Hello, let's note a the positive real number.
A positive real number is 4 less than another.
So, the other number is a - 4
When 8 times the larger is added to the square of the smaller, the result is 96.
So, we need to solve the following equation.
[tex]8a+(a-4)^2=96[/tex]
Let's do it!
[tex]8a+(a-4)^2=96\\\\8a+a^2-8a+16=96\\\\a^2=96-16=80=4^2*5\\\\a=\pm4\sqrt{5}[/tex]
As a is positive, there is only one solution which is.
[tex]\Large \boxed{\sf \bf \ \ a=4\sqrt{5} \ \ }[/tex]
Thank you.
The amount given by the sum of numbers can be presented in an equation
form from which the value of each number can be obtained.
The large number is 4·√5, the smaller number is 4·(√5 - 1)
Reason:
Let x represent the large number, we have;
The smaller number = x - 4
8 × x + (x - 4)² = 96
8·x + (x - 4)² = 96
Required:
The values of the numbers
Solution:
8·x + (x - 4)² = 8·x + x² - 8·x + 16 = 96
8·x - 8·x + x² + 16 = 96
x² + 16 = 96
x² = 96 - 16 = 80
x = ±√(80) = ±4·√5
Given that the numbers are positive, we have;
The large number, x = 4·√5
The smaller number = x - 4 = 4·√5 - 4
The smaller number = 4·√5 - 4 = 4·(√5 - 1)
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The 7th grade had a book drive. They donated 2/3 of the books to the st James school. Then donated 1/4 of the remaining books to widener. If they had 16 books left after donating to the 2 schools, how many books did they collect in the book drive?
Answer: 192 books
Step-by-step explanation:
2/3 + 1/4 = 11/12
16 remaining books = 1/12
16 x 11 = 176
176 + 16=192
Answer:
ksdljfdacnkjdsfhbjfjkn
Step-by-step explanation:
Travel
324 miles on 18 gallons of gas
Answer:
324 miles divided by 18 gallons = 18 miles per gallon (mpg)
Therefore, 41 gallons x 18 mpg = 738
Step-by-step explanation:
HELP PLS! THANK YOU SO MUCH! Consider the quadratic equation 3x^2-6=2x. (a) What is the value of the discriminant? (b) What does the discriminant of the quadratic equation tell about the solutions to 3x^2-6=2x
Answer:
see explanation
Step-by-step explanation:
Given a quadratic equation in standard form, ax² + bx + c = 0 ( a ≠ 0 )
Then the discriminant Δ = b² - 4ac informs us about the nature of the roots.
• If b² - 4ac > 0 then 2 real and distinct roots ( solutions )
• If b² - 4ac = 0 then 2 real and equal roots
• If b² - 4ac < 0 then roots are not real
Given
3x² - 6 = 2x ( subtract 2x from both sides )
3x² - 2x - 6 = 0 ← in standard form
with a = 3, b = - 2, c = - 6 , thus
b² - 4ac = (- 2)² - ( 4 × 3 × - 6) = 4 - (- 72) = 4 + 72 = 76
Since b² - 4ac > 0 then the solution is 2 real and distinct roots
Please help me solve for x (show work)
-4/7x = -1
...... ❤
[tex] \frac{ - 4}{ \: \: 7} x = - 1[/tex]
Now firstly we have to take 7 to right hand side and multiply -1 by 7
[tex] - 4x = - 1 \times 7[/tex]
[tex] - 4x = - 7[/tex]
Now we have to take -4 to the right hand side and divide -7 by -4
[tex]x = \frac{ - 7}{ - 4} [/tex]
As we know that in case of division - and - are cancelled so ,
[tex]x = \frac{7}{4} [/tex]
Hope it helps u mate
Sandra has only Re 1 and Rs 2 coins with her. If the total number of coins that she has is 50 and
the amount of money with her is Rs 75, then find the number of Re 1 and Rs 2 coins
I hope this helps you. Plz mark me as the brainliest.
How many 5 ounce glasses of soda can you get from 3, 2 liter bottles of soda (6 liters total?
Answer:
21
Step-by-step explanation:
tcctvucycyccyctctctchu ycuvuvuvy t r y y g g t g
PLEASE HELP! URGENT! Exponential function f is being represented by the table (photo attached) the function “g” is an exponential function passing through the points of (0, 15) , (2, 0). Which of the statements below correctly compared the behavior of these two functions on the interval (0, 2) ??
Answer:
C) Both functions are decreasing and both are positive on the interval (0;2)
Step-by-step explanation:
As known the exponent function has no minimum and has no maximum.
Otherwise exponent function can be only or increasing or decreasing for all x.
That means that in case y(x2)>y(x1) and if x2>x1- function is increasing.
That means that in case y(x2)<y(x1) and if x2>x1- function is decreasing.
Lets check what is going on with the function f(x)
If x1=0 f(x1)=24
If x2=2 f(x2)=0
So x2>x1 however f(x2)<f(x1)=> function is decreasing
Similarly g(x)
If x1=0 g(x1)=15
If x2=2 g(x2)=0
So x2>x1 however g(x2)<g(x1) => function is decreasing
So bothfunctions are decreasing.
Because f(x) is decreasing the function meaning with argument x1=0 has max in the interval x∈(0;2) And function meaning has the minimum if argument x2=2. So the function F(x) in interval (0;2) is changing from 24 to 0 => is positive on the interval (0,2)
The same is with g(x) . g(x) gonna be positive on the interval (0;2)
How far does Kai have to walk to school if he takes the nature trail?
School
Nature Trail
15 yd
20 yd
Kai's
House
A. 13.3 yd
B. 25.0 yd
C. 625.0 yd
D. 35.0 yd
Answer:
D?
Step-by-step explanation:
¯\_(ツ)_/¯
mg+rg=2H, solve for g
Answer:
[tex]g=\frac{2\,H}{m+r}[/tex]
Step-by-step explanation:
Starting with :
m g + r g = 2 H
extract "g" as a common factor on the left of the equal sign:
g (m + r) = 2 H
Now, in order to solve for "g" , divide both sides of the equal sign by the binomial (m + r):
g = (2 H )/(m + r)
[tex]g=\frac{2\,H}{m+r}[/tex]
Find an equation of the line containing the centers of the two circles whose equations are given below.
x2+y2−2x+4y+1
=0
x2+y2+4x+2y+4
=0
In triangle ABC, which side is the longest if these are the measures of the angles? m∠A = 60°, m∠B = (3x − 2)°, m∠C = (2x + 7)°
Answer:
AC
Step-by-step explanation:
First, let's find m∠B and m∠C by solving for x. Since the sum of interior angles in a triangle is 180°, we know that:
60 + 3x - 2 + 2x + 7 = 180
5x + 65 = 180
5x = 115
x = 23° so m∠B = 3(23) - 2 = 67° and m∠C = 2(23) + 7 = 53°. The longest side of a triangle is always opposite to the largest angle of the triangle, and since m∠B is the largest, we know that the side opposite to ∠B is the longest. That side is AC.
In triangle ABC, the longest side is AC, since it is opposite the biggest angle ∠B.
What is the angle sum property of a triangle?According to the angle sum property of a triangle, the sum of the three interior angles is 180°.
What is the relation between sides' length and the size of the angle of a triangle?In a triangle, the longest side is on the opposite side of the biggest angle, and the shortest side is on the opposite side of the smallest angle.
How do we solve the given question?We are given the angles of the triangle ABC. We are asked to find the longest side in the triangle ABC.
By the angle sum property of a triangle, we know that,
m∠A + m∠B + m∠C = 180°
or, 60° + (3x - 2)° + (2x + 7)° = 180°
or, 5x + 65° = 180°
or, 5x = 180° - 65° = 115°
or, x = 115/5 = 23.
∴ m∠A = 60°.
m∠B = (3x - 2)° = (3(23) - 2)° = (69-2)° = 67°.
m∠C = (2x + 7)° = (2(23) + 7)° = (46 + 7)° = 53°.
∵ m∠B is the largest angle, the side opposite to it, that is, AC is the longest side of the triangle.
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Identify as an increase or decrease. Then find the percent of increase or decrease. If necessary, round to the nearest percent. Original: 170 New: 90 %________
Answer:
the percent decrease is approximately 47 %
Step-by-step explanation:
Since the quantity started at 170 and then changed to 90, there was clearly a decrease in its value.
We use the following formula to calculate the percent of decrease:
[tex]\%\,decrease = \frac{original-final}{original} \,100\\\%\,decrease = \frac{170-90}{170} \,100\\\%\,decrease = \frac{80}{170} \,100\\\%\,decrease \approx 47\,\%[/tex]
To which subset(s) of real numbers does the number 4 belong? 1. Irrational numbers 2. Integers 3. Whole numbers 4. Natural numbers 5. Rational numbers
Answer:
whole number
hope it helps
what is 24,159 -3,168 =
Answer:
20991
Step-by-step explanation:
Solve the simultaneous equation,
2p - 3q = 4
3p + 2q = 9
Answer:
p = [tex]\frac{35}{13}[/tex] and q = [tex]\frac{6}{13}[/tex]
Step-by-step explanation:
Given equations:
2p - 3q = 4 -----------(i)
3p + 2q = 9 ------------(ii)
Let's solve this equation simultaneously using the elimination method
(a) Multiply equation (i) by 3 and equation (ii) by 2 as follows;
[2p - 3q = 4] x 3
[3p + 2q = 9] x 2
6p - 9q = 12 -------------(iii)
6p + 4q = 18 -------------(iv)
(b) Next, subtract equation (iv) from equation (iii) as follows;
[6p - 9q = 12]
- [6p + 4q = 18]
-13q = -6 -----------------(v)
(c) Next, make q subject of the formula in equation (v)
q = [tex]\frac{6}{13}[/tex]
(d) Now substitute the value of q = [tex]\frac{6}{13}[/tex] into equation (i) as follows;
2p - 3([tex]\frac{6}{13}[/tex]) = 4
(e) Now, solve for p in d above
Multiply through by 13;
26p - 18 = 52
Collect like terms
26p = 52 + 18
26p = 70
Divide both sides by 2
13p = 35
p = [tex]\frac{35}{13}[/tex]
Therefore, p = [tex]\frac{35}{13}[/tex] and q = [tex]\frac{6}{13}[/tex]
A manufacturer has been selling 1000 flat-screen TVs a week at $400 each. A market survey indicates that for each $10 rebate offered to the buyer, the number of TVs sold will increase by 100 per week.
(a) Find the demand function (price p as a function of units sold x).
(b) How large a rebate should the company offer the buyer in order to maximize its revenue?
(c) If its weekly cost function is C(x) = 73,000 + 110x, how should the manufacturer set the size of the rebate in order to maximize its profit?
Answer:
Explained below.
Step-by-step explanation:
(a)
It is provided that the price function for 1000 TVs is,
p (1000) = 400.
Also provided that if rebate of $10 is given then sale increases by 100 per week.
Let x be the number of unit sold per week then (x − 1000) is the increase in the number of units sold.
Then the price function is:
[tex]p(x)=400-\frac{1}{10}(x-1000)[/tex]
[tex]=400-\frac{x}{10}+100\\\\=500-\frac{x}{10}[/tex]
Thus, the demand function is, [tex]p(x)=500-\frac{x}{10}[/tex].
(b)
The revenue function is:
[tex]R(x)=x\cdot p(x)[/tex]
[tex]=x[500-\frac{x}{10}]\\\\=500x-\frac{x^{2}}{10}[/tex]
Maximize the revenue as follows:
[tex]\frac{d}{dx}(R(x))=0[/tex]
[tex]\frac{d}{dx}[500x-\frac{x^{2}}{10}]=0[/tex]
[tex]500-\frac{x}{5}=0[/tex]
[tex]\frac{x}{5}=500[/tex]
[tex]x=2500[/tex]
Observe that R'(x) > 0 for 0 ≤ x < 2500 and R'(x) < 0 for x > 2500. Hence, first derivative test will lead to the conclusion that maximum occurs at x = 2500.
Compute the value p (2500) as follows:
[tex]p(2500)=500-\frac{2500}{10}=500-250=250[/tex]
Then the rebate to maximize the revenue should be: $400 - $250 = $150.
(c)
The weekly cost function is,
[tex]C(x) = 73000 + 110x[/tex]
Compute the profit function as follows:
[tex]P(x)=R(x)-C(x)[/tex]
[tex]=500x-\frac{x^{2}}{10}- 73000 - 110x\\\\=390x-\frac{x^{2}}{10}- 73000[/tex]
Compute the marginal profit as follows:
[tex]\text{Marginal profit}=P'(x)\\=\frac{d}{dx}P(x)\\=\frac{d}{dx}[390x-\frac{x^{2}}{10}- 73000]\\=390-\frac{x}{5}[/tex]
Compute the value of x for P'(x) = 0 as follows:
[tex]P'(x)=0\\\\390-\frac{x}{5}=0\\\\x=390\times 5\\\\x=1950[/tex]
Observe that P'(x) > 0 for 0 ≤ x < 1950 and P'(x) < 0 for x > 1950. Hence, first
derivative test will lead to the conclusion that maximum occurs at x = 1950.
Compute the value p (1950) as follows:
[tex]p(1950)=500-\frac{1950}{10}=500-195=305[/tex]
Then the rebate to maximize the profit should be: $400 - $305 = $95.
A company sells x units of an item each day at the rate of Rs. 50. The cost of manufacturing each unit of an item is Rs. 36.50 and the dristributor demands a charge of Rs. 3.50 per unit. If the daily overhead charge is Rs. 2600, find the profit function. Also find the profit if 360 units of an item are produced and sold daily?
Answer:
Y(x) = 10x - 2600
Profit= RS. 1000
Step-by-step explanation:
Amount sold per item=RS. 50.
Cost of manufacturing= RS. 36.5
Distributor charges= Rs 3.5
Daily over head charge= RS.2600
Profit function Y (x)
Y (x) =x(50) -36.5(x) -3.5(x)-2600
Y(x) = (50-36.5-3.5)x-2600
Y(x) = 10x - 2600
If x= 360
Profit Y = 10(360) - 2600
Profit Y = 3600-2600
Profit = 1000
Profit= RS. 1000
Write this statement in your own words: ∃x ∈ ℕ, y ∈ ℤ|x² = y² Rewrite this using the appropriate mathematical notation: Even numbers are in the set of integers.
Answer:
See below.
Step-by-step explanation:
1)
So we have:
[tex]\exists x\in\mathbb{N},y\in\mathbb{Z}|x^2=y^2[/tex]
This can be interpreted as:
"There exists a natural number x and an integer y such that x² is equal to y²."
2)
So we want even numbers are in the set of integers.
[tex]\{2n:n\in\mathbb{Z}\}\in\mathbb{Z}[/tex]
This is interpreted as:
"The set of even numbers (2n such that n is an integer) is in the set of integers"
Paulina’s father pays her $20 per month for doing chores. In April, she makes a deal with him. Rather than paying her $20, he can pay her 1¢ on the first day of the month, 2¢ on the second, 4¢ on the third, and continue each day by doubling the amount he paid on the previous day. Use the properties of exponents to write expressions for the first 5 days of the month. The, explain if Paulina will make more or less than $20 per month using this pattern.
Answer:
Step-by-step explanation:
This is a geometric sequence with first element 1 and common ratio 2:
a(n) = 1*2^(n - 1)
Thus, a(1) = 1
a(2) = 2^(2 - 1) = 2
a(3) = 2^(3 - 1) = 4
a(4) = 2 ^( 4 - 1) = 2^ 3 = 8
a(5) = 2^(5 -1) = 2^ 4 = 16
One month is approximately 30 days. Therefore,
a(30) = 2^ (30 - 1) = 2^29 = 536870912
Using this pattern, Paulina will "make" $536870.12 vs $20 via Paulina's father's plan.
Madison leaves her house and bikes north at a constant speed of 10 miles per hour. If her dad leaves the same house two hours later, driving north at a constant speed of 15 miles per hour, how long will it take him, in hours, to reach Madison?
Answer:
It should take her father four hours to reach her.
Step-by-step explanation:
Since Madison takes an hour to travel 10 miles, by the time she reaches 3 hours, shes at 30 miles. (At this point her father has begun traveling towards her) And since he goes 15 miles per hour, four hours later (for her father), they will both be at the same distance.
(So in 6 hours, Madison goes 60 miles, and in 4 hours her father also goes 60 miles since hes faster)
Please tell me if I did anything wrong!
It will take the time that Madison's dad 8 hours to catch up with her.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
Let's call the distance from Madison's house to the point where her dad catches up with her "D".
distance Madison traveled = rate × time = 10 mph × 2 hours = 20 miles.
This means that when Madison's dad starts driving, Madison is 20 miles ahead of him.
For Madison's dad, his rate is 15 mph, and the time it takes him to catch up to Madison is "t" hours.
So his distance traveled is:
distance traveled by Madison's dad = 15 mph × t
For Madison, her rate is 10 mph, and she has already traveled for 2 hours. So her distance traveled is:
distance traveled by Madison = 10 mph × (t + 2)
Now, their distances are equal to each other:
15t = 10(t + 2) + 20
Simplifying and solving for "t", we get:
15t = 10t + 40
5t = 40
t = 8
Therefore, it will take Madison's dad 8 hours to catch up with her.
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1.008÷0.8
show work
Answer:
1.26
Step-by-step explanation:
1.008 divided by o.8 =1.26
Answer:
1.26, Dude get a calculator
Step-by-step explanation:
0 1. 2 6 0
8 1 0. 0 8 0
− 0 Listen. Its hard to do long division ona computer.
1 0
− 8
2 0
− 1 6
4 8
− 4 8
0 0
− 0
0
If angle DFG ~ angle RPQ, the value of x=_____
Answer:
[tex] x = 6.25 [/tex]
Step-by-step explanation:
Given that ∆DFG ~ ∆RPQ, therefore, [tex] \frac{DF}{PR} = \frac{DG}{QR} = \frac{FG}{QP} [/tex] (similarity theorem).
DF = 10
PR = 8
DG = 5
QR = 4
QP = 5
FG = x
[tex] \frac{10}{8} = \frac{5}{4} = \frac{x}{5} [/tex]
Using [tex] \frac{5}{4} = \frac{x}{5} [/tex] , solve for x
cross multiply:
[tex] 4*x = 5*5 [/tex]
[tex] 4x = 25 [/tex]
[tex] x = \frac{25}{4} [/tex]
[tex] x = 6.25 [/tex]
4.
Oscar Hammerstein's Island, an amusement park, plans a TV ad campaign. It will
run 30-second ads for the next 20 days on a daytime show. Hammerstein's will
also run 30-second ads for the next 5 days during a prime-time show. A 30-second
daytime ad costs $6,200, a 30-second prime-time ad costs $165,000. What is the
total ad campaign cost?
Answer:
Hey there!
30-second ads for 20 days on a day time show.
6200(20)=124000
30-second ads for 5 days on a prime time show.
165000(5)=825000
124000+825000=949000 dollars.
Let me know if this helps :)
10. Hank bought a four-family residence for rental property. Hank put 20% down on the $300,000 rental unit. How much will he be able to depreciate
using the class recovery period for residential rental property each year?
A. $9,809.09
O B. $15,609.09
O C. $11,893.09
D. $10,909.09
Mark for review Will be highlighted on the review page)
Answer:
D. $10,909.09
Step-by-step explanation:
The class recovery period for residential rental property each year = 27.5 years
The cost basis for the residential property = $300,000
The amount he will be able to depreciate
= Cost basis/ Number of years
= $300000/ 27.5 years
=$10, 909.090909
Approximately ≈ $10,909.09
The amount he will be able to depreciate using the class recovery period for residential rental property each year is: D. $10,909.09.
Using this formula
Depreciation=Rental unit amount/ MACRS residential rental property recovery period
Where:
Rental unit amount=$300,000
MACRS Residential rental property recovery period=27.5 years
Let plug in the formula
Depreciation=$300,000/27.5
Depreciation=$10,909.09
Inconclusion the amount he will be able to depreciate using the class recovery period for residential rental property each year is: D. $10,909.09.
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Rachel just purchased a homeowners insurance policy for her new home that costs $0.43 per $100. Her home is worth $387,500. What is Rachel’s annual homeowners insurance premium? a. $1,666.25 b. $2,208.75 c. $8,802.33 d. $9,011.63 Please select the best answer from the choices provided
Answer:
The answer is A.
Do you need an explanation?
387,500 /100 = 3,875
3,875 * 0.43 = 1,666.25
I multiplied, because, if you divide with a decimal, the number increases, instead of decreasing... hope this helps!
What are equivalent fractions for 8/11 and 1/10 using the least common denominator?
Answer:
2/10 because if the two fraction
The equivalent fractions of 8/11 = 16/22 , 24/33 , 32/44
The equivalent fractions of 1/10 = 2/20 , 3/30 , 4/40
What is a Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given data ,
Let the first fraction be represented as A
Now , the value of A = 8/11
Let the second fraction be represented as B
Now , the value of B = 1/10
And , the equivalent fractions of A is given by
A = 8/11 , 16/22 , 24/33 , 32/44
And , the equivalent fractions of B is given by
B = 1/10 , 2/20 , 3/30 , 4/40
Hence , the fractions are solved
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If the standard deviation for a Poisson distribution is known to be 3.60, the expected value of that Poisson distribution is
Answer: 12.96
Step-by-step explanation:
given data:
Poisson distributio = 3.60
solution:
The Poisson distribution expected value is same as Variance.
which is expressed as = SD^2
therefore;
the expected value
= SD^2
= 3.60^2
= 12.96
0.9962 to the nearest hundredth
Answer:
1.00o2
Step-by-step explanation:
You dont need this explained come on
3/4x=21 Can you please assist?
Answer:
x =28
Step-by-step explanation:
Divide the numbers
Combine multiplied terms into a single fraction
Eliminate fraction denominators
Simplify
Divide both sides of the equation by the same term
Directions: Round $45.58 to the nearest dollar.
$None of these
$46.60
$45.60
$45
$45
Answer:
none of these unless one of the 45s are 46
Step-by-step explanation:
nearest dollar means no cents so $46.60 and $45.60 are out
58 is over 50 so the two 45s go away
the only option left is none of these or 46 if you accidentally put 45 instead of 46