The remainder of the given division ( x³+5x²−32x−7 ) ÷ ( x−4 ) is equal to 9.
As given in the question,
Dividend of the given division is equal to : ( x³+5x²−32x−7 )
Divisor of the given division is equal to : ( x−4 )
Divide the given dividend ( x³+5x²−32x−7 ) by divisor ( x−4 ) remainder we get,
( x³+5x²−32x−7 )
= x³ -4x² +9x² -36x +4x-16 +9
= x²(x-4) + 9x (x-4) +4(x-4) + 9
= (x-4)(x² +9x +4) + 9
Quotient is equal to (x² +9x +4)
Remainder is equal to 9
Therefore, the remainder of the given division ( x³+5x²−32x−7 ) ÷ ( x−4 ) is equal to 9.
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Homework: Section 3.4HomeworkQuestion 6, 3.4.25 >HW Score: 50%, 5 of 10 pointsO Points: 0 of 1SaveFind an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verifythe real zeros and the given function value.n=3;3 and 4 i are zeros;f(2)=40f(x)=(Type an expression using x as the variable. Simplify your answer.)Clear allCheck answerHelp me solve thisView an example Get more help.
The roots are
[tex]\begin{gathered} x=3 \\ x=4i \\ x=-4i \end{gathered}[/tex]The polynomial can be modellled as ;
[tex]f(x)=a(x-3)(x-4i)(x+4i)[/tex][tex]f(x)=a(x-3)(x^2+16)[/tex]
Let us use f(2) to obtain a value for a
[tex]\begin{gathered} f(2)=a(2-3)(2^2+16) \\ 40=-20a \\ a=-2 \end{gathered}[/tex]The polynomal f(x) is given as
[tex]\begin{gathered} f(x)=-2(x-3)(x^2+16) \\ f(x)=-2x^3+6x^2-32x+96 \end{gathered}[/tex]help pls
1
3
144
432
The value of the given equation is 12.
What is the value of the equation?In order to solve this question, the BODMAS rule would be used. The BODMAS rule gives the order in which mathematical operations can be solved. The order is:
Bracket OfDivision Multiplication Addition SubtractionIn the numerator:
the addition would be done first: 3² + 1 = 9 + 1 = 10
Then the subtraction would be done next = 14 - 10 = 4
Now determine the square of the term in the bracket : 4²= 16
In the denominator:
The multiplication would be solved first: 3 x 1/4 = 3/4
The next step is to solve the division : 1 ÷ 3/4 = 1 x 4/3 = 4/3
The fraction becomes : 16 ÷ 4/3
16 x 3/4 = 12
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Answer:
The answer is 432
Step-by-step explanation:
I did the k 12 quiz and I got it right! good luck
By looking at the equation of the least-squares regression line, you can see that the correlation between height and arm span is.
Step-by-step explanation:
If the data shows a leaner relationship between two variables, the line that best fits this linear relationship is known as a least-squares regression line, which minimizes the vertical distance from the data points to the regression line.
The animals at a safari park include crocodiles, deer and penguins.
There are 16 more deer than there are crocodiles. 4 There are 3 times as many penguins as there are crocodiles. There are the same number of deer as there are penguins.
How many crocodiles are there at the safari park?
Answer:
8
Step-by-step explanation:
8x3 = 24
8+ 16 = 24
write four cubed in expanded form and then evaluate
Answer:
64
Step-by-step explanation:
4^3 = 4 x 4 x 4 which can be written as 2^6 which is equivalent to 64 too
(If this is what you're asking)
suppose 9 people arrive at a bank at the same time. in how many ways can they line up to wait for the next available teller? a) 40,320 b) 362,880 c) 9 d) 5,040 e) 81 f) none of the above.
The number of ways in which they can line up to wait for the next available teller is 362880.
What is termed as the permutation?We occasionally want to understand how many different ways we can order a set of items. A permutation is the number of different ways this may be done.We want to know how many different ways there are to line up 9 people.
We can choose one of the nine people in line to take the first spot. There are just eight people left to select from once we've decided who will fill this position. This means that only eight people can fill this same second position in this line. Now that the first two spots are filled, there are just seven people left to fill the third, and this line of thought can continue until the last spot is filled.= 9×8×7×6×5×4×3×2×1
= 362880
Thus, the number of ways in which they can line up to wait for the next available teller is 362880.
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after the given information, at least how many more steps are necessary to solve this proof
The following steps would be:
• TP and TP (for both triangles) are congruent by the reflexive property.
,• The triangles are congruent by the SAS theorem.
,• Angle S and angle O are congruent.
Two parallel lines are cut by a transversal as shown belc
Suppose m 8 =107 Find m2 1and m2 3
1
2
4
3
5
6
8
7
The values of the angles m∠1 and m∠3 is equal to 73°.
A transversal may be defined as a line which cuts a pair of parallel lines and forms several angles. When transversal cuts parallel lines the alternate interior angles are equal as well as the corresponding angles are equal. Also, the pair of vertically opposite angles are equal. From the figure attached. ∠4 = ∠8 as they are corresponding angles. So, m∠8 = m∠4 = 107°. Now, we know that ∠1 and ∠4 formed a pair of linear angles and the sum of the measures of the linear angles is 180°. So,
m∠1 + m∠4 = 180°
We know, m∠4 = 107°
m∠1 = 180° - 107°
m∠1 = 73°
Now, ∠1 and ∠3 are vertically opposite angles, so they are equal as the parallel lines are cut by transversal. Therefore, m∠1 = m∠3
=> m∠1 = 73°
=> m∠3 = 73°
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Calculate the average rate of change of fover the interval -3≤x≤9. Show the calculations that lead to your answer.
The function has an average rate of change f is 1/2 over the interval
How to determine the average rate of change f?The possible graph that completes the question is added as an attachment
The interval is given as
-3 ≤ x ≤ 9
This can be rewritten as
x = -3 to x = 9
This can also be represented as
(a, b) = [-3, 9]
From the attached graph, we have
f(-3) = -1.5
Also, we have
f(9) = 0.5
The estimate (to one decimal place) of the average rate of change f is calculated as
Rate = [f(b) - f(a)]/[b - a]
This gives
Rate = [f(9) - f(-3)]/[9 + 3]
So, we have
Rate = [0.5 + 1.5]/[9 + 3]
Evaluate
Rate = 2/12
Simplify
Rate = 1/6
Hence, the average rate of change f is 1/6
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Please answer quick i really need help
Answer:
( - 36, 24 )
Step-by-step explanation:
(- 9, 6)
( - 9×4, 6×4)
( - 36, 24 )
1. (01.01 LC)
Which of the following is a flat surface that extends infinitely, has length and width, but does not have depth?
Angle
O Circle
O Plane
Segment
Answer:
plane
Step-by-step explanation:
The plane is flat like a wall or the floor. It has infinite length and infinite width but has no thickness (as thick as a line--which has no thickness) basically a line is one-dimensional and a plane is two-dimensional.
See image.
Marybeth rides her skateboard 5 miles in 30 minutes. If she maintains this rate, how far will she ride her skateboard in 4 hours?
A triangular boat's sail has a total area of 7 square inches.
If the height of the sail is 3 inches less than twice the
length of its base, then find the length of the base and
height.
Answer: b = 3.5, h = 4
Step-by-step explanation: a = 1/2bh, area of a triangle formula
7 = 1/2((b)(2b-3)) state h in terms of b
7 = 1/2(2b^2-3b) simplify
7 = b^2 - 1.5b simplify
b = 3.5 final answer
Then, solve for h.
h = 7 - 3 substitute
h = 4 final answer
hope this helps!
Step-by-step explanation:
area of a triangle
base × height / 2
in our case
base × height / 2 = 7
base × height = 14
height = 2×base - 3
we can use the last identity in the area equation and get
base × (2×base - 3) = 14
2×base² - 3×base - 14 = 0
the solution to a quadratic equation like
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
base = (3 ± sqrt((-3)² - 4×2×-14))/(2×2) =
= (3 ± sqrt(9 + 112))/4 = (3 ± sqrt(121))/4 =
= (3 ± 11)/4
base1 = (3 + 11)/4 = 14/4 = 7/2 = 3.5 in
base2 = (3 - 11)/4 = -8/4 = -2
negative numbers for sizes of physical objects don't make sense, so, base = 3.5 in is our solution.
height = 2×base - 3 = 2×3.5 - 3 = 7 - 3 = 4 in
base length = 3.5 in
height = 4 in
Using the SSS congruence is criterion what additional information is needed to show that triangle RST is congruent to triangle UTS?
The additional information you will need to show that triangles RST and UTS are congruent by SSS congruence is: c. RT ≅ US.
How to Prove Two Triangles are Congruent by SSS Congruence Postulate?To prove that two triangles are congruent to each other using the SSS congruence as a criteria, we need to know or be able to show that the three sides of one triangle are congruent to the corresponding 3 sides of the other triangle.
If this criterion is met, then we have enough information needed to show the two instruments are congruent by the SSS congruence.
RS ≅ UT as marked in the diagram shown. Also, by the reflexive property, we ST ≅ TS.
We already know two pairs of sides are congruent to each other in both triangles.
In other to prove the triangles are congruent by SSS congruence, the additional information needed is: c. RT ≅ US.
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Answer:
Step-by-step explanation:The additional information you will need to show that triangles RST and UTS are congruent by SSS congruence is: c. RT ≅ US.
How to Prove Two Triangles are Congruent by SSS Congruence Postulate?
To prove that two triangles are congruent to each other using the SSS congruence as a criteria, we need to know or be able to show that the three sides of one triangle are congruent to the corresponding 3 sides of the other triangle.
If this criterion is met, then we have enough information needed to show the two instruments are congruent by the SSS congruence.
RS ≅ UT as marked in the diagram shown. Also, by the reflexive property, we ST ≅ TS.
We already know two pairs of sides are congruent to each other in both triangles.
In other to prove the triangles are congruent by SSS congruence, the additional information needed is: c. RT ≅ US.
3x = 0Graph the line by plotting any two ordered pairs with integer value coordinates that satisfy the equation
we have the equation
3x=0
is the same that
x=0
This is a vertical line (is the equation of the y-axis)
two ordered pairs that lies in this line are
(0,4) and (0,10)
graph the line
plot the points and join them
see the attached figure
Mohal has a loyalty card good for a discount at his local pharmacy. To find the total he has to pay, before tax, he multiplies the prices by 0.96. What percent discount does the card give?
The percent discount the card gives can be:
4% or 96%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Royal card for discount.
Multiplying the total price to pay with 0.96 means two cases.
0.96 = 96/100 = 96%
Cases 1:
If the percent discount is 96% we will multiply the total prices to pay by 0.96 and subtract the value from the total price.
Example:
Total price to pay = 100
0.96 x 100 = 96
Total price to pay = 100 - 96 = 4
Cases 2:
If the percent discount is 4% we will multiply the total prices to pay by 0.96 after subtracting 4% from 100%.
Example:
Total price to pay = 100
Discount = 4%
100% - 4% = 96%
96% = 0.96
Total price to pay = 0.96 x 100 = 96
Thus,
The percent discount the card gives can be:
4% or 96%.
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MARKING BRAINLEIST PLS HELP ME OUT HERE
316 is value of circle's arc BC .
What is an arc in maths?
A circle's arc is referred to as a portion or section of its circumference. A chord of a circle is a straight line that might be created by joining the arc's two ends. A semicircular arc is one whose length perfectly divides the circumference of the circle.A circle's circumference forms an arc. An arc length is the length of the arc, whereas an arc measure is the measurement of the angle the arc makes at the center of a circle. This measurement can be expressed in radians or degrees. Using the fact that pi radians = 180 degrees, we can quickly convert between the two.Short arc BC is the difference between 360° and long arc BAC
arc BC = 360 - arc BAC
= 360 - 44
= 316
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resuelve la siguiente ecuación con el metodode suma y resta x + y = 5
2x + y = 4
La solucion del sistema de ecuaciones es x = 1, y = 4, o (1, 4) en notación standard.
¿Como resolver el sistema de ecuaciones?Aqui tenemos el sistema de ecuaciones:
x + y = 5
2x + y = 4
Si tomamos la segunda ecuación, y a esta le restamos la primera, obtendremos:
(2x + y) - (x + y) = 5 - 4
(2x - x) + (y - y) = 1
x = 1
De esta forma encontramos el valor de x, para encontrar el valor de y, deberemos reemplazar x = 1 en una de las ecuaciones. Yo usare la primear.
x + y = 5
1 + y = 5
y = 5 - 1
y = 4
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82.8 cm measured to the nearest tenth of a cm.
Yall please help i need to turn this in i have too many demerits
The answers to all the subparts are:
(A) 5 cups of yellow paint will be needed with 1 cup of blue paint to make the same green shade.(B) The new pair to make the same shade of green will be 4 cups of blue paint and 20 cups of yellow paint.(C) The proportional relationship of the table will be x : 5y.(D) According to part (C), the Constant of proportionality will be x : 5y.What is constant proportionality?The ratio of two proportional values at a constant value is known as the constant of proportionality. When either their ratio or product results in a constant, two variables' values are said to be proportionally related. The ratio between the two specified quantities determines the value of the proportionality constant.So, (A) To make the same shade of green:
Cups of blue paint: 2Cups of yellow paint: 10Then, cups of yellow paint when blue paint is just 1 cup:
10/2 = 5/1 = 5
Therefore, 5 cups of yellow paint will be needed with 1 cup of blue paint to make the same green shade.
(B) New pair of numbers to make the same green shade:
Old pair:
Cups of blue paint: 2Cups of yellow paint: 10Another pair:
Cups of blue paint: 1Cups of yellow paint: 5The new pair would be:
Cups of blue paint: 2 × 2 = 4Cups of yellow paint: 10 × 2 = 20Therefore, the new pair to make the same shade of green will be 4 cups of blue paint and 20 cups of yellow paint.
(C) Proportional relationship:
Let cups of blue paint be: xCups of yellow paint be: yOld pair:
Cups of blue paint: 2Cups of yellow paint: 10Proportional relationship will be:
2x/10y = x/5y ⇒ x : 5yTherefore, the proportional relationship of the table will be x : 5y.
(D) Constant of proportionality:
According to part (C), the Constant of proportionality will be x : 5y.
Therefore, the answers to all the subparts are:
(A) 5 cups of yellow paint will be needed with 1 cup of blue paint to make the same green shade.(B) The new pair to make the same shade of green will be 4 cups of blue paint and 20 cups of yellow paint.(C) The proportional relationship of the table will be x : 5y.(D) According to part (C), the Constant of proportionality will be x : 5y.Know more about constant proportionality here:
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A car’s velocity increases from 4.2m/s to 14.8 m/s, E, in 2.5 sec. What is its acceleration?
The acceleration is 4.24 m^2/s
What is acceleration?
They are accelerations and vector quantities. The direction of an object's acceleration is determined by the direction of the net force acting on it. Acceleration describes the rate at which a speed changes over time.
The velocity is changing over time. The velocity is actually changing at a constant rate of 10 m/s per second. If an object's velocity is changing, it is said to be accelerating; it has acceleration.
According to question,
Acceleration = final velocity- initial velocity/ time
Final velocity = 14.8 and initial velocity = 4.2
Hence, acceleration = 14.8-4.2/2.5
=10.6/2.5
=4.24.
The acceleration is 4.24 m^2/s.
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equivalent to 6+12x?
Answer:
Step-by-step explanation:
6 + 12x
6 ( 1 + 2x )
Determine if 0.868668666866668666668...0.868668666866668666668... is rational or irrational and give a reason for your answer.
The numbers given as 0.868668666866668666668... and 0.868668666866668666668... are irrational numbers
How to categorize the numbers?From the question, the numbers are given as
0.868668666866668666668... and 0.868668666866668666668...
As a general rule.
Numbers that end in three dots are irrational numbers
The above is true because
These numbers are non-terminating decimals (i.e. theu do not end)These numbers cannot be represented as a fraction of integersWhen numbers cannot be represented as a fraction of integers, then such numbers are irrational numbers
Hence, the numbers are irrational numbers
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Both the given values 0.868668666866668666668.. and 0.868668666866668666668... are irrational numbers.
What are irrational numbers?An irrational number is a type of real number which cannot be represented as a simple fraction or the values that have face value are irrational numbers. Example: √2, √3, and π are all irrational.
Here,
Both numbers are irrational numbers, because
Thus, Both the given values 0.868668666866668666668.. and 0.868668666866668666668... are irrational numbers.
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Complete each statement with a number that makes the statement true.
A. __< 7°C.
B. __ <-3°C.
C. -0.8°C <___< -0.1°C
D. __> -2°C
Answer:
A. 6°C
B. -4°C
C. -0.7°C
D. -1°C
Answer:
A. 6°C < 7°C.
B. -4°C < -3°C.
C. -0.8°C < -0.7°C < -0.1°C
D. -1°C > -2°C
M= 19.7t² + 310.5t +7539.6
F= 28t² + 368t + 10127.8
modeling with mathematics during a recent period of time, the number (in thousands) of males M and females F that attend degree-granting institutions in the United States can be modeled by M= and F=
where t is time in years. Write a polynomial in standard form to model the total number of people attending degree-granting institutions. The polynomial is P=
Using addition of polynomials, the function modeling the number of people attending degree-granting institutions is:
P(t) = 48.7t² + 678.5t + 17667.4.
What is the function for the total number of people attending the institutions?The number of males is given by:
M(t) = 19.7t² + 310.5t + 7539.6.
The number of females is given by:
F(t) = 28t² + 368t + 10127.8.
The total number is given by the addition of the number of males and of females, that is:
P(t) = M(t) + F(t).
Which is an addition of polynomials. To add the polynomials, we combine the like terms, that is, adding the terms that have the same variable and exponent. Hence:
P(t) = M(t) + F(t).
P(t) = 19.7t² + 310.5t + 7539.6 + 28t² + 368t + 10127.8.
P(t) = 48.7t² + 678.5t + 17667.4.
Which is the desired function.
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ABCD is a quadrilateral.
Work out angle x.
В.
B
8 cm
A
X
6 cm
D
FIND x (
ABCD IS A QUADRILATERAL)
29%
13 cm
C
The blueprint for the moreno’s living room has a scale of 2 inches= 5 feet. The family wants to use a scale of 1 inch= 3 feet. What is the width of the living room on the new blueprint
The width of the living room on the new blueprint is 15 feet.
How to calculate the width?Based on the information, the scale of the original blueprint will be:
= 2 in / 5 ft
The width of the original blueprint is 6 inches, the actual width of the living room will be:
2/5 = 6/x
where x = width of living room
Cross multiply
x = 5 × 6 / 2
x = 15 feet.
The width is 15 feet.
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Malik had a checking account balance of $92.18. His bank will fund the first debit card purchase that creates a negative balance up to a limit of $100.00, but charges a
$28.00 fee for that overdraft. Malik made a purchase of $36.12 yesterday, and another purchase of $76.50 today. He used a debit card for each purchase. What is Malik's
account balance after the two purchases and any overdraft fees?
negative $140.62
negative $20.44
O negative $112.62
O negative $48.44
Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that costs \$3.25$3.25dollar sign, 3, point, 25. Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most \$30$30dollar sign, 30 before tax. The restaurant only sells pancakes in stacks of 444 pancakes for \$5.50$5.50dollar sign, 5, point, 50.
Let SSS represent the number of stacks of pancakes that Benjamin buys.
1) Which inequality describes this scenario?
Choose 1 answer:
Choose 1 answer:
(Choice A, Checked)
A
3.25+S \leq 303.25+S≤303, point, 25, plus, S, is less than or equal to, 30
(Choice B)
B
3.25+S \geq 303.25+S≥303, point, 25, plus, S, is greater than or equal to, 30
(Choice C)
C
3.25+5.50S \leq 303.25+5.50S≤303, point, 25, plus, 5, point, 50, S, is less than or equal to, 30
(Choice D)
D
3.25+5.50S \geq 303.25+5.50S≥303, point, 25, plus, 5, point, 50, S, is greater than or equal to, 30
2) What is the largest number of pancakes that Benjamin can afford?
The correct option is D that is bill is equal to or greater than $30
3.25 + 5.5s < =30
The first step in building the inequality is modelling Benjamin's spendings.
He buys a chocolate milk that costs $3.25, plus S stacks of pancakes, each at $5.50. Thus, in total, his spendings are of:
3.25 + 5.25s
He wants the bill to be of at most $30, that is, his spending has to be at most $30, thus:
T < 30
3.25 + 5.5s < =30
Thus the correct inequality is option D which is 3.25 + 5.5s < =30
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10 to the 3d power + 10 to the 2nd power + 10 to the 1st power
Answer: 1110
Step-by-step explanation:
Answer:
1,110
Step-by-step explanation:
1. Multiply to the powers(?)
10 x 10 x 10 = 1000
10 x 10 = 100
10 = 10
2. Add
1000 + 100 + 10 = 1110