SOLUTIONS
To solve for y in 2x – 17y = 13
[tex]2x-17y=13[/tex]Make y the subject of formular
[tex]\begin{gathered} 2x-17y=13 \\ 2x-13=17y \end{gathered}[/tex]divide both side by 17
[tex]\begin{gathered} \frac{2x-13}{17}=\frac{17y}{17} \\ y=\frac{2x-13}{17} \end{gathered}[/tex]Therefore the value of y is
[tex]y=\frac{2x-13}{17}[/tex]Find the slope through ( 0, 0) and ( -2, 4) by computing
ANSWER:
The slope is - 2
STEP-BY-STEP EXPLANATION:
We have the slope, we calculate it by means of the following formula
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]The points are (0,0) and (-2, 4), replacing:
[tex]m=\frac{4-0}{-2-0}=\frac{4}{-2}=-2[/tex]Describe how the given equation represent a transformation of the function f(x)
A function that transforms one function or graph into another, typically related function or graph is referred to as a function in mathematics.
For instance, when a quadratic graph is translated, the vertex and axis of symmetry are moved, but the parabola's general form remains the same.
What is the translational equation?
The translation equation or formula is written as g(x) = f(x+k) + C.
Replace "x" in a function with "x-h" to translate it horizontally.
The graph's left or right shift is determined by the value of the variable "h."
Since h = -4 in our example, the graph moves 4 units to the left.
Add 'k' to the end of a function to translate it vertically.
f(x+k) + C.
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solve for x: In(x+2)= -5
The given equation is:
ln (x + 2) = -5
Take the exponent of both sides
[tex]e^{\ln (x+2)\text{ }}=e^{-5}[/tex]The exponential cancels the ln on the Left Hand Side:
[tex]\text{x + 2 = e}^{-5}[/tex]Subtract 2 from both sides:
[tex]\begin{gathered} \text{x + 2 - 2 = e}^{-5}-2 \\ x=e^{-5}-2 \end{gathered}[/tex]Micheal Larry scored 18 points in a basketball game . Micheal scored twice as many points as Larry . How many points did Larry score ?
6 points
Explanations:Let the number of points scored by Michael be m
Let the number of points scored by Larry be l
Michael and Larry scored 18 points together
m + l = 18.........(1)
Michael scored twice as many points as Larry:
m = 2l..........(2)
Substitute equation (2) into equation (1)
2l + l = 18
3l = 18
l = 18/3
l = 6
Larry scored 6 points
For the diagram below, angles 4 and 6 would be referred to as _______ angles.Select one:a.supplementaryb.verticalc.alternate interiord.alternate exterior
Answer:
c. alternate interior
Explanation:
If a transversal line intersects two parallel lines, the angles formed on the interior are called the interior angles. For example, in the given diagram, angles 3, 4, 6, and 5 are interior angles.
Now the pair of angles that formed in the interior but on the opposite side of the transversal line are called alternate interior angles. For example, angels 4 and 6 are alternate interiors. angles 3 and 5 also alternate interior.
Therefore, choice C is the correct answer choice that describes angles 4 and 6.
Can you help me with number 13? Thank you I am having trouble with it.
In triangle ABC, a is the length of the side opposite to angle A (side BC), b is the length of the side opposite to angle B (side AC), and c is the length of the side opposite to angle C (side AB)
We can use the cosine rule to find the length of each side
[tex]\begin{gathered} a=\sqrt[]{b^2+c^2-2bc\cos A} \\ b=\sqrt[]{a^2+c^2-2ac\cos B} \\ c=\sqrt[]{a^2+b^2-2ab\cos C} \end{gathered}[/tex]From the given figure we can see triangle ABC, where We will use the cosine rule to find c
[tex]c=\sqrt[]{a^2+b^2-2ab\cos 90^{\circ}}[/tex]Since cos(90) = 0, then
[tex]\begin{gathered} c=\sqrt[]{a^2+b^2-2ab(0)} \\ c=\sqrt[]{a^2+b^2-0} \\ c=\sqrt[]{a^2+b^2} \end{gathered}[/tex]The expression equivalent to c is
[tex]\sqrt[]{a^2+b^2}[/tex]a radio disc jockey has 8 songs. on the upcoming playlist:2 rock songs3 reggae songs3 country songsthe disc jockey Randomly choose the 1st song to play, then Randomly choose the 2nd song from the remaining ones. what is the Probability that the 1st song is a Rock song? the 2nd song is a Country song?* write as fraction
Probabilities
We have the following elements to choose from:
Rock songs (R) = 2
Reggaes songs (G) = 3
Country songs (C) = 3
It's required to find two probabilities:
a) The first is a rock song
As stated above, there are R = 2 rocks songs and there are 8 songs in total, thus the probability of randomly picking a rock song is:
[tex]\begin{gathered} p(R)=\frac{2}{8} \\ \text{Simplify:} \\ p(R)=\frac{1}{4} \end{gathered}[/tex]b) The second song is a country song.
This is quite more complex to calculate. Let's assume the first song was not a Country song (NC). This has a probability of:
[tex]P(NC)=\frac{5}{8}[/tex]Since there are 5 non-country songs out of 8. For the second pick, we have all of the country songs unplayed out of 7, thus the probability of selecting it is:
[tex]P(C)=\frac{3}{7}[/tex]The probability of this 'brank' of events is:
[tex]P(NC,C)=\frac{5}{8}\cdot\frac{3}{7}=\frac{15}{56}[/tex]Now assume the first song was actually a country song. It has a probability of:
[tex]P(C)=\frac{3}{8}[/tex]For the second pick, we now have only 2 country songs out of 7, so the probability of selecting another country song is:
[tex]P(C)=\frac{2}{7}[/tex]The probability of this 'branch' of events is:
[tex]\begin{gathered} P(C,C)=\frac{3}{8}\cdot\frac{2}{7}=\frac{6}{56} \\ Simplify\colon \\ P(C,C)=\frac{3}{28} \end{gathered}[/tex]The total probability of selecting a country song as the second song is:
[tex]\begin{gathered} P(B)=\frac{15}{56}+\frac{3}{28} \\ P(B)=\frac{15}{56}+\frac{6}{56} \\ P(B)=\frac{21}{56} \\ P(B)=\frac{3}{8} \end{gathered}[/tex]Find the 20% trimmed mean of the following data. If necessary, round to one more decimal place than the largest number of decimal places given in the data.
Lengths of Longest 3-Point Kick for NCAA Division 1-A Football
29 30 35 37 38 40 40 43 44 45
47 48 49 49 50 53 55 55 58 59
Using the methodology of Trimmed Mean to the tune of 20%, the result derived is given as 45.5. See further explantion below.
What is Trimmed Mean?A truncated mean (another name for Trimmed Mean), like the mean and median, is a statistical measure of central tendency.
It entails calculating the mean after deleting specified sections of a probability distribution or sample at the high and low ends, often an equal proportion of both.
In the above instance, since the instruction is to trim 20% of 20 observations is 4.
Hence, 2 observations from the start and 2 from the rear will be removed. This leaves us with:
35 37 38 40 40 43 44 45 47 48 49 49 50 53 55 55. (Note that the observations must be arranged from low to high)
Hence the Trimmed Mean = (35 + 37 + 38 + 40 + 40 + 43 + 44 + 45 + 47 48 + 49 + 49 + 50 + 53 + 55 + 55)/ 16
= 728/16
=45.5
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Giving a test to a group of students, the grades and gender are summarized belowIf one student is chosen at random,Find the probability that the student was male OR got an "B".
ANSWER:
0.6875
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the probability that the gender is male and also the probability that the grade is B, separately, like this:
[tex]\begin{gathered} P(\text{male})=\frac{42}{80} \\ P(B)=\frac{19}{80} \end{gathered}[/tex]Therefore, since it is the probability that it is male OR got and "B", it is the union of both events, and it would look like this:
[tex]P(\text{male}\cup B)=P(male)+P(B)-P(male\cap B)[/tex]Now, the intersection of both events would be the probability that he is a man and gets a B, it would look like this:
[tex]P(male\cap B)=\frac{6}{80}[/tex]We replace to be able to calculate the union, like this:
[tex]\begin{gathered} P(\text{male}\cup B)=P(male)+P(B)-P(male\cap B) \\ P(\text{male}\cup B)=\frac{42}{80}+\frac{19}{80}-\frac{6}{80} \\ P(\text{male}\cup B)=\frac{55}{80}=\frac{11}{16}=0.6875 \end{gathered}[/tex]The probability that the student was male OR got an "B" is 0.6875
Find the Slope and the Y-Intercept of the line with the given equation
Answer: Slope is -4/5 and Y-int is 6
Step-by-step explanation: From the y=mx+b you can see the m is -4/5 and the b is 6. So in this case the slope would be -4/5 and y int would be 6
Please help! Functions and Relations. The function h(x) is a transformation of the square root function, f(x)= square root of x. What function is h(x)? Thanks!
In general, given a function g(x), a horizontal shift is given by the transformation below
[tex]\begin{gathered} g(x)\rightarrow g(x-a) \\ a>0\rightarrow\text{ a units to the right} \\ a<0\rightarrow\text{ a units to the left} \end{gathered}[/tex]Thus, in our case, notice that the graph of h(x) is that of f(x) shifted 1 unit to the left; then,
[tex]h(x)=\sqrt{x+1}[/tex]The answer is option C.find the image Matrix that represents the rotation of the polygon then graph the polygon and its image
SOLUTION
[tex]\text{The image matrix at 90}^o\text{ rotation is derived using the formula }[/tex][tex]\begin{gathered} \begin{bmatrix}{\cos \theta} & -\sin \theta & {} \\ \sin \theta & {\cos \theta} & {} \\ {} & {} & {}\end{bmatrix}\text{ where }\theta\text{ is 90}^{} \\ \text{This becomes the matrix of } \\ \begin{bmatrix}{0} & {-1} & {} \\ {} & {} & {} \\ {1} & {0} & {}\end{bmatrix}\text{ }\times\text{ }\begin{bmatrix}{2} & {4} & {6}{}{} \\ {2} & {5} & {1}\end{bmatrix}\text{ = }\begin{bmatrix}{0-2} & {0-5} & {0-1}{}{} \\ {2+0} & {4+0} & {6+0}\end{bmatrix}\text{ = } \\ \\ \begin{bmatrix}{-2} & {-5} & {-1}{}{} \\ {2} & {4} & {6}\end{bmatrix} \\ \\ \text{Therefore, the image matrix is }\begin{bmatrix}{-2} & {-5} & {-1}{}{} \\ {2} & {4} & {6}\end{bmatrix} \end{gathered}[/tex]The graph is shown below
When we MULTIPLY FRACTIONS, we blank the numerators, blank the denominators and blank if needed.
a. add b. keep c. multiply d. simplify
Answer:
When we multiply fractions, we multiply the numerators, multiply the denominators, and then simplify if needed.
angle Y is inscribed in the circle below. the measure of arc XZ is 205°
SOLUTION:
Case: Circle theorems
Method:
The angle subtended at the center by the arc XZ is twice the value at the circumference at Y
[tex]\begin{gathered} m\angle XOZ=2\times m\angle XYZ \\ 205=2\times Y \\ Y=\frac{205}{2} \\ Y=102.5\degree \end{gathered}[/tex]Final answer:
102.5 degrees
Please answer with if the slope is positive or negative and what the slope is.
The slope is positive ✨️
What ordered pairs do you get when you complete the table ?
for -1:
the equation will be:
[tex]y=3(-1)-1[/tex]and we symplyfy so:
[tex]y=-4[/tex]So the coordinate is:
[tex](-1,-4)[/tex]for 0:
the equation will be:
[tex]y=3(0)-1[/tex]so we simplify:
[tex]y=-1[/tex]so the coordinate is:
[tex](0,-1)[/tex]and for 1:
the equation will be:
[tex]y=3(1)-1[/tex]we simplify:
[tex]y=2[/tex]So the coordinate will be:
[tex](1,2)[/tex]So the answer is A)
A scale drawing for a restaurant is shown below. In the drawing, 2 I'm represents 3 m. Assuming the dinning hall is rectangular, find the area of the real dining hall
To solve this question, follow the steps below.
Step 01: Find the real measures of the dining hall.
The measure of the drawing is 2cm x 6cm.
Given: 2cm = 3m.
Then, 6cm = 2cm + 2cm + 2cm = 3m + 3m + 3m = 9m
The real measure of the dining hall is 3m x 9m.
Step 02: Find the area of the dining hall.
The dining hall is a rectangle and the area (A) of a rectangle is:
[tex]A=l*h[/tex]Where l and h are the sides of the rectangle.
Then, the area of the dining hall is:
[tex]\begin{gathered} A=3*9 \\ A=27m^2 \end{gathered}[/tex]Answer: The area of the dining hall is 27 m².
Finn, Michael, Luke, and Tommy are going to have a movie night this weekend. Together, they have 33 movies. If they decide to
randomly choose four movies, what is the probability that the four they choose will consist of each of their favorite movies?
Assume they have different favorites. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest
millionth
Answer:
1/982080 as a fraction
0.000001 when rounded to the nearest millionth
Step-by-step explanation:
Each time they pick a movie the odds change
the first pick is 1/33
the second is 1/32
the next is 1/31
the last is 1/30
multiply these fractions
If P = (-1, 0, 1, 2, 4} and Q = (4, 5, 6}, find Pu Q.O (-1, 0, 1, 2, 4, 5, 6}Of0 (4)O (-1, 0,1, 2, 4}
Statement Problem: If;
[tex]P=\mleft\lbrace-1,0,1,2,4\mright\rbrace,Q=\mleft\lbrace4,5,6\mright\rbrace[/tex]Find;
[tex]P\cup Q[/tex]Solution:
The union of two sets is a set containing all elements that are in the two sets.
The elements that make up a set can be any kind of mathematical objects: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
Thus, the union of set P and set Q is;
[tex]P\cup Q=\mleft\lbrace-1,0,1,2,4,5,6\mright\rbrace[/tex]
Consider the function f(x)=(x+4)(x+2). Dilate f(x) by x to create a new function of a higher degree.
f(x) = (x+4)(x+2).
f(x) = x² + 2x + 4x + 8
f(x) = x² + 6x + 8
Dilate by x:
x³ + 6x² + 8x
Given a line with slope = 5 and passing through ( 5 , 9 ) , which of the following is the correct point-slope equation of the line?
The point - slope equation of the line passing through the point (5,9) and having a slope of 5 is 5x - y = 16.
As per the question statement, we are supposed to find the point - slope equation of the line passing through the point (5,9) and having a slope equal to 5.
Before solving this, we need to know that point slope form of the equation is given as y - y1 = m (x - x1)
Where (x1, y1) are the points through which line is passing and "m" is the slope of the line.
Here x1 = 5 and y1 = 9 and m = 5
Substituting the values in the formula written above, we get
y- 9 = 5(x - 5)
y - 9 = 5x - 25
5x - y = 25 - 9
5x - y = 16
Hence the point - slope equation of the line passing through the point (5,9) and having a slope of 5 is 5x - y = 16.
Point slope form: The equation of a line in which we utilize any point which lies on the line and its slope to find the line's equation.Slope: This value indicates about the steepness of the line.To learn more about line and its characteristics, click on the link given below:
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The graph below shows the relationship between the number of hours and thenumber of miles jogged.Y161514131211109Miles8322356HoursBased on the information in the graph, what is the unit rate in miles per hour?How did u get the unit rate
Since the graph shows a proportional relationship, in order to find the unit rate in miles per hour, we just need to choose a point in the graph and divide the number of miles by the number of hours.
Looking at the graph, we can choose the point (2.5, 8), so we have:
[tex]\text{unit rate}=\frac{8\text{ miles}}{2.5\text{ hours}}=3.2\text{ miles/hour}[/tex]So the unit rate is 3.2 miles per hour.
What type of function is shown below? Y=5x
A. both proportional and non-proportional
B. non-proportional
C. neither proportional nor non-proportional
D. proportional
need Answer As Soon As Possible - ASAP
y is the midpoint of xz.x has coordinates (8,-10)and y has coordinates(-12,1)find the coordinates of z
Answer:(-32,12)
Step-by-step explanation:
Find the change in x and change in y from point x to point y. In this case it is -20 for x and +11 for y. Since the definition of a midpoint splits the line into 2 equal segments you can use the changes to calculate z. Use the midpoint coordinates and add the changes like this: (-12-20,1+11) and you will get (-32,12) for z.
1 month bet Rented 3 movies and 2 videos games for a total of $21 the next month she rented 8 movies and four game for a total of $49 find the rental cost for each movie and each video game
Let "m" represent the cost of one movie rent and "v" represent the cost of one videogame rent.
One month she rented 3 movies and 2 videogames for a total of $21, you can express the total cost for this month as:
[tex]3m+2v=21[/tex]Another month she rented 8 movies and 4 video games for a total of $49, you can express the rental costs for this month as follows:
[tex]8m+4v=49[/tex]These expressions form an equation system. To solve it, the first step is to write one of the equations in terms of one of the variables, for example, write the first equation for "v"
[tex]\begin{gathered} 3m+2v=21 \\ 3m-3m+2v=21-3m \\ 2v=21-3m \\ \frac{2v}{2}=\frac{21}{2}-\frac{3}{2}m \\ v=\frac{21}{2}-\frac{3}{2}m \end{gathered}[/tex]Next, replace the expression obtained for "v" into the second equation and solve for "m"
[tex]\begin{gathered} 8m+4v=49 \\ 8m+4(\frac{21}{2}-\frac{3}{2}m)=49 \end{gathered}[/tex]-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} 8m+4\cdot\frac{21}{2}-4\cdot\frac{3}{2}m=49 \\ 8m+42-6m=49 \end{gathered}[/tex]-Order the like terms together and simplify them:
[tex]\begin{gathered} 8m-6m+42=49 \\ 2m+42=49 \end{gathered}[/tex]-Pass 42 to the right side of the equation by applying the opposite operation to both sides of the equal sign:
[tex]\begin{gathered} 2m+42-42=49-42 \\ 2m=7 \end{gathered}[/tex]-Divide both sides by 2 to determine the value of m:
[tex]\begin{gathered} \frac{2m}{2}=\frac{7}{2} \\ m=\frac{7}{2}\approx3.5 \end{gathered}[/tex]-Replace the value obtained for "m" on the expression for "v" to determine the rental cost of one video game:
[tex]\begin{gathered} v=\frac{21}{2}-\frac{3}{2}m \\ v=\frac{21}{2}-\frac{3}{2}\cdot\frac{7}{2} \\ v=\frac{21}{2}-\frac{21}{4} \\ v=\frac{21}{4}\approx5.25 \end{gathered}[/tex]The rental cost for the movies is m=$3.50/movie and the rental cost for the videogames is v=$5.25/video game
A man has 32 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 545 cents, how many dimes does he have?
A dime is worth 10 cents and a quarter is worth 25 cents.
Let D be the number of dimes and Q be the number of quarters.
Since the total amount of coins in the pocket is 32, then:
[tex]D+Q=32[/tex]On the other hand, the total value of D dimes is 10D, while the total value of Q dimes is 25Q. Then, the total value of D dimes and Q cuarters is 10D+25Q, which must be equal to 545. Then:
[tex]10D+25Q=545[/tex]Notice that we have found a 2x2 system of equations:
[tex]\begin{gathered} D+Q=32 \\ 10D+25Q=545 \end{gathered}[/tex]Solve the system using the substitution method. To do so, isolate D from the first equation and replace the expression for D into the second equation to obtain a single equation in terms of Q:
[tex]\begin{gathered} D+Q=32 \\ \Rightarrow D=32-Q \\ \\ 10D+25Q=545 \\ \Rightarrow10(32-Q)+25Q=545 \\ \Rightarrow320-10Q+25Q=545 \\ \Rightarrow25Q-10Q=545-320 \\ \Rightarrow15Q=225 \\ \Rightarrow Q=\frac{225}{15} \\ \\ \therefore Q=15 \end{gathered}[/tex]Replace back Q=15 into the expression for D to find the amount of dimes:
[tex]\begin{gathered} D=32-Q \\ =32-15 \\ =17 \end{gathered}[/tex]Therefore, the amount of dimes that the man has is 17.
What principal would you need to invest at a rate of 4% to earn $500 in 6 months? Round your answer to the nearest cent.
From the information available, we have the following;
Rate = 4% (0.04)
Time = 0.5 (half a year/6 months)
Interest = 500
Principal = ???
Therefore, we would substitute these into the simple interest formula as shown below;
[tex]\begin{gathered} I=P\times R\times T \\ \text{Make P the ubject of the equation;} \\ \text{Divide both sides by R x T and you'll have;} \\ \frac{I}{R\times T}=\frac{P\times R\times T}{R\times T} \\ \frac{I}{R\times T}=P \\ \frac{500}{0.04\times0.5}=P \\ \frac{500}{0.02}=P \\ P=25000 \end{gathered}[/tex]ANSWER:
The principal to be invested therefore is $25,000
2. If sin B = 3/8, what is tan B?
SInce,
[tex]\begin{gathered} \sin B=\frac{opposite}{hypotenuse} \\ \text{opposite}=3 \\ \text{hypotenuse}=8 \end{gathered}[/tex]Therefore using Pythagoras theorem, we have,
[tex]x=\sqrt[]{8^2-3^2}=\sqrt[]{64-9}=\sqrt[]{55}[/tex]Therefore, tan B can be calculated as,
[tex]\tan \text{ B=}\frac{opposie}{adjacent}=\frac{3}{\sqrt[]{55}}[/tex]help mee pleasee!!
thank you <3
The equation would be y = 20.1x + 359 which represents an estimate of the number of individuals employed as medical assistants in the year.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
We have to determine the slope of the line :
⇒ m = (y₂ - y₁)/(x₂ -x₁ )
⇒ m = (560 - 359)/(10-0)
⇒ m = 20.1
This represents new assistants per year
So y-intercept of 359, your equation becomes
⇒ y = 20.1x + 359
Using the above equation, estimate the number of individuals employed as medical assistants in the year.
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Find the value of x that makes m II n [please help I really don't know what to do :') ]
