We have
[tex]\dfrac{x^4+2x^3-7x^2-8x+12}{x-2}=x^3+4x^2+x-6[/tex]
The rational root theorem suggests that other possible roots may be -6, 6, -3, 3, -2, 2, -1, and 1. It turns out that [tex]x=-2[/tex] is a root, since [tex](-2)^3+4(-2)^2+(-2)-6=0[/tex], so [tex]x+2[/tex] is also a factor and we have
[tex]\dfrac{x^4+2x^3-7x^2-8x+12}{(x-2)(x+2)}=x^2+2x-3[/tex]
Finally, we can factorize the remaining quotient easily:
[tex]x^2+2x-3=(x+3)(x-1)[/tex]
so the other factors are [tex]x+2[/tex], [tex]x+3[/tex], and [tex]x-1[/tex].
a box contains 24 yellow balls and 76 red balls. One-fourth of the ball of each color are labeled "Win a prize." Match each description of a probability with its value as a percent.
A. The probability that a randomly selected
ball labeled "Win a prize” is yellow
B. The probability that a randomly selected
ball labeled "Win a prize” is red
C. The probability that a randomly selected
ball is labeled "Win a prize" and is red
D. The probability that a randomly selected
yellow ball is labeled "Win a prize"
___76%
___25%
___24%
___19%
A=24
B=76
C=25
D= 19
Step-by-step explanation:
.......
Final answer:
The probabilities are matched as follows: A-24%, B-76%, C-19%, and D-25%. These are calculated based on the total number of balls of each color and the fraction that are labeled to win a prize.
Explanation:
The question provides a scenario where there are 24 yellow balls and 76 red balls in a box, and one-fourth of each color are labeled "Win a prize." We are asked to match descriptions of probabilities with their corresponding percent values.
A: Probability that a randomly selected ball labeled "Win a prize" is yellow = (1/4 * 24) / ((1/4 * 24) + (1/4 * 76)) * 100 = 6 / (6 + 19) * 100 = 24%.
B: Probability that a randomly selected ball labeled "Win a prize" is red = (1/4 * 76) / ((1/4 * 24) + (1/4 * 76)) * 100 = 19 / (6 + 19) * 100 = 76%.
C: Probability that a randomly selected ball is labeled "Win a prize" and is red = (1/4 * 76) / 100 = 19%.
D: Probability that a randomly selected yellow ball is labeled "Win a prize" = (1/4 * 24) / 24 * 100 = 25%.
What is the missing measure on the small rectangle?
Answer:
4 inches
Step-by-step explanation:
If you divide 18 by 6, the answer is three, so it is scaled down 3x.
So, you have to divide 12 by 3, and the answer is 4.
Answer: 4 Inches
Step-by-step explanation: The rectangle on the left shows that the length is 18 inches and the height is 12 inches. Now, to find the height on the right, First we must realize what changed has been made from the left to the right. We know that our length has decreased to 6 inches from 18. 18 can be divided by 3 and that will give us the quotient of 6. Now, we must divide our height on our original rectangle by 3 as well. Once we divide, our new height of our rectangle also known as X will be 4 Inches Long.
Have A Great Day!
what is k equal to if 7.6/2 =9.5/k
Answer:
k=2.5
Step-by-step explanation:
7.6/2 = 3.8
9.5/3.8 = 2.5
Answer:
Step-by-step explanation:
7.6/2 =9.5/k
7.6k=2×9.5
k = (2×9.5)/7.6
k = 19/7.6
k= 2.5
vrify : 7.6/2 = 3.8 and 9.5/2.5 = 3.8 .....true
which of the following is not equal to cos(-576)
A.cos 216
B. -cos(-36)
C. sin 126
d. -sin 54
e. cos 144
ANSWER
C. sin 126°
EXPLANATION
-576° is coterminal with ±216,±144.
Therefore
cos (-576°)=cos(±216°)=cos(±144°)
The principal angle for -576° is 36° .
Since the terminal side of -576° is in the second quadrant and the cosine ratio is negative in the second quadrant,
cos (-576°)=-cos (±36°)
Also from complementary angles
cos (-576°)=-cos (36°)=-sin (90-36)=-sin(54°)
A movie was shown 6 times every day from November 24 through December 19. How
many times was the movie shown in all?
(Note: The month of November has 30 days.)
Select your answer.
О 138
0 144
О156
О162
Answer:
162
Step-by-step explanation:
Nine less than the quotient of two and a number xxx.
the expression to represent "Nine less than the quotient of two and a number ( x )" is:[tex]\[ \frac{2}{x} - 9 \][/tex]
To represent "Nine less than the quotient of two and a number ( x )", we first need to find the quotient of two and ( x ), and then subtract nine from it.
Let's break it down:
1. Quotient of two and a number ( x ):
This is represented as [tex]\( \frac{2}{x} \).[/tex]
2. Nine less than the quotient:
Subtracting nine from the quotient gives [tex]\( \frac{2}{x} - 9 \).[/tex]
So, the expression to represent "Nine less than the quotient of two and a number ( x )" is:
[tex]\[ \frac{2}{x} - 9 \][/tex]
complete question given below:
Write an expression to represent: Nine less than the quotient of two and a number xxx.
Choose the correct symbol to form a true statement. 11/18 ____5/9
For this case we have the following numbers:
[tex]\frac {11} {18} = 0.611111111111\\\frac {5} {9} = 0,555555555556[/tex]
Note that [tex]\frac {11} {18}[/tex]is greater than[tex]\frac {5} {9},[/tex] so the inequality sign must be placed with the opening towards [tex]\frac {11} {18}[/tex].
Answer:
[tex]\frac {11} {18}> \frac {5} {9}[/tex]
What is the coefficient of the term of degree 5 in the polynomial below?
3x +5 - +4x3 - 9x
ANSWER
D. 4
EXPLANATION
The given polynomial is
[tex]3 {x}^{6} + 5 - {x}^{2} + 4 {x}^{5}- 9x[/tex]
The term in degree 5 in this polynomial is
[tex]4 {x}^{5} [/tex]
The coefficient of this term is the constant that is multiplying the variable raised to exponent 5.
This number is 4.
Therefore the coefficient of term in degree 5 is 4
The correct answer is D.
Question 5
What is the value of x?
Answer:
x = 27Step-by-step explanation:
An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.
Therefore we have the equation:
[tex]\dfrac{x+8}{10}=\dfrac{2x-5}{14}[/tex] cross multiply
[tex]14(x+8)=10(2x-5)[/tex] use the distributive property
[tex](14)(x)+(14)(8)=(10)(2x)+(10)(-5)[/tex]
[tex]14x+112=20x-50[/tex] subtract 112 from both sides
[tex]14x=20x-162[/tex] subtract 20x from both sides
[tex]-6x=-162[/tex] divide both sides by (-6)
[tex]x=27[/tex]
addison walked 6 miles in 4 hours what was her walking rate in hours per mile
Answer:
2/3 hour per mile.
Step-by-step explanation:
Hours per mile
= hours taken / miles walked
= 4/6 = 2/3 hour per mile.
Answer:
she walked 1.5 miles for every hour
Step-by-step explanation:
Divide the miles by the hours: 6/4 =1.5
To make sure this is correct multiply 1.5 times 4(the hours) and you will get 6(the miles she walked
Hope this helped:3
What are the solutions to the quadratic equation below x^2+20x+100=7
First you must have the quadratic equal to zero. In order to do this you must subtract 7 to both sides
x^2 + 20x + (100 - 7) = 7 - 7
x^2 + 20x + 93 = 0
Now you must find two numbers who's sum equals 20 and their multiplication equal 93
Are there any? NO!
This means that you have to use the formula:
[tex]\frac{-b±\sqrt{b^{2} - 4ac} }{2a}[/tex]
In this case:
a = 1
b = 20
c = 93
[tex]\frac{-(20) plus/minus\sqrt{20^{2} - 4(1)(93)} }{2*1}[/tex]
[tex]\frac{-20 plus/minus\sqrt{400 - 372} }{2}[/tex]
[tex]\frac{-20 plus/minus\sqrt{28} }{2}[/tex]
^^^We must simplify √28
√28 = 2√7
so...
[tex]\frac{-20 plus/minus 2\sqrt{7} }{2}[/tex]
simplify further:
[tex]-10 plus/minus\sqrt{7[/tex]
-10 + √7
or
-10 - √7
***plus/minus = ±
Hope this helped!
~Just a girl in love with Shawn Mendes
Need Help Please!!!!!!!!!!:>
divide by 2 for each of the numbers
32/2=16
16/2=8
8/2= 4
Answer is 4
ANSWER
The next term in the given geometric sequence is 4.
EXPLANATION
We want to find the next term in the geometric sequence
32,16,8,
We can observe that there is a common ratio of
[tex] \frac{16}{32} = \frac{1}{2} [/tex]
This implies that, we obtain the subsequent terms by multiplying the previous terms by ½.
To obtain the next term after 8, we multiply 8 by half to get.
[tex] 8 \times \frac{1}{2} = 4[/tex]
Therefore the next term is 4.
The bar graph shown here provides the numbers of scoops of different ice cream flavors that were sold during school lunch today.
How many more scoops of strawberry were sold than vanilla?
A) 2
B) 3
C) 4
D) 5
The number of more scoops of strawberry were sold than vanilla is 4. Therefore, option C is the correct answer.
What is bar graph?A bar graph is a graph that shows complete data with rectangular bars and the heights of bars are proportional to the values that they represent. The bars in the graph can be shown vertically or horizontally. Bar graphs are also known as bar charts and it is a pictorial representation of grouped data.
From the given graph, number of scoops of strawberry sold is 10 and the number of scoops of Vanilla sold is 6.
Difference = 10-6
= 4
Therefore, option C is the correct answer.
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A ball is dropped from the top of a building that is 1,000 feet high. Its height, in feet, as a function of the time, x, in seconds, after the ball was dropped, is given by the following equation, ƒ(x) = 1,000 - 16x 2. Which set of numbers is appropriate as the domain for this function?
Real numbers from 0 to sqrt(1000/16) = 0 to 2.5sqrt(10).
Before 0, it hadn't been dropped. After 2.5sqrt(10), it has hit the ground and stopped falling.Positive Real Numbers. This includes fractions of seconds, the other two don't.
The appropriate domain for the function describing the height of a ball dropped from a 1,000 feet high building as a function of time is 0 <= x <= 25 seconds, indicating the ball's descent time until it hits the ground.
The student has asked about the appropriate domain for a function describing a ball dropped from a height of 1,000 feet, given by the equation f(x) = 1,000 - 16x². To find the domain, we need to understand when the ball hits the ground, marking the end of its free fall and the function's practical use.
The height (f(x)) becomes 0 when the ball reaches the ground. Setting the equation to zero gives us 0 = 1,000 - 16x². Solving for x, we find x = 25 seconds. This means the ball will hit the ground after 25 seconds, indicating the end of its descent and the maximum value of x in the domain. Therefore, the appropriate domain for this function, representing the time from when the ball was dropped until it hits the ground, is 0 ≤ x ≤ 25 seconds.
A rectangle has perimeter of 20, if the length and width are halved. What is the new perimeter ?
Answer:
10
Step-by-step explanation:
The perimeter will also be halved: (1/2)(20) = 10.
Example: a rectangle of length 14 ft and width 8 ft has perimeter P = 2(14 ft) + 2(8 ft), or 28 ft + 16 ft = 44 ft.
If we halve the length and width, we get 7 ft and 4 ft, and the P is
2(7 ft) + 2(4 ft) = 14 ft + 8 ft = 22 ft, which is half of the original perimeter 44.
if x represents a number, write an expression to represent a number which is 5 less than 3 times x
Answer:
the correct answer is x = 3x - 5
Eight more than the product of a number and 4 is equal to 6
Answer:8>4n=6 or 8>4+n=6
Step-by-step explanation:
Let's solve the equation step by step. The problem statement can be translated into a mathematical equation:
"Eight more than the product of a number and 4 is equal to 6."
Let x be the number we are looking for. When the problem says "the product of a number and 4," we can express this as 4 * x or 4x. The phrase "eight more than" implies we are to add 8 to the product of the number and 4, making the expression 4x + 8. According to the statement, this expression is equal to 6. Thus, we write the equation as:
4x + 8 = 6
To find the value of x, we will follow these steps:
1. Subtract 8 from both sides of the equation to isolate the term with x on one side.
4x + 8 - 8 = 6 - 8
This simplifies to:
4x = -2
2. Divide both sides of the equation by 4 to solve for x.
4x / 4 = -2 / 4
This simplifies to:
x = -1/2
So the number we were looking for, represented as x, is -1/2.
What’s the radius of a circle with an area of 123 square feet
Answer:
6.25716517287
Step-by-step explanation:
Area of circle = π × r²
→ 123 = π × r²
⇒ Divide both sides by π
→ 39.1521160006 = r²
⇒ Square root both sides
→ 6.25716517287 = r
What is the value of x?
x=15
x=30
x=37.5
x=52.5
Answer:
x = 15Step-by-step explanation:
[tex]\text{If}\ \angle1\ \text{and}\ \angle2\ \text{are complementary, then}\ \angle1+\angle2=90^o.\\\\\text{We have:}\\\\\angle1=x^o\\\angle2=(3x+30)^o\\\\\text{Substitute:}\\\\x+(3x+30)=90\\\\(x+3x)+30=90\qquad\text{subtract 30 from both sides}\\\\4x=60\qquad\text{divide both sides by 4}\\\\x=15[/tex]
The value of x is 52.5.
Explanation:The value of x can be determined by examining the given equations:
x = 15x = 30x = 37.5x = 52.5Since x is a variable, it can take on different values. In this case, the value of x is 52.5 because that is the only value that satisfies the given equations.Learn more about Value of x here:https://brainly.com/question/26914436
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One brand of vinegar has a pH of 4.5. Another brand has a pH of 5.0. The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. What is the approximate difference in the concentration of hydrogen ions between the two brands of vinegar?
Answer:
2.16 * (10^-5).
Step-by-step explanation:
5 = -log H+
5 = log (1 / H+)
1/ H+ = 10^5
H+ = 10^-5
In a similar fashion the other brand has H+ of 10^-4.5.
So the difference in hydrogen ion concentration = 10^(-4.5) - 10^(-5)
= 2.16 * (10^-5).
2.16 × 10⁻⁵ is the difference in the concentration of hydrogen ions between the two brands of vinegar.
What is pH?pH is a numerical indicator of how acidic or basic aqueous and other liquid solutions are. The phrase, which is frequently used in biology, agronomy, and chemistry, converts the hydrogen ion concentration, which typically ranges between 1 and 1014 gram-equivalents per litre, into numbers ranging from 0 to 14.
The hydrogen ion concentration in pure water, which has a pH of 7, is 107 gram-equivalents per litre, making it neutral (neither acidic or alkaline). A solution having a pH below 7 is referred to as acidic, and one with a pH over 7 is referred to as basic, or alkaline.
5 = -log H+
5 = log (1 / H+)
1/ H+ = 10^5
H+ = 10^-5
difference= 10^(-4.5) - 10^(-5)
= 2.16 × 10⁻⁵
Therefore, 2.16 × 10⁻⁵ is the difference in the concentration of hydrogen ions between the two brands of vinegar.
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Find the area of the kite !!!! PLEASE HELP!!!!
A. 26 m^2
B. 36 m^2
C. 30m^2
D. 18 m^2
ANSWER
D. 18 m^2
EXPLANATION
The area of a kite is half the product of the diagonals.
The diagonals of the kite are
3+3=6m
and
2+4=6m
The area of the kite
[tex] = \frac{1}{2} \times 6 \times 6[/tex]
[tex] = 3 \times 6[/tex]
[tex] = 18 {m}^{2} [/tex]
The correct answer is D.
The area of kite using the diagonal length 6m and 6 m is 18 m².
Thus, option (d) is correct.
Given:
length of diagonal 1 = 3+ 3 = 6 m
length of diagonal 2 = 2+ 4 = 6 m
Using the formula of Area of Kite
[tex]{\text} Area of kite[/tex] = [tex]\dfrac{1}{2} *[/tex] [tex]{\text} product \; of \;diagonal[/tex]
Now, substituting the values of diagonal into the formula as
[tex]{\text} Area of kite[/tex] = [tex]\dfrac{1}{2} *[/tex] [tex]{\text} (6 * 6)[/tex]
= [tex]\dfrac{1}{2} *[/tex] [tex]{\text} (36)[/tex]
= 18 m²
Thus, the area is 18 m².
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Ax-bx-y=z
which of the following represents the formula that could be used to find x?
Answer:
see explanation
Step-by-step explanation:
Given
Ax - bx - y = z ( add y to both sides )
Ax - bx = z + y ← factor out x from both terms on the left side
x(A - b) = z + y ← divide both sides by (A - b)
x = [tex]\frac{z+y}{A-b}[/tex]
HELLLLLLLLLLLLLLPPPPPP MEEEEEEEEEEEEEEE!!!!!!!!!!!
Answer:
D
Step-by-step explanation:
Distribute the 1/2:
1/2(8x+4)
4x + 2
Distribute the 1/3:
1/3(9-3x)
3 - x
Add:
4x + 2 + 3 - x
3x +5
I hope this helps!
Answer:
D
Step-by-step explanation:
Distribute the 1/2:
1/2(8x+4)
4x + 2
Distribute the 1/3:
1/3(9-3x)
3 - x
Add:
4x + 2 + 3 - x
3x +5
I hope this helps!
I copy and pasted the answer above mine
which expression is 444 times as large as the expression 34 -15
A
4 x 34 - 15
B
4 x (34 - 15)
C
(4 x 34) - 15
Final answer:
The expression that is 444 times as large as the expression 34 - 15 is (4 x 34) - 15.
Explanation:
To find the expression that is 444 times as large as the expression 34 - 15, we need to multiply the expression by 444. The correct expression is option C, which is (4 x 34) - 15. Let's break it down:
First, we perform the multiplication: 4 x 34 = 136.
Then, we subtract 15 from the result: 136 - 15 = 121.
Therefore, the expression (4 x 34) - 15 is 444 times as large as the expression 34 - 15.
An engineer is designing a roller coaster. The tallest peak is 310 feet high.
The roller coaster travels 155 horizontal feet as it descends the hill.
What is the slope of the hill?
The answer is:
The slope of the hill is equal to 2.
Why?To solve the problem, we need to remember that the slope of a line, is the rate of increase or decrease of the line.
From the statement we know that the tallest peak of the roller coaster is 310 feet (y), while the roller coaster travels 155 horizontal feet (x), so, calculating we have:
[tex]Slope=\frac{height}{base}=\frac{y}{x}[/tex]
Then, substituting the given information and calculating, we have:
[tex]Slope=\frac{310ft}{155ft}=2[/tex]
We have that the slope of the hill is equal to 2.
Have a nice day!
Answer:
The slope of the hill is equal to 2
Step-by-step explanation:
Savvas realize benchmark test
The question is a picture.
Answer:
904.32 cm³Step-by-step explanation:
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - height
We have r = 6cm and H = 8cm. Substitute:
[tex]V=\pi(6^2)(8)=\pi(36)(8)=288\pi\ cm^3[/tex]
[tex]\pi\approx3.14\to V\approx(288)(3.14)=904.32\ cm^3[/tex]
Answer:
904.32 cm³
Step-by-step explanation:
The volume (V) of a cylinder is calculated using the formula
V = πr²h ( r is the radius of the base and h the height )
here r = 6 and h = 8, so
V = 3.14 × 6² × 8
= 3.14 × 36 × 8 ≈ 904.32 cm³
What is the constant term of −3x4−7x+2
-
3
x
4
-
7
x
+
2
?
Answer:
The constant term is 2
Step-by-step explanation:
The given polynomial is [tex]-3x^4-7x+2[/tex].
To find the constant term, we must make sure the polynomial is in standard form.
The constant term is the term that is independent of x.
Considering [tex]-3x^4-7x+2[/tex], the term that is independent of x is the last term which is 2.
Therefore the constant term is [tex]2[/tex].
factor completely x^6 - y^6
Answer:
[tex]\large\boxed{x^6-y^6=(x-y)(x+y)(x^2+y^2-xy)(x^2+y^2+xy)}[/tex]
Step-by-step explanation:
[tex]x^6-y^6=x^{(2)(3)}-y^{(2)(3)}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=(x^2)^3-(y^2)^3\qquad\text{use}\ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\=(x^2-y^2)\bigg((x^2)^2+x^2y^2+(y^2)^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(x-y)(x+y)\bigg((x^2)^2+2x^2y^2+(y^2)^2-x^2y^2\bigg)\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=(x-y)(x+y)\bigg((x^2+y^2)^2-x^2y^2\bigg)\\\\=(x-y)(x+y)\bigg((x^2+y^2)^2-(xy)^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(x-y)(x+y)(x^2+y^2-xy)(x^2+y^2+xy)[/tex]
Answer:
(x²)³ - (y²)³ = (x² - y²)(x^4 + x²y² + y^4)
Step-by-step explanation:
x^6 - y^6 is the difference of two cubes: (x²)³ - (y²)³. Differences of cubes can be factored as follows: a³ - b³ = (a - b)(a² + ab + b²).
Thus, (x²)³ - (y²)³ = (x² - y²)(x^4 + x²y² + y^4)
how do i find the altitude of a right triangle when given two sides but not the hypotenuse?
You can use the Pythagorean Theorem to find the hypotenuse. Then you should be able to find the altitude.
Given:
A = V3
B = 2V3
C= 25
D= V16
Which expressions result in a rational number? Select all that apply.
Answer:
The ones that give a rational number answer are:
C+D
A*B
C*D
A*A
Step-by-step explanation:
A+B does not give a rational number answer; √3+2√3 = 3√3
C+D is a rational number; √25=5 and √16=4; 5+4=9.
A+D is not a rational number; √3+√16 = √3+4
A*B is a rational number; √3*2√3 = 2√9 = 2*3 = 6
B*D is not a rational number; 2√3*√16 = 2√3*4 = 8√3
C*D is a rational number; √25*√16 = 5*4 = 20
A*A is a rational number; √3*√3 = √9 = 3