Correct the errors and fill in the blanks by completing the square.
Answer:
x = 2 - 5[tex]\sqrt{3}[/tex], x = 2 + 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
x² - 4x = 71
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 2)x + 4 = 71 + 4
(x - 2)² = 75 ( take the square root of both sides )
x - 2 = ± [tex]\sqrt{75}[/tex] = ± 5[tex]\sqrt{3}[/tex] ( add 2 to both sides )
x = 2 ± 5[tex]\sqrt{3}[/tex]
then
x = 2 - 5[tex]\sqrt{3}[/tex] , x = 2 + 5[tex]\sqrt{3}[/tex]
Lori ran 5/3 miles Monday, 15/4 miles Tuesday, 9/2 miles Wednesday,
3/5 on Thursday and 2/5 miles on Friday. What is the average number of miles
Lori ran per day this week?
Rochelle had an important swim meet coming up, so she made a schedule for herself for extra practice. She practiced for 609 minutes over a 3-week time span to get herself ready. She spent the same amount of time practicing each week. What is the constant of proportionality (k) between the number of minutes Rochelle practiced (m) and the number of weeks she spent practicing (w)?
Over the course of three weeks, she practiced for 609 minutes to become ready. The constant of proportionality is k=203.
Given that,
Rochelle planned out additional practice because she was getting ready for a big swim meet.
Over the course of three weeks, she practiced for 609 minutes to become ready. Every week she practiced for the same amount of time.
We have to find the constant of proportionality (k) between Rochelle's weekly practice time (w) and the number of minutes she practiced each week (m).
3 week =609 minutes
3w=609m
1w=609m/3
1w=203m
For 1 week she practiced 203 minutes.
Now,
Constant of proportionality is
m=kw
203=k(1)
k=203
Therefore, the constant of proportionality is k=203.
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Ian measures 9 kg of rice. One kilogram is approximately equal to 2.2 pounds. Which measurement represents the number of pounds of rice?
By using multiplication, we get that the number of pounds of rice will be 19.8 pounds.
We are given that:
1 kg of rice = 2.2 pounds of rice.
We need to find the number of pounds of rice in 9 kg of rice.
So, we will use the operation of multiplication to covert the units from kg into pounds.
So, we get that:
9 kg of rice = 2.2 × 9 pounds of rice
9 kg of rice = 19.8 pounds of rice.
Therefore, by using multiplication, we get that the number of pounds of rice will be 19.8 pounds.
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Write a numerical expression for 15 minus the sum of 6 and 7
Answer:
15-(6+7)
Step-by-step explanation:
Answer:
15 - (6+7)
Step-by-step explanation:
Analyze the diagram below and complete the instructions that follow.
Similar triangles are triangles which have the same corresponding angle measures and proportional side lengths. The value of x is 17.5.
What are similar Triangles?Similar triangles are triangles which have the same corresponding angle measures and proportional side lengths.
Let PQ be the line between RS and RT.
Now PQR and RST are similar triangles.
RT/RP=RS/RQ
14/8=x/10
Use cross multiplication
14(10)=8x
140=8x
Divide both sides by 8.
17.5=x
Therefore x is 17.5.
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Farmer Brown is making a garden 14 1/2 feet long and 8 3/4 feet wide. He puts up a fence 23 1/2 feet long and 17 3/4 feet wide. What is the distance from the fence to the edge of the garden?
The distance from the fence to the edge of the garden using the center as reference point is 4 1/2 feet.
Given data
garden 14 1/2 feet long and 8 3/4 feet wide
Fence 23 1/2 feet long and 17 3/4 feet wide
How to find the distance from the fence to the edge of the garden.We assume:
the fence has no thickness,
the distance considered is in the side of the length
the reference point for the distance is the center
Therefore:
Using the mid points we solve as follows:\
garden length / 2 - fence length / 2
= ( 23 1/2 ) / 2 - ( 14 1/2 ) / 2
= 11.75 - 7.25
= 4.5
= 4 1/2 feet
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7th-grade question
4. If a snail can move 3/10 of a meter every 1/12 hour, what is the speed of
the snail, in meters per hour?
A. 1/40
B. 5/18
C. 1 1/2
D. 18/5
Answer:
18/5 which also equals 3 3/5 would be the answer
Translate the figure 2 units legt and 4 units down. What are the coordinates of the image?
Answer:
[tex]A_{new}=(-3,0)\\B_{new}=(0,-1)\\C_{new}=(1,-4)\\D_{new}=(-3,-5)[/tex]
Step-by-step explanation:
Looking at the diagram, you can see and determine the following points, write them down:
A=(-1,4)
B=(2,3)
C=(3,0)
D=(-1,-1)
Translating 2 units left means x changes by (-2)
Translating 4 units down means y changes by (-4)
Old Point + Point Change = New Point
[tex]A_{old}+T=A_{new}\\A_{old}=(-1,4)\\T=Translation=(-2,-4)\\A_{old}+T=(-1,4)+(-2,-4) = A_{new}=(-3,0)[/tex]
[tex]B_{old}=(2,3)\\C_{old}=(3,0)\\D_{old}=(-1,-1)\\T=(-2,-4)\\B_{new}=(2,3)+(-2,-4)=(0,-1)\\C_{new}=(3,0)+(-2,-4)=(1,-4)\\D_{new}=(-1,-1)+(-2,-4)=(-3,-5)[/tex]
Please help me please In your own words
A line segment has two endpoints, whereas a ray has one endpoint and extends infinitely in the other direction, and a line extends infinitely in both directions.
A portfolio has a risk free rate of 3.5%, an expected return of 12.9%, and a sharpe ratio measure of 2.99. Find the standard deviation of the portfolio return.
The standard deviation of the portfolio return is 3.14%
What is Sharpe ratio?
Sharpe ratio measures the by extent to which the risk of an investment portfolio is compensated as it indicates the return per unit of risk inherent in the portfolio whereas the standard deviation measures the risk of expected return of the portfolio.
It should be noted that the Sharpe ratio can be determined as the expected return of the portfolio minus the risk-free rate of return divided by the standard deviation of the portfolio.
Sharpe ratio=(expected return-risk-free rate)/standard deviation
Sharpe=2.99
expected return=12.9%
risk-free rate=3.5%
standard deviation=unknown(assume it is x)
2.99=(12.9%-3.5%)/x
2.99*x=9.40%
x=9.40%/2.99
x=3.14%
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Find the distance between the pair of points, Use the distance formula.
Show your work.
(-12,20) and (-22,16)
Answer:
10.770
Step-by-step explanation:
You want the distance between points (-12,20) and (-22,16) using the distance formula.
Distance between pointsThe distance formula gives you the distance (d) between points (x1, y1) and (x2, y2).
d = √((x2 -x1)² +(y2 -y1)²)
For the given points, the distance is ...
d = √((-22-(-12))² +(16 -20)²) = √((-10)² +(-4)²) = √(100+16)
d = √116 = 2√29 ≈ 10.770330
The distance between the given points is about 10.77 units.
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The midpoint of AB is M(3, -1). If the coordinates of A are (5, 1), what are the
coordinates of B?
The coordinate of B is (1,-3)
In coordinate system mid point is the point which is exactly at the middle
The coordinates of point A are (5,1)
The coordinate of mid point M are (3,-1)
It is to be noted that mid point divides both sides in the ratio 1:1
We are required to find the coordinates of point B
Let the coordinates of B be (x,y)
For mid points, section formula further simplifies to
m's x coordinate= (a's x coordinate + b's x coordinate)/2
m's y coordinate = (a's y coordinate + b's y coordinate)/2
therefore,
3 = (5+x)/2
6=5+x
x=6-5 =1
-1 = (1+y)/2
-2 =1+y
y=-3
Hence the coordinates of B are (x,y) which is (1,-3)
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Answer this question please
Error: They failed to account for when x-5 is negative.
Solution:
[tex]|x-5|<20 \\ \\ -20<x-5<20 \\ \\ \boxed{-15<x<25}[/tex]
Is 14 a factor of 3,024
Answer:
Yes, 14 × 216 = 3024
Step-by-step explanation:
What is the area of a circle with a diameter of 10 inches?
a.
78.5 in2
c.
314 in2
b.
62.8 in2
d.
100 in2
Answer:
area is 3.14 r2
Step-by-step explanation:
here r = 5 inch
area = 3.14 × 25
so 78.5 in2
What is the solution set to the inequality m-7>-2(m+0.5)?
Select a ray. Move the point on the ray to the correct place on the number line.
The solution set to the inequality m-7>-2(m+0.5) is all real numbers greater than -0.75.
What is real numbers?Real numbers are the set of all rational and irrational numbers, which includes all positive and negative numbers, fractions, decimals, and integers. They are represented on the number line and are composed of an infinite amount of numbers between any two given numbers.
This can be represented graphically on a number line by selecting a ray starting at -0.75 and extending infinitely in the positive direction. The point on the ray at -0.75 represents the boundary between the solution set and the numbers not included in the solution set.
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Peter Sam and Ben run on a round track Peter takes hundred seconds Sam take 110 seconds and ben takes 120 seconds to run a round if they start together when will they meet again ?
Answer:
when one of them is done
Step-by-step explanation:
you can't meet together because you don't run fast the
Graph the image of the pre-image shown below, translated 4 units to the right, and 8 units down.
PLEAS ANSWER QUICK ASAP
The image of the transformation on the graph are (7, -7), (7, -2) and (-1, -14)
How to plot the graph of the function?The graph represents the given parameter
On the graph, we have the coordinates of the triangle to be
(3, 1), (3, 6) and (-5, -6)
The transformation rule is given as
Translated 4 units to the right, and 8 units down.
Mathematically, the transformation rule is given as
(x, y) = (x + 4, y - 8)
When the above transformation rule is applied to the coordinates of the triangle, we have
(3 + 4, 1 - 8), (3 + 4, 6 - 8) and (-5 + 4, -6 - 8)
Evaluate the sum and the difference
So, we have
(7, -7), (7, -2) and (-1, -14)
Next, we plot the image of the transformation on the graph
See attachment for the image of the transformation of the triangle on the graph
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Find the present value of a loan with a MONTHLY payment of $530.65 and an interest rate of 5.90% APR over 29 years, compounded MONTHLY.
Give your answer to 2 decimal places.
One person took a loan A monthly payment is $530.65. An interest rate is 5.90%. APR is over 29 years. The present value of a loan is 100.69.
Given that,
One person took a loan
A monthly payment is $530.65
An interest rate is 5.90%
APR is over 29 years.
We have to find the present value of a loan
The formula for present value of a loan is
The present value (PV) formula is used in finance to determine the present worth of money received in the future. The compound interest formula serves as the foundation for the present value formula (PV formula). The formula for compound interest is,
PV = [tex]\frac{FV}{(1+\frac{r}{n)} ^{nt}}[/tex]
Where,
PV=present value
FV=future value
r= rate of interest
n=When frequently the amount compounds
t=time
Given FV=$530.65
r= 5.90% =0.059
t=29 years
n=1(Due to the amount's annual compounding).
PV=[tex]\frac{530.65}{(1+\frac{0.059}{1})^{1\times29} }[/tex]
PV=[tex]\frac{530.65}{(1+0.059)^{29}}[/tex]
PV=[tex]\frac{530.65}{(1.059)^{29}}[/tex]
PV=[tex]\frac{530.65}{5.27}[/tex]
PV=100.69
Therefore, The present value of a loan is 100.69.
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The mass of the Earth is about 6,000,000,000,000,000,000,000,000 kg. The mass of a human toddler's brain is about 400 grams. SHOW ALL WORK
(a) What is the mass of the Earth written in scientific notation?
(b) What is the mass of a toddler’s brain in scientific notation?
(c) In comparing the measurements in Parts (a) and (b), what else must be done before a comparison is made?
(A) = 6 x 10^24
(B) = 4 x 10^2
(C) but i need help on C cause I think you have to combine the kg and grams but I dont know how
Step-by-step explanation:
that's why it is so important to always write also the units a number represent.
and for a fully nice scientific notation you write also at least 1 digit after the decimal point.
(a) 6.0 × 10²⁴ kg
(b) 4.0 × 10² g
now,
1 kg = 1000 g ("kilo" means 1000)
so, in order to be able to compare the 2 numbers, you have to bring both numbers to the same unit. either both to kg or both to g.
6.0 × 10²⁴ kg = 6.0 × 10²⁴ × 1000 g = 6.0 × 10²⁷ g
or
4.0 × 10² g = 4.0 × 10² / 1000 kg = 4.0 × 10^-1 kg
once you have both showing the same unit, you can truly compare them.
Write a number in which the value of the 3 is ten times greater than the value of the 3 in 135,864
A number in which value of 3 is ten times greater than the value of 3 is 375,786.
Here,
We have to find a number in which the value of the 3 is ten times greater than the value of the 3 in 135,864.
What is Place value?
Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.
Now,
The value of 3 in 135,864 is 30,000.
And, We want to write a number that is ten times greater than 30,000.
Hence, We have to write any other number in which the value of 3 is 300,000.
Since, There are infinitely many numbers that we can write.
Some numbers are:
375,786
2,345,576
9,387,988 ........ and so on.
Therefore, A number in which value of 3 is ten times greater than the value of 3 is 375,786.
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A scientist mixes water (containing no salt) with a solution that contains 35% salt. She wants to obtain 210 ounces of a mixture that is 15% salt. How many ounces of water and how many ounces of the 35% salt solution should she use?
The scientist should use 90 ounces of 35 percent solution and 120 ounces of water.
Percent is defined as the amount for a hundred units. Percentage is calculated by dividing the given amount by the total amount and multiplying by 100.
Let the scientist uses x ounces water.
Therefore the 35 percent solution is 210 - x.
Therefore the amount of salt in the 35 percent solution is 0.35 (210 - x )
The resulting mixture contains 15 percent salt.
Amount of salt = 15% of 210 =0.15 × 210 = 31.5 ounces.
Now 31.5 = 0.35 ( 210 - x )
or, 90 = 210 - x
or, x = 120 ounces
Therefore the 35 percent solution needed = 210 - 120 =90 ounces
Hence the scientist should use 90 ounces of 35 percent solution and 120 ounces of water.
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A line segment has the endpoints V(7, 2) and W(3, 10). Find the coordinates of its midpoint M.
The coordinates of the midpoint M of the line segment VW are M = (5, 6)
In this question,
We have been given a line segment having endpoints V(7, 2) and W(3, 10)
We need to find the coordinates of the midpoint M of the line segment VW.
We know that the midpoint of points (x1, y1) and (x2, y2) is
M = (x1 + x2 / 2, y1 + y2 / 2)
Using midpoint formula,
M = ((7 + 3) / 2, (2 + 10) / 2)
M = (10/2, 12/2)
M = (5, 6)
Therefore, the coordinates of the midpoint M of the line segment VW are M = (5, 6)
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1. Given the following set of values, what two numbers would you subtract to find the interquartile range?
17 21 19 23 16
22 19 20 24 18
22 minus 18
22 minus 16
O24 minus 16
24 minus 19
The two numbers that you would subtract to find the interquartile range (IQR) of the set of values are: A. 22 - 18.
What is the Interquartile Range of a Data Set?The interquartile range (IQR) = Upper quartile (Q3) = lower quartile (Q1).
Given the data set, 17, 21, 19, 23, 16, 22, 19, 20, 24, 18, we have the following:
Upper quartile (Q3): 22 (center of the second half of the data)
Lower quartile (Q1): 18 (the middle/center of the first part of the data)
Interquartile range (IQR) = 22 - 18
Interquartile range (IQR) = 4
Therefore, the two numbers that you would subtract to find the interquartile range (IQR) of the set of values are: A. 22 - 18.
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Which set of ordered pairs does not represent a function?
OA) { (-2,5), (-4,6), (1,2), (6,5)}
O B) { (-7,-5), (-9,4), (9,4), (1,-6)}
O c) { (5,-6),(5,9),(0,3), (-7,-9)}
D) {(5,2), (-1,-1), (-8,-1), (-7,1)}
Answer:
Answer for this question is C because, 1 input has 2 outputs. And that's why C doesn't represent a function.
The area of a rectangular wall of a barn is 119 square feet. its length is 10 feet longer than the width find the length and the width. Find the length and width of wall of the barn
The length of the rectangular wall of a barn is 7 and the width is 17 feet
Area of the rectangular wall of a barn = 119 square feet
Length of the wall of the barn = width of barn + 10 feet
Let the width of the wall of the barn be x feet
So, the length of the wall of the barn will be x + 10 feet
The area of the rectangular wall of the barn is given by:
Area of the rectangular wall of the barn = Length of the barn * Width of the barn
119 = x*(x+10)
119 = x^2 +10x
0 = x^2 +10x - 119
Using splitting the middle term method
0 = x^2 + 17x - 7x - 119
0 = x(x + 17) - 7(x + 17)
x = 17 or 7.
Since the width is 10 feet more than the length
Therefore, the length of the rectangular wall of a barn is 7 and the width is 17 feet
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Mercury is 5.8 x 10^7 km from the sun. Neptune is 4.5 x 10^10 km from the sun. How much further is Neptune from the sun than Mercury?
Divide the distances: (4.5 x 10^10)/(5.8 x 10^7)-.76 x 10^3=7.6 x 10^2
Subtract the distances by getting the same power of 10: (4.5 x 10^10) - (5.8 x 10^7)-(4.5 x 10^10)-(.0058 x 10^10) = 44.99 x 10/10km
Add the distances together: (5.8 x 10^7) 4.5 x 10^10) - 10.3 x 10^17-1.03 x 10^18km
Multiply the distances: (5.8 x 10^7) x (4.5 x 10^10) = (5.8 x 4.5) x (10^17)-26.1 x 10^17-2.61 x 10^16
The distance of Neptune from the sun than Mercury will be B. Subtract the distances by getting the same power of 10: (4.5 x 10^10) - (5.8 x 10^7)-(4.5 x 10^10)-(.0058 x 10^10) = 44.99 x 10/10km.
How to calculate the value?From the information, Mercury is 5.8 x 10^7 km from the sun and Neptune is 4.5 x 10^10 km from the sun.
It should be noted that since we want to find the difference, therefore, we've to subtract.
Therefore, distance of Neptune from the sun than Mercury will be Subtract the distances by getting the same power of 10: (4.5 x 10^10) - (5.8 x 10^7)-(4.5 x 10^10)-(.0058 x 10^10) = 44.99 x 10/10km.
In conclusion, the correct option is B.
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Standard form of y=(X+3)^2-10
At 6 AM the temperature was -6 Fahrenheit between 6 AM and 3 PM. The temperature‘s rose 11° between 3 PM and midnight the temperatures fell 7° write a number sentence that shows how to find the temperature at midnight then write the midnight temperature.
The number sentence is 5 - 7 and temperature at midnight is equal to -2°F .
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.
The temperatures are given at different time of a day. It is given that the final temperature was the temperature that existed at midnight. Firstly temperature rise between 6 AM and 3PM by 11° from - 6 °F at 6 AM and then between 3PM and midnight it fell by 7°.
So , we can show these variations as follows :
At 6AM temperature = - 6 °F
Between 6AM and 3 PM temperature rose by 11° , so temperature at 3 PM will be :
= - 6 + 11
= 5 °F
Between 3PM and midnight the temperature fell by 7° , so the number sentence will be :
= 5 - 7
And the temperature at midnight will be :
= -2°F
Therefore , the number sentence is 5 - 7 and temperature at midnight is equal to -2°F .
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