Answer:
The equation that would be used for the zero product property on will be (x-5)(x-10)=0
Option B is correct.
Step-by-step explanation:
We need to solve the equation [tex]\frac{1}{(x-4)}+1=\frac{14}{x+2}[/tex]
Solving the equation:
[tex]\frac{1}{(x-4)}+1=\frac{14}{x+2}\\\frac{1+(x-4)}{x-4}= \frac{14}{x+2}\\\frac{1+x-4}{x-4}= \frac{14}{x+2}\\\frac{x-3}{x-4}= \frac{14}{x+2}\\Cross\: Multiply\\(x-3)(x+2)=14(x-4)\\x(x+2)-3(x+2)=14x-56\\x^2+2x-3x-6=14x-56\\x^2-x-6-14x+56=0\\x^2-x-14x-6+50=0\\x^2-15x+50=0[/tex]
Now, we would factorise to find value of x
[tex]x^2-15x+50=0\\x^2-5x-10x+50=0\\x(x-5)-10(x-5)=0\\(x-5)(x-10)=0[/tex]
So, the equation that would be used for the zero product property on will be (x-5)(x-10)=0
Option B is correct.
Answer:
So, the equation that would be used for the zero product property on will be (x-5)(x-10)=0
Option B is correct.
Step-by-step explanation:
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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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:
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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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.
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.
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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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
Watch help video
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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Math homework due in 30 min
The missing values are x = 45, t = 90, n = 60, p = 75, m = 30, s = 15, k = 135, w = 30, f = 60 and y = 45.
How to determine the values of the missing angles
Herein we have a geometrical system formed by six triangles, one of them is a equilateral triangle and other one is a right triangle. By geometry we know that the sum of the measures of a triangle is equal to 180°, the angles in a equilateral triangle have the same measure and one of the angles in a right triangle is a right angle.
Then, we have following system of linear equations:
t = 90 (1)
t + 2 · x = 180 (2)
3 · n = 180 (3)
2 · p + m = 180 (4)
p + f + y = 180 (5)
(t + 5) + w + n = 180 (6)
s + k + m = 180 (7)
x + n + p = 180 (8)
f + w = 90 (9)
m + n = 90 (10)
p + s = 90 (11)
By (1) and (2):
x = 45
By (3):
n = 60
By (8):
p = 180 - 45 - 60
p = 75
By (4):
m = 180 - 2 · 75
m = 30
By (11):
s = 90 - 75
s = 15
By (7):
k = 180 - 15 - 30
k = 135
By (6) and (1):
w = 180 - 60 - 90
w = 30
By (9):
f = 90 - 30
f = 60
By (5):
y = 180 - 75 - 60
y = 45
The missing values are x = 45, t = 90, n = 60, p = 75, m = 30, s = 15, k = 135, w = 30, f = 60 and y = 45.
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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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SOMEBODY HELP WITH THIS PLEASE
To find the average height over each coaster, we must first add the height of each one together
109+135+115+365+126 = 850
Now divide 850 by the total amount of coasters, 5
850
------- = 170 Feet
5
Since the amusement park claimed their average height was 170 ft, it is not misleading. It is a good strategy because it is an honest statistic, which gives the amusement park more liability.
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
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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V
The length of a rectangle is six times its width.
If the area of the rectangle is 600 ft², find its perimeter.
Answer:
140
Step-by-step explanation:
→ Find an expression for the area
6x × x = 6x²
→ Equate to area
6x² = 600
→ Solve
x = 10
→ Find length and width
Length = 60 and width = 10
→ Find perimeter
60 + 60 + 10 + 10 = 140
Step-by-step explanation:
you can ask questions for clarification
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]
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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I am confused on how → 0 to $9875 at 10% = 987.50
and,
→ $9876 to $29600 at 12% = 2,367.00 was figured out? I never done my own taxes before! I got the first step down, but can someone please explain this to me
Answer:
$2367
Step-by-step explanation:
You want to know how to figure the 12% tax due on the amount that falls in the bracket $9876 to 29600.
ApplicationTax tables are often written in a somewhat misleading way. This one seems to tell you
0 to 9875 . . . . 10% tax rate
9876 to 29600 (and up to 40,125) . . . . 12% tax rate
What this means is that every dollar between (and including) the 9876th dollar and the 29600th dollar will have a $0.12 tax applied. It is figured by subtracting 9875 from the amount that falls in this bracket, and multiplying that difference by 12%.
(29600 - 9875) × 12%
= 19725 × 0.12
= 2367 . . . . . . . . tax due on the amount in the 9876 to 29600 bracket
Tax due
If your taxable amount is $29,600, the total tax due is ...
(amount in first bracket) × 10% + (amount in second bracket) × 12%
= 9875 × 0.10 + (29600 -9875) × 0.12
= 987.50 +2367.00
= $3,354.50 . . . . . . . . . . . total due on $29,600
__
Additional comment
It can be easier to write a new tax table that simplifies the computation. For taxable amounts up to $40,125, this table can be simplified to ...
10% . . . . for taxable income at or below $9,875.(12% of income) - $197.50 . . . . for taxable income at or below $40,125Using this last entry for $29,600, we find the total tax due to be ...
$29,600 × 0.12 - 197.50
= $3,552.00 -197.50
= $3,354.50 . . . . . . . same as above.
The amount $197.50 is (12% -10%)×9875.
Along the same lines, the rest of the tax table can be simplified to ...
(22% of income) - $4,210.00(24% of income) - $5,920.50(32% of income) - $18,984.50(35% of income) - $25,205.00(37% of income) - $35,573.00It turns out that the tax due is the maximum of the values computed using these equations. (You don't actually have to know what bracket applies to your income. Knowing the bracket does simplify the process by choosing the applicable formula.)
Note that this is a tax table for 2020. The rates for 2021 are different.
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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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]
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]
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 company makes pens. They sell each pen for $9.
Their revenue is represented by R = 9 x.
The cost to make the pens is $3 each with a one time start up cost of $6000.
Their cost is represented by C = 3 x + 6000.
a) Find the profit, P, (P = R - C) when the company sells 1000 pens.
0
9000
-9000
15000
-3000
b) Find the number of pens they need to sell to break even (when R = C).
667
1000
1100
2000
Answer:
a) 0
b) 1000
Step-by-step explanation:
revenue = R = 9x
cost = C = 3x + 6000
profit = P = R - C
(a)
P = R - C
P = 9x - (3x + 6000)
P = 9x - 3x - 6000
P = 6x - 6000
For 1000 pens, x = 1000.
P = 6(1000) - 6000
P = 6000 - 6000
P = 0
Answer: 0
(b)
R = C
9x = 3x + 6000
6x = 6000
x = 6000/6
x = 1000
Answer: 1000
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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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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Standard form of y=(X+3)^2-10
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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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.
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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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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