The quotient of [tex]x^{3}+3x^{2} -4x-12[/tex] divided by [tex]x^{2} +5x+6[/tex] is (x-2_.
Given the polynomial [tex]x^{3}+3x^{2} -4x-12[/tex] and [tex]x^{2} +5x+6[/tex] and the first expression or polynomial is divided by second.
Quotient is a number that is obtained by dividing two numbers. It can be of two numbers or two expressions. Remainder is a number or an expression left after division of two numbers.
To find the quotient of [tex]x^{3}+3x^{2} -4x-12[/tex] divided by , we have to divide the expression first.
We know that ,
Divident=Divisor*Quotient+remainder
[tex]x^{3}+3x^{2} -4x-12[/tex]=[tex]x^{2} +5x-6[/tex]*(x-2)-12
If we carefully watch the above equation and compares with the above formula then we can easily find that the value of quotient is (x-2).
Hence the quotient of [tex]x^{3}+3x^{2} -4x-12[/tex] divided by [tex]x^{2} +5x-6[/tex] is (x-2).
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Question is incomplete as the given expressions are incomplete as they should be like this:
[tex]x^{3}+3x^{2} -4x-12[/tex] and [tex]x^{2} +5x-6[/tex].
The general form of the equation of a circle is ax2 by2 cx dy e = 0, where a = b 0. if the circle has a radius of 3 units and the center lies on the y-axis, which set of values of a, b, c, d, and e might correspond to the circle?
The set of values which might correspond to the circle are A = 1, B = 1, C = 0, D = -8 and E = 7.
The equation of a circle.Mathematically, the general form of the equation of a circle is given by;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center.r is the radius of a circle.Based on the information provided that the center of the circle lies on the y-axis, we have:
(h, k) = (0, 4)
Radius, r = 3 units.
Substituting the given parameters into the formula, we have;
(x - 0)² + (y - 4)² = 3²
x ² + y² - 8y + 16 = 9
x ² + y² - 8y + 7 = 0.
Therefore, the set of values which might correspond to the circle are A = 1, B = 1, C = 0, D = -8 and E = 7.
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Complete Question:
The general form of the equation of a circle is Ax² + By² + Cx + Dy + E = 0, where A = B. If the circle has a radius of 3 units and the center at (0, 4), which set of values of A, B, C, D, and E correspond to the circle?
Lines s and t are parallel. The slope of line s is −32. What is the slope of line t?
Answer: Parallel lines have equal slopes
If the slope of line s is -32 or -3/2, then the same applies to line t
Parallel lines have equal slopes but different y intercepts. These lines do not cross or intersect.
Answer: -32
Step-by-step explanation:
The two lines are parallel which means these two lines have the same slope. Therefore, the slope of line t is -32.
What are the solutions of this quadratic equation?
x²+2x = -2
O A.
OB.
O C.
O D.
X = 1 ti
x= -1 ti
X = 0
X= ti
Answer:
The answer might be C.(x=0)
2(-5x+4)+4x-5= -3
SOLVE FOR X please
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{2(-5x + 4) + 4x - 5 = -3}[/tex]
[tex]\huge\textbf{Solving for it:}[/tex]
[tex]\mathbf{2(-5x) + 2(4) + 4x - 5 = -3}[/tex]
[tex]\mathbf{-10x + 4 + 4x - 5 = -3}[/tex]
[tex]\huge\textbf{Combine the like terms:}[/tex]
[tex]\mathbf{(-10x + 4x) + (8 - 5) = -3}[/tex]
[tex]\mathbf{-10x + 4x + 8 - 5 = -3}[/tex]
[tex]\mathbf{-6x + 3 = -3}[/tex]
[tex]\huge\textbf{Subtract \boxed{\bf 3} to both sides:}[/tex]
[tex]\mathbf{-6x + 3 - 3= -3 - 3}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathbf{-6x = -3 - 3}[/tex]
[tex]\mathbf{-6x = -6}[/tex]
[tex]\huge\textbf{Divide \boxed{\bf -6} to both sides:}[/tex]
[tex]\mathbf{\dfrac{-6x}{-6} = \dfrac{-6}{-6}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathbf{x = \dfrac{-6}{-6}}[/tex]
[tex]\mathbf{x = -6\div-6}[/tex]
[tex]\mathbf{x = 1}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf x =\frak{1}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A telephone pole has a wire attached to its top that is anchored to the ground. the distance from the bottom of the pole to the anchor point is 68 feet less than the height of the pole. if the wire is to be 4 feet longer than the height of the pole, what is the height of the pole?
The height of the pole is 96 feet
In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the legs a, b and the hypotenuse c, often called the Pythagorean equation:[1]
[tex]a^{2}+b^{2}=c^{2},[/tex]
Create a diagram of the scenario first. You would have a right triangle with a hypotenuse (longest side) of h + 4, a longest leg of h - 68, and one leg of length h to represent the pole.
Set up the equation [tex]h^2 + (h - 68)^2 = (h + 4)^2[/tex] using the Pythagorean theorem ([tex]a^2 + b^2 = c^2[/tex]).
[tex]h^2 + (h - 68)^2 = (h + 4)^2[/tex]
On simplifying we get
[tex]h^2+h^2-136h+4624 = h^2+8h+16[/tex]
[tex]2h^2-136h+4624=h^2+8h+16[/tex]
[tex]h^2-144h+4608=0[/tex]
Solving using quadratic formula
[tex]h_{1,\:2}=\frac{-\left(-144\right)\pm \sqrt{\left(-144\right)^2-4\cdot \:1\cdot \:4608}}{2\cdot \:1}[/tex]
[tex]h_1=\frac{-\left(-144\right)+48}{2\cdot \:1},\:h_2=\frac{-\left(-144\right)-48}{2\cdot \:1}[/tex]
h1 = 96 feet , h2 = 48 feet
If height would have been 48 feet then the other side would have a negative value as as 48 - 68 = -20 .
Hence the height of the pole is 96 feet
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two card are drawn from a well shuffled deck of 51 cards. find the probability thst both cards are king( the first card is not replaced by drawing a tree diagram )
Answer: P(A)=4/425≈0,0094.
Step-by-step explanation:
[tex]P(A)=\frac{C_4^1*C_3^1}{C_{51}^2} .[/tex]
The desk has 4 kings.
First card is drawn from a well shuffled deck is a card of king. ⇒
[tex]C_4^1=\frac{4!}{(4-1)!*1!} =\frac{3!*4}{3!*1}=4.[/tex]
Second card is drawn from a well shuffled deck is a card of king too. ⇒
[tex]C_{4-1}^1=C_3^1=\frac{3!}{(3-1)!*1!}=\frac{2!*3}{2!*1}=3.\\ The \ desk\ has\ 51\ card.\ \ \ \ \Rightarrow\\C_{51}^2=\frac{51!}{(51-2)*2!}=\frac{49!*50*51}{49!*1*2} =51*25=1275.\\ P(A)=\frac{4*3}{1275} =\frac{4}{425} \approx0,0094.[/tex]
Which of the following is the equation for the graph shown
Step-by-step explanation:
if the area of each face of a cubical solid is 1764 CM square find its length
What is Z in the equation
360 ÷ z = 12
Answer:
z = 30
Step-by-step explanation:
→ 360 ÷ z = 12
→ 360/z = 12
→ 12z = 360
→ z = 360/12
→ [ z = 30 ]
Hence, the value of z is 30.
Answer:you have to isolate z,make z the subject.
Step-by-step explanation: z=360 multiply by 12,
giving us 4320.z=4320,i mean thisis the answer you have to stick with if u want to find a value for z.
step by step;z/360=12
z=360 into 12
z=4320
Name the shape below.
1. irregular pentagon
2. irregular quadrilateral
3. irregular octagon
4. irregular hexagon
Answer:
3
Step-by-step explanation:
Irregular pentagon since it has 5 sides
Answer:
irregular pentagon
(first option listed)
Step-by-step explanation:
This shape still has five sides--making it a pentagon. Because the angles are not exactly the same, and so the side lengths are also not equal, we name it an "irregular" pentagon.
hope this helps! have a lovely day :)
2.
MNOP is a tetrahedron. Given that the volume of tetrahedron is 75 m²
and the area of the base is 25 m². Find the height of tetrahedron.
Answer: 9 m
Step-by-step explanation:
[tex]75=\frac{1}{3}(25)(h)\\\\h=\frac{75}{25/3}=9[/tex]
Could someone quickly sum up how to calculate probability? I’m taking a course on it and don’t understand.
Answer:
Divide the number of events by the number of possible outcomes. After determining the probability event and its corresponding outcomes, divide the total number of ways the event can occur by the total number of possible outcomes. For instance, rolling a die once and landing on a three can be considered one event.
Step-by-step explanation:
for more information check the above attachment
What value for the constant, h, in the equation shown below will result in an infinite number of solutions?
4 − 16 = h(− + 4)
Using a system of equations, it is found that a value of h = 4 will result in an infinite number of solutions.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
If two equations are equal, the system has infinite solutions.
In this problem, the equations are:
4x - 16 = h(x - 4).
Then:
4(x - 4) = h(x - 4).
h = 4.
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find the value of x , thank you so much
Answer:
x = 40
Step-by-step explanation:
All angles in a triangle add up to 180
(3x-10) + 30 + x = 180
4x = 160
x = 40
Answer: x = 40
Step-by-step explanation:
All the interior angles of a triangle add up to 180°
Therefore,
30 + 3x - 10 + x = 180
30 + 4x - 10 = 180
20 + 4x = 180
4x = 160
x = 40
Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options.
18 x minus 15 = 72
50 x minus 25 = 72
18 x minus 9 = 72
3 (6 x minus 3) = 72
x = 4.5
The equivalent expressions are 3(6x - 3) = 72 and 18x - 9 = 72
Equations and expressionsGiven the equation below as shown;
3/5(30x - 15) = 72
Expand
3/5(30x) - 3/5(15) = 72
90x/5 - 15/5 = 72
3(6x - 3) = 72
Expand
18x - 9 = 72
Hence the equivalent expressions are 3(6x - 3) = 72 and 18x - 9 = 72
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Triangles F H G and K J G share common point G. The lengths of sides H G and G J are congruent. Angles F H G and K J G are right angles.
Can you conclude that triangle GHF is congruent to triangle GJK? Explain.
yes, by ASA
yes, by AAS
yes, by AAA
not enough information given
Answer:
not enough information given
Step-by-step explanation:
as the rules say, we need at least 3 pieces of information :
2 angles and a side, or 3 angles (or there are other options like 2 sides and one angle or 3 sides).
but here we get 1 side and 1 angle. the shared point does not give us anything in that regard.
so, not enough information.
Find b. B= help me please thank you so much :)
Step-by-step explanation:
I assume that DF and DQ are tangents to the circle.
angle FGQ = 268°
therefore, angle FQ = 360 - 268 = 92°
b = 1/2 × (angle FGQ - angle FQ) = 1/2×(268 - 92) =
= 1/2 × 176 = 88°
Ratio?
Help please thanks
Answer: 4:9
Step-by-step explanation:
The ratio of the surface areas is the square of the ratio of the edge lengths.
M(-5, 4)
L(-4,2)
-4
L'(-4,-2)
M'(-5,-4)
-→-2
4
y
N'-2-3)
2
What is the rule for the reflection?
rx-axis (x, y) → (x, y)
->
ry-axis (x, y) → (x, y)
rx-axis(x, y) → (x, -y)
ry-axis (x,y) → (x, -y)
The rule for the reflection of the pre-image M(-5, 4), L(-4, 2), N(-2, 3), to form the image M'(-5, -4), L'(-4, -2), N'(-2, -3) is the option;
rx-axis(x, y) → (x, -y)Which method can be used to find the rule for the reflection?The given pre-image points are;
M(-5, 4)L(-4, 2)Possible third point; N(-2, 3)
The image points are;
M'(-5, -4)M'(-5, -4)L'(-4, -2)M'(-5, -4)L'(-4, -2)N'(-2, -3)The difference (change) between the pre-image and the image is a change in the sign of the y-value, which is equivalent to a reflection across the x-axis.
Therefore;
rx-axis M(-5, 4) → M'(-5, -4)rx-axis L(-4, 2) → L'(-4, -2)rx-axis N(-2, 3) → N'(-2, -3)The rule for the reflection is therefore;
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If a ∥ b and b ⊥ y, then _____
a ∥ y.
a ⊥ y.
x ∥ y.
x ⊥ a.
The line b is perpendicular to the line y, then the line a will also perpendicular to the line y. Then the correct option is B.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
If the line a is parallel to the line b, then the slope of the line a and b will be same.
The line b is perpendicular to the line y, then the line a will also perpendicular to the line y.
Then the correct option is B.
The diagram is given below.
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The solution to an absolute value inequality is shown on the graph below.
-5-4-3 -2 -1 0 1 2 3 4 5
What is another way to show the solution?
x> -3 or x < 2
{x|x <-3 orx <2}
[-3, 2]
O (-3, 2).
The solution to the absolute value inequality is (-3,2).
What is absolute value inequality ?Absolute Value Inequality is the expression which contains absolute function as well as inequality signs .
The absolute value inequality is represented in the form of a line
Interval of the function is -3 to 2
As the intervals are represented by open circles, so -3 and 2 are exclusive of the values of the inequality.
Therefore the another way to show the solution is
-3 < x < 2
or
(-3,2)
Therefore, the solution to the absolute value inequality is (-3,2).
The complete question is attached with the answer.
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The distance from Capital City to Little Village is 660 miles. From Capital City to Mytown is 310 miles, from Mytown to Yourtown is 200 miles, and from Yourtown to Little Village is 150 miles. How far is it from Mytown to Little Village
The distance from Mytown to Little Village is 350 miles.
The distance from Capital City to Little Village is 660 miles.
The distance from Capital City to Mytown is 310 miles,
The distance from Mytown to Yourtown is 200 miles,
and from Yourtown to Little Village is 150 miles.
Assuming all the places are collinear,
The distance from Mytown to Little Village is
200 + 150 = 350 miles
Hence, The Mytown is 350 miles far from the Little Village
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Which statements are true? Check all that apply. 0 is greater than Negative two-thirds. Two-thirds is equal to Negative two-thirds. Negative 1 less-than negative one-third Negative two-thirds greater-than one-third Negative one-third greater-than negative two-thirds
The following statements are true:
0 is greater than negative two-thirdsNegative 1 is less than negative one-thirdNegative one-third greater-than negative two-thirdsWhat is a negative number?A negative number in mathematics is any number that is less than zero i.e. x < 0.
This means that zero is greater than any negative number.
However, the higher the digit of a negative number, the smaller that number becomes. It is opposite of positive numbers or integers.
Therefore, the following statements are true:
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i am not able to solve this problem
First, 0.0004853 is < 1, so we need to multiply the number by 10 to a negative power if it's greater than 1 (if that makes sense i cant describe it better)
So, b and c is incorrect.
10 to the power of negative 4 = 0.0001, and 4.853 x 0.0001 = 0.0004853 (true), so answer is a
Answer:
a
Step-by-step explanation:
a number expressed in standard form is
a × [tex]10^{n}[/tex]
where 1 ≤ a < 10 and n is an integer
given
0.0004853 ( place the decimal point after the 4 )
= 4.853 × [tex]10^{n}[/tex]
to place the decimal point in its original position we require to shift it 4 places left , denoted by - 4 on the exponent , that is
0.0004853 = 4.853 × [tex]10^{-4}[/tex]
how do i solve this?
Answer:
mode: number that appears most
mode=4 and 7
mean: =3+4+5+6+7+8+9+10+11÷9=7
so mean is 7
An elevator has 4 passengers and 8 floors. Find the probability that no 2 passengers get off on the same floor considering that it is equally likely that a person will get off at any floor.
The probability is 5/343.
Given :8 floors and 4 passengers.
Passengers will be assumed to start on the first floor, where everyone goes up, and each passenger only gets off on the 2nd floor (no one gets off on the 1st floor!)
Now we need to find the number of all ordered lists of four numbers out of seven, eg 2<3<7<8, 3<6<7<8, 4<5<6o<8, etc.
This can be done in 7C4 ways.
The total numbers of ways 4 passengers can get off at 7 floors (starting at the 2nd!) is [tex]7^{4}[/tex].
Therefore the probability is [tex]\frac{7C4}{7^{4} }[/tex] = [tex]\frac{5}{343}[/tex]
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Explain how to decide when a normal distribution can be used to approximate a binomial distribution.
A normal distribution can be used to approximate a binomial distribution when n* p and n * q are greater than 5.
What is a normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
A probability bell curve is more properly described as the normal distribution.
The mean and standard deviation of a normal distribution are 0 and 1, respectively. It has a kurtosis of 3 and zero skew.
Not all symmetrical distributions are normal, but all normal distributions are symmetrical.
Natural occurrences frequently resemble the usual distribution.
However, most price distributions in finance are not exactly normal distributions.
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If we have five decisions to make and four choices for each decision, how can we represent the number of potential outcomes?
4 to the power of 5
5 to the power of 4
4 to the power of 4
5 to the power of 5
Using the Fundamental Counting Theorem, the number of potential outcomes is given by: [tex]4^5[/tex]
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
There are five decisions, each with four options, hence:
[tex]n_1 = n_2 = n_3 = n_4 = n_5 = 4[/tex]
The number of options is:
[tex]N = 4 \times 4 \times 4 \times 4 \times 4 = 4^5[/tex].
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Will the store manager meet her goal if the sales team sells 80 tablets and 10 laptops? If so, explain If not find how many more tablets need to be sold to meet the goal.
The store manager would reach his goal of $20,000 if the sales team sold 80 tables and 10 laptops.
How to know if the store manager achieves his goal?To calculate if the store manager achieves its goal, we must perform the following operations:
80 × $200 = $16,00010 × $400 = $4,000$16,000 + $4,000 = $20,000According to the above, sales do reach the goal if 80 tablets and 10 laptops are sold.
Note: This question is incomplete because there is some information missing. Here is the missing information:
A computer store sells both tablets and laptops. One brand of tablet costs $200. That same brand of laptop costs $400. The store manager wants to sell enough of this brand of tablets and laptops to reach the sales goal of $20,000.
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Which expression is equivalent?
Answer:
The answer is the 3rd option (2)
Step-by-step explanation:
Hope this helped! :D
Which variable expression represents the phrase “the quotient of 5 times a number and 2”?
Answer:
5x/2
Step-by-step explanation:
Say the mystery number is "x"
5 times that = 5 * x = 5x
Then the quotient (that means the result of division, so divide!) of that and 2 would give you: 5x/2