Solve the equations.
[tex]3(x+4)^{2} =10x+32\\(x+4)^{2} =3x+40\\\frac{x^{2} -1}{2} -11x=11[/tex]
Answer:
a) x = {-2 2/3, -2}
b) x = {-8, 3}
c) x = {-1, 23}
Step-by-step explanation:
If all you want are solutions, a graphing calculator can give them to you easily. The attachment shows the solutions as x-intercepts when the equation is rearranged to the form f(x) = 0.
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In general, it can be convenient to write the equation in standard form with integer coefficients. Common factors among the coefficients should be removed.
a)3(x+4)^2 = 10x +32 . . . . . given
3(x^2 +8x +16) -10x -32 = 0
3x^2 +14x +16 = 0
To factor this, we're looking for factors of 3·16 that total 14.
48 = 1·48 = 2·24 = 3·16 = 4·12 = 6·8
The last pair of factors has a total of 14, so we can rewrite the equation as ...
(3x +6)(3x +8)/3 = 0
(x +2)(3x +8) = 0
The solutions are the values of x that make the factors zero:
x = -2, x = -8/3
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b)(x +4)^2 = 3x +40 . . . . . . . . given
x^2 +8x +16 -3x -40 = 0 . . . . subtract the right side
x^2 +5x -24 = 0 . . . . . . . . simplify
(x +8)(x -3) = 0 . . . . . . factor
The solutions are the values of x that make the factors zero:
x = -8, x = 3
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c)(x^2 -1)/2 -11x = 11 . . . . . given
x^2 -1 -22x -22 = 0 . . . . . . multiply by 2, subtract the right side
x^2 -22x -23 = 0 . . . . . . simplify
(x -23)(x +1) = 0 . . . . . . factor
x = 23, x = -1
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Additional comment
Factoring often gets to the solution with the least fuss when the solutions are rational. There are several ways factoring can be done when the leading coefficient is not 1. One of them is illustrated in (a) above. We will show two other methods that give the same result.
factoring by pairs
We have identified the factors of 3·16 = 48 that have a total of 14. We can use those factors to rewrite the 14x term in the equation.
3x^2 +6x +8x +16 = 0
Now, we can group the terms in pairs, and factor each pair. It does not matter which of the factors (6 or 8) you write first. You will end with the same result.
(3x^2 +6x) +(8x +16) = 0
3x(x +2) +8(x +2) = 0
(3x +8)(x +2) = 0 ⇒ x = -8/3, x = -2
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factoring using the X method
This method is usually shown using a large graphic X. In the top quadrant is written the product of the leading coefficient and the constant: 3·16 = 48.
In the bottom quadrant is written the coefficient of the x-term: 14.
If one or the other, or both, of these top/bottom values is negative, be sure to keep the sign.
The side quadrants are then filled with values that have a product equal to the top number, and a sum equal to the bottom number. (Pay attention to the signs.) Further, in each of those quadrants, the number written is divided by the leading coefficient, and the fraction reduced to lowest terms.
Here, we would have 6/3 = 2 on one side, and 8/3 on the other side. Now the factors are written as (bx+a), where the reduced fraction on either side is a/b. In our example, the factors are (x+2) and (3x+8)
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alternate X method
This starts off in the same way the X method does, as described above. However, the factors on either side of the X are not divided by the leading coefficient (a). If those side values are 'p' and 'q', the quadratic is written in factored form as ...
(ax +p)(ax +q)/a = 0
You will notice we used this form above: (3x +6)(3x +8)/3 = 0.
Now, the divisor 'a' can be used to reduce either or both of the numerator factors. Here, the entire factor of 3 can be removed from (3x+6) to make the factorization be ...
(x +2)(3x +8) = 0
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Sometimes, one factor of the divisor will be removed from one term, and the other factor of it will be removed from the other term. An example of this might be ...
[tex]\dfrac{(6x+3)(6x+2)}{6}=\dfrac{6x+3}{3}\cdot\dfrac{6x+2}{2}=(2x+1)(3x+1)[/tex]
which net represents this rectangular prism?
Answer:
Top left
Step-by-step explanation:
Can someone plz help Me?
Answer:
A and C
Step-by-step explanation:
quotient of 2 2/3 and 3 1/2
Answer:
16/21
Step-by-step explanation:
Convert the equation g(x) = −(x − 7)2 +5 into standard form.
Answer:
7
Step-by-step explanation:
You have to add 2 and 5, the rest is stuff to distract you
I do not know how to answer these questions, can someone explain what I would do to solve them?
Answer:
Step-by-step explanation:
The nth term of the sequence 27,37,47
Answer: The 9th term of the sequence 27,37,47 is 107.
A triangle has interior measures of 45° and 50°. What is the measure of the third angle?
950
850
90°
50
Answer:
85 degrees
Step-by-step explanation:
the inside of a triangle is always 180 degrees.
180-45-59=85
What is the mean of 9, 8, -15 and -12?
The Mean is:
Answer:
-2.5
Step-by-step explanation:
add all the values and divide by the no of values present
a
What is the image of the point (-9, -6) after a rotation of 90° tounterclockwise
about the origin?
Answer:
Pumpkins are used as decorations during the fall months.
Pumpkins are used as decorations during the fall months.
Pumpkins are used as decorations during the fall months.
Pumpkins are used as decorations during the fall months.
Pumpkins are used as decorations during the fall months.
Pumpkins are used as decorations during the fall months.
Pumpkins are used as decorations during the fall months.
Pumpkins are used as decorations during the fall months.
Pumpkins are used as decorations during the fall months.
Pumpkins are used as decorations during the fall months.
Pumpkins are used as decorations during the fall months.
Pumpkins are used as decorations during the fall months.
Pumpkins are used as decorations during the fall months.
Pumpkins are used as decorations during the fall months.
Pumpkins are used as decorations during the fall months.
which inequality is a true statement select each correct answer
Answer:
A. False
B. True
C. False
D. False
E. True
Hope This Helps!!!
The slope of the line below is - Write a point-slope equation of the line
using the coordinates of the labeled point.
(4,4)
10
A. y+ 4 = (x+4)
O B. y+4= - (x + 4)
O C. y 4 = (x - 4)
OD. y-4 = -(x-4)
Answer:
D.
Step-by-step explanation:
pint slope form:
(y-y1)=m(x-x1)
do just olug in the point and the slope into the equation
(y-4)= -8/7 (x-4)
PLEASE HELP I"LL GIVE BRAINLEAST
Rico paid $180 sales tax on his new $2,400 motorcycle. What was the sales tax percentage rate where he bought his motorcycle?
7.0% tax rate
7.5% tax rate
8% tax rate
6.5% tax rate
Answer:
7.5 % Tax rate
Step-by-step explanation:
I used used the calculator to figure out the rate
$2,400 X 7.5%= 180
helppppppppp[pppppp[pppppppppp
Answer:A
Step-by-step explanation:i mean that sound logiclity correct
pls help me with my maths if you can
13. An amusement park drafting engineer must create a small
Ferris wheel with 12 cabs total, each equally spaced apart to
balance the wheel. How many degrees apart should each cab be?
Answer:
30 degrees
Step-by-step explanation:
a ferris wheel is a circle
the degree of a circle is 360
360/12=30
30 degrees each
A survey of 500 college students moving into their dorm revealed that 425 brought a microwave, 380 brought a video game console, and 50 brought neither a microwave nor game console. A survey participant is randomly selected. Let M be the event the participant brought a microwave and let C be the event the participant brought a video game console. Organize these events in a two-way table. What is the probability that the participant did not bring a microwave or did not bring a console, P(MC or CC)?
0.10
0.29
0.39
0.90
Answer:
0.90
Step-by-step explanation:
I’m doing the unit test
Answer:
0.29
Step-by-step explanation:
The probability that they brought both is .90
The probability of neither is .29, which is what this question is asking
I'm really bad at mathematics. It would be nice if anyone could help me out :) thanks
Write TWO different equations that you could use to solve for x. You don't need to solve.
Answer:
see explanation
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos52° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{18}{x}[/tex] → (1)
The 3rd angle in the triangle is
180° - (90 + 52)° = 180° - 142° = 38°
Using the sine ratio in the right triangle
sin38° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{18}{x}[/tex] → (2)
A hiker travels 1.13 kilometers south, then travels 2.25 kilometers east. What’s the hiker’s displacement for the trip?
Answer:
Total displacement = 2.52 kilometers [south east][tex]a^2 + b^2 = c^2\\1.13^2 + 2.25^2 = c^2\\c^2 = 6.3394\\c = 2.52[/tex]
Step-by-step explanation:
By the Pythagorean Theorem:
Please help me and If your answer is wrong or not appropreat I will report it
Simplify (-2x^(3)y^(7))^(2)(3x^(2)y^(2))^(5)
Answer:
972 x^16 y^24
Step-by-step explanation:
Simplify the following:
(-2 x^3 y^7)^2 (3 x^2 y^2)^5
Multiply each exponent in -2 x^3 y^7 by 2:
(-2)^2 x^(2×3) y^(2×7) (3 x^2 y^2)^5
2×7 = 14:
(-2)^2 x^(2×3) y^14 (3 x^2 y^2)^5
2×3 = 6:
(-2)^2 x^6 y^14 (3 x^2 y^2)^5
(-2)^2 = 4:
4 x^6 y^14 (3 x^2 y^2)^5
Multiply each exponent in 3 x^2 y^2 by 5:
4 x^6 y^14×3^5 x^(5×2) y^(5×2)
5×2 = 10:
4×3^5 x^6 y^14 x^(5×2) y^10
5×2 = 10:
4×3^5 x^6 y^14 x^10 y^10
3^5 = 3×3^4 = 3 (3^2)^2:
4×3 (3^2)^2 x^6 y^14 x^10 y^10
3^2 = 9:
4×3×9^2 x^6 y^14 x^10 y^10
9^2 = 81:
4×3×81 x^6 y^14 x^10 y^10
3×81 = 243:
4×243 x^6 y^14 x^10 y^10
4 x^6 y^14×243 x^10 y^10 = 4 x^(6 + 10) y^(14 + 10)×243:
4×243 x^(6 + 10) y^(14 + 10)
14 + 10 = 24:
4×243 x^(6 + 10) y^24
6 + 10 = 16:
4×243 x^16 y^24
4×243 = 972:
Answer: 972 x^16 y^24
Answer:
972x^(16)y^(24)
Step-by-step explanation:
Hope it correct !!
equation of the line that passes through (7,-1) and (-3,-1)
Answer:
y = - 1
Step-by-step explanation:
Note the y- coordinates of both points are equal, both - 1
This indicates the line is horizontal and parallel to the x- axis with equation
y = c
where c is the value of the y- coordinates the line passes through
The line passes through (7, - 1 ) and (- 3, - 1 ) with y- coordinates - 1 , then
y = - 1 ← equation of line
How i can answer this question, NO LINKS, if you answer correctly i will give u brainliest!
Answer:
A Todays soup will be less tomatoey
Step-by-step explanation:
will mark brainleist pls hep
Answer: 242
Brainliest plsssssss
The expression below represents the perimeter of a square in centimeters.
4(6+2.5)
What is the square's perimeter?
Answer:
34
Step-by-step explanation:
4(8.5) = 34
What is 6 percent of 200 plz show your work
Answer: 12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
200 * 0.06 = 12
2+5+8+….+3n-1=n(3n+1)/2
Answer:
all you do is() first divide then go from left to right answers 4
What is the solution for -10 < x - 9?
x > -19
x < -1
x < -19
x > -1
Answer:
x > -1
Step-by-step explanation:
-10 < x - 9 add 9 to both sides of the inequation
9 + (-10) < x - 9 + 9 minus 9 will eliminate the positive 9 on the right side of the inequation therefore the answer is:
-1 < x and x > -1
The manger of a water park keeps track of the amount of money collected, M, and the number of tickets,T, each day.
Answer: The variable t us the dependent variable because it affects the amount of money collected, m, each day.
If triangle ABC is congruent to DEF, then what side is congruent to BC?
A. FD
B. EF
C. ED
D. CA
Answer:
EF
Step-by-step explanation:
BC is the hypotenuse of the left triangle. The corresponding side on the right triangle would be EF.
Answer:
EF
Step-by-step explanation:
The corresponding side to BC is EF.
Look at the bolded letters
ABC ⇒ DEF
notice the similarities?