Find the intersection points when the line y = 12-4x meets the curve y =12-x^3. Hence, sketch in the same diagram, the line y = 12 - 4x and the curve y=12-x^3 Calculate the area of the region bounded by the curve and the line
Answers
The equations of the line and the curve are
[tex]\begin{gathered} y=12-4x \\ y=12-x^3 \end{gathered}[/tex]We will equate their right sides to find the values of x
[tex]12-4x=12-x^3[/tex]Subtract 12 from both sides
[tex]\begin{gathered} 12-12-4x=12-12-x^3 \\ -4x=-x^3 \end{gathered}[/tex]Divide both sides by -1
[tex]\begin{gathered} \frac{-4x}{-1}=\frac{-x^3}{-1} \\ 4x=x^3 \end{gathered}[/tex]Subtract 4x from both sides
[tex]\begin{gathered} 4x-4x=x^3-4x \\ 0=x^3-4x \end{gathered}[/tex]Switch the two sides
[tex]x^3-4x=0[/tex]Take x as a common factor
[tex]\begin{gathered} x(\frac{x^3}{x}-\frac{4x}{x})=0 \\ x(x^2-4)=0 \end{gathered}[/tex]Factor the bracket using the rule of the difference between two squares
[tex](a^2-b^2)=(a+b)(a-b)[/tex][tex]\begin{gathered} (x^2-4)=(x+2)(x-2) \\ x(x+2)(x-2)=0 \end{gathered}[/tex]Now, equate each factor by 0
[tex]\begin{gathered} x=0 \\ x+2=0,x-2=0 \\ x=-2,x=2 \end{gathered}[/tex]Substitute the values of x in the equation of the line to find their corresponding values of y
[tex]\begin{gathered} y=12-4(0)=12 \\ y=12-4(-2)=12+8=20 \\ y=12-4(2)=12-8=4 \end{gathered}[/tex]The points of intersection between the line and the curve are
(0, 12), (-2, 20), (2, 4)
Let us draw the graph
The red line represents the equation of the line
The blue curve represents the equation of the curve
To find the area bounded between the line and the curve we will use the integration
Since the line is above the curve at the point (-2, 20), then
We will subtract the curve from the line and use the values of x -2 and 2 as the limits of integration
[tex]A=\int_{-2}^2[(12-4x)-(12-x^3)]dx[/tex]Simplify the terms inside the brackets first.
[tex]\begin{gathered} A=\int_{-2}^2[12-4x+12+x^3]dx \\ A=\int_{-2}^2[-4x+x^3]dx \end{gathered}[/tex]In integration, we will add the power by 1 and divide the term by the new power
[tex]A=[\frac{-4x^{1+1}}{1+1}+\frac{x^{3+1}}{3+1}]_{-2}^2[/tex]Simplify it
[tex]\begin{gathered} A=[\frac{-4x^2}{2}+\frac{x^4}{4}]_{-2}^2 \\ A=[-2x^2+\frac{x^4}{4}]_{-2}^2 \end{gathered}[/tex]Substitute x by 2 and -2, then subtract the answer
[tex]A=[-2(2)^2+\frac{2^4}{4}]-[-2(-2)^2+\frac{(-2)^4}{4}][/tex]Solve each bracket
[tex]A=8[/tex]The area of the region bounded between the line and the curve is 8 square unit
Related Questions
Andre used 1/2 of a stick of butter to make multiple batches of brownies. The recipe calls 1/8 for of a stick of butter for each batch. How many batches did he make?
Please help!! Will give brainlest
Answers
1/8 + 1/8 + 1/8 + 1/8 = 4/8
4/8 = 1/2
Use a graph in a [-2π, 2π, π/2] by [-3, 3, 1] viewing rectangle to complete the identity
Answers
We have the expression:
[tex]\frac{1-2\cos 2x}{2\sin x-1}[/tex]Let's work first with the numerator. We have that we can write cos2x like this:
[tex]\cos 2x=1-\sin ^2x[/tex]doing this substitution we get the following:
[tex]\begin{gathered} 1-2\cos 2x=1-2\cdot(1-\sin ^2x)=1-2+4\sin ^2x=4\sin ^2x-1 \\ =(2\sin x+1)(2\sin x-1) \end{gathered}[/tex]Now that we have these two factors, we can use them on the original identity to get:
[tex]\frac{1-2\cos2x}{2\sin x-1}=\frac{(2\sin x+1)(2\sin x-1)}{2\sin x-1}=2\sin x+1[/tex]therefore, the resulting identity is 2sinx+1
Kayla's class went on a field trip to an aquarium. One tank had 30 clown fish. She miscounted the total number of clown fish in the tank and recorded it as 24 fish. What is Kayla's percent error?a 6%b 25%c 30%d 30%
Answers
Error = Value with error - Correct value
Error = 24-30 = -6
(Note tha the minus sign means the value is less than the correct value)
[tex]\text{ \%error = }\frac{\text{error}}{\text{True value}}\text{ x 100\%}[/tex][tex]=\frac{6}{30}\text{ x 100\% = 20\%}[/tex]help meeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
Answer: I think it is -5, but im not very sure srry
Step-by-step explanation:
The distance to Star A is about 8 × 10^4 light years. The distance to Star B is about 2 × 10^6 light years. Choose which star is farther away. Then fill in the blankwith a number written in standard notation.
Answers
Given:
[tex]\begin{gathered} \text{The distance of star A is 8}\times10^4\text{ light years} \\ \text{The distance of star B is 2}\times10^{6^{}}\text{ light years} \end{gathered}[/tex]To choose which start is farther away,
[tex]\begin{gathered} \text{Star B -Star A=}(2\times10^6)-(8\times10^4) \\ =10^4(2\times10^2-8) \\ =192\times10^4 \end{gathered}[/tex][tex]\text{Star B is 192}\times10^4\text{ light years times far away from star A.}[/tex]Please help See attached picture
Answers
Using the N scale trains are 1: 160
the width be of an N scale train track, in inches is 0.35 inchesThe Locomotive has a length of 5.7 inches in the modelA model boxcar has a length of 56 feetHow to determine dimensions using scale factorsInformation gotten from the question
N scale trains are 1: 160
The width of a standard railroad track is 4 Feet, 8 inches
A Locomotive has a length of 76 feet
A model boxcar has a length of 4.2 inches
width be of an N scale train track, in inches
4 feet 8 inches = 4 * 12 inches + 8 inches = 56 inches
1 foot = 160 feet is same as 12 inches = 12 * 160 inches = 1920 inches
12 inches = 1920 inches
? = 56 inches
? = 56 * 12 / 1920
? = 0.35 inches
A Locomotive has a length of 76 feet
76 feet = 912 inches
12 inches = 1920 inches
? = 912 inches
? = 5.7 inches
A model boxcar has a length of 4.2 inches
12 inches = 1920 inches
4.2 inches = ?
? = 4.2 * 1920 / 12
? = 672 inches
converting to feet
? = 672 inches * 12
? = 56 feet
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For the function, f(x) = -x + 4, find f(-2), f(-0.5) and f(3)
Answers
Given function is
[tex]f(x)=-x+4[/tex][tex]\begin{gathered} f(-2)=2+4=6 \\ f(-0.5)=0.5+4=4.5 \\ f(3)=-3+4=1 \end{gathered}[/tex]correct option is D 6, 4.5, 1.
An experimental blood test has been developed for lockjaw by the National Institute of HealthDue to the experimental nature of the test, it is not 100% accurateIn a trial of the blood test, the following probabilities were computed 51% of the participants in the trial have lockjaw the participants with lockjaw, 76% have a positive blood test the participants who do not have lockjaw, 84% have a negative blood test Round your answers to three decimals a ) What is the probability that a random participant will have a negative blood test ? b ) If a randomly selected participant has a positive blood test , what is the probabi that they do not have lockjaw ?
Answers
The probabilities in the context of this problem are given as follows:
a) Negative blood test: 0.543 = 54.3%.
b) Do not have lockjaw, given that the test is positive: 0.1682 = 16.82%.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which the parameters of the formula are described as follows:
P(B|A) is the probability of event B happening, given that event A happened.[tex]P(A \cap B)[/tex] is the probability of both events A and B happening.P(A) is the probability of event A happening.For item a, the percentages associated with negative blood tests are given as follows:
84% of 49% (do not have lockjaw).24% of 51% (have lockjaw).Hence the probability is:
p = 0.84 x 0.49 + 0.24 x 0.51 = 0.534 = 53.4%.
For item b, the probabilities associated with positive blood tests and not having lockjaw are given as follows:
0.466 = 46.6% positive.16% of 49% have positive tests and do not have lockjaw.Hence the conditional probability is:
P(B|A) = 0.49 x 0.16/0.466 = 0.1682 = 16.82%.
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Use the elimination method when solving the translated system Two angles are (complementary angles are angles whose sum is 90.) Their difference is 40. Find the angles. The larger angle is ? , and the smaller angle is ?.
Answers
Let's write the equation system first. We have two angles, let's call the, A and B, wich are complementary. This is:
[tex]A+B=90º[/tex]Also their difference is 40º:
[tex]A-B=40º[/tex]The system is;
[tex]\begin{cases}A+B=90º \\ A-B=40º\end{cases}[/tex]Now, if we add the two equations, since we have a "B" and a "-B", they will eliminate:
[tex]\begin{gathered} (A+B=90º)+(A-B=40º) \\ A+B+A-B=90º+40º \\ A+A+B-B=130º \\ 2A=130º \\ A=\frac{130º}{2}=65º \end{gathered}[/tex]The value of one of the angles is 65º. To find the other angle, we can go back to the first equation, A + B = 90º:
[tex]65º+B=90º[/tex]And solve:
[tex]B=90º-65º=25º[/tex]The larger angle is 65º and the smaller angle is 25º
Anton counted 36 dogs and cats at the animal shelter. He noticed that there are 18 fewer cats than dogs. If c= the number of cats and d= the number of dogs, then which system of equations represents the situation?
Answers
Answer: 2d + 18 = 36
Step-by-step explanation:
c = number of cats, d = number of dogs
1. d + c = 36 because there are 36 cats and dogs combined
2. c = d - 18 because there are 18 fewer cats than dogs
3. d + d - 18 = 36 because we inserted the equation of step 2 in the equation of step 1
4. 2d + 18 = 36 is the simplified equation of step 3
I need help writing a equation for a circleEnds of diameter: (1,-2) and (10,8)
Answers
The equation of the circle with the given end point is;
[tex](x-5.5)^2+(y-3)^2=\text{ }\frac{181}{4}[/tex]Here, we want to write the equation of a circle, given the end points of the circle
Given the end-points, we can use the formual for the distance to get the radius of the circle
We have this as follows;
[tex]\begin{gathered} D\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ \\ (x_1,y_1)\text{ = (1,-2)} \\ (x_2,y_2)\text{ = (10,8)} \\ D\text{ = }\sqrt[]{(10-1)^2+(8-(-2))^2} \\ D\text{ = }\sqrt[]{9^2+10^2} \\ D\text{ = }\sqrt[]{181} \end{gathered}[/tex]To get the radius of the circle, we have to divide the diameter by 2
We have this as;
[tex]r\text{ = }\frac{D}{2}\text{ = }\frac{\sqrt[]{181}}{2}[/tex]Now, the other thing needed to write the equation of the circle is the center of the circle
The center of the circle can be calculated by the use of the midpoint formula
[tex]\begin{gathered} (x,y)\text{ = (}\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}) \\ \\ (x,y)\text{ = (}\frac{1+10}{2},\frac{8-2}{2})\text{ = (5.5,3)} \end{gathered}[/tex]The general equation of the circle is;
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ (a,b)\text{ = (5.5,3)} \\ r\text{ = }\frac{\sqrt[]{181}}{2} \\ \\ (x-5.5)^2+(y-3)^2=\text{ }(\frac{\sqrt[]{181}}{2})^2 \\ \\ (x-5.5)^2+(y-3)^2=\text{ }\frac{181}{4} \end{gathered}[/tex]What's the equation of the tangent to [tex]y = x^2[/tex] at [tex]x = 2[/tex]?
Answers
Answer:
y=4x-4.
Step-by-step explanation:
1. the required equation of the tangent line has the form:
y=kx+i, where k=f'(x₀), i - interception;
2. if x₀=2, then y₀=2²=4;
3. f'(x)=2x, then f'(x₀)=2*2=4;
4. the required equation with unknown 'i' is y=4x+i;
it is possible to calculate unknown 'i' using coordinates (x₀;y₀):
5. 4=4*2+i, ⇒ i=-4;
6. finally, y=4x-4.
P.S. the suggested solution is not the shortest one.
A right triangle is formed by the x-axis, the y-axis, and the line y = -2x + 7.A. Sketch and label a graph of the triangle in the coordinate plane.B. Find the length of the hypotenuse.C. Find the area of the triangle.
Answers
The given equation is
[tex]y=-2x+7[/tex]We have to find the axis interceptions to graph this function.
For x = 0, we have
[tex]y=-2(0)+7=0+7=7[/tex]The y-interception is (0,7).
For y = 0, we have
[tex]\begin{gathered} 0=-2x+7 \\ 2x=7 \\ x=\frac{7}{2} \end{gathered}[/tex]The x-interception is (7/2, 0).
Now, we graph.
Where h is the hypothenuse.
To find the hypothenuse of the right triangle formed, we use the distance formula and both points.
[tex]d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]Replacing the coordinates, we have
[tex]\begin{gathered} d=\sqrt[]{(0-7)^2+(3.5-0)^2}=\sqrt[]{(-7)^2+(3.5)^2} \\ d=\sqrt[]{49+12.25}=\sqrt[]{61.25}\approx7.83 \end{gathered}[/tex]Therefore, the hypotenuse is 7.83 units long, approximately.
At last, the area of the triangle is found with the formula
[tex]A=\frac{1}{2}b\cdot h[/tex]Where b is the base and h is the height of the triangle. b = 3.5, h = 7.
Replacing these values, we have
[tex]A=\frac{1}{2}(3.5)\cdot(7)=\frac{24.5}{2}=12.25u^2[/tex]Therefore, the area of the triangle is 12.25 square units.
Use a suitable half-angle formula to find the exact value of cos(15°).
Answers
Remember that
[tex]\cos (\frac{x}{2})=\pm\sqrt[]{\frac{1_{}+\cos x}{2}}[/tex]For x=30 degrees
[tex]\cos (\frac{30^o}{2})=\cos (15^o)=\sqrt[]{\frac{1+\cos 30^o}{2}}[/tex]we know that
[tex]\cos 30^o=\frac{\sqrt[]{3}}{2}[/tex]substitute
[tex]\cos (15^o)=\sqrt[]{\frac{1+\frac{\sqrt[]{3}}{2}}{2}}[/tex][tex]\cos (15^o)=\sqrt[]{\frac{2+\sqrt[]{3}}{4}}[/tex][tex]\cos (15^o)=\frac{\sqrt[]{2+\sqrt[]{3}}}{2}[/tex]In a board game, students draw a number, do not replace it, and then draw asecond number. Determine the probability of each event occurring.
Answers
The probability P(choosing then an odd number, a 6) is 9 / 56
The figure of the board game is shown below.
From the question, we have
There are eight numbers on the board game.
Odd number total: (1, 9, 1) = 3
6 digits in total equal 3
Probability is "necessary outcome" divided by "all possible outcomes."
P = 3 / 8 (choosing an odd number).
without replacement
Board game numbers remaining: 8 - 1 = 7.
P(choosing a 6) = 3/7
Hence,
probability, P(choosing then an odd number, a 6) = 3/8 * 3/7 = 9 / 56
Probability:
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
Complete question: In a board game, students draw a number do not replace it, and then draw a second number. Determine the probability of each event occurring. Drawing an odd number then drawing a 6? dependent events.
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Estimate the total cost of the following items for your dorm room. Round the individual cost to the nearest ten dollars. Round your answer to the nearest dollar (no cents).
Answers
First, we need to round each individual item to the nearest ten dollars.
Loft bed $149.68 = $150.00
Beanbag chair $39.73 = $40.00
Storage cubes $19.85 = $20.00
Lava lamp $19.68 = $20.00
Now, we need to add up all the items to find the total cost.
Total cost = $150.00 + $40.00 + $20.00 + $20.00
Total cost = $230
Hence, the estimated total cost for the dorm room items is $230.
The unknown triangle ABC has angle A= 44º and sides a = 15 and c= 20. How many solutions are there for triangle?
Answers
Step 1: '
Find the sides and the angles.
Apply sine rule to find angle C
Step 2
[tex]\begin{gathered} \frac{a}{\sin A}\text{ = }\frac{c}{\sin C} \\ \frac{15}{\sin44}\text{ = }\frac{20}{\sin C} \\ \frac{15}{0.695}\text{ = }\frac{20}{\sin C} \\ \sin C\text{ = }\frac{20\times0.695}{15} \\ s\text{inC = 0.92666666} \\ C=sin^{-1}(0.9266666667) \\ C\text{ = 68} \end{gathered}[/tex]Step 3
44 +
Step 4
Find side b
[tex]\begin{gathered} \frac{a}{\sin A}\text{ = }\frac{b}{\sin B} \\ \frac{15}{\sin44}\text{ = }\frac{b}{\sin 68} \\ \frac{15}{0.695}\text{ = }\frac{b}{0.927} \\ b\text{ = }\frac{15\times0.927}{0.695} \\ b\text{ = 20} \end{gathered}[/tex]Final answer
Since angle C = angle B, the length of the sides must also be equal.
Hence,
0 triangle
In this diagram, point P is the orthocenter of AABC.How is the orthocenter of atriangle found?
Answers
SOLUTION
Recall the definition of orthocenter of a triangle
The orthocenter of a triangle is the point where the perpendicular drawn from the vertices to the opposite sides of the triangle intersect each other.
Therefore from the options the right answer is:
By drawing a line from each vertex that is perpendicular to the opposite sides.
PUNTOS POSIBLE A parking meter that is 1.6 meters (m) tall casts a shadow 3.6 m long. At the same time, a tree casts a shadow 9 m long. 1.6 m 3.6 m 9 m What is the height of the tree?
Answers
Answer:
4 meters
Explanation:
The triangle formed by the parking meter and its shadow is similar to the triangle formed by the tree and its shadow. So, the ratio of the height of the object and its shadow is constant and we can write the following equation:
[tex]\frac{Tree}{\text{Shadow Tre}e}=\frac{\text{ Parking meter}}{Shadow\text{ Parking meter}}[/tex]So, replacing the values, we get:
[tex]\frac{Tree}{9\text{ m}}=\frac{1.6\text{ m}}{3.6\text{ m}}[/tex]Solving for the height of the tree, we get:
[tex]\begin{gathered} \frac{Tree}{9\text{ m}}\times9m=\frac{1.6\text{ m}}{3.6\text{ m}}\times9m \\ \text{Tree = 4 m} \end{gathered}[/tex]Therefore, the height of the tree is 4 meters.
The shape below is made of two rectangles joined together.
9 cm
5 cm
8 cm
5 cm
Find the total area of the shape.
Optional working
Answers
Answer:
a=7, b=3
Step-by-step explanation:
Subtracting, we get the area of QRXY is 63 cm².
Using the area formula of a rectangle, we get 9a=63, and thus a=7.
Using the area formula again on triangle PXYS, 7b=21, and thus b=3.
The value of side 'a' is 7cm and side b is 3 cm.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
It is given that the area of PQRS is 84 square cm and the area of PSYX is 21 square cm.
The area of QRXY is calculated as,
Area QRXY = 84 - 21
Area QRXY = 63 square cm
The side a will be calculated as,
a x 9 = 63
a = 63 / 9
a = 7 cm
The side of b will be,
b x 7 = 21
b = 21 / 7
b = 3 cm
Therefore, the value of side 'a' is 7cm and side b is 3 cm.
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What number is best to use to simplify a fraction Least common multiple be least common denominator see greatest common factor de greatest
Answers
The greatest common factor and least common multiple are the best used to simplify a fraction.
Suppose we wanted to add the fractions:
10/12 and 20/15.
Now, consider the fraction:
10/12
We can eliminate that component from both the numerator and the denominator and simplify the fraction if we can identify the greatest common factor between 10 and 12.
So,
The factors of 10 are 1, 2, 5, 10.
The factors of 12 are 1, 2, 3, 4, 6, 12.
Therefore, GCF of 10 and 12 is 2.
Hence,
10/12 = ( 10 ÷ 2 ) / ( 12 ÷ 2 ) = 5/6
Similarly,
For 20/15,
The factors of 20 are 1, 2, 4, 5, 10, 20.
The factors of 15 are 1, 3, 5, 15.
The greatest common factor is 5.
So,
20/15 = ( 20 ÷ 5 ) / ( 15 ÷ 5 ) = 4/3
Now, when we add the fractions:
10/12 + 20/15 = 5/6 + 4/3
Now, as the fractions are already simplified.
By using the least common multiple.
10/12 + 20/15 = 5/6 + ( 4/3 ) × ( 2/2 )
10/12 + 20/15 = 5/6 + 8/6
10/12 + 20/15 = 13/6
Hence, using the greatest common factor we can simplify the fractions, and the least common multiple we can perform operations on the fractions.
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Graph f(x)=-2x + 4. What is x when f(x)=-8? Complete the explanation on how you found x.
Answers
f(x) = - 2x + 4
To find the value of x at f(x) = -8
Substitute f(x) in the equation above by -8
-8 = -2x + 4
Subtract 4 from both sides to move 4 from the right side to the left side
-8 - 4 = -2x + 4 - 4
-12 = -2x
Divide both sides by -2 to find x
[tex]-\frac{12}{-2}=-\frac{2x}{-2}[/tex]6 = x
The value of x at f(x) = -8 is 6
The first point x = 0
f(0) = -2(0) + 4
f(0) = 0 + 4
f(0) = 4
The point is (0, 4)
The second point y = 0
f(x) = 0
0 = -2x + 4
Add 2x to both sides
0 + 2x = -2x + 2x + 4
2x = 4
Divide both sides by 2
x = 2
The point is (2, 0)
at y = -8 x = 6
Convert 7935 ml into litres
Answers
Answer:
7.935L
Step-by-step explanation:
1L=1000ml
7935/1000=7.935
Answer:
Step-by-step explanation:
1000 ml = 1 litre
7000 ml = 7 litres
935 ml = 0.935 litres
7935 ml = 7.935 litres
Hope this helped
Find the PERIMETER of a square with sides 6 yards long. ANS.P = _______,
Answers
The given dimension of the square is 6 yards.
The perimeter of the square is express as : 4 x side
Perimeter of the square with the side 6 yards = 4 x 6
Perimeter of square = 24 yards
Answer. The perimeter of the square = 24yards
The graph shown is the graph of which function?A. f(x)=tan xB. f(x)= sec xC. f(x)= csc xD. f(x)=cot x
Answers
The graph shown in the graph of f(x) = cot x. (Option D)
75 - (5+2 (5) +7(8) +1)
Answers
Answer:
3
Step-by-step explanation:
75 - (5 + 10 + 56 + 1)
75 - (15 + 56 + 1)
75 - (71 + 1)
75 - 1 x 72
75 - 72
3
Find the coordinates of the vertices of each
figure after the given
transformation.
reflection across y = -1
Answers
The x-components of the vertices are all that need to be taken into consideration for reflection along a vertical axis (x = -1).
How can coordinates be determined after reflection?The x-coordinates and y-coordinates move when a point is reflected across the line y = x. The line y = x reflects the point (x, y), and the reflection is (y, x).
The new value of x for any point (x, y) would be the angle 'd' with respect to the reflection axis (x -(-1)), then inverted for reflection around the reflection axis x = -1. x’ = -1 -d… where x = -1 -(x + 1) = -x -2 and d = (x - (-1)) = (x + 1)
For instance, if a = (1, 3), a' = (-1, -2, 3) = (-3, 3).
If you have a triangle with some vertices on one side and some on the other, straddling the axis, this reflection will still hold true for vertices on either side of the reflection axis.
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A park has 39 visitors on Friday. The number of visitors on Saturday is 5 times that plus 12. Part A. Write an expression you could use to find the number of visitors to the park on Saturday.Part B. How many visitors were at the Park on Friday and Saturday.
Answers
Okay, here we have this:
Considering the provided information, we are going to wirte the requested expression, so we obtain the following:
[tex]SaturdayVisitors=FridayVisitors*5+12[/tex]Then replacing with the given information:
[tex]\begin{gathered} SaturdayVisitors=39*5+12 \\ SaturdayVisitors=195+12 \\ SaturdayVisitors=207 \end{gathered}[/tex]Finally we obtain that the park has 39 visitors in friday, and 207 on saturday.
Please help me dont have much time
Answers
Answer:
+, +, -4, 5, -20
Step-by-step explanation:
hope this helps
The maximum grade allowed between two stations in a rapid transit rail system is 3.6% between station A and station , which are 300 feet apart, the tracks rise 7ft. What is the grade of the tracks between these stations? round the answer to the nearest tenth of a percent. Does this grade meet the rapid-transit rail standards
Answers
To determine the grade we first need to find the slope of the track, the slope is given by:
[tex]slope=\frac{rise}{run}[/tex]In this case, we know that the track rise 7 ft in a 300 ft run, then we have:
[tex]slope=\frac{7}{300}=0.023[/tex]Now that we know the slope we just multiply it by 100 to find the grade:
[tex]\begin{gathered} grade=100*(0.023) \\ grade=2.3 \end{gathered}[/tex]Hence the grade of the track is 2.3% and since this is less than 3.6% we conclude that this track meets the rapid-transit rail standards
