Graph the rational functiony=x^2-3/x-1. Both branches of the rational function pass through which quadrant?Quadrant 2Quadrant 3Quadrant 4Quadrant 1
Answers
Quadrant 1
Explanations:Given the rational function
[tex]y=\frac{x^2-3}{x-1}[/tex]From the function, you can see that the vertical asymptotes of the function is at x = 1 (the point where the denominator is zero),
The quadratic numerator also shows that the curves cuts the x-axis at two points as shown in the graph below;
From the graph shown, you can see that the both branches of the function pass through the Quadrant 1. For other quadrants, either one of none of he branches passes through
Related Questions
How many solutions does this system of equations have y=2x+5Y=x^3+4x^2+x+2
Answers
ANSWER:
D. 3 solutions
EXPLANATION:
Given:
[tex]\begin{gathered} y=2x+5 \\ \\ y=x^3+4x^2+x+2 \end{gathered}[/tex]To find:
The number of solutions this system has
Let's equate the two equations and solve for x;
[tex]\begin{gathered} 2x+5=x^3+4x^2+x+2 \\ \\ x^3+4x^2-2x+x+2-5=0 \\ \\ x^3+4x^2-x-3=0 \end{gathered}[/tex]Since the highest power of x is 3, therefore, the system of equations will have 3 solutions
Hey could you please help me on this math problem thank you
Answers
Given two set of data represented in a dot plot. We are to find the dot plot with the highest element.
Plot A:
21 = 21, 21, 21, 21
22 = 22, 22
23 = 0
24 = 24
Total element in Plot A:
21, 21, 21, 21, 22, 22, 24 = 7 elements 9dots)
Plot B:
21 = 21
22 = 22, 22
23 = 23, 23, 23
24 = 24, 24, 24
Total elements in plot B:
21, 22, 22, 23, 23, 23, 24, 24, 24 = 9 elements (dots)
Plot A: 7 elements (dots)
Plot B: 9 elements (dots)
Therefore, from our analysis above, the plot with less elements (dots) is Plot A.
Bill can repair a transmission in 8 hours. It takes Henry 10 hours to do the same job. If they begin the job together and then Bill leaves after 3 hours, how long will it take Henry to finish?
Answers
Answer: Henry will take 3.25 hours to finish the work alone.
Explanation
Given
• Bill can repair a transmission in 8 hours.
,• It takes Henry 10 hours to do the same job.
,• If they begin the job together and then Bill leaves after 3 hours, how long will it take Henry to finish?
Procedure
Bill does 1/8 of the job per hour, while Henry does 1/10 of the work per hour. They work together 3 hours. If we assume their works are additive (no interference from one another), and considering that:
[tex]rate\times time=\text{work done}[/tex]Then we can build the following relation:
[tex](\frac{1}{8}+\frac{1}{10})\times3=\text{ work done}[/tex]Simplifying:
[tex]\text{ work done}=(\frac{5+4}{40})\times3=(\frac{9}{40})\times3=\frac{27}{40}[/tex]The job at the 3 hours will be 27/40 done. Then, Henry has to finish the rest of the work, which is:
[tex]\frac{40}{40}-\frac{27}{40}=\frac{13}{40}[/tex]Finally, to calculate the time it will take Henry to do the job, we have to do the following:
[tex]\frac{1}{10}\times t=\frac{13}{40}[/tex][tex]t=\frac{\frac{13}{40}}{\frac{1}{10}}=\frac{130}{40}=\frac{13}{4}\approx3.25h[/tex]3. What can you say about the data displayed in the box plot?The data is skewed to the left.The data is skewed to the right.The mean is less than the median,The mean and median are about the same.
Answers
Solution
The data is skewed to the right.
Thirty 8th graders signed up for running club,however nine dropped out before the first2practice. If 46 2/3% of the club are 8th graders,how many total students are in the runningclub?
Answers
Given
30 8th graders
9 dropped out before the first practice
Total = 30 - 9 = 21 8th graders
Procedure
46% of the club are 8th graders
T: Total of studetns
[tex]\begin{gathered} 21=T\cdot46\text{ 2/3 \%} \\ T=\frac{21}{0.46666} \\ T=45 \end{gathered}[/tex]The total students in the running club would be 45 students and 21 from 8th graders
Chad originally had a rectangle garden with the area of 2X ^2square meters .He decided to make a new garden that was larger than his original garden. The area of the new garden is 2x^2+6x+4 square meters. Which of the following expressions represents the difference between the area of his new garden and the area of the original garden .I just need a brief explanation with the answer
Answers
The area of original graden = 2x^2
Area of new garden =
[tex]2x^2+6x+4[/tex]Substract the area =
[tex]2x^2+6x+4-2x^2=6x+4[/tex]Difference between the area of his new garden and the area of the original garden is (6x + 4_
Answer: d) 6x + 4
Mariah solved the inequality 15-2x>5 and got x>5 as a solution. Describe how you can use a number line to prove that her solution is incorrect.
Answers
Solve the inequality;
[tex]\begin{gathered} 15-2x>5 \\ \text{Subtract 15 from both sides of the inequality} \\ 15-15-2x>5-15 \\ -2x>-10 \\ \text{Divide both sides by -2} \\ \frac{-2x}{-2}<\frac{-10}{-2} \\ x<5 \end{gathered}[/tex]As a rule in math, when an inequality is divided by a negative number, the sign is flipped backwards. This simply means whe dividing by a negative number, the sign "greater than" is flipped back to "less than" and vice versa.
If according to Mariah's solution the answer is x > 5, that means we woud have the following;
[tex]\begin{gathered} 15-2(6)>5 \\ 15-12>5 \\ 3>5 \\ \text{Note that we have used 6 as the value of x because her answer is x}>5\text{ on the number line} \\ \text{However, 3 is not greater than 5, hence her solution is incorrect} \\ \end{gathered}[/tex]7⅕-6⅔=?O A. 1⅕O B. ⅘O C. 13⅗O D. 1 ⅘
Answers
We have two mixed fractions
[tex]7\frac{1}{5}-6\frac{2}{5}[/tex]Separate 1 from the seven
[tex]6\frac{6}{5}-6\frac{2}{5}[/tex]Subtract the integers
6 - 6 = 0
Combine the fractions
[tex]\frac{6}{5}-\frac{2}{5}=\frac{4}{5}[/tex]Answer: Option B
For the following set of data, find the sample standard deviation, to the nearest thousandth.77, 124, 77, 82, 100, 139, 81
Answers
Sample standard deviation:
[tex]s=\sqrt{\frac{\Sigma(x_i-\bar{x})^2}{n-1}}[/tex]To find the standard deviation of the given set:
1. Fidn the mean:
[tex]\bar{x}=\frac{77+124+77+82+100+139+81}{7}=\frac{680}{7}\approx97.14[/tex]2. Find the (x-mean) for each data:
[tex]\begin{gathered} (77-97.14)=-20.14 \\ (124-97.14)=26.86 \\ (77-97.14)=-20.14 \\ (82-97.14)=-15.14 \\ (100-97.14)=2.86 \\ (139-97.14)=41.86 \\ (81-97.14)=-16.14 \end{gathered}[/tex]3. Square the results you get in previous step:
[tex]\begin{gathered} (-20.14)\placeholder{⬚}^2=405.6196 \\ 26.86^2=721.4596 \\ (-20.14)\placeholder{⬚}^2=405.6196 \\ (-15.14)\placeholder{⬚}^2=229.2196 \\ 2.86^2=8.1796 \\ 41.86^2=1752.2596 \\ (-16.14)\placeholder{⬚}^2=260.4996 \end{gathered}[/tex]4. Add the squares you get in previus step:
[tex]405.6196+721.4596+405.6196+229.2196+8.1796+1752.2596+260.4996=3782.8572[/tex]5. Divide the resull above into n-1:
[tex]\frac{3782.8572}{7-1}=\frac{3782.8572}{6}=630.4762[/tex]6. Find the square root of the quotient you get in previous step:
[tex]s=\sqrt{630.4762}\approx25.109[/tex]Then, the standard deviation is 25.109Given the rule for a dilation (x,y) → (4x, 4y) What is the scale factor?
Answers
Rule
[tex]\begin{gathered} (x,y)\to(4x,4y) \\ \end{gathered}[/tex]The scale factor would be 4
a kite in the shape of a rhombus has diagonals that are 25 in long and 15 in Long what is the area of the kite
Answers
The area of a rhombus is given by:
[tex]A=\frac{d_1d_2}{2}[/tex]where d1 and d2 are the diagonals. Then in this case we have:
[tex]A=\frac{25\cdot15}{2}=187.5[/tex]Therefore the area is 187.5 squared inches.
Graph the image of the figure on the right under the given translation.T(5,3) (x,y)
Answers
Notice that the translation transforms the coordinates (x,y) to (x+5,y+3). Then, if the vertex of the original triangle are ( -3,5), (-5,-2), and (-9,4) then the vertex of the transformed triangle are (2,8), (0,1), and (-4,7).
The graph of the new triangle is:
Answer: First image of the options in the question tab.
2) Direction: In the diagram below, justify each step of the equation. Statement Reason 3n - 5 = -8(6+5n) A) 3n-5=-48-40n B) 3n-43= -40n C) -43=-43n D) N=1
Answers
First:
Statement: 3n - 5 = -8(6 + 5n)
Reason: Given
Second:
Statement: 3n - 5 = -48 - 40n
Reason: Distributive property
Third:
Statement: 3n - 5 - 3n = -48 - 40n - 3n
Reason: Subtraction property of equality
Fourth:
Statement: 0 - 5 = -48 - 43n
Reason: Additive inverse property(left) and combine like terms(right)
Fifth:
Statement: -5 = -48 - 43n
Reason: Additive Identity property
Sixth:
Statement: - 5 + 48 = -43n - 48 + 48
Reason: Addition property of equality
Seventh:
Statement: 43 = -43n
Reason: Addition
Eight:
Statement: n = -1
Reason: Division
in the figure below, quadrilateral RATS is a rhombus with diagonals SA and TR interesting at E.
Answers
We need to find the length of the sides SR, RT, and the angle m∠TAS.
Finding the length of SR:
We consider that, in a rhombus, all of the sides are equal. So the sides ST and SR have to be equal:
[tex]ST=SR[/tex]Substituting the values of these sides:
[tex]3x+30=8x-5[/tex]We need to solve this equation for x.
Subtract 3x to both sides:
[tex]\begin{gathered} 30=8x-3x-5 \\ 30=5x-5 \end{gathered}[/tex]Add 5 to both sides:
[tex]\begin{gathered} 30+5=5x \\ 35=5x \end{gathered}[/tex]Divide both sides by 5:
[tex]\begin{gathered} \frac{35}{5}=x \\ 7=x \end{gathered}[/tex]Now that we have the value of x, we can find the value of SR:
[tex]\begin{gathered} SR=8x-5 \\ \text{substituting x=7} \\ SR=8(7)-5 \\ \text{Solving the operations:} \\ SR=56-5 \\ SR=51 \end{gathered}[/tex]SR=51
Finding the length of RT:
To find this length we need the value of z. And we can find the value of z considering that the diagonals bisect each other, so each side of a diagonal is equal to the other side of the diagonal. In this case, the blue and the red line in the image are equal:
We have that:
[tex]SE=AE[/tex]Substituting the values of SE and AE:
[tex]3z=4z-8[/tex]And now we solve for z by subtracting 3z to both sides:
[tex]\begin{gathered} 0=4x-3z-8 \\ 0=z-8 \\ \text{Add 8 to both sides:} \\ 8=z \end{gathered}[/tex]With this value of z, we can find the length RT.
RT is the yellow line in the image:
Again we consider that the two sides of the diagonal are equal. Thus, RT is equal to:
[tex]\begin{gathered} RT=5z+5+5z+5 \\ \text{Combining like terms:} \\ RT=10z+10 \\ \text{substituting z=8} \\ RT=10(8)+10 \\ RT=80+10 \\ RT=90 \end{gathered}[/tex]RT=90
Finally, we need to find the angle m∠TAS shown in blue in the image:
Since it is a rhombus, all of the angles in point E are equal to 90°:
So, considering only the triangle inside the rhombus marked in blue
We apply the property of triangles that tells us:
The sum of the internal angles of a triangle is equal to 180°.
So adding all of the blue angles we should get 180:
[tex]90+9y+8+5y-2=180[/tex]And now we solve for y, first, combine like terms:
[tex]96+14y=180[/tex]Subtract 96 to both sides:
[tex]\begin{gathered} 14y=180-96 \\ 14y=84 \end{gathered}[/tex]Divide both sides by 14:
[tex]\begin{gathered} y=\frac{84}{14} \\ y=6 \end{gathered}[/tex]And now that we have the value of y, we can find the value of m∠TAS:
[tex]\begin{gathered} m\angle TAS=9y+8 \\ \text{Substituting y=6} \\ m\angle\text{TAS}=9(6)+8 \\ m\angle TAS=54+8 \\ m\angle TAS=62 \end{gathered}[/tex]m∠TAS=62°
Answer:
SR=51
RT=90
m∠TAS=62°
x,y,z and w are -8-6,2 and 6, respectively find the length of two segments . Then tell whether they are congruent
Answers
To find the length of a segment in the number line, you have to subtract the smaller coordinate to the greater coordinate. In the case of the segment XY, its length is:
XY = -6 - (-8) = -6 + 8 = 2
In the case of the segment ZW, its length is:
ZW = 6 - 2 = 4
Given that their lengths are different, then they are not congruent.
Simplify and solve the problemb^2 a^4 / b^6 a^3
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
b^2 a^4 / b^6 a^3
Step 02:
simplify the expression:
[tex]\frac{b^2a^4}{b^6a^3}=\frac{a}{b^4}[/tex]The answer is:
a / b^4
sales tax in a certain community is 7% if the sales tax on a new car was 1400 what was the selling price of the car
Answers
hello
the cost of the sale tax = 1400
the percentage of the tax = 7%
selling price = ?
[tex]\begin{gathered} 7=\frac{1400}{x}\times100 \\ \frac{7}{100}=\frac{1400}{x} \\ \text{cross multiply both sides } \\ 7\times x=100\times1400 \\ 7x=140000 \\ \text{divide both sides by 7} \\ \frac{7x}{7}=\frac{140000}{7} \\ x=20000 \end{gathered}[/tex]from the calculation above, the selling price of the car is 20,000
Rena's Rowbot drift 23 feet from Shore followed by 9 more feet the rowboat card current position can be represented by - 23 + - 9 what integer represents the Rowboat current position.
Answers
Answer:
The integer that represent the rowboat's current position is;
[tex]-32[/tex]Explanation:
Given in the question;
the rowboat card current position can be represented by;
[tex]-23+-9[/tex]We need to solve to know the rowboat current position;
[tex]\begin{gathered} -23+-9 \\ =-23-9 \\ =-32 \end{gathered}[/tex]The integer that represent the rowboat's current position is;
[tex]-32[/tex]One side of a triangle is 4 more inches than the shortest side. The third side is 3 times the length of the shortest side. If the perimeter of the triangle is 29 inches, write and solve an equation to find the lengths of all 3 side of the triangle.
Answers
Answer
The three sides of the triangle have the measures
5 inches
9 inches
15 inches
Explanation
The perimeter of a figure is the sum of the dimensions of its exterior sides.
Let the length of the shortest side of the triangle be x inches
One side of a triangle is 4 more inches than the shortest side, that is, (x + 4) inches.
The third side is 3 times the length of the shortest side. That is, (3x) inches
So, the three sides of the triangle are
x
x + 4
3x
So, the sum of these sides is equal to the perimeter of the triangle, 29 inches.
x + x + 4 + 3x = 29
5x + 4 = 29
5x = 29 - 4
5x = 25
Divide both sides by 5
(5x/5) = (25/5)
x = 5 inches
x + 4 = 5 + 4 = 9 inches
3x = 3 (5) = 15 inches
Hope this Helps!!!
Find the area of the shapes belowMust show all steps including formula and units!
Answers
Answer:
[tex]\begin{gathered} a)1.33m^2 \\ b)123m^2 \\ c)62.5ft^2 \end{gathered}[/tex]Explanation:
We were given the following information:
Figure 1:
This is a trapezium
The area is calculated as shown below:
[tex]\begin{gathered} Base_1=2.0m \\ Base_2=1.8m \\ Height=0.7m \\ Area=\frac{Base_1+Base_2}{2}\times Height \\ Area=\frac{2.0+1.8}{2}\times0.7 \\ Area=1.9\times0.7 \\ Area=1.33m^2 \end{gathered}[/tex]Figure 2:
This is a rectangle
The area is calculated as shown below:
[tex]\begin{gathered} Length=15m \\ Width=8.2m \\ Area=Length\times Width \\ Area=15\times8.2 \\ Area=123m^2 \end{gathered}[/tex]Figure 3:
This is a rectangle
The area is calculated as shown below:
[tex]\begin{gathered} Length=12.5ft \\ Width=5ft \\ Area=Length\times Width \\ Area=12.5\times5 \\ Area=62.5ft^2 \end{gathered}[/tex]Plot the points with polar coordinates (-3, -2pi) and (2, pi/4) using the pencil.
Answers
P1 = (-3, -2π)
P2 = (2, π/4)
The first number is the length of the line joining the origin and the point, and the second number is the angle between the line and the horizontal axis. For the first point, we see that the angle is -2π. Since this is a circle, for an angle of -2π we finish at the same point. The length is 3 but points to the left side of the origin because the coordinate is -3.
For the second point, we have a line of length 2, and the angle is π/4. Graphically, this is:
Find the measure of angle one and angle two if angle 3 =78° and angle 4=102°
Answers
Given the diagram
Given that <3 =78 degrees and
<4 = 102 degrees.
To get angle 1 (<1):
< 1 and <4 are corresponding angles
When two lines are crossed by another line (called the Transversal), the angles in matching corners are called Corresponding Angles.
Therefore: <1 = <4 = 102 degrees
[tex]<1=102^0[/tex]To get angle 2 (<2)
<2 and <3 are also corresponding angles
therefore
<2 = <3 =78 degrees
This means that
[tex]<2=78^0[/tex]The Marching Band is traveling from Minnesota to Florida to perform in a national competition. A train ticket from Minnesota to Florida costs $150 and takes 15 hours of travel time per student. To rent a bus to make the trip, it costs $120 per student and takes 20 hours of travel time per student. The band has $4,800 to spend on the trip and can only spend 720 hours of total travel time. Use the information below.Let x = Students traveling by trainLet y = Students traveling by busTherefore,$150x + $120y < $4,800 and15x + 20y < 720.The graph of these functions is to the right.It is impossible for a negative number of students to go on the trip, so x and y both have to be greater than zero. Therefore, the functions are confined to the first quadrant.Number of students function:N = x + yWhat is the maximum number of students who can attend the trip? A. A maximum of 36 students can attend the trip. B. A maximum of 32 students can attend the trip. C. A maximum of 38 students can attend the trip. D. A maximum of 40 students can attend the trip.
Answers
ANSWER
A maximum of 38 students can attend the trip. (Option C).
EXPLANATION
Given:
Number of students function: N = x + y
$150x + $120y < $4,800 ................equ 1
15x + 20y < 720.................................equ 2
where
x = Students traveling by train
y = Students traveling by bus
Multiply equation 2 by -10
[tex]equ\text{ 2 }\times-10\Rightarrow-150x\text{ - 200y < -7200..........................equ 3}[/tex]Add equation 1 and 3
150x + 120y < 4,800
-150x - 200y <-7200
-----------------------------
0x - 80y < -2400
y > 2400/80
y > 30
Substitute the value of y into equation 1 to solve for x
150x + 120y < 4,800
150x + 120(30) < 4800
150x < 4800 - 3600
x < 1200/150
x < 8
Number
Graph each equation using x- and y- intercept -5x+y=-10 Other equation-3x-6y=12
Answers
10) We have to calculate the x and y intercepts for the line and graph the line:
[tex]-5x+y=-10[/tex]The x-intercept corresponds to the point where y = 0, so we can calculate it as:
[tex]\begin{gathered} -5x+0=-10 \\ -5x=-10 \\ x=\frac{-10}{-5} \\ x=2 \end{gathered}[/tex]The y-intercept corresponds to the point where x = 0, so we can calculate it as:
[tex]\begin{gathered} -5(0)+y=-10 \\ y=-10 \end{gathered}[/tex]With the intercepts, we have two points: (2,0) and (0,-10) and we can use them to graph as:
11) We have to calculate the x and y intercepts for the line and graph the line:
[tex]-3x-6y=12[/tex]The x-intercept is:
[tex]\begin{gathered} -3x-6(0)=12 \\ -3x=12 \\ x=\frac{12}{-3} \\ x=-4 \end{gathered}[/tex]The y-intercept is:
[tex]\begin{gathered} -3(0)-6y=12 \\ -6y=12 \\ y=\frac{12}{-6} \\ y=-2 \end{gathered}[/tex]Then, knowing the intercepts, we know the points (-4,0) and (0,-2) and we can graph the line as:
Draw a picture to show the division. write a division expression using unit form. Then expression your answer as a fraction.a) 1÷5 b) 3÷4 c) 6÷4
Answers
First let's draw a picture to represent each division:
a)
b)
c)
Now, writting the divisions in the unit form, we have:
a) 1÷5 = 5 fifths ÷ 5 = 1 fifth = 1/5
b) 3÷4 = 12 fourths ÷ 4 = 3 fourths = 3/4
c) 6÷4 = 24 fourths ÷ 4 = 6 fourths = 6/4
Write all classifications that apply to the real number -5.natural number, terminating decimalrational, integer, natural numberrational, integer, whole number, natural number, terminating decimalrational, integer, terminating decimal
Answers
Consider that the given number is '-5'.
In all the mentioned choices, the classifications are given as, natural numbers, terminating decimal, rational, integer, whole number.
Let us discuss -5 for each of these classifications one at a time:
Natural Number:
The integer number equal to 1 or greater than 1, are termed Natural Numbers. Since -5 does not satisfy this condition, that is, -5 is not greater than 1. So it cannot be called a natural number.
Rational Number:
A real number is said to be rational is it can be written in the form p/q such that 'q' must be non-zero. The number -5 can be represented as -5/1, that satisfies the condition. So thcan be considered as rational.
Find the equation of the hyperbola that has its foci at (0,-4) ans (10,-4) and whose conjugate axis is 6 units long
Answers
We are given the following information
Foci at (0, -4) and (10, -4)
The conjugate axis is 6 units
Recall that the standard form of the equation of hyperbola centered at (h, k) is given by
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]Where the center is (h, k)
The center (h, k) is the midpoint of the transverse axis given by
[tex]\begin{gathered} (h,k)=(\frac{0+10}{2},\frac{-4+(-4)}{2}) \\ (h,k)=(\frac{0+10}{2},\frac{-4-4}{2}) \\ (h,k)=(\frac{10}{2},\frac{-8}{2}) \\ (h,k)=(5,-4) \end{gathered}[/tex]Let us find the values of a and b
The semi transverse axis (a) is given by
[tex]a=\frac{10-0}{2}=\frac{10}{2}=5[/tex]The semi conjugate axis (b) is given by
[tex]b=\frac{6}{2}=3[/tex]So, the equation of the hyperbola is
[tex]\begin{gathered} \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1 \\ \frac{(x-5)^2}{5^2}-\frac{(y-(-4))^2}{3^2}=1 \\ \frac{(x-5)^2}{25^{}}-\frac{(y+4)^2}{9^{}}=1 \end{gathered}[/tex]Therefore, the equation of the hyperbola is
[tex]\frac{(x-5)^2}{25^{}}-\frac{(y+4)^2}{9^{}}=1[/tex]is this true or false?5. When the leading coefficient of a quadratic polynomial is negative, it graphs as a parabola opening upward.
Answers
False
Explanation
Parabolas may open upward or downward.
A)If the sign of the leading coefficient, a, is positive (a > 0), the parabola opens upward.
B)If the sign of the leading coefficient, a, is negative (a < 0), the parabola opens downward.
so, in this case ,When the leading coefficient of a quadratic polynomial is negative, it graphs as a parabola opening upward. is false because the parabola opens downward
I hope this helps you
The number of people estimated to vote in an election was 7,000. The actual number of people who voted was 5,600.Part A By what percent did the estimate vary from actual turnout? Part B In the previous election 6,400 people voted. What is the percent decrease in actual voters?
Answers
Step 1
Part A
Write an expression in ratio form that can be used to determine the percent with which the estimate varied from the actual turnout
Estimate to vote = 7,000 people
Actual turnout = 5,600 people
The ratio is given as
[tex]\frac{estimated\text{ number of people to vote}-\text{actual number of peple that voted}}{\text{actual number of people that voted}}\times100[/tex]Step 2
Substitute and get the answer to step 1
[tex]\begin{gathered} =\frac{7000-5600}{5600}\times100 \\ =\frac{1400}{5600}\times100 \\ x=\text{ 25\%} \end{gathered}[/tex]Hence the percent with which the estimate varied with the actual turnout =25%
Step 3
Calculate the percentage decrease
State an expression for percentage decrease
[tex]Percentage\text{ decrease =100}\times\frac{\text{final}-\text{initial}}{\text{initial}}[/tex]Step 4
Substitute and get the answer to part
[tex]\text{Percentage decrease = 100}\times\frac{5600-6400}{6400}[/tex][tex]\text{percentage decrease =12.5\%}[/tex]The percentage decrease in the actual voters = 12.5%
4. An athlete jumped 3.8 feet, which was 0.7 feetlower than the next jumper .Howfeet didthe next athlete jump?
Answers
For next Athlete jumps 3.8 + 0.7 feet =
Then next should have jumped = 3.8 + 0.7 = 4.5 feet
Answer is 4.5 feet