When [tex]x^3[/tex]+4x-24 is divided by x-2 then the remainder is -8.
What is remainder theorem?
Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that when a polynomial P(x) is divided by a factor (x - a), which isn't really an element of the polynomial, a smaller polynomial is produced along with a remainder. The remainder theorem asserts that when a polynomial p(x) is divided by (x - a), the remainder equals f. (a). Using Euclid's Division Lemma, this may be demonstrated. To put it another way, p(x) = q(x) (x - a) + r if q(x) is the quotient and 'r' is the remainder.
Here the given [tex]x^3[/tex]+4x-24 and x-2
When a function f(x) is divided by x+a, then the remainder is given by f(−a):
So, in this case remainder will be f(2) .
=> f(x)= [tex]x^3[/tex]+4x-24
put x=2 then
=> f(2)= [tex]2^3[/tex]+4(2)-24
=> f(2) =8+8-24
=> f(2) = 16-24 =-8
Hence the remainder is -8.
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For what value of x is line m parallel to line n?
Answer:
x = 42
Step-by-step explanation:
You want to know the value of x that makes alternate interior angles 105° and (3x-21)° congruent.
Congruent anglesWhen alternate interior angles are congruent, the lines forming them are parallel. Congruent angles have the same measure, so we want ...
3x -21 = 105
3x = 126 . . . . . . add 21
x = 42 . . . . . . . divide by 3
The value of x is 42 when the lines are parallel.
The distance between Bills house and his aunts house is 835 miles.About how many miles would he drive if he made 4 one-way trips?
Answer:
3340 miles
Step-by-step explanation:
Multiply 4x835=3340 miles
Ursula wants to make 48 hotdogs for a party. If
a bag of 12 hotdog buns costs $1.50 each and a
package of 8 hotdogs costs $2 each, how much
will the 48 hotdogs cost altogether?
Answer:
Hotdogs: $12
Buns: $6
Altogether (Hotdogs plus Buns): $18
Step-by-step explanation:
She wants 48 hot dogs, and each package contains 8 hotdogs.
48/8 = 6
She'd have to buy 6 packages
6 packages x $2 each = $12
She'd be spending $12 on the hotdogs
She'd also have to get an equivalent amount of buns
Each bag has 12 buns. She needs 48 buns.
48 buns /12 per bag = 4 bags
She would need to buy 4 bags of buns
$1.50 per bag x 4 bags = $6
She'd be spending $6 on buns
Adding the amount she spends on both the buns and hotdogs, she spends $18
re Stock Market Alexander is a stockbroker. He earns 14% commission each week. Last week. he sold $5.300 worth of Locks. How much did he make last week in commission? If he averages that me amount each week, how much did he make in commission in 2011?
Help meee
Alexander made $742 last week in commission. He made $40068 in commission in 2011.
Sold = $5300
Commission percent = 14%
Commission = 14% of 5300
= (14/100)*5300
= 14*53
= 742
No. of weeks in 2011 = 54
Commission = 54 * 742
= 40068
Hence, he makes $742 in weeks and $40068 in year 2011.
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What is the greatest common factor of 42,21 and 49?
Answer:
GCF = 7
Step-by-step explanation:
The greatest common factor is equal to the product of the prime factors that all of the original numbers have in common.
The greatest common factor of 49, 21 and 49 is 7.
convert y=-2x into standard form
A new company wants to offer a line queuing service where customers book someone to wait in line on their behalf through a smart phone app. What concept is represented by the possibility that no one wants to pay someone else to wait in line ?.
A new company wants to offer a line queuing service where customers book someone to wait in line on their behalf through a smart phone app.
The possibility that no one wants to pay someone else to wait in line can be represented by the concept of probability.
The probability of an event occurring is defined by probability.
The outcome of an event may be known to us or unknown to us. When this happens we say that there is a chance that the event will happen or not.
We can identify probability by simply dividing the favorable number of possibilities by the entire number of possible outcomes.
Hence, probability is a numerical representation of the chance that a specific event will take place.
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factorise y^2 + 27y.
Answer:
y(y+27)
Step-by-step explanation:
as per it is y2 it is two times counted so
y(y+27)
Which of the following statements about the changing features of the family is not true of todays Commonwealth Caribbean societies?
A) men and women choose their own partners
B) husband and wives usually treat each other as equals
C) parents are becoming more autocratic
D) generally, families have fewer children
The statement about the changing features of the family that is not true of todays Commonwealth Caribbean societies is C. parents are becoming more autocratic.
How to illustrate the information?It should be noted that nowadays, men and women choose their own partners, husband and wives usually treat each other as equals and generally, families have fewer children
While role changes are often difficult, many positive things can occur as a result. Families may learn to work better together and support one another. Learning new tasks can help children gain confidence. Families may discover that, despite the changes, life can still be enjoyable.
In conclusion, the correct option is C.
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how many positive integers of 3 digits may be made from the digit 1,2,3,4,5, each digit may be used just once
60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.
According to the question,
We have the following information:
3 digits integers are to be made from 1,2,3,4 and 5
So, we will use permutation to find the possible number of digits that can be made if we apply all the given conditions.
Now, we have:
Total number of digits = 5
Number of digits to be made = 3
So, we have:
[tex]^{5} P_{3}[/tex]
Solving this expression:
5*4*3
60
Hence, 60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.
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A nonregular hexagon has five exterior angle measures of 55, 60, 69, 57, and 57. What is the measure of the interior angle adjacent to the sixth exterior angle?
62
128
118
108
The measure of the interior angle adjacent to the sixth exterior angle of the heaxagon is 118°.
What is an interior angle?Interior angles are those that lie inside a polygon.
To calculate an interior angle of a hexagon, we use the formula below.
Formula:
a = 360-(b+c+d+e+f)............ Equation 1Where:
a = The sixth exterior angleb = 55°c = 60°d = 69°e = 57°f = 57°Substitute these values into equation 1
a = 360-(55+60+69+57+57)a = 360-298a = 62°Recall that, the sum of an interior and exterior angle is 180°
a'+a = 180............... Equation 2Where:
a = Interior angle of the sixth exterior angle.Substitute the value of a into equation 2
a' = 180-62a' = 118°Hence, the value of the interior angle is 118°.
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The equation x^2-6x=72 ha a olution between 4 and 5
Ue a trial and improvement method to find thi olution
Give your anwer correct to 1 decimal place
The solution of the quadratic equation [tex]x^2 - 6x = 72[/tex] is
x = 12 or x = -6
What is a quadratic equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
The given quadratic equation is
[tex]x^2 - 6x = 72[/tex]
Now,
[tex]x^2 - 6x = 72\\x^2 - 6x - 72 = 0\\x^2 - 12x + 6x -72 = 0\\x(x -12)+6(x -12)=0\\(x-12)(x+6)=0\\x-12=0 \ or \ x+6 = 0\\x = 12 \ or \ x = -6[/tex]
The solution of the quadratic equation [tex]x^2 - 6x = 72[/tex] is
x = 12 or x = -6
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Simplify: 2√2 + 3√5 in the calculus topic, surds.
The radical expression 2√2 + 3√5 cannot be simplified
How to simplify the expression?From the question, we have the following parameters that can be used in our computation:
2√2 + 3√5
The above expression is a radical expression
The radicals in the expression are √2 and √5
The numbers 2 and 5 do not have common factors
This means that 5 cannot be expressed in terms of 2, and vice versa
So, we cannot simplify the given expression 2√2 + 3√5
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need help on this math question please
The sequence of transformations is described as follows:
B. Reflection over the y-axis, translation 6 units right and 4 units up, dilation with center (0,0) and scale factor 2.
What are the transformations?The two polygons have vertical symmetry, hence the reflection was over the y-axis.
Two equivalent vertices are given as follows:
R(4,-4) and V(2,-4).
After the reflection over the y-axis, the coordinates would be of:
R'(-2,-4).
The polygon increases after the transformation, hence the dilation has a scale factor greater than 1, which is of 2, as VZ = 8, RU = 4.
With a dilation with scale factor of 2, the coordinates of R'' would be given as follows:
R''(-4,-8).
The coordinates of V are:
(2,-4).
Hence the translation is:
6 units right.4 units up.Hence option B is correct.
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A math test with 26 questions is worth 100 points. There are multiple choice questions that are worth 2 points each and fill in the blank questions that are worth 5 points each. How many of each type of question is there?.
Answer:
Step-by-step explanation:
−64÷(−8)
solve and show how you solved
Which expression is equivalent to 3 log2 x – 4 log2 y + 2 log2 z?
log base 2 of the quantity x cubed y to the fourth all divided by z squared end log
log base 2 of the quantity x times z to the fifth all divided by y end log
log base 2 of the quantity x cubed z squared all divided by y to the fourth end log
log base 2 of the quantity xy divided by z end quantity raised to the fourth end log
Answer:log base 2 of the quantity x cubed z squared all divided by y to the fourth end log
Step-by-step explanation:
a precision instrument is guaranteed to read accurately to within 2 units. a sample of four instrument readings on the same object yielded the measurements 353, 351, 351, and 355. find a 90% confidence interval for the population variance. what assumptions are necessary? does the guarantee seem reasonable?
As per the given confidence interval, the value of P is lees than significant.
Confidence interval:
In statistics, a range around a measurement that conveys how precise the measurement is referred as confidence interval.
Given,
A precision instrument is guaranteed to read accurately to within 2 units. a sample of four instrument readings on the same object yielded the measurements 353, 351, 351, and 355. find a 90% confidence interval for the population variance.
Here we need to find the assumptions of the given situation,
From the given question we have identified the following,
Reading of instruments = 353, 351, 351, and 355.
Confidence interval = 90% = 0.09
Number of units = 2.
Based on these details, the standard deviation of this temple is 0.7.
So, the Z score is the same as the sample mean minus the population mean divided by the standard error, which is 2.857.
Therefore, P value was less than significant.
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Hey, can anyone help me with this maths question please? Will mark brainliest!
Answer:n1=-9,n2=10
Step-by-step explanation:
define your variables and set up a system of equations, then solve
Solving by the system of linear equations, the Cost per pound of peanuts is $3.79 and M&M's is $4.99.
What do you mean by system of linear equations?
A system of linear equations consists of two or more equations, each of which has two or more variables, and all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy each of the system's linear equations is necessary to identify the system's unique solution.
Let, the cost per pound of peanut be $x and for M&M's be y
so, according to the question, we are getting two linear equations,
$8x + $5y = $55.27..................(i)
$6x + $4y = $42.70....................(ii)
Solving this two systems of linear equations , x=$3.79 and y=$4.99
Hence, the Cost per pound of peanuts is $3.79 and M&M's is $4.99.
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What is the quotient and remainder when 2x3 + x2 − 10x − 11 is divided by x + 1?
The quotient of the division is 2x² - x - 11 and 0 is the remainder.
Given,
The expression; 2x³ + x² - 10x -11 ÷ x + 1
We have to find the quotient and remainder
One of the arithmetic operations carried out on two given polynomials is to divide them. In this, the divisor is typically a polynomial of lower degree than the dividend.
Lets solve ;
2x³ + x² - 10x -11 / x + 1 (2x²)
= -x² - 10x - 11 / x + 1 (-x)
= -11x - 11 / x + 1 (-11)
= 0
Here,
The quotient = 2x² - x - 11
Remainder = 0
That is,
The quotient of the division is 2x² - x - 11 and 0 is the remainder.
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Parallelogram ABCD has vertices A(1,1) , B(17,1) , C(22,13) , and D(6,13) what is the perimeter in units of parallelogram ABCD
The perimeter of the parallelogram ABCD is, 58 units.
What is perimeter?
The length of a shape's boundary taken as a whole is referred to as its perimeter. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.
Consider the given vertices, A(1, 1), B(17, 1), C(22, 13), D(6, 13).
The perimeter of parallelogram is the sum of all sides of parallelogram.
So, first to find the length of each side of parallelogram, using the distance formula,
[tex]d = \sqrt{(x_2 -x_1)^2+(y_2-y_1)^2}[/tex]
So,
[tex]AB = \sqrt{(17-1)^2+(1-1)^2}=\sqrt{16^2-0} = 16\\ BC = \sqrt{(22-17)^2+(13-1)^2} = \sqrt{5^2+12^2}= \sqrt{25+144}=13\\ CD = \sqrt{(6-22)^2+(13-13)^2} = \sqrt{16^2+0}=16\\ AD = \sqrt{(6-1)^2+(13-1)^2}=\sqrt{5^2+12^2} =\sqrt{25+144}=13[/tex]
Therefore, the perimeter of the parallelogram ABCD is,
P = AB + BC + CD + AD
P = 16 + 13 + 16 + 13
P = 58
Hence, the perimeter of the parallelogram ABCD is, 58 units.
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2 divided by 5 over 6
Answer: 0.06 repeated, I'm sorry if it's wrong! I used a calculator.
Step-by-step explanation:
Calculating 2 divided by 5 / 6 should give you the answer 0.06666666666.
50POINTS
Do these pairs of values (x and y) represent two quantities that are
proportional?
xy
3 5
4 7
6 10
9 15
Answer:
D. No because not all of the pairs are simplified ratiosStep-by-step explanation:
The proportional relationship is:
y = kx, where k- constant of proportionalityLet's find the value of k for each pair and compare:
k = y/x1) x = 3, y = 5 ⇒ k = 5/32) x = 4, y = 7 ⇒ k = 7/43) x = 6, y = 10 ⇒ k = 10/6 = 5/34) x = 9, y = 15 ⇒ k = 15/9 = 5/3As we see thee of the pairs have same value of k, 5/3 and one is different 7/4.
The answer is no.
Answer choices given in the comment:
A. No because not all the pairs represent the same ratioB. Yes because the ratios 3/5 and 6/10 are equalC. Yes because as x increases y increasesD. No because not all of the pairs are simplified ratiosWhich of the expressions below means the
same as y/3
y+3
y-3
y÷3
3xy 3-y 3÷y
Answer:
y÷3
Step-by-step explanation:
y/3 is the same as y÷3
What's the
degree measure of
NEED HELP ASAP
The measure of ∠x is 190°
Define Exterior angle
The Exterior Angle is the angle between any side of a shape, and a line extended from the next side. The sum of the exterior angles of a triangle is 360°.In the given diagram, all angles marked is an exterior angle
And, we know sum of exterior angle is 360°
So, now just equate the given values to 360 degree
x + 60 + 110 = 360
x + 170 = 360
x = 360 - 170
x = 190°
Hence, the measure of ∠x is 190°
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for corporation p to file a consolidated tax return with corporation s, p must own what percentage of s's voting stock?
For corporation p to file a consolidated tax return with corporation s, p must own 80% of s's voting stock
The consolidated tax return is defined as a single income tax return filed by an affiliated group of corporations that combines their tax liability.
The percentage is the ratio that can be represented as the fraction of hundred.
The voting stock is defined as the shares that give the stockholder, that is the right to vote on the policymaking of the corporation
Here, p must own 80% of s's voting stock
Hence, for corporation p to file a consolidated tax return with corporation s, p must own 80% of s's voting stock
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Determine which postulate can be used to prove that the triangles are congruent.
The postulate which can be used to prove that the given triangles are congruent is SAS. Option A is correct.
First, let us understand the congruency of the triangle:
When two triangles have the same sides and angles, they are congruent. That is, one's three sides are equal to the other's three sides, and one's three angles are equal to the angles of the other.
In triangles ABD and CBD;
Side BD = side BD (common)
∠ABD = ∠CBD (90 degrees)
Side AB = side CB (common)
For this triangle pair, the postulate that fit are:
SAS since the two sides and the included angle are equal in both triangles.
Thus, the postulate which can be used to prove that the given triangles are congruent is SAS. Option A is correct.
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Use the parabola to graph the quadratic function f(x)=-2(x+4)^2-3
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
*i’ve been trying to understand this question for so long and when i try to find the answer they don’t make sense!!*
Given that the directrix is -2 and the vertex is (-4,-3), the graph will be the parabola plotted in the negative quadrant.
What is parabola?Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. Three crucial components make up a parabola: a focus, a directrix, and a vertex. This upward-opening parabola illustrates how all points along its curve will be equally distant from the directrix and the focus.
Here,
The equation of the parabola is,
f(x)=-2(x+4)²-3
a=-2
(h,k)=(-4,-3)
The graph will be the parabola plotted in the negative quadrant as the directrix is -2. and the vertex is (-4,-3).
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what percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line?
The percentage of the variation in y can be explained by the corresponding variation in x and the least - squares line
The value of the coefficient of determination r2 = 0.9617*0.9617 = 0.9249
percentage of the variation in y can be explained by the corresponding variation in x and the least - squares line is = 92.49%
So, percentage is unexplained = (100 - 92.49)%
= 7.51%
Therefore, the percentage of the variation in y that can be explained by the corresponding variation in x and the least-squares line is 92.49% . The percentage which is unexplained is 7.51% i.e. (100%−92.49%) .
Hence the variation in X and the least-squares line is 7.51%
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