Answer
Option B is correct.
64x³ + 27 = (4x + 3) (16x² - 12x + 9)
Explanation
We are told to factorize
64x³ + 27
To do this, we use the factorization of (x³ + y³) as a guide. First of,
(x + y)³ = (x + y) (x + y)² = (x + y) (x² + 2xy + y²)
(x + y)³ = x³ + y³ + 3x²y + 3xy²
So, we can write
x³ + y³ = (x + y)³ - 3x²y - 3xy² = (x + y)³ - 3xy(x + y)
= (x + y) [(x + y)² - 3xy]
= (x + y) (x² + y² + 2xy - 3xy)
= (x + y) (x² - xy + y²)
So, comparing (64x³ + 27) with (x³ + y³), we can see that
64x³ = (4x)³
27 = (3)³
(64x³ + 27) = (4x)³ + 3³
x³ + y³ = (x + y) (x² - xy + y²)
(4x)³ + 3³ = (4x + 3) [(4x)² - (4x × 3) + 3²]
= (4x + 3) (16x² - 12x + 9)
Hope this Helps!!!
What do all the points on this line have in common?
B. The points have an x-coordinate in common.
C. The general equation of a vertical line is x = c, where c is a constant.
Working with special triangles. Find y. I have attached the picture.
In this case, we'll have to carry out several steps to find the solution.
Step :
Data:
diagram:
right triangle
Step 02:
special right triangles:
we must analyze the triangle to find the solution.
special right triangle example:
right triangle:
side y:
[tex]\begin{gathered} 88\text{ = }\sqrt{2}y\text{ } \\ \\ \frac{88}{\sqrt{2}}\text{ = y} \end{gathered}[/tex]That is the full solution.
What is the total number of college student round your answer to the nearest million
EXPLANATION:
From the data provided, 46% of all college students were enrolled part-time.
We also know that this percentage is represented by 7.8 million students. If the total number of students is given as x, then we can derive the following equation;
[tex]Total=\begin{cases}46\text{\%=7.8m} \\ 100\text{\%=x} \\ \square\end{cases}[/tex][tex]\frac{7.8}{46}=\frac{x}{100}[/tex]Cross multiply the above equation and you'll have;
[tex]\begin{gathered} \frac{7.8\times100}{46}=x \\ 16.9665=x \\ \text{Rounded to the nearet million, } \\ x\approx17 \end{gathered}[/tex]ANSWER:
The total number of students (rounded to the nearest million) therefore is 17 million.
The braking distance of a car is proportional to the square of its speed.17. According to Graham's law, the rate of diffusion of two gases is inverselydproportional to density and is given bywhere ', and r2 are12rates of diffusion of two gases and d, and d2 are their respectivedensities. Which equation represents d, in terms of the other variables?
Ok in this problem you have to take Graham's law which is given to you and manage to write the density d1 as a function of the others. We have:
[tex]\frac{r_1}{r_2}=\sqrt[]{\frac{d_2}{d_1}}[/tex]Since we want to have d1 alone in one side of the equation the first thing we have to do is pass the square root to the other side. Square roots pass as square powers:
[tex](\frac{r_1}{r_2})^2=\frac{d_2}{d_1}[/tex]Then we have to pass d1 multiplying on the other side:
[tex]d_1\frac{r^2_1}{r^2_2}^{}=d_2[/tex]Now we only need to pass both r1 and r2:
[tex]d_1=d_2\frac{r^2_2}{r^2_1}[/tex]This is the same expresion that the one in item B so that is the correct answer
A triangle has angle measures of 27 degrees , 50 degrees, and x degrees, use the triangle sum theorem to find the value of x.
ANSWER:
Angle x is 103 degrees
EXPLANATION
The sum of all the angles in a triangle is 180 degrees
Hence, Let angle A = 27 degrees
Angle B = 50 degrees
Angle C = x degrees
Triangle sum theorem state that
50 + 27 + x = 180
77 + x = 180
x = 180 - 77
x = 103 degrees
Which of the following options could you do before subtracting the equations so that one variable will be eliminated when you subtract them?
We need to do something to both equations so we can eliminate one variable
We can multiply the first equation by 3 and the second equation by 4
3( 4x-2y = 7) yields 12x -6y = 21
4( 3x-3y = 15) yields 12x -12y = 60
Now when we subtract
12x -6y = 21
-(12x -12y = 60)
---------------------------
12x -6y = 21
-12x +12y = -60
------------------------
6y = 39
The x terms are eliminated
Choice D multiply the top equation by 3 and the bottom equation by 4
CAN SOMEONE HELP WITH THIS QUESTION?✨
The coterminal angle is 943° .
What is a coterminal angle?Coterminal angles are angles with the starting side on the positive x-axis and a shared terminal side. They are in standard position. Examples include the coterminal nature of the angles 30, -330, and 390. The phrase "coterminal angle" refers to angles with the same starting side and terminal side. If the specified angle is given in radians or degrees, finding coterminal angles is as easy as adding or subtracting 360° or 2 to each angle. It is possible to find all possible coterminal angles. The coterminal angle is described in mathematics as the angle formed by two angles drawn side by side in the same plane. Furthermore, both of them share the same location for their terminal sides. As an illustration, 405 and -315 are the coterminal angles of 45.
1294° = 360° + 934°
So the coterminal angle for 1294° is 934° .
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Please Help! An eight foot ladder leans against a building. if the ladder makes an angle of 60 degrees with the ground, haw far from the building is the base of the ladder. Round you answer to the nearest tenth.
The base of the ladder is 4 ft away from the buliding
Here, we want to calculate the distance from the building to the base of the ladder
To properly answer this, an image of the question is needed
We have this as follows;
From the diagram, what we want to calculate is the distance d
To calculate this, we need the appropriate trigonometric identity
Firstly, we need to identify the parts of the triangle present
As we can see, we have the hypotenuse which is the side that faces the right angle and also is the longest side
The side we want to get is the adjacent
Mathematically, the trigonometric ratio that connects the adjacent to the hypotenuse is the cosine
Thus, we have it that;
[tex]\begin{gathered} \cos \text{ 60 = }\frac{d}{8} \\ \\ d\text{ = 8 cos 60} \\ d\text{ = }4.0\text{ ft} \end{gathered}[/tex]Pieter sailed his sailboat 1,260 yards in 30 minutes . What is the average number of yards of yards he traveled per minute ? A. 21 B. 30 C. 42
Given:
Distance Pieter sailed = 1260 yards
Time taken to sail = 30 minutes
Let's solve for the average number of yards he traveled per minute.
To find the average number of yards he traveled per minute, apply the formula:
[tex]\begin{gathered} A=\frac{\text{distance in yards}}{time\text{ in minute}} \\ \\ A=\frac{1260}{30}\frac{\text{yards}}{\text{minutes}} \\ \\ A=42\text{ yards per minute} \end{gathered}[/tex]Therefore, the average number of yards he traveled per minute is 42 yards per minute.
ANSWER:
C. 42
8. If the slope of the equation y = -3/5x + 4 is changed to 3/5 and the y-intercept is changed to -4, which statement best describes this situation? You can use a calculator to graph or create your own graph.*A The new line is perpendicular to the original line. B The new line is parallel to the original line. C The new line and the original line have the same y-intercept. D The new line and the original line have the same x-intercept.
Answer:
Explanation:
Given that the line
[tex]y=-\frac{3}{5}x+4[/tex]is changed to
[tex]y=\frac{3}{5}x-4[/tex]|- 1/5| ? |-0.8|what’s the missing inequality symbol?
Given:-
[tex]|-1\frac{1}{5}|,|-0.8|_{}[/tex]To find the correct inequality between the given datas.
So now we simplify. so we get,
[tex]|-1\frac{1}{5}|=|-\frac{6}{5}|=|-1.2|[/tex]So we get,
[tex]\begin{gathered} |-1.2|=1.2 \\ |-0.8|=0.8 \end{gathered}[/tex]So the inequality is,
[tex]1.2>0.8[/tex]can you please help me with this question. it's geometry
To find the angle A we need to find first the value of x. To do this we need to use the fact the the addition of the interior angles of any triangle is 180°.
The right side angle is equatl to 4x+4 since its vertically opposite to the one shown in the picture. The upper angle is 100° since it has to be supplementary to the angle of 80° shown in the picture.
With this in mind we have the equation:
[tex](4x+4)+(4x+4)+100=180[/tex]Solving for x we have:
[tex]\begin{gathered} (4x+4)+(4x+4)+100=180 \\ 8x+108=180 \\ 8x=180-108 \\ 8x=72 \\ x=\frac{72}{8} \\ x=9 \end{gathered}[/tex]Once we know the value of x we plug it in the expression for the angle A:
[tex]4(9)+4=40[/tex]Therefore the angle A is 40°.
#1) Write the ratio of 60 km in 28 minutes in simplest form.#2) Is this ratio a rate? Explain your answer using words. [C
1. Expressing 60km per 28 minutes in its simplest form requires us to get it per 1 minute. This, we can easily obtain by:
[tex]\frac{60\operatorname{km}}{28\min}=\frac{15\operatorname{km}}{7\min}=2\frac{1}{7}\frac{km}{\min }[/tex]2.143 km per minute
2. The ratio is a rate. A rate is a measure of a quantity with respect to another, especially with respect to time.
As can be seen, this ratio is speed. Speed is a measure of distance covered per time.
What is the perimeter of the isosceles triangle ABC such that angle A= angle C ?
Given angle A=angle C.
The objective is to find the perimeter of the isosceles triangle ABC.
First let's find the value of x.
An isosceles triangle contains two equal sides. Here angle A and angle C are equal. So the sides AB and AC are equal.
[tex]\begin{gathered} AB=BC \\ 5x-1=3x+11 \\ 5x-3x=11+1 \\ 2x=12 \\ x=\frac{12}{2} \\ x=6 \end{gathered}[/tex]Now, find the perimeter of the triangle by adding all the sides of the triangle.
[tex]P=5x-1+3x+11+x+19[/tex]Substittue the value of x =6.
[tex]\begin{gathered} P=5(6)-1+3(6)+11+6+19 \\ P=30-1+18+11+6+19 \\ P=83 \end{gathered}[/tex]Hence, the perimeter of the triangle is 83.
[tex]\begin{gathered} \text{Let's check the whether the obtained x value if correct.} \\ AB=BC \\ 5x-1=3x+11 \\ 5(6)-1=3(6)+11 \\ 30-1=18+11 \\ 29=29 \end{gathered}[/tex]Thus the sides of isoscles triangles are equal. Hence the value of x is correct.
Ann, justin, and kevin sent a total of 88 text message during the weekend. Ann sent 8 more message than justin. kevin sent 3 times as many message as justin. how many message did they each send
let the no. of message sent by Ann is A,
the no. of the message sent by Justin is J
the no. of the message sent by Kevin is K
sum of messages is = 88
A + J + K = 88
it is given that Ann sent 8 more messages than justiJustinn.
A = J + 8
Kevin sent 3 times as many as Justin.
K = 3 J
substitute all the values ,
(J + 8 ) + J + ( 3 J) = 88
5J + 8 = 88
5J = 88 - 8
5J = 80
J = 80/5
J = 16
messages sent by Ann is A = J + 8 = 16 + 8 = 24 message
messages sent by Ann is 24 messages
messages sent by Justin is J = 16 message
messages sent by Justin is 16 messages
messages sent by Kevin is K = 3J = 3 x 16 = 48 message
messages sent by Kevin is 48 message.
The product of two factors is x2 – X – 20. If one of the factors is x-5, what is the other factor?
we can rewrite the statement
[tex](x-5)(A)=x^2-x-20[/tex]where A is the missing factor, A must be of the form
[tex](x+a)[/tex]where a is a constant, to obtain "a" we must bear in mind that the multiplication of the two constants must give us the third term and the sum of these must give us the second term
so
[tex]\begin{gathered} -5\times a=-20 \\ -5+a=-1 \end{gathered}[/tex]if we solve any equation, the value of a is 4
so a is 4 and the factor is
[tex](x+4)[/tex][tex](x-5)(x+4)=x^2-x-20[/tex]To solve the inequality -7x<24, the inequality sign must be reversed.A. TrueB. False
ANSWER
True
EXPLANATION
To solve the inequality given:
-7x < 24
we have to divide both sides of the inequality by -7.
Dividing both sides of an inequality causes the sign to change direction (or be reversed) and so we will have:
x > -24 / 7
Therefore, it is true that the sign will be reversed.
1. Solve -4x < -3(6x - 2) and sketch the solution set on a number line.
We need to solve the inequality:
[tex]-4x<-3\mleft(6x-2\mright)[/tex]Let's multiply right side out and take variables to one side and numbers to another. The process is shown below:
[tex]\begin{gathered} -4x<-3\mleft(6x-2\mright) \\ -4x<-18x+6 \\ -4x+18x<6 \\ 14x<6 \\ x<\frac{6}{14} \\ x<\frac{3}{7} \end{gathered}[/tex]The solution set is:
[tex]\begin{gathered} x<\frac{3}{7} \\ or \\ x<0.4286 \end{gathered}[/tex]This means that x is less than 3/7, or
x is less than 0.4286
On the number line it looks:
Calculate the mean for each set of data round to the nearest tenths
The mean is the average of the numbers.
It is easy to calculate: add up all the numbers, then divide by how many numbers there are
[tex]\bar{x=\frac{\sum ^{\square}_{\text{ of numbers}}}{Number\text{ of items}}\text{ }}[/tex]the numbers given in the question are
[tex]2,11,5,6,13,4,9[/tex]there are 7 numbers in total.
Therefore, the mean will be
[tex]\begin{gathered} \operatorname{mean}=\frac{2+11+5+6+13+4+9}{7} \\ \operatorname{mean}=\frac{50}{7} \\ \operatorname{mean}=7.143 \\ to\text{ the nearest tenths, the mean is} \\ \operatorname{mean}=7.1 \end{gathered}[/tex]Hence,
the mean of the above set of values to the nearest tenth is = 7.1
Thelma performed a construction on a quadrilateral.Her work is shown below..EBсDWhich statement is justified by her construction?AD – AEAE - BEAD – BCO ADAD ~ DC
Looking at the image, we can see that the arc created in point E was created with the same radius of segment AD (that is, A is the center of a circle that contains both arcs that pass through points D and E).
From that construction, we can affirm that segments AD and AE are congruent.
Therefore the correct option is the first one.
If f (x) = -3x - 2, find each value
Given:
The function is given as
[tex]f(x)=-3x-2[/tex]Required:
We want to find the value of
[tex]f(-7)[/tex]Explanation:
[tex]f(-7)=-3(-7)-2=21-2=19[/tex]Final answer:
19
The distances between Centerville, Springfield, and Capital City form a right triangle. The distance between Centerville and Springfield is 913 kilometers and the distance between Springfield and Capital City is 976 kilometers. View the map.
Answer:
The distance between Centerville and Capital City is 1336 kilometers.
Step by step explanation:
To solve the situation, we can use the Pythagorean theorem, which is represented by the following expression and diagram:
Now, if a=913 kilometers and b=976 kilometers. Solve for c:
[tex]\begin{gathered} 913^2+976^2=c^2 \\ c=\sqrt[]{913^2+976^2} \\ c=\sqrt[]{833569+952576} \\ c=\sqrt[]{1786145} \\ c=1336\text{ kilometers} \end{gathered}[/tex]Pryz is a rhombus. If RK=5, RY=13 and M
Remember that
In a Rhombus
All sides are equal
Diagonals bisect each other perpendicularly
so
Part 22
Find out KY
In the right triangle RYK
Applying the Pythagorean Theorem
RY^2=RK^2+KY^2
substitute given values
13^2=5^2+KY^2
KY^2=13^2-5^2
KY^2=144
KY=12
Part 23
Find out PK
Remember that
Diagonals bisect each other perpendicularly
that means
PK=KY=12
Part 24
mRemember that
Diagonals bisect each other perpendicularly
so
mthat means
m
Part 25
mwe have that
mtherefore
m
Find the next three terms in this sequence: 5120, 1280, 320, 80...-160, -400, -64020, 5, 1.2540, 20, 1076, 72, 68
Given the first four terms of this sequence:
[tex](5120,1280,320,80,\ldots)[/tex]We can see a pattern. To analize this pattern, let's first check the difference between those terms.
[tex]\begin{gathered} 5120-1280=3840 \\ 1280-320=960 \\ 320-80=240 \end{gathered}[/tex]From those differences, we can verify the following equations:
[tex]\begin{gathered} 3840=4(960) \\ 960=4(240) \end{gathered}[/tex]From this, we can write the general rule for this sequence:
[tex]a_n=\frac{5120}{4^{n-1}}[/tex]This sequence gives us:
[tex]\begin{gathered} a_1=5120 \\ a_2=1280 \\ a_3=320 \\ a_4=80 \\ a_5=20 \\ a_6=5 \\ a_7=1.25 \end{gathered}[/tex]Then, we have the following 3 terms. (20, 5, 1.25)
the equation below describe the graph of a line on a coordinate planes.y - 2 = -3/2 (x + 1) which graph represents this line ?
The y-intercept is 1/2.
The answer is C. we can use the y-intercept to know the graph. You can see that option C when x = 0 , y is 1/2.
Fill in the blanks in the sequence _,29,_,_,_,539, 1083
we are given the following sequence:
[tex]_{}29,,,,539,1083[/tex]To go from 539 to 1083 we multiply 539 by 2 and add 5, like this:
[tex]1083=539\times2+5[/tex]Therefore, for a number in position "n", the formula for its value is:
[tex]a_n=2a_{n-1}+5[/tex]Solving we get:
[tex]a_{n-1}=\frac{a_n-5}{2}[/tex]Replacing the current value for 539 we get:
[tex]a_5=\frac{a_6-5}{2}[/tex][tex]a_5=\frac{539-5}{2}=267[/tex]Now to find the 4th value:
[tex]a_4=\frac{a_5-5}{2}[/tex]Replacing:
[tex]a_4=\frac{267-5}{2}=131[/tex]For the third value:
[tex]a_3=\frac{a_4-5}{2}[/tex]Replacing:
[tex]a_3=\frac{131-5}{2}=63[/tex]The second value is already given as 29, therefore, the first value is:
[tex]a_1=\frac{a_2-5}{2}[/tex]Replacing:
[tex]a_1=\frac{29-5}{2}=12[/tex]Therefore, the sequence is:
[tex]12,29,63,131,267,539,1083[/tex]
-2x + y = 3 5x - y = -3
we have
-2x + y = 3 -----> equation A
5x - y = -3 -----> equation B
Solve the system of equations
Solve by elimination
Adds equation A and equation B
-2x + y = 3
5x - y = -3
-----------------
-2x+5x=3-3
3x=0
x=0
Find the value of y
substitute the value of x in equation A or equation B
-2(0)+y=3
y=3
therefore
the solution is the point (0,3)A new bank customer with $2,500 wants to open a money market account. The bank is offering a simple interest rate of 1.8%.
a. How much interest will the customer earn in 30 years?
b. What will the account balance be after 30 years?
a. The customer will earn $_ in interest.
Using the simple interest formula, the interest will the customer earn in 30 years is $1350, the account balance be after 30 years is $3850 and the customer earn $1350 interest.
In the given given that;
A new bank customer with $2,500 wants to open a money market account.
The bank is offering a simple interest rate of 1.8%.
So the Principal Amout(P)=$2500
Interest Rate(R)=1.8%
(a) So we have to find the interest will the customer earn in 30 years.
So the time (T)=30 years
So the formula of Simple Interest;
I=PRT/100
I=2500*1.8*30/100
I=1350
So the interest will the customer earn in 30 years is $1350.
(b) Now we have to find the account balance be after 30 years.
The account balance = Principal Amount+Interest Amount
The account balance = 2500+1350
The account balance = $3850
(c) Now we have to find the customer will earn $_ in interest.
The customer earn $1350 interest.
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it's under the saying you add an extender different you subtract which a person does this explain
Operations
add → symbol "+"
subtract → symbol "-"
Multiply/divide → symbol "*/÷"
a triangle has side lengths of 6,7, and 14 is it possible or impossible
Answer:
Impossible
Explanation:
The side lengths a, b and c can form a triangle if the inequality holds:
[tex]a+b\ge c[/tex]Given the side lengths 6,7 and 14:
[tex]\begin{gathered} 6+7=13\le14\text{ (This invalidates it)} \\ 6+14=20\ge7 \\ 6+13=19\ge7 \end{gathered}[/tex]Since the inequality does not hold in all cases, it is Impossible to form sides of a triangle.