Factorise fully the following:
a) x² + 3x
b) 2x? - 8x
c) 6x + 9x
d) 12x - 4x?
Answers
Answer:
a) [tex]x(x+3)[/tex]
b) [tex]2x(x-8)[/tex]
c) [tex]3x(2+3x^{2})[/tex]
d) [tex]4x^{2} (3x-1)[/tex]
Step-by-step explanation:
a) [tex]x^{2} +3x=x(x+3)[/tex]
b) [tex]2x^{2} -8x=2x(x-8)[/tex]
c) [tex]6x+9x^{3} =3x(2+3x^{2})[/tex]
d) [tex]12x^{3} -4x^{2} =4x^{2} (3x-1)[/tex]
Factors of the following algebraic expression are
a. Factors of x² + 3x are x and x+3
b. Factors of 2x² -8x are 2, x and ( x-4)
c. Factors of 6x +9x³ are 3, x and (2 + 3x²)
d. Factors of 12x³ - 4x² are 4, x, x and (3x -41)
What is factor of an algebraic expression?The factor of an given algebraic expressions are one or more numbers or linear or other expressions that multiply to form the given algebraic expression and cannot be broken down further into simpler expressions.
For finding factors of an algebraic expression we can simply take out common expressions from all the terms of the expression and try to simplify it.
a. x² + 3x = x( x+3), (taking x common from both terms)
b. 2x² -8x = 2x ( x-4) (taking 2x common from both terms)
c. 6x +9x³ = 3x (2 + 3x²) ( taking 3x common from both terms)
d.12x³ - 4x² = 4x× x × (3x -41) ( taking 4x² common from both terms)
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Related Questions
round to the nearest tenth place it is repeating decimal 4/6
Answers
Answer:
0.7
Step-by-step explanation:
I divided 4 by 6
0.6666666666666...
Simplify to 0.7
. Find the range of the data.
7,4, 12, 1, 8, 8, 4, 14, 13, 9, 11, 10, 2,7,5, 3, 1, 8,5,3
Answers
Answer:
Range: 13
Step-by-step explanation:
Population size:20
Lowest value: 1
Highest value: 14
Answer: 13
Hope this helps.
What is the greatest common factor of 8m^{2}8m
2
8, m, squared, 4m4m4, m, and 10m^410m
4
10, m, start superscript, 4, end superscript?
Answers
Answer:
2mStep-by-step explanation:
Given the functions 8m², 4m and 10m⁴, in order to find the greatest common factor, we will find a factor common to all the functions as shown;
8m² = 2*2*(2*m)*m
4m = 2*(2*m)
10m⁴ = (2*m)*5*m³
from the three expansion, it ca be seen that only 2 and m are common to all the function as shown in parentheses.
The greatest common factor factor will be the product of 2 and m i.e 2*m = 2m
The table shows the height in feet, y, of a pebble dropped from a tall bridge after x seconds.
Which descriptions are true of the function shown in the table? Check all that apply.
quadratic
linear
rational
y = –16x + 150
y = –16x2 + 150
y = + 150
nvm . jus got it wrong and it's A and E
Answers
Answer:
The answer is A & E
Step-by-step explanation:
quadratic
y=-16x^2 + 150
Answer: A and E
Step-by-step explanation:
edge 2023
Which polyhedron has more faces than a tetrahedron but fewer faces than an
octahedron?
A. Dodecahedron
B. Hexahedron
c. lcosahedron
D. Pyramid
Answers
Answer:
B. Hexahedron
Step-by-step explanation:
It helps to know the number faces in the named solids.
tetrahedron: 4 faces
octahedron: 8 faces
A. Dodecahedron : 12 faces
B. Hexahedron : 6 faces
D. lcosahedron : 20 faces
D. Pyramid: 4 for a triangular pyramid; more for other pyramids
Which polyhedron has more than 4 faces and less than 8 faces?
Answer: B. Hexahedron
The reason the answer is not a pyramid is that a pyramid may have exactly 4 faces or more than 7 faces.
Answer:
B
Step-by-step explanation:
Cube or Hexahedron ( 6 faces) has more faces than tetrahedron ( 4 faces), but fewer than octahedron ( 8 faces)
If using the method of completing the square to solve the quadratic equation x^2+15x+25=0x
2
+15x+25=0, which number would have to be added to "complete the square"?
Answers
Answer:
x = -15/2 ± (1/2)*5√5
Step-by-step explanation:
I will assume that you meant x^2+15x+25=0.
To complete the square, take half of the coefficient of x, square the result, add this square into the equation after '15x,' and then subtract the square from the result:
x^2+15x+25=0 => x^2 + 15x + (15/2)^2 - (15/2)^2 + 25 = 0.
Rewrite the first two terms as (x + 15/2)^2 - 225/4 + 100/4 = 0, or
(x + 15/2)^2 - 125/4 = 0
Taking the square root of both sides, we obtain the solutions:
x + 15/2 ±√[125/4], or
x = -15/2 ± (1/2)*5√5
The quadratic equation x²+15x+25=0, (15/2)² is a number to be added to "complete the square"
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 quadratic equation x²+15x+25=0
x²+15x+(15/2)²+25-(15/2)²=0
(x+15/2)²+25-225/4
(x+15/2)²+(100-225)/4
(x+15/2)²+(-125/4)
(x+15/2)²-(√125/√4)²
(x+15/2+√125/√4)(x+15/2-√125/√4)
(x+15/2+√125/2)(x-15/2-√125/2)
(x+(15+√125)/2)(x-(15+√125)/2)
Hence (15/2)² is a number to be added to "complete the square"
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if the radius of a circle 3 meters. what is the circles diameter?
Answers
Answer:
6 m
Step-by-step explanation:
the radius is half of the diameter
So, let’s plug 3m into this equation
r = 3 meters
r•2=d
3•2=d
6 meters = diameter
can someone heelp me with this i just dont understand it
Answers
Answer:
I CAN!
Step-by-step explanation:
First, where does the line start?
y=1
It looks like it goes up, and then right each one unit. No?
So that would be
Y=1+1
Warning! DO NOT say y=2. That is no good. You probably want to simplify it, but dont. Okay?
Happy to help
ОωО
Someone please help me
Answers
X = 0, Y = 5
X = -2, Y = -3
Equation: Y = aX + b
Using point 1:
5 = a0 + b
=> b = 5
Then again
Y = aX + b
-3 = a(-2) + 5
-3 - 5 = -2a
- 8 = -2a
=> a = 4
Y = 4X + 5
Answer:
y=4x+5
Step-by-step explanation:
Liner graph, therefore, y=mx+b; b is the y intercept; m is the slope
b=5, another pair is (-1,1)
need to find m first
Substituting we get:
⇒1= m(-1) + 5
⇒1= -1m + 5
⇒1-5= -m
⇒-4 = -m
⇒m=4
Eq: y=4x+5
Students were asked to write 6x^5 + 8x - 3x^3 + 7x^7 in standard form. Shown below are four
student responses.
Anna: 7x^7+ 6x^5 - 3x^3 + 8x
Mario: -3x^3 + 6x^5 + 7x^7 + 8x
William: 8x + 7x^7+ 6x^5 - 3x^3
Olivia: 8x - 3x^3 + 6x^5 + 7x^7
Which student is correct?
Answers
Answer:
Anna
Step-by-step explanation:
In standard form the first term is the term with the largest exponent.
The following terms are then in descending order of exponents.
The term with the largest exponent is 7[tex]x^{7}[/tex] ← first term
The expression in standard form is
7[tex]x^{7}[/tex] + 6[tex]x^{5}[/tex] - 3x³ + 8x ← Anna
Antonio has a kite, in the directions on how to put the kite together it says that the drawing is to scale where 10 cm = 1 meter. If the kite when put together is 1.5 m. Tall, how tall is it in the drawing?
Answers
Answer: 15cm.
Step-by-step explanation:
Hi, to answer this question we have to multiply the real height of the kite (1.5m) by the scale factor of the drawing (10):
Mathematically speaking:
Since 1 m = 10 cm
So:
1.5 m x 10 cm/m = 15 cm
The kite is 15 centimeters tall in the drawing.
Feel free to ask for more if needed or if you did not understand something.
Ross drives 280 miles in 4 hours. If Ross continues to drive at the same rate, how many miles can he drive in 12 hours?
Answers
Answer:
Step-by-step explanation:3,360
On his afternoon jog Chris took 42 minutes to run 3.75 miles. How many miles can he run in 90 minutes?
Answers
Answer:
8.03
Step-by-step explanation:
43 min = 3.75 miles
90 min = X
99 min×3.75÷42=8.03
Find the length of the third side to the nearest tenth.
Answers
Answer:
5.3
Step-by-step explanation:
You use the Pythagoras theorem which is a^2+b^2=c^2.
Since you're solving for a side length that's not the hypotenuse you will manipulate the equation to c^2-a^2=b^2. From here you just plug in numbers.
8^2 - 6^2 = b^2
64 - 36 = b^2
b = sqrt(28)
b = 5.2915.... = 5.3
Aprivate high school charges $57,000 for tuition, but this figure is expected to rise 10% per
year. What will the tuition be in 3 years?
Answers
Answer:
$75,867
Step-by-step explanation:
that will be the answer
plz help me I can't do anything and I have to pass this assignment for online School
Answers
Answer:
It will take 8
Step-by-step explanation:
2 cubic units we take 1 / 4 which four equals one and eight equals 2, so it will take a eight 1/4 to fill the prism.
$1500.00 in a simple interest savings account. Two years later, the total account balance is $1665.00.
What is the interest rate of the savings account?
What will be the total amount of money in the account after 8 years? $
please answer
Answers
Answer:
interest rate=45.04
I after 8 years=5994
step on step explainaton:
I=PRT
1500=1665×r/100×2
r=45.04
I after 8 years= I=PRT
=1665×45/100×8=5994
Can someone answer this question please please help me I really need it if it’s correct I will mark you brainliest .
Answers
Answer:
We divided the figure into 1 triangle and 2 rectangles.
Adding up the area of them, we get the total area:
A = 14 x (10 + 8 + 12 - 16)/2 + 8 x 5 + 6 x (12 + 8)
= 258 (yd2)
Hope this helps!
:)
A trampoline gym charges $6 for 1/2 of an hour. At that rate, what does 1 hour cost?
Answers
Answer:
Step-by-step explanation:
12
One hour's cost for the trampoline gym will be $12.
What is ratio?The ratio can be defined as the number that can represent one quantity as a percentage of another. They can be compared only when the two numbers in a ratio have the same unit. Ratios are used to compare two objects.
Given, A trampoline gym charges $6 for 1/2 of an hour.
Since,
For 1/2 hour gym charges = 6$
So from the definition of the ratio
Thus,
For 1-hour gym will charge = 6*2
For 1 hour gym will charge = 12$
therefore, One hour cost for the gym will be $12.
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Mr. Maxwell White bought a house at the cost of GHȼ250,000,000.00. He paid 20% of the cost out of his own resources an took a loan for the remaining amount at 2 1/2 % simple interest per annum. Calculate the total amount Mr. Maxwell White paid for the house, if he paid the loan 8 years later.
Answers
Answer:GHȼ290,000,000
Step-by-step explanation:
Given the following :
Cost of house = 250,000,000
Amount paid out of his own resources = 20% of house cost
Amount loaned = 250,000,000 - (20% of 250,000,000)
Rate = 2 1/2% = 5/2% = 0.025
Period or time = 8 years
Therefore,
Amount paid out of his own resources :
0.2 × 250,000,000 = 50,000,000
Amount loaned = (250,000,000 - 50,000,000) = 200,000,000 = principal
Simple Interest on loan = (principal × rate × time)
200,000,000 × 0.025 × 8 = 40,000,000
Total amount paid back= (200,000,000 + 40,000,000) = 240,000,000
Total amount paid for the house :
Total loan paid + amount paid from own resource:
240,000,000 + 50,000,000 = 290,000,000
Evaluate the finite geometric series for the specified number of terms. 1 + 2 + 4 + 8 + 16 + ...; n = 27
Answers
2^(27 -1)
2^26 = 67108864
How many meters are in a kilometre
Answers
Answer:
3000meter
Step-by-step explanation:
[tex] \frac{300000}{100} = 3000[/tex]
According to your question there are 1/1000 km in a meter and 1000 meters in a km.
Also for future reference you can follow the table given below-
Always the first is km
Second is ha.m ( hectameter)
Third is da.m ( dacameter)
Fourth is m ( meter)
Fifth is dm ( decimeter)
Sixth is cm ( centimetre)
Seventh is mm ( millimetre)
Remember when you are converting smaller unit ( lower) to bigger unit ( upper) you need to divide and while converting a bigger unit to a smaller unit you need to divide.
The sequence can be easily remembered by a line:
King
Henery
Died
Mother
Didn't
Cried
Much
HOPE IT HELPS!!!
IF IT HELPED YOU PLEASE MARK BRAINLIEST!!!!
what do 10n represent in p (n)=10n-1200
Answers
Step-by-step explanation:
The term 1200 represents the 11
i need help with the following question above please
Answers
Answer:
2a+c ( not sure if this is what you are looking for!)
Step-by-step explanation:
WORTH 60 POINTS AND BRAINLIEST. DO NOT PLAGIARIZE OR WRITE FAKE ANSWERS I WILL REPORT THANK YOU!!
A. David notices that the shape of the Ligersville toxic dump site is somewhat like a triangle. He claims that he can approximate the perimeter of the dump site without doing any extra measurements. What assumption about side AB of the dump site would David need to make in order to justify his claim?
B. Based on the assumption in part A, determine the approximate length of side AB of the dump site. Explain your reasoning in at least two sentences.
C. Determine the approximate perimeter of the Ligersville toxic dump site. Explain your reasoning.
Answers
Answers and Step-by-step explanations:
A. David would need to assume that side AB is the hypotenuse of the almost-right triangle that A, B, and C make. That way, he can use the Pythagorean Theorem to solve for AB.
B. AB² = 24² + 32² = 1600 ⇒ AB = √1600 = 40 yards
We can use the Pythagorean Theorem because we assume that ABC is in the form of a right triangle, with AB as the hypotenuse. Then since whenever we have a right triangle, we can use the Pythagorean Theorem to solve for an unknown side, that applies here as well.
C. The approximate perimeter is 24 + 32 + 40 = 96 yards. Using the approximation of AB from part B, we simply add up all the side lengths of this "triangle", as that is the definition of "perimeter". Thus, when we add them all together, we get a total of 96 yards.
Answer:
A. Assumption: length of the curve AB is equal to the hypotenuse of the triangle formed AB was a straight line.
B. 40 yards
C. 96 yards
Step-by-step explanation:
A. Assumption: length of the curve AB is equal to the hypotenuse of the triangle formed AB was a straight line.
B. AB² = 32² + 24²
AB² = 1600
AB = 40
Since we have assumed that AB is equal to the hypotenuse, we can use pythagoras theorem to find an approximate length of AB
C. Perimeter is the sum of all lengths:
32 + 24 + 40 = 96
Can someone help me answer this please.
Answers
Answer:
yes it is correct
Step-by-step explanation:
Answer:
Yes.
Step-by-step explanation:
Here are some of the Pythagorean Triples:
(3,4,5)
(5,12,13)
(7,24,25)
(8,15,17)
(9,40,41)
(11,60,61)
(12,35,37)
(13,84,85)
You'll see that 8, 15, 17 is a Pythagorean Triple so yes, it is a right triangle.
In a class full of men and woman 4/7 are woman what is the ratio of men and woman in the simplist form ?
Answers
Answer:
4:7
Step-by-step explanation:
i don't think that you can simplify it any further so you just change the / to a :
Please help! Correct answers only please!
You roll a 6-sided die two times.
What is the probability of rolling an odd number and then rolling a 3?
Simplify your answer and write it as a fraction or whole number.
Answers
Answer:
1/12
Step-by-step explanation:
to get a odd number is a 1/2 chance. to roll a 3 is a 1/6 chance. multiply those together to get 1/12.
A trucking company needs to move a pile of dirt. The dirt is stored in a pile shaped like a cone. The pile is 12 yards high, and its base has a diameter of 8 yards. How many truckloads will the company need, if each truck holds 6.28yd3 of dirt?
Answers
Answer:
it will take 96 truckload trips to move the entire pile of dirt.
Step-by-step explanation:
The formula for the volume of a cone of height h and radius r is
V = πr²h. Here, the radius, r, is half the given diameter, or r = d/2, or r = (8 yds)/2, or 4 yds, and the height is 12 yds. Thus, in this case, the volume of the conical pile of dirt is
V = π(4 yd)²·12 yd, or
V = 3.14(16 yd²)(12 yd), or
V = 602.88 yd³
If each truck holds 6.28 yd³ and we want to know how many truckloads the company needs in order to move the conical pile, we divide the above volume (V) by 6.28 yd³:
V 602.88 yd³
------------- = --------------------------------------- = 96
6.28 yd³ (6.28 yd³ per truckload)
We interpret this to mean that it will take 96 truckload trips to move the entire pile of dirt.
The number of truckloads the company will need is A = 32 truckloads
What is a Cone?A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the center of base) called the apex or vertex.
The volume of a cone is given by the equation
Volume of Cone = ( 1/3 ) πr²h
where r is the radius of the cone
h is the height of the cone
Surface area of the cone = πr ( l + r )
where l = √ ( b² + r² )
Given data ,
The first step is to find the volume of the pile of dirt using the formula for the volume of a cone: V = ( 1/3 ) πr²h, where r is the radius of the base and h is the height.
The height of the cone is given as 12 yards, and the diameter of the base is 8 yards, so the radius is half of that, or 4 yards. Plugging in these values, we get:
V = (1/3)π (4 yards)² (12 yards)
V ≈ 201.06 yards³
Next, we need to find out how many truckloads the company will need.
We know that each truck can hold 6.28 cubic yards of dirt, so we can divide the total volume of dirt by the volume of one truckload to find the number of truckloads needed:
201.06 cubic yards / 6.28 cubic yards/truckload ≈ 31.99 truckloads
Since the company can't order a fractional number of truckloads, they will need to round up to the nearest whole number.
Hence , the company will need 32 truckloads to move the pile of dirt
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PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1111111111
Answers
Answer:
261
Step-by-step explanation:
Answer:
i think its 261
Step-by-step explanation: