Greatest common factor (GCF): 12a³b + 8a²b² - 20ab³. = 4ab(3a² + 2ab - 5b²) that is option 2
Describe GCF.A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, the numbers 12, 20, and 24 share the components 2 and 4. Since four is the biggest, we refer to the GCF of 12, 20, and 24 as four.
There are two stages to get the GCF since 12a3b + 8a2b2 - 20ab3. contains both integers and variables (HCF). Find GCF for the variable component first, then for the numeric part.
How to locate GCF
1. Find the GCF for the 12, 8, 20 numerical portion.
2. Calculate the GCF for the variable component (a3b, a2b2, and ab3).
3. Add the values together and multiple them
Find the common factors for the numerical part: 12 ,8,20 is
factors of 12 -1,2,3 ,4,6,12
factors of 8 - 1,2,4,8,
factor of 20 - 1,2,4,5,10,20
the common factor will be 1,2,4
so GCF = 4
Next, find the common factors for the variable part: a³b , ,a²b² ,ab³.
the common factors will be ab
so GCF = ab
for the equation 12a³b + 8a²b² - 20ab³.
4ab is common , if we take 4ab common then remaining parts are
12a³b = 3a²
8a²b² = 2ab
20ab³. = 5b²
greatest common factor: 12a³b + 8a²b² - 20ab³. = 4ab(3a² + 2ab - 5b²)
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Simplify:
[tex]\frac{sec(x)-csc(x)}{sec(x)+csc(x)}[/tex]
Hence, the value of [tex]\frac{sec(x)-csc(x)}{sec(x)+csc(x)}=1[/tex].
What is the trigonometry?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Here given that,
[tex]\frac{sec(x)-csc(x)}{sec(x)+csc(x)}[/tex]
As we know,
[tex]sec(x)=\frac{1}{csc(x)}\\\\\\1-1csc^2(x)=cot^2(x)\\\\\\1+csc^2(x)=cot^2(x)[/tex]
So,
[tex]\frac{sec(x)-csc(x)}{sec(x)+csc(x)}\\\\\\=\frac{\frac{1}{csc(x)}-csc(x)}{\frac{1}{csc(x)}+csc(x)}\\\\\\=\frac{\frac{1-csc^2(x)}{csc(x)}}{\frac{1+csc^2(x)}{csc(x)}}\\\\\\=\frac{{1-(1)csc^2(x)}}{{1+csc^2(x)}}\\\\\\=\frac{cot^2(x)}{cot^2(x)}\\\\\\=1[/tex]
Hence, the value of [tex]\frac{sec(x)-csc(x)}{sec(x)+csc(x)}=1[/tex].
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Please help!! I tried setting it up to 180 but I don’t feel right about it! Thanks! :)
Would like some help identifying these triangles :)
Answer:
A=Right, B=Acute, C=Obtuse, D=Obtuse
Step-by-step explanation:
A.right
B.acute
C.obtuse
D.obtuse
What is the equation of the horizontal line that passes through (8,-3) what is the slope of the line?
Answer: 0
Step-by-step explanation:
A horizontal line always has a slope of 0
Please answer this problem
Answer: 2 is equal to or less than 5
Step-by-step explanation:
When the dot is colored in that means it’s equal to or _, while when it’s hollowed out it’s equal to a simple greater or less than symbol.
For the function f(x) =8(x+10), find f
Answer:
Step-by-step explanation:
The function for f(x)=8(x+10) is;
B. f^-1(x)=x-10/8
Find the arc length and sector area for the following:
(Use \large \pi=3.14...do not use the \large \pi button on your calculator!)
arc length =
sector area =
the value of arc length = 3.14 and the area of the sector = 4.71cm²
What is area of sector and length of an arc?The formula for the area of the sector of a circle is /360° (r2) where r is the radius of the circle and is the angle of the sector.
Arc length is the distance between two points along a section of a curve. It is given as
/360°×2r
= 180°, therefore /3 = 180/3= 60°
arc length = 60°/360 × 2×3.14×3
arc length = 3.14cm
The area of the sector = /360°×r²
60/360×3.14×3²
sector area = 3.14×3÷2
sector area = 4.71cm²
therefore the length of the arc and the area bounded by the arc and radius(sector) is 3.14cm and 4.17cm².
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Answer:the value of arc length = 3.14 and the area of the sector = 4.71cm²
Step-by-step explanation:
the value of arc length = 3.14 and the area of the sector = 4.71cm²
Please help me understand this
Answer:
? understand whatt I think you ment to put a picture or something
A square has sides of 18 units. Squares x + 1by x + 1units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x. V(x) =
The box's volume V expressed as a function of x V(x) =(x+1)(16 -2x) ².
A square form is what?A square has four equal sides, four vertices, and is a closed, two-dimensional object. It has parallel sides on either side. A square is also equivalent to a rectangle having equal length and width.
What are the four different kinds of squares?An equal-length rectangle with two neighboring sides. a quadrilateral having four straight angles and equal sides. a parallelogram with two sides that are equally spaced apart and one right angle. the shape of a right-angled rhombus.
Briefing:A distance of (x+1) is cut in from both sides, so the base dimensions are
18 - 2(x+1) = 16 - 2x
The depth of the fold is (x+1), so that is the depth of the box.
The volume V(x) = (x+1)(16 -2x)²
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Emika has a monthly budget for her cell phone bill.
Last month she spent `120\%` of her budget, and the bill was `\$60`.
What is Emika’s monthly budget?
Using percentages, we know that Emika's monthly budget is $50.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent symbol, "%," is frequently used to indicate it.
A % is a number without dimensions and without a standard measurement.
For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
So, if we multiply a fraction of a number by 100, you get a percentage. % is the symbol used to denote percentages.
Let x stand in for Emika's monthly cell phone budget.
Divide $60 by 120% to find his monthly spending limit.
x = $60 / 120%
x = $60 / 1.20
x = $50
Therefore, using percentages, we know that Emika's monthly budget is of $50.
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What is the surface area of the figure In square centimeters of 4cm 3cm 6cm 5cm
The surface area of the prism is 84 square centimeters.
What is a prism?
A prism is a polyhedron in geometry that has n parallelogram faces that connect the n-sided polygon basis, the second base, which is a translated duplicate of the first base, and the n faces. The bases are translated into all cross-sections that are parallel to them.
In the figure,
The surface area of the figure consists of 2 triangles, 3 rectangles.
The area of the triangle and rectangle is the surface area of the triangle.
The area of the triangle is (1/2) × base × height
The base of the triangle ABC is BC and the height is AB.
The area of triangle ABC is (1/2) × 4 × 3 = 6 square centimeters.
The area of triangle DEF is (1/2) × 4 × 3 = 6 square centimeters.
The area of the rectangle ACDE is 5 × 6 = 30 square centimeters.
The area of the rectangle ABEF is 4 × 6 = 24 square centimeters.
The area of the rectangle BCDF is 3 × 6 = 18 square centimeters.
The total surface area of the figure is ( 6 + 6 + 30 + 24 + 18) square centimeters = 84 square centimeters
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what is the decimal equivalent of 38/50
Answer: it is equal to 0.76
Answer: 0.76
Step-by-step explanation: 38 ÷ 50 = 0.76
Jayden is deciding between two truck rental companies. Company A charges an initial fee of $85 for the rental plus $1.50 per mile driven. Company B charges an initial fee of $65 for the rental plus $2.50 per mile driven. Let AA represent the amount Company A would charge if Jayden drives xx miles, and let BB represent the amount Company B would charge if Jayden drives xx miles. Write an equation for each situation, in terms of x,x, and determine which company would be cheaper if Jayden needs to drive 5 miles with the rented truck.
Answer:
A = 85 +1.50xB = 65 +2.50xB is cheaper for 5 milesStep-by-step explanation:
You want cost equations and the cheaper company for driving 5 miles when A charges $85 plus $1.50 per mile, and B charges $65 plus $2.50 per mile.
(a) EquationsIn each case, the cost is the sum of the initial fee and the mileage charge. The mileage charge is the cost per mile, multiplied by the number of miles (x). Using the given fees and costs per mile, we have ...
A = 85 +1.50x
B = 65 +2.50x
(b) Cheaper companyThe difference in fees is $85 -65 = $20. The difference in mileage charges is $2.50 -1.50 = $1.00 (per mile). Then the two companies will charge the same for $20/($1 /mile) = 20 miles.
Five miles is less than that "break even" mileage, so the cheaper company will be the one with the lower initial fee. (The graph shows the charges for each company for 5 miles.) For more than 20 miles, the cheaper company is the one with the lower mileage charge.
Company B will be cheaper for a drive of 5 miles.
When Derrick turned 15, his grandparents put $10,000 into an account that yielded 1.4% interest, compounded quarterly, When Derrick turns 18, his grandparents
will give him the money to use toward his college education. How much does Derrick receive from his grandparents on his 18th birthday?
=======================================================
Explanation:
The compound interest formula is
A = P*(1+r/n)^(n*t)
where,
A = account balance after t yearsP = deposit amountr = annual interest rate in decimal formn = number of times the money is compounded per yeart = number of yearsThe deposit amount is P = 10000 dollars.
The value of r here is r = 0.014 which is the decimal form of 1.4%
n = 4 since we're compounding quarterly, i.e. 4 times a year.
The timespan from when Derrick was 15 to when he became 18 is 18-15 = 3 years, which is the value of t.
Summary of input values:
P = 10000r = 0.014n = 4t = 3Let's find the value of "A".
A = P*(1+r/n)^(n*t)
A = 10000*(1+0.014/4)^(4*3)
A = 10428.1800719861
A = 10428.18
Find the equation of a line that passes through (-7,2) and is parallel to the line 7x+2y=0
Answer:
7x + 2y = - 45-----------------------
GivenLine 7x + 2y = 0,Point (-7, 2) on a parallel line.Find the equation of the parallel line.We know parallel lines have equal slopes.
Find the slope of the given line:
7x + 2y = 02y = - 7xy = - 3.5xThe slope is - 3.5.
Use point-slope equation to find the equation of the parallel line.
y - 2 = - 3.5(x - (-7))y - 2 = - 3.5x - 24.5y = - 3.5x - 22.5Convert it to standard form:
y = - 3.5x - 22.52y = - 7x - 45 7x + 2y = - 45retangular form of r=8 sin theta
Answer:
Step-by-step explanation:
r2=x2+y2,tanθ=yx,x=rcosθ,y=rsinθ
a Ferris wheel can accommodate 35 people in 20 minutes. how many people could ride the Ferris wheel in 6 hours
Answer:
630 people could ride the Ferris wheel in 6 hours.
Step-by-step explanation:
First, let's find the people-per-hour amount:
Since there are 3 "20 minutes" in an hour, we multiply the amount it can accommodate by 3 as well:
35 * 3 = 105
Next, since we have 6 hours, we multiply our people-per-hour by 6:
105 * 6 = 630 people in 6 hours, final answer.
in a class of 30 students, approximately what is the probability that two of the students have their birthday on the same day
The probability that two students out of 30 students have their birthday on the Same day is 0.706, that is nearly 71%
What is conditional probability?The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability.
How do you calculate conditional probability?the likelihood of the preceding event is multiplied by the probability of the subsequent,or conditional, occurrence to determine the conditional probability.
In a year we have 365 days
probability at least 2 people share the same birthday=1 - probability no people share the same birthday
the first student can be born on any day,so we'll give him a probability of 365/365
the probability of the next born is 364/365
the probability of the third born is 336/365
[tex] \frac{365 \: factorial}{335 \: factorial \: . {365}^{30} } [/tex]
this is the simplified form of the 30 probabilities product.= 0.294
therefore
probability at least 2 people share the same birthday=1 - probability no people share the same birthday
1 - 0.294= 0.706
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Please help and show how you got the answer.
Answer:
1.8 cans of paint are needed
Step-by-step explanation:
A large statue has a volume of 135 m³ and an area of 81 m², while a small statue has a volume of 5 m³. You want to know the number of cans of paint required to paint the small statue, if each can covers 5 m².
Scale factorThe ratio of linear dimensions on the small statue to those on the large statue is the cube root of their volume ratio:
sf = ∛(5/135) = ∛(1/27) = 1/3
AreaThe area of the small statue is the larger statue's area multiplied by the square of the scale factor:
smaller area = larger area × (sf)²
smaller area = (81 m²)(1/3)² = 9 m²
PaintEach can of paint covers 5 m², so the number of cans required is ...
(9 m²)/(5 m²/can) = 1.8 cans
You will need 1.8 cans of paint to paint the small statue.
__
Additional comment
If you must pay for whole cans of paint, you must buy 2 cans of paint.
Evaluate } 3² · 3⁻⁵ / 4⁻²
16/27
27/16
16/59,049
59,049/16
Answer: 27/16
Step-by-step explanation: evaluate
A fish dives down into the ocean at a constant rate. From the surface, it
dives 2,060 feet in 5 minutes. The number -2,060 represents the
location of the sailfish in relation to the surface. What number
represents the location of the fish in relation to the surface 2 minutes
after beginning the dive?
Answer:
- 824 ft
Step-by-step explanation:
2 minutes out of 5 is a fraction 2/5
2/5 of the -2060 would be
2/5 *( -2060) = - 824 ft
Answer:
uhhh i think -824
Step-by-step explanation:
-2060/5
-412
-412x2
-824
8. Write an equation in standard form to represent the line shown on the graph below.
Answer:
2x - y - 2 = 0
Step-by-step explanation:
A (1,0)
B (0,-2)
(y-0)/(-2-0) = (x-1)(0-1)
y/-2 = (x-1)/-1
-y/2 = -x + 1
-y = 2(-x+1)
-y = -2x + 2
2x - y - 2 = 0
For the function N(t)=4|t+5|+3, evaluate N(2).
Answer:
see explanation
Step-by-step explanation:
N(t)=4|t+5|+3, evaluate N(2).
Evaluate: Plug in a number for each variable.
4(|t+5|)+3
t=2
Evaluate for t=2
4(|2+5|)+3
4(|2+5|)+3
=31
(Hope this answer does you some good )
Nachelle has x dimes and y nickels. She has at least 11 coins worth a maximum of $0.80 combined. Solve this system of inequalities graphically and determine one possible solution.
PLEASE SHOW ON A GRAPH AND USE AND START THE INEQUALITY WITH Y.
NO LINKS.
The solution of the given inequalities will be the common region between the two (refer to the graph).
What is an inequality ?
In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
Nachelle has x dimes and y nickels.
We know that, A nickel is worth 5 cent, A dime is worth 10 cent and have maximum of $0.8 combined.
So, 5% x + 10% y ≤ 0.8
5x + 10y ≤ 80
She has at least 11 coins.
So, x + y ≥ 11
Hence, We have two inequalities as:
5x + 10y ≤ 80 and x + y ≥ 11
Similarly, x≥ 0 and y≥ 0.
Now, We'll find the points that lie on the given lines and draw the lines ( refer the given figure )
After drawing the graph, we'll check the inequalities where the portion is true.
If take point (0,0),
5x + 10y ≤ 80
5(0) + 10(0) ≤ 80
0 ≤ 80 which is true, hence we will shade the region which is down because the point (0,0 ) lies in downward region.
Similarly,
x + y ≥ 11
0 + 0 ≥ 11
0 ≥ 11 which is false hence, we will shade the region which is up because the point (0,0 ) lies in downward region.
In result, We get the common region which is the solution.
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I need help with this question
Answer:
slope is 7/4
y intercept (0,2)
Step-by-step explanation:
m= 7/4 y=mx + b to find slope.
Lilah invested $400 in the stock market. She saw an 8% decrease in her money, what is the value of her stocks now
The value of Lilah's stock after the decrease of 8 % is $ 368
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the initial amount of money Lilah invested in stocks be = A
The value of A is = $ 400
Now , the percentage decrease in the value of stocks = 8 %
So , the equation will be
The value of the stocks after the decrease = initial amount of money Lilah invested in stocks - ( percentage decrease in the value of stocks x initial amount )
Substituting the values in the equation , we get
The value of the stocks after the decrease = 400 - ( 8/100 ) x 400
The value of the stocks after the decrease = 400 - ( 8 x 4 )
The value of the stocks after the decrease = 400 - 32
The value of the stocks after the decrease = $ 368
Therefore , the value of A is $ 368
Hence , The value of Lilah's stock after the decrease of 8 % is $ 368
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ethe relationship between the data in the table is linear write a equation
in slope-itercept form that represent the data in the table
Answer:
give the data in the graph form and your answer is right..
Directions - Match the equations for parallel lines. (Note: you will not use all choices on the right side).
The equations for parallel lines:
y = -1/2 x - 2 ----- y = -1/2 x + 6
y = 1/2 x + 4 ----- y = 1/2 x - 4
y = 2x -4 ----- y =2/1x + 2
y = 5x + 2 ----- y = 5x - 1
y = 1/5 x + 10 ---- y = 1/5 x + 3
What is slope of line?
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
If an equation in the form y = mx + c then m is the slope of the line.
Equation of line slope Slope parallel line
y = -1/2 x - 2 -1/2 -1/2
y = 1/2 x + 4 1/2 1/2
y = 2x -4 2 2
y = 5x + 2 5 5
y = 1/5 x + 10 1/5 1/5
Now identify the lines from the option whose slope are -1/2, 1/2, 2, 5, 1/5.
The slope of the line y = -1/2 x + 6 is -1/2.
The slope of the line y = 1/2 x - 4 is 1/2.
The slope of the line y = 2x -4 is 2.
The slope of the line y = 5x + 2 is 5.
The slope of the line y = 1/5 x + 10 is 1/5.
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Find the vertex.
f(x) = 4(x - 2)² +11
([?],[_])
(2, 11) is the vertex of f(x) = 4(x - 2)² +11.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
The given equation is f(x) = 4(x - 2)² +11.
The vertex form is y=a(x-h)²+k
y=a(x-h)²+k of a parabola is said to be in vertex form because the vertex can be determined by examining the equation: (h, k) is the vertex.
(h, k) are the vertices of the given equation.
a=4,
h=2 and
k=11
so the (2,11) is the vertex of the function.
Hence, the vertex of f(x) = 4(x - 2)² +11 is (2, 11).
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The sum of the measures of angle P and angle S is 140°.
The measure in degrees of angle P is represented by the expression ( 5x+30)°·
The measure of angle S is 80°.
What is the value of x?