Answer:
Step-by-step explanation:
{z+1}/{z-1} = i.
z+1 = i (z-1)
z+1 =iz -i
z - iz = -1 -i
z ( 1 -i) = - 1 -i
z = (- 1 - i ) /(1-i) = - (1+i)/(1-i)
z = - (1+i)(1+i)/(1-i)(1+i)
z = - (1+2i +i²)/ ( 1²-i²).........i² = -1
z =-2i/2
z = - i (one solution)
All the complex numbers z satisfying the equation {z+1}/{z-1} = i is z = -i.
What are Complex Numbers?Complex numbers are numbers which are of the form [tex]a + ib[/tex], where a and b are real numbers and i is the imaginary number called iota whose value is [tex]i^2[/tex]= -1.
Given equation is,
(z + 1) / (z - 1) = i
Multiplying both sides by (z - 1),
z + 1 = i (z - 1)
Let z = (a + bi)
Substituting,
(a + bi + 1) = i (a + bi - 1)
(a + bi + 1) - i (a + bi - 1) = 0
a + bi + 1 - (ai + b(i)² - i) = 0
a + bi + 1 - ai - b(i)² + i = 0
Now i² = -1
a + bi + 1 - ai + b + i = 0
Combining the like terms,
(bi - ai + i) + (a + 1 + b) = 0
i (b - a + 1) + (a + b + 1) = 0
Left hand side is a complex number.
A complex number is a + bi = 0, when a = 0 and b = 0.
So, we get,
(b - a + 1) = 0 and (a + b + 1) = 0
b - a = -1 and a + b = -1
So, combining,
a + b = b - a
a + a = b - b
2a = 0
a = 0
Substituting,
b = -1
So the complex number, z = a + bi = -i
Hence the complex number z = -i.
Learn more about Complex Numbers here :
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Anthony purchased 6 fruit bars and 3 chocolate-nut bars for a camping trip. He spent $4.12 on the bars. Anthony wrote the following equation: 6x+3y=4.12 . What did he define as the variable x?
Answer:
He defined variable x as the cost of each fruit bar.
Step-by-step explanation:
6 is the amount of fruit bars Anthony has, so 3y must be for the chocolate-nut bars. So the only thing that makes sense is if variable x is the cost of each fruit bar.
Answer:
A cost a friut bar
Step-by-step explanation:
just finished the test and that was correct have a great day or night!
What is the sum of the geometric sequence −1, 6, −36, ... if there are 6 terms? (1 point) −39,991 6,665 −6,665 39,991
Answer:
=6665
Step-by-step explanation:
The sum of a geometric series is given by:
Sn=a(1-rⁿ)/(1-r)
Sn is the sum of the first n terms, r is the rate and n is the number of terms.
r the quotient between any two consecutive numbers.
r=6/-1= -6
Sn=-1(1-(-6)⁶)/(1--6)
=46655/7
=6665
Sum of the first six terms=6665
6 radians is the same as ____°.
Round to the nearest hundredth of a degree.
Answer:
343.77°
Step-by-step explanation:
1 radian = [tex]\frac{180}{Pi}[/tex]°
6 radians will be;
6 × [tex]\frac{180}{Pi}[/tex]° =343.7746771 °
Or 343.77° (rounded up to nearest hundredth)
Answer:
343.77
Step-by-step explanation:
You roll a number cube three consecutive times. What is the probability that you roll an even number the first two times and a 3 the last time?
Answer:
1/24.
Step-by-step explanation:
Probability(Rolling an even number)
= 3/6 = 1/2.
Probability(Rolling a 3) = 1/6.
Required Probability = 1/2 * 1/2 * 1/6
= 1/24.
The probabilities are multiplied because the 3 events are independent.
Answer:
1/24
Step-by-step explanation:
A die has 6 faces with numbers 1 through 6. Three faces have even numbers, and 3 faces have odd numbers.
Each roll of the die can result in 6 different outcomes.
The total number different outcomes of rolling a die 3 times is 6 * 6 * 6 = 216.
There are 3 possible even number outcomes on the first roll, and another 3 possible even number outcomes on the second roll. The third roll needs to be a 3, so there is one single desired outcome of the third roll.
Total number of desired outcomes: 3 * 3 * 1 = 9
probability(even, even, 3) = 9/216 = 1/24
Joyce had business cards made through a printing company. They charge an initial fee of $12 and $3.99 for each box of 100 business cards. If Joyce needs 5 boxes, how much will she be charged?
Answer:
$31.95
Step-by-step explanation:
The total cost is the initial fee plus the cost of the boxes.
12 + 5×3.99 = 31.95
2354 bdxbdbdbht55675443t35222222222222222222222222
Using the data: 2, 2, 3, 3, 3, 4, 5, 6, 6, 10
What is the median?
5
4
3.5
4.5
[tex]\huge{\boxed{4.5}}[/tex]
First, add all the numbers together. [tex]2+2+3+3+3+4+5+6+6+10=\bf{44}[/tex]
Divide by the amount of numbers. [tex]\frac{44}{10}=\boxed{4.4}[/tex]
[tex]4.5[/tex] is the closest, so that is the answer.
what does x² - 5x equal
Answer:
x(x-5)
Step-by-step explanation:
We cannot solve this expression because there is no equals sign.
We can,however simplify the expression
x^2 -5x
Factor out an x
x(x-5)
HELP PLEASE
Select all that apply.
Which quadrilaterals always have four congruent angles?
rectangle
rhombus
parallelogram
square
Answer:
rectangle, square
Step-by-step explanation:
A rectangle always has 4 congruent angles. A square is a rectangle, so a square always has 4 congruent angles.
A parallelogram and a rhombus may or may not have 4 congruent angles.
Answer: rectangle, square
Answer:
Only a square and rectangle
Step-by-step explanation:
Both have angles of only 90 deg.
Evaluate the expression below 3^3-10+(2*4^2)
Answer:
49
Step-by-step explanation:
We are going to use PEMDAS to simplify
[tex]3^3-10+(2 \cdot 4^2)[/tex]
First step is P.
P refers to the parenthesis or anything acting as a grouping symbol.
We notice the following operations there are multiplication and exponents.
According to PEMDAS, after parenthesis we do the exponents so let's do the exponent in the ( ).
[tex]3^3-10+(2 \cdot 16)[/tex]
Now we still have to finish P up. That is we need to do the one last operation in the ( ).
[tex]3^3-10+(32)[/tex]
Nothing left to perform in the () so we can just write:
[tex]3^3-10+32[/tex]
Now there are no more grouping symbols left.
The next letter is E and it stands for exponents so we must evaluate anything we can that has an exponent.
[tex]27-10+32[/tex]
Now after E we have M and D which means to multiply and divide as you the expression from left to right.
There is no multiplication and division so moving on.
A and S means to do the addition and subtraction as it occurs left to right:
[tex]17+32[/tex]
[tex]49[/tex]
Below is the graph of f ′(x), the derivative of f(x), and has x-intercepts at x = –3, x = 1 and x = 2. There are horizontal tangents at x = –1.5 and x = 1.5. Which of the following statements is true?
A. f is concave down from x = –3 to x = 0.
B. f is decreasing from x = –1.5 to x = 1.5.
C. f has a relative maximum at x = 1.
D. None of these is true.
Answer:
C. f has a relative maximum at x = 1.
Step-by-step explanation:
A. False. f(x) is concave down when f"(x) is negative. f"(x) is the tangent slope of the graph, f'(x). So f(x) is concave down between x = -1.5 and x = 1.5.
B. False. f(x) is decreasing when f'(x) is negative. So f(x) is decreasing in the intervals x < -3 and 1 < x < 2.
C. True. f(x) has a relative maximum where f'(x) = 0 and changes from + to -.
What is the mean of 3 8 10 19
Answer:
Mean=10
Step-by-step explanation:
To find the mean of a set of numbers, you need to add all of them up and then divide by the amount of numbers that are in the sequence. In this case...
3+8+10+19=40
Then we need to divide by 4 because there are 4 numbers in the sequence. \
40/4=10
Answer:
The mean is 10
Step-by-step explanation:
The mean is just another word for average.
Add the four numbers together and divide by 4
(3+8+10+19)/4
40/4
10
The graph of the equation $x + 2y + 3 = 0$ is perpendicular to the graph of the equation $ax + 2y + 3 = 0$. What is the value of $a$?
Answer:
a = -4.
Step-by-step explanation:
If the are perpendicular then the slope of one graph will be - 1 / slope of the other.
Convert each equation to slope-intercept form:
x + 2y + 3 = 0
2y = = -x - 3
y = (-1/2)x - 3/2 (Slope/intercept form)
So the slope of the line perpendicular to this will be - 1 / (-1/2) = 2.
Consider the other line:
ax + 2y + 3 = 0
2y = -ax - 3
y = (-a/2) x - 3/2 (Slope/intercept form)
So the slope for this line - a/2 and it equals 2.
-a/2 = 2
-a = 2*2 = 4
a = -4 (answer).
To determine the value of $a$ such that the graph of the equation $ax + 2y + 3 = 0$ is perpendicular to the graph of the equation $x + 2y + 3 = 0$, we'll need to find the slopes of the two lines represented by these equations since two lines are perpendicular if and only if the product of their slopes is $-1$ (the slopes are negative reciprocals of each other).
Let's find the slope of the first line.
The equation of the first line is $x + 2y + 3 = 0$. We can rearrange this to find $y$ in terms of $x$:
\[2y = -x - 3\]
\[y = \frac{-x}{2} - \frac{3}{2}\]
The slope of this line, denoted by $m_1$, is the coefficient of $x$:
\[m_1 = -\frac{1}{2}\]
Now, let's find the slope of the second line.
The equation of the second line is $ax + 2y + 3 = 0$. Rearranging this to solve for $y$ in terms of $x$, we get:
\[2y = -ax - 3\]
\[y = -\frac{a}{2}x - \frac{3}{2}\]
The slope of this line, denoted by $m_2$, is the coefficient of $x$:
\[m_2 = -\frac{a}{2}\]
Now, for the lines to be perpendicular, their slopes must satisfy the following condition:
\[m_1 \cdot m_2 = -1\]
Substituting the known slopes into the equation, we get:
\[-\frac{1}{2} \cdot \left(-\frac{a}{2}\right) = -1\]
\[\frac{a}{4} = -1\]
\[a = -4\]
Therefore, the value of $a$ that ensures the graph of the equation $ax + 2y + 3 = 0$ is perpendicular to the graph of the equation $x + 2y + 3 = 0$ is $a = -4$.
Including scholarships and financial aid, Mark has $37,000 to spend on
college. If the total cost of his college education is _____, he will have
enough resources to pay.
A. $43,000
B. $40,000
C. $46,000
D. $34,000
Answer:
D
Step-by-step explanation:
The answer is anything less than $37,000 because that is how much he has to spend. D. $34,000 is the only answer less than that, so D is the correct answer.
Reflect the given the coordinate points over the line y=x. F(−5,−3) G(−5,−2) H(−2,−2) F′( , ) G′( , ) H′( , )
Answer:
[tex]F'(-3,-5),G'(-2,-5),H'(-2,-2)[/tex]
Step-by-step explanation:
The given points are: F(−5,−3) G(−5,−2) H(−2,−2)
The mapping for reflection in the line [tex]y=x[/tex] is [tex](x,y)\to (y,x)[/tex].
We just have to swap the coordinates of the preimage to obtain the image
[tex]F(-5,-3)\to F'(-3,-5)[/tex].
[tex]G(-5,-2)\to G'(-2,-5)[/tex].
[tex]H(-2,-2)\to H'(-2,-2)[/tex].
Therefore the image points are
[tex]F'(-3,-5),G'(-2,-5),H'(-2,-2)[/tex]
which of these points is closest to the y-axis? a) (-6,0) b) -2,12) c) (4,2) d) (5,1)
Answer:
(-2,12)
Step-by-step explanation:
it is the closest because it is only 2 units away
The coordinates of points on the Cartesian plane, are given by a pair of values
The closest point to the y-axis is (-2, -12)Reason:
The given coordinates are; (-6, 0), (-2, -12), (4, 2), (5, 1)
Method:
A point is close to the y-axis where the magnitude x-coordinate value is low
By observation, the coordinates of the point having the lowest magnitude of the x-value, is the point (-2, -12)
By plotting the points on the graph, we can observe that the closest point i (-2, -12)Learn more about the Cartesian plane here:
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One of our brainliest, Konrad509, made this:
Solve for the numeral base [tex]x[/tex] in:
[tex]\frac{B_x\sqrt{74_x}}{1D_x}+J_x51_x=4G3_x[/tex].
[tex]\dfrac{B_x \sqrt{74_x}}{1D_x}+J_x51_x=4G3_x[/tex]
A=10, B=11, C=12, etc.
[tex]\dfrac{11\cdot x^0\cdot \sqrt{7\cdot x^1+4\cdot x^0}}{1\cdot x^1+13\cdot x^0}+19\cdot x^0\cdot (5\cdot x^1+1\cdot x^0)=4\cdot x^2+16\cdot x^1+3\cdot x^0\\\\\dfrac{11\sqrt{7x+4}}{x+13}+19(5x+1)=4x^2+16x+3\\\\\dfrac{11\sqrt{7x+4}}{x+13}+95x+19=4x^2+16x+3\\\\11\sqrt{7x+4}+95x(x+13)+19(x+13)=(4x^2+16x+3)(x+13)\\\\11\sqrt{7x+4}+95x^2+1235x+19x+247=4x^3+52x^2+16x^2+208x+3x+39\\\\11\sqrt{7x+4}=4x^3-27x^2-1043x-208\\\\121(7x+4)=(4x^3-27x^2-1043x-208)^2[/tex]
[tex]121(7x+4)=(4x^3-27x^2-1043x-208)^2\\\\847x+484=16 x^6 - 216 x^5 - 7615 x^4 + 54658 x^3 + 1099081 x^2 + 433888 x + 43264\\\\16 x^6 - 216 x^5 - 7615 x^4 + 54658 x^3 + 1099081 x^2 + 433041 x +42780=0[/tex]
Now, the "only" thing that remains to do is solving the above equation.
While making this problem I only made sure it has a solution. I didn't try to solve it myself and I didn't know it will end up with such "convoluted" polynomial. Sorry to everyone who tried to solve it... m(_ _)m
I think the best way to approach it is using the rational root theorem since we know that [tex]x\in\mathbb{N}[/tex]. Moreover we can deduce that [tex]x\geq19[/tex] since there is [tex]J[/tex] and [tex]J=19[/tex].
After you succesfully solve it, you should get the answer [tex]x=20[/tex].
Solve the matrix equation by using inverse matrices.
[2 -2] * [x] = [-18]
[-1 3] * [y] = [13 ]
Answer:
x=-7, y=2
Step-by-step explanation:
You are given the matrix equation
[tex]\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right] \cdot \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}-18\\13\end{array}\right][/tex]
Find the inverse matrix for the matrix
[tex]\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right][/tex]
1. The determinant is
[tex]\left|\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right]\right|=2\cdot 3-(-1)\cdot (-2)=6-2=4[/tex]
2.
[tex]a_{11}=2 \Rightarrow A_{11}=3\\ \\a_{12}=-2 \Rightarrow A_{12}=-(-1)=1\\ \\a_{21}=-1 \Rightarrow A_{21}=-(-2)=2\\ \\a_{22}=3 \Rightarrow A_{22}=2[/tex]
3. Inverse matrix is
[tex]\dfrac{1}{4}\left[\begin{array}{cc}3&1\\2&2\end{array}\right]^T=\dfrac{1}{4}\left[\begin{array}{cc}3&2\\1&2\end{array}\right][/tex]
So, the solution of the equation is
[tex]\left[\begin{array}{c}x\\y\end{array}\right]=\dfrac{1}{4}\left[\begin{array}{cc}3&2\\1&2\end{array}\right]\cdot \left[\begin{array}{c}-18\\13\end{array}\right]=\\ \\=\dfrac{1}{4}\left[\begin{array}{cc}3\cdot(-18)+2\cdot 13\\1\cdot (-18)+2\cdot 13\end{array}\right]=\dfrac{1}{4}\left[\begin{array}{c}-28\\8\end{array}\right]=\left[\begin{array}{c}-7\\2\end{array}\right][/tex]
You are facing North. Turn 90 degrees left. Turn 180 degrees right. Turn around to reverse your direction. Turn 45 degrees left. Turn around to reverse your direction. In which direction are you facing?
Answer:
Final direction is 45 degrees south of west or 45 degrees west of south.
Step-by-step explanation:
i) You are facing North
Turn 90 degrees left
ii) 90 degrees left to north is west.
Turn around to reverse your direction
iii) On reversing direction you will be facing east.
Turn 45 degrees left
iv) On turning 45 degrees left, you will be facing north east.
Turn around to reverse your direction
v) On reversing direction you will be facing south west.
Final direction is 45 degrees south of west or 45 degrees west of south.
AB passes through A(-3,0) and B(-6, 5). What is the equation of the line that passes through the origin and is parallel to AB?
Answer:
Step-C. -5x-3y=0 which is the same thing as y= -5/3x + 0.
by-step explanation:
i hope this helps
Square lMNO is shown in the diagram below what are the coordinates of the midpoint of a diagonal LN
Answer:
The coordinates of the midpoint of LN are [tex](-2\frac{1}{2},4\frac{1}{2})[/tex]
answer (4)
Step-by-step explanation:
* Lets explain how to find the midpoint of a line
- The coordinates of the midpoint of a line whose endpoints are (x1 , y1)
and (x2 , y2) are [tex]x=\frac{x_{1}+x_{2}}{2},y=\frac{y_{1}+y_{2}}{2}[/tex]
∵ LMNO is a square
∵ The coordinates of point L are (-6 , 1)
∵ The coordinates of point N are (1 , 8)
- Let the coordinates of point L are (x1 , y1) , the coordinates of point
N are (x2 , y2) and the coordinates of the midpoint of LN are (x , y)
∴ x1 = -6 , x2 = 1 and y1 = 1 , y2 = 8
- Use the rule of the midpoint above to find the midpoint (x , y)
∵ [tex]x=\frac{-6+1}{2}=\frac{-5}{2}=-2\frac{1}{2}[/tex]
∵ [tex]y=\frac{1+8}{2}=\frac{9}{4}=4\frac{1}{2}[/tex]
∴ The coordinates of the midpoint are [tex](-2\frac{1}{2},4\frac{1}{2})[/tex]
* The coordinates of the midpoint of LN are [tex](-2\frac{1}{2},4\frac{1}{2})[/tex]
Answer:
The answer should be D the fourth one
Step-by-step explanation:
Karin wants to use the distributive property to mentally find the value of 19⋅42+19⋅58. Which expression can she use?
Answer:
19 x (42 + 58)
Step-by-step explanation:
The common term is 19
Answer : The expression she use can be, [tex]19\times (42+58)[/tex]
Step-by-step explanation :
Distributive property Law : It says that multiplying a number by the group of numbers added together is the same as doing each multiplication separately.
For example:
3 × (2 + 4) = 3×2 + 3×4
As we are given the expression:
[tex]19\times 42+19\times 58[/tex]
[tex]\Rightarrow 19\times (42+58)[/tex]
Thus, the expression she use can be, [tex]19\times (42+58)[/tex]
Beth is designing a business card. She makes a scale drawing of her old business card by using the scale factor 5/4. Her scale drawing is 2 1/2in by 5in rectangle.
The print shop says the scale drawing is a reduction of the original card because the original card must be 3 1/8in by 6 1/4in. Which explains the print shop’s error?
A. The scale factor is greater than 1 so the scale drawing is an enlargement, and the original card is 2in by 4in
B. The scale factor is greater than 1 so the scale drawing is an enlargement, and the original card is 3 3/4in by 6 1/4in
C. The scale factor is a fraction so the scale drawing is an reduction, and the original card is 2in by 4in
D. The scale factor is a fraction so the scale drawing is an reduction, and the original card is 3 3/4in by 6 1/4in
Answer:
The correct option is A.
Step-by-step explanation:
It is given that Beth makes a scale drawing of her old business card by using the scale factor 5/4.
If the scale factor is less than 1, then it represents compression and if the scale factor is greater than 1, then it represents enlargement.
Since the scale factor is greater than 1 so the scale drawing is an enlargement.
Let the initial dimension of business card is a by b.
Her scale drawing is [tex]2\frac{1}{2}[/tex] in by 5 in rectangle. Multiply each dimension by reciprocal of scale factor to find the dimension of original card.
[tex]a=2\frac{1}{2}\times \frac{4}{5}=\frac{5}{2}\times \frac{4}{5}=2[/tex]
[tex]b=5\times \frac{4}{5}=4[/tex]
The dimension of original card is 2 in by 4 in.
Therefore the correct option is A.
Answer: A
Step-by-step explanation:
A research company wants to test the claim that a new multivitamin helps to improve short term memory. State the objective of the experiment, suggest a population, determine the experimental and control groups, and describe a sample procedure.
(SHOW WORK)
Answer:
I would think that you would want to have the multivitamin and then a placebo, then conduct an experiment testing the results of the multivitamin and observe the effects on both groups taking the medicine.
Step-by-step explanation:
your control group would be the placebo and your experimental group would be the multivitamin...
Answer with explanation:
Objective of the experiment:
The Multivitamin made by research company is beneficial or not for abolishing short term memory.
Population
The population can be chosen from the largest city hospital where people are suffering from short term memory loss.
Suppose 100 people are suffering from short term memory loss.
Experimental and control group
Suppose 40 people are being tested that is in experimental group and 60 people are in Control group.
Sample Procedure
After selecting 40 people in the experimental group , and then providing them Multivitamin for few days ,and then checking whether it is helping them to attain their memory or not is the procedure.
in diagram below, ab and bc are tangent to o. what is the measure of abc.
A. 46
B.67
C.42
D.92
help FAST please!!!!
Check the picture below.
Answer:
Option A. will be the answer.
Step-by-step explanation:
It is given in the diagram attached, AB and BC are the tangents to circle O.
We have to find the measure of ∠ABC.
By the theorem,
Measure of ∠ABC which inscribed within the tangents will be [tex]=\frac{1}{2}(arcADC-arcAC)[/tex]
[tex]=\frac{1}{2}(226-134)[/tex]
[tex]=\frac{1}{2}(92)[/tex]
= 46°
Option A. will be the answer.
Use the substitution method to solve the system of equations. Choose the
correct ordered pair
x + 2y = 12
y = x + 3
O A. (5,8)
O B. (5,2)
O C. (2,1)
O D. (2,5)
Answer:
D. (2,5)
Step-by-step explanation:
For X:
2+2(5)=12
2+10=12
For Y:
5=2+3
Answer:
D
Step-by-step explanation:
Given the 2 equations
x + 2y = 12 → (1)
y = x + 3 → (2)
Substitute y = x + 3 into (1)
x + 2(x + 3) = 12 ← distribute and simplify left side
x + 2x + 6 = 12
3x + 6 = 12 ( subtract 6 from both sides )
3x = 6 ( divide both sides by 3 )
x = 2
Substitute x = 2 into (2) for corresponding value of y
y = 2 + 3 = 5
Solution is (2, 5 ) → D
is the grouping method to factor 5x^3+15x^2-2x-6
Answer:
[tex](x+3)(5x^2-2)[/tex]
Step-by-step explanation:
[tex]5x^3+15x^2-2x-6[/tex]
The grouping method means you are going to group some terms together and then factor what you can out of each pair to hopefully make the expression you started with factorable.
Let's try it.
[tex]5x^3+15x^2+-2x-6[/tex]
I like to insert a + in front of the last two terms if it isn't already one. I think it makes it less confusing.
I'm going to group the first two terms together and I'm going to group the last two terms together like so:
[tex](5x^3+15x^2)+(-2x-6)[/tex]
Now I'm going to factor what I can out of each pairing.
[tex]5x^2(x+3)+-2(x+3)[/tex]
(*I always factor out negative number if the first term in the second pair has a negative on it.)
Now notice in each pairing, there is a common factor of (x+3) so I can factor that out.
The expression then becomes:
[tex](x+3)(5x^2-2)[/tex]
Final answer:
Yes, the grouping method can be used to factor the polynomial 5x³ + 15x² - 2x - 6, resulting in (x + 3)(5x² - 2) as the factored form.
Explanation:
The question is asking if we can use the grouping method to factor the polynomial 5x³ + 15x² - 2x - 6. Factoring by grouping is a technique where we group terms that have common factors and then factor each group individually.
To apply the grouping method to this polynomial, we would look for groups of terms that have common factors and try to factor out those common factors. Let's group the first two terms and the last two terms:
Group 1: 5x³ + 15x²
Group 2: -2x - 6
Factoring out the greatest common factor from each group, we get:
Group 1: 5x² (x + 3)
Group 2: -2 (x + 3)
Now, we can factor out the common binomial factor (x + 3):
(x + 3)(5x² - 2)
This is the factored form of the polynomial using the grouping method.
witch numbers belong to the equation 6x <= 66
A 11
B 53
C 9
D 12
E 50
F 7
plz explain i need to know how this works lol
Answer:
A 11
C 9
F 7
Step-by-step explanation:
6x≤ 66
Divide each side by 6
6x/6 ≤ 66/6
x ≤ 11
Any number less than or equal to 11 is a solutions
A 11 yes
B 53 no
C 9 yes
D 12 no
E 50 no
F 7 yes
prescription for marilyn jones piroxicam 20 mg capsule take 1 capsule 2 times a day how many milligrams mg will marilyn take of the Piroxicam in 90 days
Answer:
[tex]\boxed{\text{3600 mg}}[/tex]
Step-by-step explanation:
Step 1. Calculate the number of capsules
Marilyn takes 2 capsules per day
[tex]\text{No. of capsules} = \text{90 days} \times \dfrac{\text{2 capsules}}{\text{1 day}} = \text{ 180 capsules}[/tex]
Step 2. Convert capsules to milligrams
There are 20 mg in each capsule.
[tex]\text{No. of milligrams} = \text{180 capsules} \times \dfrac{\text{20 mg}}{\text{1 capsule}} = \textbf{3600 mg}\\\\\text{Marilyn will take } \boxed{\textbf{3600 mg}} \text{ of Pirixocam}[/tex]
Each of the 27 turtles in the pet store needs to be fed. There is one bag of turtle food that weighs 84 ounces. If each turtle gets the same amount of food, how many ounces of turtle food will each turtle get?
Step-by-step explanation:
84 ounces / 27 turtles = 3.111 ounces per turtle
Or in fractional form, 3 ¹/₉ ounces per turtle.
Each turtle gets 3.11 ounces if Each of the 27 turtles in the pet store needs to be fed
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
Each of the 27 turtles in the pet store needs to be fed.
There is one bag of turtle food that weighs 84 ounces.
Each turtle gets the food = 84/27
= 3.11 ounces
Thus, each turtle gets 3.11 ounces if Each of the 27 turtles in the pet store needs to be fed
Learn more about the fraction here:
brainly.com/question/1301963
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Factor completely 21x3 + 35x2 + 9x + 15. (3x − 5)(7x2 − 3) (3x − 5)(7x2 + 3) (3x + 5)(7x2 − 3) (3x + 5)(7x2 + 3)
Answer:
(7x^2+3)( 3x+5)
Step-by-step explanation:
21x^3 + 35x^2 + 9x + 15.
We will do factor by grouping
Rearranging the terms so I have the terms with a factor of 3 first and 5 last
Factor a 3x from the first two terms and 5 from the last two terms
21x^3 + 9x + 35x^2+ 15
3x(7x^2 +3) +5(7x^2+3)
Now factor out a (7x^2+3)
(7x^2+3)( 3x+5)
Answer:
Cubic = (3x + 5)(7x^2 + 3)
Step-by-step explanation:
If you make up two groups of 2, you might be able to factor this using the distributive property. Let's try it.
First group: 21x^3 + 35x^2 Take out 7x^2 as a common fact
First group: 7x^2(3x + 5)
Second group: 9x + 15 The HCF is 3
Second group: 3(3x + 5)
Now put your factors together in one long string.
Cubic = group 1 + group 2
Cubic = 7x^2 (3x + 5) + 3(3x + 5)
Note: If you had something like 7x^2 * y + 3 *y then you should see that the factors are y* (7x^2 + 3). So to solve the cubic, you should observe that (3x + 5) is a common factor.
Let y = 3x + 5
y(7x^2 + 3) Now substitute back for the y.
Cubic = (3x + 5)(7x^2 + 3)