The degree a polynomial is determine by the highest highest power of variable in the equation.
However, for a multivariable polynomial, the degree is the highest sum of powers of different variables in any of the terms in the expression.
For this polynomial,
[tex]-56a^2y^3+23a^2y\text{ - 29a + 17}[/tex]The degree of polynomial is 5 at the term -56^2y^3 which has 2 and 3 exponent at variable a and y respectively.
will send image 8.2 + x + 2; x= 3.1
For x = 3.1
10) 8.2 + x
I need help.on a problem
the equation
[tex]-1.26\times n=-10.08[/tex]total days
we solve n dividing all expression by -1.26
[tex]\begin{gathered} \frac{-1.26\times n}{-1.26}=\frac{-10.08}{-1.26} \\ \\ n=8 \end{gathered}[/tex]then the total number of days is 8
y=-2/3x +7y = 2x - 3For each equation, write the slope and y-intercept.Graph both equations on the same graph (do this on paper)
The given equations of the lines are in their slope-intercept form, that is:
[tex]\begin{gathered} y=mx+b \\ \text{ Where m is the slope and} \\ b\text{ is the y-intercept of the line} \end{gathered}[/tex]Then, we have:
• First equation
[tex]\begin{gathered} y=-\frac{2}{3}x+7 \\ \boldsymbol{m=-\frac{2}{3}} \\ \boldsymbol{b=7} \end{gathered}[/tex]• Second equation
[tex]\begin{gathered} y=2x-3 \\ \boldsymbol{m=2} \\ \boldsymbol{b=-3} \end{gathered}[/tex]Now, to graph the first equation, we can find two points through which the line passes:
• First point
If x = 3, then we have:
[tex]\begin{gathered} y=-\frac{2}{3}x+7 \\ y=-\frac{2}{3}\cdot3+7 \\ y=-2+7 \\ y=5 \end{gathered}[/tex]That means that the line passes through the point (3,5).
• Second point
If x = 6, then we have:
[tex]\begin{gathered} y=-\frac{2}{3}x+7 \\ y=-\frac{2}{3}\cdot6+7 \\ y=-2\cdot2+7 \\ y=-4+7 \\ y=3 \end{gathered}[/tex]That means that the line passes through the point (6,3).
To graph the second equation, we can find two points through which the line passes:
• First point
If x = 3, then we have:
[tex]\begin{gathered} y=2x-3 \\ y=2\cdot3-3 \\ y=6-3 \\ y=3 \end{gathered}[/tex]That means that the line passes through the point (3,3).
• Second point
If x = 4, then we have:
[tex]\begin{gathered} y=2x-3 \\ y=2\cdot4-3 \\ y=8-3 \\ y=5 \end{gathered}[/tex]That means that the line passes through the point (4,5).
Now that we know two points through which each line passes, we can graph them and then join them to obtain the graph of both equations:
The equation of the line of best fit is y= 25x+7.5. What does the y-intercept represent?
y= 25x+7.5
The general equation of a line is given as
y = mx + c
where m is the slope and c is the y-intercept
Comparing with the equation
the y intercept is 7.5
Translate the sentence into an inequality. A number w increased by 8 is greater than −16.
Input data
A number w increased by 8 is greater than −16.
Procedure
A number w increased by 8...
[tex]w+8[/tex]is greater than −16.
[tex]w+8>-16[/tex]Select the equation that represents the graph of the line. 3+ 2 1- -5 -4 -3 -2 -1 1 2 3 4 5 -3+ -4- -57 o y = 1 / 2 x + 2 O'y=x-1 o y = 1 / 2 x - 1 O y=x+2
First, we have to find the slope with the formula below.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the points (0, -1) and (2, 0).
[tex]m=\frac{0-(-1)}{2-0}=\frac{1}{2}[/tex]Once we have the slope, we use the slope-intercept formula to find the equation.
[tex]y=mx+b[/tex]Where m = 1/2, and b = -1.
[tex]y=\frac{1}{2}x-1[/tex]Hence, the answer is the third choice.Find the point of intersection of the following pair of equations, then sketch your solutions indicating all point where the equations intersect both sets of axes: a) y = 2x – 1 and x + 2y = 5b) ^2 + ^2 = 4 and 3x + y = 2
Answer:
a) Intersection of the equations (1.4, 1.8)
b) Intersection of the equations (0, 2) and (1.2, -1.6)
Explanation:
Part a) y = 2x – 1 and x + 2y = 5
To find the intersection point, let's replace the first equation on the second one, so
x + 2y = 5
x + 2(2x - 1) = 5
Now, we can solve the equation for x
x + 2(2x) - 2(1) = 5
x + 4x - 2 = 5
5x - 2 = 5
5x - 2 + 2 = 5 + 2
5x = 7
5x/5 = 7/5
x = 1.4
Then, replace x = 7/5 on the first equation
y = 2x - 1
y = 2(1.4) - 1
y = 2.8 - 1
y = 1.8
Then, the graph of the lines is:
Where the intersection points with the axes for y = 2x - 1 are (0, -1) and (0.5, 0) and the intersection points with the axes of x + 2y = 5 are (0, 2.5) and (5, 0)
Part b) ^2 + ^2 = 4 and 3x + y = 2
First, let's solve 3x + y = 2 for y, so
3x + y - 3x = 2 - 3x
y = 2 - 3x
Then, replace y = 2 - 3x on the first equation and solve for x
x² + y² = 4
x² + (2 - 3x)² = 4
x² + 2² - 2(2)(3x) + (3x)² = 4
x² + 4 - 12x + 9x² = 4
10x² - 12x + 4 = 4
10x² - 12x + 4 - 4 = 0
10x² - 12x = 0
x(10x - 12) = 0
So, the solutions are
x = 0
or
10x - 12 = 0
10x = 12
x = 12/10
x = 1.2
Replacing the values of x, we get that y is equal to
For x = 0
y = 2 - 3x
y = 2 - 3(0)
y = 2 - 0
y = 2
For x = 1.2
y = 2 - 3(1.2)
y = 2 - 3.6
y = -1.6
Therefore, the intersection points are (0, 2) and (1.2, -1.6)
Then, the graph of the functions are:
Since ^2 + ^2 = 4 is a circle with radius 2, the intersection points with the axes are (2,0), (0, -2), (-2, 0) and (0, 2). Additionally, the intersections potins with the axis of the line 3x + y are (0, 2) and (0.667, 0)
In a coordinate plane, quadlateral PQRS has vertices P(0,7), Q(4,6), R(2,3), S(-1,3). Find the coordinates of the vertices of the image after each reflection.Reflection across the line y = x
First we need to draw the graph
Then reflect with respect to the X axis
which is basically changing the sign of the Y values for each point
So, we can calculate the new points
[tex]\begin{gathered} P^{\prime}(0,-7) \\ Q^{\prime}(4,-6) \\ R^{\prime}(2,-3) \\ S^{\prime}(-1,-3) \end{gathered}[/tex]For the following exercise, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptotes of the function. use that information to sketch graph.
Answer:
The expression is given below as
[tex]a(x)=\frac{x^2+2x-3}{x^2-1}[/tex]The horizontal intercepts will be at y=0
[tex]\begin{gathered} a(x)=\frac{x^2+2x-3}{x^2-1} \\ \frac{x^2+2x-3}{x^2-1}=0 \\ x^2+2x-3=0 \\ x^2+3x-x-3=0 \\ x(x+3)-1(x+3)=0 \\ (x-1)(x+3)=0 \\ x-1=0,x+3=0 \\ x=1,x=-3 \end{gathered}[/tex][tex]\begin{gathered} x^2-1=0 \\ x^2=1 \\ x=\pm1 \\ x=1,x=-1 \end{gathered}[/tex]Hence,
The horizontal intercepts is at x = -3
The vertical intercept is at x=0
[tex]\begin{gathered} a(x)=\frac{x^2+2x-3}{x^2-1} \\ y=\frac{0^2+2(0)-3}{0^2-1} \\ y=\frac{-3}{-1} \\ y=3 \end{gathered}[/tex]Hence,
The vertical intercept is at y=3
A vertical asymptote is a vertical line that guides the graph of the function but is not part of it. It can never be crossed by the graph because it occurs at the x-value that is not in the domain of the function. A function may have more than one vertical asymptote.
[tex]\begin{gathered} a(x)=\frac{x^2+2x-3}{x^2-1} \\ a(x)=\frac{(x-1)(x+3)}{(x-1)(x+1)_{}} \\ \text{hence, the vertical aymspote will be at} \\ x+1=0 \\ x=-1 \end{gathered}[/tex]Hence,
The vertical asymptotes is at x= -1
The horizontal asymptotes will be calculated using the image below
[tex]\begin{gathered} a(x)=\frac{x^2+2x-3}{x^2-1} \\ a=1,b=1,n=m=1 \\ y=\frac{a}{b} \\ y=\frac{1}{1} \\ y=1 \end{gathered}[/tex]Hence,Do you have any questions about the steps to solve your question?
The horizontal asymptotes is y=1
The graph is represented below as
Gemma had $2, 054 in her checking account. She wrote acheck for $584 to pay the rent on her apartment. After thelandlord cashed the check, how much money did Gemmahave left in her checking account?
Solution
Given that Gemma had $2, 054 in her checking account.
She wrote a check for $584 to pay the rent on her apartment.
That means she would have $2, 054 - $584 = $1, 470 left in her checking account
Option C
15. Find the volume of the figure below.20 yd15 yd9 yd12 yd- 20.9
The volume of a triangular prism is the following equation:
[tex]V=Ah[/tex]where A represents the area of the base and h represents the height of the prism.
In this case, the area of the base is the following:
[tex]A=\frac{12\cdot9}{2}=\frac{108}{2}=54yd^2[/tex]then, the volume of the prism is:
[tex]V=54(20)=1080yd^3[/tex]the graph shows that school's profit P for selling x lunches on one day.The school wants to change the price for lunch so that when it sells more than 30 lunches in one day, it begins to make a profit.How much would the school need to charge for each lunch situation?
Find the slope of the line. That will give us the present price for each lunch.
Use the points (0,-150) and (50,0):
[tex]\begin{gathered} m=\frac{0--150}{50-0} \\ \Rightarrow m=3 \end{gathered}[/tex]Then, the current profit equation is given by:
[tex]y=3x-150[/tex]We want to change the price of each lunch so that the point (30,0) belongs to the graph (that means that when selling 30 lunches, it begins to make profit).
Let M be the new price. Then:
[tex]\begin{gathered} 0=30M-150 \\ \Rightarrow30M=150 \\ \Rightarrow M=\frac{150}{30} \\ \therefore M=5 \end{gathered}[/tex]Therefore, the school should charge 5 dollars for each lunch.
Elena is conduction a study about the effects of toxins in the water on the hormones of fish. Elena surveys 350 male fish in a river and finds that 150 of the male fish have egg cells growing inside them. According to Elena’s survey, what is the ratio of male fish with egg cells to male cells in the river?
Answer:
3:7
Explanation:
We know that Elena surveys 350 male fish in a river.
Out of these 350 fish, 150 have egg cells growing inside them.
Therefore,
male fish with egg cells: male fish in the river = 150: 350
The next step is to write this ratio as a fraction and simplify it.
Writing the ratio as a fraction gives
[tex]\frac{150}{350}[/tex]dividing both the numerator and the denominator by 50 gives
[tex]\frac{150\div50}{350\div50}[/tex][tex]=\frac{3}{7}[/tex]Hence, the ratio of the male fish with egg cells to total male fish in the river is 3:7.
Jenny makes money by mowing lawns. She can mow 8 lawns in 5 hours. At this rate, how long does it take her to mow 12 lawns?
Answer is 20 hours.
Given:
Jenny can make 8 lawns in 5 hours.
The objective is to calculate the time required for her to mow 12 lawns.
Consider the required time as t.
The rate of equation can be represented as,
[tex]\begin{gathered} r=\frac{12}{8} \\ r=4 \end{gathered}[/tex]Now, the time required can be calculated as,
[tex]\begin{gathered} r=\frac{t}{5} \\ 4=\frac{t}{5} \\ t=20\text{ hours} \end{gathered}[/tex]Hence, the time required for her to mow 12 lawns is 20 hours.
The volume of this cone is 53,851 cubic yards. What is the height of this cone? Use pi = 3.14 and round your answer to the nearest hundredth.
Volume of a cone = 1/3 π r^2 h
Where:
r= radius = 35 yd
h= height
π = 3.14
Replacing with the values given:
53,851 = 1/3 (3.14) 35^2 h
Solve for h
53,851 / (1/3 (3.14) 35^2)= h
h= 42
I need the answers please show work so I don’t fail
Solution
- The way to solve the question is that we should substitute the values of x and y given into the formula given to us.
- The formula given to us is:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ where, \\ (x_1,y_1)\text{ are the points given to us} \\ m\text{ is the slope} \end{gathered}[/tex]- Thus, we can solve the question as follows:
Question 1:
[tex]\begin{gathered} m=5 \\ x_1=3,y_1=6 \\ \\ \text{ Thus, the equation is:} \\ y-6=5(x-3) \end{gathered}[/tex]Question 2:
[tex]\begin{gathered} m=\frac{2}{7} \\ x_1=-5,y_1=4 \\ \\ \text{ Thus, the equation is:} \\ y-4=\frac{2}{7}(x-(-6)) \\ \\ y-4=\frac{2}{7}(x+6) \end{gathered}[/tex]Question 3:
[tex]\begin{gathered} m=-\frac{3}{2} \\ x_1=-7,y_1=-10 \\ \\ \text{ Thus, the equation is:} \\ y-(-10)=-\frac{3}{2}(x-(-7)) \\ \\ y+10=-\frac{3}{2}(x+7) \end{gathered}[/tex]Final Answer
Question 1:
[tex]y-6=5(x-3)[/tex]Question 2:
[tex]y-4=\frac{2}{7}(x+6)[/tex]Question 3:
[tex]y+10=-\frac{3}{2}(x+7)[/tex]Write the following fractions in thesimplest form:1. 20/52. 12/963. 100/2
So the first fraction is:
1)
[tex]\frac{20}{5}[/tex]So we have to find a number that is multiple of 20 and 5, in this case is the number 5. the we have to divide the two numbers in 5:
[tex]\frac{5}{5}=1\to\text{ }\frac{20}{5}=4[/tex]So at the end the fraction is going to be equal to:
[tex]\frac{20}{5}=4[/tex]2)
[tex]\frac{12}{96}[/tex]and 12 and 96 are multiples of two, so we can divide by 2
[tex]\frac{12}{2}=6\to\frac{96}{2}=48[/tex]now we need to find other number that is multiple of 6 and 48, and agins is the number 2:
[tex]\frac{6}{2}=3\to\frac{48}{2}=24[/tex]Now 3 and 24 are multiples of 3, so we make the same procedure:
[tex]\frac{3}{3}=1\to\frac{24}{3}=8[/tex]So at the end is going to be:
[tex]\frac{12}{96}=\frac{1}{8}[/tex]3)
[tex]\frac{100}{2}[/tex]100 and 2 are multiples of 2, so we divide them by 2:
[tex]\frac{100}{2}=50\to\frac{2}{2}=1[/tex]So the final Resold will be:
[tex]\frac{100}{2}=\frac{50}{1}=50[/tex]A table of values of a linear function is shown below. Find the output when the input is n. input: 1 2 3 4 n output: 3 1 -1 -3
We have the points of a linear function and need to find the equation that represent.
Because it is a linear function, we can find its equation with two points.
We get the points (1,3) and (2,1):
[tex]\begin{gathered} We\text{ call input as x and output as y:} \\ P_1=(x_1,y_1)=(1,3),P_2=(x_2,y_2)=(2,1) \\ y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1) \\ y-3=\frac{(1-3)}{(2-1)}(x-1) \\ y-3=-\frac{2}{1}(x-1)=-2(x-1) \\ y=-2x-2\cdot(-1)+3 \\ y=-2x+2+3 \\ y=-2x+5 \end{gathered}[/tex]We can check that the points (3,-1) and (4,-3) also satisfy the equation that we found above:
[tex]\begin{gathered} \text{For point (3,-1):} \\ y=-2\cdot3+5=-6+5=-1 \\ \text{For point (4,-3):} \\ y=-2\cdot4+5=-8+5=-3 \end{gathered}[/tex]The above shows that the points satisfy the equation.
So, for input=n the output is:
[tex]\text{output}=-2\cdot n+5[/tex]Please help me with this problem I am trying to help my son to understand I have attached what I have helped him with so far just need to be sure i am correct:Solve the system of equations.13x−y=90y=x^2−x−42 Enter your answers in the boxes. ( __,__) and (__,__)
y=xTo solve the system of equations, follow the steps below.
Step 01: Substitute the value of y from equation 2 in equation 1.
In the second equation:
[tex]y=x^2-x-42[/tex]In the first equation:
[tex]13x-y=90[/tex]So, let's substitute y by x² - x - 42.
[tex]\begin{gathered} 13x-y=90 \\ 13x-(x^2-x-42)=90 \\ 13x-x^2+x+42=90 \end{gathered}[/tex]Adding the like terms:
[tex]-x^2+14x+42=90[/tex]Subtracting 90 from both sides:
[tex]\begin{gathered} -x^2+14x+42-90=90-90 \\ -x^2+14x-48=0 \end{gathered}[/tex]Step 02: Use the quadratic formula to solve the equation.
For a quadratic equation ax² + bx + c = 0, the quadratic formula is:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \end{gathered}[/tex]In this question, the equation is -1x² + 14x + -48 = 0, then, teh coeffitients are:
a = -1
b = 14
c = -48
Substituting the values and solving the equation:
[tex]\begin{gathered} x=\frac{-14\pm\sqrt{14^2-4*(-1)*(-48)}}{2*(-1)} \\ x=\frac{-14\pm\sqrt{196-192}}{-2} \\ x=\frac{-14\pm\sqrt{4}}{-2}=\frac{-14\pm2}{-2} \\ x_1=\frac{-14-2}{-2}=\frac{-16}{-2}=8 \\ x_2=\frac{-14+2}{-2}=\frac{-12}{-2}=6 \end{gathered}[/tex]Step 03: Substitute the values of x in one equation and find y.
Knowing that:
[tex]y=x^2-x-42[/tex]Let's substitute x by 6 and 8 and find the ordered pairs that are the solution of the system.
First, for x = 8:
[tex]\begin{gathered} y=8^2-8-42 \\ y=64-8-42 \\ y=14 \end{gathered}[/tex]Second, for x = 6:
[tex]\begin{gathered} y=6^2-6-42 \\ y=36-48 \\ y=-12 \end{gathered}[/tex]So, the solutions for the system of equations are (8, 14) and (6, -12).
Answer: (8, 14) and (6, -12).
Analyze the data in the line plot "attached "Use the data to construct a line plot.Number of students in a classroom:22, 28, 31, 33, 28, 29, 31, 28, 29, 32, 27, 18, 29, 31, 30, 31, 32, 27, 29, 33
Answer:
Most classrooms have between 29-31 students.
Step-by-step explanation:
To construct a line plot, create a number line that includes all the numbers or values in the data set. Then place an x over each data value on the number line, if a value occurs more than one place x's as necessary:
Donna got a prepaid debit card with $25 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 21 cents per yard. If after that purchase there was $21.22 left on the card, how many yards of ribbon did Donna buy?
Given data:
Initial amount of money: $25.00
Final amount of money: $21.22
Price of ribbon: $0.21 per yard
1. Find the money Donna spend in the craft store: Subtract the final amount of money from the initial amount of money:
[tex]25.00-21.22=3.78[/tex]2. Divide the result of step 1 by the price per yard of the ribbon:
[tex]\frac{3.78}{0.21}*\frac{100}{100}=\frac{378}{21}[/tex]Then, Donna bought 18 yards of ribbonCan you please help me out with a question
As you can see in the given figure, there are two intersecting chords inside the circle.
Recall that the "Intersecting Chords Theorem" is given by
[tex]AE\cdot EC=BE\cdot DE[/tex]For the given case, we have
AE = 7
BE = 6
EC = 9
Let us substitute these values into the above equation and solve for DE
[tex]\begin{gathered} AE\cdot EC=BE\cdot DE \\ 7\cdot9=6\cdot DE \\ 63=6\cdot DE \\ \frac{63}{6}=DE \\ 10.5=DE \\ DE=10.5 \end{gathered}[/tex]Therefore, the length of DE is 10.5 units.
Yellow chip = +1 Red chip = -1Find the sum of 4 + -5 using the counter chips.4=-5=4 + -5 =
Notice that 5 is greater than 4.
To find 4-5, remember that when a greater number is subtracted from another, the result is a negative number. Then, the result is the same as the result of 5 minus 4 but with a negative sign.
Since 5-4 is equal to 1, then:
[tex]4-5=-1[/tex]Therefore, the answer is: -1.
What are the critical points of f prime = 2x -2/x
The critical points of f prime are at x = ± 1
What are critical points?Critical points of a function are the points at which the function changes direction.
How to find the critical points of f prime?Since we have the function f'(x) = 2x - 2/x
Since the functionis f'(x), this implies that it is a derivative of x.
So, to find the critical points of f'(x), we equate f'(x) to zero.
So, we have that
f'(x) = 0
⇒ 2x - 2/x = 0
⇒ 2x = 2/x
cross-multiplying, we have that
⇒ 2x² = 2
Dividing through by 2, we have that
⇒ x² = 2/2
⇒ x² = 1
Taking square root of both sides, we have that
⇒ x = ±√1
⇒ x = ± 1
So, the critical points are at x = ± 1
Learn more about critical points here:
https://brainly.com/question/26978374
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Convert the following angle from degrees to radians. Express your answer in simplestform.150°
Recall that:
[tex]2\pi radians=360^{\circ}.[/tex]Therefore:
[tex]150^{\circ}=\frac{150*2\pi}{360^}\text{ radians.}[/tex]Simplifying the above result, we get:
[tex]150^{\circ}=\frac{5}{6}\pi.[/tex]Answer: [tex]\begin{equation*} \frac{5}{6}\pi. \end{equation*}[/tex]21a. Ellen is selling fruit juice and each juice is $3. Write an equation for thesituation.
price of each juice = $3
Number of juices = x
total cost = y
Equation
y= 3x
graph the equation y= -x² + 10x - 16. you must plot 5 points including the roots and the vertex
Given the function:
[tex]y=-x^2+10x-16[/tex]The graph of the function is plotted and attached below:
From the graph:
• The roots are (2,0) and (8,0).
,• The vertex is a maximum that occurs at (5,9)
,• The graph intersects the y-axis at (0,-16).
The other points are added as a guide when plotting your own graph.
you roll a number cube numbered from 1 to 6 p( a number greater than 4)
The probability of an event A can be calclated obythe number of possible favorable outcomes of A dividaed by the total possible outcomes of the random experience.
If we rolled a number cube (1 to 6), the total possible outcomes is 6 because we cn get {1, 2, 3, 4, 5, 6}.
From those outcomes, only two are greater than 4: {5, 6}.
Thu, the required probability is:
[tex]p=\frac{2}{6}=\frac{1}{3}[/tex]The approximate value is p = 0.33
it’s a system of equation graph and they need to be matched with its solution
Explanation
Step 1
[tex]\begin{gathered} f(x)=2^x-3 \\ j(x)=x+2 \end{gathered}[/tex]a) to graph f(x) , we start from the function
[tex]\begin{gathered} f(x)=2^x \\ then,\text{ we shift the graph 3 units down, so} \end{gathered}[/tex]b) j (x) is a line, so we need 2 points
[tex]\begin{gathered} j(0)=0+2=2 \\ P1(0,2) \\ and \\ j(1)=1+2=3 \\ P2(1,3) \end{gathered}[/tex]then, draw a line that passes through P1 and P2
finally, the solution is the point where the graph intersect each other, so
so, we can conclude that
the answer is
Use the slope formula to find the slope of the line through the points (9,5) and (-7,2).
The formula for determining slope is expressed as
slope = (y2 - y1)/(x2 - x1)
Where
y2 and y1 are the final and initial values of y respectively
x2 and x1 are the final and initial values of x respectively
From the information given,
x1 = 9, y1 = 5
x2 = - 7, y2 = 2
Thus,
Slope = (2 - 5)/(- 7 - 9)
Slope = - 3/ - 16
Slope = 3/16