The quotient of x³ - 64/x - 4 is (x² + 4x + 16).
The quotient of x⁴ − 256/x − 4 is (x³ + 4x² + 16x + 64).
The quotient of x⁵ - a⁵ /x - a is (x⁴ + ax³ + a²x² + a³x + a⁴).
What is Division method?
Division method is used to distributing a group of things into equal parts.
We have to given that;
The quotient of x² − 16/ x − 4 is x + 4.
Now, We have compute each quotient as;
The quotient of x³ - 64/x - 4 is;
[tex]\frac{x^{3} - 64}{x-4} = \frac{x^{3} - 4^{3} }{x-4} = \frac{(x-4) (x^{2} +4x+16)}{(x-4)} = (x^{2} +4x+16)[/tex]
Hence, The quotient of x³ - 64/x - 4 is (x² + 4x + 16).
And, The quotient of x⁴ − 256/x − 4 is;
[tex]\frac{x^4-4^4}{x-4} = \frac{((x^2)^2-(4^2)^2)}{(x-4)} = \frac{(x^{2} -4^4) (x^{2} + 4^2)}{(x-4)} = \frac{(x-4)(x+4)(x^{2} +4^2)}{(x-4)} = (x+4)(x^{2} + 16)[/tex]
[tex](x+4)(x^{2} + 16) = x^{3} + 4x^{2} +16x + 64[/tex]
Hence, The quotient of x⁴ − 256/x − 4 is (x³ + 4x² + 16x + 64).
The quotient of x⁵ - a⁵ /x - a is;
_______
x - a ) x⁵ - a⁵ ( x⁴ + ax³ + a²x² + a³x + a⁴
x⁵ - ax⁴
- +
-------------------
ax⁴ - a⁵
ax⁴ - a²x³
- +
-------------------
a²x³ - a⁵
a²x³ - a³x²
- +
-----------------
a³x² - a⁵
a³x² - a⁴ x
- +
--------------------------
a⁴ x - a⁵
a⁴ x - a⁵
- +
-----------------------
0
Hence, The quotient of x⁵ - a⁵ /x - a is (x⁴ + ax³ + a²x² + a³x + a⁴).
Therefore, The quotient of x³ - 64/x - 4 is (x² + 4x + 16).
The quotient of x⁴ − 256/x − 4 is (x³ + 4x² + 16x + 64).
The quotient of x⁵ - a⁵ /x - a is (x⁴ + ax³ + a²x² + a³x + a⁴).
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To rent a certain meeting room, a college charges a reservation fee of $47 and an additional fee of $5.70 per hour. The history club wants to spend at most
$75.50 on renting the meeting room.
What are the possible amounts of time for which they could rent the meeting room?
Use t for the number of hours the meeting room is rented, and solve your inequality for t.
Answer:
to be honest i don't know :^
NO LINKS!! Please help me
Answer:
[tex]\textsf{b)} \quad -\dfrac{\sqrt{7}}{4}[/tex]
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
θ is the angle.O is the side opposite the angle.A is the side adjacent the angle.H is the hypotenuse (the side opposite the right angle).[tex]\textsf{If}\; \cos(\theta)=-\dfrac{3}{4} \implies \sf A=3 \; \textsf{and} \; H=4.[/tex]
Use Pythagoras Theorem to calculate the length of the opposite side:
[tex]\sf \implies O^2+A^2=H^2[/tex]
[tex]\implies \sf O=\sqrt{H^2-A^2}[/tex]
[tex]\implies \textsf{O}=\sqrt{4^2-3^2}[/tex]
[tex]\implies \textsf{O}=\sqrt{7}[/tex]
Therefore, substituting the values of O and H into the sine ratio:
[tex]\implies \sin\theta=\dfrac{\sqrt{7}}{4}[/tex]
As the terminal side of the angle is in Quadrant III, and sine is negative in Quadrants III and IV, the exact value of sin(θ) is:
[tex]\implies \implies \sin\theta=-\dfrac{\sqrt{7}}{4}[/tex]
Members of a soccer team raised $2143.50 to go to a tournament. They rented a bus for $888.50 and budgeted $62.75 per player for meals. Write and solve an equation which can be used to determine xx, the number of players the team can bring to the tournament.
Equation:
Answer:x=
The equation to determine the number of players the team can bring to the tournament is xx = (2,143.50 - 888.50)/62.75.
What is an equation?An equation is a mathematical statement that shows that two or more mathematical expressions are equal.
Equations express the equality of mathematical expressions by using the equation mark (=).
Data and Calculations:The total amount raised for the tournament = $2,143.50
The amount for renting a bus = $888.50
The cost of budgeted meals per player = $62.75
The equation to determine xx is the number of players the team can bring to the tournament (xx = (2,143.50 - 888.50)/62.75.
Check:
xx = (2,143.50 - 888.50)/62.75
xx = 1,255/62.75
xx = 20
Thus, the equation to determine the number of players the team can bring to the tournament is xx = (2,143.50 - 888.50)/62.75.
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Can Any one help me on this and explain it?
Answer: to be honest looks kinda hard
Step-by-step explanation:
I think both are 4
Ruben is driving along a highway that passes through Barstow. His distance d, in miles, from Barstow is given by the equation
d = |210 − 60t|,
where t is the time, in hours, since the start of his trip and
0 ≤ t ≤ 5.
When will Ruben be exactly 90 miles from Barstow?
Answer:
after 2 hours, andafter 5 hoursStep-by-step explanation:
Given that Ruben's distance from Barstow is d = |210 -60t|, you want to know the time t when he is exactly 90 miles from Barstow.
SetupThe absolute value will be 90 when the argument of the function is either -90 or +90.
The question resolves to two equations:
210 -60t = -90210 -60t = 90SolutionThese two-step linear equations can be solved in the usual way:
-60t = -300 . . . . subtract 210-60t = -120Then ...
t = -300/-60 = 5 . . . . divide by the coefficient of tt = -120/-60 = 2Ruben is 90 miles from Barstow after driving 2 hours, and again after driving 5 hours.
What’s the coefficient in this expression, 12x+z^4.
12
x
z
4
Answer:
12 is the coefficient.
Step-by-step explanation:
1.8x7+3 (1 point)
o 67
o 80
o 59
o 18
A map is drawn to a scale of 28 miles per inch.
inches: 0.5 miles: 14
inches: 1 mile 28
inches: 1.5 miles 42
The British imperial and American customary systems of measurement both use the inch as their standard unit of length (symbolized as in or ′′). It is equivalent to 1/36 of a yard or 1/ 12 of a foot. The term inch, which is often used to translate comparable units in other measurement systems and is derived from the Roman uncia ("twelfth"), is generally considered to refer to the breadth of the human thumb.
Since the international yard was adopted in the 1950s and 1960s, standards for the precise length of an inch have varied, but the inch is now based on the metric system and is defined as precisely 25.4 mm.
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3. During a school trip, Class 6 students of a school saw the sign shown below at the entrance of an amusement park ride. Which of the following can be the MAXIMUM number of these students who can take the ride at the same time?
Sign
The Lazy Poseidon Maximum Capacity 1000 kgs Have Fun!
a. 5
b. 20
c. 50
d. 100
Answer:
50
explanation:
1000 divided by 50 = 20
One person can at least be 20 kg.
20 students can ride in one turn
The maximum number of these students who can take the ride at the same time will be 50. Then the correct option is C.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
During a school trip, Class 6 students of a school saw the sign shown below at the entrance of an amusement park ride.
The average weight of the student is 20 kg.
The Lazy Poseidon Maximum Capacity 1000 kgs Have Fun!
The maximum number of these students who can take the ride at the same time will be
⇒ 1000 / 20
⇒ 50
The maximum number of these students who can take the ride at the same time will be 50. Then the correct option is C.
The missing sentence is given below.
The average weight of the student is 20 kg.
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5 thousands equals how many tens
someone please help!
Answer:
4a + 2b + 5
Step-by-step explanation:
4a−1+2b+6
=4a+−1+2b+6
Combine Like Terms:
=4a+−1+2b+6
=(4a)+(2b)+(−1+6)
=4a+2b+5
Use function notation to write the equation of the line.
please help
Answer:
f(x) = -3/2 x - 2
Step-by-step explanation:
The line rises to the left so the slope is negative, also:
the slope of the line is -3/2 and the y-intercept is at (0, -2)
5. A car. travels 220 miles in 4 hours. What is
the constant of proportionality that relates y,
the total number of miles, to x, the number of
hours?
k =
the car is traveling at 55 mph
I am a two digit multiple of eleven. I am not odd. My digits, when multiplied, make a cube and a square out of me. What number am I? (30 pts) Explain and prove your answer. (70 pts)
The digit that when multiplied, make a cube and a square out of the number is 88.
How to calculate the value?It should be noted that this has to do with mental reasoning.
It should be noted that 8 × 8 = 64. This is the square of 8.
Also, it should be noted that 4 × 4 × 4 = 64. This gives the cube value.
Therefore, the number is 88.
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Use
x
for your variable
The sum of a number increased by nine and the number decreased by two.
The answer is [tex](x+9)+(x-2)[/tex] .
A variable is a symbol used to represent a number in an expression or equation. The value of this number is subject to change. An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.We have given two statements one is " number increased by nine "
Let the number be x .
Mathematically , first statement is represented by
x + 9
Second statement is " number decreased by two "
Mathematically , second statement is represented by
x - 2
According to the question
Sum of first and second statement = [tex](x+9)+(x-2)[/tex]
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Which statement is the inverse of the conditional statement: If point B bisects line segment AC into two congruent segments, then point B is the midpoint.
The inverse of the given statement will be- Option 3, If point B is the midpoint, then point B bisects line segment AC into two congruent segments.
Here, we are given a statement: If point B bisects line segment AC into two congruent segments, then point B is the midpoint.
According to the statement,
if B bisects AC ⇒ AB = BC
then, B is the midpoint.
The inverse of this will be-
if B is the midpoint of AB ⇒ AB = BC
then, B bisects AB
This can be written as-
If point B is the midpoint, then point B bisects line segment AC into two congruent segments.
Thus, option 3 is the correct answer.
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Your question was incomplete. Check below for full content-
Which statement is the contrapositive of the conditional statement:
Which statement is the inverse of the conditional statement: If point B bisects line segment AC into two congruent segments, then point B is the midpoint.
1. If point B is not the midpoint, then point B does not bisect line segment AC into two congruent segments.
2. Point B bisects line segment AC into two congruent segments if, and only if, point B is the midpoint.
3. If point B is the midpoint, then point B bisects line segment AC into two congruent segments.
4. If point B does not bisect line segment AC into two congruent segments, then point B is not the midpoint.
The length of a shadow of a building is 10 m. The distance from the top of the building to the tip of the shadow is 26 m. Find the height of the building
Answer:
The height of the building is 24m
Step-by-step explanation:
This can be solved using the Pythagorean theorem
which states that the three sides of a right triangle are related by the equation
[tex]c^2 = a^{2} + b^{2}[/tex] (see figure)
where c is the hypotenuse and a, b are the other two sides
Here we have c = the distance from the top of the building to the tip of the shadow = 26m
One side, the length of the shadow ie b = 10 m
So we have
[tex]26^2 = a^2 + 10^2[/tex] where a is the height of the building
Switch sides to get
[tex]a^2 + 10^2 = 26^2[/tex]
[tex]a^2 + 100 = 676[/tex]
Subtract 100 from both sides
[tex]a^2 = 676 - 100 = 576[/tex]
[tex]a = \sqrt{576}[/tex]
a = 24
The height of the building is 24m
CAN SOMEONE PLEASE ANSWER WITH THE STEPS??
-5 2/3 · 3 3/4
simplified answer pls
Answer:
[tex]-21\frac{1}{4}[/tex]
Step-by-step explanation:
First you need to get them into improper fractions. To do that multiply the whole number by the bottom number, and then add the top number:
[tex]-5\frac{2}{3} = -\frac{17}{3} \\3\frac{3}{4} = \frac{15}{4}[/tex]
Next, multiply the numerators (top numbers) by the denominators (bottom numbers)
[tex]-\frac{255}{12}[/tex]
Next just fix it and make it a mixed number. Just divide -255 by 12
The answer is -21.25
Just make that into a fraction and you are finished
Rachel bought 7 pounds of
grapes at $1.34 per pound, and
6 pounds of kiwi at $2.87 per
pound. How much did Rachelork
spend on the fruit?
A package of 88 batteries costs $ 4 . 724.72 .
What is the cost per battery?
We get that the cost of the battery is $ 8.24 per battery.
We are given that the cost of 88 batteries = $ 724.72
We need to find the cost of one battery.
We will do this by diving the cost of 88 batteries by 88.
Using division, we get that:
cost of one battery = $ 724.72 ÷ 88
Simplifying the expression, we get that:
cost of one battery = $ 8.24 per battery.
Therefore, we get that the cost of the battery is $ 8.24 per battery.
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former minnesota vikings quarterback brett favre throws a football at a speed of 35 meters per second . if the weight if the football is 0.4 kg, what would the kinetic energy of brett favre's pass be?
The kinetic energy of brett favre's will be 245 J.
To accelerate Associate in Nursing object, we've to use force. to use force, we want to try to to work. once work is completed on Associate in Nursing object, energy is transferred, and also the object moves with a replacement constant speed. we have a tendency to decision the energy that's transferred K.E., and it depends on the mass and speed achieved.Kinetic energy of Associate in Nursing object is that the live of the work Associate in Nursing object will treat virtue of its motion.Kinetic energy may be a scalar amount, and it's entirely represented by magnitude alone and is given by K.E = 1 /2 mv² .....(1) where "m" is that the body’s mass, and "v" is that the body’s speed.It is given that speed is 35 meters per second and mass of football is 0.4 kg .
Using equation (1) , we get
K.E = 1 /2 (0.4)(35)²
= 490 / 2
= 245 J
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please help!
maths geometry
Step-by-step explanation:
trapezium means especially
AD || BC
AC = BC tells us that ABC is an isoceles triangle (both legs are identically long, which makes also their angles with their baseline AB equal).
therefore, A1 = B = 80°.
and because the sum of all angles in a triangle is always 180°, we get
180 = 80 + 80 + C1
C1 = 20°
(e)(1)
because of the law of a line intersecting parallel lines with the same angles, and AC is intersecting the parallel lines AD and BC, we know that
C1 = A2 = 20°
(e)(2)
because also the sum of all angles around a single point on one side of a line is 180°, we know D1 + D2 = 180°.
we also know that D2 is an angle in an equilateral triangle (that means all 3 sides are equally long, and therefore all 3 angles are equal too = 180/3 = 60°) and therefore
D2 = 60°.
therefore, D1 = 180 - 60 = 120°.
so, for the triangle ACD we have
180 = A2 + D1 + C2 = 20 + 120 + C2
C2 = 40° = 2×20 = 2×C1
(f)(1)
a kite is a quadrilateral, and as such the sum of all angles is 360°.
again remember the symmetry of a kite, so the angles at H and at F must be equal.
H = F = x
so, we have
360 = 110 + 50 + H + F = 110 + 50 + 2x
200 = 2x
x = 100°
(f)(2)
after drawing EG we see that this line splits the kite into 2 equal (ahem, congruent) triangles due to the symmetry of a kite exactly along that line.
and that splits both angles E and G in half for each of the triangles.
again, the sum of all angles in a triangle is 180°, so
180 = 110/2 + 50/2 + x = 55 + 25 + x = 80 + x
x = 100°
mr keon spent 5/8 of his salary of
2 416.00 on food,rent,clothes and transport how mush money did he spend
The salary Mr. Keon spent 1510 on food, rent, clothes, and transport.
The term "linear function" in mathematics applies to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
If y is the amount of money Mr. Keon spent on food and clothes and x is Mr. Keon's salary.
Then the linear function for the relation between x and y is:
y = ( 5/8) × (x)
y = (5/8)x
The salary of Mr. Keon is 2416.
Now, Mr. Keon spent 5/8 of his salary on food, rent, clothes, and transport.
Let x be the money she spent.
Then,
x = 5/8 of Mr. Keon's salary
x = ( 5/8 ) × 2416
x = ( 2416 × 5 ) / 8
x = 12080 / 8
x = 1510
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if a = 2 + i, and b = 3 -2i, what is a/b?
Answer:
75-79 i87
Step-by-step explanation:
find the perimeter or circumference and area of each figure if each unit on the graph measure 1 centimeter. round answers to the nearest tenets, if necessary
The circumference of the circle = 17.8 units
The area of the circle = 25.1 square unit
Given,
the points are A(2,3) and B(4,1)
Formula to get the circumference of a circle = 2πr
Where r = radius of the circle
Radius of the given circle = Distance between the points A(2, 3) and
B(4, 1)
r = √(2 - 4)² + (3 -1)²
r = √(-2)² + (2)²
r = √4+4
r = √8
r = √2(4)
r = 2√2
Therefore the circumference is = 2π(2√2)
= 17.77
≈ 17.8 units
Area of the circle = πr²
= π(2√2)²
= 8π
= 25.13
≈ 25.1 square unit
Hence we get the circumference and area of the circle as 17.8 units and 25.1 square unit respectively.
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A plastic boulder was launched from a second-floor window, using a catapult. The function below represents the height of the
plastic boulder from the ground, h(t), in feet, over time, t, in seconds.
h(t) = -2x² + 2x + 40
How many seconds did it take for the plastic boulder to hit the ground?
Answer:
5 seconds
Step-by-step explanation:
Given the height function h(t) = -2x² + 2x + 40, you want the positive value of t such that h(t) = 0.
SolutionThe given function can be factored as ...
h(t) = -2(x -5)(x +4)
This will be zero when the factors are zero:
x -5 = 0 ⇒ x = 5
x +4 = 0 ⇒ x = -4
The positive value of t for which the height is zero is t = 5.
It took 5 seconds for the plastic boulder to hit the ground.
__
Additional comment
There are several methods available for factoring the equation. One is to factor out the leading coefficient, then factor the remaining quadratic.
-2(x² -x -20)
To factor this, you're looking for factor pairs of -20 that have a sum of -1.
-20 = -20(1) = -10(2) = -5(4)
The last of these, {-5, 4} has a sum of -1. These are the constants that go into the binomial factors.
12x-4
————
2
Simplify
Answer: 6x-2 ==> option 4
Step-by-step explanation:
(12x-4)/2=
12x/2 - 4/2= 6x-2 ==> option 4
Answer:
Step-by-step explanation:
Question 5(Multiple Choice Worth 2 points)
(Multi-Step Percent Problems MC)
Oliver borrowed $2,500 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 20% for 3 months Calculate the simple
interest using /-prt.
O $60
O$125
O$1,250
O$1,500
The 20% rate the bank borrowed Oliver the loan for 3 months gives an interest of $125.
How can the simple interest be calculated?The amount Oliver borrowed = $2,500
The interest rate applied to the loan = 20%
Required: To calculate the simple interest using the formula, I = P•R•T
Where;
I = The simple interest
P = The principal borrowed = $2,500
T = The time or loan duration = 3 months = 1/4 year
R = The rate at which the loan is applied = 20% = 0.2
Therefore;
I = $2,500 × 0.2/year × 3/12 year = $125
The correct option for the interest paid on the loan is therefore;
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Answer:
125
Step-by-step explanation:
on a map, two cities are 5 1/2 inches apart. the map uses a scale of 2 inches =75 miles
what is the actual distance between the two cities?
Answer:
187.5 miles
Step-by-step explanation:
We can use the rationing method to solve for this problem.
2 inches on map = 75 miles actual distance
1 inch on map = (75 ÷ 2) = 37.5 miles actual distance
5.5 inches on map = (37.5 × 5) = 187.5 miles actual distance
Please help! How are you supposed to fill in something that isnt there? If you took the derviative of x wouldn't it be one?
Answer:
f'(5) = 1
Step-by-step explanation:
You are right. The derivative of f(x) = f'(x) = 1 a constant
If you plot y = f'(x) = 1 it will be a vertical line passing through x = 1 (See graph)
This means f'(x) is constant and equal to 1 for all values of y
So whether it is f'(5) or f'(100) the value = 1
f'(5) = 1