The steps for deriving the Quadratic formular are shown. Which best choose for the missing reason?
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In the part inside the yellow circle, we multiplied by 1 the term -c/a, that is
[tex]-\frac{c}{a}=-\frac{c}{a}\times1=-\frac{c}{a}(\frac{4a}{4a})=-\frac{4ac}{4a^2}[/tex]where 1 was written as 4a/4a.
Since we must add this result to
[tex]\frac{b^2}{4a^2}[/tex]the answer is option C, change to LCD ( Least Common Denominator) because both terms must have the same denominator, which is 4a^2.
Related Questions
In the 2008 presidential election of a country, 121,621,050 people turned out to vote. At the time, there were 190,296,524 registered voters. What percent of the registered voters voted?
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The percentage of registered voters that voted are
[tex]\frac{\text{voted}}{\text{registered voters }}\times100[/tex]Now,
# voted = 121,621,050
# registered voters = 190,296,524;
therefore,
[tex]\text{percent}=\frac{121,621,050}{190,296,524}\times100=63.91\approx64[/tex]Hence, about 64% of the registered voters voted.
Hi could you help me for this one as well.
Answers
Symmetric Property
Order of congruence does not matter.
Part B The seesaw moves and the angle created by the left of the seating board and the central support is now 70°. Seating Board R S 70 Central Support Find the distance from point Q to the ground when the angle created by the left side of the seating board and the central support is 70 ° (the length of the dashed line). Show your work or explain your answer. Round your answer to the nearest tenth of a foot. Enter your answer, and your work or explanation in the space provided
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In order to determine the distance from the point Q until the ground, it is necesary to know the length of the support. It is obtained from the part A of the question, as follow:
d = 5 ft · sin 30° = 2.5 ft
Next, consider, that the line that connects point R and the ground trought Q is the hypotenuse of a triangle. In this case, the length of the support is the adjacent side to the angle 70°. With this information and by using the cosine of the angle 70°, you can obtain the distance from R to the ground trough Q, as follow:
RG: distance from R to the ground (hypotenuse)
cos 70° = length of the support / RG solve for GR
cos 70° = 2.5 ft/ RG
RG = 2.5 ft/ cos 70°
RG = 7.3 ft
Next, to the previous value, subtract the lenght of segment RQ = 5 ft:
Distance from point Q to the ground trough dotted line = 7.3 ft - 5 ft = 2.3 ft
Hence, th answer is 2.3 ft
Select all the intervals where f is decreasingA: -4.5 < x < -4B: -0.5 < x < 0C: 1 < x < 2D: none of the above
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The intervals where f is decreasing can be found by looking at the graph for the values of x where x increases and f decreases.
Looking at the graph, the first interval where the function is decreasing is between -3.5 and -1, so we have -3.5 < x < -1.
Then, the second interval where the function is decreasing starts approximately at x = 2.2, and goes towards positive infinity, so we have x > 2.2.
Looking at the options, we have:
-4.5 < x < -4
In this interval the function is increasing.
-0.5 < x < 0
In this interval the function is increasing.
1 < x < 2
In this interval the function is increasing.
Therefore the correct option is D.
What is the value of a + b+c? you may assume that the ray is tangent to the circle?a. 86b.150c.133d.47
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ANSWER:
c. 133°
STEP-BY-STEP EXPLANATION:
We have that there is a chord that divides the circle in two equal parts because it passes through the middle of the circle. Since it is half of the circle, the arc is 180°, we can see that this arc is the sum of the angles a + b, this angle must measure half of 180°, therefore:
[tex]a\degree+b\degree=\frac{180\degree}{2}=90\degree[/tex]Now the angle c° must measure half of the 86° arc, therefore:
[tex]\begin{gathered} c\degree=\frac{86\degree}{2}=43\degree \\ \end{gathered}[/tex]That means that a° + b° + c° is equal to:
[tex]a°+b°+c°=90+43=133\degree[/tex]Therefore, the correct answer is c. 133°
Shaun estimated that the attendance at a college basketball game was 4,000. The actual attendance was 3,475. What is the percent error of Shaun's estimate? Round to the nearest whole percent.
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Percentage = 100 * (4000 - 3475)/3475 = 100 * (525/3475) = 52500/3475 = 15.1 %
Answer:
15.1%
if there are 36 successful outcomes in a sample size of 80 what is the sample proportion
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The sample proportion is the number of successes over the sample size. That is:
36/80 = 9/20
henry has one bag of groceries that weighs 9 pounds he has another bag of groceries that weighs 62 ounces how many ounces of grocery bags weigh altogether
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You can first use a rule of three to convert 9 pounds of groceries to ounces:
[tex]\begin{gathered} 1\text{ pound}\rightarrow16\text{ ounces} \\ 9\text{ pounds}\rightarrow x\text{ ounces} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{9\text{ pounds}\cdot16\text{ ounces}}{1\text{ pound}} \\ x=\frac{9\cdot16\text{ ounces}}{1} \\ x=\frac{9\cdot16}{1}\text{ ounces} \\ x=9\cdot16\text{ ounces} \\ x=144\text{ ounces} \end{gathered}[/tex]Now, add up all the groceries Henry has:
[tex]\begin{gathered} \text{Total weight of groceries}=9\text{ pounds }+62\text{ ounces} \\ \text{Total weight of groceries}=144\text{ ounces }+62\text{ ounces } \\ \text{Total weight of groceries}=206\text{ ounces } \end{gathered}[/tex]Therefore, in total the bags of groceries of Henry weight 206 ounces.
2500/10.5 please show work
Answers
The given expression is
2500/10.5
We would multiply the numerator and denominator by 10. We have
2500 x 10/10.5 x 10
= 25000/105
We would divide the numerator and denominator by common factors until they can't be simplified further. Dividing by 5, we have
5000/21
It can't be simplified further since there is no common factor of 5000 and 21. We would convert the fraction to mixed fraction
5000/21 = 238 remainder 2
Thus, if we write it as mixed fraction, we have
238 2/21
Write an inequality for the word problem and answer the question about the inequality. Twice a number added to 6 is less than 23is 10 a possible solution.
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Twice a number added to 6 is less than 23
[tex]2x+6<23[/tex]is 10 a possible solution. ?
In order to answer this question, we must solve for x
[tex]\begin{gathered} 2x+6<23 \\ 2x+6-6<23-6 \\ 2x<17 \\ \frac{2x}{2}<\frac{17}{2} \\ x<\frac{17}{2} \\ x<8.5 \end{gathered}[/tex]the solution is all numbers less than 8.5, therefore 10 is not a possible solution.
Find the circumference of this circleusing 3 for T.C ~ [?]14C = 27r
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Hello! To calculate the circumference, we have to use the formula below:
[tex]C=2\cdot\pi\cdot r[/tex]pi = 3
radius (r) = 14
Replacing these values in the formula, we will have:
[tex]\begin{gathered} C=2\cdot3\cdot14 \\ C=6\cdot14 \\ C=84 \end{gathered}[/tex]What is the volume of this cube? 2 cm 2cm 2cm
Answers
Answer:
The volume is
[tex]8\operatorname{cm}^3[/tex]Explanation:
The volume of a cube with length l is given by the formula:
[tex]V=l^3[/tex]Given the length 2 cm
The volume is:
[tex]V=2^3=8\operatorname{cm}^3[/tex]Complete the remainder of the table for the given rules
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To complete the table you have to input each value of x in the given equation and solve for y:
Function:
[tex]y=-2x+9[/tex]For x= -2
[tex]\begin{gathered} y=-2\cdot(-2)+9 \\ y=4+9 \\ y=13 \end{gathered}[/tex]x= -2 → y=13
For x= 0
[tex]\begin{gathered} y=-2\cdot0+9 \\ y=0+9 \\ y=9 \end{gathered}[/tex]x=0 → y=9
For x= 2
[tex]\begin{gathered} y=-2\cdot2+9 \\ y=-4+9 \\ y=5 \end{gathered}[/tex]x=2 → y=5
For x= 4
[tex]\begin{gathered} y=-2\cdot4+9 \\ y=-8+9 \\ y=1 \end{gathered}[/tex]x=4 → y=1
The maximum value in this range is: Use the range rule of thumb to determine whether 1 girl in 10 births is a significantly low number of girls.
Answers
Answer:
The maximum value in the range is 8.113
1 girl in 10 births is a significantly low number of girls.
Explanation:
Note that the range rule of thumb says that the range of about 4 times the standard deviation.
We'll use the below formula to determine the standard deviation;
[tex]\begin{gathered} \sigma=\sqrt[]{\lbrack\sum^{}_{}x^2\cdot P(x)\rbrack-\mu^2} \\ \text{where }\mu=\text{ population mean} \end{gathered}[/tex]Let's go ahead and determine the mean as seen below;
[tex]\mu=\sum ^{}_{}\lbrack x\cdot P(x)\rbrack[/tex][tex]\begin{gathered} \mu=(0\cdot0.005)+(1\cdot0.12)+(2\cdot0.039)+(3\cdot0.113)+(4\cdot0.196)+(5\cdot0.235)+(6\cdot0.209) \\ +(7\cdot0.113)+(8\cdot0.036)+(9\cdot0.016)+(10\cdot0.026) \end{gathered}[/tex][tex]\begin{gathered} \mu=0.12+0.078+0.339+0.784+1.175+1.254+0.791+0.288+0.144+0.26 \\ \mu=5.233 \end{gathered}[/tex]Let's now determine the below;
[tex]\begin{gathered} \sum ^{}_{}x^2\cdot P(x)=(0^2\cdot0.005)+(1^2\cdot0.12)+(2^2\cdot0.039)+(3^2\cdot0.113)+(4^2\cdot0.196)+(5^2\cdot0.235) \\ +(6^2\cdot0.209)+(7^2\cdot0.113)+(8^2\cdot0.036)+(9^2\cdot0.016)+(10^2\cdot0.026) \end{gathered}[/tex][tex]\begin{gathered} \sum ^{}_{}x^2\cdot P(x)=0.012+0.156+1.017+3.136+5.875+7.524+5.537+2.304+1.296+2.6 \\ =29.457 \end{gathered}[/tex]So the standard deviation will be;
[tex]\sigma=\sqrt[]{29.457-5.233^2}=\sqrt[]{29.457-27.384}=\sqrt[]{2.073}=1.44[/tex]Let's determine the maximum and minimum value of the distribution as seen below;
[tex]\begin{gathered} Maximum\text{ value = }\mu+2\sigma=5.233+2(1.44)=5.233+2.88=8.113 \\ \text{Minimum value }=\mu-2\sigma=5.233-2(1.44)=5.233-2.88=2.353 \end{gathered}[/tex]We can see from the above that the number of girls born among 10 children should be between the range of 2.353 and 8.113, therefore 1 girl in 10 births is a significantly low number of girls.
The maximum value in this range is 8.113
A survey was conducted to determine the food choices of the 80 students at a picnic. The types of food are in the graph belowSalad 10%Sandwich 20%Hamburger 15%Hotdog 15%Pizza 30%Based on the graph how many more students chose pizza than students who chose salad
Answers
First, find the amount of students who chose pizza and the amount of students who chose salad based on the total amount of students in the survey and the corresponding percentages.
Pizza: 30%
[tex]\frac{30}{100}\times80=24[/tex]Then, 24 students chose pizza.
Salad: 10%
[tex]\frac{10}{100}\times80=8[/tex]Then, 8 students chose salad.
Subtract the amount of students who chose salad (8) from the amount of students who chose pizza (24) to find how many more students chose pizza than students who chose salad.
[tex]24-8=16[/tex]Therefore, there are 16 more students who chose pizza than students who chose salad.
Garrick gets paid $4.70 an hour with time-and-a-half for overtime(over 40 hours). How much did he earn one week when he worked 46hours?a. $195.05b. $220.90c. $230.30d. $188
Answers
Solution
For this case we can calculate the total with the following formula:
Fixed amount= 40*4$.70= $188
And now for the remain hours we can do this:
Extra = 6* 1.5*$4.70= $42.3
Then the total amount is:
Fixed amount+ Extra = 188$ + 42.3$ = $230.3
Then the answer is:
c. $230.30
find the surface area of a composite figure round to the nearest tenth if necessary to units
Answers
The composite image is that of a cuboid and a triangular prism
For the cuboid, the surface area will be
A = LB + 2BH + 2LH
L = 1.8
B= 1.1
H= 0.8
A = 1.8X1.1 + 2 X 1.1 X 0.8 + 2 X 1.8 X 0.8
A = 1.98 + 1.76 +2.88
Area of cuboid = 6.62
Hello, I need some help with this precalculus question for my homework, please HW Q1
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In order to get the value of the given expression, let's convert it to an exponential form. Here's the pattern:
[tex]log_by=x\Leftrightarrow y=b^x[/tex]Let's convert the given expression in the problem using the pattern above.
[tex]log_4\text{ }x=3\Leftrightarrow x=4^3[/tex]So, let's solve 4³.
[tex]4^3=4\times4\times4=64[/tex]Therefore, the value of x is 64.
Answer: The solution set is {64}. Option A.
Please answer last oneDetermine the points Either A,B,C, or D and fill in the blank if needed
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We know that the graph has a horizontal asymptote y = 0 and we can also check that:
[tex]R(-6)=\frac{-6+6}{(-6)(-6+8)}=\frac{0}{-12}=0[/tex]Therefore, the graph of R intersects the horizontal or oblique asymptote at (-6,0)
8. On a map with a scale of 1cm - 15km, two towns are 7.5 cm apart. How far apart are they in real life? I
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ANSWER:
112.5 km
EXPLANATION:
Given that the map has a scale of 1cm : 15 km.
This means that 1 cm represents 15 km.
Since 1cm represents 50km, and the towns are 7.5 cm, the distance between both towns in real life will be:
[tex]\frac{15}{1\text{ }}\text{ }\ast\text{ 7.5 = }112.5\text{ km}[/tex]The distance between the two towns in real life will be 112.5 km
A county is planning to expand its train service. To better understand the current service, the county planner looked at which train stations are along or not along various train lines
Answers
Solution
(a)
5 stations are along the orange line
(b)
8 stations
A pyramid has a square base with sides of length s. The height of the pyramid is equal to of the length of a side on the base. Which formularepresents the volume of the pyramid?OA. V = ¹8³OB. V=¹8³OC. V=8³OD. V=35³OE V=65³
Answers
Given,
The measure of the length of the side of square is s.
The height of the pyramid is 1/2 of the length of the side.
Required
The volume of the square pyramid.
The formula for the volume of the square pyramid is,
[tex]Volume\text{ =}\frac{side\times side\times height}{3}[/tex]Substituting the values then,
[tex]\begin{gathered} Volume\text{ =}\frac{s\times s\times s}{3\times2} \\ =\frac{s^3}{6} \end{gathered}[/tex]Hence, the volume of the pyramid is s^3/6.
Sorry if its a bit blurry if u need I can tell you what it says.
Answers
Let x represent the length of the kite
Let t repesent the length of the tail of the kite
We were told that the tail of the kite is 1.5 feet plus twice the length of the kite. This means that
t = 1.5 + 2x
Together, the length of the kite and the tail are 15.5 feet long. It means that
x + t = 15.5
Substituting t = 1.5 + 2x into x + t = 15.5, it becomes
x + 1.5 + 2x = 15.5
x + 2x = 15.5 - 1.5
3x = 14
x = 14/3
x = 4 2/3
Substituting x = 14/3 into t = 1.5 + 2x, it becomes
t = 1.5 + 2 * 14/3
t = 1.5 + 28/3
t = 3/2 + 28/3
t = 65/6
t = 10 5/6
Length of kite is 4 2/3 feet
Length of tail is 10 5/6 feet
In 2010, the population of a city was 170,000. From 2010 to 2015, the population grew by 4.5%. From 2015 to 2020, it fell by 3.3%. To the nearest 100 people, what was the population in 2020?
Answers
Given a percentage of change we can calculate the final population by the end of a period with the following formula:
P = P0 + xP0
Where P is the final population, P0 is the initial population at the beginning of the period and x is the percentage of change, if the population grew x will be a positive value and if the population fell x will be a negative value.
For the period 2010 to 2015, the population was initially 170,000 and it grew by a 4.5%. Then by replacing 0.045 for x (4.5/100) and 170000 for P0, we get:
P2015 = 170000 + 0.045×170000 = 177650
From 2015 the population decay by 3.3%, then we can calculate the population by 2020 to get:
P2020 = 177650 + 177650×(-0.033) = 171787
Then, rounding to the nearest 100 people we get 171,800
At store A, oranges are $3.99 for 5 apples. At store B oranges are $20 for 7 apples which is the better deal?
Answers
Answer:
Store A
Explanation:
To know which is the best deal, we need to find the price per apple for each store, so we need to divide the price by the number of apples.
For store A:
[tex]\frac{\text{ \$3.99}}{5\text{ Apples}}=0.798\text{ per apple}[/tex]For Store B:
[tex]\frac{\text{ \$20}}{7\text{ Apples}}=2.85\text{ per apple}[/tex]So, the best deal is Store A because the price per apple is less than the price of Store B.
Use the diagram below, correctly identify the angle using the three CAPITAL letter designation.
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he following list contains the average annual total returns (in percentage points) for 9 mutual funds. The mutual funds appear in an online brokerage firm'sall-star" list.-9, 23, 12, 4, 11, 5, 36, 7, 31Send data to calculator(a) What is the mean of this data set? If your answer is not aninteger, round your answer to one decimal place.(b) What is the median of this data set? If your answer is notan integer, round your answer to one decimal place.(c) How many modes does the data set have, and what aretheir values? Indicate the number of modes by clicking in theappropriate circle, and then indicate the value(s) of themode(s), if applicable.00zero modesone mode:two modes: andX
Answers
Given
average annual total returns for 9 mutual funds.
-9, 23, 12, 4, 11, 5, 36, 7, 31
Find
a) Mean
b) Median
c) Mode
Explanation
a) Mean = sum of observations/ total number of observation
so ,
[tex]\begin{gathered} mean=\frac{-9+23+12+4+11+5+36+7+31}{9} \\ \\ mean=\frac{120}{9} \\ \\ mean=13.33333\approx13.3 \end{gathered}[/tex]to find median , we need to arrange in ascending order :
-9 , 4 , 5 , 7 , 11 , 12 , 23 , 31 , 37
there are 9 entries which is an odd number
so , median = (n+1/2)th term
[tex]\begin{gathered} \frac{9+1}{2} \\ \frac{10th}{2} \\ 5th \end{gathered}[/tex]so , median = 11
there is no mode because no term is repeating.
Final Answer
Hence ,
mean = 13.3
median = 11
mode - zero mode
2 2 3 4 5 Enter an estimate. Round each mixed number to the nearest whole in your estimate. -38 4 9 Estimate: Find the difference and enter it in simplest form. 3 60
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To make the estimate of the substraction of the mixed numbers we use the fraction that is accompaning the whole number. If the number is less than 1/2 we say that the number is closer to the whole number before the fraction, if it is 1/2 or more then we add one to the whole number.
For the first number
[tex]5\frac{1}{4}\approx5[/tex]This is approximate to 5 because 1/4 is less than 1/2
For the second number
[tex]3\frac{8}{9}\approx4[/tex]This is approximate to 4 because 8/9 is greater than 1/2.
ESTIMATE
[tex]\begin{gathered} 5\frac{1}{4}-3\frac{8}{9}=\text{?} \\ 5-4\approx1 \end{gathered}[/tex]To pass a mixed number into a fraction we use the following procedure
[tex]a\frac{b}{c}=\frac{(a\cdot c)+b}{c}[/tex]Pass both mixed numbers
[tex]\begin{gathered} 5\frac{1}{4}=\frac{(5\cdot4)+1}{4}=\frac{20+1}{4}=\frac{21}{4} \\ 3\frac{8}{9}=\frac{(3\cdot9)+8}{9}=\frac{27+8}{9}=\frac{35}{9} \end{gathered}[/tex]To find the exact value
[tex]\frac{21}{4}-\frac{35}{9}=\frac{21\cdot9-35\cdot4}{9\cdot4}=\frac{49}{36}[/tex]answer
The exact value of the substraction is
[tex]\frac{21}{4}-\frac{35}{9}=\frac{49}{36}=1\frac{13}{36}[/tex]Ronald was 1.5 times olderthan Megan. If Ronald was 27years old, how old is Megan?Write an equation to solve.
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Solution:
Let x represent Ronald's age, and y represent Megan's age.
Thus,
[tex]\begin{gathered} x\Rightarrow Ronald^{\prime}s\text{ age} \\ y\Rightarrow Megan^{\prime}s\text{ age} \end{gathered}[/tex]Given that Ronald was 1.5 times older than Megan, we have the equation to be represented
[tex]x=1.5y\text{ ---- equation 1}[/tex]If Ronald was 27 years old, we have
[tex]x=27[/tex]Substituting the value of 27 for x into equation 1, we have
[tex]\begin{gathered} 27=1.5y \\ solve\text{ for y by dividing both sides by the coefficient of y,} \\ \frac{27}{1.5}=\frac{1.5y}{1.5} \\ \Rightarrow y=18 \end{gathered}[/tex]This implies that Megan's age is
[tex]18\text{ years}[/tex]C Campus StudentCampus StudentGA-051 st AFJROTCGA-051 st AFJROTC5 New Tabebra_TC_Online LearningSubtracting with a Model3Subtract: 95 - 43Click or tap blocks to subtract them.032O 42O 52O 62
Answers
95 - 43= 52
9 5
- 4 3
______
5 2
____________
5-3 =2
9-4 = 5
______________
Answer
The third choice, 52