How do you simplify # (x+3)/(x^2+7x+12)#?
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hope it is helpful
Related Questions
The midpoint of is m(–8, 1). one endpoint is k(–6, 5). find the coordinates of the other endpoint l.
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The midpoint of kl is m(–8, 1). one endpoint is k(–6, 5). find the coordinates of the other endpoint l.
we know that
the formula of midpoint is
Xm=(x1+x2)/2----> 2*Xm=x1+x2------> x2=2*Xm-x1
Ym=(y1+y2)/2----> 2*Ym=y1+y2------> y2=2*Ym-y1
let
(x1,y1)-------> (–6, 5).
(Xm,Ym)-----> (-8,1)
find (x2,y2)
x2=2*Xm-x1-----> 2*(-8)-(-6)----> -10
y2=2*Ym-y1----> 2*(1)-5-----> -3
the point l is (-10,-3)
Consider the multiple regression model with two regressors x1 and x2, where both variables are determinants of the dependent variable. when omitting x2 from the regression, there will be omitted variable bias for modifyingabove beta with caret 1:
a. if upper x 2 is measured in percentages.
b. only if upper x 2 is a dummy variable.
c. if upper x 1 and upper x 2 are correlated.
d. always.
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Bill buys a red marble and a blue marble. If the total weight of 3 such red marbles and 2 such blue marbles is 84g, and the total weight of 12 such red marbles and 5 such blue marbles is 282g, what is weight of the red marble and the blue marble respectively?
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Final answer:
The weight of the red marble is 16 grams, and the weight of the blue marble is 18 grams, based on the solution of the system of linear equations derived from the given total weights of the marbles.
Explanation:
To solve the problem of determining the weight of each marble, we can set up a system of linear equations based on the given information:
Let r be the weight of a red marble in grams.
Let b be the weight of a blue marble in grams.
The total weight of 3 red marbles and 2 blue marbles is 84g.
The total weight of 12 red marbles and 5 blue marbles is 282g.
Based on these statements, we can write two equations:
3r + 2b = 84 (1)
12r + 5b = 282 (2)
We can solve this system of equations by multiplying equation (1) by 4 to eliminate variable b.
(4)(3r + 2b) = (4)(84)
12r + 8b = 336 (3)
Subtract equation (2) from equation (3) to solve for r:
(12r + 8b) - (12r + 5b) = 336 - 282
3b = 54
b = 18 (weight of blue marble)
Substitute value of b in equation (1) to solve for r:
3r + 2(18) = 84
3r + 36 = 84
3r = 48
r = 16 (weight of red marble)
Therefore, the weight of the red marble is 16 grams and the weight of the blue marble is 18 grams.
Need help on this asap!!
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Please, see the attached file.
Thanks.
Jonathan opened an auto repair shop. In the first month, 11 cars were serviced at his shop. The number of cars serviced at Jonathan's shop increased at 9 cars per month.
How many total cars were serviced at Jonathan's shop at the end of the 7th month?
329 cars
65 cars
266 cars
201 cars
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Number of cars in second month = 11 + 9 =20
Number of cars in third month = 20 + 9 = 29
If we observe, the number of cars form an Arithmetic sequence with first term as 11 and common difference 7. We are to find the total cars received till the end of 7th term in the shop i.e. we are to find the sum of first 7 terms of the sequence.
So, using the formula of sum Arithmetic series we can write:
Cars received in 7th months = [tex] \frac{7}{2}(2(11)+(7-1)(9)) = 266 [/tex] cars
Thus, 266 cars were received at the end of 7th month at Jonathan's auto repair shop.
What is the middle term of the product of (x - 4)(x - 3)?
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Answer:
The middle term of the product of (x - 4)(x - 3) is -7
Step-by-step explanation:
Consider the given expression (x - 4)(x - 3)
We have to find the middle term of the product of (x - 4)(x - 3).
First multiply the given terms, we get,
[tex](x - 4)(x - 3)=x(x-3)-4(x-3)[/tex]
Simplify, we get,
[tex]x(x-3)-4(x-3)=x^2-3x-4x+12[/tex]
Simplify further, we get,
[tex]x^2-3x-4x+12=x^2-7x+12[/tex]
Thus, the middle term of the product of (x - 4)(x - 3) is -7
Multiply the polynomials.
(x – 7)(x2 + 3x – 3)
A. x3 – 4x2 – 3x + 21
B. x3 – 7x2 – 24x + 21
C. x3 – 4x2 – 24x + 21
D. x3 – 7x2 – 3x + 21
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Answer:
C) x³ -4x² - 24x + 21.
Step-by-step explanation:
Given : (x – 7)(x² + 3x – 3).
To find : Multiply the polynomials.
Solution : We have given (x – 7)(x² + 3x – 3).
Distributes x over (x² + 3x – 3) and -7 over (x² + 3x – 3).
Then
x (x² + 3x – 3) -7(x² + 3x – 3).
x³ + 3x² -3x - 7x² - 21x +21.
Combine like terms
x³ + 3x² - 7x² -3x -21x + 21.
x³ -4x² - 24x + 21.
Therefore, C) x³ -4x² - 24x + 21.
Answer:
x³ -4x² - 24x + 21.
Step-by-step explanation:
Ape-x
Without graphing, classify the following system as independent, dependent, or inconsistent. y=-3x+4 and 6x+2y=8
a. independent
b. dependent
c. inconsistent
please help
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Answer:
Dependent
Step-by-step explanation:
[tex]y=-3x+4[/tex] and [tex]6x+2y=8[/tex]
Lets solve the second equation for y and then substitute it in first equation
[tex]6x+2y=8[/tex]
Subtract 6x on both sides
[tex]2y=-6x+8[/tex]
Divide by 2 on both sides
[tex]y=-3x+4[/tex]
Now we plug it in first equation for y
[tex]-3x+4=-3x+4[/tex]
Add 3x on both sides
[tex]4=4[/tex]
Both sides are same, they are equal. the system has infinite solutions.
They are said to be dependent
How many of the first 1992 prime numbers have reciprocals less tahn 0.05?
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Suppose N represents a power of 10. what is the value of n when 31,100 is rounded to the nearest power of 10?
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We get the approximate value of [n] as 5.
What is logarithm? What is a mathematical equation and expression?A quantity representing the power to which a fixed number (the base) must be raised to produce a given number. We can write -[tex]$\log_{b}({b^x})=x[/tex]
A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have 31,100 is rounded to the nearest power of 10 and [N] represents a power of 10.
We can write -
10ⁿ = 31100
10ⁿ = 311 x 10²
10ⁿ ⁻ ² = 311
log(10ⁿ ⁻ ²) = log(311)
(n - 2) log 10 = log (311)
n - 2 = log(311)/log(10)
n - 2 = 2.5
n = 4.5
n = 5 (approx.)
Therefore, we get the approximate value of [n] as 5.
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When rounding 31,100 to the nearest power of 10, we get the value of n is 4.
To find the value of n when 31,100 is rounded to the nearest power of 10, we first need to determine which powers of 10 are closest to 31,100. The nearest powers of 10 to 31,100 are 104 (10,000) and 105 (100,000). Since 31,100 is closer to 104 than to 105, we round it down to 104.
Therefore, when 31,100 is rounded to the nearest power of 10, the value of n is 4.
The process involves converting the number into scientific notation and then adjusting the exponent, which represents the number of places the decimal point moves. In our case, to convert 31,100 to a number between 1 and 10, we would express it as 3.11 × 104, confirming that the value of n is 4.
Find the quotient of 3/5 and 9/10 . Express your answer in simplest form.
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Short answer: 2/3
Why?
When dividing two fractions, you don't divide, you find the reciprocal of the second fraction (9/10) and multiply. So, it's 3*10/9*5. Simplify. {3 * 10 => 30} ~ {9 * 5 => 45} Now we have 30/45. This can be simplified. Simplified, 30/45 reduces down to 2/3.
Hope this helped you! ♥
The quotient of 3/5 and 9/10 is the value obtained by dividing both values, Hence, the quotient of the division is 2/3
The numerator = 3/5 The denominator = 9/10The division operation can be expressed thus :
3/5 ÷ 9/10
Take the reciprocal of the denominator and change the sign to multiplication ;
Reciprocal of 9/10 = 10/9
Hence, we have ;
3/5 × 10/9 = 30/45
In simplest form ; 30/45 = 10/15 = 2/3Therefore, the quotient is 2/3
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The radius of this ball is 24 inches. Which equation gives the ball's surface area, in square inches?
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The sum of two consecutive numbers is 131 .What are the two numbers ?
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n + (n + 1) = 131n + n + 1 = 1312n + 1 = 131 |-12n = 130 |:2n = 65n+1 = 66
Answer: 65 and 66.
The sum of two consecutive numbers is 131. What are the two numbers?
Answer is provided in the image attached.
10 POINTS!!! FULL ANSWER IN STEP BY STEP FORMAT!!
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The sign of the first derivative changes at x=0, at which point the slope is undefined (the curve is vertical). The curve approaches +∞ at x=0 both from the left and from the right, so the other absolute extreme is (0, +∞).
b) The second derivative (g'') changes sign at x=2, so there is a point of inflection there.
c) There is a vertical asymptote at x=0 and a flat spot at x=2. The curve goes through the points (-2, 5) and (4, 1), is increasing to the left of x=0 and non-increasing to the right of x=0. The curve is concave upward on [-2, 0) and (0, 2) and concave downward on (2, 4]. A possible graph is shown, along with the first and second derivatives.
PLEASE HELP!!! BRAINLIEST! 20 POINTS!
A rectangle has a width of 3 cm and a length of 10 cm.
What is the effect on the perimeter when the dimensions are multiplied by 10?
A) The perimeter is increased by a factor of 10.
B) The perimeter is increased by a factor of 40.
C) The perimeter is increased by a factor of 100.
D) The perimeter is increased by a factor of 400.
THANK YOU SO MUCH!!!! <333
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How do I factorise
6-42x
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FACTORING: 6 - 42x
STEPS:
6 - 42x
-42x + 6
= -6(7x - 1)
FINAL ANSWER: -6(7x - 1)
Answer:
[tex]6(-7x+1)[/tex]
Step-by-step explanation:
Given: The equation [tex]6-42x[/tex].
To find: Factorize the given equation.
Solution:
The given expression is:
[tex]6-42x[/tex]
which can be rewritten as:
[tex]-42x+6[/tex]
Upon solving the above expression and Taking 6 common from both the terms of the expression ,we get
[tex]6(-7x+1)[/tex]
which is the required factorized form of the given expression.
A jacket is discounted 40% the jacket is now 38.70 dollars what was the original price
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To find the original price, you'll first need to convert 40% into a decimal. You can do this by moving the decimal point twice to the left. So now you have 0.40. Now you'll need to divide 38.70 by 0.40. Once you've done that, you'll get the original price
The original price of the jacket was $96.75
I hope this helps!
Find the length of the hypotenuse of a right triangle whose legs are 5 and sqare root of 2
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4 + 5 = c²
9 = c²
c = 3
Sorry this is so late and was never answered. I just saw it pop up in the related questions.
Answer:
The length of the hypotenuse is 3√3 units.
Step-by-step explanation:
It is given that the length of the legs of a right triangle are 5 units and √2 units.
According to the Pythagoras theorem, in a right angled triangle
[tex](hypotenuse)^2=(leg_1)^2+(leg_2)^2[/tex]
Substitute leg₁=5 and leg₂=√2 in the above formula.
[tex](hypotenuse)^2=(5)^2+(\sqrt{2})^2[/tex]
[tex](hypotenuse)^2=25+2[/tex]
[tex](hypotenuse)^2=27[/tex]
Taking square root both the sides.
[tex]hypotenuse=\sqrt{27}[/tex]
[tex]hypotenuse=3\sqrt{3}[/tex]
Therefore the length of the hypotenuse is 3√3 units.
The price of a gym membership has a one-time sign-up fee and a monthly fee. The price can be modeled by the function y = 10x + 15, where x is the number of months. What is the y-intercept, and what does it represent?
10; it represents the monthly fee
10; it represents the one-time sign-up fee
15; it represents the monthly fee
15; it represents the one-time sign-up fee
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What is the equation of the circle with a diameter of 6 units and a center located at (2, -5) on the coordinate plane?
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[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{2}{ h},\stackrel{-5}{ k})\qquad \qquad radius=\stackrel{3}{ r} \\\\\\\ [x-2]^2+[y-(-5)]^2=3^2\implies (x-2)^2+(y+5)^2=9[/tex]
The equation of a circle centered at (2, -5) with a diameter of 6 units is (x-2)² + (y+5)² = 9.
Explanation:The equation of a circle in the coordinate plane is given by (x-h)² + (y-k)² = r², where (h, k) are the coordinates of the center of the circle, and r is the radius. In this case, the center of the circle is at (2, -5) and the diameter is 6 units. Therefore, the radius (r) is half the diameter, which is 3 units.
Substituting h=2, k=-5, and r=3 into the equation, we get the equation of the circle: (x-2)² + (y+5)² = 9.
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For the solids show, choose all the statements that will be true if we can infer the solids' congruence by Cavalieri's Principle. The radii are congruent. The bases are congruent. The altitudes are congruent. The bases are parallel.
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Cavalieri's principle states that if two solids have equal height and if the cross-sections intersected by planes parallel to the bases and equally distant from them have always the same ratio, then the two volumes will have the same ratio.
Therefore, we can say that:
1) the radii are congruent (bases and cross-sections are congruent circles);
2) the bases are congruent;
3) the altitudes are congruent;
4) the bases are parallel.
Hence, all four statements are TRUE.
Answer:
All four are true :)
Step-by-step explanation:
Please help, I need to turn in today
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Jon performs 3 transformations on a pentagon. First, he reflects it over the x-axis. Then, he translates it 3 units to the left and 4 units up. Finally, he reflects the image over the line x = 1. Are the original and transformed images congruent? Justify your answer.
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The original and transformed images are congruent.
yes; Reflections and translations are rigid motions. Rigid motions preserve the size of the original image.
PLEASE HELP! BRAINLIEST!!!!!!! PLEASE
Jade used candle molds, as shown, to make candles that were perfect cylinders and spheres:
What is the approximate difference in the amount of wax needed to make a candle from each of these molds? (Use π = 3.14.)
27.0 cubic inches
47.1 cubic inches
84.78 cubic inches
91.12 cubic inches
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First you have to find the volume of the cylinder
To find the volume of a cylinder you use the equation
[tex]V = \pi r^{2} h[/tex]
V is volume
r is radius
h is height
Put in the values you know and 3.14 for pi
[tex]V = 3.14 * 3^{2} * 7[/tex]
Square the number
V = 3.14 * 9 * 7
Multiply
V = 197.82
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Next you find the volume of the sphere
To find the volume of a sphere you use the equation
[tex]V = \frac{4}{3} \pi r^{3} [/tex]
V is volume
r is radius
Put in the values you know and 3.14 for pi
[tex]V = \frac{4}{3} * 3.14 * 3^{3} [/tex]
Cube the number
[tex]V = \frac{4}{3} * 3.14 * 27[/tex]
Multiply
V = 113.04
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Finally you subtract the two volumes from each other
197.82 - 113.04 = 84.78
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The answer is C)84.78
Hope this helps!
(5x^2+38x+18) divided (x+7) what is the quotient and the remainder
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To determine the quotient and remainder for (5x^2+38x+18) divided by (x+7), polynomial long division must be used, involving dividing terms, multiplying and subtracting until the remainder is obtained.
Explanation:To find the quotient and remainder of the division of polynomials (5x2+38x+18) by (x+7), we can use polynomial long division.
Divide the first term of the dividend, 5x2, by the first term of the divisor, x, to get the first term of the quotient, which is 5x. Multiply the entire divisor (x+7) by 5x and subtract from the dividend. Bring down the next term from the dividend and repeat the process until there are no more terms to bring down. The last line after the subtraction will be the remainder.
By doing this, you will obtain the quotient and the specific remainder for this division.
He probability of choosing a vowel (a, e, i, o, or u) from a deck of cards containing the 26 letters of the alphabet is shown below. what is the probability of choosing the letters a and e one after the other without replacement?
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There is 1 a out of 26 letters; P(a) = 1/26
There is 1 e out of 26 letters; however, since it comes after drawing the a and is done without replacement, it is out of 25: 1/25
Together, their probabilities are 1/26(1/25) = 1/650
Please help me with this question
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◉ Data point (10, 10); Residual = 4.50
_____
Apparently, this question makes no use of the line of best fit.
Identify intervals on which the function is increasing, decreasing, or constant.
g(x) = 1 - (x - 7)^2
Select one:
a. Increasing: x < 7; decreasing: x > 7
b. Increasing: x < -7; decreasing: x > -7
c. Increasing: x > 1; decreasing: x < 1
d. Increasing: x < 1; decreasing: x > 1
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does anyone know where to find the poly-graphical point of a circle?
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y = cy + r * sin(a)
Find the inverse function f^-1(x) for the given function f(x). f(x) =3x-8
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Answer: [tex]y=\dfrac{x+8}{3}=\dfrac{1}{3}x+\dfrac{8}{3}[/tex]
Final answer:
To find the inverse of the function f(x) = 3x - 8, you swap x and y and solve for y, resulting in the inverse function f^-1(x) = (x + 8) / 3.
Explanation:
To find the inverse function f-1(x) for the given linear function f(x) = 3x - 8, we will follow these steps:
Replace f(x) with y: y = 3x - 8.
Swap x and y to make it x = 3y - 8.
Solve for y to get the inverse function.
Starting with x = 3y - 8, we add 8 to both sides to obtain x + 8 = 3y. Then, we divide both sides by 3 to isolate y, resulting in y = (x + 8) / 3. Therefore, the inverse function is f-1(x) = (x + 8) / 3.