The factors of the expression is 3x²(x+5)(x+5) .
Factors of a number are defined as the numbers which divide the given number completely.
For an algebraic expression the factors of the expression are smaller polynomials which divide the given expression completely.
Factors of algebraic expression can be calculated by the following methods:
Middle-term factorizationcompletion of squareUsing factor theoremThe given polynomial is of the form:
3x⁴ + 30x³ + 75x²
Taking 3x² common from all the terms we get:
3x² (x² + 10x + 25)
Now we use middle- term factorization method to factor (x² + 10x + 25)
3x² (x² + 5x + 5x + 25)
or, ( 3x² ){x ( x + 5 ) + 5 ( x + 5 )}
or, 3x² (x + 5) (x + 5)
or, 3x² (x + 5)²
Hence the factors of the expressions are: 3x² (x + 5)²
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Factor completely: 3x⁴ + 30x³ + 75x²
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29) A company planned to donate 640 bags of groceries, 320 cases of bottled water, and 800 small toys to a
local relief center. Suppose that the number of bags of groceries, cases of bottled water, and small toys are to be
placed in boxes with the same number of each good in each box. For instance, you could place 10 bags of
groceries and 5 cases of water in each of 64 boxes, but that would require 12.5 toys per box-oops! To be as
efficient as possible, assume that the company wants to use as few boxes as possible and must have a whole
number of groceries, water, and toys in each box.
a) How many boxes are needed? b) What are the contents of each box?
160 boxes needed to pack these items
Therefore contents in each box have 4 bags of groceries, 2 cases of bottled water, and 5 toys.
Given no of groceries bags = 640
number of cases of bottled water = 320
number of small toys = 800
We have to find out how many boxes are needed and the contents of each box.
(i) How many boxes are needed:
To do this we need to find the greatest common factor of these three items
as
640 - 2⁷ * 5
320 - 2⁶ * 5
800 - 2³ * 5²
GCF = 2⁵ * 5 = 160
Therefore 160 boxes needed to pack these items
(ii) Contents of each box:
No of bags of groceries in each box = 640 / 160 = 4
No of cases of bottled water = 320 / 160 = 2
No of toys in each box = 800 / 160 = 5
Therefore, contents in each box have 4 bags of groceries, 2 cases of bottled water, and 5 toys.
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Solve the inequality and express your answer in interval notation.
x^2 + 12x +7 < 0
Solution:
B. [tex](-6-\sqrt{29},-6+\sqrt{29})[/tex]
Hope this helps! If so, lmk! Thanks and good luck!
Answer: (-6-[tex]\sqrt{29}[/tex], -6+[tex]\sqrt{29}[/tex]) ==> D
Step-by-step explanation:
x^2 + 12x +7 < 0
x^2+12x+36-29<0
(x+6)^2-29<0
(x+6)^2<29
x+6<[tex]\sqrt{29}[/tex]
x<-6+[tex]\sqrt{29}[/tex]
x+6>-[tex]\sqrt{29}[/tex]
x>-6-[tex]\sqrt{29}[/tex]
(-6-[tex]\sqrt{29}[/tex], -6+[tex]\sqrt{29}[/tex]) ==> D
-6-[tex]\sqrt{29}[/tex] and -6+[tex]\sqrt{29}[/tex] aren't included in the solution since if these values are plugged in to x^2 + 12x +7, the expression will equal 0. That's not supposed to happen. The expression is supposed to be LESS than 0.
A cube has a volume of 197 meters cubed (197 m3) What is the approximate value of one edge of the cube? The approximate value of one edge of the cube is meters. Round your answer to the nearest hundredth. What is the approximate area of one face of the cube? The approximate area of one face of the cube is meters. Round your answer to the nearest hundredth.
The edge length and area of the face of the cube are 5. 82 meters and 203 square meters respectively
How to determine the valueThe formuka for the volume of a cube is expressed as;
Volume = a^3
Where 'a' is the length of it's edge
From the information given, we have that the volume of the cube has a value of 197 cubic meters.
Now, substitute the value of the volume
We have;
197 = a^3
Take the cube root of both sides
a = 5. 82 meters
The formula for area of the face of a cube is given as;
Area = 6a ^2
Area = 6(5.82)^2
Area = 6(33. 85)
Area = 203 square meters
Thus, the edge length and area of the face of the cube are 5. 82 meters and 203 square meters respectively
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the base of a pyramid is the regular polygon abcdef gh, which has 14-inch sides. all eight of the pyramid’s lateral edges, va, v b, . . . , v h, are 25 inches long. to the nearest tenth of an inch, calculate the height of pyramid vabcdef gh.
the height of pyramid vabcdef gh is 45.2º.
What is a polygon?A polygon is a closed polygonal chain made up of a limited number of straight line segments that are joined to form a planar figure in geometry (or polygonal circuit). A polygon can be defined as the region that is circumscribed by a bounding circuit, the bounded plane, or both.
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In reality, the lateral face VAB is an isosceles triangle with a 14-length base and 25-length legs. This triangle's altitude must cut over angle V and the base, forming a right triangle with a hypotenuse that is 25 inches long and a short leg that is 7 inches long. We can calculate the altitude, which is also the slant height of the pyramid, using the Pythagorean theorem.
s.h. = alt. = √(252 - 72) = 24
Now, by adding the pyramid's height and half of its base, we may utilize this slant height as the hypotenuse of another right triangle.
We look at a regular octagon to identify half the base. You'll see that four of the sides are horizontal or vertical, while the other four are at an angle of 45 degrees to the first four. So, in this example, 14 + 28/2 = 14 + 142, the distance between parallel sides of a regular octagon would be equal to s + 2s/2.
hence, the base's half would equal 7 + 72.
The height of the pyramid and the dihedral angle with the base are both provided by this right triangle.
h = √(242 - (7 + 7√2)2) = 17.0"
θ = cos-1((7 + 7√2)/24) = 45.2º
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a swimming pool has two pipes coming in. one fills the pool in four hours, the other in six hours. an outlet pipe empties the pool in five hours. the outlet pipe is accidentally left open. in how many hours is the pool full?
The pool is full for 4 hrs.
Add the rates of filling of the 2 filling pipes and
subtract the rate of draining of the emptying pipe;
1st pipe's rate: ( 1 pool filled ) / ( 3 h);
2nd pipe's rate: ( 1 pool filled ) / ( 6 h );
3rd pipe's rate of emptying: ( 1 pool emptied ) / ( 4 h);
Let t = the time in hrs to fill the pool with all 3 pipes open
1/3+16-1/4 = 1/t;
Multiply both sides by 24t;
t = 4 hrs
volume is a measure of occupied three-dimensional space. it's miles frequently quantified numerically using SI derived units (consisting of the cubic meter and liter) or by way of diverse imperial devices (inclusive of the gallon, quart, cubic inch).
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write an equation of the line passing through the point (5, -6) that is parallel to the line y=-x-5.
The equation of the line is y+x+1=0.
It is required to find the equation of the line.
What is line?A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.
Given:
The given line is
y=-x-5.
Slope of line
y+x-5=0
We have to find the equation of the line.
According to given question we have
Slope =-1
Thus the slope of the required line is
-1
The point (5, -6)
The equation of the line is
y+6=-1(x−5)
=>y+6=-x+5
=>y+x+1=0
Therefore, the equation of the line is y+x+1=0.
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What are the leading coefficient and degree of the polynomial -u^8+18+10u^3
Answer:
Step-by-step explanation:
The variable here is u, and the highest power of u is u^8. The first term is thus -u^8, and the coefficient of this is -1. Thus, the leading coefficient of the polynomial is -1. The degree is 8.
FOR MY LAST QUESTION I forgot to add the screenshot so, help please! 25 points
Answer: c. P=43
d. P=3x^2+5x+8
Step-by-step explanation:
c. P=12x+19 ==> See how I got this formula in my previous answer to parts a and b
P=12(2)+19
P=24+19
P=43
d. P=a+b+c+d
P=x^2 +4x+8+2x^2 +x
P=x^2 +2x^2 +4x+x+8
P=3x^2+5x+8
andrea runs 4 miles every day, but she wants to increase her distance in order to run a 26-mile marathon. she decides to add 2 miles each day to her distance until she achieves her goal. if she starts with 6 miles today, how many miles will she have run, in total, by the time she achieves her 26-mile goal?
If she starts with 6 miles today and add 2 miles each day to her distance until she achieves her goal and then she has to run 176 miles in total to achieve her 26 miles goal.
Given,
Total distance for the marathon = 26 miles
Distance she add each day =2
She starts with 6 miles
Then,
Equation of nth term in the arithmetic sequence
[tex]t_{n}=a+(n-1)d[/tex]
Substitute the values and find the value of n
26=6+(n-1)2
26=6+2n-2
26=4+2n
2n=22
n=11
To find the total distance she run to achieve her 26 miles goal, we have to apply the sum of n terms of arithmetic sequence,
[tex]S=\frac{n}{2}[2a+(n-1)d]\\ S=\frac{11}{2}[2(6)+(11-1)2]\\ S=\frac{11}{2}[12+20]\\ S=\frac{11}{2}[32]\\ S=176[/tex]
If she starts with 6 miles today and add 2 miles each day to her distance until she achieves her goal and then she has to run 176 miles in total to achieve her 26 miles goal.
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Find the perimeter and area of the
polygon with the given vertices.
W(5, — 1), X(5, 6), Y(2, — 1), Z(2, 6)
The perimeter is units. The area is
squareunits.
The perimeter of the polygon will be 20 units and the area will be 21 square units.
From the given vertices a rectangle will be formed. A rectangle is a closed figure in which each interior angle is a right angle. The Perimeter of the rectangle can be given by formula 2(l + b) and the area is given by l×b where l is the length and b is breadth of rectangle. Now from the given points the dimensions of rectangle will follow the order W (5, -1), X (5, 6), Z (2, 6) and Y (2, -1).
The length of the rectangle is given by l = √ (6 + 1) ² + (5 - 5) ²
l = √49
l = 7 units
The breadth of the rectangle is given by b = √ (6 - 6) ² + (2 - 5) ²
b = √9
b = 3 units
Now, the perimeter of rectangle = 2 (l + b)
P = 2(7 + 3)
P = 20 units
Area of the rectangle = l×b
A = 7×3
A = 21 square units.
Thus, the perimeter and area are 20 units and 21 square units respectively.
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A particular antibiotic is eliminated from the blood with a half-life of 16 hours. how many hours does it take for 100-milligram dose to decrease to 30-milligrams in the blood?
Using the decay formula, the particular antibiotic with half-life of 16 hours, will decrease to 30-milligrams in the blood after 27.79 hours.
We can use the decay formula to solve the problem:
A(t) = A(0) . (0.5)^(t/T)
Where:
A(t) is the remaining quantity at time t
A(o) is the initial quantity
t is the time interval
T is the half-life rate
In the given problem:
A(0) = 100 milligram
T = 16 hours
A(t) = 30 milligram
We need to find t such that the remaining quantity of this antibiotic is 30 mg.
Substitute the given parameters into the formula:
A(t) = A(0) . (0.5)^(t/T)
30 = 100 . (0.5) ^(t/16)
Taking the logarithm:
log (30) = log [100 . (0.5) ^(t/16)]
Use the logarithm property, log(A.B) = log A + log B
log (30) = log (100) + log [(0.5) ^(t/16)]
Use the logarithm property, log(Aⁿ) = n.log A
log (30) = log (100) + (t/16) . log (0.5)
log (30) = 2 + (t/16) . log (0.5)
(t/16) . log (0.5) = log (30) - 2
t/16 = 1.737
t = 1.737 . (16) = 27.79 hours
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25 points plus brainliest
Answer:
The answer is C.
(0,4) and (3,0)
Step-by-step explanation:
To find the x, substitute 0 to the y.
* 4x + 3(0) = 12
> 4x = 12
> x = 3 (3,0)
To the y, substitute 0 to the x.
* 4(0) + 3y = 12
> 3y = 12
> y = 4 (0,4)
I hope you get this right!
Answer:
(0,4) and (3,0)
Step-by-step explanation:
Hope this helps :D
help me pls !!! I’ll give good pts
Answer:
0.32×0.5=0.16
If M is a midpoint of segment AB and AM=3x+1, if AB=20 cm what is the value of x?
Answer:
x = 3
Step-by-step explanation:
AB is the line segment and is 20 cm
Since M is the midpoint, AM = MB = 20/2 = 10
3x + 1 = 10
==> 3x = 10- 1 = 9
==> x = 9/3 = 3
Answer:
AB=20 then AM =10
now,
[tex]3x + 1 = 10 \\ 3x = 10 - 1 \\ 3x = 9 \\ x = 3 [/tex]
7 1/2 divided by 15 find the Quotient
Answer:
0.5
Step-by-step explanation:
7 1/2 • 2 = 15
7 times 2 is equal to 14
1/2 times 2 is equal to 1
14 plus 1 is equal to 15
brainliest to coorrrect answer
The measures of angles q, r and s are 100°, 135° and 125° and the sum of the three angles equals 360°.
What are the measures of missing angles of a geometric system?
In this problem we find a geometric system generated by three lines no collinear to each other, which generate the triangle DEF. In accordance with the Euclidean geometry, the sum of the measures of internal angles in a triangle equals 180°:
m ∠ FDE + m ∠ DEF + m ∠ DFE = 180° (1)
If m ∠ FDE = 80° and m ∠ DEF = 45°, then the measure of the angle DFE is:
m ∠ DFE = 55°
Finally, we find the values of the angles q, r and s by definition of supplementary angles:
q = 180° - 80°
q = 100°
r = 180° - 45°
r = 135°
s = 180° - 55°
s = 125°
The sum of the measures of angles q, r and s is:
q + r + s = 360°
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two third of a number minus 5 gives 11
what is the number?
Answer: n=24
Step-by-step explanation:
n=number
2/3 * n - 5=11
2n/3=16
2n=48
n=24
A bag has 1 red, 3 blue, and 4 green marbles. Outcome A is drawing a green marble on the first draw. Outcome B is drawing a green marble on the second draw without replacing the first marble.
The Probability that Outcome B is drawing a green marble on the second draw without replacing the first marble is
P(B|A) = 3/7.
What is probability ?The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty.
Probability is another word for possibility. It is a field of mathematics that examines the occurrence of a random event. The value is given as a number between 0 and 1. To determine how likely an event is to occur, probability has been introduced in mathematics.
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PLEASE HELP! URGENT!!
Find the range of values of [tex]k[/tex] for which the line [tex]y=kx+k[/tex] intersects the curve [tex]x^{2} +y^{2} =8k\\[/tex]
Answer:
x-
[tex]x = - {y}^{2} + 8k[/tex]
HELP NEEDED ASAP/NOW......NO LINKS AND NO JOKING PLS
AUBSERD ANSWERS WILL BE REPORTED<<
1) If, while training for a marathon, you ran 64 miles in 2 4/5 months, how many miles did you run each month? (Assume you ran the same amount each month) Write your answer as a whole number, proper fraction, or mixed number in simplest form.
Answer:
22 6/7 miles========================
GivenTotal distance is 64 miles,Total time is 2 4/5 months.SolutionIn order to find the distance you run each month you need to divide the total distance by the number of months:
64 : 2 4/5 = 64 : 14/5 = 64 * 5/14 = 32*5/7 = 160/7 = 22 6/7 mileshow to solve 233.91/3.45
Answer:if it is division it is:
Divide
233.91
by
3.45
=
67.8
Step-by-step explanation:
What is the answer to this problem?
Answer:
bsosbsodndodnelsnsodnendk
|3x + 3|-5> 4
please help me it’s due at 3:30
Answer:
x > 2 or x < −4
Step-by-step explanation:
Let's solve your inequality step-by-step.
|3x + 3| −5 > 4
Step 1: Add 5 to both sides.
|3x + 3| −5 + 5 > 4 + 5
|3x + 3| > 9
Step 2: Solve Absolute Value.
|3x + 3| > 9
We know either3x + 3 > 9 or 3x + 3 < −9
3x + 3 > 9(Possibility 1)
3x + 3 −3 > 9 −3(Subtract 3 from both sides)
3x > 6
3x > 6 (Divide both sides by 3)
3 3
x > 2
3x + 3 < −9(Possibility 2)
3x + 3 −3 < −9 −3(Subtract 3 from both sides)
3x < −12
3x < -12 (Divide both sides by 3)
3 3
x < −4
The angle shown has the same measure as an angle drawn on paper. Order the steps for copying the angle from the paper using a compass and straightedge.
The order of the steps for copying the angle from the paper using a compass and a straight edge are;
5. Label the original angle as ‹A. On a separate piece of paper, draw a horizontal ray directed to the right, using the straight edge. Label the left endpoint D
4. Draw an arc centered at the vertex A that passes through both sides of ‹A using the compass. Label the points of intersection B and C.
1. Using the same compass setting, draw an arc centered at point D that intersects the ray and looks like the arc through B and C. Label the intersection of the arc and the ray as E.
3. Adjust the compass to the length BC. Draw an arc with radius BC centered at point E that intersects the arc through E. Label the point of intersection F.
2. Draw [tex] \overrightarrow{DF} [/tex]. You now have [tex] \angle A \cong \angle D [/tex]
How can the order of copying an angle be found?The steps for copying an angle includes;
Drawing a line segment on which the angle is to be copied, and label the endpoint as DDrawing an arc centered on the vertex, A, of the original angle, to intersect with the rays of the angle at B and C.With the same compass width, place the compass at D and draw an arc to intersect the ray from D at point E.With radius BC draw an arc from point E intersecting the arc drawn through E at FJoin point D to F to complete the construction of a copy of ‹A, such that, [tex] \angle A \cong \angle D [/tex]The order of the steps based on the appearance of the step in the question are therefore;
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Interest earned: $39.60
Principal: ?
Interest rate: 11%
Time: 6 months
The principal amount is calculated as $720.
What is defined as the simple interest?Simple interest is a simple and quick method to calculate the interest on a loan.
Consumers who charge their loans on time as well as early each month benefit from simple interest.Auto loans as well as short-term personal loans have been typically interest-only loans.Simple interest is calculated by multiplying the daily interest rate by the principal multiplied by the number of days between payments.The formula for calculating the simple interest is;
SI = PRT/100
Where,
SI = simple interest
P = principal amount
R = rate of interest (%)
T = time period in years
For the given values in the question
Simple Interest earned: $39.60Interest rate: 11%Time: 6 months = 0.5 years.Substitute the given values in the question;
39.60 = (P×11×0.5)/100
P = 39.60×100/(11×0.5)
P = 720
Therefore, the value of the principal amount is estimated as $720.
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PLEASE HELP ITS DUE IN 6 MINUTESS: schools A and B are competing in an academic contest. Correct answers earn 9 points. Incorrect answers lose 4 points. In the final round, School A gives the same number of correct and incorrect answers. School B gives no incorrect answers and the same number of correct answers as School A. School A started the final round with 128 points. School B started with 56 . The game ends with the two schools tied. Let x represent the number of correct answers given by School A in the final round. Write an equation that models the outcome of the contest. Then find the number of answers that each school got correct in the final round.
The number of answers that each school got correct in the final round is 18.
How to calculate the value?School A point = 128
School B point = 56
Let x = the number of correct answers given by School A in the final round.
Therefore, the equation for A will be:
128 + 9x - 4x = 128 + 5x
The equation for B will be:
= 56 + 9x.
We will equate the equations.
128 + 5x = 56 + 9x
9x - 5x = 128 - 56
4x = 72
x = 72/4
x = 18
School A and B gave 18 correct answers
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What is the student error in the multiplication below?
Multiply the ones: 957 times 23 = 2871. Above the 9 in 957 is 1, above the 5 in 957 is 2.
Multiply the tens: 957 times 23 = 2871. 2871 + 1914 = blank. Above the 9 in 957 is 1, above the 5 in 957 is 1.
Answer:
When multiplying the tens, the student didn't use the 0 place holder for the ones place.
Step-by-step explanation:
When using or doing long multiplication the answer was correct (2871) BUT before multiplying the tens, a zero should be placed in the ones place of the results. So, the tens should be 19140
2871+19140=22011
Answer: 1) When multiplying the ones, the student did not carry over a ten to the next place in the first multiplication.
2) When multiplying the ones, the student should have calculated 3 times 2 plus 5 as 11 and placed a 1 in the tens place.
3) When multiplying the tens, the student did not use the 0 place holder for the ones place.
4) When multiplying the tens, the student should have calculated 2 times 1 plus 9 as 11 and used a 1 should in the hundreds place.
Answer:
The correct option is;
4) When multiplying the tens, the student did not use the 0 place holder for the ones place
Step-by-step explanation:
Here we have when doing long multiplication, the student correctly multiplies the ones as 2871, however, before commencing multiplication of the tens, a 0 should be placed in the ones place of the result as a place holder such that the outcome of the multiplication of the tens should be;
19140
Hence, the correct result should be 2871 + 19140 = 22011
The correct option is therefore, that "When multiplying the tens, the student did not use the 0 place holder for the ones place."
Step-by-step explanation:
Can someone please answer the question for me? I am terrible at Algebra!
Answer:
Grace's work was done correctly.
Step-by-step explanation:
She expanded the equation and grouped the like terms, then added them together to get the answer.
[tex]6-3x-2\left(6x-8\right)\\=6-3x-12x+16\\3x - 12x = -15x\\= -15x + 6 + 16\\6 + 16 = 22\\= -15x + 22[/tex]
Hope this helps!
Justin operates an orange juice stand. Justin started out with 48 oranges. On monday, he used 3/4 of the orange. On Tuesday he used 1/12 as many oranges as Monday. How much more oranges did he sell on Monday compared to Tuesday.
Answer:
75% of 48 = 36 oranges used on M. 36/12=3, 3 is 1/12 of 36, so he sold 33 more oranges on M then on T when he only sold 3.
I need help with this one
Answer:
c) -66%, -0.45, -1/3, 1.8
Step-by-step explanation:
Numbers provided:
-66%-1/3-0.451.8Rewrite them in decimals:
-66% = -0.66-1/3 = -0.33-0.45 = -0.451.8 = 1.8In ascending order (from least to greatest):
-0.66 < -0.45 < -0.33, 1.8-66% < -0.45 < -1/3 < 1.8Solution: -66%, -0.45, -1/3, 1.8