Scientists are sending a rover to the moon. Their plan is to study a rectangular area of the moon by placing a grid over the map as shown. On the grid, 1 unit represents 1 kilometer (km).
the Rover will land at (3.5,1) , explore up to (3.5,4), and then over (2,4).
PART A. what are the coordinates of the fourth vertex of the rectangle that the scientist plan to explore ?
PART B.
what is a horizontal length of the rectangle? what is the vertical length of the rectangle
PART C. find the area of the Moon exploration area in square kilometers. Show your work.
Answers
The fourth vertex is (2, 1), and horizontal length is 1.5 km and the vertical length is 3 km. Then the area of the Moon exploration area will be 4.5 square km.
What is the area of the rectangle?Let L be the length and W be the width of the rectangle.
Then the area of the rectangle will be
Area of the rectangle = L×W square units
Scientists are sending a rover to the moon.
Their plan is to study a rectangular area of the moon by placing a grid over the map as shown.
On the grid, 1 unit represents 1 kilometer (km).
PART A. Then the coordinates of the fourth vertex of the rectangle will be (2, 1).
PART B. Then the horizontal length of the rectangle will be 1.5 km and the vertical length of the rectangle will be 3 km.
PART C. Then the area of the Moon exploration area in square kilometers will be
Area = 3 x 1.5
Area = 4.5 square km
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Related Questions
Given that the triangle ABC is at A=(-1,5) B=(1, 1) C = (2, 3), and if the triangle is
reflected across the line x = 4, find the new position of point C'.
Answers
Answer: (6,3)
Step-by-step explanation:
Since C is 2 units from the line of reflection, and it lies on the left of the line of reflection, C' will lie 2 units to the right of the line of reflection.
Therefore, C'=(6,3).
help please, i need to turn this in
Answers
Answer:
a = -3
b = 9
c = -3
Step-by-step explanation:
[tex]a. (2^{5} )(2)^{-8} =2^{a} \\2^{(5-8)} =2^{a} \\2^{-3}=2^{a}[/tex]
[tex]a=-3[/tex]
[tex]b.\frac{4^{7} }{4^{-2} } =4^{b} \\4^{(7-(-2))} } =4^{b} \\4^{(7+2)} =4^{b}[/tex]
[tex]4^{9} =4^{b}[/tex]
[tex]b=9[/tex]
[tex]c. \frac{7^{9} }{7^{c} } =7^{12}[/tex]
[tex]7^{9-c} =7^{12}[/tex]
[tex]9-c=12[/tex]
[tex]c=9-12[/tex]
[tex]c=-3[/tex]
Hope this helps
4. Evaluate e^-2 to one decimal place
A) 0.7
B) -1.4
C) 0.1
D) 1.4
Answers
If the probability that a person over 40-year-old is diabetic, is 0.55
and the probability that a person has hypertension is 0.62. If a person
is selected randomly, find the probability that he is diabetic and and has hypertension
Answers
Answer:
0.341
Step-by-step explanation:
Multiply the probabilities: 0.55 * 0.62 = 0.341
Two triangles are similar. The base of one is 2 inches and the height is 5 inches. If the base of the other is 7 inches, what is the height?
Answers
Step-by-step explanation:
similar shapes means that they have the same angles, and there is one scale factor that applies to all sides and other lines in the shapes (like heights).
therefore the ratios between 2 correlated lines are all the same.
so,
2/7 = 5/height
2×height / 7 = 5
2×height = 7×5 = 35
height = 35/2 = 17.5 in
Help me with the problem please!!
Answers
Step-by-step explanation:
Scale factor red to blue meaning 42 to 7
42÷7=6
Scale factor is 6
Perimeter of the blue quadrilateral = ?
If perimeter of red = 204
Then we use this following proportion
[tex]204 \div 42 = x \div 7[/tex]
[tex] \frac{204}{42} = \frac{x}{7} [/tex]
Then we cross multiply
42x=7×204
42x=1428
x=34
Area of the blue quadrilateral = ?
If area of the red quadrilateral = 2880
Then we use the following proportion
[tex]2880 \div 42 = x \div 7[/tex]
[tex] \frac{2880}{42} = \frac{x}{7} [/tex]
Then we cross multiply
42x=2880×7
42x=20160
x=480
Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the
following is true.
P(-C≤Z≤c)=0.9715
Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
Answers
Using the normal distribution, considering it's symmetry, it is found that the value of C is of 2.19.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The standard normal distribution has mean and standard deviation given, respectively, by:
[tex]\mu = 0, \sigma = 1[/tex].
Hence, considering the symmetry of the normal distribution, the value of c is Z with a p-value of (1 + 0.9715)/2 = 0.98575, hence c = Z = 2.19.
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A company lost $5,676 over a year. How much money did they lose each month to split evenly?
Answers
Answer:
$473
Step-by-step explanation:
We divide 5676 by 12 and we get 473
$473 they lose each month (?)
Step-by-step explanation:
calculator
For the data set represented on the box plot, which region contains the most dispersed data?
Answers
The region that contains the most dispersed data is between the upper quartile and the median.
Which region contains the most dispersed data?A box plot is used to study the distribution and level of a set of scores. The box plot consists of whiskers which measure the minimum and maximum numbers.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
Difference between the lower quartile and the median : 300 - 275 = 25Difference between the upper quartile and the median : 340 - 300 = 40Difference between the upper quartile and the maximum : 355 - 340 = 15Difference between the minimum and the lower quartile : 275 - 250 = 25To learn more about box plots, please check: brainly.com/question/27215146
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²-6x +10 is to be written in the form (x-p)² +g. Find the values of p and q.
Answers
Answer:
[tex]p = 3\\\\q= 1[/tex]
Step-by-step explanation:
[tex]x^2 -6x +10\\\\=x^2 -2 \cdot 3x +3^2 -3^2 +10\\\\=(x-3)^2 -9+10\\\\=(x-3)^2 +1\\\\\text{By comparing with}~ (x-p)^2 +q, \\\\p = 3\\\\q = 1[/tex]
Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 14 and its height is 6?
Answers
The possible base and height of a second triangle are 12 and 7, respectively
How to determine the possible base and height of a second triangle?An inverse variation is represented as:
Base * Height = k
Where k is the constant of variation.
In this case, k is the area
So, we have:
Base * Height = Area
For the first triangle, we have:
14 * 6 = Area
Evaluate
Area = 84
Substitute Area = 84 in Base * Height = Area
Base * Height = 84
Express 84 as the product of two numbers
Base * Height = 12 * 7
By comparison;
Base =12 and Height = 7
Hence, the possible base and height of a second triangle are 12 and 7, respectively
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If Toni wants to grow flowers in her garden, she will need a special type of top soil. If she wants the topsoil to be 1 foot deep, how much topsoil is needed? Remember, the length of the garden is 44 feet and the width is 2 feet.
Answers
Answer:
Depending on the unit your answer needs to be in, it would be 88 cubic feet or 3.25926 cubic yards
If your question asks you to round to the nearest hundredth it would be 3.26 cubic yards.
Step-by-step explanation:
To find the volume of soil:
Volume= Length x Width x Depth/Height
Volume= 44ft x 2ft x 1ft
Volume= 88 cubic feet or 3.25926 (there are 27 cubic feet in a cubic yard, 88/27=3.25926)
hope this helps! :)
Expand and simplify: (-7y - 8) (y - 4)
Answers
Answer:
[tex] { - 7y}^{2} + 20y + 32[/tex]
Step-by-step explanation:
1.) -7y times y = -7y(squared)
2.) -7y times -4 = 28y
3.) -8 times y = -8y
4.) -8 times -4 = 32
5.) Combine like terms
[tex] { - 7y}^{2} + 28y - 8y + 32 = { - 7y}^{2} + 20y + 32[/tex]
Triangle ABC is translated 2 units to the right
on a coordinate plane to form triangle DEF.
The measure of AB= 6 units, BC = 5 units,
CA= 4 units, and m/ABC = 41°. Which of the
following is not a corresponding measure of
triangle DEF?
Answers
Answer:
56
Step-by-step explanation:
What is the volume of a sphere with a radius of 5.9 in, rounded to the nearest tenth of a cubic inch?
Answers
[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=5.9 \end{cases}\implies V=\cfrac{4\pi (5.9)^3}{3}\implies V\approx 860.3~in^3[/tex]
find the
-2
-4
-3
-1
-9-8
determinant OF
-15
- 5
6
Answers
Determinants are defined only for square matrices, so I assume you are given the 3×3 matrix
[tex]A = \begin{bmatrix}-2 & -4 & -3 \\ -1 & -9 & -8 \\ -15 & -5 & 6 \end{bmatrix}[/tex]
Let's compute the determinant by taking the cofactor expansion along the first column:
[tex]\det A = -2 \det\begin{bmatrix}-9 & -8 \\ -5 & 6\end{bmatrix} + \det\begin{bmatrix}-4 & -3 \\ -5 & 6\end{bmatrix} - 15 \det \begin{bmatrix}-4 & -3 \\ -9 & -8\end{bmatrix}[/tex]
[tex]\det A = -2 ((-9)\times6-(-8)\times(-5)) + ((-4)\times6 - (-3)\times(-5)) \\ ~~~~~~~~~~~~~~~- 15 ((-4)\times(-8)-(-3)\times(-9))[/tex]
[tex]\det A = -2(-54-40) + (-24 - 15) - 15 (32 - 27)[/tex]
[tex]\det A = \boxed{74}[/tex]
What is the equation of the line that is perpendicular to the line and passes through the point (15,-5)?
Answers
The equation of the line that is perpendicular to the line and passes through the point (15,-5) is y = -x + 10
The complete question is
What is the y-intercept of the equation of the line that is perpendicular to the line y = x + 10 and passes through the point (15, –5)?
What is the meaning of Perpendicular ?A perpendicular means a line which intersects the other line at 90 degree.
Line given y = x+10
slope = 1
Slope of the line perpendicular to the above line = -1
and it passes through the point (15, –5)
The equation will become
y = mx +c
-5 = -1 * 15 + c
15-5 = c
c = 10
Therefore the equation is y = -x +10
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Answer: d
Step-by-step explanation:
Can somebody please help with Khan Academy? Thx :)
Answers
Answer:
x ≤ 0
Step-by-step explanation:
The number line's direction is left, any number that is left on a number line behind zero has a less value. Greater than or equal!
A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company manufactures is 3%. Suppose a random sample of 10 LED light bulbs is selected. What is the probability that:
a. None of the LED light bulbs are defective?
b. Exactly one of the LED light bulbs is defective?
c. Two or fewer of the LED light bulbs are defective?
d. What are the mean and standard deviation of the binomial distribution for the number of defective LED light bulbs?
Answers
Answer:
a) There is a 59.87% probability that none of the LED light bulbs are defective.
b) There is a 31.51% probability that exactly one of the light bulbs is defective.
c) There is a 98.84% probability that two or fewer of the LED light bulbs are defective.
d) There is a 100% probability that three or more of the LED light bulbs are not defective.Step-by-step
explanation:
For each light bulb, there are only two possible outcomes. Either it fails, or it does not. This means that we use the binomial probability distribution to solve this problem.
What are the domain and range of the function represented by the set of ordered pairs?
{(-6, 12), (-3, -2), (1, 0), (14, -4)}
A. Domain: {-6, -3, 1, 14}
Range: {-4, -2, 0, 12}
B. Domain: -6 ≤ x ≤ 14
Range: -4 ≤ y ≤ 12
C. Domain: {-4, -2, 0, 12}
Range: {-6, -3, 1, 14}
D. Domain: -4 ≤ x ≤ 12
Range: -6 ≤ y ≤ 14
Answers
Answer:
A
Step-by-step explanation:
the domain is the definition of the valid x (input) values.
the range is the definition of the valid y (result) values.
as the function is defined by listing the specific points, the function only consists of individual points and not of connecting lines.
therefore the domain and range cannot be continuous intervals (otherwise the function would suddenly also include points not in the original list).
so, B and D are wrong.
and A is right, because the domain contains the x values, and the range the y values.
jackson bought 3 pounds of candy for $9.60.
What was the price of this candy in cents per once ?
Answers
Answer:
to find for one divide 9 dollars 60 pounds by 3 to get the coast of one candy
function h is a transformation of the parents tangent function such that h(x)=-tan(1/2x). Which graph represents function h?
Answers
The graph that represents function h is the graph in; Option C
How to Interpret Graph Transformations?The parent function is; f(x) = tan (x)
The transformed function is; h(x) = -tan(¹/₂x)
Now, from general tangent function we know that; y = tan(Bx)
Thus, period = π/(¹/₂)
From the given transformation that produced the h(x) function and when we look at the given graphs, the one that represents the function h is Option C.
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Which expression is a possible leading term for the polynomial function graphed below?
Answers
Like wise, option 2 is not the answer because it has a negative symbol.
This leaves us with option 4, 22x^9 as the right answer.
HELP ILL GIVE BRAINLIEST!
Solve 2u² = 90, where u is a real number.
Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
u=
Answers
Answer:
I think maybe u=6.71 but I'm not sure. wait for another answer
Two similar cylinders have surface areas of 24 cm² and 54 cm². The volume of the smaller cylinder is 167 cm³.
What is the volume of the larger cylinder?
O 367 cm³
46 cm³
O 48
cm³
O 54
cm³
Answers
The volume of the larger cylinder will be 36π cm³. Then the correct option is A.
The complete question is attached below.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
The ratio of the volume to surface area will be
V / SA = πr²h / 2πrh
Then we have
Two similar cylinders have surface areas of 24 cm² and 54 cm².
The volume of the smaller cylinder is 16π cm³.
Then the volume of the larger cylinder will be
Let x be the volume of the larger cylinder.
Then we have
x / 54 = 16π / 24
x = 36π cm³
Then the correct option is A.
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The population of Detroit, Michigan, decreased from 1,027,974 in 1990 to 688,701 in 2013 (Source: U.S. Census Bureau). Find the average rate of change in the population of Detroit, Michigan, over the 23-year period.
Answers
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
to get the slope of any straight line, we simply need two points off of it, so let's use the ones provided in that
[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{years}{x}&\stackrel{population}{y}\\ \cline{1-2} 1990&1027974\\ 2013&688701\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{1990}~,~\stackrel{y_1}{1027974})\qquad (\stackrel{x_2}{2013}~,~\stackrel{y_2}{688701}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{688701}-\stackrel{y1}{1027974}}}{\underset{run} {\underset{x_2}{2013}-\underset{x_1}{1990}}} \implies \cfrac{-339273}{23}\implies -14751\qquad \stackrel{rate~of}{change}[/tex]
let's notice, is negative since the population decreased.
Which of the numbers below are whole numbers? Check all that apply.
A. 29
B. 367.53
C. 71.1
D. 6523
DE 1/2
F. 126
Answers
Answer:
A,D,F
Step-by-step explanation: Because it not a fraction or decimal in it its an whole number
The measure of an exterior angle of a regular polygon is 45º. How many sides does the polygon have?
Answers
Answer:The answer is 8 sides
Step-by-step explanation:
In order to qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches. The inequality 64 < x < 68, where x represents height, can be used to represent the height range. Which is another way of writing the inequality?
x > 64 and x < 68
x > 64 or x < 68
x < 64 and x < 68
x < 64 or x < 68
Answers
Solve for x and y.
7x-4
#
4y+8
24#
+
31
Answers
Answer:
7x-4 = -28
4y+8 = 4(y + 2)
Step-by-step explanation: