Answer:
[tex]\boxed{\bold{\left(3x-2\right)^2}}[/tex]
Step By Step Explanation:
Rewrite [tex]\bold{9x^2-12x+4}[/tex][tex]\bold{\left(3x\right)^2-2\cdot \:3x\cdot \:2+2^2}[/tex]
Rewrite Equation[tex]\bold{\left(3x\right)^2-2\cdot \:3x\cdot \:2+2^2}[/tex]
Apply Perfect Square Formula [tex]\bold{\left(a-b\right)^2=a^2-2ab+b^2: \ a=3x,\:b=2}[/tex][tex]\bold{\left(3x-2\right)^2}[/tex]
ANSWER
[tex]9 {x}^{2} - 12x + 4 = (3x - 2) ^{2} [/tex]
EXPLANATION
The given expression is
[tex]9 {x}^{2} - 12x + 4[/tex]
This is in the form
[tex]a {x}^{2} + bx + c[/tex]
[tex]a=9,b=-12 ,c=4[/tex]
[tex]ac=9 \times 4 = 36[/tex]
Split with -6x-6x
[tex]9 {x}^{2} - 6x - 6x + 4[/tex]
[tex] = 3x( 3x - 2) - 2(3x - 2)[/tex]
Factor further to obtain,
[tex] = (3x - 2)(3x - 2)[/tex]
[tex] = (3x - 2) ^{2} [/tex]
a store clerk has 45 shirts to pack in boxes. Each box holds 6 shirts . What is the fewest boxes the clerk will need to pack all the shirts
Answer:
8 boxes
Step-by-step explanation:
45/6 is 7.5 boxes, but you can not have half a box so the fewest number of boxes is 8.
A rectangular prism has side lengths of 4 inches, 6 inches, and 7 inches. If all side lengths are doubled, what happens to the surface area
Original measurements:
L = 4; W = 6; H = 7
surface area = 2(LW + LH + HW)
surface area = 2(4 * 6 + 4 * 7 + 6 * 7)
surface area = 2(24 + 28 + 42)
surface area = 2(94)
surface area = 188
Doubled measurements:
L = 8; W = 12; H = 14
surface area = 2(LW + LH + HW)
surface area = 2(8 * 12 + 8 * 14 + 12 * 14)
surface area = 2(96 + 112 + 168)
surface area = 2(376)
surface area = 752
The surface area was 188 square inches and it became 752 square inches.
752/188 = 4
As the side lengths increased by a factor of 2, the surface area increased by a factor of 4.
Rewrite the expression 2(10+15) using distributive property of multiplication over addition
Answer:
2(10+15)= (2x10)+(2x15) 20+30=50
Step-by-step explanation:
The expression 2(10+15) rewritten using the distributive property is 20 + 30, which simplifies to 50.
Explanation:Rewriting the expression 2(10+15) using the distributive property of multiplication over addition involves multiplying the 2 by each term inside the parentheses. To do this, multiply 2 by 10 to get 20, and then multiply 2 by 15 to get 30. Combine these two products to complete the process.
Here's the calculation step by step:
Multiply the first term: 2 × 10 = 20.Multiply the second term: 2 × 15 = 30.Add the products: 20 + 30 = 50.Therefore, the expression 2(10+15) using the distributive property is 20 + 30 which simplifies to 50.
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I need help plz show steps
The "-4" tacked onto the 2x^2 term will move the entire parabola down 4 units. This is because y = 2x^2 becomes y-4 = 2x^2-4
The y-4 means we move every y coordinate down 4 spots. The x coordinate stays the same.
Solve the equation 2x3 + 7x2 – 10x – 24 = 0 in the real number system.
Answer:
x = 2
x = -4
x = -3/2
Step-by-step explanation:
We need to find the roots of the equation
2x^3 + 7x^2 – 10x – 24 = 0
We can factorize the equation into
(x-2)(x+4)(2x + 3) = 0
Roots
x = 2
x = -4
x = -3/2
The answer to your question is also attached in the images below
Answer:
x=2 ; x=-4 or x=-3/2
Step-by-step explanation:
We are given a cubic polynomial
[tex]2x^3+7x^2-10x-24=0[/tex]
Here as we are having a cubic equation to factorize, we have to find some value of x such that when we put that value in place of x , it gives us a 0. We have to try it randomly like first we try it for x=1 then x=2 and so on.
On trying for x=2 , we see that the equation becomes 0=0 and hence x=2 is one of the solution. And also as x=2 is one of the solution, (x-2) must be one of the factor. Now we use this property to determine the other factor like this.
[tex]2x^3+7x^2-10x-24=0[/tex]
Adding and subtracing [tex]4x^2[/tex] to [tex]2x^3[/tex] we get
[tex]2x^3-4x^2+4x^2+7x^2-10x-24=0[/tex]
Now we take out [tex]2x^2[/tex] as GCF
[tex]2x^2(x-2)+11x^2-10x-24=0[/tex]
Now subtracting and adding [tex]22x[/tex] to [tex]11x^2[/tex]
[tex]2x^2(x-2)+11x^2-22x+22x-10x-24=0[/tex]
taking [tex]11x^2[/tex] as GCF out
[tex]2x^2(x-2)+11x(x-2)+22x-10x-24=0[/tex]
[tex]2x^2(x-2)+11x(x-2)+12x-24=0[/tex]
[tex]2x^2(x-2)+11x(x-2)+12(x-2)=0[/tex]
Now taking [tex](x-2)[/tex] out as GCF
[tex](x-2)(2x^2+11x+12)[/tex]
Now we need to split the middle term of [tex](2x^2+11x+12)[/tex] to factorize it in such a way that their product is 2*12 and sum is 11. We have 8 and 3 as these factors.
Hence it can be factored like this
[tex](2x^2+11x+12)\\2x^2+8x+3x+12\\2x(x+4)+3(x+4)\\(2x+3)(x+4)[/tex]
Hence our answer will be
[tex](x-2)(2x+3)(x+4)=0[/tex]
And thus the solutions will be
x-2=0 : x=2
x+4=0 ; x=-4
2x+3=0 ; x=-[tex]\frac{3}{2}[/tex]
What is the probability of spinning a B?
Answer:
3/8 or 37.5%
Step-by-step explanation:
There are a total of 8 possible outcomes. B appears only 3 times in those 8 outcomes. Therefore, the chances of landing on B is 3 out of 8 or 3/8.
The probability of B in percent is 37.5 %.
What is Probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, Total outcomes = {A, A, B, B, B, C, C, C}
n(S) = 8
Now, possibility of B = {B, B, B}
n(B) = 3
Probability of B = Favorable outcomes/ total outcomes
= n(B) / n(S)
= 3/8
= 0.375
= 37.5 %
Thus, the probability of B in percent is 37.5 %.
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You throw a stone from a height of 16 feet with an initial vertical velocity of 32 feet per second. the function h= -16t squared + 32t + 16 represents the h ( in feet) of the stone after t seconds) Find the Maximum height of the stone the maximum height. please help me somebody brainly teacher expert anyone please
hope this helps :)
Step-by-step explanation:
dh/dt=-32t+32
When velocity, dh/dt, is equal to zero, the object is at its maximum height.
dh/dt=0 only when 32t=32, t=1 second, so the maximum height is h(1)
h(1)=-16+32=16ft
Using algebra
The maximum height will occur at the midpoint between the two zeros of the height function because of a quadratics symmetry...
h(t)=0 when
-16t^2+32t=0
-16t(t-2)=0
so t=0 and 2
The midpoint is t=1
And of course this will give you the same as we found earlier. The maximum height is h(1) ft
Answer:
dh/dt=-32t+32When velocity, dh/dt, is equal to zero, the object is at its maximum height.dh/dt=0 only when 32t=32, t=1 second, so the maximum height is h(1)h(1)=-16+32=16ftUsing algebraThe maximum height will occur at the midpoint between the two zeros of the height function because of a quadratics symmetry...h(t)=0 when-16t^2+32t=0-16t(t-2)=0so t=0 and 2The midpoint is t=1
Hope this helped Wilbert!
you have 1 can of chicken soup, and 3 vegetable and 1 can of tomato, what is probability of getting tomato soup
Hey there!
First, let’s find the total amount of soup cans:
1 chicken soup
3 vegetable soup
1 tomato soup
1 + 3 + 1 = 5
Therefore, the odds of you randomly selecting the tomato soup is 1/5
Hope this helps you!
God bless ❤️
Brainliest would be appreciated
xXxGolferGirlxXx
Write the ratios for sin X, cos X,and tan X
On a coordinate grid, the movie theater is located at (0,0) and the mall is located at (4,3). If the bowling alley is located at the midpoint between the theater and the mall, what is the approximate distance from the bowling alley to the mall? (Note: 1 unit equals 1 mile)
A) 1.3 miles
B) 1.5 miles
C) 2 miles
D) 2.5 miles
Answer:
D.) 2.5 miles
Step-by-step explanation:
The first step required for solving this problem is to calculate the midpoint between the theater and the mall (2, 1.5). Then use the distance formula to calculate the distance from the bowling alley to the mall.
The distance from the bowling alley to the mall is 2.5 miles. The coordinates of the midpoint, which is the location of the bowling alley, are calculated first. Then, using the Pythagorean theorem, the distance to the mall is found by calculating the square root of the sum of the squares of the horizontal and vertical distances.
Explanation:The task is to calculate the distance from the bowling alley to the mall if the bowling alley is at the midpoint between the movie theater at (0,0) and the mall at (4,3). First, we find the coordinates of the midpoint, which is the average of the x-coordinates and the y-coordinates of the two points respectively. Thus, the midpoint is located at:
(0 + 4) / 2 = 2 for the x-coordinate(0 + 3) / 2 = 1.5 for the y-coordinateSo, the bowling alley is at point (2, 1.5). Secondly, we use the Pythagorean theorem to find the distance from the bowling alley to the mall:
The change in x (horizontal distance) from the bowling alley to the mall is 4 - 2 = 2 units.The change in y (vertical distance) from the bowling alley to the mall is 3 - 1.5 = 1.5 units.Applying the distance formula (or Pythagorean theorem):
Distance = √( Δx² + Δy² ) = √( 2² + 1.5² ) = √( 4 + 2.25 ) = √6.25 = 2.5 miles
Therefore, the approximate distance from the bowling alley to the mall is 2.5 miles, which corresponds to answer (D).
How do you find interval of increase or decrease??
To find intervals of increase or decrease, analyze the function's derivative or slope. Linear regression uses a straight line equation to estimate these trends graphically. Graphs are helpful for visually representing increase or decrease rates and other numerical relationships.
To find intervals of increase or decrease in a function, you need to analyze the function's derivative. If the derivative is positive over an interval, the function is increasing; if the derivative is negative, the function is decreasing. An example of observing such behavior is through graphical analysis, where you look for portions of the graph that have an upward or downward slope, respectively.
Linear regression is a tool used to determine the rate of increase or decrease over a set of data points. By fitting a line X = S\u00d7t + I, where S is the slope and I the intercept with the vertical axis, one can estimate the trend or rate of change, assuming a linear relationship.
To describe the rate of growth in various contexts, such as population growth or economic data, graphs can display these trends visually. For different applications, such as contour mapping in geography, the interval of change might be adjusted to represent details accurately. A constant rate of growth assumption, however, isn't always correct and must be adjusted depending on the circumstances.
There are 4 cups in 1quart.If you want to convert quarts to cups,should you multiply or divide by 4
you would multiply by 4 because if there are 4 cups in a quart then u have 1 quart or 4 cups . thats the only explanation even possible for this problem
Determine the multiplicity of the roots of the function k(x) = x(x + 2)3(x + 4)2(x − 5)4. 0 has multiplicity −2 has multiplicity −4 has multiplicity 5 has multiplicity
Answer:
0 has multiplicity 1
-2 has multiplicity 3
-4 has multiplicity 2
5 has multiplicity 4
Step-by-step explanation:
The multiplicity of the root of a polynomial function, refers to the number of time the root repeats itself.
The given function is
[tex]k(x)=x(x+2)^3(x+4)^2(x-5)^4[/tex]
To find the roots of this function, we equate the function to zero.
[tex]x(x+2)^3(x+4)^2(x-5)^4=0[/tex]
We now use the zero product principle, to obtain;
[tex]x=0[/tex], with multiplicity 1
[tex](x+2)^3=0[/tex]
[tex]\Rightarrow x=-2[/tex], with multiplicity 3
[tex](x+4)^2=0[/tex]
[tex]\Rightarrow x=-4[/tex], with multiplicity 2
[tex](x-5)^4=0[/tex]
[tex]\Rightarrow x=5[/tex], with multiplicity 5.
Answer:
The roots of the function;
[tex]k(x)=x(x+2)^3(x+4)^2(x-5)^4[/tex]
0 has multiplicity 1.-2 has multiplicity 3.-4 has multiplicity 2.5 has multiplicity 4.Step-by-step explanation:
Given information:
The function;
[tex]k(x)=x(x+2)^3(x+4)^2(x-5)^4[/tex]
As, we know that multiplicity of any function is defined as the number of times the roots repeats in the solution.
Hence, we need to find the roots of the function
So, equating the function to [tex]0[/tex]
[tex]x(x+2)^3(x+4)^2(x-5)^4=0[/tex]
As, [tex]x=0[/tex] , is having multiplicity [tex]1[/tex].
[tex](x+2)^3=0\\x=-2[/tex]
Having a multiplicity 3.
Now,
[tex](x+4)^2=0\\x=-4[/tex]
Having a multiplicity 2.
And,
[tex](x-5)^4=0\\x=5[/tex]
Having multiplicity 4.
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w÷5=? "With work if needed"
Answer: This question doesn't have an answer.
Step-by-step explanation:
When 6 is subtracted from a square of a number the result is 5 times the number
Answer:
Step-by-step explanation:
The starting number is 6
6*6=36
36-6=30
6*5=30
Answer:
My guy tha answer is x=6
Step-by-step explanation:
how i know, because i got it right
How many lines of symmetry does this figure have?
Answer:
1 line of symmetry through the middle making 2 v s
Step-by-step explanation:
Answer: The figure has 1 line of symmetry.
Step-by-step explanation:
A figure is said to has a line of symmetry if we can draw a line that divides the entire figure into two equal halves, so that each half appears as a reflection image or the mirror of the other.
In the given picture , if given a figure of alphabet W.
It has only a vertical symmetry ( see below the line of symmetry divides W into two Vs) but no horizontal symmetry and any other symmetry.
Therefore , it has only one line of symmetry.
Hence, the figure has 1 line of symmetry.
what is the degree angle of sircle
Answer: there are 360 degrees in a circle, that there are 90 degrees in a right angle, and that the angle of an equilateral triangle contains 60 degrees.
Step-by-step explanation:
There are 360 degrees in a circle
Multiply
(5x-1)(6x^2+3x+7)
SHOW WORK
sorry for using printed paper, I tried my best to avoid the lines
Answer:
30x³ + 9x² + 32x - 7
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
5x(6x² + 3x + 7) - 1 (6x² + 3x + 7) ← distribute both sets of parenthesis
= 30x³ + 15x² + 35x - 6x² - 3x - 7 ← collect like terms
= 30x³ + 9x² + 32x - 7
What is the average rate of change for this quadratic function for the interval from x=3 to x=4
ANSWER
A. 27.5
EXPLANATION
The average rate of change of the given quadratic function on the interval;
x=2 to x=4 is the slope of the secant line connecting the points (2,f(2)) and (4,f(4)).
This implies that the average rate of change is
[tex] = \frac{f(4) - f(2)}{4 - 2} [/tex]
From the table,
[tex]f(4) = 64[/tex]
and
f(2)=9.
The average rate of change becomes
[tex] = \frac{64 - 9} {4 - 2} [/tex]
[tex] = \frac{55}{2} = 27.5[/tex]
The correct choice is A.
Why is this expression not positive or negative when x=-5 -1.3x-6.5
Answer:
This is because this equation equals 0 when x = -5
Step-by-step explanation:
To find this, plug the value in for x.
-1.3x - 6.5
-1.3(-5) - 6.5
6.5 - 6.5
0
The expression -1.3x - 6.5 evaluated at x=-5 equals zero, which is why it is neither positive nor negative.
To verify this let's evaluate it step by step.
Substitute x = -5 into the expression:
-1.3(-5) - 6.5
Then, multiply -1.3 by -5:
-1.3 * (-5) = 6.5
Then, subtract 6.5:
6.5 - 6.5 = 0
The expression -1.3x - 6.5 evaluated at x=-5 equals zero, which is why it is neither positive nor negative.
If 2a+ 2/a =4, what is the value of 2a^2− 2/a^2 ?
ANSWER
0
EXPLANATION
Given :
[tex] \frac{2a + 2}{a} = 4[/tex]
We solve for 'a' to obtain,
[tex]2a + 2 = 4a[/tex]
This implies that,
[tex]2 = 4a - 2a[/tex]
[tex]2 = 2a[/tex]
This implies that,
[tex]a = 1[/tex]
We substitute a=1 into
[tex] \frac{ 2{a}^{2} - 2}{ {a}^{2} } [/tex]
This gives us,
[tex]\frac{ 2{(1)}^{2} - 2}{ {(1)}^{2} } = \frac{2 - 2}{2} = \frac{0}{2} = 0[/tex]
Derek‘s parents are finalizing a budget for his college expenses his first year of college will cost $1000 in expenses will increase by 12% each year which statement is correct regarding the amount they should budget for dares for your college education to the nearest dollar
Answer:
$4779
Step-by-step explanation:
First you need to write an equation to model this situation. In this case it's f(x)=1000(1.12)^x. College usually lasts 4 years, so to find the total amount of money they need to budget, you need to find the sum of f(0), f(1), f(2), and f(3).
This is roughly equivalent to 1000+1120+1254+1405, which equals 4779.
Answer: A
Step-by-step explanation:
It looks like its A to me but I actually am not 100% on this one
Solve the problem below. Write the answer in the space provided.
1/2 of 4 feet = ___________
inches
Answer:
24 inches
Step-by-step explanation:
1/2 of 4 feet is 2 feet
you know that 1 feet = 12 inches
So 2 feet = 24 inches
Please help
ASP PLEASE FOR 10 points!!✨
Part A: You can add the time in hours to find the total. 1/3 + 3/4 + 4/6 + 1/2 = 2 1/4 hours which can also be expressed as 2 hours and 15 minutes (1/4 of an hour is 15 minutes.)
Part B: It takes him 3/4 hr to do homework, 4/6 hr to play soccer, and 1/2 hr to play piano. 3/4 + 4/6 + 1/2 = 1 11/12 hrs or 1 hour and 55 minutes (11/12 of an hour is 55 minutes.) Therefore Kevin is wrong.
PLEASE PLEASE HELP ME!!!!
According to Casio Calculations the Answer is C.
Which of the following options best describes the zeros of the quadratic function above?
A. 2 real zeros
B. 1 real zero
C. 1 real zero and 1 imaginary zero
D. 2 imaginary zeros
Answer:
it might be d
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
hi
What is the answer to this problem
the answer is negative 168
Answer:
Step-by-step explanation:
What is the area of the circle?
Circumference is found by multiplying the diameter by PI,
so a circumference of 6PI means the diameter is 6 inches.
Area is found using the formula PI x r^2
r = 1/2 the diameter
r = 6/2 = 3
The area becomes 3^2 x PI = 9PI inches.
The answer is C.
The diameter of a circular garden is 16 feet what is the approximate area of the garden
Answer:
Option C
201 feet²
Step-by-step explanation:
Given in the question,
diameter of the circular graph = 16 feet
Formula to calculate the area of garden
Area = π r²where π is constant = 3.14
r is the radius
To find the radius
diameter/216/2
8 feet
Plug in values to calculate area
(3.14) 8²
200.96 feet²
Area of the circular garden having 16 feet diameter is 201 (approximate)
Can you help me I’m begging you for your help please tell me I need your help please I’m begging you I’ve never been like this in my entire life please I’m begging you please help me with this question
Answer
D. -3x + 4(2x-6) + 5
Step-by-step explanation:
-3x has nothing attached to it so leave it alone
4 times 2x equals 8x and 4 times -6 equals -24
add 5
8x-3x=5x
-24 + 5 = -19
5x - 19
Answer: The answer is D
Step-by-step explanation:
I forgot set by step so I hope u figure that part out though