Answer:
(x - 3)(4x² + 6x + 9)
Step-by-step explanation:
This is a difference of cubes which factors in general as
a³ - b³ = (a - b)(a² + ab + b²)
8x³ = (2x)³ ⇒ a = 2x
27 = 3³ ⇒ b = 3
Hence
8x³ - 27
= (2x)³ - 3³
= (2x - 3)( (2x)² + (2x × 3) + 3²)
= (2x - 3)(4x² + 6x + 9)
What is the maximum height of the apple equation which formula is -16x^2+56x+40
40; base it off of the y-intercept [C]. What is the unit of measurement?
Answer:
The maxima is the point where it is the highest it can possibly get. I promise this isn't a scam but I have a picture that shows what I mean
Step-by-step explanation:
So this graph shows that (1.75, 89) is the maximum height
I hope this helps:)
Which of the following represents the value of the missing side?
Answer:
The value of the missing side is [tex]x=2\ units[/tex]
Step-by-step explanation:
In this problem i assume that the length side x is tangent to the circle
so
the length side x is perpendicular to the radius
Applying the Pythagoras Theorem in the right triangle
we have that
[tex](1.5+1)^{2}=1.5^{2}+x^{2}[/tex]
Solve for x
[tex](2.5)^{2}=1.5^{2}+x^{2}[/tex]
[tex]x^{2}=2.5^{2}-1.5^{2}[/tex]
[tex]x^{2}=4[/tex]
[tex]x=2\ units[/tex]
Answer:
x=2
Step-by-step explanation:
Andrew estimated the weight of his dog to be 60 lb. The dog’s actual weight was 68 lb.
What was the percent error in Andrew’s estimate? Round your answer to the nearest tenth of a percent.
%
Answer:
11.76%
Step-by-step explanation:
use % error formula:[tex]\frac{|approx-exact|}{exact}[/tex]
where approx is 60
and exact is 68
so
[tex]\frac{|60-68|}{68}[/tex]
[tex]\frac{|-8|}{68}[/tex] =0.1176
0.1176=11.76%
hope this helps!
Pleas help I will mark brainliest
The area for one side is S^2 where S is the length of one side.
The area for one side = 1/2^2 = 1/4 square foot.
A cube has 6 sides. Total surface are = 1/4 x 6 = 1 1/2 square feet.
Volume of a cube is S^3
1/4^3 = 1/64 cubic foot.
Simplify the following expression Algebra Fraction
Which polygon will tessellate a plane?
Tessellation is possible only for equilateral triangles, squares and regular hexagons. Therefore, there are only three regular polygons that tessellate.
Tessellation is possible, if each interior angle of a polygon is a factor of 360 degrees.
Now, in the given image, pentagon and octagon cannot tessellate.
And the triangle does not seem to be an equilateral triangle. But in general we can say that triangle tessellates.
So, the answer might be triangle (if its equilateral)
Classify the following triangle.
Answer:
its an obtuse
Step-by-step explanation:
The triangle is:
A. Scalene.
E. Acute
Step-by-step explanation:Scalene triangle--
A triangle is said to be scalene if the length of all the three sides of a triangle are different.
Right triangle--
A triangle is said to be a right triangle if one of the angle is right angle i.e. measure of one of the angle is: 90 degrees.
Equilateral triangle--
A triangle is said to be equilateral if all of the sides of a triangle are equal.
Obtuse triangle--
A triangle is said to be obtuse if measure of one of the angle is more than 90 degrees but less than 180 degrees.
Acute triangle--
A triangle is said to be acute triangle if the measure of all the three angles of a triangle are less than 90 degrees.
Based on the diagram we observe that all the sides of a triangle are different and all the three angles of a triangle are less than 90 degrees.
Hence, the triangle is scalene and it is a acute triangle.
by which reason can it be proven that triangles DAB and DAC are congruent
Answer:
ASA
Step-by-step explanation:
You are given 2 equal sets of angles.
<ABD and <ACD (right angles)
<BAD and <CDA (bisected angle)
You can get <ADB = <ADC because every triangle has 180 degrees. You know two of the angles: you can show that the 3 rd set are equal a subtraction postulate.
AD = AD (Reflexive property)
The triangles are congruent by ASA
If AAS is acceptable then it is correct in this case.
AD = AD
The two right angles are equal
The two angles created by the angle bisector are equal.
These three facts give AAS, but please see my comment below.
Answer:
The correct answer is AAS.
Step-by-step explanation:
A town has a population of 2000 and grows at 4.5% every year. What will be the
population after 13 years, to the nearest whole number?
Answer:
3544
Step-by-step explanation:
This is a problem of compound growth. The formula is
[tex]F=P(1+r)^t[/tex]
Where F is the value in the future (in this case, the population after 13 years)
P is the intial amount (here, the initial population of 2000, so P = 2000)
r is the rate of growth (here, it is 4.5%, in decimal, 0.045)
t is the time frame (here, it is 13 years, so t = 13)
we can plug the numbers into the formula and solve for F:
[tex]F=P(1+r)^t\\F=2000(1+0.045)^{13}\\F=2000(1.045)^{13}\\F=3544.4[/tex]
rounded to the nearest whole number, the population after 13 years would be 3544
Answer:
The population after 13 years = 3544
Step-by-step explanation:
Points to remember
Compound interest
A = P[1 +R/n]^nt
Where A - amount
P - principle amount
R = rate of interest
t - number of years
n - number of times compounded yearly
Here we have to consider compounded growth.
To find the population
Here P = 2000 , R = 4.5% = 0.045% and n = 13 years
A = P[1 +R/n]^nt
= 2000[1 + 0.045/1]^(1 * 13)
= 2000 * 1.77
= 3544
Therefore the population after 13 years = 3544
What can you say about the relationship between M and P? Which letter is the correct answer?
Answer:
log(M/N) = 4, log(P/N) = 5
log M - log N = 4
log P - log N = 5
log P - log M = log(P/M) = 1
P/M = 10
P = 10M
The correct answer is C.
Since it is evident that P is in fact ten times larger than M, the right response is P = 10M Option C is correct.
To solve this problem
Given that log(M/N) = 4, log(P/N) = 5 and both logarithms have the same base, let's consider the relationship between M and P
Since Log (M) = 4 this implies that M =[tex]10^4[/tex]
Similarly, Log ( P) = 5 this implies that P = [tex]10^ 5[/tex]
Now, we can compare P and M :
[tex]P = 10^5[/tex]
[tex]M = 10^4[/tex]
Since it is evident that P is in fact ten times larger than M, the right response is:
C . P = 10M
Therefore, This reflects the relationship that P is 10 times M.
Find the different forms of the equation of the straight line passing through ( 5 , 7 ) and perpendicular to the straight line whose equation is 4y-3x+9=0
Answer:
y-7=-(4/3)(x-5) (point slope form)
y=-(4/3)x+(41/3) (slope intercept form)
4x+3y-41=0 (general form)
Step-by-step explanation:
step 1
Find the slope of the perpendicular line to 4y-3x+9=0
If two lines are perpendicular, then the product of their slopes is equal to -1
4y-3x+9=0
4y=3x-9
y=(3/4)x-9/4 -----> the slope is m=3/4
The perpendicular slope is
m*(3/4)=-1
m=-4/3
step 2
Find the equation of the line into slope point form
y-y1=m(x-x1)
we have
(x1,y1)=(5,7)
m=-4/3
substitute
y-7=-(4/3)(x-5) ----> equation of the line into point slope form
Convert to slope intercept form ----> y=mx+b
y-7=-(4/3)(x-5)
y-7=-(4/3)x+(20/3)
y=-(4/3)x+(20/3)+7
y=-(4/3)x+(41/3) -----> equation of the line into slope intercept form
Convert to general form ----> Ax+By+C=0
y=-(4/3)x+(41/3)
Multiply by 3 both sides
3y=-4x+41
4x+3y-41=0 -----> equation of the line in general form
In a randomly generated list of numbers from 0 to 4, the chance that each
number can occur is 1/4.
A True
B. False
Answer: false
Step-by-step explanation:
Final answer:
The probability of any number from 0 to 4 appearing in a randomly generated list is 1/5, not 1/4. The false notion might come from misinterpreting randomness or falling prey to the gambler's fallacy.
Explanation:
Your question pertains to the concept of probability in a random distribution of numbers. Specifically, you are asking whether the probability of each number occurring in a randomly generated list of numbers from 0 to 4 is 1/4. This statement is false. Since there are five possible outcomes (0, 1, 2, 3, and 4), and assuming that each number has an equal chance of being selected, the correct probability of each number occurring would be 1/5, not 1/4.
The misconception that the probability is 1/4 likely arises from a misunderstanding of randomness and probability. People often have a preconceived notion of what randomness looks like, influenced by incidents of the gambler's fallacy, where they believe past events affect the likelihood of future events. Which is not mathematically accurate. For example, the gambler's fallacy is when someone thinks that after flipping a coin and getting heads multiple times, tails is 'due' to occur. However, each flip is independent, and the probability remains at 50% for heads or tails, regardless of past flips.
Understanding true randomness means recognizing that each outcome in a set of distinct outcomes has an equal chance of occurring, and that chance is determined by dividing 1 by the total number of possible outcomes. In the scenario with the list of numbers from 0 to 4, since there are 5 possible outcomes, the correct probability should be calculated as 1/5.
What is -5/3 / (-1/8)?
Please help me. i don't understand...
Answer:
40/3
Step-by-step explanation:
Here you're dividing the fraction -5/3 by the fraction -1/8.
Right off, we can simplify this by recalling that (-)(-) = (+), and so we have:
Divide 5/3 by 1/8.
There's a rule for dividing by a fraction: Invert the fraction and multiply. So, applying that rule here, we get:
5 8
---- * ---- = 40/3
3 1
equations standard form
f(x) x²- 3x - 54
Answer:
[tex]f\left(x\right)=x^2-3x-54[/tex]
Step-by-step explanation:
Given function is [tex]f\left(x\right)=x^2-3x-54[/tex].
Now we need to rewrite that equation in standard form.
Given equation is a polynomial function. So to write that in standard form, we need to rearrange terms in descending order of exponents of the variable (x).
We see that exponents of variable x are 2, 1 and 0.
Terms are already written in descending order of exponents.
Hence final answer is given function itself. [tex]f\left(x\right)=x^2-3x-54[/tex]
NEED HELP MARK BRAINLIEST
Answer:
C) 200.96 ft²Step-by-step explanation:
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
We have the diameter d = 16ft.
d = 2r, therefore r = (16 ft) : 2 = 8 ft.
Substitute:
[tex]A=\pi(8^2)=64\pi\ ft^2[/tex]
[tex]\pi\approx3.14\to A\approx(64)(3.14)=200.96\ ft^2[/tex]
Answer:
C) 200.96 ft²
Step-by-step explanation:
Area formula of a circle: A = πr²
radius = circumference/2 = 8 ft
Plug in: A = π(8)²
Multiply: A = 64π
Approximate+ Multiply: π ≈ 3.14 --> A ≈ 200.96 ft²
A whAt the theoretical probability
B experimental probability
Fractions in simplest form
With steps
Please
Answer:
a. [tex]\frac{1}{6}[/tex]
b. [tex]\frac{67}{450}[/tex]
Step-by-step explanation:
Theoretical probability is what we expect to happen and experimental probability is what actually happens.
a. In theoretical probability, it doesn't matter what happened in the past. So basically we want to know the probability of rolling a 3 when a number cube is rolled.
There are 6 faces (from 1 to 6) in a number cube. And there is 1 "3". So the probabilty of rolling a 3 is:
1/6
b. In experimental probability, we need to know what happened before. When the cube was rolled 450 times, it came up "3", 67 times.
Hence the experimental probabilty of rolling a "3" is:
67/450
What is the sum of the infinite geometric series?
Answer:
-288
Step-by-step explanation:
n=1/2 divided by -144. You then just plug that number which is .00347 into n in the equation and use a scientific calculator to find the answer.
The sum of the infinite geometric series is:
-288
Step-by-step explanation:We know that the sum of the infinite geometric series:
[tex]\sum_{n=1}^{\infty} ar^{n-1}[/tex]
is given by the formula:
[tex]Sum=\dfrac{a}{1-r}[/tex]
The series is given by:
[tex]\sum_{n=1}^{\infty} (-144)\cdot (\dfrac{1}{2})^{n-1}[/tex]
By looking at the series we observe that the first term of the series is:
[tex]a=-144[/tex]
and the common ratio of the series is:
[tex]r=\dfrac{1}{2}[/tex]
Hence, the sum of the series is:
[tex]Sum=\dfrac{-144}{1-\dfrac{1}{2}}\\\\Sum=\dfrac{-144}{\dfrac{1}{2}}\\\\Sum=-144\times 2\\\\Sum=-288[/tex]
3x-4y=16 and 5x+2y=44 using elimination strategy and comparing strategy
[tex]
3x-4y=16 \\
5x+2y=44 \\ \\
3x-4y=16 \\
10x+4y=88 \\ \\
13x=104 \\
x=\boxed{104\div13=8}\\ \\
3\times8-4y=16 \\
24-4y=16 \\
-4y=-8 \\
y=\boxed{2}
[/tex]
The points scored by a football team are shown in the stem-and-leaf plot below.
0| 6
1 | 2 3 4 7
2| 0 3 4 4 7 8 8 8
3| 0 7 8
Key
1 | 3 = 13 points
What was the median number of points scored by the football team?
4 + 4= 8/2= 4
the median number is 4
The answer is 24.
Hope this helps!
Help with 4 and 6
And is 5 correct?
Answer:
4) 0, -1, 1, 1, 1
5) correct
6) [tex]x = -2 \pm 2\sqrt5[/tex]
Step-by-step explanation:
4) fill in the previous sequence element in the next. This sequence gets "stuck" at 1.
6) use the quadratic formula.
Please help me with this and thank you
Answer:
The answer is D
Step-by-step explanation:
(12 + 6) x ( 11 - 7) = 72
18 x 4 = 72
72 = 72
Answer:
The answer is D.
Step-by-step explanation:
The only equation that equals 72 is letter D. if you add 12 + 6 you get 18 so now the equation is 18 * (11 - 7) = 72 then you do 11 - 7 and get 4 so now the equation is 18 * 4 = 72 and 18 * 4 equals 72 so your answer is correct.
A rectangular swimming pool is 17 meters long, 14 1/2 meters wide, and 3 1/2 meters deep. What is its volume?
Answer:
862.75 meters^3
Step-by-step explanation:
(17)(14.5)(3.5)=862.75
Answer:
862.75
Explanation:
17multiply by 14.5 multiply by 3.5
Which is the equation of the given line? (-10,-7) (3,-7)
Answer: [tex]y=-7[/tex]
Step-by-step explanation:
The equation of the line in Slope-intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
Find the slope with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Given the points (-10,-7) (3,-7), substitute values into the formula. Then:
[tex]m=\frac{-7-(-7)}{-10-3}\\\\m=\frac{0}{-13}\\\\m=0[/tex]
Substitute the slope and any point into [tex]y=mx+b[/tex] and solve for "b":
[tex]-7=0x+b\\b=-7[/tex]
Then, substituting "m" and "b" into the equation [tex]y=mx+b[/tex], you get that the equation of this line is:
[tex]y=0x-7[/tex]
[tex]y=-7[/tex]
Answer:
Step-by-step explanation:
the answer is y=-7
Solve the equation. When necessary, round to the nearest hundredth. 7^x = 14
Answer:
x = 1.36
Step-by-step explanation:
We are given the following equation;
7^x = 14
we are required to determine the value of x;
the first step is to introduce natural logs on both sides of the equation;
[tex]ln(7^{x})=ln(14)\\\\xln(7)=ln(14)\\\\x=\frac{ln(14)}{ln(7)}\\\\x=1.3562[/tex]
Rosie has some charms, c, for her charm bracelet. Ray gives Rosie 3 new charms.How many charms does Rosie have now? write an expression
Answer:
Rosie now has c+3 charms
Explanation:
We are given that the original number of charms that Rosie has is c
We know that Ray gave Rosie 3 new charms
This means that the number of charms that Rosie originally had increased by 3
To express this increase, we use addition where we add 3 to the original number of charms that she had
New number of charms = original number of charms + 3
New number of charms = c + 3
Hope this helps :)
Answer:
c+3
Step-by-step explanation: she already had c charms, since we do not know what c is equal to, we can only simplify the question down to c(what she had) +3(what ray gave her)
Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 then how many of each kind did she buy?
She bought 2 fancy shirts and 5 plain shirts.
2 x 28=$56, and 5x15=$75. 75 plus 56 is 131
Square ABCD is a dilation of square ABCD. What is the scale factor
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
2 divided by 6 is [tex]\frac{1}{3}[/tex]
To confirm it,
[tex]6 * \frac{1}{3} =2[/tex]
what is the equation of the graphed line
Answer:
y = 2x + 3
Step-by-step explanation:
The y-intercept is clearly marked: it's b = 3 (or 0, 3).
Going from the point (-3, -3) to the point (0, 3),
x increases by 3 and y increases by 6. Thus, the slope of the line through these two points is m = rise / run = 6 / 3, or m = 2.
Starting with the slope-intercept form of the equation of a straight line:
y = mx + b, we substitute 2 for m and 3 for b, obtaining:
y = 2x + 3
Answer:
y = 2x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 3, - 3) and (x₂, y₂ ) = (0, 3) ← 2 points on the line
m = [tex]\frac{3+3}{0+3}[/tex] = [tex]\frac{6}{3}[/tex] = 2
note the line crosses the y- axis at (0, 3) ⇒ c = 3
y = 2x + 3 ← equation of line
Which statement is true about the two lines whose equations are given below?
4x - 2y= 5
4x + 2y=5
Choices
They are parallel
They are perpendicular
They intersect but not perpendicular
The line coincide
Answer:
They intersect but not perpendicular.
8. Mr. Benson ran 5 2/3 miles. Miss Pagan
ran 6 1/3 miles and Mr. Caswall ran 5 4/5
miles. How many miles did the 5 grade
teachers run altogether?
Answer:
17 4/5
Step-by-step explanation:
Fist, add the whole numbers.
5 + 6 + 5 = 16
Now add the fractions.
2/3 and 1/3 have the same denominator so you can add easily.
2/3 + 1/3 = 3/3 = 1
Now 16 + 1 = 17
Then what's left is Mr. Caswall's 4/5 and then we add that to 17.
So it's 17 4/5
Hope this helps!
Answer:
17 4/5 miles.
Step-by-step explanation:
First add the integer parts of the mixed numbers:
5 + 5 + 6 = 16 miles.
Now add the fractions:
2/3 + 1/3 + 4/5
LCD of 3 and 5 is 15 so we have:
10/15 + 5/15 + 12/15
= 27/15
= 9/5
= 1 4/5 miles.
So our answer is 16 + 1 4/5
= 17 4/5 miles.