Answers
Answer:
x = 8 ± \(\sqrt{10}\)
Step-by-step explanation:
x² - 16x + 54 = 0 ( subtract 54 from both sides )
x² - 16x = - 54
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 8)x + 64 = - 54 + 64
(x - 8)² = 10 ( take the square root of both sides )
x - 8 = ± \(\sqrt{10}\) ( add 8 to both sides )
x = 8 ± \(\sqrt{10}\)
then
x = 8 - \(\sqrt{10}\) , x = 8 + \(\sqrt{10}\)
Related Questions
Which inequality matches the graph?
Answers
Answer:
B) x ≥ 3
Step-by-step explanation:
The circle is shaded which indicates that the inequality is equal to. The circle is on -3 and extends towards numbers that are greater than -3. Thus, all numbers are can be equal to or greater than -3.
Which expression is equal to:
³ × ³ × ³ × ³ × ³ × ³ × ² × ³ ×
3
X
4
3
4
Answers
3 x 3 x 3 x 3 x 3 x 3 x 2 x 3 x 3 x 434 = 5,694,948
I need help and fast
Answers
Answer:
I believe it's 7 cups.
Step-by-step explanation:
I did 3/2 times 4 + 1/4 times 4 which gave me 7.
Please let me know if this works for you. Double check first.
Another way you could do this is by adding both fractions 3/2 + 1/4
to get 7/4 and multiply 7/4 by 4. so, 3/2 + 1/4= 7/4 7/4 x 4 = 7
How to find derivative of x^5(1- (5/x+8))
Answers
Answer:
\(5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)
Step-by-step explanation:
\(f(x)=x^5\\f'(x)=5x^4\\g(x)=1-\frac{5}{x+8}\\g'(x)=\frac{5}{(x+8)^2}\\\\\frac{d}{dx}f(x)g(x)\\\\=f'(x)g(x)+f(x)g'(x)\\\\=5x^4(1-\frac{5}{x+8})+x^5(\frac{5}{(x+8)^2})\\\\=5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)
Arianna is packing scented candles and candle holders into gift boxes. She has 84 candles and 48 holders, and each box must contain both items. She puts the same number of candles in each box, and the same number of holders in each box. What is the maximum number of gift boxes Arianna can pack, and how many scented candles and candle holders will each box have?
A.
4 boxes; 21 scented candles and 12 candle holders
B.
6 boxes; 14 scented candles and 8 candle holders
C.
12 boxes; 7 scented candles and 4 candle holders
D.
24 boxes; 3 scented candles and 2 candle holders
Answers
The answer is A
Hope this helps!
Natalie invests $2,000 into a savings account
which earns 11% per year. In 20 years, how
much will Natalie's investment be worth if
interest is compounded monthly? Round to the
nearest dollar.
Answers
Answer:
We can use the formula for compound interest to find the future value (FV) of Natalie's investment:
FV = P * (1 + r/n)^(n*t)
Where:
P is the principal amount (the initial investment), which is $2,000 in this case
r is the annual interest rate as a decimal, which is 11% or 0.11
n is the number of times the interest is compounded per year, which is 12 since interest is compounded monthly
t is the number of years, which is 20
Substituting the values into the formula, we get:
FV =
2
,
000
∗
(
1
+
0.11
/
12
)
(
12
∗
20
)
�
�
=
2,000 * (1.00917)^240
FV = $18,255.74
Therefore, after 20 years of compounded monthly interest at a rate of 11%, Natalie's investment of 2,000 will be worth approximately 18,256.
Answer:
$17,870
Step-by-step explanation:
You must use the formula for compound interest.
A = P(1 + r/n)^nt
I suggest you look it up at some point so that you can do these more easily in the future!
Suppose a population contains 20,000 people. All else being equal, a study
based on a population sample that includes which of the following numbers
of respondents would be the most reliable?
A. 200
OB. 20
C. 2000
D. 2
Answers
A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.
In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.
A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.
Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.
Option A: 200 respondents
This represents only 1% of the population.
While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.
Option B: 20 respondents
This represents only 0.1% of the population.
With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.
Option C: 2000 respondents
This represents 10% of the population.
While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.
The study may provide reasonably reliable results, but there is room for potential sampling error.
Option D: 2 respondents
This represents an extremely small sample size, accounting for only 0.01% of the population.
With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.
Based on the options provided, option C with 2000 respondents would be the most reliable study.
Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.
However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.
For similar question on population sample.
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3,947 ÷ 45 = (?) R (?)
Answers
Answer:
87.7(1)
=
87 Remainder 32
Write the ratio as a fraction in the simplest form 26.1miles : 3.6hours
Answers
Answer:36 hours
Step-by-step explanation:
A school district can send a representative to the state spelling bee for every 50 students in the school district that year. There are 5 schools woth a b c d e students respectively. Write an algebraic expression to show how many representatives r, the students will have in any year?
Answers
An algebraic expression to show representatives r, the students will have in any year is r=(a+b+c+d+e)/50.
What is Expression?An expression is combination of variables, numbers and operators.
Given, that school district can send a representative to the state spelling bee for every 50 students in the school district that year.
There are 5 schools woth a b c d e students respectively.
We need to find the algebraic expression to show how many representatives r, the students will have in any year.
r=(a+b+c+d+e)/50
THe above expression is used to represent the representives.
Hence, (a+b+c+d+e)/50 is an algebraic expression to show representatives r, the students will have in any year
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Solve for the value of X in the parallelogram below. X = _____
Answers
Answer:
One of the properties of parallelograms is that opposite sides are congruent.
Step-by-step explanation:
Answer:
x is equal to 1 and y is equal to 2
I made a fort by connecting two boxes.
The first box is 555 meters long, 999 meters wide, and 999 meters high.
The second box is 333 meters long, 888 meters wide, and 222 meters high.
How many cubic meters of space does my fort have?
Answers
Answer:
453m^3
Step-by-step explanation:
The cubic meters of space does the gorilla have to play in her fort is equal to adds the volume of the first box and the volume of the second box.
The volume of the box is equal to: V = LWH
Find the volume of the first box:
V1 = 5x9x9 = 405m^3
Find the volume of the second box:
V2 = 3x8x2 = 48m^3
Add V1 and V2:
405m^3 + 48m^3 = 453m^3
On a television game show, contestants earn 5 points for each correct answer, but lose 2 points for each wrong answer. On last week's show, the winning contestant earned 80 points and answered 30 questions. Given that x represents the number of questions answered correctly, and y represents the number of questions answered incorrectly, determine which system of equations correctly represents this situation.
Answers
Answer:
5x-2y =80
x+y=30
Step-by-step explanation:
Basically, 5x is the points earned by correct questions (5 points per right answer) and -2x is the points lost by wrong answers (2 points taken away for every wrong answer). The total points the contestant earned is 80, which is why we set this equation equal to 80. Hence, 5x-2y=80.
They also tell us that the contestant answered a total of 30 questions, so x and y combined would be the total number of questions. Hence, x+y=30.
Answer:
5x-2y =80
x+y=30
Step-by-step explanation:
This situation can be represented by a system of two linear equations, with one equation representing the number of points earned and one equation representing the number of questions answered.
First, determine the equation representing the number of points earned.
Since contestants earn 5 points for every correct answer and x is the number of questions answered correctly, 5x represents the amount of points earned from correct responses. Since contestants lose 2 points for every incorrect answer and y is the number of questions answered incorrectly, 2y represents the amount of points lost from incorrect responses.
The amount of points earned minus the amount of points lost yields the total number of points at the end of the game, 80.
Next, determine the equation representing the number of questions answered.
Since x represents the number of questions answered correctly and y represents the number of questions answered incorrectly, the sum of these values equals the total number of questions, 30.
Together, these two equations create the system that can be used to determine the number of questions answered correctly and the number of questions answered incorrectly by the contestant in this situation.
Suppose MarketOne is a marketing company that has small businesses for clients. MarketOne charges an upfront cost of $350 for new clients and an additional $195 per month to run and maintain the client's website. A linear equation could be used to relate the total cost, in dollars, of MarketOne's services and the number of months that the client's website is running. Which solution is viable for this situation? For full points, write the equation and show your work.
Answers
C = 195m + 350
where the constant term of 350 represents the upfront cost and the coefficient of 195 represents the monthly cost.
To check if this equation is viable for the situation, we can use some reasonable values for the number of months and see if the resulting costs make sense.
For example, if the client's website is running for 6 months, the total cost would be:
C = 195(6) + 350
C = 1,170 + 350
C = 1,520
This means that the client would pay $1,520 in total for 6 months of service from MarketOne.
Similarly, if the client's website is running for 12 months, the total cost would be:
C = 195(12) + 350
C = 2,340 + 350
C = 2,690
This means that the client would pay $2,690 in total for 12 months of service from MarketOne.
Based on these calculations, we can see that the linear equation is viable for the situation. The equation allows us to calculate the total cost of MarketOne's services based on the number of months the client's website is running, which is a useful tool for budgeting and planning.
Find the equation of a line parallel to y=x−1 that contains the point (−3,−2). Write the equation in slope-intercept form.
Answers
Answer:
y = x + 1
Step-by-step explanation:
Parallel lines have same slope.
y = x - 1
Compare with the equation of line in slope y-intercept form: y = mx +b
Here, m is the slope and b is the y-intercept.
m =1
Now, the equation is,
y = x + b
The required line passes through (-3 ,-2). Substitute in the above equation and find y-intercept,
-2 = -3 + b
-2 + 3 = b
\(\boxed{b= 1}\)
Equation of line in slope-intercept form:
\(\boxed{\bf y = x + 1}\)
The equation is :
↬ y = x + 1Solution:
We KnowIf two lines are parallel to each other, then their slopes are equal. The slope of y = x - 1 is 1. Hence, the slope of the line that is parallel to that line is 1.
We shouldn't forget about a point on the line : (-3, -2).
I plug that into a point-slope which is :
\(\sf{y-y_1=m(x-x_1)}\)
Slope is 1 so
\(\sf{y-y_1=1(x-x_1)}\)
Simplify
\(\sf{y-y_1=x-x_1}\)
Now I plug in the other numbers.
-3 and -2 are x and y, respectively.
\(\sf{y-(-2)=x-(-3)}\)
Simplify
\(\sf{y+2=x+3}\)
We're almost there, the objective is to have an equation in y = mx + b form.
So now I subtract 2 from each side
\(\sf{y=x+1}\)
Hence, the equation is y = x + 1Simplify (2.6 x 10-6) + (3.2 x 10-2) (1.94 x 10-4) write answer in scientific notation
Answers
Answer:
\(8.808 \times 10^{-6}\)
Step-by-step explanation:
Given expression:
\((2.6 \times 10^{-6})+(3.2 \times 10^{-2})(1.94 \times 10^{-4})\)
The grouping of numbers by parentheses in a different way does not affect their product. Also, changing the order or position of the product of two numbers does not change the end result.
\(\implies (2.6 \times 10^{-6})+(3.2 \times 1.94 \times 10^{-2} \times 10^{-4})\)
Multiply the numbers 3.2 and 1.94:
\(\implies (2.6 \times 10^{-6})+(6.208\times 10^{-2} \times 10^{-4})\)
\(\textsf{Apply the exponent rule} \quad a^b \cdot a^c=a^{b+c}:\)
\(\implies (2.6 \times 10^{-6})+(6.208\times 10^{-2-4})\)
\(\implies (2.6 \times 10^{-6})+(6.208\times 10^{-6})\)
Factor out the common term 10⁻⁶:
\(\implies 10^{-6}(2.6+6.208)\)
Add the numbers 2.6 and 6.208:
\(\implies 10^{-6}(8.808)\)
\(\implies 8.808 \times 10^{-6}\)
Scientific notation is written in the form a × 10ⁿ , where 1 ≤ a < 10 and n is any positive or negative whole number. Therefore, the final answer is in scientific notation.
In a town of 117 000 people, 14000 like to
Watch hockey. What percent of the town's
Populations like to watch hockey?
Answers
Divide number that like hockey by population then multiply by 100:
14,000 / 117,000 = 0.11965
0.11965 x 100 = 11.965%
Round up to 12%
Raymond wanted to buy 8 t-shirt but he was short of $8.10. instead he bought 5 T-shirt and had $12.60 left. how much would he need to pay for 20 t-shirt?
Answers
Answer:
$138
Step-by-step explanation:
Let the money with Raymond be $y
Let the cost of 1 tshirt be $x
then cost of 8 tshirt = cost of 1 t-shirt*8 = 8x
Raymond wanted to buy 8 t-shirt but he was short of $8.10
It means that 8x is equal to money he had plus $8.10
thus,
y + 8.10 = 8x
y = 8x - 8.10
Next situation
cost of 5 t-shirt = 5x
. instead he bought 5 T-shirt and had $12.60 left,
it means cost of 5 T-shirt plus $12.60 = total money Raymond had
y = 5x + 12.60
comparing y in both the equation
y = 8x - 8.10 and y = 8x - 8.10
5x + 12.60 = 8x - 8.10
=> 8x-5x = 12.60+8.10
=> 3x = 20.70
=> x = 20.70/3 = 6.9
Thus, cost of 1 T-shirt = $6.9
cost of 20 T-shirt = 20*$6.9 = $138 (Answer)
Please help thank you if you do!!
Answers
9514 1404 393
Answer:
1 1/5 hours walking to 1 hour jogging
Step-by-step explanation:
You can multiply by 3 to eliminate the fraction, then reduce in the usual way.
4 ÷ (3 1/3)
= 12 ÷ 10 . . . . . . . multiply both numbers by 3
= 1 2/10 = 1 1/5 . . . . do the division by 10
A rectangular box has dimensions 2ft by 4ft by 3ft. Increasing each dimension of the box by the same amount yields a new box with a volume four times the old. Use the ALEKS graphing calculator to find how much each dimension of the original box was increased to create the new box. Round your answer to two decimal places.
Answers
The increase in the dimensions of the new rectangular box is given by the equation x = 1.65 feet
What is the Volume of a Rectangle?The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
Let the dimensions of the rectangle A be 2ft x 4ft x 3 ft
So , the length of the rectangle L = 2 feet
The width of the rectangle W = 4 feet
The height of the rectangle H = 3 feet
Now , the volume of rectangle = Length x Width x Height
Substituting the values in the equation , we get
Volume of rectangle A = 2 x 4 x 3 = 24 feet³
And , let the increase in dimensions be represented as x
So , the length of the rectangle B = ( 2 + x )
The width of the rectangle B = ( 4 + x )
The height of the rectangle B = ( 3 + x )
Volume of rectangle B = ( 2 + x ) ( 4 + x ) ( 3 + x )
On simplifying the equation , we get
Volume of rectangle B = x³ + 9x² + 26x + 24
And , volume of rectangle B = 4 ( volume of rectangle A )
So , x³ + 9x² + 26x + 24 = 4 ( 24 )
x³ + 9x² + 26x + 24 = 96
Subtracting 96 on both sides of the equation , we get
x³ + 9x² + 26x + -72 = 0 be equation (1)
So , the value of x from ALEKS graphing calculator is 1.65
Hence , the increase in dimensions of the rectangle is 1.65 feet
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The vertices of triangle ABC are given: A (0;-1) B(12; -10) C(10;4)
Find:
a) the equation of the median and bisector drawn from vertex A;
b) the equation of the altitude from vertex B;
c) the point of intersection of the median and height;
d) the coordinates of the center of mass (the point of intersection of the medians).
Answers
verified
Verified by Toppr
Median bisects the line.
D≡(
2
−3+5
,
2
−9−8
)≡(1,
2
−17
)
E≡(−
2
1+5
,
2
6−8
)≡(2,−1)
F≡(−
2
1−3
,
2
6−9
)≡(−2,
2
−3
)
∴ equation of AD:(y−y
1
)=(
x
2
−x
1
y
2
−y
1
)
AD
(x−x
1
)
⇒(y−6)=
⎝
⎜
⎜
⎛
1+1
2
−17
−6
⎠
⎟
⎟
⎞
(x+1)⇒(y−6)=−
4
29
(x+1)
⇒
4
29
x+y−6+
4
29
=0
AD⇒29x+4y+5=0
equation of BE:(y+9)=(−
2+3
1+9
)
BE
(x+3)
⇒(y+9)=
5
8
(x+3)⇒5y+45=8x+24
BE⇒8x−5y−21=0
Equation of CF:(y+8)=
⎝
⎜
⎜
⎛
−2−5
−
2
3
+8
⎠
⎟
⎟
⎞
CF
(x−5)
⇒(y+8)=−
14
13
(x−5)⇒14y+112=−13x+65
CF:13x+14y+47=0
Calvin estimated he would need 8 hours to
complete his science project. It actually took
him 12 1/2 hours to get everything done. What
was his percent error?
Answers
Answer:45%
Step-by-step explanation:
Hope this helps.
I’m not really good at percentages but I’m sorry I couldn’t give you the full answer. You got this though! <3
Which is the graph of the linear inequality 2x - 3y < 12?
Answers
At the office supply store, a ream of paper costs $5.89 and a cartridge of ink costs $38.40. Delilah needs to buy 8 reams of paper and 6 cartridges of ink for her office. She needs to know how much money to bring, so estimate the cost of these supplies.
Answers
Answer:
Step-by-step explanation:
Delilah needs to buy 8 reams of paper which cost $5.89 each, $5.89 x 8 = $47.12
Delilah needs to buy 6 cartridges of ink which cost $38.40 each, $38.40 x 6 = $230.4
We then add $230.4 and $47.12
$230.4 + $47.12 = $277.52.
Delilah needs to bring $277.52 to cover the cost of her supplies.
What is the value of the expression “two less than six times the difference of a number and five” when n = 9?
22
16
32
31
Answers
Answer:
the answer is 22
Answer: 22
Step-by-step explanation:
This is the answer because if you work backwards then number minus five is actually 9-5, so you're left with 4. And then you need to do 6 times he difference of 9-5, which is 4. So, 6 X 4 would equal 24. And then you need to do 2 less than that answer. So 24-2 would equal 22.
find the product in lowest terms 24/18x2/17x34/3
Answers
Answer:
Step-by-step explanation:
To find the product of the given fractions in lowest terms, we can multiply the numerators and denominators together, and then simplify the resulting fraction:
(24/18) * (2/17) * (34/3)
First, we can simplify the fractions by reducing any common factors in the numerators and denominators:
24/18 = (212)/(29) = 12/9 = 4/3
2/17 = 2/17
34/3 = (2*17)/3 = 34/3
Now we can multiply the simplified fractions:
(4/3) * (2/17) * (34/3) = (4234)/(3173) = 272/153
The product of the given fractions in lowest terms is 272/153.
please help me please really need help please
Answers
Answer:
x=0
Step-by-step explanation:
What is 5÷40= and what's the math problem look like when you work it out on paper
Answers
Answer:
.125
Step-by-step explanation:
40÷5
0
40÷5
0
40÷5
0
0
40÷5
- 0
5
remainder 5
HELP ME PLEASEEEEEEEEEEEE
Answers
have a nice day
Question 2 of 10
How many solutions does the system of equations below have?
y=3x+4
y+6= 3x
OA. Exactly 1 solution
B. No solution
OC. More than 1 solution
OD. At least 1 solution
SUBMIT
Answers
Answer:
B, No solution
Step-by-step explanation:
If two lines are graphed, the point they intersect is the solution. However, if the slope is the same, they will never intersect
In the first and second equation, the slopes are both 3 so they will never intersect.