The GCF is 4
The polynomial factors to [tex]4(3x^2+x+5)[/tex]
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Further explanation:
Ignore the x terms
We're looking for the GCF of 12, 4 and 20
Factor each to their prime factorization. It might help to do a factor tree, but this is optional.
12 = 2*2*34 = 2*220 = 2*2*5Each factorization involves "2*2", which means 2*2 = 4 is the GCF here.
We can then factor like so
[tex]12x^2 + 4x + 20\\\\4*3x^2 + 4*x + 4*5\\\\4(3x^2 + x + 5)[/tex]
The distributive property pulls out that common 4. We can verify this by distributing the 4 back in, so we get the original expression back again.
The polynomial inside the parenthesis cannot be factored further. Proof of this can be found by looking at the roots and noticing that they aren't rational numbers (use the quadratic formula).
a plant grew 3 1/4 inches over a - 6 1/2 month period. what was the average
Answer:
0.5 inches per a month
Step-by-step explanation:
you turn them to a decimal to make them easier and then divide them to get the answer.
12 + 5 + 32 × 10 − 5 =
(12 + 5) + 32 × (10 − 5) =
Add 12 and 5 to get 17.
17 + 32 × 10 − 5Multiply 32 and 10 to get 320.
17 + 320 − 5Add 17 and 320 to get 337.
337−5Subtract 5 from 337 to get 332.
332 ===> Answer
Exercise number 2.(12 + 5) + 32 × (10 − 5)Add 12 and 5 to get 17
17 + 32 (10 − 5)Subtract 5 from 10 to get 5.
17 + 32 × 5Multiply 32 and 5 to get 160.
17+160Add 17 and 160 to get 177.
177 ===> Answer
Bob is throwing a party. He has 22 pints of soda. At the end of the party, there are 8
pints of soda.
How many cups of soda were drank during the party?
Answer:
14
Step-by-step explanation:
If Bob has 22 pints, and one glass is one pint, the 22-8 = 14
Answer:
14
Step-by-step explanation:
you would subtract 8 pints of soda left from the total pints which is 22 to get 14 pints used during the party
22-8=14
Select the correct answer from each drop-down menu.
A researcher is examining the claims made by a water softener salt manufacturer. He performs an experiment using water from a variety of
sources. For each water source, he has sample with no treatment and a sample treated with the recommended amount of the water softener
salt.
He then tests each sample to measure the softness and compares the results, determining that the claims made by the manufacturer are true.
The conclusion drawn from the study is
v because the sample is
v . In this instance, an
v study was
performed.
The conclusion drawn from the study is valid because the sample is homogenous. In this instance, an experimental study was performed.
What is an experimental study?An experimental study can be defined as a quantitative research method that is used by a researcher to determine and show the effects of changes in the dependent variable, while placing other relevant independent variables under control.
Based on the experimental study conducted by using water from a variety of sources, the conclusion which can be drawn from this study is valid because the sample is homogenous.
In this instance, we can infer and logically deduce that an experimental study was performed.
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1 in. = 2 ft. what is the area of the actual living room?
Answer:
........................
Answer:
[tex]144ft^{2}[/tex] (144ft^2)
Step-by-step explanation:
Since the living room is 6 inches by 6 inches, the formula of the living room can be seen as: [tex]6in^{2}[/tex]. And since each inch is equal to 2 feet, (6*2=12) we can turn the equation into: [tex]12ft^{2}[/tex]. 12 times 12 is 144, so the answer is [tex]144ft^{2}[/tex]
Please belpppp don’t understand
Answer:
[tex]3w^2\sqrt[4]{2w^3}[/tex]
Step-by-step explanation:
hope this helps!:)
HELP ASAP PLEASEE
Circle X with a radius of 6 units and circle Y with a radius of 2 units are shown. Circles X and Y are shown. Circle X has a radius of 6 units and circle Y has a radius of 2 units. Which steps would prove the circles similar?
-Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 4.
- Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 4.
-Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.
-Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 3.
Answer & step-by-step explanation:
to arrive at the similarity, the transformation must be as follow:
the small circle will be dilated for a specific scale factor,
the radius of X circle is R= 6, and the radius of the small circle is r = 2
besides, two circles are similar if and only if R = r, (their radius ar equal)
therefore r = 2*k = 6, and from where k = 6 / 2 = 3 units
the answer is
Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.
Answer:
Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.
Step-by-step explanation:
To prove circles are similar:
Translate the circles so that they share a common center point. (The circles are now concentric as they have the same center).
Dilate the smaller circle to increase its size to coincide with the larger circle. The amount that the circle needs to be dilated by is the scale factor.
As the radius of circle Y is 2 and the radius of circle X is 6, determine the scale factor by dividing the larger radius by the smaller radius:
scale factor = 6 ÷ 2 = 3
Solution:
Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.
By the way, you forgot to give us the image:
If AD=2:5 the coordinates of point F are. Point E has the coordinates (3.8, -3) and the coordinates of point D are
Using the assumed coordinates of point F, the coordinates of point D are (3,3)
How to determine the coordinates of D?The given parameters are:
Ratio, m : n = 2 : 5
E = (3.8, -3)
The coordinates of point D is calculated using:
[tex]D = \frac{1}{m + n} * (mx_2 +nx_1,my_2 +ny_1)[/tex]
So, we have:
[tex]D = \frac{1}{2 + 5} * (2x_2 +5*3.8,2y_2 +5*-3)[/tex]
Evaluate the sum and the products
[tex]D = \frac{1}{7} * (2x_2 +18,2y_2 -15)[/tex]
Assume the coordinates of point F are:
F = (1.5,18);
The equation becomes
[tex]D = \frac{1}{7} * (2*1.5 +18,2*18 -15)[/tex]
Evaluate
[tex]D = \frac{1}{7} * (21,21)[/tex]
This gives
D = (3,3)
Hence, the coordinates of point D are (3,3)
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Part 2: Approximately what value of will give her a box with the greatest volume? Explain your reasoning.
( only need part 2 already have part one thx)
The value of x that gives the box the greatest volume is approximately 2.08
How to determine the value that gives the greatest volume?The equation of the volume of the box is given as:
V(x) = x(12 - 2x)(13 - 2x)
Expand
V(x) = (12x - 2x^2)(13 - 2x)
V(x) = 156x - 24x^2 - 26x^2 + 4x^3
V(x) = 156x - 50x^2 + 4x^3
Differentiate the function
V'(x) = 156 - 100x + 12x^2
Set to 0
156 - 100x + 12x^2 = 0
Rewrite as:
12x^2 - 100x + 156 =0
Divide through by 4
3x^2 - 25x + 39 =0
Using a graphing calculator, the values of x are:
x = 2.08 and x = 6.26
Substitute these values of x in V(x)
V(2.08) = 2.08 * (12 - 2 * 2.08)(13 - 2 * 2.08) = 144.16
V(6.26) = 6.26 * (12 - 2 * 6.26)(13 - 2 * 6.26) = -1.56
The volume cannot be negative.
So, we have:
V(2.08) = 144.16
Hence, the value of x that gives the box the greatest volume is approximately 2.08
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Complete the function table
Answer:
-3. -5
-2. -4
-1. -3
0. -2
1. -1
formula is f(x)=x-2
does someone mind helping me with this problem? Thank you!
Anyea
Step-by-step explanation:
Answer:
180 inches squared (^2)
Step-by-step explanation:
To find the area of a rectangle, simply multiply the length by the width (15*12)
Don't forget it is squared! Good luck!
Find the least positive integer that has a remainder of 2 when you divide by 5, a
remainder of 5 when you divide by a 8, and a remainder of 8 when you divide by 11.
When you divide 12 by 5, the remainder is 2. When you divide 37 by 8, the remainder is 5. When you divide 30 by 11, the remainder is 8.
What is a quotient?The term quotient refers to the number that is obtained when you divide a number by another.
When you divide 12 by 5, the remainder is 2. When you divide 37 by 8, the remainder is 5. When you divide 30 by 11, the remainder is 8.
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Help me solve this problem please
the mean numbers of point scored is greater than 12 points(C.)
Good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
Is the relationship between the step number and number of squares a quadratic function.
AnalyzeStep 1 = 2 squares
Step 2 = 6 squares
Step 3 = 12 squares
2, 6, 12
4 6
2
To build a quadratic functionax² + bx + c
2a = 2 ⇒ a = 1
3a + b = 4 ⇒ 3(1) + b =4 ⇒ b = 1
a + b + c = 2 ⇒ 1 + 1 + c = 2 ⇒ c = 0
Equation: x² + x
Hence, Yes it is a quadratic function.
Answer:
It is quadratic with nth term = n^2 + n.
Step-by-step explanation:
Number of squares in each term = 2, 6 and 12
Differences between these are 4 and 6
6 - 4 = 2
This is an indication of a quadratic function with n^2 the first term.
Value of n^2 for first 3 terms
= 1 4 9 and the terms are:
2 6 12
Differences 1 2 3
This last term = n
So the quadratic function for this sequence is
n^2 + n.
A $52 video game is advertised for 20% off
If sales tax is 6%; how much will the
video game cost?
Answer:
Equation: 52+(52•.20) that is the first part for your answer you should get 10.4 or $10.40. Then you would take 52-10.4=41.60 then keeping that number in mind you do 41.60• .06 and get, rounded, 2.50. Then you would add 41.60+2.50 and get $44.10 as your answer . I hope I could help
Step-by-step explanation:
NEEED HELPppppppppppp
PLSSSSS
Answer:
probably the furthest graph to the left.
Step-by-step explanation:
seems like a 25% 10% split.
Hey! So I need to study for my Algebra 1 finals can someone link me a video or give me a way to study for algebra 1. I have a week or so
Answer:
Review your state Standards.
Notes
Khan on your topic or grade level
Dealta Math
Math Nation
What is the unfilled volume inside the cylinder? 320π cubic units 597π cubic units 640π cubic units 725π cubic units
The unfilled volume inside the cylinder is determined as 640π cubic units.
Volume of the cylinder
The volume of the cylinder is determined as follows;
V = πr²h
where;
r is radius of the cylinder given as 8 unitsh is height of the cylinder determined as 15 unitsV = π(8²)(15)
V = 960 π cubic units
Volume of coneV = ¹/₃πr²h
where;
r is radius of the cone given as 8 unitsh is slant height of the cone determined as 15 unitsV = ¹/₃π(8)²(15)
V = 320 π cubic units
Unfilled volume of the cylinderΔV = 960 π - 320 π = 640 π cubic units
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Answer:
It’s C
Step-by-step explanation:
i got a 100% on my quiz so trust me
ur wlcm :)
Arrange the hyperbolas in increasing order of the horizontal widths of their asymptote rectangles.
The increasing order of the horizontal widths of their asymptote rectangles is dependent on the values gotten from y = ± x.
What is a Hyperbola?
This is defined as a two-branched open curve formed by the intersection of a plane perpendicular to the bases of a double cone.
The rectangular hyperbola has two asymptotes which are defined as y = ± x in this scenario.
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what is the slope of the liner equation y=7x-2
Answer:
Hence, slope of y=7x−2 is 7 and y -intercept is −2.
Step-by-step explanation:
The equation of any straight line can be written as y=mx+c, where m is its slope and c is its y-intercept.
Comparing the equation y=7x−2 with the standard form of the equation, we get:
m=7,c=−2
Hence, slope of y=7x−2 is 7 and y -intercept is −2
Hope this helps :)
2. a science museum has a spherical model of the moon with a diameter of 6.4 ft. what is the volume of the model to the nearest cubic foot? show your work.
The volume of the model to the nearest cubic foot is 137 ft³
Volume of a sphereVolume of a sphere = 4/3πr³
π = 3.14Diameter = 6.4 ftRadius, r = diameter / 2
= 6.4 ft / 2
= 3.2 ft
Volume of a sphere = 4/3πr³
= 4/3 × 3.14 × 3.2³
= 4/3 × 3.14 × 32.768
= 411.56608 / 3
= 137.188693333333
Approximately,
Volume of the sphere = 137 ft³
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If I get 10 dollars a week how much money will I have saved up in 9-years I WILL GIVE 55 POINTS
Answer:
$4,680
Step-by-step explanation:
Rate : 10 dollars a week
Per year : 10 x 52 = $5209 x 520 = $4,680You will have saved up $4,680 in 9 years.
Rewrite the radical expression as an exponential expression, and then simplify.
StartRoot 121 EndRoot = one-half (121) = 60.5
StartRoot 121 EndRoot = 121 squared = 14,641
StartRoot 121 EndRoot = 121 Superscript one-half Baseline = 11
StartRoot 121 EndRoot = 121 Superscript one-half Baseline = 60.5
The radical expression written as an exponent, and simplified, is given by:
[tex]\sqrt{121} = (121)^{\frac{1}{2}} = 11[/tex].
How to transform an exponent to a power?It happens according to the following rule:
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
The inverse is also valid, hence, in this problem, the expression written as an exponent and simplified is given by:
[tex]\sqrt{121} = (121)^{\frac{1}{2}} = 11[/tex].
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Find the ratio of the trig function indicated.
Answer:
[tex]\huge\boxed{\bf\:Ratio = 4:5}[/tex]
Step-by-step explanation:
We have a right angled triangle given.
At first, let's note that, sin θ = oppposite side of the triangle / hypotenuse of the triangle.
Now, in the given triangle, from the view of ∠θ,
Opposite side of the triangle = 8 Hypotenuse = 10Then,
[tex]\sin \theta = \mathrm{\frac{opposite \: side}{hypotenuse}}\\\sin\theta = \frac{8}{10}\\\sin\theta = \frac{4}{5}\\\\\\\Longrightarrow \boxed{\mathrm{Ratio = 4:5}}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
What is the range of the function graphed below?
Picture has the stuff
Answer:
∝ < y < 2
Step-by-step explanation:
The range is negative infinity to 2.
*PLSSSS HELP WILL GIVE 30 POINTS I'M DESPERATE*
What type of number is -6?
Select *ALL* correct answers
_integer _irrational
_rational _whole
_natural _real
Answer:
rational real whole
Step-by-step explanation:
PLEASE HELP ME IVE BEEN SITTING HERE FOR HOURS
Answer:
0-9: 4
10-19: 4
20-29: 1
30-39: 4
40-49: 2
Step-by-step explanation:
Since frequency means how many times it showed up in the list
this all adds up to 15, making it an easy check.
hope this helps:)
(Look at image) Need help for question 6. Tried looking into it but still failed. I couldn’t understand what the question was asking me so I need some help asap by tomorrow.
Also do not mind the other answers. Those were already answered by epic people (thanks again)
Answer:
For 4 its 6 due to having 0 INCHES for 6 days (The answer to number 6 which is what your looking for is 1 12/8 simplify that and It'd be 2 1/2)
Step-by-step explanation:
This is because adding up the total rain falls will get you to 2 1/2
polynomials ( math )
pls help
Answer:
f(x) = x¹² + 4
Step-by-step explanation:
Degree 12:
This means that one of the terms needs to be raised to the power of 12. The term should be a variable. Therefore, a term you can use is x¹².
2 Terms:
This means there should be 2 separate entities in the expression. These terms are non-combinable unless you input an "x" value. The 2 terms you could use for this expression are x¹² and a constant.
Constant:
Constants are numbers that are not beside any variables. In other words, they are not being multiplied to the "x" value. The constant you could use is (4).
Putting all of these together, one of the many expressions that could satisfy the prompt is f(x) = x¹² + 4.
25° 35° to 205° circle
Answer:
x = 60
Step-by-step explanation:
the chord- chord angle x is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
The sum of the arcs in a circle = 360° , then
intercepted arc = 360° - (35 + 25 + 205)° = 360° - 265° = 95°
then
x = [tex]\frac{1}{2}[/tex] (95 + 25 ) = [tex]\frac{1}{2}[/tex] × 120 = 60