The addition symbol (+) can be used in between the two parentheses to show that you will be using the distributive property.
Distributive property:
The distributive property states that multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.
It can be written as,
a x (b + c) = (a x b) + (a x c)
Where a, b and c are the values of the variables.
Given,
Here we have the expression:
8 x 57 = (8 x 50) _____(8x7)
Here we need to find the symbol that can be used in between the two parentheses to show that it will be using the distributive property.
Based on the definition of the distributive property we have know that the symbol (+) can be used to make this one as distributive property used equation.
Therefore, the expression is written as,
8 x 57 = (8 x 50) + (8x7)
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A landscaper mows lawns for at least 3 hours but not more than 6 hours. the landscaper can mow 44,000 ft2 per hour. the function f(t)=44,000t represents the number of square feet the landscaper can mow in t hours. what is the practical range of the function?
Answer: [tex]132000 \le f(t) \le 264000[/tex]
Explanation:
The domain is [tex]3 \le t \le 6[/tex] to represent the time values between 3 and 6 hours, including the endpoints. This represents the set of possible inputs to the function.
The function f(t) = 44000t is an increasing function. This means the smallest range value corresponds to the smallest domain value.
Plug in t = 3 to find that:
f(t) = 44000t
f(3) = 44000*3
f(3) = 132000
This says he mows 132,000 sq ft of lawn in 3 hours.
Now plug in the largest domain value to find the largest range value
f(t) = 44000t
f(6) = 44000*6
f(6) = 264000
He mows 264,000 sq ft of lawn in 6 hours.
The range is the set of f(t) values between 132,000 and 264,000
We can write that as [tex]132000 \le f(t) \le 264000[/tex]
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
The answer is 43
Step-by-step explanation:
Remember that the sum of the angles of all triangles is 180 degrees.
80+57+x=180
137+x=180
x=43
Please help me find the quadratic inequality for this
y ≥ x2 - 4x + 1
Answer:
x/> -y/2 + 1/2
If (-6,-38) and (5,28) are twoanchor points on the trend line,then find the equation of the line..y = 6x + [?]
Step 1
Write the slope, y-intercept form of the equation of a line.
[tex]undefined[/tex]
2. Dexter needs to find each angle in this figure that is adjacent
to LLON. He claims that LMON is adjacent to LLON.
a. List each angle that is adjacent to LLON.
мор
b. Why is Dexter's claim incorrect?
Answer:
It would be MOP is adjacent
Step-by-step explanation:
on a test consisting of 250 questions, jassi answered 40% of the first 125 questions correctly. what percent of the other 125 questions does she need to answer correctly for her grade on the entire exam to be 60%
test of 250 questions
40% of the fist 125 are ok, this means that 125(0.4) = 50 questions of the first 125 are ok
If jassi needs 60% of the 250 ok, that is 250(0.6) = 150
If of the first half she already has 50 questions ok, and needs 150, she needs to have 100 questions our of the second 125
If she needs 100 out of 125, this percent is 100/125 = 0.8, this means 80%
Answer:
Jassi needs 80% of the second 125 questions to be ok
A ball was dropped from the Empire State Building observatory. The height of the ball in feet is described by the function f(x) = 1048 - 16[tex]x^{2}[/tex], where x is the time in seconds.
Find the inverse function [tex]f^{-1}[/tex](x) and explain its meaning.
[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] is the inverse function and it means the time in seconds it will take the ball to attain a certain height in feet.
What is the inverse function f^-1(x) and its meaning?
Given:
[tex]f(x) = 1048 - 16x^{2}[/tex]
Since the function f(x) is the height (h), we can write the function as :
[tex]h = 1048 - 16x^{2}[/tex]
We will make x the subject:
[tex]16x^{2} = 1048 - h[/tex]
[tex]x^{2} = \frac{1048 - h}{16}[/tex]
[tex]x = \sqrt{\frac{1048 - h}{16} }[/tex]
[tex]x = \sqrt{65.5 - 0.0625h }[/tex]
Since:
[tex]x = f^{-1} (h) = \sqrt{65.5 - 0.0625h }[/tex]
Thus:
[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex]
Therefore, the inverse function is [tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] and it is a function describing the amount of time (in seconds) it takes for the ball to reach a height of h feet.
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10 Which relation is a function?
y =
X
-1
0
1
1
2
3
(1)
y
1
0
1
2
4
9
(x,-1
(x², 2
(2)
y
(3)
{(0,1), (2,3), (3,2), (3,4)}
(4)
An electric current that alternates sinusoidally with a frequency of 60
cycles per second and is at maximum at t = 0.1 seconds can be described by
the equation
I(t) = 10cos(120πt - 12π) + 5,
where I is current in Amperes and t is time in seconds. What is the
approximate range of the current?
The current is defined as rate of flow of charge I = dq/dt.
The approximate range of the current is 299.5.
How to estimate the approximate range of the current?The current is defined as rate of flow of charge I = dq/dt
Let the equation be [tex]$q=\int i d t$[/tex]
Given: I(t) = 10 cos(120πt - 12π) + 5
We will substitute it in the above equation
q = [tex]$$\int[/tex] 10 cos(120πt - 12π) + 5 dt
now here limits of time is from t = 0.1 to t = 60 s
so here it will be given as
[tex]$\int 10 cos(120\pi t - 12\pi ) + 5 dt[/tex]
Rewrite using trig identities
[tex]$=\int_{0.1}^{60} 10 \cos (120 \pi t)+5 d t$$[/tex]
Apply the Sum Rule:
[tex]$\int f(x) \pm g(x) d x=\int f(x) d x \pm \int g(x) d x$[/tex]
substitute the values in the above equation, we get
[tex]$=\int_{0.1}^{60} 10 \cos (120 \pi t) d t+\int_{0.1}^{60} 5 d t$[/tex]
simplifying the equation,
[tex]$\int_{0.1}^{60} 10 \cos (120 \pi t) d t=0[/tex]
[tex]$\int_{0.1}^{60} 5 d t=299.5$[/tex]
= 0 + 299.5
= 299.5
Therefore, the approximate range of the current is 299.5.
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What is the absolute value of -6? Use the number line to help answer the question.
-6
07
6543210
st
4+
3+
2+
7777777
Answer:
your answer is in the screenshot
Step-by-step explanation:
What is a correct congruence statement for the triangles shown?
Enter your answer in the box.
Answer:
ASA
Step-by-step explanation:
there are two congruent angles with an included side in between
Answer: Triangle RHS and NKW are congruent through the Congruence Theorem Angle-Side-Angle.
Step-by-step explanation:
The side HS is congruent to the side KW.
The angle H is congruent to angle K.
The angle S is congruent to angle S.
5x+3=53
I don’t know pls help
Answer:
x10
Step-by-step explanation:
How to solve your problem
5x+3=53
Subtract 3 from both sides
5x+3=53
5x+3-3=53-3
Simplify
Subtract the numbers
5x+3-3=53-3
5x=53-3
Subtract the numbers again
5x=53-3
5x50
Divide both sides by the same factor
5x=50
5x=50\
[tex]\frac{50x}{5}[/tex][tex]\frac{50}{5}[/tex]
Simplify
Cancel terms that are in both the numerator and denominator
[tex]\frac{5x}{5}[/tex]=[tex]\frac{50}{5}[/tex]
x=[tex]\frac{50}{5}[/tex]
Divide the numbers
x=[tex]\frac{50}{5}[/tex]
x=10
answer is 10
Which relation is a function?
Responses
(1, 0), (3, 0), (1, 1), (3, 1), (1, 3)
(1, 0), (3, 0), (1, 1), (3, 1), (1, 3)
(1, 1), (2, 2), (3, 3), (4, 4), (5, 8)
(1, 1), (2, 2), (3, 3), (4, 4), (5, 8)
(2, 7), (6, 5), (4, 4), (3, 3), (2, 1)
(2, 7), (6, 5), (4, 4), (3, 3), (2, 1)
(9, -3), (9, 3), (4, -2), (4, 2), (0, 0)
Answer:{(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
Step-by-step explanation: hope this helps
The mean height of married american women in their early twenties is 64.5 inches and the standard deviation is 2.5 inches. the mean height of married men the same age is 68.5 inches, with standard deviation 2.7 inches. the correlation between the heights of husbands and wives is about r = 0.5. find the height of the husband without using least mean
Y'=33.67+0.54*X' .
For married couples in their early 20s, the regression equation and the prediction of a husband's height. In statistics, a regression equation is used to determine whether or not there is a link between two sets of data.
What is the purpose of a regression equation?In statistics, a regression equation is used to determine whether or not there is a link between two sets of data. For instance, you might discover that a child grows roughly 3 inches a year if you measure their height each year. A regression equation can be used to model the three-inch growth tendency.
Detailed explanation:
r=0.5 \s x'=64.5 \s Sx=2.5 \s y'=68.5 \s Sy=2.7The slope of the regression line is the linear correlation coefficient multiplied by the standard deviation for y' divided by the standard deviation for x', according to the general regression line equation: Y'=a+b*X'The mean of the lowered by the slope and mean of x is the intercept with axis y.The following is the equation regression line:Y'=33.67+0.54*X'.To learn more about Regression equation refer to:
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Past due I don't really understand, what's the answer??
Answer:
$50.16
Step-by-step explanation:
id.k if it's actually right but i believe the tip would be $8.36 if it's 20% so adding it together is $50.16
Lee and Sandy work at the same factory. Lee earns $17 per hour, and Sandy earns $20 per hour. Factory manager announces that all the workers' wages will go up by $1.50 per hour, starting next month.What will be the percent increase in Lee's hourly wage, rounded to one decimal place?
0.9(x+1.4)−2.3+0.1x=1.6
please help, I'm really not sure how to do this.
Answer:
x = 2.64
Step-by-step explanation:
Do the distributive property first.
0.9(x + 1.4)
0.9(x) + 0.9(1.4)
0.9x + 1.26 - 2.3 + 0.1x = 1.6
Simplify the left side by adding like terms. I'm going rewrite the equation and group the like terms together.
0.9x + 0.1x + 1.26 - 2.3 = 1.6
1x - 1.04 = 1.6
1x is the same as x, so I am going to remove the 1. Solve for x.
x - 1.04 + 1.04 = 1.6 +1.04
x = 2.64
Brynn rides her bike 84 miles in 4 hours.
a. Create a ratio of Brynn's miles per hour.
b. Using the ratio you found in part a, determine
how far Brynn can ride in 7 hours.
c. If Brynn rides 57 miles at the rate indicated,
how long will she ride? Justify your response.
Part (a)
distance = rate*time
rate = distance/time
rate = 84/4
rate = 21
Answer: 21 mph
==================================================
Part (b)
distance = rate*time
distance = 21*7
distance = 147
Answer: 147 miles
==================================================
Part (c)
distance = rate*time
time = distance/rate
time = 57/21
time = 2.71428571428571
time = 2.714
Answer: Approximately 2.714 hours
Answer;
A.21:1
B:147 Miles
C.2.7 hours or 182 minutes
Mai runs around a 400-meter track at a constant speed of 250 meters per minute. How many minutes does it take Mai to complete 4 laps of the track? Write your answer as an improper fraction
The minutes it take Mai to complete 4 laps of the track would be 6 minutes 24 seconds.
What is speed?Speed can be calculated as the ratio of distance traveled to the time taken.
Speed = distance /time
Also, Time = distance/ speed
In this case, the distance is 4 laps of 400 meters, so;
4 x 400=1600 meters
Speed = 250 per minute
Now,
Time =1600 meters /250 meter per minute
= 6,40 minutes is the same 6 minutes 24 seconds
Hence, the minutes it take Mai to complete 4 laps of the track would be 6 minutes 24 seconds.
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PLEASE HELP
Which transformation represents a reflection over the x-axis?
Answer: E
Step-by-step explanation:
Option A is a reflection over the y-axis.
Option B is a rotation of 180 degrees about the origin followed by a dilation.
Option C is a reflection over the line y=x.
Option D is a reflection over the y-axis.
Option E is a reflection over the x-axis.
In solving any inequality if the variable is eliminated and a false statement such as
ANSWER:
No solution
STEP-BY-STEP EXPLANATION:
We have the following inequality:
[tex]x+7If we solve we have the following:[tex]7<-2[/tex]The value of 7 is not less than -2, so this is false.
Which means that the set has no solution
Kyle just graduated from college and got his first job, he has $45,000 in student loan debt, wants to buya new car, and is considering opening up a retirement account. He has a disposable income of$300/month, what would you recommend he do with this money? Why?
Problem
Kyle just graduated from college and got his first job, he has $45,000 in student loan debt, wants to buy a new car, and is considering opening up a retirement account. He has a disposable income of $300/month, what would you recommend he do with this money? Why?
Solution
For this case the best option would be put the $45000 in a bank with a compound interest
And with the earnings each month of 300$ he can put the half of this into the account and the remain to spend on other things
my tutors keep getting cut off due to connection and i need help!!
Let:
(x1,y1) = (0,4)
(x2,y2) = (4,0)
The slope m is:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1}=\frac{0-4}{4-0}=\frac{-4}{4}=-1 \\ \end{gathered}[/tex]Using the point slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-4=-1(x-0) \\ y=-x+4 \\ \text{ In standard form:} \\ x+y=4 \end{gathered}[/tex]Loren solved the equation 10 = startfraction 19 over 9 endfraction (149) b for b as part of her work to find the equation of a trend line that passes through the points (1, 130) and (10, 149). what error did loren make?
The eqations are 149=19/9 (10) +b and 130=19/9(1)+b
Given that,
As part of her work, Loren found the solution to the equation 10 = start fraction 19 over 9 end fraction (149) b for b and the points are (1, 130) and (10, 149)
Finding the slope of a line that goes through two locations for Loren is as follows: m=y2-y1/x2-x1
=149-130/10-1
=19/9
m=19/9
There are two ways to solve for b in the equation y=mx+b for the location (1,130), where y=130, x=1, and m=19/9, and for the position (10,149), where 149=19/9 (10) +b.
Therefore, the equation of a trend line that passes through the points (1, 130) and (10, 149) are 149=19/9 (10) +b ,130=19/9(1)+b
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Write an expression for the calculation triple 4 and then add 6 times 6
Answer:
4x3+6x6=48
Step-by-step explanation:
PEMDAS
4x3=12
6x6=36
12+36=48
therefore, the answer is 48
You are a grant writer for an organization that helps adults complete their high school educations. For the last 5 years, you have applied for and received $45,000.00 in grants. Your boss would like you to try to increase that amount to $60,000.00. How much of an increase does the new amount represent over the previous amount?
Based on the amount you have received in grants, and the amount the boss wants to increase it to, the increase the new amount represents over the previous amount is $15,000 or 33.3%.
How to find the increase?Your boss wants to increase the grants to $60,000 from the current amount of $45,000.
This means that the new amount will represent an increase over the previous amount by:
= 60,000 - 45,000
= $15,000
In percentage terms this is:
= Increase over previous amount / Previous amount x 100%
= 15,000 / 45,000 x 100%
= 33.3%
In conclusion, the difference between the grants applied for in the past 5 years and the amount the boss is asking for, gives the increase of $15,000.
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An artist is going to cut four similar righttriangles from a rectangular piece of paperlike the one shown to the right. What is thedistance from B and D to the diagonal AC?Write an equation and solve, showing ALLthe work.
First let's find the length of AC using the Pythagorean theorem in the right triangle with legs of 5 and 12:
[tex]\begin{gathered} AC^2=5^2+12^2 \\ AC^2=25+144 \\ AC^2=169 \\ AC=13 \end{gathered}[/tex]So the diagonal of the rectangle is 13 units. Now, since the area of a triangle is calculated as the product of a base and the corresponding height, we can use the legs as base and height or we can use the segment AC and the corresponding height, and the result is the same, so we have:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ A=\frac{5\cdot12}{2} \\ A=\frac{13\cdot h}{2} \\ \\ \frac{5\cdot12}{2}=\frac{13\cdot h}{2} \\ 60=13h \\ h=\frac{60}{13} \end{gathered}[/tex]So the distance from B or D to the diagonal AC is 60/13 units.
Which is the equation of a line that is perpendicular to the line represented by ?
Answer:
It will be
.. y = -4/3x +c . . . . . for some value of c
_____
The slope of the perpendicular line will be the negative reciprocal of the slope of the given line, which is 3/4.
y+1=3/2(x-1) in slope intercept form
Answer:
y=[tex]\frac{3}{2}[/tex]x - [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
To get slope intercept form (y=mx+b), simplify and solve for y.
y+1=[tex]\frac{3}{2}[/tex](x-1)
Simplify
y+1=[tex]\frac{3}{2}[/tex]x - [tex]\frac{3}{2}[/tex]
Solve for y
y=[tex]\frac{3}{2}[/tex]x - [tex]\frac{5}{2}[/tex]
What is the smallest and greatest number that rounds to 380 when
rounding to the nearest ten?
The smallest and greatest number that rounds to 380 when rounding to the nearest ten are 375 and 384 respectively.
What is rounding a number?Adjusting a number's digits so that it produces an approximation of a result is known as rounding.
The given number is 380.
When rounding a number to the nearest ten, pay attention to the last digit; if it is less than five, round down; if it is five or more, round up.
Therefore, the smallest number that rounds to 380 when rounding to the nearest ten is 375.
Similarly, the greatest number that rounds to 380 when rounding to the nearest ten is 384.
Hence, the smallest and greatest number that rounds to 380 when rounding to the nearest ten are 375 and 384 respectively.
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