Total number of students = 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30
The probability that a student is female given that it is a junior is computed as follows:
[tex]\text{ P(}female|junior\text{)=}\frac{P(female\cap junior)}{P(junior)}[/tex]The probability that a student is female and junior is:
[tex]P(female\cap junior)=\frac{6}{30}=\frac{1}{5}[/tex]The probability that a student is a junior is:
[tex]P(junior)=\frac{2+6}{30}=\frac{8}{30}=\frac{4}{15}[/tex]Finally, The probability that a student is female given that it is a junior is:
[tex]P(female|junior)=\frac{\frac{1}{5}}{\frac{4}{15}}=\frac{1}{5}\cdot\frac{15}{4}=\frac{3}{4}=0.75\text{ or 75\%}[/tex]Complete both transformations below.
Then enter the final coordinates of the figure.
(1,-3)
A
C (2,-5)
B
(5,-1)
A" ([?], [])
B" ([ ], [])
C" ([],[])
1) Reflect across y - axis
2) <4.5>
Answer:
A''(3, 2), B''(-1, 4), C''(2, 0)
Step-by-step explanation:
For the first step, negate the y coordinate.
For the second step, add 4 to the x coordinate and 5 to the y coordinate.
[tex]A(1,-3) \longrightarrow A'(-1, -3) \longrightarrow A''(3, 2) \\ \\ B(5,-1) \longrightarrow B'(-5,-1) \longrightarrow B''(-1, 4) \\ \\ C(2, -5) \longrightarrow C'(-2, -5) \longrightarrow C''(2, 0)[/tex]
Problem 2: The area of a
rectangular desk is given
by the trinomial x²-7x-18.
What are the dimensions
of the desk? (10 points)
Answer: (x-9) and (x+2)
Step-by-step explanation:
You would first have to break the trinomial down into 2 factors.
Since there are two minuses in the trinomial, start off like this : (x- __) (x+__)
Now, what two numbers add to -7, and multiply to -18?
9 and 2, with one term being negative.
Since the 2nd term in the trinomial is a negative, there must be a number added that has a greater negative term than the other positive term, therefore, making 9 the negative term, since 2-9 is -7.
And -9 times 2 is -18.
Now fill in the blanks : (x-9)(x+2)
Since (x-9) and (x+2) are multiplied by each other, they are the dimensions of the desk, being L x W.
Now let's double check the factors:
(x-9)(x+2)
Distribute the terms.
x^2 +2x -9x -18
x^2-7x-18
There, hoped that helped :D
PLEASE HELP ITS DUE SOON! I DONT GET ANY OF THIS! HELP WOULD BE MUCH APPRECIATED! NEED THIS DONE BEEN STUCK ON THIS FOR WAY TO LONG!
YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!
So, we know BC is parallel to EF and 1 is congruent to 3.
Angles between parallel lines have special relationships. The relationships between 2 and 3 is that they are Same-side Interior Angles. This means that angles on the same line, formed by parallel lines intersecting that line (and the angles are on the same side of their respective line) are congruent. So, 2 and 3 are congruent... But by the transitive property, if 1 = 3 and 3 = 2... 1 = 2! And if 1 = 2, they are also Same-side interior angles and thus, the lines they lie on are parallel! So, since 1 and 2 are congruent, AB is parallel to DE.
Answer:
See below.
Step-by-step explanation:
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
[tex]\begin{array}{c|c}\sf Statement & \sf Reason\\\cline{1-2} BC \parallel EF & \phantom{\dfrac11}\sf Given\\\\\angle 2=\angle 3 & \textsf{Corresponding Angles Postulate}\\\\\angle 1=\angle 3 & \sf Given\\\\\angle 1=\angle 2 & \textsf{Transitive property of equality}\\&(\angle 2=\angle 3 \; \textsf{and} \; \angle 1=\angle 3)\\\\AB \parallel DE & \textsf{Corresponding Angles Postulate}\\& \textsf{as} \;\angle 1=\angle 2\end{array}[/tex]
As DE intersects the two parallel lines BC and EF, ∠2 is congruent to ∠3 (corresponding angles postulate).
As ∠1 = ∠3 and ∠2 = ∠3, then ∠1 = ∠2 (transitive property of equality).
Therefore, as ∠1 and ∠2 are congruent, AB and DE must be parallel (BC is the transversal).
Identify the correct box and whisker plot of the given data.
Given the data below.
[tex]\lbrace1,3,5,6,6,7,8,11,12\rbrace[/tex]The median of the data above is the middle number
[tex]median=6[/tex]The first quartile is:
[tex]\begin{gathered} 1,3,5,6 \\ Q1=\frac{3+5}{2}=\frac{8}{2}=4 \end{gathered}[/tex]The third quartile is:
[tex]\begin{gathered} 7,8,11,12 \\ Q3=\frac{8+11}{2}=\frac{19}{2}=9.5 \end{gathered}[/tex]The box and whisker plot for the data is:
The second option is correct.
dilate the triangle (2,3) , (-5,4) , (0,-12) with a scale factor of 2 centered from the origin
For us to be able to determine the new coordinates of the triangle after being dilated with a scale factor of 2 centered from the origin, multiply each x and y coordinate value by the scale factor of 2 to find the new coordinates.
We get,
A (2, 3) → A' (4, 6)
B (-5, 4) → B' (-10, 8)
C (0, -12) → C' (0, -24)
Let's now plot it in a graph,
A circle of radius r has area A, where A =xr^2
The area A of the circle whose radius is 10 can be calculated by given equation A =pi r^2 is 314.2 cm^2.
What is area?
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
If we draw a square using a pencil on a sheet of paper. It will have two dimensions. The area of a shape on paper is the area that it occupies and it will be called as area of that square.
For getting the area of the circle we need to put the value of r in the given equation:
r = 10 cm
Putting the value of pi and r in the equation:
A = pi r^2
A = 3.142 (10)^2
A = 3.142 (100)
A = 314.2
Therefor the area of the circle calculated by given equation is 314.2 cm.
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Complete question
A circle of radius r has area A, where A =pir^2, calculate the area of circle whose radius is 10 cm.
1. **Gabriella and Lisbet are selling bracelets and earrings to make money for their summer vacation. The bracelets will cost $2 and earrings will cost $3. They want to make at least $500 and would like to make less than 50 bracelets to make a profit. Graph the solution set to the system of linear inequalities in the coordinate plane below. Label your axes and create a scale. a. Is it possible for Gabriella and Lisbet to make a profit? Justify your answer using your graph above.
Answer:
It is possible for Gabriella and Lisbet to make a profit
Explanation:
Let's call x the number of bracelets that they will make and y the number of earrings that they will make.
If the bracelets will cost $2 and the earring will cost $3, they will make:
2x + 3y
Then, this quantity should be at least $500, so:
2x + 3y ≥ 500
Additionally, they would like to make less than 50 bracelets, so:
x < 50
So, the system of inequalities is:
2x + 3y ≥ 500
x < 50
Now, to graph the system, we need to identify the lines that separate the regions. So, for x < 50, we get that the line is x = 50, a vertical line that passes through the point (0, 50).
For 2x + 3y ≥ 500, we need to identify two points that belong to the line
2x + 3y = 500 as (250, 0) and (100, 100)
So, the graph of the inequalities is:
Therefore, the solution of the system is the yellow region. Since there is a region in the graph, Gabriella and Lisbet can make a profit.
Solve the following equation for a. Be sure to take into account whether a letter is
capitalized or not.
D = Ga +3h³ a
[tex]a=\frac{D}{G+3h^{3}}[/tex]
Looking at the equation, we can see that “a” is a part of both terms. Therefore, we can factor it out. Then we divide to get “a” by itself.
See details:
Simplify m8m−6. yehhhhhh
The value of [tex]m^{8} m^{-6}[/tex] after simplification is [tex]m^{2}[/tex].
According to the question,
We have the following expression:
[tex]m^{8} m^{-6}[/tex]
Now, please note that there are some rules for simplifying expressions with powers. For example, powers are added if the base of the terms in the multiplication are the same. And if the base of the terms are same but they are in division then the powers are subtracted.
In this case, the base is same (m) and the terms are in multiplication.
So, we are supposed to add their powers.
Now, we have the following expression:
[tex]m^{(8-6)}[/tex]
[tex]m^{2}[/tex]
Hence, the value after solving the given expression is [tex]m^{2}[/tex].
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Beginning with the graph of f(x) = x², what transformations are needed to form g(x) = –(x – 6)² + 3?
A) The graph of g(x) opens upward and is shifted to the right 6 units and up 3 units.
B) The graph of g(x) opens upward and is shifted to the left 6 units and up 3 units.
C) The graph of g(x) opens downward and is shifted to the right 6 and up 3 units.
D) The graph of g(x) opens downward and is shifted to the left 6 units and up 3 units.
Answer:
C) The graph of g(x) opens downward and is shifted to the right 6 and up 3 units.
Step-by-step explanation:
You want to know what transformations are needed to form g(x) = –(x – 6)² + 3 from f(x) = x².
TransformationsThe function transformations we are typically concerned with are ...
translation horizontally and verticallyscaling horizontally and verticallyreflection across vertical and horizontal linesEach of these has a recognizable influence on the function.
TranslationTranslation by 'h' units to the right and 'k' units up transforms the function to ...
g(x) = f(x -h) +k
ScalingExpanding a graph horizontally by a factor of p and vertically by a factor of q transforms the function to ...
g(x) = q·f(x/p)
ReflectionReflecting a graph horizontally across the y-axis replaces x with -x.
Reflecting a graph vertically across the x-axis replaces f(x) with -f(x).
Given graphComparing g(x) = -(x -6)² +3 to the original f(x) = x², we see that ...
(h, k) = (6, 3)f(x) was replaced by -f(x)This means the graph was shifted right 6 units and up 3 units. The graph was reflected across the x-axis, so the curve opens downward.
Option c, The graph of g(x) opens downward and is shifted to the right 6 and up 3 units. is the correct answer.
What is graph?
In the field of mathematics, a graph is a representation (visual) or diagram that shows the facts or values in an ordered and systematic way.
The relationships between two or more items are frequently represented by the points on a graph.
As given in the question,
[tex]f(x)=x^2[/tex] and [tex]g(x)= -(x-6)^2 + 3[/tex]
Since, [tex]f(x) = x^2[/tex] we are applying the following three rigid transformations on f(x) to obtain g(x):
Reflection around the x-axis in the graph: [tex]f'(x) = -x^2[/tex]Translation in the +x semi-axis in the graph: [tex]f''(x) = -(x-6)^2[/tex]Translation in the +y semi-axis in the graph: [tex]g(x) = -(x-6)^2+3[/tex]Therefore, The graph of g(x) opens downward and is shifted to the right 6 and up 3 units.
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what is 34.49 divided by 0.2 help!!! due friday
Answer:
17.245
Step-by-step explanation:
34.49 divided by 0.2 is 17.245
Which ordered pair is the y-intercept of y=x² + 6.0 – 4?(1,6)O (60)0 (0, -4)O (6,4)
The equation given is,
[tex]y=x^2+6x-4[/tex]The y-intercept is determined when x coordinate is zero.
Substitute x equals to 0 in the equation,
[tex]y=0^2+6(0)-4[/tex][tex]y=-4[/tex]Thus, the ordered pair of y-intercpet is,
[tex](0,-4)[/tex]The correct option is c.
A jar contains only pennies, nickels, dimes, and quarters. There are 24 pennies, 13 dimes, and 28 quarters. The rest of the coins are nickels. There are 91 coins in all. How many of the coins are not nickels? If n represents the number of nickels in the jar, what equation could you use to find n?
__ of the coins are not nickels.
Answer:"There are 24 pennies, 21 dimes, and 29 quarters", so there are 25+21+29 = 75 coins so far. This is the amount of coins that aren't nickels. The rest are nickels, which is some amount n. This adds to the 75 to get 75+n. Set this equal to 92 because there are 92 coins in all. That's how we end up with 75+n = 92.
-----
Extra info
The equation 75+n = 92 is the same as n+75 = 92. Subtract 75 from both sides to isolate n. You should get n = 17 after doing so.
Step-by-step explanation:
PLEASE HELP ME ANSWER THESE QUESTIONS !
1. How does radian measure of an angle compare to the degree measure? Include an explanation of 1 radian in your answer.
2. Explain how the cosine of an angle in the second quadrant differs from the cosine of its reference angle in the unit circle.
3. Describe the secant and cosecant functions.
4. When a right triangle with a hypotenuse of 1 is placed in the unit circle, which sides of the triangle correspond to the x- and y-coordinates?
Through the knowledge and trigonometry, we have :
1 radian = 180 degrees[tex]t^{'} = 180-t[/tex][tex]Secant \alpha = \frac{hypotenuse}{base}\\ Cosecant \alpha = \frac{hypotenuse}{perpendicular}[/tex]The x-coordinate is the central angle's adjacent side, while the y-coordinate is its opposite side.1. Since a circle's circumference is 360 degrees or two pi radians, a radian is equivalent to 180 degrees. Since radians require knowledge of higher mathematics and contain tangents, sines, and cosines, which are taught in college, they are not as frequently employed in measuring circles and angles as degrees.
2. The measurement of the lowest, positive, acute angle t created by the angle's terminal side is known as the reference angle, t the horizontal axis, too. As a result, positive reference angles can be used as models for angles in other quadrants because their terminal sides are in the first quadrant.
In the 1st Quadrant, All the trigonometric functions are positive,
[tex]t^{'} =t[/tex]
In the 2nd Quadrant. Only Sin is positive,
[tex]t^{'} = 180-t[/tex]
So, [tex]cost^{'} = Cos(180-t) = -Sint[/tex]
3. Secant is the Inverse of Cos and Cosecant is the Inverse of Sine, Hence they are :
[tex]Secant \alpha = \frac{hypotenuse}{base}\\ Cosecant \alpha = \frac{hypotenuse}{perpendicular}[/tex]
4. The x-coordinate is the central angle's adjacent side, while the y-coordinate is its opposite side.
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Find the value of 12.56 is multiplied by 8.8 and result is divided by 1.57.
Given:
12.56 is multiplied by 8.8 and the result is divided by 1.57.
To find the final result:
First, we multiply 12.56 by 8.8.
We get,
[tex]12.56\times8.8=110.528[/tex]Next, the result 110.528 is divided by 1.57.
So, we get
[tex]\frac{110.528}{1.57}=70.4[/tex]Hence, the answer is 70.4.
For #5 - 7, using the given scale factor and center, dilate the following figures and state the new coordinates.
Given: A scale factor of 1/2 and center N of a figure is given.
Required: To dilate the given figure using the given scale factor and center.
Explanation: Dilation is a transformation, used to change the size of the given figure. If the value of dilation>1 then the new figure enlarges. If dilation<1 then the given figure contracts while a dilation=1 means that the new figure is of the same size.
Now here the center is given to be N. And the scaling factor is 1/2.
The coordinates of center N are (3,2). Point M is 2 units left and 4 units down from point N. Hence for dilation of a factor of 1/2, point M' will be 1 unit to the left and 2 units down from point N -
[tex]\begin{gathered} M^{\prime}=(3-1,2-2) \\ M^{\prime}=(2,0) \end{gathered}[/tex]Similarly, point O is 2 units to the right and 6 units down from point N. Hence for dilation of a factor of 1/2, point O' will be 1 unit to the right and 3 units down from point N.
[tex]\begin{gathered} O^{\prime}=(3+1,2-3) \\ =(4,-1) \end{gathered}[/tex]Final Answer: M'=(2,0)
O'=(4,-1)
Kurt has pulled 15 marbles from a large bag, and 6 of them are brown. What is the experimental probability that the next marble selected from the bag will be brown? Simplify your answer and write it as a fraction or whole number. A. P(brown) = 1/5 B. P(brown) = 2/5 C. P(brown) = 1/2 D. P(brown) = 3/5
total marbles: 15
brown marbles: 6
Probability : brown marbles / total marbles = 6 /15 (simplify) = 2/5
Find the equation of the line whose slope is -3 and which passes through the point (5,-2).
Answer:
y = -3x + 13
Step-by-step explanation:
We can use the the point slope form of an equation for this:
y - y1 = m (x - x1)
Replace the y1, x1, and m variables with what we were given:
y - (-2) = -3 (x - 5)
Distribute
y + 2 = -3x + 15
Combine like terms
y = -3x + 13
convert 430 cm² to m²
Answer:
4.3
Step-by-step explanation:
A new model is to be built to serve the towns of Sunnyvale and Gloomington, who’s centers are 6 miles apart. The developers want to locate the mall not more than 3 miles from the center of Sunnyvale and also not more than 5 miles from the center of Gloomington. Drawl a simple map showing Sunnyvale, Gloomington, and all potential locations for the new mall, based on the given information. Be sure to show the scale of your map. Explain how you determine do the possible locations for the mall.
See explanation below
Explanation:
We are told the centres of the two towns are 6miles apart.
This means the distance between Sunnyvale and Gloomington = 6 miles.
We will draw a line with a distance of 6cm to indicate their distance apart.
The two end points of the line will indicate the location of Sunnyvale and Gloomington respectively.
For the developers to locate the mall not more than 3 miles from the center of Sunnyvale, we will draw a circle which has radius of 3cm. This way the mall doesn't exceed 3 miles from Sunnyvale.
For the developers to locate the mall not more than 5 miles from the center of Gloomington, we will draw a circle which has radius of 5cm. This way the mall doesn't exceed 5 miles from Gloomington.
The scale of the drawing will be 1cm represent 1 mile
You can use a compass(drawing tool) to draw the circles. adjusting the legs to suit the measurement of each radius.
The area under the each of the circles are all the possible locations of the map. The location of the new mall cannot go beyond the area under circles but can be within it.
A s’mores maker kit has a list price of $39.95 and is offered to wholesalers with a series discount of 20/10/10. The same appliance is offered to Kitchen Crafters (a retailer) with a series discount of 20/10. Find the difference in price.
Since the list price is $39.95
Since the series of discounts 20/10/10
Then we will find the new price by this way
Since the first discount is 20%, then
The new price will be 80% of 39.95
[tex]\frac{80}{100}\times39.95=31.96[/tex]Since the second discount is 10%
Then the new price is 90% of 31.96
[tex]\frac{90}{100}\times31.96=28.764[/tex]Since the third discount is 10%
Then the new price is 90% of 28.764
[tex]\frac{90}{100}\times28.764=25.8876[/tex]Since the second option has only a 20/10 discount, then
The new price is 28.764
To find the difference subtract 25.8876 from 28.764
The difference = 28.764 - 25.8876
The difference = 2.8764
The answer is $2.8764
can you help me find the derivatives of these questions please
(Number 5)
[tex]\frac{dy}{dx}=\text{ }x(2^x)\ln 2\text{ }+2^x[/tex]Explanations:The given equation is:
[tex]y=x(2^x)[/tex]This function represents the product of x and 2^x, therefore, to find the derivative, we will use the product rule.
When y = UV, dy/dx is given as:
[tex]\frac{dy}{dx}\text{ = U}\frac{dV}{dx}+V\frac{dU}{dx}[/tex]In the equation y = x (2^x):
[tex]\begin{gathered} U\text{ = x} \\ \frac{dU}{dx}=\text{ 1} \\ V=2^x \\ \frac{dV}{dx}=2^x\ln 2 \end{gathered}[/tex]Substituting the U, V, dU/dx, and dV/dx into the given formula for dy/dx:
[tex]\begin{gathered} \frac{dy}{dx}=x(2^x)\ln 2+2^x(1) \\ \frac{dy}{dx}=\text{ }x(2^x)\ln 2\text{ }+2^x \end{gathered}[/tex]triangle IJK with vertices I(-9-8),J(-5-6),and K(-7-3) is drawn on the coordinate grid below. what is the area in square units of triangle IJK
Here, we want to calculate the area of the given triangle
Mathematically, the product of the height and base of a triangle divided by 2 gives its area
Now, as we can see the shape, while IJ represents the base, KJ represents the height
We need to calculate the distance between these points before we can get the area of the triangle
To get the distances between the points, we have to use the distance formula
We can proceed with this as follows;
[tex]\begin{gathered} D\text{ = }\sqrt[]{(_{}x_2-x_1)^2+(y_2-y_1)^2} \\ \\ \text{For IJ} \\ (x_1,y_1)\text{ = (-9,-8)} \\ (x_2,y_2)\text{ = (-5,-6)} \\ |IJ|\text{ = }\sqrt[]{(-5+9)^2+(-6+8)^2} \\ |IJ|\text{ = }\sqrt[]{16\text{ + 4}} \\ |IJ|\text{ = }\sqrt[]{20} \\ \\ \text{For KJ} \\ (x_1,y_1)\text{ = (-7,-3)} \\ (x_2,y_2)\text{ = (-5,-6)} \\ |KJ|\text{ = }\sqrt[]{(-5+7)^2+(-6+3)^2} \\ |KJ|\text{ = }\sqrt[]{4+9} \\ |KJ|\text{ = }\sqrt[]{13} \end{gathered}[/tex]Thus, we have the area of the triangle as follows;
[tex]\begin{gathered} \text{Area = }\frac{1}{2}\times base\times height \\ \\ \text{Area = }\frac{1}{2}\times\sqrt[]{20}\times\sqrt[]{13\text{ }}=\frac{\sqrt[]{260}}{2}\text{ = }\frac{2\sqrt[]{65}}{2}\text{ = }\sqrt[]{65\text{ }}\text{ square units} \end{gathered}[/tex]When Andy Green broke the land speed record, his vehicle was traveling across a flat portion of the desert with a forward velocity of 341.11 m/s. How long would it take him at that velocity to travel 4.500 km?
Answer:
13.192 seconds
Step-by-step explanation:
You want to know the time to travel 4.500 km at a speed of 341.11 m/s.
Travel timeThe relation between time, speed, and distance is ...
time = distance/speed
time = (4500 m)/(341.11 m/s) ≈ 13.192 s
It would take Andy about 13.192 seconds to travel 4.500 km.
__
Additional comment
The distance of 4.500 km is rounded to the nearest meter, so may have an error of 0.5 meters. At 342.11 m/s, it takes about 1.47 ms to travel that distance. This suggests that timing to the nearest millisecond is consistent with the precision of the other numbers in the problem.
One could argue that speed is 5 significant figures, but distance is 4 significant figures. That suggests their ratio, time, is only accurate to 4 significant figures: 13.19 s. Analysis of the worst-case error in the ratio suggests that this reported value throws away some accuracy, so a better result is 13.192 s.
3 + 51 x 1/10 + 9 x 1/100
Answer:
5.49
Step-by-step explanation:
3+ 51= 54
54 x 1/10= 5.4 + 9 x 1/100
5.4 + 0.09=
5.49
5. Find the value of x for which ABCD must be a parallelogram.AB-9 - 6xX-30DC
Given:
We're a given figure ABCD
∠ADB = x - 30
∠DBC = -9 - 6x
To find:
The value of x for which ABCD must be a parallelogram.
Step-by-step solution:
For ABCD to be a parallelogram, Its Alternate angles (Z - angles) must be equal.
Thus,
∠ADB = ∠DBC
x - 30 = -9 - 6x
7x = 21
x = 3
Final answer:
For ABCD to be a parallelogram, The value of x should be equal to 3.
9 divided by 927. ……………………
depending on the question but it's most likely 103
Step-by-step explanation:
7x-3y=11 find ordered pairs
Answer:
[tex](0,-\frac{11}{3} ),(1,-\frac{4}{3} ),(2,1)[/tex]
Step-by-step explanation:
Given Equation:
[tex]7x-3y=11[/tex]Required:
Solve the equation for [tex]y[/tex].Find ordered pairs.Steps:
Subtract 7x from both sides of the equation.
-3y = 11 - 7x
Divide each term in -3y = 11 - 7x by -3 and simplify.
-3y/-3 = 11/-3 + -7x/-3
Simplify the left side.
Cancel the common factor of -3.
-3y/-3 (canceled) = 11/-3 + -7x/-3
Divide y by 1.
y = 11/-3 + -7x/-3
Simplify the right side.
Simplify each term.
Move the negative in front of the fraction.
y = -11/3 + -7x/-3
Dividing two negative values results in a positive value.
y = -11/3 + 7x/3
Choose any value for x that is in the domain to plug in to the equation.
Choose 0 to substitute in for x to find the ordered pair.
Remove parentheses.
y = -11/3 + 7(0)/3
Simplify -11/3 + 7(0)/3.
⇒ Combine the numerators over the common denominator.
y = -11/3 + 7(0) / 3
Simplify the expression.
Multiply 7 by 0.y = -11 + 0/3
Add -11 and 0.y = -11/3
Move the negative in front of the fraction.y = -11/3
Use the x and y values to form the ordered pair.
(0, -11/3)
Choose 1 to substitute in for x to find the ordered pair.
Remove parentheses.
y = -11/3 + 7(1)/3
Simplify -11/3 + 7(1)/3.
Combine the numerators over the common denominator.
y = -11/3 + 7(1)/3
Simplify the expression.
Multiply 7 by 1.
y = -11 + 7/3
Add -11 and 7.
y = -4/3
Move the negative in front of the fraction.
y = -4/3
Use the x and y values to form the ordered pair.
(1, -4/3)
Choose 2 to substitute in for the x in the ordered pair.
Remove parentheses.
y = -11/3 + 7(2)/3
Simplify -11/3 + 7(2)/3.
Combine the numerators over the common denominator.
y = -11/3 + 7(2)/3
Simplify the expression.
Multiply 7 by 2.
y = -11 + 14/3
Add -11 and 14.
y = 3/3
Divide 3 by 3,
y = 1
Use the x and y values to form the ordered pair.
(2, 1)
These are three possible solutions to the equation.
(0, -11/3), (1, -4/3), and (2,1)
Thanks,
Eddie
Solve the system. Check the solution.x + y = 8(x=y-3
Answer:
[tex]\begin{gathered} \text{Solution:} \\ (2.5,5.5) \end{gathered}[/tex]Step-by-step explanation:
Given the following system of equations:
[tex]\begin{gathered} x+y=8\text{ (1)} \\ x=y-3\text{ (2)} \end{gathered}[/tex]Since on equation 2, x is already isolated, substitute it into equation 1:
[tex]\begin{gathered} (y-3)+y=8 \\ \end{gathered}[/tex]Solve for y.
[tex]\begin{gathered} 2y=8+3 \\ y=\frac{11}{2}=5.5 \end{gathered}[/tex]Knowing the value of y, plug it into equation (2) and solve for x:
[tex]\begin{gathered} x=y-3 \\ x=5.5-3 \\ x=2.5 \end{gathered}[/tex]Determine whether the triangles are simllar. If they are, select thecorrect similarity statement and the theorem used.
Step 1
From the image;
[tex]Triangle\text{ ABE\textasciitilde Triangle ACD}[/tex][tex]\begin{gathered} Find\text{ the value of x to know if the sides are proportional} \\ \frac{12}{8}=\frac{6+x}{x} \\ 12x=48+8x \\ 4x=48 \\ x=\frac{48}{4}=12 \end{gathered}[/tex]Hence;
[tex]\begin{gathered} \frac{12+6}{12}=\frac{8+4}{8} \\ \frac{18}{12}=\frac{12}{8} \\ \frac{3}{2}=\frac{3}{2} \end{gathered}[/tex]The triangles also share similar angles therefore the answer will be;
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