We must solve the following system of equation:
[tex]\begin{gathered} x=y-8 \\ -x-y=0 \end{gathered}[/tex]Solving by elimination method.
If we add the first equation wih the second one, we obtain
[tex]x-x-y=y-8+0[/tex]which is equal to
[tex]-y=y-8[/tex]If we move y to the left hand side, we have
[tex]\begin{gathered} -y-y=-8 \\ \\ \end{gathered}[/tex]and it reads
[tex]\begin{gathered} -2y=-8 \\ y=\frac{-8}{-2} \\ y=4 \end{gathered}[/tex]We obtained the first result y=4. Now, we can substitute this value into one of the two equation. If we substitute y=4 in the first equation, we have
[tex]x=4-8[/tex]which gives x=-4. Finally, the answer is x=-4 and y=4. The coordinate of this solution is (-4,4).
find the slope from the points (5,-1)and (8,-6)
In order to find the slope of the a line that connects the given points, use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are the given points.
Replace the following coordinates in the formula for m:
(x1,y1) = (5,-1)
(x2,y2) = (8,-6)
[tex]m=\frac{-6-(-1)}{8-5}=\frac{-6+1}{3}=\frac{-5}{3}=-\frac{5}{3}[/tex]
Hence, the slope is -5/3
Choose and solve an equation for thefollowing real-world context: CoachMilewski divided a class into four teamswith 7 students per team. How manystudents are in the class?
Let n be the number of student in the class. Since there are 4 teams with 7 students per team, we can write this statements as
[tex]\frac{n}{4}=7[/tex]then, by moving 4 to the right hand side, we have
[tex]n=7\times4[/tex]then, the total number of students is n=
how to solve this problem, find the variance. Round your answer to one decimal place. Previous answer: mean = 5.8.
To calculate the variance in this case, we need to use the variance for a discrete variable and its probability.
The equation we need to use in this case is:
[tex]\sigma=\sum ^{}_i(x_i-\mu)^2P(x_i)[/tex]Where x_i is each value in the first row and P(x_i) is each value in the second row.
First, let's calculate each square difference:
[tex]\begin{gathered} (4-5.8)^2=(-1.8)^2=3.24 \\ (5-5.8)^2=(-0.8)^2=0.64 \\ (6-5.8)^2=(0.2)^2=0.04 \\ (7-5.8)^2=(1.2)^2=1.44 \\ (8-5.8)^2=(2.2)^2=4.84 \end{gathered}[/tex]Now, we need to multiply each for its corresponding P(x):
[tex]\begin{gathered} 3.24\cdot0.3=0.972 \\ 0.64\cdot0.2=0.128 \\ 0.04\cdot0.1=0.004 \\ 1.44\cdot0.2=0.288 \\ 4.84\cdot0.2=0.968 \end{gathered}[/tex]Finally, we sum them all to get the variance:
[tex]\sigma=\sum ^{}_i(x_i-\mu)^2P(x_i)=0.972+0.128+0.004+0.288+0.968=2.360\approx2.4[/tex]So, the variance to one decimal place is 2.4.
Enter the coordinates of the vertices of (Ry-axis) r (90°, 0)(QRST).i
To find the coordinates of the vertices reflected through the y-axis, we just have to use the reflection rule:
P(x,y)=P'(-x, y)
So,
Q'(-1, 3)
R'(-3, -3)
S'(0, -2)
T'(2, 1)
Can you help graph abs give the domain and range
SOLUTION
We want to draw the graph of
[tex]g(x)=-2^x-1_{}[/tex]The graph is shown below
Domain of the function.
The domain is determined from the x-axis. The function is defined for all values of x, hence the domain is negative infinity to positive infinity.
The domain in interval notation is
[tex]\mleft(-\infty\: ,\: \infty\: \mright)[/tex]The Range of the funtion.
The range is determined from the y-axis. Looking at the graph, the graph has a horizontal asymptote drawn at y = - 1, and the y-values run below and does not exceed this -1, telling us it is between negative 1 and negative infinity.
Hence the range in interval notation is
[tex]\mleft(-\infty\: ,\: -1\mright)[/tex]c. The percentage of hippos born weighing 25 pounds or less is(Round to one decimal place as needed.)
Given data:
Mean: 84 lb
Standard deviation: 12lb
Find % of hippos born weighing 25 poind or less.
1. Find the z-score corresponding to x=25:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ z=\frac{25-84}{12} \\ \\ z=-\frac{59}{12} \\ \\ z=-4.92 \end{gathered}[/tex]2. Use a z-table to find the probability of x less or equal to 25 (z-score -4.92):
For a z-score of -3.50 or less the corresponding value is 0.0001
[tex]P(x\leq25)=0.0001[/tex]3. Multiply by 100 the value you get in step 2 to get the percentage:
[tex]0.0001*100=0.01[/tex]Then, the percentaje of hippos born weighing 25 poind or less is 0.01%One month Reuben rented 5 movies and 2 video games for a total of $23. The next month he rented 3 movies and 8 video games for a total of $58. Find the rental cost for each movie and each video game.
Rental cost of each movie = $2
Rental cost of each video game = $6.5
Explanations:Let the rental cost of each movie be "x"
Let the rental cost of each video game be "y"
If in one month Reuben rented 5 movies and 2 video games for a total of $23, this can be expressed as:
5x + 2y = 23 .............................. 1
If in the next month he rented 3 movies and 8 video games for a total of $58, then;
3x + 8y = 58 ............................... 2
Solve the equations simultaneously using the elimination method
5x + 2y = 23 .............................. 1 * 4
3x + 8y = 58 ............................... 2 * 1
Multiply equation 1 by 4 and equation 2 by 1 to have;
20x + 8y = 92 .............................. 3
3x + 8y = 58 ............................... 4
Subtract equation 3 from 4
20x - 3x = 92 - 58
17x = 34
x = 34/17
x = 2
Substitute x = 2 into equation 1 to get the value of "y"
Recall that 5x + 2y = 23
5(2) + 2y = 23
10 + 2y = 23
2y = 23 - 10
2y = 13
y = 13/2
y = 6.5
This shows that the rental cost of each movie is $2 and the rental cost of each video game is $6.5
In the following long division problem most of the steps have been completed but fill in each blanks so that the resulting statement is true
Computing the last difference, we have:
Tin the last step, we have the difference:
[tex](-22x+4)-(-22x-55)=-22x+4+22x+55=59.[/tex]Answer
From the picture above, we see that:
• mark obtains ,59,,
,• the quotient is ,3x - 11,,
,• and the remainder is ,59,,
,• the answer to this long division is ,3x - 11 + 59/(2x+5)
Determine the equation of the line with y intercept at (0,-4) and a slip of - 1/4.
We need to determine the equation of the line that passes through (0, -4) and has a slope of -1/4. For that we will first use the slope-point form, and then isolate the y-variable on the left side to determine the slope-intercept form. The two forms are shown below:
[tex]\begin{gathered} y-y_1=m\cdot(x-x_1) \\ y=m\cdot x+b \end{gathered}[/tex]Since we have the value of the slope, and a point we can determine the first equation.
[tex]\begin{gathered} y-(-4)=-\frac{1}{4}\cdot(x-0) \\ y+4=-\frac{1}{4}x \\ \end{gathered}[/tex]Now we need to isolate the y-variable on the left side.
[tex]y=-\frac{1}{4}x-4[/tex]I need help with my math
Answer:
(-4,3)
Explanation:
The equation of a line in slope-intercept form is given by
[tex]y-y_0=m(x-x_0)_{}[/tex]where (x0,y0) is a point on the line,
Now in our case, we have the equation
[tex]y-3=2(x-(-4)_{})_{}[/tex]meaning
x0 = -4 and y0 = 3; therefore (x0,y0) = (-4, 3) is a point that lies on the line.
Hence, the first option is correct.
1/4, 2/4, 3/4, 4/4, describe the pattern, write the next term, and write a rule for the nth term of the sequence.
Arithmetic Sequence
In an arithmetic sequence, each term can be obtained as the sum of the previous term plus a fixed number, called the common difference.
To find if this is an arithmetic sequence, we subtract every consecutive term. If the result is constant, we have a common difference.
Let's subtract the second term minus the first term:
d = 2/4 - 1/4 = 1/4
Let's subtract the third term minus the second term:
d = 3/4 - 2/4 = 1/4
Let's subtract the fourth term minus the third term:
d = 4/4 - 3/4 = 1/4
Now we are sure this is an arithmetic sequence. The formula for the nth term of an arithmetic sequence is:
an = a1 + (n-1) d
Substituting:
[tex]a_n=\frac{1}{4}+(n-1)\cdot\frac{1}{4}=\frac{1}{4}+\frac{n}{4}-\frac{1}{4}=\frac{n}{4}[/tex]Thus, the general term is
an = n/4
To calculate the next term, we set n=5:
a5 = 5/4
Summarizing:
Rule: an = n/4
Next term: 5/4
Which is true about the functional relationship shown in the graph?Cost of Apples
ANSWER
The cost of apples is a function of their weight.
EXPLANATION
On the cartesian plane, the horizontal axis is the x-axis and the vertical axis is the y-axis.
The values on the y-axis are the values of the dependent variable while the values on the x-axis are the values of the independent variable.
This implies that, generally, for a function, y is a function of x.
Therefore, the cost of apples is a function of their weight.
Makong bought a new baseball glove for $32.00. He received a discount of 20% off the original price. Which Fraction, or decimal is equivalent to 20%? A 2/5B 1/20C 0.2D 2.0???
The discount is 20%.
20% means 20 out of 100
This can be written as
[tex]\text{ }\frac{20}{100}\text{ = }\frac{1}{5}\text{ = 0.2}[/tex]The correct answer is 0.2. Option C is the correct option
Graph the line that represents this equations cloron a tool to begin drawing Undo Select Reset | Point Line A 10 TO
We have that the graph is
The important points are:
6543-64 3-22507Find the slope of the line.Slope = m =Enter your answer as an integer or as a reduced fraction in the form A/B.
The slope equation is given by:
[tex]m=\frac{y_2-y_1}{x_{_2}-x_1}[/tex]To get the slope of the graph, we will pick two points along the line:
Let's pick the first point at (x, y) = (-6, 6)
Let's pick the second point at (x, y) = (0, -2)
We plug this into the slope equation, we have:
[tex]\begin{gathered} m=\frac{-2-6}{0--6}=-\frac{8}{6} \\ m=-\frac{4}{3} \end{gathered}[/tex]The slope (m) = -4/3
Where do they go because it doesn’t make no sense
Solution:
Alternate exterior angles
When two lines are crossed by another line (called the Transversal): Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.
The image below shows the description of alternate exterior angles
Corresponding angles
In geometry, corresponding angles are formed where a line known as an intersecting transversal, crosses through a pair of straight lines. Corresponding angles are the pairs of angles that are found in the same relative position on different intersections.
The image below shows the relationship between corresponding angles
Hence,
With this illustration, we have the final answers to be
[tex]\begin{gathered} \angle6\text{ and }\angle8\text{ (corresponding)} \\ \angle4\text{ and }\angle5(alternate\text{ exterior)} \\ \angle1\text{ and}\angle3\text{ (corresponding)} \\ \angle1\text{ and }\angle8\text{ (alternate exterior)} \end{gathered}[/tex]The point A(-6, 8) has been transformed using the compositionr(90, O) counter clockwise • Rx-axis . Where is A'?O (8,6)O (8,-6)O (-8,6)O (6,8)
The first step is to rotate point A(- 6, 8) 90 degrees counterclockwise. If a point, (x, y) is rotated 90 degrees counterclockwise, the new coordinate woule be (- y, x)
For point A, x = - 6, y = 8
Rotating point A 90 degrees counterclockwise, the new coordinate is
(- 8, - 6)
The next step is to reflect this point across the x axis. If a point is reflected across the x axis, the sign of the x coordinate remains the same while the sign of the y coordinate reverses. Thus, (x, y) becomes (x, - y)
Thus, the new coordinate of (- 8, - 6) after a reflection over the x axis is
A' = (- 8, - - 6)
A' = (- 8, 6)
The correct option is the third one
factor: x^2-36 I need help( i Don't know how to factor)
ANSWER
[tex](x+6)(x-6)[/tex]EXPLANATION
We want to factor the expression given:
[tex]x^2-36[/tex]To do this, we use the difference of two squares method:
[tex]a^2-b^2=(a+b)(a-b)[/tex]Therefore, we have:
[tex]\begin{gathered} x^2-36 \\ x^2-6^2 \\ \Rightarrow(x+6)(x-6) \end{gathered}[/tex]That is the answer.
Please help3 |3 - 5r| - 3 = 18
ANSWER
r = -0.8 or 2
EXPLANATION
We have the absolute value equation:
3 |3 - 5r| - 3 = 18
First, let us isolate the absolute value:
3 |3 - 5r| = 18 + 3
3 |3 - 5r| = 21
Divide through by 3:
|3 - 5r| = 21 / 3
|3 - 5r| = 7
An aboslute value equation can have two meanings, it could mean that the value in the absolute value function is positive or negative.
That means that we can split the function as follows:
3 - 5r = 7 or 3 - 5r = -7
Collect like terms:
-5r = 7 - 3 or -5r = -7 - 3
-5r = 4 or -5r = -10
Divide through by -5:
r = 4 / -5 or r = -10 / -5
r = -0.8 or 2
That is the value of r.
A store randomly assigns their employees work identificationnumbers to track productivity. Each number consists of 5 digits ranging from 1-9.If the digits cannot repeat, find the probability that a randomly generated numberis 25938.
In order to determine the probability of generating 25938 in exact order, let's determine first how many ways can we generate 5-digit numbers from 1 - 9.
So, for our first number, we have 9 numbers to choose from.
For our second number, we only have 8 numbers to choose from since digits cannot be repeated.
For our third number, we only have 7 numbers to choose from.
For our 4th number, we now have 6 numbers only available
Lastly, for our 5th number, only 5 numbers are available.
[tex]9\times8\times7\times6\times5=15,120[/tex]So, there are 15, 120 ways of generating 5-digit numbers out from 1-9 without digits being repeated. Out of these 15,120 ways, only one is 25938.
Hence, the probability that a randomly generated number is 25938 is:
[tex]P(25938)=\frac{1}{15,120}[/tex]or in decimal form,
[tex]P(25938)=0.0000661[/tex]or in percent form.
[tex]P(25938)=.00661\%[/tex]The table below shows the high temperature, in degrees Fahrenheit, each day in Fairbanks, Alaska, during a week in January. Day: Sunday High temp: -8 Day: Monday High temp: 2 Day: Tuesday High temp: -6 Day:Wednesday High temp: -3 Day Thursday High temp: 4 Day: Friday High temp:5 Day Saturday High temp:-1The following sunday, Erin recorderd the High tenperature and then calculated the mean high temperature, which she found was -1.5 F. What was the temperature on Sunday?
Let y be the temperature
[tex]\operatorname{mean}=\frac{\Sigma x}{n}[/tex]mean =-1.5
n=8
substitute in the above
[tex]-1.5=\frac{-8+2+(-6)+(-3)+4+5+(-1)+y}{8}[/tex][tex]-1.5=\frac{-7+y}{8}[/tex]Multiply both-side of the equation by 8
[tex]-1.5(8)=-7+y[/tex][tex]-12=-7+y[/tex]Add 7 to both-side of the equation
[tex]-12+7=y[/tex][tex]-5=y[/tex][tex]y=-5[/tex]Of the methods for solving systems of equations, which is best used when one equation is solved for either x or y, or can easily be solved for x or y?A) SubstitutionB) GraphingC)None of the methods are appropriate for this situation.D) Elimination
The given information is you have one equation that can easily be solved for either x or y, we don't know any information about the second equation.
Then, the most appropiate method is substitution, since you can solve this equation for one of the variables (x or y) and then substitute it in the other equation and solve.
So, the answer is A. Substitution
Find the angle. Round your answer to the nearest whole number.
Trigonometric Ratios
The trigonometric ratios are used on right triangles to relate angles and side lengths.
We are given the lengths of the three sides of the right triangle, so we can use any of the trigonometric ratios available. Let's choose, for example, the sine ratio, whose formula is:
[tex]\displaystyle\sin \theta=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]We want to calculate the value of the angle marked as '?', called theta in the formula above.
Please note the opposite leg to the angle is 16 and the hypotenuse is 34, thus:
[tex]\displaystyle\sin \theta=\frac{16}{34}=0.47059[/tex]The angle is calculated as the inverse sine function:
[tex]\theta=\arcsin (0.47059)=28.07^o[/tex]Rounding to the nearest whole number:
Angle '?' = 28°
what is the measure of the angle identified with the? In the diagram
Let the required angle = x
As shown in the figure :
There is a right triangle , the hypotenuse of the triangle = 90 feet
The adjacent side to the angle x = 45 feet
So, we can use the cosine function to find the angle
[tex]\begin{gathered} \cos x=\frac{adjacent}{hypotenuse} \\ \\ \cos x=\frac{45}{90}=\frac{1}{2}=0.5 \\ \\ x=\cos ^{-1}0.5=60 \end{gathered}[/tex]So, the answer is : the measure of the angle = 60
during periods when the unajusted federal minimum wage is constant ,identify the trend that you observed in the adjusted federal minimum wage and then explain why that Trend occurred
From the graph given the trends noticed between the adjusted and unadjusted federal minimum wage are
For every period when the unadjusted federal minimum wage is constant, there is a decrease in the adjusted federal minimum wage.
I need to know the right answer soon it’s due tonight
Multiplying 9/8 and the first equation we get:
[tex]-\frac{63}{8}x-9y=\frac{81}{8}\text{.}[/tex]Adding the above equation and the second equation of the system we get:
[tex]-\frac{63}{8}x-4x=\frac{81}{8}-22.[/tex]Adding like terms, we get:
[tex]-\frac{95}{8}x=-\frac{95}{8}\text{.}[/tex]Therefore:
[tex]x=1.[/tex]Subtituting x=1 in the first equation, we get:
[tex]-7-8y=9.[/tex]Solving the above equation for y, we get:
[tex]\begin{gathered} -8y=9+7, \\ -8y=16, \\ y=-2. \end{gathered}[/tex]Answer:
[tex]x=1,\text{ y=-2.}[/tex]how did the equation shift from the parent function?y=f(x-4)the answer choices is A. vertical stretch by 4b. shift right by 4 C. Shift left by 4 D. Shift down by 4 E. horizontal stretch by 4
We can translate a function on its two axis. If we want to translate it on the vertical axis we need to add or subtract the constant that determines the translation by the end of the function, as seen below:
[tex]f(x)+c[/tex]If the constant is positive, then the function will be translated up, if its negative it'll be translated down.
We can also shift the function on its horizontal axis. To do that we have to add a constant in the argument of the function as seen below:
[tex]f(x+c)[/tex]If the constant is negative, the shift will happen on the right direction. If the constant is positve, the shift will be on the left direction.
The function given to us is:
[tex]y=f(x-4)[/tex]This falls on the second type of translation and the constant is negative, therefore there is a shift to the right by 4 units. The correct answer is b.
--- f(x) = 3x – 4 g(x) = -x2 + 2x – 5 h (x) = 2x2 +1 j(x) = 6x2 k(x) = 3x2 – x +7 Calculate (g+h) (2). 82
We have:
[tex]g(x)=-x^2+2x-5[/tex]And:
[tex]h(x)=2x^2+1[/tex]In order to calculate (g+h)(2) we first add both equations:
[tex]g(x)+h(x)=(-x^2+2x-5)+(2x^2+1)^{}[/tex][tex]\Rightarrow g(x)+h(x)=x^2+2x-4[/tex]When now replace x by 2:
[tex](g+h)(2)=(2)^2+2(2)-4\Rightarrow(g+h)(2)=4[/tex]You and your friends have organized a 2 day event called TheSummer Splash Party! You flip a coin each day to randorlydecide whether you will have play Water Tag (W) or Duck DuckSplash (D).What is the probability that you play Water Tag (W) both days?
Answer:
1/4
Explanation:
There are two possible games to choose from ( Water Tag and Duck Duck Splash). Therefore, the probability of each 1 / 2.
The probability that you play Water Tag on day 1 is 1/2.
The probability that you play Water Tag on day 2 is 1/2.
Therefore, the probability that you play Water Tag on both days is
[tex]\frac{1}{2}*\frac{1}{2}=\frac{1}{4}[/tex]Using the tools you learned in this lesson, find all solutions (real and non-real) for the polynomial: 2x^3-3x^2+32x+17 To earn full credit please share all work, calculations and thinking. If you prefer you can do the work by hand on a piece of paper, take a picture of that work and upload it.
The given polynomial function is;
[tex]f(x)=2x^3-3x^2+32x+17[/tex]Firstly, we would find a factor of the function by a trial and error method.
Thus, we have:
[tex]\begin{gathered} \text{when x=-1} \\ f(-1)=2(-1)^3-3(-1)^2+32(-1)+17 \\ f(-1)=2(-1)-3(1)-32+17 \\ f(-1)=-2-3-32+17 \\ f(-1)=-20 \\ \text{Thus,(x}+1)\text{ is not factor} \end{gathered}[/tex][tex]\begin{gathered} \text{when x=}\frac{-1}{2} \\ f(-\frac{1}{2})=2(-\frac{1}{2})^3-3(-\frac{1}{2})^2+32(-\frac{1}{2})+17 \\ f(-\frac{1}{2})=2(-\frac{1}{8})-3(\frac{1}{4})-\frac{32}{2}+17 \\ f(-\frac{1}{2})=-\frac{2}{8}-\frac{3}{4}-\frac{32}{2}+\frac{17}{1} \\ f(-\frac{1}{2})=\frac{-2-6-128+136}{8} \\ f(-\frac{1}{2})=\frac{0}{8}=0 \\ \text{Since, this is equal to zero, it implies that;} \\ 2x+1\text{ is a factor of the given polynomial} \end{gathered}[/tex]We are going to use the long division method to get the other factor(s).
Thus, we have:
The final remainder of the long division is 0.
Thus, the factors of the polynomial are:
[tex](2x+1)and(x^2-2x+17)[/tex]Find the zeros of these factors, we have:
[tex]\begin{gathered} 2x+1=0 \\ 2x=-1 \\ x=-\frac{1}{2} \end{gathered}[/tex][tex]\begin{gathered} x^2-2x+17 \\ \text{This is not factorizable, thus we would make use of the quadratic formula to solve it} \end{gathered}[/tex]The quadratic formula is given by the equation;
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex][tex]\begin{gathered} \text{From the equation;} \\ x^2-2x+17 \\ a=1;b=-2;c=17 \\ \text{Thus, we have} \\ x=\frac{-(-2)\pm\sqrt[]{(-2)^2-4(1)(17)}}{2(1)} \\ x=\frac{2\pm\sqrt[]{4-68}}{2} \\ x=\frac{2\pm\sqrt[]{-64}}{2} \\ \text{Recall from complex number;} \\ i=\sqrt[]{-1} \\ \text{Thus, }\sqrt[]{-64}\text{ can be further expressed as }\sqrt[]{64}\text{ }\times\sqrt[]{-1} \\ \Rightarrow8i \\ \text{Thus, } \\ x=\frac{2\pm8i}{2} \\ x=\frac{2+8i}{2}\text{ OR }\frac{2-8i}{2} \\ x=\frac{2(1+4i)}{2}\text{ OR }\frac{2(1-4i)}{2} \\ x=1+4i_{} \\ OR \\ x=1-4i \end{gathered}[/tex]Hence, the solutions are:
[tex]x=-\frac{1}{2},1+4i\text{ and 1-4i}[/tex]