The complete factorization of the equation 81x² - 100 is; (9x - 10)(9x + 10)
How to factorize quadratic equations?We are given the quadratic equation;
81x² - 100
Now, according to quadratic identities, we know that;
(a + b) * (a - b) = a² - b²
Now, our equation can also be expressed as;
81x² - 100 = 9²x² - 10²
Thus, applying the quadratic identity gives us;
(9x + 10)(9x - 10)
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Find the value of x.
B
A
2
30°
5
30°
5
x = [?]
X
C
D
Given the functions f(x) = x3 + x2 – 3x + 4 and g(x) = 2^x– 4, (Consider domain, range, x-intercepts, and y-intercepts.)
The first function is a type of cubic function and the second function is a type of linear function. The key feature(s) do f(x) and g(x) have in common as they both have value of domain and range as (-∞, ∞).
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The function given in the problem is:
f(x) = x³ + x² – 3x + 4
The highest degree (power) of this function is 3. Thus, this function is a type of cubic function.
The second function given in the problem is:
g(x) = 2x – 4
The highest degree (power) of this function is 1. Thus, this function is a type of linear function.
Both the function has the value of domain and range from -∞ to ∞ (-∞,∞).
Thus, the first function is a type of cubic function and second function is a type of linear function. The key feature(s) do f(x) and g(x) have in common as they both have value of domain and range as (-∞, ∞).
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A body and tackle with a velocity ratio of 5 is used to raise a mass of 50kg through a vertical distance of 20n at a steady rate if the effort is equal to 80n. Determine (a) distance moved by effort (b)the workdone by the effort in lifting the load (c)the losses in energy involve the operating in machine
A. The distance moved by the effort is 100 m
B. The workdone by the effort in lifting the load is 8000 J
C. The losses in energy involve the operating in machine 1800 J
A. How to determine the distance moved by the effortVelocity ratio = 5Load distance = 20 mEffort distance =?Velocity ratio = Effort distance / Load distance
5 = Effort distance / 20
Cross multiply
Effort distance = 5 × 20
Effort distance = 100 m
B. How to determine the work done by the effortEffort distance = 100Effort = 80 NWorkdone by effort =?Workdone = force × distance
Workdone by effort = 80 × 100
Workdone by effort = 8000 J
C. How to determine the losses in the energyWe'll begin by calculating the workdone in lifting the load. This is illustrated below:
Mass (m) = 50 KgAcceleration due to gravity (g) = 9.8 m/s²Height (h) = 20 mWorkdone =?Workdone = mgh
Workdone = 50 × 9.8 × 20
Workdone = 9800 J
Now, we can determine the energy lost as follow:
Workdone = 9800 JWorkdone by effort = 8000 JEnergy lost =?Energy lost = 9800 - 8000
Energy lost = 1800 J
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Kristina wants to invest $6200 in a savings account that pays 7.6% simple interest. How long will it take for this investment to double in value? Round your answer to the nearest tenth.
The number of years it would take the investment to double in value is 13.2 years.
How long will it take for the investment to double?When the amount doubles, the interest earned would be $6200.
Time = interest earned / (amount invested x simple interest)
$6200 / (6200 x 0.076) = 13.2 years
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Rewrite 1/2 x 1/2 x 1/2 as an exponential expression with a base of 2.
The equivalent expression of 1/2 * 1/2 *1/2 is 2^-3
How to rewrite the expression?The expression is given as:
1/2 * 1/2 *1/2
Apply the product law of indices
1/2 * 1/2 *1/2 = (1/2)^3
Apply the power law of indices
1/2 * 1/2 *1/2 = (2^-1)^3
This gives
1/2 * 1/2 *1/2 = 2^-3
Hence, the equivalent expression of 1/2 * 1/2 *1/2 is 2^-3
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DEFG is a rumbus. Find the vaule
Step-by-step explanation:
in a rhombus (not rumbus !) all sides are equally long.
that means
7x - 4 = 3x + 12
4x = 8
x = 2
Answer:
Step-by-step explanation:
The sides of a square are equal to each other, it is with the same with rhombus.
With this information, we can Say that [tex]DE[/tex] is equal to line [tex]GD[/tex], with
[tex]DE =7x-4GD=3x+12[/tex]
[tex]7x-4=3x+12\\[/tex]
Take [tex]3x[/tex] from both sides.
[tex]4x-4=12[/tex]
Add 4 to isolate X
[tex]4x=16[/tex]
Divide by 4
[tex]x=4\\[/tex]
So we can say that the value of [tex]x[/tex] is 4
Find the domain of the function. Express the exact answer using interval notation.
f(x) = 2/3x+8
Answer:
(-oo, -8/3) U (-8/3, oo)
Step-by-step explanation:
Hope this helps.
The domain of the equation f(x) = 2/(3x + 1) is (-∝, -8/3) U (-8/3, ∝)
How to calculate the domain of the equation?From the question, we have the following parameters that can be used in our computation:
f(x) = 2/(3x + 1)
The above equation is a rational function
The rule of a function is that
The domain is the set of all input numbers
For the domain, we set the denominator not equal to 0
So, we have
3x + 8 ≠ 0
Evaluate
x ≠ -8/3
When represented as interval notation, we have
Domain = (-∝, -8/3) U (-8/3, ∝)
Hence, the domain is (-∝, -8/3) U (-8/3, ∝)
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a coffee shop, the first 100 customers' orders were as follows. Small Medium Large Hot 5 48 22 Cold 8 12 5 What is the probability that a customer ordered a large given that he or she ordered a cold drink? Rounded to the nearest percent, [? ]% Enter
Using it's concept, there is a 20% probability that a customer ordered a large given that he or she ordered a cold drink.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, 8 + 12 + 5 = 25 people ordered a cold drink, and of them, 5 were large, hence the probability is:
p = 5/25 = 0.2 = 20%.
20% probability that a customer ordered a large given that he or she ordered a cold drink.
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Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of T Q is 16 and the length of R Q is 20.
What is the length of Line segment S R?
9 units
12 units
15 units
18 units
The length of the line segment SR is 15 units.
How to find the length of a line segment?In Δ SRQ as seen in the attached image, we see that;
∠SRQ is a right angle
SQ is the hypotenuse
RT ⊥ SQ
Thus, by triangular rules, we know that;
(RQ)² = TQ × SQ
RQ = 20 units and TQ = 16 units
Thus;
(20)² = 16 × SQ
400 = 16 × SQ
SQ = 400/16
SQ = 25 units
By using Pythagoras theorem in Δ SRQ, we have;
(SR)² + (RQ)² = (SQ)²
RQ = 20 units and SQ = 25 units
Thus;
(SR)² + (20)² = (25)²
(SR)² + 400 = 625
(SR)² = 225
SR = √225
SR = 15 units
The length of the line segment SR is 15 units.
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"You helped 3.6 customers per half hour yesterday."
Employee: "So I helped __________ customers in 7.5 hours yesterday."
Answer: 54
Step-by-step explanation:
So I helped 54 customers in 7.5 hours yesterday.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
You helped 3.6 customers per half hour yesterday.
That means,
for one hour:
Using multiplication
(3.6) x 2 per 1/2 x 2 hours
7.2 per hour.
Therefore,
if n hours so,
(7.2) per n hours
Here, n = 7.5
(7.2) x (7.5) per 7.5 hours
54 customers per 7.5 hours.
Therefore, I helped 54 people in 7.5 hours.
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If a boat with a value of $23, 000 depreciates at a rate of 18% per year, what is the value
after 5 years?
The value of the car after 5 years is 8527.02 dollars
How to find the value after depreciation?Depreciation is the reduction in the value of an asset over time due to elements such as wear and tear. For example a car is said to "depreciate" in value after a discovery of a faulty transmission.
The value after 5 years can be found as follows:
Rate = 18% = 18 / 100 = 0.18
Initial Value = $23,000
time = 5 years
Therefore,
y = 23000(1 + 18%)⁵
y = 23000(1 - 0.18)⁵
y = 23000(0.82)⁵
y = 23000 × 0.3707398432
y = 8527.0163936
y = 8527.02 dollars
Therefore, the value of the car after 5 years is 8527.02 dollars
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Using an exponential function, it is found that the value of the car after 5 years will be of $8,527.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.For this problem, the initial cost and the decay rate are given as follows:
A(0) = 23000, r = 0.18.
Hence the value of the boat after t years is given as follows:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 23000(1 - 0.18)^t[/tex]
[tex]A(t) = 23000(0.82)^t[/tex]
The value after 5 years will be of:
[tex]A(5) = 23000(0.82)^5 = 8527[/tex]
The value of the car after 5 years will be of $8,527.
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An animal shelter has a total of 5 * 47 animals comprised of cats, dogs, and rabbits. If the number of rabbits is 5 less than one half the number of cats, and there are 20 more cats than dogs, how many dogs are at the shelter?
The number of dogs in the animal shelter which comprise of cats, dogs, and rabbits is 84 dogs.
EquationTotal animals = 5 × 47
= 235
Number of rabbits = 1/2(d + 20) - 5Number of cats = d + 20Number of dogs = d235 = d + (d + 20) + 1/2(d + 20) - 5
235 = d + d + 20 + 1/2d + 10 - 5
235 = 2 1/2d + 25
235 - 25 = 2 1/2d
210 = 2 1/2d
d = 210 ÷ 2 1/2
d = 210 ÷ 5/2
= 210 × 2/5
= 420/5
d = 84 dogs
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The terminal side of Ø is in quadrant II and cos ø = -5/13 What is sin ø?
the value of sin ∅ is 12/ 13
Quadrants and the "cast" Rule:In the first quadrant, the values for sin, cos, and tan are positive.In the second quadrant, the values for sin are positive only.In the third quadrant, the values for tan are positive only.In the fourth quadrant, the values for cos are positive only.From the given question,
We have, cos ∅= 5/13
From the trigonometric identities, we have that
[tex]sin^2\alpha + cos^2\alpha = 1[/tex]
Then , let's substitute the value of cos ∅
[tex]sin^2\alpha +(\frac{-5}{13} )^2 = 1[/tex]
Let make sin the subject of formula and find the squares of the fraction
sin²∅ = [tex]1 - \frac{25}{169}[/tex]
Find the LCM
sin²∅ = [tex]\frac{169 - 25}{169}[/tex]
Find the difference
sin²∅ = [tex]\frac{144}{169}[/tex]
Find the square root
sin∅ = [tex]\sqrt{\frac{144}{159} }[/tex]
sin∅ = [tex]\frac{12}{13}[/tex]
In quadrant II , sin is positive, so we have
sin ∅ = 12/ 13
Thus, the value of sin ∅ is 12/ 13
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An H0-scale model railroad engine is 9 inches long. The H0 scale is 87 feet to 1 foot. How long is a real engine?
The real engine is 65.25 feet long
How to determine the length?The scale is given as:
Scale = 87 feet to 1 foot
The scale length is given as
Scale length = 9 inches
Convert inches to feet
Scale length = 9/12 feet
The actual length is then calculated as:
Actual = 87 * 9/12 feet
Evaluate
Actual = 65.25 feet
Hence, the real engine is 65.25 feet long
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50 POINTS!!!!!!!!!!!!!!!!!!!!!!!! SOLVE THIS QUICKLY WITH AN EXPLANATION
Answer:
x = 30 degrees
Step-by-step explanation:
angles MNO, LNM, and KNL make a straight line: 105+45+y = 180 --> y = 30 degrees
KNL = 30 degrees
angle KLN is 90 degrees, a triangle is equal to 180 degrees
2x+30+90 = 180
2x = 60
x = 30 degrees
(02.04 LC)
Determine the equation of the line shown in the graph:
graph of a vertical line with an x intercept of negative 1
y = −1
y = 0
x = −1
x = 0
Answer:
x = - 1
Step-by-step explanation:
the equation of a vertical line is
x = c
where c is the value of the x- coordinates the line passes through
the line passes through the x- intercept of - 1 , then
x = - 1 ← equation of vertical line
solve the equation 13Z/Z+1 =11-3i, Z£C where Z=X+yi X&Y£R?
Presumably you mean the equation
[tex]\dfrac{13z}{z+1} = 11-3i[/tex]
Observe that for [tex]z\neq-1[/tex],
[tex]\dfrac{13z}{z+1} = \dfrac{13(z+1) - 13}{z+1} = 13 - \dfrac{13}{z+1}[/tex]
so we can simplify the equation to
[tex]13 - \dfrac{13}{z+1} = 11 - 3i \implies \dfrac{13}{z+1} = 13 - (11 - 3i) = 2+3i[/tex]
Multiply both sides by [tex]\frac{z+1}{2+3i}[/tex].
[tex]\dfrac{13}{z+1}=2+3i \implies \dfrac{13}{2+3i} = z+1 \implies z = \dfrac{13}{2+3i} - 1[/tex]
Rationalize the denominator by introducing its complex conjugate.
[tex]z = \dfrac{13(2-3i)}{(2+3i)(2-3i)} - 1 = \dfrac{26-39i}{2^2+3^2} - 1 = \boxed{1 - 3i}[/tex]
Jan and Jo live 1,170 miles apart. At the same time, they start driving toward each other on the same road. Jo’s constant rate is 60 mph. Jan’s is 70 mph. How long will it take them to meet?
A. 8 hours
B. 9 hours
C. 16 hours
D. 19 hours
Answer: B. 9 hours
Step-by-step explanation:
Question analysis (Optional if you can understand the question)
Since they are 1170 miles apart, with their speed, the question is asking how long would it take them to travel 1170 miles together.
In other words, the distance that Jo and Jan together add up to 1170 miles.
Given information
Total distance = 1170 miles
Jo's rate = 60 mph
Jan's rate = 70 mph
Set variables
Let x be the time they took to meet each other
Set equation
60x + 70x = 1170
Solve equation
130x = 1170
Divide 130 on both sides
130x / 130 = 1170 / 130
[tex]\boxed{x=9 \: hrs}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
You have a credit card that charges an interest rate of 16.15% compounded monthly. The table below shows your activity for the month of April. Date Activity Amount Balance April 1 Beginning Balance 1,000.00 April 5 Purchase 29.10 1,029.10 April 12 Payment −225.00 804.10 April 15 Purchase 97.25 901.35 April 23 Purchase 19.00 920.35 April 26 Purchase 28.40 948.75 April 30 Ending Balance 948.75 What is the average daily balance for this account? $ What is the finance charge for the month of April? $
1. The average daily balance for this credit card account is $187.74.
2. The finance charge for the month of April is $249.22.
How is the average daily balance calculated?The average daily balance for April is the total of the balance for every day in the billing cycle divided by the number of days in the billing cycle.
A billing cycle for a credit card account is usually one month.
Data and Calculations:Interest rate = 16.15% compounded monthly
Date Activity Amount Balance
April 1 Beginning Balance $1,000.00
April 5 Purchase 29.10 1,029.10
April 12 Payment −225.00 804.10
April 15 Purchase 97.25 901.35
April 23 Purchase 19.00 920.35
April 26 Purchase 28.40 948.75
April 30 Ending Balance 948.75
Total $5,632.05
Average daily balance = $187.735 ($5,632.05/30 days)
Daily interest rate = 0.04425 (16.15%/365)
Finance charge = $249.22 ($187.74 x 0.04425 30 days)
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Select the correct answer.
What is the range of the function shown in the graph?
keeping in mind that the range is vertical values covered by the function, Check the picture below.
If you go out to eat with 3 friends and your meal was $72.50, there is 6.75% sales tax
and you should tip the waiter 15%. How much should each person pay?
Tax $
Total meal cost
Tip $
Total cost of meal with tip
Price for each person
After the tax and the tip are counted, we conclude that each friend must pay $30.
How much should each person pay?We know that the meal cost is $72.50.
Now, there is a 6.75% sales tax and a 15% tip on the waiter (we assume that the tip is based on the total meal cost, after the tax is applied).
Then the total meal cost is:
C = $72.50*( 1 + 6.75%/100%) = $72.50*(1 + 0.0675) = $77.39
Now we also need to add the tip, which is a 15% of that, so the total cost with the tip included is:
C' = $77.39*(1 + 15%/100%) = $88.998 = $90
(Where we rounded up).
Then, if there are 3 friends, each one must pay:
$90/3 = $30
Each friend must pay $30.
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Lindsay is checking out books at the library, and she is primarily interested in mysteries and nonfiction. She has narrowed her selections down to six mysteries and nine nonfiction books. If she randomly chooses three books from her selections, what’s the probability that they will all be nonfiction? Enter a fraction or round your answer to 4 decimal places, if necessary.
Please explain in detail
The probability that all 3 books would be nonfiction is 0.1846.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that all 3 books would be nonfiction = (number of non fiction books / total number of books) x (number of non fiction books - 1 / total number of books - 1) x (number of non fiction books - 2 / total number of books - 2)
9 /15 x 8/14 x 7/13 = 0.1846
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The sum
of three numbers is 24. If two numbers are 16 and 22, what is the third?
Answer:
-14
Step-by-step explanation:
[tex]16+22+x=24\\38+x=24\\x=-14[/tex]
You are training your dog to catch a frisbee. You are playing in a large field, and you are standing next to your dog when you throw the frisbee. If the path of the frisbee is y = –x2 + 9x + 8 and the path of the dog is modeled by y = 3x + 8, will the dog catch the frisbee? If so, what are the coordinates of the point or points where they meet?
Yes, they intersect at the coordinates (0, 8) and (3,17)
Yes, they intersect at the coordinates (0, 8) and (4, 20)
Yes, they intersect at the coordinates (0, 8) and (6, 26)
No, the paths do not cross
Solving a quadratic equation, the correct option is given by:
Yes, they intersect at the coordinates (0, 8) and (6, 26).
What is a quadratic function?A quadratic function is given according to the following rule:
y = ax² + bx + c
The solutions are:
x1 = (-b + sqrt(Delta))/2a
x2 = (-b - sqrt(Delta))/2a
In which:
Delta = b² - 4ac
The equation for this system if:
-x² + 9x + 8 = 3x + 8
x² - 6x = 0
x(x - 6) = 0
Then:
x = 0 -> y = 3 x 0 + 8 = 8.x - 6 = 0 -> x = 6, y = 3 x 6 + 8 = 26.Which means that the correct option is:
Yes, they intersect at the coordinates (0, 8) and (6, 26).
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Find QR.
A).12
B).-8
C).9
D).6
Answer:
D. 6
Step-by-step explanation:
Let's first find x :-
[tex]\sf 3 + 2x + 22 = x + 17[/tex]
[tex]\sf 2x + 25 = x + 17[/tex][tex]\sf 2x - x = 17 - 25[/tex][tex]\sf x = - 8[/tex]Now that we found x, let's find QR :-
QR = 2x + 22
[tex]\sf QR = 2( - 8) + 22[/tex][tex] \sf - 16 + 22[/tex][tex]\sf 6[/tex]Therefore, QR = 6 !!!
PLEASE HELPPPPPPPPPPPP!!!!!!! IM BEING TIMEDDDDDD
Answer:
119°
Step-by-step explanation:
the angles of a triangle make 180° (so does a straight line) therefore
180 (triangle) = a + c + 51
to find c:
180 (straight line) = 112 + c
c = 180 - 112
c = 68°
now we have
180 (triangle) = a + 68 + 51
to find a:
a = 180 - (68 + 51)
a = 180 - 119
a = 61°
to find b:
180 (straight line) = 61 + b
b = 180 - 61
b = 119°
Explain how to draw a line segments that measures 2 7/16 inches.
The line segment which represents 2 7/16 inches should first be drawn with the use of a ruler.
What is a Ruler?This is referred to an instrument which is used to measure distances between points or draw straight lines and also usually graduated in inches.
On the inches graduation, the zero mark should be located and the 1/16 inch which is found before the half-inch mark between 2 and 3 inches. When this is done, a line should be drawn to meet both points which will therefore measure 2 7/16 inches long.
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4/3*(1/2-6)=(4/3*1/2)-(4/3-6)
Answer:
The product would be: -22/3 = 16/3, if true or false: false the left side -7.3 does not equal to the right side 5.3 which means the given statement is false, if it is evaluated -22/3 = 16/3, if multiplied it would still be -22/3 = 16/3 (you never said how to solve it so here are ways)
Eddie built the ramp shown to train his puppy to do tricks.
The dimensions are
25 in.15 in.20 in. 20 in.20 in. 23 in.25 in
HELP PLEASE!!!
The surface area of the trapezoidal prism is: 4,190 in.².
What is the Surface Area of a Trapezoidal Prism?Surface area = (b1+b2)h + PH, where:
Length of the base of the trapezoid (b1) = 20 in.Length of the base of the trapezoid (b2) = 60 in.Height of the trapezoid (h) = 15 in.Perimeter of the trapezoid (P) = 60 + 25 + 20 25 = 130 in.Height of the prism (H) = 23 in.Plug in the values
Surface area = (b1+b2)h + PH = (20 + 60)15 + (130)(23)
Surface area = 4,190 in.²
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Solve the following system of equations.
d + e = 6
d – e = 4
infinite number of solutions
infinite number of solutions
(5, 1)
(5, 1)
no solution
no solution
(3, –1)
(3, –1)
Answer: (5,1)
Step-by-step explanation:
Adding the equations gives 2d=10, and thus d=5.
So, it follows e=1.
Therefore, the solution is (5,1).
The solution is (5,1)
Given that d+e =6 and d-e =4
We need to find the solution of the given equations
Elimination method is used to eliminate a variable in an equation to find the value of another variable
Now here ,
We we will solve the equation i.e
d+e = 6
d-e = 4
Solving this equation We get,
2d = 10
Therefore,
d= 5
Now substituting the value of d in equation d+e =6
therefore,
5+e =6
Therefore e = 1
Hence the solution is (5,1)
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