Final answer:
To factor the expression 3x² - 19x + 20, we find two numbers that multiply to 60 and add up to -19, which are -4 and -15. The expression can then be rewritten and factored by grouping to obtain the factors (x - 5)(3x - 4).
Explanation:
The question asks to factor the quadratic expression
3x² - 19x + 20
To factor this expression, we need to find two numbers that multiply to give the product of the coefficient of x² (which is 3) and the constant term (which is 20), and at the same time, add up to give the coefficient of x (which is -19). The two numbers that satisfy these conditions are -4 and -15, as (-4) * (-15) = 60 and (-4) + (-15) = -19.
Now, we can rewrite the expression by splitting the middle term:
3x² - 4x - 15x + 20
Factor by grouping: x(3x - 4) - 5(3x - 4)
The factors are: (x - 5)(3x - 4)
how do you put .36÷4 into a model
Answer:
Step-by-step explanation:
you have to make 4 rows and 36 column then solve 36 divided by 4=9
Suppose f(x)=x^2 find the graph of f(x)+1
Answer:
f(x)+1 = x^2 + 1
Step-by-step explanation:
The graph of f(x)+1 will be given by adding 1 to the initial function f(x)
f(x)+1 = x^2 + 1
See the attachment for the graph;
Part A:
At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle (blue) with a radius of 11 m. The inner edge of the sidewalk is a circle (orange) with a radius of 9 m. Find the approximate AREA of the larger circle (blue).
Use 3.14 for pi.
Show your work!
Part B:
At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle (blue) with a radius of 11 m. The inner edge of the sidewalk is a circle (orange) with a radius of 9 m. Find the approximate AREA of the smaller circle (orange).
Use 3.14 for pi.
Show your work!
Part C:
At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle (blue) with a radius of 11 m. The inner edge of the sidewalk is a circle (orange) with a radius of 9 m. Find the approximate AREA of the sidewalk (shaded region between the blue and orange circles).
Use 3.14 for pi.
Show your work!
Please answer all of them. ;;
All of them have the same attached image.
Answer:
Part A: 379.94
Part B: 254.34
Part C: 125.6
Step-by-step explanation:
The are for the area of a circle is A = Pi*r^2
So for part A, do
A = 3.14 * 11^2
A = 3.14 * 121
A = 379.94
Same thing for Part B, just change the radius:
A = 3.14 * 9^2
A = 3.14 *81
A= 125.6
And for Part C, Subtract the area of the smaller from the area of the larger circle:
379.97 - 254.34 = 125.6
Answer:
I'm just answering this so that you can give them brainlest
Step-by-step explanation: Have a good day
A painter charges $15.92 per hour, plus an additional amount for the supplies. If he made $175.72 on a job where he worked 6 hours, how much did the supplies cost?
Answer: $15.92*6= $95.52
$175.72 - $ 95.52= $ 80.20
Step-by-step explanation:
-3x-9+15x
Please help asap
Answer:
= 0.75
Step-by-step explanation:
-3x-9+15x = 0
12x = 9
x = 3
4
= 0.75
Hey there!
The answer is 12x - 9
Hope this helps you!
God bless ❤️
xXxGolferGirlxXx
Plz help me with this!!!!!!!!
Answer: √y
Step-by-step explanation:
[tex]\sqrt[6]{y^3}=y^{\frac{3}{6}}=y^{\frac{1}{2}}=\boxed{\sqrt y}[/tex]
X+3
——=8 what’s the value for
2. X
Type the correct answer in each box.Use numerals instead of words. If necessary, use / for the fraction bar.
Line AB and Line BC form a right angle at their point of intersection, B.
If the coordinates of A and B are (14, -1) and (2, 1), respectively, the y-intercept of Line AB is _____ and the equation of is y = ___x+___.
If the y-coordinate of point C is 13, its x-coordinate is ___.
Answer:
y intercept is 1 1/3
equation is y = -1/6x + 4/3
x coordinate is -70 (-70,13)
Step-by-step explanation:
find M
m = 1 - (-1)/ 2 -1 4
m = -2/12 = -1/6
Find y intercept--Plug m and one point from above into y = mx + b
1 = - 1/6 (2) + b
1 = -2/6 + b
1 2/6 = b
1 1/3 = b
4/3 = b
To find the x coordinate if y is 13
13 = -1/6 x + 4/3
11 2/3 = -1/6 x
-70 = x
The y intercept of line AB = [tex](0,\dfrac{4}{3})[/tex]
The equation of line AB will be
[tex] y=\dfrac{-1}{6}x+\dfrac{4}{3}[/tex]
The x-coordinate of C = 4
Step-by-step explanation:The slope of line AB with coordinates of A and B are (14, -1) and (2, 1)
[tex]m_1=\dfrac{1-(-1)}{2-14}=\dfrac{2}{-12}=\dfrac{1}{-6}[/tex]
The equation of line AB will be
[tex](y-1)=\dfrac{1}{-6}(x-2)\\\\\Rightarrow y=\dfrac{1}{-6}(x-2)+1\\\\\Rightarrow\ y=\dfrac{-1}{6}x+\dfrac{1}{3}+1\\\\\Rightarrow y=\dfrac{-1}{6}x+\dfrac{4}{3}[/tex]
Put x=0, we get the [tex]y=\dfrac{4}{3}[/tex] i.e. [tex](0,\dfrac{4}{3})[/tex] is the y intercept of line AB.
Since, Line AB and Line BC form a right angle at their point of intersection, B. The the product of their slope must be -1.
Therefore, the slope of BC =[tex]m_2=\dfrac{-1}{m_1}=6[/tex]
Let x coordinate of C be a,then the coordinates of C = (a,13)
Now, slope of BC with points B(2,1) and C(a,13) will be
[tex]\dfrac{13-1}{a-2}=6\\\\\Rightarrow\ a-2=\dfrac{12}{6}\\\\\Rightarrow\ a-1=2\\\\\Rightarrow\ a=4[/tex]
Hence, the x-coordinate of C = 4
You want to put a 2 inch thick layer of topsoil for a new 27 ft by 34 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
Answer:
3.78 cubic yards or just 4 to make things simple.
20 x 30 = 600 sqft x .17 or (2/12) = 102 cubic feet / 27 (cubic feet in a yard) = 3.78 cubic yards
Step-by-step explanation:
To cover a 27 ft by 34 ft garden with a 2 inch thick layer of topsoil, we would need approximately 5.75 cubic yards of topsoil from the store.
Explanation:This question involves understanding dimensions and volume. In this case, the dimensions of the garden are given in feet (27 ft by 34 ft), and the desired thickness of the topsoil is 2 inches, which is approximately 0.167 feet. To calculate the volume in cubic feet, we multiply the length, width, and height.
The formula to calculate volume is: Volume = Length * Width * Height.
So, Volume = 27 ft * 34 ft * 0.167 ft = 153.234 cubic feet
Now, to convert this volume into cubic yards (since the store sells soil in cubic yards), we use the fact that 1 cubic yard = 27 cubic feet.
So, Volume = 153.234 cubic feet / 27 = approximately 5.676 cubic yards.
Given that the store only sells in increments of 1/4 cubic yards, we will need to round 5.676 up to the nearest quarter yard. This gives us 5.75 cubic yards.
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if the first 15 sandwiches sold at a restaurant one day, 9 were club sandwiches. at the same rate, how many sandwiches would have to be sold for 90 of the total number of sandwiches to be club sandwiches?
Answer:
54 I think
Step-by-step explanation:
I just did 15 divided by 9 and got 5/3 and then did 90 divided by 5/3 and got 54
Final answer:
To find out how many sandwiches would have to be sold for 90 of the total number of sandwiches to be club sandwiches, set up a proportion using the given information: 9 club sandwiches out of 15 total sandwiches is equal to 90 club sandwiches out of x total sandwiches. Solve for x to find that 150 sandwiches would need to be sold in total for 90 of them to be club sandwiches.
Explanation:
To find out how many sandwiches would have to be sold for 90 of the total number of sandwiches to be club sandwiches, we can set up a proportion using the information given.
First, we know that out of the first 15 sandwiches sold, 9 were club sandwiches. This can be written as a ratio:
9 club sandwiches / 15 total sandwiches = 90 club sandwiches / x total sandwiches
Cross-multiplying, we get 9x = 90 * 15
Dividing both sides by 9, we find that x = 150
Therefore, if 150 sandwiches are sold, 90 of them would be club sandwiches.
find the area of the parallelagram
Answer:
The area of the parallelogram is 117.
Step-by-step explanation:
You do 9x13= area
9x13= 117
Any number raised to the power of zero is zero true or false
Answer: Any number times zero is zero, it can never equal something else.
Step-by-step explanation: My teacher taught me this before so i know :)
The statement is false.
Statement given,
Any number raised to the power of zero is zero.
The following statement is false, as, any number raised to the power of zero is one always. Thus,
[tex]\bold{x^0 =1}[/tex],
where x is any real number, except zero.
So, x is defined for any number except 0.
Hence, the statement is false.
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17x -8x -9 = 76 - 40
Answer:
5
Step-by-step explanation:
17x -8x -9 = 76 - 40
17x -8x = 76 - 40 + 9
9x = 45
x = 45/9
x=5
Answer:
x = 5
Step-by-step explanation:
17x - 8x - 9 = 76 - 40
9x - 9 = 36
+9 +9
9x = 45
/9 /9
x = 5
which of the statements using operations on rational or irrational numbers always results in a rational number?
a) irrarional + irrational
b) irrational ÷ irrational
c) rational + irrational
d) rational ÷ rational
[tex]1.999999\inf[/tex]
So adding a rational number, like 2, it would be irrational still:
[tex]2+1.999999\inf=3.999999\inf[/tex]
That being said, answer C is wrong
Now, what is 2/2? Or 4/1? Whole numbers are one of the 3 types of rational numbers.
[tex]2\ /\ 2=1\\\\4\ / 1=\ 4[/tex]
Thus the answer appears to be D
Now lets use the process of elimination to double check the answer:
The wording of your question is what will help us out here:
Which of the statements using operations on rational or irrational numbers always results in a rational number?
Because of that, any of the choices that involve a irrational number can result with another irrational number like so:
[tex]a)\ 1.999\inf+ 1.999\inf=3.888\inf\\\\b)\ 2.999\inf / 1.999\inf= 1.50025\inf[/tex]
And there you go, the only answer that hasn't been proven wrong is answer D.
Now, if you like this answer and would like to see more please make sure to Like, Comment, and Rate this answer! Also, be sure to send me a friend request, I'm always up for a Challenge!Thanks!The statement using operations on rational or irrational numbers always results in a rational number is d) rational ÷ rational.
What are rational and irrational numbers?We know all the real can be subdivided into two parts one is rational numbers and the other is an irrational number.
Rational numbers are those numbers that have repeating or terminating digit patterns after the decimal place and irrational numbers are those numbers that do not have this property.
a) irrational + irrational is an irrational number, √3 + √3.
b) irrational ÷ irrational is sometimes rational and sometimes irrational,
√3 ÷ √3 = 1 but √6 ÷ √3 = √2.
c) rational + irrational is always an irrational number.
d) rational ÷ rational is always a rational number.
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PLEASE HELP!! Im having a really hard time.
A science museum has a spherical model of the earth with a diameter of 8.5 m.What is the volume of the model? Use 3.14 for pi and round your answer to the nearest whole number. Show your work.
Answer:
V = 321 m^3
Step-by-step explanation:
Volume of a sphere
V = 4/3 pi r^3
The radius is equal to
r = d/2
r = 8.5/2 =4.25
V =4/3 (3.14) (4.25)^3
V =321.3920833 m^3
Rounding to the nearest whole number
V = 321 m^3
Answer:
V = 321 m^3
V = 4/3 pi r^3 diameter is double of radius (radius is half of diameter)
V = 4/3 pi (4.25)^3
V= 75.66 meters squared (rounded)
Which expression is equivalent to (3x^2-7)?
Answer:
The correct answer is third option
(10x² - 4) - (7x² + 3)
Step-by-step explanation:
From the given option we get the correct answer is third option.
(10x² - 4) - (7x² + 3)
Check the correct answer
(10x² - 4) - (7x² + 3) = 10x² - 4 - 7x² - 3)
= 10x² - 7x² - 4 - 3 = 3x² - 7
Therefore the correct answer is third option
(10x² - 4) - (7x² + 3)
The correct answer is C on edg
:)
Please help 10 points <3
Can someone tell me how
the way I get the subsequent term, nevermind the exponents, the exponents part is easy, since one is decreasing and another is increasing, but the coefficient, to get it, what I usually do is.
multiply the current coefficient by the exponent of the first-term, and divide that by the exponent of the second-term + 1.
so if my current expanded term is say 7a³b⁴, to get the next coefficient, what I do is (7*3)/5 <----- notice, current coefficient times 3 divided by 4+1.
anyhow, with that out of the way, lemme proceed in this one.
[tex]\bf ~~~~~~~~\textit{binomial theorem expansion} \\\\ \qquad \qquad (1+ax)^n\implies \begin{array}{llll} term&coefficient&value\\ \cline{1-3}&\\ 1&+1&(1)^n(ax)^0\\\\ 2&+\frac{(1)(n)}{1}\to n&(1)^{n-1}(ax)^1\\\\ 3&+\frac{n\cdot (n-1)}{2}&(1)^{n-2}(ax)^2 \end{array}[/tex]
so, following that to get the next coefficient, we get those equivalents as you see there for the 2nd and 3rd terms.
so then, we know that the expanded 2nd term is 24x therefore
[tex]\bf n(1)^{n-1}(ax)1 = 24x\implies n(1)(ax)=24x\implies nax=24x\implies n=\cfrac{24}{a}[/tex]
we also know that the expanded 3rd term is 240x², therefore we can say that
[tex]\bf \cfrac{n(n-1)}{2}~~(1)^{n-2}(ax)^2 = 240x^2\implies \cfrac{n(n-1)}{2}(1)(a^2x^2) = 240x^2 \\\\\\ \cfrac{(n^2-n)(a^2x^2)}{2}=240x^2\implies \cfrac{(n^2-n)(a^2)}{2}=\cfrac{240x^2}{x^2}\implies \cfrac{a^2n^2-a^2n}{2}=240 \\\\\\ a^2n^2-a^2n=480[/tex]
but but but, we know what "n" equals to, recall above, so let's do some quick substitution
[tex]\bf a^2n^2-a^2n=480\qquad \boxed{n=\cfrac{24}{a}}\qquad a^2\left( \cfrac{24}{a} \right)^2-a^2\left( \cfrac{24}{a} \right)=480 \\\\\\ a^2\cdot \cfrac{24^2}{a^2}-24a=480\implies 24^2-24a=480\implies 576-24a=480 \\\\\\ -24a=-96\implies a=\cfrac{-96}{-24}\implies \blacktriangleright a = 4\blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ n=\cfrac{24}{a}\implies n=\cfrac{24}{4}\implies \blacktriangleright n=6 \blacktriangleleft[/tex]
Write the expression in complete factored form. 4u(y+6)+a(y+6)
Answer:
(y + 6)(4u + a)
Step-by-step explanation:
Given
4u(y + 6) + a(y + 6) ← factor out (y + 6) from each term
= (y + 6)(4u + a) ← in factored form
A triangular prism has bases that are equilateral triangles. Which statements are true about the surface area of the triangular prism? Choose all that apply. A all three rectangular faces have the same surface area
B the surface area of each rectangular face is 66cm2
C the combined surface area of both bases is greater than the surface area of one rectangular face
D the surface area of one base is 15.6cm2
Answer:
A. all three rectangular faces have the same surface area
B. the surface area of each rectangular face is [tex]66\ cm^{2}[/tex]
D. the surface area of one base is [tex]15.6\ cm^{2}[/tex]
Step-by-step explanation:
Verify each statement
case A) all three rectangular faces have the same surface area
The statement is true
Because, the equilateral triangle has the three equal sides and the three equal internal angles.
case B) the surface area of each rectangular face is [tex]66\ cm^{2}[/tex]
The statement is true
Because, the area of each rectangular face is equal to
[tex]6(11)=66\ cm^{2}[/tex]
case C) the combined surface area of both bases is greater than the surface area of one rectangular face
The statement is False
Because
The combined surface area of both bases is [tex]2[\frac{1}{2}(6)(5.2)]=31.2\ cm^{2}[/tex]
The surface area of one rectangular face is [tex]66\ cm^{2}[/tex]
therefore
[tex]31.2\ cm^{2}< 66\ cm^{2}[/tex]
case D) the surface area of one base is [tex]15.6\ cm^{2}[/tex]
The statement is True
Because
The surface area of one base is [tex]\frac{1}{2}(6)(5.2)=15.6\ cm^{2}[/tex]
C.
D.
B.
C.
A.
D.
C.
C.
B.
A. B. and D.
This is the whole practice! 100% percent!
Have an amazing day! :):)
What expression represents five times the quotient of some number and ten
Answer:
since we dont know the variable it isnt very easy to anser..
Step-by-step explanation:
Lets assume the variable is V okay?
5 time we know times means multiplication so
5 x
The quotients is division so
5 x V divided 10
Please help me with this one please ( up there )
Answer:
the blue one is 1/2 and the red one is 1/4
Step-by-step explanation:
count the bricks and put a "1/" in front of the number of bricks and... BOOM you have your answer
Pythagorean theorem
Answer:
use pythagorean theroem lol a²+b²=c²
Answer:
I think the answer would be 4.5 miles
Step-by-step explanation:
Which formula can be used to describe the sequence below? –8, –5, –2, 1, 4, ...
Answer:
an = -8 +3(n-1)
an = -11 +3n
f(n) = -11 +3n
Step-by-step explanation:
–8, –5, –2, 1, 4, ...
This is an arithmetic sequence.
We are increasing by 3 each time
-8 +3 = -5
-5+3 = -2
-2 +3 = 1
The common difference is 3
The formula for an arithmetic sequence is
an = a1 +d (n-1)
an = -8 +3(n-1)
an = -8 +3n -3
an = -11 +3n
The nth term is -11 +3n
f(n) = -11 +3n
D. an = an-1+3; a1 = -8
EG. 2020
Find the perimeter of the larger Octagon.
The scale factor is obviously 7, because the 28 divided by 4 equals 7.
This means that the larger octagon's perimeter will be 7 times the smaller octagon's perimeter.
So 34 * 7 = 238.
To find the perimeter of a larger octagon, add up the lengths of all its sides. The formula for finding the perimeter of any regular polygon is P = ns, where P is the perimeter, n is the number of sides, and s is the length of one side.
Explanation:An octagon is a polygon with 8 sides. To find the perimeter of an octagon, you need to add up the lengths of all its sides. If you know the length of one side of the octagon, you can multiply it by 8 to get the perimeter. For example, if the length of one side is 5 cm, the perimeter of the octagon would be 5 cm x 8 = 40 cm.
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The first side of a triangle is 3 inches shorter than the second side, and 2 inches longer than the third side. How long is each side, if the triangle has a perimeter of 28 inches?
➷ 1st side = x - 3
2nd side = x
3rd side = x - 1
Form an equation:
x - 3 + x + x - 5 = 28
Simplify:
3x - 8 = 28
Add 8 to both sides:
3x = 36
Divide both sides by 3:
x = 12
first length = 12 - 3 = 9 inches
second length = 12 inches
third length = 12 - 5 = 7 inches
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which expression is equivalent to 8x - 12y +32
The expression equivalent to 8x - 12y + 32 is 4(2x - 3y + 8) after factorization by the greatest common factor.
Explanation:To find an expression equivalent to 8x - 12y + 32, we can primarily factor by finding common factors in this expression. One of the significant aspects in factorizing expressions is searching for the greatest common factor which is 4 in this case. We divide each term in the expression by the greatest common factor to obtain the equivalent expression.
So, "4(2x - 3y + 8) is an equivalent expression to 8x - 12y + 32".
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Nadia makes the sign for her bedroom door she wants to put a ribbon border around the edges of the side she has 12 inches of ribbon is that enough
Answer - No because a door is around 5 feet
11, 7, 3, -1,...
If 11 is defined as the first term in the sequence given above which of the following functions describes this sequence?
(Answer choices in photo)
The mathematical formula to solve this is :
f(n)= f1 + (n-1)d
We have:f(n)= 11 + (n-1)-4
f(n)= 11 -4n +4
f(n)=15 -4n
The right answer is D.
What is the equation of the graph below?
Answer:
y=cos(0.4x)
Step-by-step explanation:
Answer:
The equation of the graph given is:
[tex]y=\cos(0.4x)[/tex]
Step-by-step explanation:
Clearly from the graph of the function that is provided to us we see that the graph repeats itself after every 5π.
i.e. the period of the function is: 5π.
Now we will check in each of the given options whose period is 5π.
We know that the period of a cosine function of the type:
[tex]y=cos(bx)[/tex] is given by:
[tex]Period=\dfrac{2\pi}{5}[/tex]
1)
[tex]y=\cos(\dfrac{x}{0.4})[/tex]
The period of this function is:
[tex]Period=\dfrac{2\pi}{\dfrac{1}{0.4}}\\\\\\Period=0.8\pi\neq 5\pi[/tex]
Hence, option: 1 is incorrect.
2)
[tex]y=\cos (5x)[/tex]
The period of this function is:
[tex]Period=\dfrac{2\pi}{5}\\\\\\Period=\dfrac{2}{5}\pi\neq 5\pi[/tex]
Hence, option: 2 is incorrect.
4)
[tex]y=\cos (\dfrac{x}{5})[/tex]
The period of this function is:
[tex]Period=\dfrac{2\pi}{\dfrac{1}{5}}\\\\\\Period=10\pi\neq 5\pi[/tex]
Hence, option: 4 is incorrect.
3)
[tex]y=\cos(0.4x)[/tex]
The period of this function is:
[tex]Period=\dfrac{2\pi}{0.4}\\\\\\Period=5\pi[/tex]
Hence, option: 3 is the correct option.