The image of the given points under the rotation through +90° about the center origin include the following;
A' (-5, 4).
B' (-3, -2).
C' (5, -3).
D' (1, 4).
What is a rotation?In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise to the vertices of each figure, the coordinates of the vertices of the image are as follows:
(x, y) → (-y, x)
A (4, 5) = A' (-5, 4).
B (-2, 3) = B' (-3, -2).
C (-3, -5) = C' (-(-5), 3) = (5, -3)
D (4, -1) = D' (-(-1), 4) = (1, 4)
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Nisha read the part of a book in 1 hour. How much part of the book will be read by
her in 3 2/5
hours?
Suppose that \( f(x)=h^{-1}(x) \) and that both \( j \) and \( h \) are defined for all values of \( x \). Let \( h(11)=2 \) and \( f(12)=-7 \). Evaluate the following if possible. If it is not possib
h(2) + j(−7) = −7(1 + j)
Suppose that f(x) = h^−1(x) and that both j and h are defined for all values of x. Let h(11) = 2 and f(12) = −7. We need to evaluate the following. h(2) + j(−7)For finding the value of h(2), we can use f(x) = h^−1(x) where x = h(2)f(h(2)) = 2h(2) = f^−1(2)We need to find h(2). Therefore, we need to find f^−1(2). We know f(12) = −7f(h(2)) = 2⟹ h(2) = −7Substitute h(2) = −7 in h(11) = 2h(11) = h(2 + 9) = h(2) + 9 = 2 + 9 = 11Therefore, h(2) = −7 and h(11) = 2.h(2) + j(−7) = −7 + j(−7) = −7(1 + j)Therefore, h(2) + j(−7) = −7(1 + j).
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Prove that cyclic trapezium is always isosceles and its diagonal are equal
In our proof, as the trapezium are congruent and the rest of the sides are equal ∴AC = BD. Hence, the cyclic trapezium is isosceles and its diagonals are equal.
How do we prove cyclic trapezium is always isosceles and its diagonal are equal?Step 1:
The diagonals are AC and BD, and the line CE is parallel to AD.
We know that a parallelogram's opposite angles are equal.
∠D = ∠AEC......(1)
We also know that the sum of a cyclic quadrilateral's opposite angles is 180 degrees.
∠D + ∠ABC = 180..........(2)
We can deduce from (1) and (2) that
AEC + ABC = 180....... (3)
AEC and CEB are now a linear pair.
AEC + CEB = 180................. (4)
We can conclude from (3) and (4) that,
CEB = ABC
The sides opposite the equal angles are also equal, as we know.
CEB = ABC
CE = CB ... (5)
However, because AECD is a parallelogram, opposite sides must be equal.
∴CE = AD ... .(6)
From equation (5) and (6), we can conclude that
AD = CB ......(7)
As a result, the cyclic trapezium ABCD is isosceles.
Step 2:
Establishing that its diagonals are equal.
We have AC and BD as diagonals.
In triangle DBA and CBA,AD = CB from (7)⇒AB = AB (common side).
ADB + ACB (angles in the same segment of a circle are equal). As a result of the SAS rule, ABD and ABC are congruent.
Because they are congruent and the other sides are equal, AC = BD. As a result, a cyclic trapezium is isosceles and has equal diagonals.
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*3 SIMPLE GEOM QUESTIONS!!*
please help me with this study guide!
I appreciate it!
Thank you so muchhh <3
Therefore , the solution of the given problem of coordinates comes out to be the coordinates of the reflection of G(3, -2) across the y-axis (-3, -2).
Explain coordinate.By utilising one or even more variables or coordinates, a coordinate system is able to precisely locate points or other mathematical items on such a room, including Euclidean space. Coordinates, which seem to be pairs of integers, are used to locate a point or object on a double plane. The y and x vectors are used to represent the position of a point on a two-dimensional surface. a group of figures used to designate particular places.
Here,
G(3, -2) will have the following coordinates after being reflected across the y-axis:
=> (-3, -2).
A point's x-coordinate changes sign when it is reflected across the y-axis, but its y-coordinate stays the same.
Consequently, the coordinates of the reflection of G(3, -2) across the y-axis (-3, -2).
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The coordinates of the resulting point after the reflection across the y - axis will be G'(3, 2) and The coordinates of the resulting point after the reflection across the x - axis will be G'(3, 2).
What do you mean by reflection of coordinates?A reflection on the coordinate plane (x , y ) is a type of transformation. It takes a geometric figure such as a line, segment, point or shape and transforms it into a congruent geometric figure called the image.
a. It is given that a point (-3, 2) reflected across the y - axis.
Now, when any given coordinate is reflected across the y - axis then, the sign of the x - coordinate is inverted and the y - coordinate remains same.
Therefore, the coordinates of the resulting point after the reflection across the y - axis will be G'(3, 2)
b. It is given that a point (3, -2) reflected across the x - axis.
Now, when any given coordinate is reflected across the x - axis then, the sign of the y - coordinate is inverted and the x - coordinate remains same.
Therefore, the coordinates of the resulting point after the reflection across the x - axis will be G'(3, 2).
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Using a ruler and a pair of compass only construct:
a. Line MN =8. 8cm
b. A perpendicular to MN at N
c. Angle MNP=60 degrees,such that line NP =6. 3cm
The Construction of line MN and perpendicular at point N as well as angle MNP = 60°such that NP would be 6.3 cm is given below as image.
In Euclidean geometry, an angle is a shape made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles can be formed in the plane where two rays are positioned. Moreover, when two planes overlap, angles are created. Dihedral angles are what they are called.
In geometry, two lines are considered to be perpendicular if they meet or intersect at right angles of 90°. The Latin term "perpendicularis," which denotes a plumb line, is where the word "perpendicular" originally made its appearance.
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Rachel, Sam and Thomas applied for a common position at the company. Only one of them will be hired for the position. The probabilities that each of them is hired for the role are given by 1 out of 7, 2 out of 7, and 4 out of 7 respectively.The probabilities that Rachel, Sam and Thomas can help boost the company’s revenue are given by 4 out of 5, 1 out of 2, and 3 out of 10 respectively if they are hired.(a) Find the probability that Thomas is selected for the position given that the company’s revenue did not improve.(b) Find the probability, p, that the company’s revenue will generally improve.Rachel, Sam and Thomas interviewed at another company for another position. The probabilities that each of them is hired for the role are now given by x, 2x and 4x respectively.It can be assumed that the hiring process for each individual candidate are independent of one another.(c) Suppose there is no limit to the number of hires the company can make (i.e. the company can hire any one of them, any two of them, all three of them or no one at all). Find an inequality that must satisfied by x.
(a) The probability that Thomas is selected for the position given that the company's revenue did not improve is 4/7.
(b) To find the probability, p, that the company's revenue will generally improve, we can calculate the probability that at least one of Rachel, Sam, or Thomas is selected for the position.
This can be done by calculating the sum of the probabilities of each of them being hired, which is 1/7 + 2/7 + 4/7 = 7/7 = 1. Therefore, the probability that the company's revenue will generally improve is 1.
(c) To find an inequality that must be satisfied by x, we must take into account the probabilities that each of Rachel, Sam, and Thomas is hired for the role.
For example, if x = 1/2, then the probability that Rachel is hired is 1/2, Sam is hired is 1, and Thomas is hired is 2. Therefore, the inequality that must be satisfied by x is 0 < x ≤ 1/2.
For further information on (a) The probability that Thomas is selected for the position given that the company's revenue did not improve is 4/7.
(b) To find the probability, p, that the company's revenue will generally improve, we can calculate the probability that at least one of Rachel, Sam, or Thomas is selected for the position. This can be done by calculating the sum of the probabilities of each of them being hired, which is 1/7 + 2/7 + 4/7 = 7/7 = 1. Therefore, the probability that the company's revenue will generally improve is 1.
(c) To find an inequality that must be satisfied by x, we must take into account the probabilities that each of Rachel, Sam, and Thomas is hired for the role. For example, if x = 1/2, then the probability that Rachel is hired is 1/2, Sam is hired is 1, and Thomas is hired is 2. Therefore, the inequality that must be satisfied by x is 0 < x ≤ 1/2.
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The table summarizes results from 986 pedestrian deaths that were caused by automobile accidents.
Driver Pedestrian Intoxicated?
Intoxicated? Yes No
Yes 54 83
No 246 603
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was not intoxicated.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
prob = %
From the given data, the probability that the pedestrian was not intoxicated or the driver was not intoxicated is 99.7%.
To find the probability that the pedestrian was not intoxicated or the driver was not intoxicated, we can add the probabilities of the two mutually exclusive events:
Pedestrian not intoxicated and driver intoxicated
Pedestrian intoxicated and driver not intoxicated
From the table, we can see that there were 603 pedestrian deaths where the driver was not intoxicated and 54 pedestrian deaths where the driver was intoxicated, for a total of 657 deaths where the driver was not intoxicated. Similarly, there were 246 pedestrian deaths where the pedestrian was not intoxicated and 83 pedestrian deaths where the pedestrian was intoxicated, for a total of 329 deaths where the pedestrian was not intoxicated.
Therefore, probability that pedestrian was not intoxicated or driver was not intoxicated is:
P = (657 + 329) / 986
= 0.9969
Converting to percentage and rounding to one decimal place,
P = 99.7%
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Compare the dimensions of the prisms. How many times greater is the surface area of the red prism than the surface area of the blue prism?
4 m
3m
2m
12 m
The dimensions of the red prism are
The surface area of the red prism is
9 m
6 m
times the dimensions of the blue prism.
times the surface area of the blue prism.
Answer:
3, 9
Step-by-step explanation:
Surface A = 2(wl + hl + hw)
Where in the red prism, l is 12, w is 6, h is 9 and in the red prism l is 4, w is 2, h is 3
Lenght 12/4 =3
Width 6/2 =3
Height 9/3 =3
Calculate surface are of red prism
SA = 2( 6x12 + 9x12 + 9x6)
SA = 2( 72 +108+54)
SA = 2(234) = 468 m²
Calculate surface area of blue prism
SA = 2(2x4 + 3x4 + 3x2)
SA = 2(8 +12+6)
SA = 2(26)
SA =52
Area of red /area of blue = 468/52
Ans =9
could use some help, think this might be right(new to precalculus
Find dxdy . y= cosx1+ tanx7dxdy =
Answer:
y= 1/cosx+7/tanx
dy/dx = 1secxtanx-cosec^2x
Answer this ASAP will give the brainliest answer
Given that y = 11 cm and θ = 38°, work out x rounded to 1 DP.
x ≈ 17.8 cm (rοunded tο 1 decimal place).
What is trigοnοmetric functiοn ?The trigοnοmetric functiοns in mathematics are real functiοns that relate the angle οf a right-angled triangle tο the ratiοs οf its twο side lengths. They are alsο knοwn as circular functiοns, angle functiοns, οr gοniοmetric functiοns.
All geοsciences, including navigatiοn, sοlid mechanics, celestial mechanics, geοdesy, and many οthers, use them extensively. They are sοme οf the mοst straightfοrward periοdic functiοns, and as a result, Fοurier analysis is frequently used tο study periοdic phenοmena.
Tο sοlve fοr x, we can use the trigοnοmetric functiοn cοsine since we have the adjacent side and the hypοtenuse.
cοs(θ) = adjacent/hypοtenuse
cοs(38°) = x/hypοtenuse
We knοw that the perpendicular is y = 11 cm, sο we can use the Pythagοrean theοrem tο find the hypοtenuse:
[tex]\rm hypotenuse^2 = perpendicular^2 + base^2[/tex]
[tex]x^2 = y^2 + (adjacent)^2[/tex]
[tex]x^2 = 11^2 + (x cos(38^\circ))^2[/tex]
[tex]x^2 = 121 + (x 0.7880107536)^2[/tex]
[tex]x^2 = 121 + 0.6201117996x^2[/tex]
[tex]0.3798882004x^2 = 121[/tex]
[tex]x^2 = 318.5022183[/tex]
x ≈ 17.84 cm (rounded to 1 decimal place)
Therefore, x ≈ 17.8 cm (rounded to 1 decimal place).
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(6e−3f−4)⋅2=left parenthesis, 6, e, minus, 3, f, minus, 4, right parenthesis, dot, 2, equals
The final result of the expression (6e−3f−4)⋅2 is e3f−8.
The calculation is as follows: (6e−3f−4)⋅2 = (6e-3f-4)*2. In order to calculate this expression, it is necessary to use the Order of Operations. The Order of Operations is a set of rules that determine the order in which operations should be performed when evaluating an expression. First, any parentheses need to be evaluated. In this expression, there are parentheses surrounding 6e−3f−4. This means that any operations within the parentheses should be done first. Inside the parentheses, there is an exponent, e−3f, and a subtraction, 4. Exponents should be done first, so e−3f should be evaluated first. This is equivalent to e multiplied by e multiplied by e, multiplied by f, which is equal to e3f. Then, 4 should be subtracted from e3f, which is equal to e3f−4. After the parentheses have been evaluated, the remaining multiplication should be done. This is equivalent to (e3f−4)*2, which is equal to e3f−8.
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A circle has a radius of 6 feet and a circumference of approximately 37.70 feet. Complete the sentence to describe
how to estimate the value of 7.
Move the correct answer to each box. Not all answers will be used.
6 12 37.70
To estimate the value of x, divide
37.70/12
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According to the manufacturer, a sandwich cookie weighs on average 11.3 grams. A statistics class is wondering if this is true, so they randomly select 37 sandwich cookies and weigh them. Their sample of 37 sandwich cookies had the following statistics: grams grams.
Based on the sample of 37 sandwich cookies, it can be concluded that the average weight of a sandwich cookie is close to 11.3 grams, as the manufacturer claimed. This conclusion is supported by the mean, standard deviation, and range of the sample.
What is standard deviation?Standard deviation is a measure of how spread out a set of numbers is. It gives us an idea of how much variation there is from the average or expected value. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.
The manufacturer of a sandwich cookie claims that the average weight of a sandwich cookie is 11.3 grams. To test this claim, a statistics class randomly selected 37 sandwich cookies and weighed them. The sample of 37 sandwich cookies had a mean of 11.2 grams, standard deviation of 0.5 grams, and range of 10.1 to 12.5 grams.
The mean of 11.2 grams is very close to the manufacturer’s claim of 11.3 grams. The standard deviation of 0.5 grams indicates that the sample of sandwich cookies had a very small amount of variance. The range of 10.1 to 12.5 grams indicates that the sample had sandwich cookies with weights that were close to the mean, which further supports the conclusion that the mean is close to 11.3 grams.
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Does there exist a triangle with side lengths 12 , 5 , 15 ?
Answer:
yes, a triangle with the side lengths 12, 5, and 12 does exist.
Step-by-step explanation:
side a = 12
side b = 5
side c = 12
area = 29.34In
12.
Find the Volume of the solid below;
Round to the nearest one hundredth
Use your pi #button when applicable.
10 ft
17 ft
6 ft
8 ft
The volume of the given solid above which is a triangular prism would be = 510 ft³.
How to calculate the volume of the solid shape ?To calculate the volume of the given prism the formula should be used such as;
Volume = 1/2 × base× height × length
Where base = 10ft
height = 6 ft
length = 17ft
Volume = 1/2 × 10×6×17
= 5×6×17
= 510 ft³
Therefore the volume of the given shape above would be = 510 ft³ when the formula for triangular prism is used.
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which way does shift
g(x)=lx+9l-5
Answer:
g(x) was shifted 9 units to the left and 5 units down
Step-by-step explanation:
Horizontal shifts take place when the x value is changed within the parentheses, or in this case, absolute value.
The graph is shifted 9 units left because of the + 9.
Vertical shifts happen when the entire equation is added or subtracted to.
The graph is shifted 5 units down because of the - 5.
See the graph for a visualization.
during the lunch rush, a fast food joint sold 10 sodas and earned $30 which is the rate of dollars per soda?
Answer:
1:3 is your rate for dollars per soda
Step-by-step explanation:
Use a property to write an equivalent expression 12 times (100-5).which property did you use?
Answer: distributive property
Step-by-step explanation:1 2 times 95 can indeed be rewritten as 12(100-5) and we can use the distributive property IN OUR HEADS, so we get 1200 - 60 = 1140.
Alex’s printer can print 8 photos in 12 minutes. Khalid printer can print 24 photos in 1 hour. which process could you use to help determine how much longer will it take khalils printer to print 120 photos than Alex’s. select all that apply.
A. write an equation that adds the number of photos that each print prints in 1 hour
B. make a table of equal ratios to find how long it takes each printer to print 120 photos and find the difference
C. Subtract the number of photos that khalil printer prints in two hours from the number of photos that alex’s printer print in 2 hours.
D. graph a table of values for each printer and compare the number of minutes when the number of photos is 120.
Answer:
B. Make a table of equal ratios to find how long it takes each printer to print 120 photos and find the difference would be an appropriate process to determine how much longer it will take Khalil's printer to print 120 photos than Alex's.
Step-by-step explanation:
To use this process, we can set up a table showing the ratio of photos printed to time taken for each printer. Then we can use these ratios to find how long it would take each printer to print 120 photos, and find the difference between the two times to determine how much longer it would take Khalil's printer.
Averi was trying to factor 4x^2+20x-164x
2
+20x−164, x, squared, plus, 20, x, minus, 16. She found that the greatest common factor of these terms was 4 and made an area model:
What is the width of Averi's area model?
The width of Averi's area model is 4 units.
The area model for factoring 4x²+20x-16 is shown above. The width of Averi's area model is 4 units. To factor the given expression, Averi used an area model.
In this model, the width represents the greatest common factor of the given expression while the length represents the remaining factors of the expression. Averi determined that the greatest common factor of 4x²+20x-16 was 4.
Therefore, she created a rectangle with a width of 4 and a length of (x²+5x-4). The dimensions of the rectangle are determined by the factors of the given expression.
The area of the rectangle represents the original expression. Therefore, the area of the rectangle can be calculated by multiplying the width and length of the rectangle. The area of the rectangle is equal to: Area of rectangle = width x length Area of rectangle = 4(x²+5x-4)Area of rectangle = 4x²+20x-16
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What value of x makes 23x+5=11 true?
A. 4
B. 513
C. 9
D. 1023
E. 24
6/23 is the value of x that ensures that the equation 23x + 5 = 11 holds true. The solution to this problem cannot be found in the available selections since none of the answer possibilities match this value.
We must find x in order to determine what value of x results in the equation 23x + 5 = 11 being true.
Initially, we must remove 5 from both sides of the equation to isolate the variable x:
23x + 5 - 5 = 11 - 5
When we combine the left and right sides, we obtain:
23x = 6
Then, by multiplying both sides of the equation by 23, we must find x:
23x/23 = 6/23
When we combine the left and right sides, we obtain:
x = 6/23
As a result, 6/23 is the value of x that ensures that the equation 23x + 5 = 11 holds true.
The solution to this problem cannot be found in the available selections since none of the answer possibilities match this value.
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Find the surface area of a cylinder with a base diameter of 8 feet and a height of 8 feet right your answer in terms of pi and be sure to include the correct unit
Answer:
96π cubic feet
Step-by-step explanation:
Surface area of a cylinder
A = 2πr(h+r)
where r = radius, h = height
Here
r = diameter/w = 8/2 = 4 feet
h = 8 feet
A = 2π · 4 (8 + 4)
= 8π (12)
= 96π cubic feet
Quantity of fuel uterlized by water tanker March 2022
The quantity of fuel utilized by the water tanker in March 2022 is 10,580 litres. The total amount of money that was utilized on fuel for the water tanker in March 2022 is R206,929.00.
To determine the quantity of fuel utilized by the water tanker in March 2022, we need to first calculate the total distance that the water tanker has covered in March 2022.
The total distance covered can be calculated using the formula:
distance = rate × time
From Annexure A, we can see that the water tanker was supplied to the construction site on the following dates in March 2022:
March 1, 2, 3, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 27, 28, 29, 30, and 31
Counting the number of days, we get a total of 23 days. Since the water tanker was supplied every day, we can assume that it covered the same distance every day.
The rate of fuel consumption of the Mercedes water tanker averages 5 km/l, which means that it can travel 5 km for every litre of fuel it consumes. Therefore, the distance covered by the water tanker on a full tank of fuel is:
distance = rate × fuel capacity
= 5 km/l × 460 litres
= 2300 km
So, the total distance covered by the water tanker in March 2022 is:
distance = 23 days × 2300 km/day
= 52,900 km
Next, we can determine the quantity of fuel utilized by the water tanker in March 2022 using the formula:
quantity of fuel = distance ÷ rate
Using the values we have calculated, we get:
quantity of fuel = 52,900 km ÷ 5 km/l
= 10,580 litres
Therefore, the quantity of fuel utilized by the water tanker in March 2022 is 10,580 litres.
To determine the total amount of money that was utilized on fuel for the water tanker in March 2022, we can multiply the quantity of fuel utilized by the fuel price in March 2022:
total cost = quantity of fuel × fuel price
From the problem statement, the fuel price in March 2022 was R19.55 per litre. Substituting the values we have calculated, we get:
total cost = 10,580 litres × R19.55/litre
= R206,929.00
Therefore, the total amount of money that was utilized on fuel for the water tanker in March 2022 is R206,929.00.
Complete question:
Records of the number of water tankers that were supplied to the construction site appear in the calendar on ANNEXURE A. The water tanker has a fuel capacity of 460 litres. The rate of fuel consumption of the Mercedes water tanker averages 5 km/l. The prices of fuel per litre in March and June 2022 appear below. MARCH 2022 FUEL PRICES DIESEL 50 ppm (a 4. 1) (b ) COST R19,55 JUNE 2022 FUEL PRICES DIESEL 50 ppm Source: COST R24,14 Calculate the total distance that the water tanker has covered in March 2022. Hence, determine the quantity of fuel that was utilized by the water tanker in March 2022. Determine the total amount of money that was utilized on fuel for the water tanker in March 2022. Quantity of fuel utilized by water tanker March 2022
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PLEASE HELP ME ASAP PLEASEEE
Answer:
Step-by-step explanation:
B and E
The most powerful volcanic eruption on earth in the last 10,000 years was approximately VEI 7.3 (Mt. Rinjani in Indonesia). The most powerful volcanic eruption in the last 100 years was the 1991 eruption of Mt. Pinatubo in the Philippines (I remember it very well). It was rated a 6.0. How much larger was the Mt. Rinjani eruption than the Mt. Pinatubo eruption?
This means that the Mt. Rinjani eruption was approximately 20 times larger and more powerful than the Mt. Pinatubo eruption.
What is exponent?An exponent is a mathematical operation that involves raising a base number to a certain power. The exponent tells how many times the base number should be multiplied by itself. For example, in the expression 2³, 2 is the base number and 3 is the exponent, and it means that 2 should be multiplied by itself three times: 2 x 2 x 2 = 8. Exponents are commonly used in algebra, calculus, and other branches of mathematics.
Here,
The Volcanic Explosivity Index (VEI) is a logarithmic scale used to measure the relative size and power of volcanic eruptions. Each increase of 1 on the VEI scale represents a tenfold increase in the eruption's size and power.
The difference in VEI between the Mt. Rinjani eruption and the Mt. Pinatubo eruption is 7.3 - 6.0 = 1.3.
To calculate the difference in size and power, we need to raise 10 to the power of 1.3:
10¹.³ = 19.95
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If a person walks 1 2 2 1 mile in each 1 4 4 1 hour, compute the unit rate in miles per hour.
The unit rate is 8.4 miles per hοur.
What dοes distance means?Distance and displacement are twο quantities that seem tο mean the same but are distinctly different with different meanings and definitiοns. Distance is the measure οf “hοw much grοund an οbject has cοvered during its mοtiοn” while displacement refers tο the measure οf “hοw far οut οf place is an οbject.”
Tο find the unit rate in miles per hοur, we need tο divide the distance by the time.
The distance is 1 2 2 1 miles and the time is 1 4 4 1 hοurs.
Sο, the unit rate in miles per hοur is:
(1 2 2 1 miles) / (1 4 4 1 hοurs) = 8.4 miles per hοur (rοunded tο οne decimal place)
Therefοre, the unit rate is 8.4 miles per hοur.
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Which points are solutions to the linear inequality y < 0. 5x +
2? Select three options.
The three points that are solutions to the linear inequality y < 0.5x + 2 are (-3, -2), (-1, -2), and (1, -2)
To check which points are solutions to the linear inequality y < 0.5x + 2, we can substitute the coordinates of each point into the inequality and check whether the inequality is true or false.
For the point (-3, -2):
y < 0.5x + 2
-2 < 0.5(-3) + 2
-2 < -0.5
This inequality is true, so (-3, -2) is a solution.
For the point (-2, 1):
y < 0.5x + 2
1 < 0.5(-2) + 2
1 < 1
This inequality is false, so (-2, 1) is not a solution.
For the point (-1, -2):
y < 0.5x + 2
-2 < 0.5(-1) + 2
-2 < 1.5
This inequality is true, so (-1, -2) is a solution.
For the point (-1, 2):
y < 0.5x + 2
2 < 0.5(-1) + 2
2 < 1.5
This inequality is false, so (-1, 2) is not a solution.
For the point (1, -2):
y < 0.5x + 2
-2 < 0.5(1) + 2
-2 < 2.5
This inequality is true, so (1, -2) is a solution.
Therefore, the three points that are solutions are (-3, -2), (-1, -2), and (1, -2).
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The given question is incomplete, the complete question is:
Which points are solutions to the linear inequality y < 0. 5x +2? Select three options. (-3,-2) (-2,1) (-1,-2) (-1, 2) (1,-2)
In a school, 220 students offer Biology or Mathematics or both. 125 offer biology and 110 Mathematics. How many offer Biology but not Mathematics?
The number of students are 110 students offer Biology but not Mathematics.
Let's use a Venn diagram to solve this problem. We know that 125 students offer Biology and 110 offer Mathematics, and we want to find out how many offer Biology but not Mathematics.
First, we can fill in the number of students who offer both Biology and Mathematics, which is the overlap between the two circles. We can do this by subtracting the total number of students who offer both from the total number of students who offer either:
220 (total) - (125 + 110) = 220 - 235 = -15
Wait a minute! A negative number of students doesn't make sense in this context. What this tells us is that there must be some double-counting going on - in other words, some students are being counted twice, once in each of the Biology and Mathematics categories.
To correct for this, we need to add back in the number of students who are counted twice, which is the overlap between the two circles. We can calculate this by adding the number of students who offer Biology and Mathematics together:
125 + 110 = 235
Now we can redo the calculation:
220 (total) - 235 (double-counted) = -15
This tells us that there are 15 students who are being counted twice. To find the number of students who offer Biology but not Mathematics, we need to subtract this number from the number of students who offer Biology:
125 - 15 = 110
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Answer: if im correct i think its 95
This question has two parts. First, answer Part A. Then, answer Part Part A SOFTWARE A software company releases two products: a home version of their photo editor, which costs $20, and a professional version, which costs $45. The company sells 1000 copies of the photo editing software, earning a total revenue of $38,075. Write and solve a system of equations to determine how many home versions and professional versions of the software the company sold. Let h = the number of home versions sold and D = the number of professional versions sold
A system of equations to determine the number of home versions and professional versions of the software the company sold is given by:
20h + 45p = 38,075
h + p = 1000
The number of home versions sold is 277 and the number of professional versions sold is 723.
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would assign variables to the number of home versions sold and the number of professional versions sold respectively, and then translate the word problem into a linear equation as follows:
Let the variable h represent the number of home versions sold.Let the variable p represent the number of professional versions sold.Since a home version of their photo editor cost $20, and a professional version, cost $45, a linear equation that models the situation is given by:
20h + 45p = 38,075
Additionally, the company sold 1000 copies of the photo editing software;
h + p = 1000
Solving the equations simultaneously, we have:
20h + 45(1000 - h) = 38,075
20h + 45,000 - 45h = 38,075
25h = 6,925
h = 277 home versions.
p = 1000 - h
p = 1000 - 277
p = 723 professional versions.
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6. if you replace one 75-watt incandescent light bulb with fluorescent light bulb that gives the same amount of light by drawing only 20 watts. you use the light bulb for an average of 4 hours a day. a. how many kwhs of energy would you save in one day? b. how many kwhs of energy would you save in one year? c. the cost of one kwh is $0.10. how much money does the fluorescent light bulb save in one year?
On replacing the incandescent light bulb with a fluorescent light bulb (a) the energy saved in one day is 0.22 kWh, (b) the energy saved in one year is 80.3 kWh. and (c) the cost savings in one year is $8.03.
a. The energy saved in one day by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:
Energy saved in one day = Energy consumed by incandescent bulb - Energy consumed by fluorescent bulb
Energy saved in one day = (75 watts x 4 hours) - (20 watts x 4 hours)
Energy saved in one day = 300 watt-hours - 80 watt-hours
Energy saved in one day = 220 watt-hours
To convert watt-hours to kilowatt-hours (kWh), we divide the watt-hours by 1000:
Energy saved in one day = 220 watt-hours / 1000
Energy saved in one day = 0.22 kWh
b. The energy saved in one year by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:
Energy saved in one year = Energy saved in one day x Number of days in one year
Energy saved in one year = 0.22 kWh/day x 365 days/year
Energy saved in one year = 80.3 kWh
c. The cost savings in one year by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:
Cost savings in one year = Energy saved in one year x Cost per kWh
Cost savings in one year = 80.3 kWh x $0.10/kWh
Cost savings in one year = $8.03
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