A perfect square trinomial is represented by the equation [tex]x^2-6x+9[/tex] and this can be determined by using the factorization method.
Given :
A perfect square trinomial can be represented by a square model with equivalent length and width.
The following steps can be used in order to determine the polynomial that can be represented by a perfect square model:
Step 1 - First, check option a) [tex]x^2-6x+9[/tex] is a perfect square or not.
Step 2 - Try to factorize the above equation.
[tex]x^2-6x+9 = x^2-3x-3x+9[/tex]
[tex]x^2-6x+9 = x(x-3)-3(x-3)[/tex]
[tex]x^2-6x+9 = (x-3)^2[/tex]
Step 3 - The equation in option a) represents the perfect square trinomial.
From, the above steps, it can be concluded that the correct option is a).
For more information, refer to the link given below:
https://brainly.com/question/2263981
Are the figures below similar?
NO LINKS!! NEED ANSWER ASAP
Here is my answer. I hope it is helpful.
This is a really quick question and I need your help
Step-by-step explanation:
To find the slope, calculate rise and run. The formula is as follows...
[tex]\frac{Rise}{Run} =\frac{y2-y1}{x2-x1}[/tex]
Allen is showing his work in simplifying −8.3 + 9.2 − 4.4 + 3.7. Identify any errors in his work or in his reasoning.
Step Work Reasoning
−8.3 + 9.2 − 4.4 + 3.7 Original problem
1 −8.3 + 9.2 + 4.4 + 3.7 Additive inverse
2 −8.3 + 4.4 + 9.2 + 3.7 Commutative property
3 −8.3 + (4.4 + 9.2 + 3.7) Associative property
4 −8.3 + 17.3 Simplify
5 9 Simplify
He did not make any errors.
Step 1: He wrote −4.4 incorrectly as + 4.4.
Step 2: He identified changing the order of the numbers as the commutative property, which is incorrect.
Step 3: He identified changing the grouping of the numbers as the associative property, which is incorrect.
Step-by-step explanation: First, you use the PEMDAS method which is parenthese, exponent, multiplication division, addition and subtraction.
So, there is parenthese, exponent, multiplaction or division.
Now, first you add -8.3 + 9.2= 0.9, then subtract 0.9 by 4.4= -3.5, now add -3.5 + 3.7= 0.2
Use the original problem and use the PEMDAS method.
Hope this helps!!
The graphs above are of the lines y = -x+2 and y=x+1. The point of intersection of the linear equations is
(0,2)
(0.5, 1.5)
(-1,0)
(2,0)
See below
[tex]\\ \sf\Rrightarrow y=-x+2[/tex]--(1)
[tex]\\ \sf\Rrightarrow y=x+1[/tex]--(2)
Now
[tex]\\ \sf\Rrightarrow -x+2=x+1[/tex]
[tex]\\ \sf\Rrightarrow -2x=-1[/tex]
[tex]\\ \sf\Rrightarrow x=0.5[/tex]
Put in eq(2)
[tex]\\ \sf\Rrightarrow y=0.5+1[/tex]
[tex]\\ \sf\Rrightarrow y=1.5[/tex]
(x,y)=(0.5,1.5)
What is the slope of a line that is parallel to y = 5x + 3?
Answer:
slope = 5
Step-by-step explanation:
The equation of a lin in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 5x + 3 ← is in slope- intercept form
with slope m = 5
Parallel lines have equal slopes , then
The slope of a line parallel to y = 5x + 3 is 5
a man who is 1.6 m tall observes the angle of elevation of the top of a tower is 45°.if the height of the tower is 21 m,find the distance between the man and the tower.
Step-by-step explanation:
hope it will help you.....
Simplify this expression
[tex]\frac{(a^8a^6)}{a^2} ^\frac{1}{7}[/tex]
Answer:
Step-by-step explanation: The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form.
Robert graded his friend Sam's practice test and a him a 72% Sam checked it again in found that he really made a 80% Robert said relax i only made an error of 8%Is robert correct
Answer:
No
Step-by-step explanation:
Use the formula, difference/original. The difference is 8%. The original is 72%.
The equation would be: 8/72
Which is 1/9
1/9 = 11.1%
So he made a mistake of 11%
pe
Two companies allow you to pay monthly for your food
A charges a one time fee of $150 and $45 per month Company B charges a
one time fee of $125 and $50 per
month
Answer:
A: 150+(45•p)
B: 125+(50•p)
Step-by-step explanation:
You multiply the monthly fee by a letter representing an unknown number because we dont know how many months you are staying with each company and we add the one time fee because you are only paying once, so in conclusion you add the one time fee to the result of the monthly fee by how many months.
I NEED HELP!!!
solve x^3 - 6x^2 - 7x + 60 by factoring. show all work
(using the method in the picture below)
Answer: x = -3, 5, 4
Step-by-step explanation:
Don't have time for it
Help please I’ll give the highest point ! :)))) tysm I need it done by 10:20
Answer:
hope it helps you.........
Answer:
10/14 - 7/14 = 3/14 :D
Step-by-step explanation:
you have to find the common denominator, in this case its 14. then, whatever number you multiplied the denominator by, you have to multiply the numerator by. so, 5/7x2= 10/14, and 1/2x7 = 7/14, then its just 10-7 which equals 3
Please help me! I’m failing!!!
a. If G(t) = a (1 + r)ᵗ, then G(0) = a corresponds to the starting area of the glacier, which is given to be 142 acres. So a = 142.
The area of the glacier shrinks by 4.4% each year. This means that after 1 year, the area is reduced to
142 - (4.4% of 142) = 142 (1 - 0.044) ≈ 135.75 acres
After another year,
135.75 - (4.4% of 135.75) = 135.75 (1 - 0.044) ≈ 129.78 acres
or equivalently, 142 (1 - 0.044)² acres.
And so on. After t years, the glacier would have an area of
G(t) = 142 (1 - 0.044)ᵗ ⇒ G(t) = 142 × 0.956ᵗ
b. If the year 2007 corresponds to t = 0, then 2012 refers to t = 5. Then the area of the glacier is
G(5) = 142 × 0.956⁵ ⇒ G(5) ≈ 113.39 acres
c. Simply take the difference between G(5) and G(0) :
G(5) - G(0) ≈ 142 - 113.39 ≈ 28.61 acres
d. The average rate of change of G(t) from 2007 to 2012 is given by the difference quotient of G(t) over the interval 0 ≤ t ≤ 5 :
[tex]ARC_{[2007,2012]} = \dfrac{G(5) - G(0)}{5 - 0} \approx \dfrac{113.39 - 142}5[/tex]
so that ARC ≈ -5.72 acres/year. This rate tells us that a little less than 6 acres of glacial ice is lost each year, based on the reduction over the first 5 years.
e. The year 2017 refers to t = 10, so now we compute
[tex]ARC_{[2012,2017]} = \dfrac{G(10) - G(5)}{10 - 5} \approx \dfrac{90.55-113.39}5[/tex]
which comes out to about ARC ≈ -4.57 acres/year. Since this rate is smaller than the ARC between 2007 and 2012, this means that the glacial ice is disappearing at a slower rate in later years.
A company needs to package 2,400 pencils. A box in the shape of a rectangular prism can hold 60 pencils. A cylindrical container can hold 80 pencils. Each box costs the company $0. 50, while each cylindrical container costs $0. 75. Which packaging should the company use to minimize cost? Explain. The rectangular prism boxes should be used because they will cost the company $2. 50 less than using the cylindrical containers. The cylindrical containers should be used because they will cost the company $2. 50 less than using the rectangular boxes. The rectangular prism boxes should be used because they will cost the company $5. 00 less than using the cylindrical containers. The cylindrical containers should be used because they will cost the company $5. 00 less than using the rectangular boxes.
The true statement is (a) The rectangular prism boxes should be used because they will cost the company $2. 50 less than using the cylindrical containers.
The given parameters are:
[tex]Pencils = 2400[/tex] --- the pencils needed
The number of pencils the prism can hold is:
[tex]Prism =60[/tex]
Divide the number of pencils needed by the number of pencils in 1 rectangular prism, to calculate the number of prisms needed (n1)
[tex]n_1 = \frac{Pencils}{Prism}[/tex]
So, we have:
[tex]n_1 = \frac{2400}{60}[/tex]
[tex]n_1 = 40[/tex]
A rectangular prism costs $0.50.
So, the total cost is:
[tex]Total\ cost = 40 \times 0.50[/tex]
[tex]Total\ cost = \$20[/tex]
The number of pencils the cylinder can hold is:
[tex]Cylinder=80[/tex]
Divide the number of pencils needed by the number of pencils in 1 cylinder box, to calculate the number of cylinders needed (n2)
[tex]n_2 = \frac{Pencils}{Cylinder}[/tex]
So, we have:
[tex]n_2 = \frac{2400}{80}[/tex]
[tex]n_2 = 30[/tex]
A cylinder costs $0.75.
So, the total cost is:
[tex]Total\ cost = 30 \times 0.75[/tex]
[tex]Total\ cost = $22.5[/tex]
By comparison, the rectangular prism costs $2.5 less than the cylinder
Hence, the true statement is (a)
Read more about volumes at:
https://brainly.com/question/1908836
I need the answer urgent plssss
Answer:
4,6,14,18, and 20
Step-by-step explanation:
does anyone know the answer
Answer: C. Distributive Property
Step-by-step explanation: To simplify this expression, you would multiply 6 by y and 2.
what is the cost of 12 bottles? explain
Answer:
$24
Step-by-step explanation:
The unit rate is shown to be $2 per bottle. The cost of 12 bottles is 12 times the cost of one bottle. That means the cost of 12 bottles is ...
(12 bottles) × ($2/bottle) = $24
I NEED HELP WITH NUMBER 2
[tex]5y+2x = -7~~~~~......(i)\\\\y = -2x +5 ~~~~~~.....(ii)\\\\(i) -(ii):\\\\5y+2x -y = -7-(-2x+5)\\\\\implies 4y +2x = -7 +2x -5\\\\\implies 4y +2x -2x = -12\\\\\implies 4y = -12\\\\\implies y = - \dfrac{12}4 = -3\\\\\\\text{Substitute}~ y=-3~ \text{in equation (ii):}\\\\\\-3 = -2x +5\\\\\implies 2x = 5 +3 \\\\\implies 2x = 8\\\\\implies x = \dfrac 82 =4\\\\\text{Hence,}~ x = 4[/tex]
A recipe that makes 4 servings calls for Two-thirds cup of flour. How much flour is required to make 20 servings?
6 cups
3 and one-third cups
two-thirds cups
StartFraction 2 over 15 EndFraction cups
PLEASE HURRY ITS A TEST AND TIMED
What is the relation between the sine and cosine values of angles in each quadrant? How would you use the 60° angle to find sine and cosine of 120°, 240°, and 300°? What angles could we find sine and cosine for using information for π/4 and π/6?
The angles, 60°, [tex]\displaystyle \frac{\pi}{4}[/tex] and [tex]\displaystyle \frac{\pi}{6}[/tex] are special angles that have known trigonometric ratio values.
First part;
The sine and cosine gives the coordinates of the tip of the radius of a unit circle as it rotates P(cos(θ), sin(θ))Second part;
With the knowledge of the sine and cosine of 60°, we have; sin(60°) = sin(120°), sin(240°) = -sin(60°), sin(300°) = -sin(60°)cos(120°) = -cos(60°), cos(240°) = -cos(60°), cos(300°) = cos(60°)Third part;
[tex]\displaystyle \frac{\pi}{4}[/tex] can be used to find the sine and cosine of [tex]\displaystyle \frac{3 \cdot \pi}{4}[/tex], [tex]\displaystyle \frac{5 \cdot \pi}{4}[/tex], and [tex]\displaystyle \frac{7 \cdot \pi}{4}[/tex] [tex]\displaystyle \frac{\pi}{6}[/tex], can be used to find the sine and cosine of [tex]\displaystyle \frac{5 \cdot \pi}{6}[/tex], [tex]\displaystyle \frac{7 \cdot \pi}{6}[/tex], and [tex]\displaystyle \frac{11 \cdot \pi}{6}[/tex]Reasons:
First Part;
Considering a unit circle with the center at the origin of the graph, we have;
The sine of the angle, θ, rotated by the radius is the vertical distance of a point P on the circle which is the location of the radius, from the horizontal axis.
The cosine of the angle, θ, is the horizontal distance of P from the vertical axis, such that we have;
The coordinates of point P = (cos(θ), sin(θ))
In the four quadrant, we have;
First Quadrant; All trigonometric ratios are positive
Second Quadrant; sine is positive
Third Quadrant; Tan is positive
Fourth Quadrant; Cosine is positive
Second part;
We have; At 120°, the point P is the same elevation from the horizontal axis, therefore;
sin(60°) = sin(120°) = 0.5·√3
However, the x-coordinate of the point P is in the negative direction, therefore, we get;
cos(120°) = -cos(60°) = -0.5
Similarly from the quadrant relationship, we have;
240° is in the third quadrant, and it is 60° below the negative horizontal line, therefore;
sin(240°) = -sin(60°) = -0.5·√3
cos(240°) = -cos(60°) = -0.5
300° is in the fourth quadrant, and it is 60° below the positive x-axis, therefore;
sin(300°) is negative and cos(300°) is positive
Which gives;
sin(300°) = -sin(60°) = -0.5·√3
cos(300°) = cos(60°) = 0.5
Third part;
[tex]\displaystyle \frac{\pi}{4} =45^{\circ}[/tex]
[tex]\displaystyle \frac{\pi}{6} =30^{\circ}[/tex]
The sine and cosine of 45° can be used to find the sine and cosine of (180° + 45°) = 225°, (360° - 45°) = 315°
Also, due to the mid location of the angle 45° on the quadrant, we have;
Another angles is the sines and cosine of (90° + 45°) = 135°
Therefore, [tex]\displaystyle \frac{\pi}{4}[/tex], can be used to find the sine and cosine of 135°, 225°, and 315°
[tex]\displaystyle 135^{\circ} = \mathbf{\frac{3 \cdot \pi}{4}}[/tex], [tex]\displaystyle 225^{\circ} = \frac{5 \cdot \pi}{4}[/tex], [tex]\displaystyle 315^{\circ} = \frac{7 \cdot \pi}{4}[/tex]
Therefore,
[tex]\displaystyle \frac{\pi}{4}[/tex] can be used to find the sine and cosine of [tex]\displaystyle \mathbf{\frac{3 \cdot \pi}{4}}[/tex], [tex]\displaystyle \mathbf{\frac{5 \cdot \pi}{4}}[/tex], and [tex]\displaystyle \mathbf{ \frac{7 \cdot \pi}{4}}[/tex]
Similarly, the sine and cosine of, [tex]\displaystyle \frac{\pi}{6}[/tex] = 30° can be used to find the sine and cosine of 150°, 210°, and 330°.
[tex]\displaystyle 150^{\circ} = \frac{5 \cdot \pi}{6}[/tex], [tex]\displaystyle 210^{\circ} = \frac{7 \cdot \pi}{6}[/tex], and [tex]\displaystyle 330^{\circ} = \frac{11 \cdot \pi}{6}[/tex]
[tex]\displaystyle \frac{\pi}{6}[/tex], can be used to find the sine and cosine of [tex]\displaystyle \mathbf{ \frac{5 \cdot \pi}{6}}[/tex], [tex]\displaystyle \mathbf{ \frac{7 \cdot \pi}{6}}[/tex], and [tex]\displaystyle \mathbf{\frac{11 \cdot \pi}{6}}[/tex]
Learn more about the sine and cosine of angles here:
https://brainly.com/question/4372174
Answer:
Step-by-step explanation:
The cosine value of an angle is the x coordinate of the point the angle corresponds to on the unit circle, and the sine value of an angle is the y coordinate of that point. 120, 240, and 300 all form 60 degree reference angles which in turn forms 30-60-90 triangles which help to find the sine and cosine of these corresponding angles. Pi/4 radians converts to 45 degrees which forms a 45-45-90 special triangle on the unit circle which has its own known trigonometric ratio. Pi/6 radians converts to 30 degrees which forms a 30-60-90 triangle on the unit circle which also has a known trigonometric ratio. These ratios help find the sine and cosine of the angles on the unit circle which corresponds to a point on the coordinate plane.
A scientist counted 3,921 total eggs in
49 sea turtle nests. Each nest had about
the same number of eggs. Which is the
best estimate of the number of eggs
she counted in each eggs?
Answer:
The Answer is 80
Step-by-step explanation:
So I turned 3,921 to 4,000 then 49 to 50.
After that I divided the too 4,000÷50= 80
If f(x) = x2 - 1 and g(x) = 2x - 3, what is the domain of (fog)(x)?
Answer:
domain will be ( -∞, ∞)
Step-by-step explanation:
The given functions are f(x) = x² - 1 and g(x) = 2x - 3
We have to find domain of (fog)(x)
We will find the function (fg)(x) first.
(fog)(x) = f[g(x)]
= (2x - 3)²
= 4x² + 9 - 12x - 1
= 4x² - 12x + 8
= 4 (x² - 3x + 2)
The given function is defined for all values of x.
Therefore, domain will be ( -∞, ∞)
https://brainly.com/question/2458431
PLEASE HELP GIVING 50 POINTS!!
Answer:
y = 18
Step-by-step explanation:
Direct variation means y will change by the same factor x does. When x changes by a factor of 15/10 = 1.5, the value of y will change by that same factor
x = 10, y = 12
x= 15, y = 1.5×12 = 18
The new value of y is y = 18.
_____
Written as a proportion, you have ...
y/15 = 12/10
y = 15×12/10 = 18
__
Written as a direct variation equation, you have ...
y = kx
12 = k·10 ⇒ k = 1.2
y = 1.2·15 = 18 . . . . for x=15
can someone help me answer this
[tex]32^{-\tfrac 25}\\\\=(2^5)^{-\tfrac 25}\\\\=2^{-2}\\\\=\dfrac 1{2^2}\\\\=\dfrac 14[/tex]
4) The yellow submarine was at sea level when the passengers boarded. The journey began with a descent of 40 meters. After examining the sea life, they rose 30 meters. Zach thought he saw an octopus, below. They dove again, a distance of 25 meters to watch the eight ‘legged’ sea creature.
a) Write an expression to describe the journey of the yellow submarine. _________________________________
b) At what depth did they stop to look at the octopus? ______________________
a) Write an expression to describe the journey of the yellow submarine.
-> ((0 - 40) + 30) - 25
[] Sea level = 0
[] The descend 40 meters = -40
[] After examining the sea, they rose 30 meters = + 30
[] They dove 25 meters to look at an octopus = -25
b) At what depth did they stop to look at the octopus?
-> -35 meters
[] The started at 0 (0), descended 40 (-40), rose 30 (-10), and then sove 25 (-35) to see the octopus
[] Another way to think of this is to simplify our previous expression completely
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Which of the sets of ordered pairs represents a function?
A = {(3, −5), (4, 6), (3, 9), (2, 7)}
B = {(2, 4), (−1, 4), (5, 4), (4, 4)}
a
Both A and B
b
Only B
c
Only A
d
Neither A nor B
Answer:
B
Step-by-step explanation:
A does not represent a function because the x-value of 3 appears twice, and by the defenition of a function, the x-value cannot appear twice for it to be considered a function. B could be a function because the x-values are not repeated.
Therefore the answer is B, only B is a function.
(In , (c) in a group of students of them are Science Society members and the rest are Mathematics Society members of the Science Society 5 members or 16 of them are girls. Find the total number of Mathematics Society members. Dalam satu kumpulan murid, daripada mereka 9 ialah ahli Persatuan Sains dan selebihnya ialah ahli 2. Persatuan Matematik. daripada ahli Persatuan . 5 Sains atau 16 orang daripadanya ialah perempuan. Cari jumlah bilangan ahli Persatuan Matematik [3 marks / 3 markah) Answer / Jawapan:
Answer:
50 studentsStep-by-step explanation:
Given:
4/9 of students are Science Society membersThe rest are Mathematics Society members2/5 of Science Society members are girls = 16 peopleFind the number of Science Society members:
2/5x = 16x = 16*5/2 = 40Find the total number of group members:
4/9x = 40x = 40*9/4 = 90Find the number of Mathematics Society members:
90 - 40 = 50An amusement park has two themed resorts, Stargazer Suites and Retro Retreat. The graph and table below display the cost of the stay, y, for different numbers of nights, x, for the two different resorts.
Which statement correctly compares the nightly rates at Stargazer Suites and Retro Retreat?
The nightly rate at Stargazer Suites is $15 more than the nightly rate at Retro Retreat.
The nightly rate at Stargazer Suites is $25 more than the nightly rate at Retro Retreat.
The nightly rate at Retro Retreat is $30 more than the nightly rate at Stargazer Suites.
The nightly rate at Retro Retreat is $80 more than the nightly rate at Stargazer Suites.
The nightly rate at each resort is the same.
Answer:
to confusing
Step-by-step explanation:
Answer:
The nightly rate at Stargazer Suites is $25 more than the nightly rate at Retro Retreat.
Step-by-step explanation:
For the function y = 4x – 2, what is the value of the function when x is equal to -3?
Giving brainliest to the right answer!
Answer:
y = 4 (-3) - 2
y = -12 - 2
y = -14
Step-by-step explanation:
work out the height of a triangular crosse section with the volume of 35cm
The answer is 2.5 cm.
Sorry if I am incorrect
Does 12/15 and 14/17 form a proportion?
Answer:
yes they form a proportion