The remainder when a cubic polynomial is divided by (x-2)(x-3) can be found using the given remainders with (x-2) and (x-3) separately, resulting in a = 3 and b = -2. Hence, the remainder is 3x - 2. Then, using the condition that f(1)=1 and f(x) is cubic with a leading coefficient of 1, we can determine the entire function and Q(x).
Explanation:Given that a polynomial f(x) has remainders when divided by (x-2) and (x-3), we can establish that:
f(x) = (x-2)(x-3)Q(x) + ax + b, where a and b are constants that represent the remainder when f(x) is divided by (x-2)(x-3).The condition f(x) divided by (x-2) has remainder 4:f(2) = 4, which gives us (2-2)(2-3)Q(2) + 2a + b = 4.The condition f(x) divided by (x-3) has remainder 7: f(3) = 7, which gives us (3-2)(3-3)Q(3) + 3a + b = 7.From these conditions, we derive two equations:
2a + b = 43a + b = 7Solving these simultaneously gives us a = 3 and b = -2. Thus, the remainder when f(x) is divided by (x-2)(x-3) is 3x - 2.
Considering f(x) is cubic and the coefficient of x^3 is 1, f(x) = x^3 + px^2 + qx + r, and since f(1)=1, we can find out Q(x) by plugging the values a, b, and f(1) into the polynomial f(x) and comparing it with the standard cubic form. This will lead us to determine the function Q(x).
eanyone know??? get it correct u get 50 points
Answer:
J would be the answer, my friend.
log2 (24/3) = log5 (x)
log(8)/log(2) = log(x)/log(5)
log(x) = [log(5)][3]
log(x) = log(5^3)
x = 5^3 = 125
Step-by-step explanation:
Answer:
x = 125
Step-by-step explanation:
[tex] \log_2 24 - \log_2 3 = \log_5 x [/tex]
Use the rule of subtracting logs:
[tex] \log_b x - \log_b y = \log_b \dfrac{x}{y} [/tex]
[tex] \log_2 \dfrac{24}{3} = \log_5 x [/tex]
[tex] \log_2 8 = \log_5 x [/tex]
[tex] 3 = \log_5 x [/tex]
Use the definition of log:
[tex] \log_b x = y ~~\Longleftrightarrow ~~ b^y = x [/tex]
[tex] x = 5^3 [/tex]
[tex] x = 125 [/tex]
The temperature increased 16°C
during the morning. At noon the
temperature was 13°C. What was
the beginning temperature, t?
Answer:
-3°
Step-by-step explanation:
13°-16°=(-3°)
A metalworker has a metal alloy that is 30% copper and another alloy that is 55% copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 50% copper alloy? The metal worker should use (blank) kilograms of the metal alloy that is 30% copper and (blank) kilograms of the metal alloy that is 55% copper. (show your work)
Answer:
20kg
Step-by-step explanation:
12 is at most a number decreased by seven
Answer:
12 ≤ x - 7
Step-by-step explanation:
let "x" represent the number
The term decreased means subtraction.
The problem indicates that 12 cannot be greater than a number decreased by 7. Use ≤ which means less than or equal to.
≤ less than or equal to 12 means that 12 is the maximum value.
-1 2/3 + (-2 1/6)
A. Use the real number of properties to write an equivalent expression for this sum.
B. Find the sum. Express your answer as a mixed number in lowest terms.
MUST SHOW PART A AND PART B!!
Answer:
-3 5/6 (-3.83333)
Step-by-step explanation:
(-1x3+2)/3+-(2x6+1)/6
-5/3+-13/6
-5x2/6+-13x1/6
-10/6+-13/6
(-10+-13)/6
-23/6
-(3x6+5)/6
=-3 5/6 or (-3.83333)
A quadrilateral has vertices A(4,9), B(2,5), C(8,2), and D(10,6). Which statement about the quadrilateral is true?
Answer:
it is letter B
The given quadrilateral is not a parallelogram, is convex, and is not a square.
The question asks for the statement that is true about the given quadrilateral with vertices A(4,9), B(2,5), C(8,2), and D(10,6). To determine the truth of statements, we need to consider the properties of the given quadrilateral.
One statement that is true is that it is not a parallelogram. This can be proven by showing that opposite sides are not parallel, as the slopes are not equal.
Another statement that is true is that it is a convex quadrilateral. A convex quadrilateral is one where all interior angles are less than 180 degrees. To prove this, we can calculate the angles and show that they are all less than 180 degrees.
Lastly, a true statement is that it is not a square. A square is a special type of parallelogram with 4 equal sides and 4 right angles. We can determine this by calculating the lengths of the sides and showing that they are not all equal.
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How do you calculate constant rate of change from a proportional graph given the coordinates (x, y)?
Question 1 options:
x/y
y + x
xy
y/x
Answer:
y/x
Step-by-step explanation:
If y is directly proportional to x, then:
y = kx
k is the coefficient of proportionality, or the constant rate of change. Solving for k:
k = y/x
please help me.
A mixture of gasoline and oil is supposed to contain K ounces of oil for every gallon of gasoline.
Which coordinate is represented on the graph?
Answer:
(1,K) hope i could help
Step-by-step explanation:
Answer:
[tex](1,K)[/tex]
Step-by-step explanation:
According to the problem, the mixture must contain K ounces of oil for every gallon of gasoline. That is, each gallon of gasoline equals K ounces, this can be expressed as
[tex](1,K)[/tex]
Where [tex]x=1[/tex] expresses each gallon of gasoline and [tex]y=K[/tex] represents ounces of oil.
Therefore, the coordinate on the graph must represent [tex](1,K)[/tex], that is, K ounces of oil per gallon of gasoline.
What is the perimeter of a rectangle with a length of 9 - 2y and width of 7?
Answer:
The perimeter of the rectangle is 32 - 4y
Step-by-step explanation:
To find the perimeter, we will simply follow the steps below;
First write down the formula for finding the perimeter of a rectangle
The formula for finding perimeter in a rectangle is;
perimeter = 2l +2w
where l= length of the rectangle and w is equal to width of the rectangle
From the question given, length =9 - 2y and width =7
We can now proceed to insert the values into the formula;
perimeter = 2l +2w
=2(9-2y) + 2(7)
Then we will now simplify
perimeter =2(9-2y) + 2(7)
=18 - 4y + 14
= 18 + 14 - 4y
=32 - 4y
Therefore, the perimeter of the rectangle is 32 - 4y
The perimeter of the rectangle is 32-4y.
Step-by-step explanation:
Given information:
The length of the rectangle = 9-2y
The width of the rectangle = 7
Now
The perimeter (P) of the rectangle is :
[tex]P = 2( \text{Length} + \text{width})[/tex]
[tex]P= 2(9-2y+7)\\P=18-4y+14\\P=32-4y[/tex]
Hence, the perimeter of the rectangle is 32-4y.
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the area of a circular plot is 9856 metre square.calculate the cost of fencingthe plot at Rs.32.50 per metre.
Answer:
Rs 11440Step-by-step explanation:
Area of a circular plot is [tex]9856\text{ }m^{2}[/tex].
The area of a circle with radius [tex]r[/tex] is given by [tex]\pi r^{2}[/tex]
[tex]\pi r^{2}=9856\\r^{2}=9856\times\frac{7}{22}=3136\\r=56\text{ }m[/tex]
So, the radius of the circular plot is [tex]56\text{ }m[/tex].
Cost of fencing the plot is [tex]32.50\frac{Rs}{m}[/tex].
Total circumference of the circular plot is given by [tex]2\pi r[/tex]
Circumference = [tex]2\times\frac{22}{7}\times56=352\text{ }m[/tex]
Cost of fencing = [tex]352\text{ }m\times 32.50\frac{Rs}{m}=11440\text{ }Rs[/tex]
∴ Cost of fencing = Rs 11440
What is 53 divided by 30?
Answer:
1.76666666666666666
Answer:
53/30=1.7666666...
Step-by-step explanation:
The slope of line éb is zac
What is the equation of D. simplified?
B(2a, 2b)
y-yı = m(x - xı)
y-0=(220)(x-c)
y=[0]x-(22b)
y=(220 fer-(2 bezed
y=(22]x- (226)
O y=(,20 ]- (250)
Ela, b)
A(0, 0)
Dac, 0)
C(2c, 0)
Answer:
[tex]y = \frac{2b}{2a - c} x - \frac{2bc}{2a - c}[/tex]
Step-by-step explanation:
The straight line BD passes through points B(2a,2b) and D(c,0).
Therefore, the equation of the straight line BD will be given by
[tex]\frac{y - 2b}{2b - 0} = \frac{x - 2a}{2a - c}[/tex]
⇒ [tex]y - 2b = \frac{2b}{2a - c}x - \frac{4ab}{2a - c}[/tex]
⇒ [tex]y = \frac{2b}{2a - c} x - \frac{4ab}{2a - c} + 2b[/tex]
⇒ [tex]y = \frac{2b}{2a - c} x + \frac{-4ab + 4ab - 2bc}{2a - c}[/tex]
⇒ [tex]y = \frac{2b}{2a - c} x - \frac{2bc}{2a - c}[/tex]
Therefore, third option is correct. (Answer)
We know that the equation of a straight line passing through the points ([tex]x_{1},y_{1}[/tex]) and ([tex]x_{2},y_{2}[/tex]) is given by
[tex]\frac{y - y_{1} }{y_{1} - y_{2}} = \frac{x - x_{1} }{x_{1} - x_{2}}[/tex]
Latoya's cow gives 1 1/2gallons milk each day. How much is this in quarts?
Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answer:
6 quarts
Step-by-step explanation:
1 gallon = 4 quarts
1 1/2 gallon * (4 quarts / 1 gallon) = (1 + 1/2) * 4 = 1*4 + 1/2*4 = 4 +2 = 6 quarts
11 X +11 Y equals -5
Answer:
Step-by-step explanation:
11x+11y=-5
what is the answer to 5.48 * 15.12
Answer:
82.8576
Step-by-step explanation:
Nancy is going to glaze 6-ounce servings of pretzels and put them into gift boxes. If pretzels
are sold in -pound bags, how many bags will Nancy need for 100 gift boxes?
A. 16
B. 17
C. 22
D. 27
Please show how you got this answer
Drag each interval to a box to show if the function shown is increasing, decreasing, or neither over that interval.
I NEED HELP ASAP
Answer:
Increasing : [tex]-5<x<-1[/tex] or [tex]-1<x<1[/tex]
Decreasing : [tex]-8<x<-5[/tex] or [tex]4<x<7[/tex]
Neither : [tex]1<x<4[/tex]
Step-by-step explanation:
Increasing function : In this function, the y-value increases as the x-value increases.
From the given graph it is clear that the function is increasing on
[tex]-5<x<-1[/tex]
[tex]-1<x<1[/tex]
Decreasing function : In this function, the y-value decreases as the x-value increases.
From the given graph it is clear that the function is decreasing on
[tex]-8<x<-5[/tex]
[tex]4<x<7[/tex]
Neither increasing nor decreasing function : In this function, the y-value remains constant as the x-value increases.
From the given graph it is clear that the function is neither increasing nor decreasing on
[tex]1<x<4[/tex]
To determine if a function is increasing, decreasing, or neither over intervals on a graph, analyze the direction of the graph. If the graph goes up, the function is increasing. If it goes down, the function is decreasing. If it remains flat, the function is neither increasing nor decreasing.
Explanation:The question asks to determine if the function is increasing, decreasing, or neither over each interval on the given graph. To do this, we need to analyze the direction of the graph. If the graph goes up as we move from left to right, the function is increasing. If the graph goes down, the function is decreasing. If the graph remains flat, the function is neither increasing nor decreasing. Drag the intervals to the appropriate box based on these observations.
Parallelograms:
ABCD∼A1B1C1D1.
Find BC, B1D1
Answer:
[tex]BC = 4.8[/tex] and [tex]B_{1}D_{1} = 6.25[/tex]
Step-by-step explanation:
The parallelograms ABCD and [tex]A_{1} B_{1} C_{1}D_{1}[/tex] are similar.
Now, AB = 8 (Given in the figure), so CD = 8.
Now, we can write, [tex]\frac{BC}{B_{1}C_{1}} = \frac{CD}{C_{1}D_{1}}[/tex]
⇒ [tex]\frac{BC}{3} = \frac{8}{5}[/tex]
{Since, given that [tex]B_{1}C_{1} = 3[/tex] and [tex]C_{1}D_{1} = 5[/tex]}
⇒ [tex]BC = \frac{8 \times 3}{5} = 4.8[/tex] (Answer)
Again, we can write, [tex]\frac{BD}{B_{1}D_{1}} = \frac{CD}{C_{1}D_{1}}[/tex]
⇒ [tex]\frac{10}{B_{1}D_{1}} = \frac{8}{5}[/tex] {Since, BD = 5 + 5 = 10}
⇒ [tex]B_{1}D_{1} = \frac{5 \times 10}{8} = 6.25[/tex] (Answer)
Mr. Johnson's lunch bill is $29.90, which includes a 15% típ
What is the price before tip, b, of Mr. Johnson's lunch?
Answer:
price before tip (b) = $26
Step-by-step explanation:
29.90 is INCLUDING tip, so the real bill, b, would be less.
Now, since 29.90 is including 15% tip, and we let the original bill be "b", we can say:
b INCREASED by 15% gives us 29.90
We need to come up with an equation and solve for b.
15% means 15/100 = 0.15
Now, we can write:
b + 15% of b = 29.90
or
b + 0.15b = 29.90
then
1.15b = 29.90
b = 29.90/1.15
b = 26
So, price before tip (b) = $26
Answer:
the answer is 26
Step-by-step explanation:
Factors of 42
I need to know what factors make 42
Those are the factors of 42 c:
(1, 42), (2, 21), (3, 14) and (6, 7).
If h(x)=x-7 and g(x)=x^2, witch expresión is equivalent to(g*h)(5)?
Answer: 4
Step-by-step explanation:
(g*h)(5) = 4
Firstly, h(5) = 5 - 7 = -2
Then, evaluate g(-2) = (-2)^2 = 4
Write a polynomial equation of degree 4 that has the following roots : -1 repeated three times and 4
Answer:
x^4 -x^3 -9x^2 -11x -4
Step-by-step explanation:
We can use the zero product property
(x-a) (x-b) (x-c) (x-d) where a b c d are the roots
(x- -1)(x- -1)(x- -1) ( x-4) since the root -1 is repeated 3 times and 4 is a root
(x+1)(x+1)(x+1) ( x-4)
Foil the first two terms and the last two terms
(x^2 + 2x+1)( x^2 -3x-4)
Foil again
x^4 -3x^3 -4x^2 +2x^3 -6x^2 -8x +x^2 -3x-4
Combine like terms
x^4 -x^3 -9x^2 -11x -4
Answer:
Step-by-step explanation:
roots = -1, -1, -1, 4
(x + 1)(x + 1)(x + 1)(x - 4) = 0
(x^2 + 2x + 2)(x^2 - 3x - 4) = 0
x^2(x^2 - 3x - 4) + 2x(x^2 - 3x - 4) + 2(x^2 - 3x - 4) = 0
x^4 - 3x^3 - 4x^2 + 2x^3 - 6x^2 - 8x + 2x^2 - 6x - 8 = 0
x^4 - x^3 - 8x^2 - 14x - 8 = 0
Which situation has a unit rate of $7?
A
Trevor spent $49 on 2 theater tickets.
B
Sally bought a pack of 5 t-shirts for $35.
C
Brandon bought 7 gallons of gas for $14.
D
Gina bought nail polish for $5 and a pack of gum for $2.
The right answer is Option B.
Step-by-step explanation:
A unit rate describes how many units of one type of quantity corresponds to one unit of other type of quantity.
A. Trevor spent $49 on 2 theater tickets.
2 theater tickets = $49
1 theater ticket = [tex]\frac{49}{2} = \$24.5[/tex]
B. Sally bought a pack of 5 shirts for $35.
5 shirts = $35
1 shirt = [tex]\frac{35}{5} = \$7\\[/tex]
C. Brandon bought 7 gallons of gas for $14.
7 gallons = $14
1 gallon = [tex]\frac{14}{7}=\$2[/tex]
D . Gina bought nail polish for $5 and a pack of gum for $2.
1 nail polish = $5
1 pack of gum =$2
The pack of 5 shirts for $35 has a unit rate of $7.
The right answer is Option B.
Keywords: unit rate, division
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What is the value of x in the equation 3x - 1 y = 18, when y = 27?
o 5
ООО
Answer:
X would equal 15
Step-by-step explanation:
-1 × 27 = -27
-27 + 27 =0
18 + 27 = 45
3x ÷ 3 = x
45 ÷ 3 = 15
x = 15
3 1⁄2 kilometers = hectometers
Answer:
35 hectometers
Step-by-step explanation:
1 kilometer=10 hectometers
3 1/2=7/2
7/2*10=35
Answer:
[tex]\large\boxed{3\dfrac{1}{2}\ kilometers=35\ hectometers}[/tex]
Step-by-step explanation:
[tex]PREFIXES\\\\mega\ (M)=10^6\\\\kilo\ (k)=10^3\\\\hecto\ (h)=10^2\\\\deko\ (da)=10\\\\decy\ (d)=10^{-1}=0.01\\\\centi\ (c)=10^{-2}=0.01\\\\mili\ (m)=10^{-3}=0.001\\\\mikro\ (\mu)=10^{-6}=0.000001[/tex]
[tex]3\dfrac{1}{2}=3.5\\\\1\ kilometers=10\ hectometers\ (1\ km=10\ hm)\\\\3\dfrac{1}{2}\ km=3.5\ km=3.5\cdot10\ hm=35\ hm[/tex]
One day, the Jerry Bakery produced 800 pieces of bread and sold a total of 750 pieces.
Find the percentage of bread left.
A. 63%
B.6%
C.93%
D. 93%
The right answer is Option B.
Step-by-step explanation:
Pieces of bread produced = 800
Pieces of bread sold = 750
Pieces left = Pieces produced - Pieces sold
Pieces left = 800 - 750 = 50
Percentage of bread left = [tex]\frac{Pieces\ left}{Pieces\ of\ bread\ produced}*100[/tex]
[tex]Percentage\ of\ pieces\ left=\frac{50}{800}*100\\Percentage\ of\ pieces\ left=\frac{5000}{800}\\Percentage\ of\ pieces\ left= 6.25\%\\[/tex]
Rounding off to nearest whole percent;
Percentage of pieces left= 6%
The right answer is Option B.
Keywords: percentage, subtraction
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A piggy bank contains $5.60 in nickels and dimes. The number of nickels is 8 less than 3 times the dimes. How many nickels and dimes are there in the piggy bank?
The piggy bank has nickels and dimes.
Answer:
64 nickels and 24 dimes are there in the piggy bank.
Step-by-step explanation:
There are $5.60 in the piggy bank in nickels and dimes.
Let x number of nickels and y number of dimes are there.
Now, 1 nickel ≡ 0.05 dollars and 1 dime ≡ 0.1 dollars.
So, 0.05x + 0.1y = 5.6
⇒ 5x + 10y = 560
⇒ x + 2y = 112 ....... (1)
Again, from the condition given we can write that,
So, 3y - 8 = x ........ (2)
Now, solving (1) and (2) we get 3y - 8 + 2y = 112
⇒ 5y = 120
⇒ y = 24
And from equation (2) we get x = 3y - 8 = 64.
So, there are 64 nickels and 24 dimes in the piggy bank. (Answer)
Answer:
64 nickels and 24 dimes in the piggy bank.
Step-by-step explanation:
Bella plans to put $300 into a savings account. She can place her money into an account represented by p(x) = 3x+300, or into another account represented by
n(x) =300(1.04)^x. Which account has the highest value in 5 years? Which account has the highest in 12 years? Show your work!
Answer:
3(5) + 300 = 15 + 300 = 315
300(1.04)^5 = 300 * 1.21665 = 365
In 5 years, the second account is higher.
3(12) + 300 = 336
300(1.04)^12 = 300 * 1.601 = 480
In 12 years, the second account is higher
Mitchell owns 6 pairs of hockey skates. What equation could Gabe write to find the total number of hockey skates Mitchell has?
Answer: 6x2=y
Step-by-step explanation:
If Mitchell owns 6 pairs of hockey skates, then The equation for the number of hockey stakes can be written as, X - 12 = 0
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
Mitchell owns 6 pairs of hockey skates,
The equation for number of hockey stakes = ?
Suppose, the number of hockey stakes = X
According to given condition,
there are 6 pairs,
It is known that,
1 pair = 2 hockey stakes
So,
The equation is,
X = 2 x Number of pairs,
X = 2 x 6
X = 12
Hence, the equation is X - 12 = 0
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2,952 = 72=
It’s is another hard question on my math homework pls help
Answer:41
Step-by-step explanation: