse of A, we can use the following formula:
A⁻¹ = (1/|A|) adj(A)
where |A| is the determinant of A and adj(A) is the adjugate matrix of A.
First, let's calculate the determinant of A:
|A| = 1(1×1 - 0×0) - 0(1×0 - 0×1) + 2(1×0 - 1×1)
|A| = -1
Next, we need to find the adjugate matrix of A.
To do this, we need to find the matrix of cofactors of A, then take its transpose:
[tex]C = \left[\begin{array}{ccc}1&-2&0&0&1&0&-1&2&1\end{array}\right]\\[/tex]
adj(A) = [tex]C^T = \left[\begin{array}{ccc}1&0&-1&-2&1&2&0&0&1\end{array}\right][/tex]
Now we can calculate A⁻¹ using the formula:
A⁻¹ = (1/|A|) adj(A)
So, we have
[tex]A^{-1} = (-1) \left[\begin{array}{ccc}1&0&-1&-2&1&2&0&0&1\end{array}\right] = \left[\begin{array}{ccc}-1&0&1&2&-1&-2&0&0&-1\end{array}\right][/tex]
Checking whether AA⁻¹ = I₃Finally, we can check whether AA⁻¹ = I₃ using
[tex]A^{-1}A = \left[\begin{array}{ccc}-1&0&1&2&-1&-2&0&0&-1\end{array}\right] \left[\begin{array}{ccc}1&0&2&1&1&0&1&0&1\end{array}\right] = \left[\begin{array}{ccc}1&0&0&0&1&0&0&0&1\end{array}\right] = I_3[/tex]
Therefore, we have found the inverse of A and verified that AA⁻¹ = I₃.
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Find the equilibrium level of national income in the basic Keynesian macroeconomic model
Y=c+I
C= 40+ 0.5y
I= 200
Therefore, the equilibrium level of national income in this basic Keynesian macroeconomic model is 480.
What is sum?In mathematics, the sum is the result of adding two or more numbers or quantities together. The symbol used to represent a sum is the capital Greek letter sigma (∑), which stands for "sum up."
by the question.
In the basic Keynesian macroeconomic model, equilibrium occurs when national income (Y) equals total spending in the economy. Therefore, we can set Y equal to the sum of consumption (C) and investment (I), as follows:
Y = C + I
Substituting the given consumption and investment functions into this equation, we get:
Y = (40 + 0.5Y) + 200
Simplifying and rearranging, we get:
Y - 0.5Y = 240
0.5Y = 240
Y = 480
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15. Find the value of x that makes the
quadrilateral a parallelogram.
6x-8
4x
If the value of x is 4, the quadrilateral meets all the requirements of a parallelogram and will be a parallelogram.
What is a quadrilateral?A quadrilateral is a four-sided shape with straight line segments as its sides. It is a two-dimensional shape with four angles, each measuring 90°. Quadrilaterals can be categorized into different shapes such as squares, rectangles, parallelograms, trapezoids, rhombuses, and kites.
A parallelogram is a four-sided shape with opposite sides parallel and equal in length. To find the value of x that makes the quadrilateral a parallelogram, we need to use the property of a parallelogram, which states that the opposite sides of a parallelogram are equal in length.
Therefore, we need to equate the opposite sides of the quadrilateral: 6x-8=4x. After solving this equation, we get x=4. Thus, the value of x that makes the quadrilateral a parallelogram is 4.
In order for a quadrilateral to be a parallelogram, opposite sides must be parallel. Using this property, we can set the opposite sides equal to each other and solve for x.
[tex]$2x + 5 = 3x - 2$[/tex]
Simplifying this equation, we get:
[tex]$x = 7$[/tex]
Therefore, if [tex]$x=7$[/tex], the quadrilateral is a parallelogram.
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Consider the given function.
ƒ(1): =
5,
I < -2
3, -2 <=<0
0,
0 <=<2
> 2
-3,
Which graph represents the given function?
Find each measurement indicated using Law Of Sines. Round your answers to the nearest tenth.
answer 4 -8
Using Law of sines, the missing angles are:
4) ∠B = 45.74°
6) ∠C = 21.02°
8) ∠A = 60.84°
How to use the Law of Sines?The law of sines is a rule for solving the lengths and angles of triangles and it states that:
a/sin A = b/sin B = c/sin C
4) Using law of sines, we have:
8/sin B = 11/ sin 80
(8/11) sin 80 = sin B
sin B = 0.7162
B = sin⁻¹0.7162
∠B = 45.74°
6) Using law of sines, we have:
13/sin C = 32/sin 62
sin C = (13/32) sin 62
sin C = 0.3587
C = sin⁻¹0.3587
C = 21.02°
8) Using law of sines, we have:
30/sin 104 = 27/sin A
sin A = (27/30) sin 104
sin A = 0.8733
A = sin⁻¹0.8733
A = 60.84°
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Help
Please …….
Zxrxrxrdrdrxxtxtcvyhnin
The box-and-whisker plot shows that the dataset has a median of approximately 5.5 and is relatively symmetric, with the middle 50% of the data falling between approximately 4 and 7.
The box-and-whisker plot offers a visual summary of the distribution of the given dataset. The following is one way to understand the plot:
The median, which is the midway number when the data is organised from least to largest, is shown by the line inside the box. The median in this situation is roughly 5.5.
The box's bottom edge corresponds to the first quartile (Q1) and its top edge to the third quartile, and it represents the middle 50% of the data (Q3). The interquartile range is the space between Q1 and Q3 (IQR). In this instance, Q1 is roughly 4 and Q3 is roughly 7, hence the IQR is roughly 3.
The whiskers reach from the box's boundaries to the dataset's lowest and largest values that aren't regarded as outliers. Although there are many different definitions of an outlier, it is generally accepted that any number that is more than 1.5 times the IQR below Q1 or above Q3 qualifies as an outlier. There aren't any anomalies in this circumstance.
Individual data points outside the box and whiskers are shown as dots above and below the whiskers. There are no such data points in this situation.
Hence, the box-and-whisker plot reveals that the dataset is very symmetrical and has a median of about 5.5, with the middle 50% of the data ranging between roughly 4 and 7.
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Which relationships describe angles 1 and 2?
Select each correct answer.
A. supplementary angles
B. complementary angles
C. vertical angles
D. adjacent angles
The relationship which describe angles 1 and 2 is supplementary angles.
The correct answer choice is option A.
What are supplementary angles?Supplementary angles are angles in which the sum of their measure is equal to 180°.
Based on this, angles 1 and 2 are supplementary because they both add up to 180°.
Complementary angles are two angles which add up to 90 degrees.
Vertical angles are angles opposite each other when two angles intersect.
Adjacent angles are angles which have a common side and common vertex.
Hence, angles 1 and 2 are supplementary.
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a) What is the height of the container if it’s a cylinder with a radius of 3cm?
b) If the container from Part A is filled with coffee and coffee costs $0.02 per cubic centimeter, what is the cost of coffee?
a. The Vοlume = 198 cm³ and height = 7, if it’s a cylinder with a radius οf 3cm.
b. The cοst οf cοffee is $3.96 when $0.02 per cubic centimetre.
What is the fοrmula fοr the vοlume οf the cylinder?The fοrmula fοr the vοlume οf a cylinder is
V = πr²h,
where V is the vοlume, r is the radius, and h is the height.
a) Tο find the height οf the cylinder, we need tο knοw the vοlume οf the cοntainer and the radius. The fοrmula fοr the vοlume οf a cylinder is:
V = πr²h
[tex]$\mathrm{\frac{V }{ h}} = \pi r\² }[/tex]
[tex]$\mathrm{\frac{V }{ h}} = \frac{22}{7} \times 3 \times 3}[/tex]
[tex]$\mathrm{\frac{V }{ h}} = \frac{22}{7} \times 3 \times 3}[/tex]
[tex]$\mathrm{\frac{V }{ h}} = \frac{198}{7}[/tex]
Thus, Vοlume = 198 cm³ and height = 7
b) If the cοntainer frοm is filled with cοffee and cοffee cοsts $0.02 per cubic centimetre, Then the cοst οf cοffee
= $0.02 × 198 cm³
= $3.96
Thus, The Vοlume = 198 cm³ and height = 7, if it’s a cylinder with a radius οf 3cm.
The cοst οf cοffee is $3.96 when $0.02 per cubic centimetre.
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You travel in a car at an average rate of 55 miles per hour on the highway and 35 miles per hour in the city.
a. How long does it take you to travel 16.5 highway miles and 7 city miles?
b. How long does it take you to travel 44 highway miles and 28 city miles?
According to the given information, it takes 0.5 hours to travel 16.5 highway miles and 7 city miles and 1.6 hours to travel 44 highway miles and 28 city miles.
What is the average rate?
The average rate is a measure of the average speed at which something occurs over a period of time. It is calculated by dividing the total amount of something by the total time it took to occur.
The formula for the average rate or average speed is:
Average speed = Total distance traveled / Total time taken
a. To find the time it takes to travel 16.5 highway miles and 7 city miles, we can use the formula:
time = distance/speed
The time it takes to travel 16.5 highway miles is:
time on highway = 16.5 / 55 = 0.3 hours
The time it takes to travel 7 city miles is:
time in city = 7 / 35 = 0.2 hours
The total time it takes to travel both distances is:
total time = time on highway + time in city = 0.3 + 0.2 = 0.5 hours
Therefore, it takes 0.5 hours (or 30 minutes) to travel 16.5 highway miles and 7 city miles.
b. To find the time it takes to travel 44 highway miles and 28 city miles, we can use the same formula:
time on highway = 44 / 55 = 0.8 hours
time in city = 28 / 35 = 0.8 hours
total time = time on highway + time in city = 0.8 + 0.8 = 1.6 hours
Therefore, it takes 1.6 hours (or 96 minutes) to travel 44 highway miles and 28 city miles.
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Hello, If 1lb - $3.40 would 0.274lb equal 2.647? I was struggling with this question, At first I did 0.34(y) and 0.1(x) but I learned that going up from 0.34 every 0.1 decimal will not help because I am trying to figure out 0.274 so then I am trying to see if $2.4 would work. Thank you. Oops, I am in middle school not college, Apologies.
A rainwater tank has a diameter of 160 cm and a height of 190 cm. The tank is half full. The water is used at a rate of 25,5 litres per day. In how many days will the tank run dry, assuming that no rain falls in that time?
It will run dry after 141.7 days.
In how many days will the tank run dry?The rainwater tank has a diameter of 160 cm and a height of 190 cm, then its volume is:
V = 3.14*(180cm)*(160cm/2)² = 3,617,280 cm³
We know that 1 L = 1000 cm³
then:
3,617,280 cm³ = 3,617.280 L
The water is used at a rate of 25,5 litres per day, so after x days there is:
W = 3,617.280 - 25.5*x liters
It is zero when:
0 = 3,617.280 - 25.5*x
x = 3,617.280/25.5
x = 141.7 days.
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Write a polynomial of least degree with real coefficients and with the root -20-7i. Write your answer using the variable x and in standard form with a leading coefficient of 1.
Answer:
Step-by-step explanation:
Logically, if a polynomial of real coefficients has a complex root, it’s conjugate is a root as well. That means if -20-7i is a root, -20+7i is also a root. Also, since we’re dealing with minimal degree, we wish to construct a quadratic expression with such roots. To do this, we can use Vieta’s formulas, which relates the trinomial coefficients with its roots. The two roots added together is -b/a in ax^2 + bx + c, and the two roots multiplied together is c/a. The two roots added together is -40. The two roots multiplied together is 449. So, our quadratic expression is x^2+40x+449
Converting Standard Form-Slope Intercept Form
Solve for y.
Step 1: Move the x term to the other
side by performing the opposite
operation to BOTH sides.
-7x+y=-17
+ [?];
+7x
Therefore , the solution of the given problem of slope comes out to be y = 7x - 17 is the equation in slope-intercept form.
Explain slope.A line's steepness is determined by its slope. In gradient-based equations, a situation known as gradient overflow can happen. One can determine the slope by dividing the sum of a run (width differential) and rise (climbing distinction) between two places. The equation with the hill variation, y = mx + b, is used to model the fixed path issue. where grade is mm, a = bc, and the line's y-intercept is situated; (0, b).
Here,
Given :
=> -7x + y = -17
7x both faces together
=> -7x + 7x + y = 7x - 17
Condense: y = 7x - 17
So,
=> y = 7x - 17 is the equation in slope-intercept form.
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A bakery sells chocolate cupcakes and mocha cupcakes. One day it sold 162 chocolate and 138 mocha. What percent of the cupcakes sold that day were chocolate?
N=6, p=0.3, x<4
P(x<4) =
Answer:
Step-by-step explanation:
To find P(x<4), we need to use the cumulative distribution function (CDF) of the binomial distribution.
For N = 6 and p = 0.3, the probability mass function (PMF) is:
P(X = k) = (6 choose k) * 0.3^k * 0.7^(6-k)
where (6 choose k) is the binomial coefficient.
Using this formula, we can find the probabilities for each value of X less than 4:
P(X = 0) = (6 choose 0) * 0.3^0 * 0.7^6 ≈ 0.1176
P(X = 1) = (6 choose 1) * 0.3^1 * 0.7^5 ≈ 0.3025
P(X = 2) = (6 choose 2) * 0.3^2 * 0.7^4 ≈ 0.3241
P(X = 3) = (6 choose 3) * 0.3^3 * 0.7^3 ≈ 0.1852
Therefore, P(x<4) is the sum of these probabilities:
P(x<4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) ≈ 0.9294
So the probability of getting less than 4 successes in 6 trials with a success probability of 0.3 is approximately 0.9294.
simplify the polynomial
The polynomial after simplification is obtained as [tex]5 x^{2}[/tex] + 9x + 3.
What is simplification?
In mathematics, reducing an expression, fraction, or problem to a simpler form is referred to as simplification. With calculations and solution, the problem is made simple. Make something simpler by simplifying it.
We are given a polynomial as
5x - 5 + [tex]11 x^{2}[/tex] + 4x - [tex]6 x^{2}[/tex] + 8
Now, in order to simplify the given polynomial, we will combine the like terms of the polynomial.
On combining the like terms, we get
[tex]5 x^{2}[/tex] + 9x + 3
Hence, the polynomial after simplification is obtained as [tex]5 x^{2}[/tex] + 9x + 3.
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Write the six trig functions for the following
SOH CAH TOA
Please and thank you
The six trig functions are:
(1) Figure 1, sin θ = 1/√5
(2) Figure 1, cos θ = 2/√5
(3) Figure 1, tan θ = 1/2
(4) Figure 2, sin θ = 3/√13
(5) Figure 2, cos θ = 2/√13
(6) Figure 2, tan θ = 3/2
What is a trig function?Trig function (short for "trigonometric function") is a mathematical function that relates the angles of a right triangle to the lengths of its sides. The main trig functions are sine (sin), cosine (cos), and tangent (tan).
The trig functions are abbreviated using SOH CAH TOA.
SOH : sin θ = opposite / hypotheses
CAH: cos θ = adjacent / hypothenuse
TOA : tan θ = opposite / adjacent
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You want to determine the savings for using a battery that can be recharged. The battery costs sixteen dollars. You save four dollars each time you recharge the battery. Represent the cost of the rechargeable battery as a negative number and savings as a positive number.
Define a unit for the net savings of the rechargeable battery.
What is your net savings if you recharge the battery ten times?
If your net savings is twelve dollars, how many times did you recharge the battery?
Complete the rows for the amount you save each time you recharge the battery and the cost of a rechargeable battery. Then, enter a variable for the number of rechargings and use this variable to write an expression for the net savings of the rechargeable battery.
Find the value of x..
Answer:
x = 16
Step-by-step explanation:
∠1 + ∠2 = 90
42 + 3x = 90
3x = 90 - 42
x = 48/3 = 16
CAN SOMEONE HELP WITH THIS QUESTION?✨
The rate of change of the angle of elevation is 0.00011 rad/ft, for that we have to know the elevation.
What is Elevation?The height above or below a specified(predefined) reference point, most frequently a reference geoid, which is a mathematical representation (expression) of the Earth's sea level as an equipotential gravitational surface, determines(defines) a location's elevation.
The angle of elevation of the camera is, Θ= [tex]tan^-^1(\frac{x}{2000} )[/tex]
The distance between the camera and the launching pad is, b= 2000 ft
The distance between the camera and the racket is, h = 4255 ft
To find the rate of change of the angle of elevation of the camera, we need to differentiate the function of that angle.
Θ= [tex]tan^-^1(\frac{x}{2000} )[/tex]
Differentiating function with respect to x we have,
[tex]\frac{d}{dx}[/tex] Θ=[tex]\frac{d}{dx} tan^-^1(\frac{x}{2000} )[/tex]
Θ'=[tex]\frac{1}{1+\frac{x^2}{2000^2} }[/tex][tex]*\frac{1}{2000}[/tex]
[tex]\frac{1}{2000+\frac{x^2}{2000} }[/tex] (Equation 1)
[tex]h^2=b^2+p^2[/tex]
[tex]4255^2+2000^2+x^2[/tex]
Θ=[tex]\frac{1}{2000+\frac{14105025}{2000} }[/tex]
≈ 0.00011 rad/ft.
Thus, the rate of change of the angle of elevation is 0.00011 rad/ft.
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Which best describes the relationship between the line that passes through the points (–6, 5) and (–2, 7) and the line that passes through the points (4, 2) and (6, 6)?
A. same line
B. neither perpendicular nor parallel
C. parallel
D. perpendicular
Answer:
B
Step-by-step explanation:
calculate the slopes m of the 2 lines using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 6, 5 ) and (x₂, y₂ ) = (- 2, 7 )
m = [tex]\frac{7-5}{-2-(-6)}[/tex] = [tex]\frac{2}{-2+6}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]
repeat with
(x₁, y₁ ) = (4, 2 ) and (x₂, y₂ ) = (6, 6 )
m = [tex]\frac{6-2}{6-4}[/tex] = [tex]\frac{4}{2}[/tex] = 2
• Parallel lines have equal slopes
[tex]\frac{1}{2}[/tex] ≠ 2 , then lines are not parallel
the product of the slopes of perpendicular lines equals - 1
[tex]\frac{1}{2}[/tex] × 2 = 1 ≠ - 1 , thus lines are not perpendicular
the lines are neither perpendicular nor parallel
This figure is made from a part of a square and a part of a circle.
What is the area of this figure, to the nearest square unit?
Perimeter of the given polygon figure will be 38 units.
What exactly is a polygon in mathematics?
A closed, two-dimensional, flat, closed polygon is a shape that is constrained by geometry and has straight sides. Its sides don't curve inward at all. Another term for a polygon's sides is its polygonal edges. The points where two sides converge are known as a polygon's vertices (or corners).
Perimeter of a polygon = Measure of the circumference of the polygon
From the figure attached,
Perimeter of the figure = measure of the three straight lines + measure of the circumference of the quarter circle
Measure of linear sides = 5 + 10 + 10 + 5 = 30 units
Circumference of the quarter circle = 1/4(2πr)
= 1/2(π)(5)
= 7.85 units
Perimeter of the figure = 30 + 7.85
= 37.85
≈ 38 units
Therefore, perimeter of the given figure will be 38 units.
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Select from the drop-down menu to correctly complete each comparison 4.408
The prοduct οf the matrices is nοt the identity matrix. Therefοre, X and A nοt inverses οf each οther.
What is an identity matrix?An identity matrix is a square matrix in which all the elements οf principal diagοnals are οne, and all οther elements are zerοs. It is denοted by the nοtatiοn “In” οr simply “I”. Any matrix will yield a matrix as a result of being multiplied by the identity matrix.
The identity matrix is a matrix having entry οne in its diagοnal and rest οf the entries are zerο.
[tex]X.A = \left[\begin{array}{cc}2&-1\\6&-4\\\end{array}\right] \left[\begin{array}{cc}1/2&1/4&\\-2&-1/2&\end{array}\right][/tex]
[tex]X.A = \left[\begin{array}{cc}3&1\\11&7/2\end{array}\right][/tex]
Hence, The prοduct of the matrices is not the identity matrix. Therefοre, X and A not inverses of each other.
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The complete question is in the attached image.
23841.0596 in standard form
Answer:
23841.0596 in standard form is 2.38410596 x 10^4.
Step-by-step explanation:
Answer:
2.38410596 x 10^4
Step-by-step explanation:
pls brainlist
Rewrite in the simplest form 7(−8f−2)+10(−5f+7)
Answer:
-106f+56
Step-by-step explanation:
7(-8f-2)= -56f-14
10(-5f+7)= -50f+70
-56f-14. +. 50f+70
=-106f+56
Answer:
-2(53f-28)
Step-by-step explanation:
Distribute7(−8f−2)+10(−5f+7)
7x-8f=-56f 7x-2=-14
10x-5f=-50f 10x7=70
-56f-14+-50f+70 Adding a negative to something means to subtract. Like right here at -14 + -50 is the same as -14 - 50
2. Add the numbers
-56f-14+-50f+70 -14+70=56
-56f+56-50f
3. Combine like terms
-56f+56-50f -56+ -50= -106
-106f +56
4. Common Factor
-106f + 56
-2(53f-28)
HELP ME ASAP
Owen's Muffin Extravaganza recorded how many of each type of muffin it recently sold.
bran muffins 25
blueberry muffins 12
poppy seed muffins 3
chocolate chip muffins 10
Considering this data, how many of the next 16 muffins sold would you expect to be bran muffins?
Answer:
Step-by-step explanation:
A hands-on experience is the only modality that would give visitors a complete understanding of the plight of modern enslaved people.
pls right answer worth 100 points and brainlest
Answer: 204 ft
Step-by-step explanation: First lets find the area of the triangle, the formula for area of a triangle is base times height divided by 2. Now the height isn't given but we can find it by subtracting 18 by 10 which gives us 8. 8 times 6 is 48 divided by 2 is 24. Therefore, the area of the triangle is 24 ft. Now we find the area of the rectangle which is length times width. 18 times 10 is 180. Now we add the area of both shapes, 180 plus 24 is 204, so your answer is 204 ft.
Answer:
Step-by-step explanation:
Answer this question please
The single translation that maps shape A onto shape C is given as follows:
Translation one unit right.Translation ten units down.What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically on the coordinate plane.
The four translation rules for coordinates are defined as follows:
Translation left a units: (x,y) -> (x - a, y).Translation right a units: (x,y) -> (x + a, y).Translation up a units: (x,y) -> (x, y + a).Translation down a units: (x,y) -> (y - a).Translations can often be composed, that is, a combination of multiple translations can result in a single translation, as is the case for this problem.
Considering the translation of 3 units left(shape B) and then 4 units right(shape C), the horizontal translation is given as follows:
-3 + 4 = 1 -> 1 unit right.
Considering the translation of 7 units down(shape B) and then 3 units down(shape C), the vertical translation is given as follows:
-7 - 3 = 10 units down.
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Which sequence of transformations results in figures that are similar but not congruent
Answer:
When two shapes are similar but not congruent, the sequence of steps showing the similarity usually has a single dilation and then the rest of the steps are rigid transformations. The dilation can come at any time.
Step-by-step explanation:
When two shapes are similar but not congruent, the sequence of steps showing the similarity usually has a single dilation and then the rest of the steps are rigid transformations. The dilation can come at any time.