I'm assuming we factor...
The answer is (2a + c)(4a^2 - 2ac + c^2.)
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Answer:
(2a + c)(4a² - 2ac + c²)
Step-by-step explanation:
8a³ + c³ ← is a sum of cubes and factors in general as
a³ + b³ = (a + b)(a² - ab + b²)
Given
8a³ + c³
= (2a)³ + c³
= (2a + c)((2a)² - 2ac + c²), that is
= (2a + c)(4a² - 2ac + c²)
409 divided by 2 = a 24 R1 B 25 r1 C 204 R1 d 205 r1
Answer:
answer c-204 r1
Step-by-step explanation:
409 divided by 2 is 204.5 or 204 r1
Semicircles
whose centers A
are the midpoints .
of the sides of
square ABCD are .
drawn. If the
measure of each
side of the square
is 4 cm, what is the area, nearest to
the tenth of a sq cm, of the shaded
portion of the figure?
Answer:
The area of the shaded portion of the figure is [tex]9.1\ cm^2[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The shaded area is equal to the area of the square less the area not shaded.
There are 4 "not shaded" regions.
step 1
Find the area of square ABCD
The area of square is equal to
[tex]A=b^2[/tex]
where
b is the length side of the square
we have
[tex]b=4\ cm[/tex]
substitute
[tex]A=4^2=16\ cm^2[/tex]
step 2
We can find the area of 2 "not shaded" regions by calculating the area of the square less two semi-circles (one circle):
The area of circle is equal to
[tex]A=\pi r^{2}[/tex]
The diameter of the circle is equal to the length side of the square
so
[tex]r=\frac{b}{2}=\frac{4}{2}=2\ cm[/tex] ---> radius is half the diameter
substitute
[tex]A=\pi (2)^{2}[/tex]
[tex]A=4\pi\ cm^2[/tex]
Therefore, the area of 2 "not-shaded" regions is:
[tex]A=(16-4\pi) \ cm^2[/tex]
and the area of 4 "not-shaded" regions is:
[tex]A=2(16-4\pi)=(32-8\pi)\ cm^2[/tex]
step 3
Find the area of the shaded region
Remember that the area of the shaded region is the area of the square less 4 "not shaded" regions:
so
[tex]A=16-(32-8\pi)=(8\pi-16)\ cm^2[/tex]
---> exact value
assume
[tex]\pi =3.14[/tex]
substitute
[tex]A=(8(3.14)-16)=9.1\ cm^2[/tex]
of the 20 basketball games so far this year,tracy has attended 14.what percent of basketball games has tracy attended
Answer: Tracey attended 70% of the basketball games.
Step-by-step explanation:
you would multiply 14 by 100then you would multiply 20 by xthat equals 1400=20xthen you divide both sides of the equal sign by 20and get 70%Answer:
70%
Step-by-step explanation:
As a fraction, 14 / 20.
If you multiply the 2 Terms by 5, you would get 70 / 100 which equals 70%.
Best of Luck!
complete the equcomplete the equation of the line whose slope is -2 and y intercept is (0,3)ation of the line whose slope is -2 and y intercept is (0,3)
Complete the equation of the line whose slope is -2 and y intercept is (0,3)
Answer:The equation of the line whose slope is -2 and y intercept is (0,3) is y = -2x + 3
Solution:Given that line has slope of -2 and y - intercept of (0, 3)
We have to find the equation of line
The equation of line can be found by using the slope intercept form
The slope intercept form is given as:
y = mx + c
Where "m" is the slope of line and "c" is the y-intercept
Here given that slope = m = -2
y - intercept is the y-coordinate of a point where a line intersects the y-axis.
So here y intercept is (0, 3) and we get c = 3
Substituting the values in slope intercept form we get,
y = -2x + 3
Thus the equation of line is found
Need help on 5
Is it function and explain why.
Answer:
#5
It is not a function because the some x-values can have more than one possible y-value. The x-values can have the positive and negative y-value.
Step-by-step explanation:
The equation is the equation for a circle. When you graph a circle, it does not pass the vertical line test.
Example: if x is 6
6² + y² = 100
36 + y² = 100
y² = 100 - 36
y² = 64
y = ± √64 This is true because: (-8)² = 64 AND 8² = 64
y = -8 OR 8
By the way, for #4 it is not a function.
The points (13, 4) and (13, -4) mean that x will have more than one y value. The x-value 13 will have y-values 4 and -4.
All 203 students at Polk School eat lunch at the same time. One
day 19 students were absent. If 8 students sit at each table in
the lunchroom, how many tables were used that day at lunch?
Answer:
The number of tables were used that day at lunch is 23 tables.
Step-by-step explanation:
Given as :
The total number of students in the Polk school = 203
On one day the number of students absent = 19
So, The number of student present on that day = Total student - absent students
I.e The number of student present on that day = 203 - 19 = 184
The number of students sit on each table = 8
Let The number of tables were used that day at lunch = n
So, According to question
The number of tables were used that day at lunch = [tex]\dfrac{\textrm The number of student present on that day}{\textrm Total number of students sit on each table}[/tex]
I.e n = [tex]\frac{184}{8}[/tex]
∴ n = 23 tables
So, The number of tables were used that day at lunch = n = 23 tables
Hence, The number of tables were used that day at lunch is 23 tables. Answer
Write a linear function f with the values f(2)=4 and f(−7)=9. A function is f(x)=
Answer:
f(x) = -5/9 x + 5 1/9
Step-by-step explanation:
f(2)=4 and f(−7)=9 means the line pass through (2,4) and (- 7,9)
f(x) = mx + b
m = (y-y') / (x-x') = (9 - 4) / (- 7 - 2) = - 5/9
for (2,4) : b = f(x) - mx = y - mx = 4 - (- 5/9) x 2 = 4 + 10/9 = 46/9 = 5 1/9
f(x) = -5/9 x + 5 1/9
check for (-7, 9) f(-7) = (-5/9) * (-7) + 5 1/9 = 35/9 + 46/9 = 81/9 = 9
Final answer:
The linear function that satisfies the given points f(2)=4 and f(-7)=9 is f(x) = (-5/9)x + (46/9).
Explanation:
To write a linear function f(x) that satisfies f(2)=4 and f(-7)=9, one must determine the slope and y-intercept of the line. A linear function has the form y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope using the two points (2, 4) and (-7, 9):
Slope (m) = (y2 - y1) / (x2 - x1) = (9 - 4) / (-7 - 2) = 5 / -9.
Now we have the slope which is -5/9. We can use one of the points and the slope to find the y-intercept (b). Let's use the point (2, 4):
4 = (-5/9)(2) + b
b = 4 + (10/9) = 46/9
Therefore, the linear equation of the function is:
f(x) = (-5/9)x + (46/9).
the smith family is driving to a vacation spot the number of miles they have left is 540-60x where x represents the number of driving hours what does 60x represent
Answer:
The number of miles traveled for x hours
Step-by-step explanation:
Question 8 of
Question 8 (2 points)
What values of x satisfy the equation 2x2 + 3x – 10 = 2x + 5
a
x
=3/2 or x=-5
x=-5/2 or x=2
x=10 or x=-1/2
X=-3 or x=5/2
Next Page
Back
Answer:
[tex]x=-3\ or\ \frac{5}{2}[/tex]
Step-by-step explanation:
Given:
Given equation is.
[tex]2x^{2} +3x-10=2x+5[/tex]
Find values of x?
Solution.
[tex]2x^{2} +3x-10=2x+5[/tex]
[tex]2x^{2} +3x-10-2x-5=0[/tex]
[tex]2x^{2} +x-15=0[/tex]
Find the roots of the equation.
compare the above equation with [tex]ax^{2} +bx+c=0[/tex]
Therefore, [tex]a=2,b=1,c=-15[/tex]
[tex]x=\frac{-b\pm\sqrt{(b)^{2}-4ac}}{2a}[/tex]
Put a,b and c value in above equation.
[tex]x=\frac{-1\pm\sqrt{(1)^{2}-4(2)(-15)}}{2(2)}[/tex]
[tex]x=\frac{-1\pm\sqrt{1-8(-15)}}{4}[/tex]
[tex]x=\frac{-1\pm\sqrt{1+120}}{4}[/tex]
[tex]x=\frac{-1\pm\sqrt{121}}{4}[/tex]
[tex]x=\frac{-1\pm\sqrt{(11)^{2}}}{4}[/tex]
[tex]x=\frac{-1\pm 11}{4}[/tex]
For positive sign
[tex]x=\frac{-1+ 11}{4}[/tex]
[tex]x=\frac{10}{4}[/tex]
[tex]x=\frac{5}{2}[/tex]
For negative sign
[tex]x=\frac{-1- 11}{4}[/tex]
[tex]x=\frac{-12}{4}[/tex]
[tex]x=-3[/tex]
[tex]x=-3\ or\ \frac{5}{2}[/tex]
Therefore, the value of [tex]x=-3\ or\ \frac{5}{2}[/tex] satisfy the given equation.
What is the standard form of the equation 6, -3 with a slope of two over three
Answer:
The equation of line is y= [tex]\dfrac{2}{3}[/tex] x - 7
Step-by-step explanation:
Given as :
The points as [tex]x_1[/tex] = 6
And [tex]y_1[/tex] = - 3
The slope of the line = m = [tex]\dfrac{2}{3}[/tex]
Now, The equation of line in slope-point form
y - [tex]y_1[/tex] = m × (x - [tex]x_1[/tex])
Or, y - (-3) = [tex]\dfrac{2}{3}[/tex] × (x - 6)
Or, y + 3 = [tex]\dfrac{2}{3}[/tex] × (x - 6)
Or, 3 × (y + 3) = 2 × (x - 6)
Or, 3 y + 9 = 2 x - 12
Or, 3 y = 2 x - 12 - 9
Or, 3 y = 2 x - 21
∴ y = [tex]\dfrac{2}{3}[/tex] x - [tex]\dfrac{21}{3}[/tex]
i.e y = [tex]\dfrac{2}{3}[/tex] x - 7
So, The equation of line = y = [tex]\dfrac{2}{3}[/tex] x - 7
Hence, The equation of line is y= [tex]\dfrac{2}{3}[/tex] x - 7 Answer
which of the following are true statements? Check all that apply logM^(p)=p*logM log ((M)/((N)))=logM-logN log ((M)/((N)))=(logM)/(logN) (logM)^(p)=p*logM
The expressions logM^(p)=p*logM and log ((M)/((N)))=logM-logN both correctly apply rules of logarithm, while log ((M)/((N)))=(logM)/(logN) and (logM)^(p)=p*logM don't.
Explanation:The subject matter involves logarithmic identities in Mathematics, specifically, rules of logarithms. Logarithms have certain properties that allow us to simplify complex expressions.
Let's go through each expression:
logM^(p)=p*logM: This is a correct identity. It's known as the power rule of logarithms, which states that the log of a number raised to an exponent is equal to the exponent multiplied by the log of the number. log ((M)/((N)))=logM-logN: This is also a correct identity. It's known as the quotient rule of logarithms, which states that the log of a quotient is the difference of the logs. log ((M)/((N)))=(logM)/(logN): This statement is false. It's an incorrect assumption about the rules of logarithms. (logM)^(p)=p*logM: This statement is also false. The power in this case refers to the exponent on the entire log term, which is different from the power rule. Learn more about Rules of Logarithms here:https://brainly.com/question/30287525
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Brook states that the distance on the line is 4 units. Caleb states that the whole line does not have a distance because it continues on forever. Vivian states that the line is 6 units long.
Answer:
kaleb is correct
Step-by-step explanation:
The awsner is Brook did the distance between L and M, Vivian however did the distance between M and N. Hope this helps you
A circle is divided into 6 equal parts. what is the total angle measure of 1 part?
Answer:
[tex]dis \: is \: easy \\ angle \: in \: a \: circle = 360 \\ the \: angle \: is \: divided \: into \: six \: part \\ divide \: the \: 360 \: by \: 6 \\ \frac{360}{6} = 60 \\ therefore \: the \: angle \: of \: one \: part \: \\ = 60 \: degree[/tex]
Marty's class collected $16.00 in a school-wide penny collection contest.If Tommy's class collected,x, and then multiplied the difference by 2,they would have the same amount of money as Marty's class.How much money did Tommy's class collect?
A.$23.00
B.$13.00
C.$18.00
D.$5.00
Final answer:
Tommy's class collected $8.00.
Explanation:
To find out how much money Tommy's class collected, we can set up an equation:
x * 2 = 16.00
Solving for x, we divide both sides of the equation by 2:
x = 8.00
Therefore, Tommy's class collected $8.00.
What is 0.21666667 as a rounded percent
Answer:
23%
Step-by-step explanation: ???
What is the radian measure of the central angle of a circle of radius 1.5 meter that intercepts an arc of length 600 centimeters
Radian measure of the central angle is 4 radian
Solution:
Given that,
A circle of radius 1.5 meter that intercepts an arc of length 600 centimeters
To find: Radian measure of the central angle
Let us find the circumference of circle
The circumference of circle is given as:
[tex]\text{ circumference of circle } = 2 \pi r[/tex]
Where "r" is the radius of circle
[tex]\text{ circumference of circle } = 2 \times \pi \times 1.5 = 3 \pi[/tex]
Therefore circumference of circle = [tex]3 \pi[/tex] meters , which subtends central angle of [tex]2 \pi[/tex] radian
Given that arc of length 600 centimeters. Let us convert 600 centimeter to meter
We know that, to convert centimeter to meter divide the length value by 100
[tex]\text{ 600 centimeter } = \frac{600}{100} \text{ meter } = 6 \text{ meter}[/tex]
Therefore arc of 6 meter will subtend a central angle of:
[tex]\rightarrow \frac{6}{3 \pi} \times 2 \pi = 4[/tex]
Therefore radian measure of the central angle is 4 radian
Is x=4 and y=5 perpendicular
Answer:
The statement is true
The lines are perpendicular
Step-by-step explanation:
we have
[tex]x=4[/tex] ----> equation A
The equation A represent a vertical line (is parallel to the y-axis)
The slope is undefined
[tex]y=5[/tex] ----> equation B
The equation B represent a horizontal line (is parallel to the x-axis)
The slope is equal to zero
Remember that
The y-axis and the x-axis are perpendicular lines
so
Line A and line B are perpendicular lines too
therefore
The statement is true
What is the approximate circumference of the circle shown below?
A. 37.8 cm
B. 92.9 cm
C. 46.5 cm
D. 23.2 cm
Answer:c
Step-by-step explanation:
Answer:
Step-by-step explanation:
C
What is the domain and range of Y=3X-7.25? can someone please help?
Answer:
Domain and range of the equation
Y = 3X-7.25
will be Set of all Real numbers.
Step-by-step explanation:
Because at any value of x, you will get a respective value of y. For example if you put X=0, then y=7.25. You can put any value of X in the equation and for each value equation will be true and will give respective value of y.
omplete the paragraph proof.
Given: M is the midpoint of
Prove: ΔPKB is isosceles
Triangle P B K is cut by perpendicular bisector B M. Point M is the midpoint of side P K.
It is given that M is the midpoint of and . Midpoints divide a segment into two congruent segments, so . Since and perpendicular lines intersect at right angles, and are right angles. Right angles are congruent, so . The triangles share , and the reflexive property justifies that . Therefore, by the SAS congruence theorem. Thus, because _____________. Finally, ΔPKB is isosceles because it has two congruent sides.
corresponding parts of congruent triangles are congruent
base angles of isosceles triangles are congruent
of the definition of congruent segments
of the definition of a right triangle
Answer:
Complete paragraph proof withe Diagram is below.
Δ PMB ≅ Δ KMB ...........SAS congruence theorem
∴ PB ≅ KG ......corresponding parts of congruent triangles are congruent
Step-by-step explanation:
Complete the paragraph proof.
Given: M is the midpoint of
Prove: ΔPKB is isosceles
Triangle P B K is cut by perpendicular bisector B M. Point M is the midpoint of side P K.
It is given that M is the midpoint of and . Midpoints divide a segment into two congruent segments, so . Since and perpendicular lines intersect at right angles, and are right angles. Right angles are congruent, so . The triangles share , and the reflexive property justifies that . Therefore, by the SAS congruence theorem. Thus, because __corresponding parts of congruent triangles are congruent _.
Finally, ΔPKB is isosceles because it has two congruent sides.
Δ PMB ≅ Δ KMB ...........SAS congruence theorem
∴ PB ≅ KG ......corresponding parts of congruent triangles are congruent
Answer: A
Step-by-step explanation:
if you draw two right triangles using the line as the hypotenuse, do the triangles have to be similar? Why or why not?
Answer:
All the right triangles will be similar.
Step-by-step explanation:
See the attached diagram.
Let us assume any two right triangles are drawn on the line OP, and AB and A'B' as the hypotenuse on the same line OP.
Since the slope of the line OP is constant and assume that it makes x° with the positive x-axis.
Hence, [tex]\tan x = \frac{AC}{BC} = \frac{A'C'}{B'C'}[/tex]
⇒ [tex]\frac{AC}{A'C'} = \frac{BC}{B'C'}[/tex]
Therefore, the sides of the two right triangles are in the same ratio and hence, Δ ABC and Δ A'B'C' are similar.
Hence, all the right triangles will be similar. (Answer)
67+46
Find the solution and model how you found your answer
113
Step-by-step explanation:
7 plus 6 is 14 carry the one over to the 6 of the 67 then add the one the six and the four that equals 11
that gets you
113
Easy + brainliest
2x(^3) + 10x(^2) − 4x(^2)y − 20xy
factor this pls, (show all work)
Answer:
2x(x + 5)(x - 2y)
Step-by-step explanation:
Given
2x³ + 10x² - 4x²y - 20xy ← factor out 2x from each term
= 2x(x² + 5x - 2xy - 10y)
Factor the first/second and third/fourth terms inside the parenthesis
= 2x(x(x + 5) - 2y(x + 5)) ← factor out (x + 5) from each term in the parenthesis
= 2x(x + 5)(x - 2y)
1000 into an account that is growing 4.2% per year. What should you do to the pervious years amount
Answer:
The amount into account after a year is $1042
Step-by-step explanation:
Given as :
The principal amount into the account = p = $1000
The amount is growing at the rate = r = 4.2 % per year
Let The Amount into account after 1 year = $A
So, According to question
The amount into account after 1 year = The principal amount × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm 1}[/tex]
Or, A = $1000 × [tex](1+\dfrac{\textrm 4.2}{100})^{\textrm 1}[/tex]
Or, A = $1000 × 1.042
Or, A = $1042
So, The amount into account after a year = A = $1042
Hence,The amount into account after a year is $1042 . Answer
which way is the closest estimate of this product 518 * 5
518x5=2,590, So your estimate is about 2,600, Because we want to round up, So we look in the tens place and we see a nine, so that means we go up on, Also 5 and up means we gonna round up and 5 and below means we gonna round down.
The answer to 518*5 is 2590 or rounded, 3000, or 2600.
You can get your answer my multiplying 518 by 5 and rounding it to the nearest thousands place, hundreds place or tens place.
Hope this helped!
An old house has a basement stairway that has steps with 7.25 inch vertical risers and 7 inch horizontal treads. What is the slope of the stairway? Round to two decimal places.
Answer:
1.04 inch
Step-by-step explanation:
Given: Old house has a basement stairways with 7.25 inch vertical riser and 7 inch horizontal treads.
Remember; horizontal treads is known as run in steps.
Now, calculating the slope of the stairways.
Formula: [tex]Slope= \frac{Rise}{Run}[/tex]
Rise= 7.25 inch
Run= 7 inch.
Subtituting the value in the formula
Slope= [tex]\frac{7.25}{7}= 1.0357 \approx 1.04[/tex] (∵ Round to two decimal)
∴ Slope of stairways is 1.04.
paolo read 40 books in one year 35% of the books paolo read were non fiction. how many nonfiction and fiction books did he read?
Answer:
Paolo reads in total 26 fiction and 14 non- fiction books.
Step-by-step explanation:
Here, the total number of books read by Paolo = 40 books
The percentage of non-fiction books read = 35%
Now, 35% of total books read = 35% of 40
⇒ [tex]\frac{35}{100} \times 40 = 14[/tex]
So, the number of non -fiction books read by Paolo = 14
Now, the number of fiction booosk read
= Total books read - Non- Fiction books read
= 40 - 14 = 26
So, the number of fiction books read by Paolo = 26
Hence, Paolo reads in total 26 fiction and 14 non- fiction books.
1/3 the weight of a bar of gold plus 30 pounds equals the weight of that bar of gold. How much does the bar of gold weigh?
Answer:
Step-by-step explanation:
Final answer:
To find the weight of the bar of gold, solve the equation (1/3)x + 30 = x, where x represents the weight of the bar. After simplifying, the weight of the bar is found to be 45 pounds.
Explanation:
To solve this problem, let's assume the weight of the bar of gold is x pounds. According to the given information, one-third of the weight of the bar of gold plus 30 pounds equals the weight of the bar of gold. This can be written as:
(1/3)x + 30 = x
To solve for x, we can start by subtracting (1/3)x from both sides of the equation:
(1/3)x + 30 - (1/3)x = x - (1/3)x
This simplifies to:
30 = (2/3)x
To isolate x, we can multiply both sides of the equation by 3/2:
(3/2)(30) = (3/2)(2/3)x
45 = x
Therefore, the bar of gold weighs 45 pounds.
Which expressions are equivalent to z+(z+6)?
Answer: [tex]2 z + 6[/tex] and [tex]2 (z + 3)[/tex]
Step-by-step explanation:
We have te following expression:
[tex]z+(z+6)[/tex]
Which can be written as:
[tex]z+z+6=2z+6[/tex]
Applying common factor 2 in the right side of the equation:
[tex]z+z+6=2(z+3)[/tex]
A bookstore costs $105 a day to keep open, and it spends $12 for each book
that it sells. If each book sells for $15, what is the break-even point for this
bookstore?
After selling 35 books, the store will break-even.
Step-by-step explanation:
Given,
Cost required per day to keep store open = $105
Amount spent on each book = $12
Let,
n be the number of books.
Total costs = 12n + 105
Selling price of each book = $15
Total revenue = 15n
For braking even;
Costs = Revenue
[tex]12n+105=15n\\105=15n-12n\\105=3n\\3n=105[/tex]
Dividing both sides by 3
[tex]\frac{3n}{3}=\frac{105}{3}\\n=35[/tex]
After selling 35 books, the store will break-even.
Keywords: revenue, cost, division
Learn more about division at:
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