(9 - 4i)(2 + 5i)
To solve this question you must FOIL (First, Outside, Inside, Last) like so
First:
(9 - 4i)(2 + 5i)
9 * 2
18
Outside:
(9 - 4i)(2 + 5i)
9 * 5i
45i
Inside:
(9 - 4i)(2 + 5i)
-4i * 2
-8i
Last:
(9 - 4i)(2 + 5i)
-4i * 5i
-20i²
Now combine all the products of the FOIL together like so...
18 + 45i - 8i - 20i²
***Note that i² = -1; In this case that means -20i² = 20
18 + 45i - 8i + 20
Combine like terms:
38 - 37i
^^^This is your answer
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the inequality in sentence form?
n/4.2 ≤ 21?
thanks!
Answer:
n ≤ 88.2
Step-by-step explanation:
Answer:
"n divided by four-point-two is greater-than or equal to twenty-one".
~
WILL GET BRAINLIEST IF EXPLAINED AND CORRECT
Give the equation for a circle with the given center and radius.
Center at (-1, 3), radius = 4
A. (x+3)2+(y−1)2=4
B. (x−3)2+(y+1)2=4
C. (x−1)2+(y+3)2=16
D. (x+1)2+(y−3)2=16
Answer:
It is D. (x + 1)^2 + (y - 3)^2 = 16.
Step-by-step explanation:
The general equation of a circle is
(x - h)^2 + (y - k)^2 = r^2 where the center is (h, k) and the radius is r.
So substituting the given values the required equation is:
(x + 1)^2 + (y - 3)^2 = 4^2.
Answer:
D. [tex](x+1)^2+(y-3)^2=16[/tex]
Step-by-step explanation:
We are asked to write equation of a circle whose center is at point [tex](-1,3)[/tex] and whose radius is 4 units.
We know that equation of a circle is standard form is in format [tex](x-h)^2+(y-k)^2=r^2[/tex], where [tex](h,k)[/tex] is the center of circle.
Upon substituting [tex]h=-1[/tex], [tex]k=3[/tex] and [tex]r=4[/tex] in the standard form of circle, we will get:
[tex](x-(-1))^2+(y-3)^2=4^2[/tex]
[tex](x+1)^2+(y-3)^2=16[/tex]
Therefore, our required equation would be [tex](x+1)^2+(y-3)^2=16[/tex] and option D is the correct choice.
Compare the function
f(x) = −6x − 3
g(x) is the graph
h(x) = h(x) = 2 cos(x + π) − 1
The given three functions all have the same y-intercept at (0,-3).
We have given that,
f(x) = −6x − 3
g(x) is the graph
h(x) = h(x) = 2 cos(x + π) − 1
What is the coordinate?
A coordinate plane is a two-dimensional plane formed by the intersection of a vertical line called y-axis and a horizontal line called x-axis.
all you have to do is substitute 0 for x and you can also sub y for the function notation
So the first is y=-6x-3
When x=0 then all you have left is y=-3 so the point is (0,-3)
The second function is shown on the graph and the y-intercept (where x=0) is at -3, so the point for that is (0,-3)
And the third function has x=0, So you get[tex]y=2cos(\pi )-1.[/tex]The [tex]cos(\pi )=-1,[/tex]
So that gives
[tex]y=2(-1)-1\\y=-2-1\\ y=-3[/tex]
then and the point is (0,-3)
Therefore they all have the same y-intercept at (0,-3).
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candace is practicing her typing. she records the number of words she can type each minute and plans to plot the data on the following grid where the x-axis represents the number of minutes and the y-axis represents the number of words typed. which table shows data that could be best presented using a grid with the scales candace does?
Answer:
C
Step-by-step explanation:
Its C because the graph is not up to scale in order to fit the other options B looks like it could but I cant see the whole graph so Id go with C
Its C because the graph is not up to scale in order to fit the other options B looks like it could but I cant see the whole graph so Id go with C.
What are Grid numbers?Grid Reference a page number, column, and line combination used to identify a container's location in a bay layout. Each area must have a unique Grid Number for quick identification.
Without limiting the generality of the aforementioned, each credit party agrees that the administrative agent shall have the right to sell or otherwise dispose of all or any portion of the collateral at a public or private sale, at any broker's board.
It on any securities exchange, for cash, upon credit, or for future delivery as the administrative age approaches, subject to the mandatory requirements of applicable law.
Therefore, Its C because the graph is not up to scale in order to fit the other options B looks like it could but I cant see the whole graph so Id go with C.
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Evaluate the expression.
a3b2c-1d
Evaluate a2b2c1d
If a = 2, b = 4, C = 10, d = 15
Express your answer
as a reduced fraction.
Please help
Step-by-step explanation:
for a³b²c-1d
given
a=2
b=4
c=10
d=15
a³b²c-¹d
=(2³4²10^-1*15
=2³4²15/10
=8*16*15/10
=8*8*3
=64*3
=192
now
a³b²c¹d
=(2³4²10 15)
=(8*16*10*15)
=120*16*10
=1200*16
=19200
Answer:
3/4 if meant [tex]a=2,b=4,c=10,d=15[/tex]
is [tex]a^3b^{-2}c^{-1}d[/tex]
Step-by-step explanation:
So the expression we want to evaluate for [tex]a=2,b=4,c=10,d=15[/tex]
is [tex]a^3b^{-2}c^{-1}d[/tex]
Please make sure I typed the expression and the values for the letters right.
[tex]a^3b^{-2}c^{-1}d[/tex]
Plug in the given values:
[tex](2)^3(4)^{-2}(10)^{-1}(15)[/tex]
In the following step I said 2^3 equals 8 because 2^3 means 2*2*2. I also got rid of the negative exponents by taking reciprocal.
[tex]8 \cdot \frac{1}{4^2} \cdot \frac{1}{10^1} (15)[/tex]
In the following step I said 4^2=16 because 4^2 means 4*4. I also wrote 10^1 as 10.
[tex]8 \cdot \frac{1}{16} \cdot \frac{1}{10} (15)[/tex]
In the following step, I'm going to rewrite everything as a fraction if it isn't already a fraction. 8=8/1 and 15=15/1.
[tex]\frac{8}{1} \cdot \frac{1}{16} \cdot \frac{1}{10} \cdot \frac{15}{1}[/tex]
To multiply fractions, you just multiply straight across on top and straight across on bottom.
[tex]\frac{8(1)(1)(15)}{1(16)(10)(1)}[/tex]
Actually performing the multiplication:
[tex]\frac{120}{160}[/tex]
Time to reduce:
[tex]\frac{12}{16}[/tex] I divided top and bottom by 10 to get this.
One more time for reducing:
[tex]\frac{3}{4}[/tex] I divided top and bottom by 4 to get this.
there are 480000 books in two public libraries if each cupboard in the library hold 80 books then how many cupboard are required to keep all of the books if one library has 267112 books then how many books are there in the other library
Answer:
there would be 212,888 books in the 2nd library, and 6,000 cupboards needed to hold all the books.
Step-by-step explanation:
simple division is all you need to answer. 480,000 divided by 80 is 6,000. for the second part, if the total amount of books between both libraries is 480,000 and one library has 267,112 books, 480,00 - 267,112 is 212,888
Hope this helps :)
feel free to ask if you have any questions
meaningful use was created to help improve quality safety and efficiency true or false
Answer:
TRUE
Step-by-step explanation:
Meaningful use is used to define the minimum standards of the American government for electronic health records and it has five main objectives:
Provide privacy and security for personal health informationExpand public healthImprove care coordinationIncrease patient engagementImprove quality, safety, efficiency and reduce health disparities.Therefore, the statement is true.
Help please don't mind what I wrote I am so confused:
Answer:
The correct option is D.
Step-by-step explanation:
a = 9c²+4
b= 7+3c
Firstly solve 2nd equation for c in terms of b:
b=7+3c
b-7=3c
b-7/3 = c
Now substitute the value of c in equation 1:
a= 9c²+4
a=9(b-7/3)² +4
a=9(b-7)²/9+4
9 will be cancelled by 9, so the equation we get is:
a=(b-7)²+4
Apply whole square formula for (b-7)²
a=b²-14b+49+4
Solve like terms:
a=b²-14b+53
Therefore the correct option is D....
In the figure, ADHG = AFHE. Which statement is true by CPCTC?
Answer:
this was last last year sorry u never got an answer
simplify this expression 6g 11g
Answer:
[tex](6g)(11g)=\bigg((6)(11)\bigg)(gg)=66g^2[/tex]
Does the quadratic function have a maximum or minimum? Give the value
Answer:
Max is 4.
Step-by-step explanation:
Maximum means it has a highest point and what is the highest point.
Minimum means it has a lowest point and what is the lowest point.
It doesn't have a minimum because it keeps going down forever and ever.
It does have a maximum because it does stop at the top. The y-value that is stops at is 4 so the max is 4.
find the volume in cubic yards of the cube whose edges are eight feet
The volume of the cube with edges of eight feet is approximately 18.96 cubic yards.
To find the volume of a cube, you need to know the length of one of its edges. In this case, the edge length is given as eight feet.
Volume of a cube = (Edge length)³
Volume = 8³ = 512 cubic feet.
Now, we need to convert cubic feet to cubic yards. Since 1 cubic yard is equal to 27 cubic feet:
Volume in cubic yards = 512 cubic feet / 27 cubic feet per cubic yard ≈ 18.96 cubic yards.
So, the volume of the cube is approximately 18.96 cubic yards.
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If the factors of a polynomial are x5 and x + 2, what values of x make that
polynomial O?
Answer:
x = 5, x=-2
Step-by-step explanation:
The factors are x-5 and x+2:
Set each factor equal to zero and then solve each of them for x to find out what values of x make the polynomial equal to zero.
x-5 = 0 , x+2 = 0
x=0+5 , x=0-2
x=5 , x= -2....
The values of x that make the polynomial 0, given its factors are x⁵ and x + 2, are x = 0 and x = -2.
If the factors of a polynomial are x⁵ and x + 2, to find the values of x that make the polynomial equal to zero, we set each factor equal to zero and solve for x.
For the factor x⁵ = 0, the only solution is x = 0.
For the factor x + 2 = 0, solving for x gives us x = -2.
Therefore, the values of x that make the polynomial 0 are x = 0 and x = -2.
f(x) = x3 – 2x + 6
g(x) = 2x3 + 3x2 - 4x + 2
Find (f – g)(x).
Answer:
-x^3-3x^2+2x+4
Step-by-step explanation:
Just calculate each coefficient of the polynomial separately.
x^3-2x+6-(2x^3+3x^2-4x+2) = (1-2)x^3+(0-3)x^2+(-2-(-4))x+(6-2) = -x^3-3x^2+2x+4.
Answer:
- x³ - 3x² + 2x + 4
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x)
= x³ - 2x + 6 - (2x³ + 3x² - 4x + 2) ← distribute by - 1
= x³ - 2x + 6 - 2x³ - 3x² + 4x - 2 ← collect like terms
= - x³ - 3x² + 2x + 4 ← in standard form
The drama club you are part of is hosting a pancake breakfast. You are in charge of buying the sausage, which costs $5 per pound, and bacon, which costs $4 per
pound. The meat budget you are given totals $500 dollars. The inequality 5x + 4y < 500 represents the possible combinations of pounds of sausage (x) and bacon
(y) you can buy
A. 20 pounds of sausage and 90 pound of bacon
B. 40 pound of sausage and 40 pound of bacon
C. 60 pound of sausage and 80 pound of bacon
D. 80 pound of sausage and 20 pound of bacon
Answer:
C.Step-by-step explanation:
Look at the pictures.
x - sausage
y - bacon
A. 20 pounds of sausage and 90 pound of bacon
x = 20 → y = 100 > 90
B. 40 pound of sausage and 40 pound of bacon
x = 40 → y = 75 > 40
C. 60 pound of sausage and 80 pound of bacon
x = 60 → y = 50 < 80
D. 80 pound of sausage and 20 pound of bacon
x = 80 → y = 25 > 20
Option A (20 pounds of sausage and 90 pounds of bacon) and Option B (40 pounds of sausage and 40 pounds of bacon) are the possible combinations of pounds of sausage and bacon that you can buy.
Explanation:The inequality 5x + 4y < 500 represents the possible combinations of pounds of sausage (x) and bacon(y) you can buy.
Let's check each option to see if it satisfies the inequality:
Option A: 20 pounds of sausage and 90 pounds of baconTherefore, options A and B are the possible combinations of pounds of sausage and bacon that you can buy.
What is the ratio for the sine of Z ?
Answer:
55/73
Step-by-step explanation:
Soh Cah Toa gives us our definitions for the trigonometric ratios: sine, cosine, and tangent.
That is the first part means sine is opposite / hypotenuse.
The second part means cosine is adjacent / hypotenuse.
The last part means tangent is opposite / adjacent.
No matter what angle you are looking to label the right triangle from, the hypotenuse will always be the same. The hypotenuse is the side opposite the 90 angle. Opposite meaning not touching; across from.
The other two terms are adjacent and opposite and depending on what angle you are looking from these change.
Adjacent means touching (exclude the hypotenuse from this).
Opposite means across from; not touching.
So from Z:
The side that has measurement 55 is opposite to Z.
The side that has measurement 48 is adjacent to Z.
The hypotenuse is the side that has measurement 73.
So from Y:
The side that has measurement 48 is opposite to Y.
The side that has measurement 55 is adjacent to Y.
The hypotenuse is the side that has measurement 73.
We don't label are triangle with respect to the 90 degree, X.
Anyways we asked to find sin(Z).
[tex]\sin(Z)=\frac{\text{opposite to }Z}{\text{ hypotenuse}}=\frac{55}{73}[/tex]
The value of -8/-15 · 29/64 is _____. -1/-6 1/6 -2/-3 2/3
Answer:
29/120
Step-by-step explanation:
-8/-15 · 29/64
Lets rewrite the problem
-8/64 *29/-15
We can simplify the first fraction
-1/8 * 29/-15
Multiply the numerators
-1*28 = -29
Multiply the denominators
8*-15 =-120
Put the numerator over the denominator
-29/-120
A negative over a negative is a positive
29/120
Are you sure you have the factions correct
[tex]\text{Hey there!}[/tex]
[tex]\dfrac{-8}{-15}\times\dfrac{29}{64}[/tex]
[tex]\dfrac{8\times29}{15\times64}[/tex]
[tex]{8 \times 29 = 232}\\\\\ 15\times 64 = 960[/tex]
[tex]\text{Both numbers goes into 8 (or the GCF is 8.)}\text{ So divide both numbers by 8.}[/tex]
[tex]231\div8 = 29\leftarrow \text{numerator (top number)}\\\\ 960\div8=120\leftarrow\text{denominator (bottom number)}[/tex]
[tex]\boxed{\boxed{\text{Answer: }\bf{\dfrac{29}{120}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
The sum of the interior angles, s, in an n-sided polygon can be determined using the formula s=180(n−2), where n is the number of sides.
Using this formula, how many sides does a polygon have if the sum of the interior angles is 1,260°? Round to the nearest whole number.
Answer:
The polygon has 9 sides
Step-by-step explanation:
We need to equate the given expression to the given value and solve for n.
The sum of the interior angles, s, in an n-sided polygon is given by the expression:
[tex]s = 180(n - 2)[/tex]
We want to use this formula, to calculate how many sides has a polygon if the sum of the interior angles is 1,260°.
We solve the following equation for n.
[tex]180(n - 2) = 1260[/tex]
Divide through by 180 to get:
[tex] \frac{180(n - 2)}{180} = \frac{1260}{180} [/tex]
[tex]n - 2 = 7[/tex]
Add 2 to both sides to get:
[tex]n = 7 + 2[/tex]
[tex] \therefore \: n = 9[/tex]
Hence the polygon has 9 sides
Answer: d
Step-by-step explanation:
Which action is not a step in using paper folding to find the midpoint of a line
segment?
A. Draw a line from the segment to any point on the fold line.
B. Draw a line segment on tracing paper.
C. Fold the tracing paper so that the endpoints lie on top of each
other.
D. Mark the intersection of the fold and the segment with a point.
Answer:
A. Draw a line from the segment to any point on the fold line.
Step-by-step explanation:
When using the paper folding method to find the midpoint of a line segment we take the following steps:
Draw a line segment on the tracing paperFold the tracing paper so that the endpoints lie on top of each otherMark the intersection of the fold and the segment with a pointThese steps include statements B, C, and D. Drawing a line from the segment to any point on the fold line, which is statement A, is not included in these steps because it is not needed.
Thus, choice A is not a step in using paper folding to find the midpoint of a line segment.
About 20% of the time you sleep is spent in rapid eye movement (REM) sleep, which is associated with dreaming. If an adult sleeps 7 to 8 hours, which inequality shows how much time, in hours, is spent in REM sleep?
1.4 < h < 1.6
35 < h < 40
0.35 < h < 0.4
14
Answer:
The answer should be 1.4<h<1.6
Step-by-step explanation:
Multiply 7 and 8 by 0.2 to find out what 20% is. 7*0.2=1.4 and 8*0.2=1.6. So it should be at or between those two numbers making the inequality 1.4<h<1.6
When an adult sleeps between 7 to 8 hours, they spend between 1.4 and 1.6 hours in REM (Rapid Eye Movement) sleep, which is associated with dreaming.
Explanation:Given that an adult sleeps 7 to 8 hours, roughly 20% of this time is spent in REM or Rapid Eye Movement sleep, typically associated with dreaming. To find out how much time is spent in REM sleep, we calculate 20% of the total sleep time. If 20% of 7 hours is 1.4 hours and 20% of 8 hours is 1.6 hours, then the correct inequality showing how much time, in hours, is spent in REM sleep is 1.4 < h < 1.6 where 'h' represents number of hours in REM sleep.
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what is -1/6 times -1/5
[tex]\frac{1}{30}[/tex]
Explanation:Multiply the numerators together. [tex]-1*-1=1[/tex]
Multiply the denominators together. [tex]6*5=30[/tex]
Put the two products together in a new fraction. [tex]\frac{-1}{6}*\frac{-1}{5}=\frac{1}{30}[/tex]
Answer:
1/30
Multiply the numerators together.
Multiply the denominators together.
Put the two products together in a new fraction.
Step-by-step explanation:
If 50% of days are sunny and 50% of days are rainy, what is the ratio of sunny days to rainy
days? (4 points)
Answer:
1:1
Step-by-step explanation:
Since both equal up to 100% and both are 50%, it's 1:1.
1 stands for 50% and the other 1 stands for 50% too.
solve the equation 169x^2+36=0
Subtract.
(6x + 5) - (x+3)
(6x+5)-(x+3).
6x+5-x-3.
Add the like terms.
6x-x+5-3.
We get.
5x+2.
Answer:
6x+5-x-3
=5x+2
I don’t which one it is?
Answer:
7.4
Step-by-step explanation:
The information given is in from SAS.
This is a job for law of cosines.
This is the law of cosines [tex]a^2=b^2+c^2-2bc cos(A)[/tex]
The angle A is opposite side a and b,c are the other sides.
So 13 degrees is opposite the y there.
[tex]y^2=16^2+22^2-2(16)(22)\cos(13)[/tex]
Now I'm going to put 16^2+22^2-2*16*22*cos(13) in my calculator:
[tex]y^2=54.04347439[/tex]
Now one more step. To get rid of the square, you need to square root both sides:
[tex]y=\sqrt{54.04347439}=7.351426691[/tex]
Sp the answer is approximately 7.4
Answer:
7.351
I don't know how they have rounded; the closest answer is A
Step-by-step explanation:
The only way I know to do this is with the cos law
y^2 = x^2 + z^2 - 2*x*z cos(Y)
x = 22
z = 16
y = ?
I have serious doubts that this will make a triangle. I ran it though a calculator and it does work -- surprise for me. Substitute the givens.
y^2 = 256 + 484 - 2*10*22*cos(13)
y^2 = 740 - 704*cos(13)
y^2 = 740 - 704*0.9744
y^2 = 740 - 685.95
y^2 = 54.05 Take the square root of both sides
y = √54.05
y = 7.351
Help me answer this question please.There were 3 bands that performed at talent show. What percent of the 16 group acts were band performances?
Divide the number of bands by the total acts:
3 /16 = 0.1875
Multiply by 100:
0.1875 x 100 = 18.75% were bands. ( Round answer as needed.)
??help me how to do this
Answer:
x = sqrt( 4^2 + 7^2)
Step-by-step explanation:
They want the equation to solve the triangle
We can use the Pythagorean theorem
a^2 + b^2 = c^2
where a and be are the legs and c is the hypotenuse
4^2 + 7^2 = x^2
Take the square root of each side
sqrt(4^2 + 7^2) = sqrt(x^2)
sqrt( 4^2 + 7^2) = x
Answer:
[tex]\large\boxed{x=\sqrt{7^2+4^2}=\sqrt{65}}[/tex]
Step-by-step explanation:
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have
[tex]leg=7,\ leg=4,\ hypotenuse=x[/tex]
Substitute:
[tex]x^2=7^2+4^2\to x=\sqrt{7^2+4^2}[/tex]
[tex]x=\sqrt{49+16}\\\\x=\sqrt{65}[/tex]
using a table find the range of the function for given domain f(x)=2x+7 with domain x=2,3,5,9
Answer:
Range : {11,13,17,25}
Step-by-step explanation:
Given
f(x) = 2x+7
and
Domain = {2,3,5,9}
To find the range, the values in domain will be put in the function one by one
So,
f(2) = 2(2)+7 = 4+7 = 11
f(3) = 2(3)+7 = 6+7 = 13
f(5) = 2(5)+7 = 10+7 = 17
f(9) = 2(9)+7 = 18+7 = 25
Therefore the range is {11,13,17,25} ..
Which point represent the location of the vertex of the
given function? *
f(x) = -2(x – 4)2 – 7?
Answer:
(4,-7) is the vertex
Step-by-step explanation:
The equation of the parabola is of the form
y= a(x-h)^2 +k
where (h,k) is the vertex
f(x) = -2(x – 4)^2 – 7
(4,-7) is the vertex
Answer:
The vertex point is (4, -7)
Step-by-step explanation:
Compare withe the general form of the vertex form:
f(x) = a(x - h)^2 + k where (h, k) is the vertex.
f(x) = -2(x - 4)^2 - 7.
- so the vertex is (4, -7).
An ant can travel 2 feet in 30 seconds and a beetle can travel 5 feet in 90 seconds. Which bug travels farther per second?
Answer:
The beetle does
Answer:
The Ant travels farther per second
Step-by-step explanation:
To Find how far the ant and beetle travels we have to find out how many feet per second the Ant and Beetle travel.
To find that out for the Ant I divided 30 by 2 and got 15 which means the ant travels 1 foot in 15 second.
To find that out for the beetle I divided 90 by 5 and got 18 which means the beetle travels 1 foot in 18 seconds.
Therefore the Ant travels faster.