Answer:
- 14 + 18i
Step-by-step explanation:
Note that i² = ([tex]\sqrt{-1}[/tex] )² = - 1
Given
4i(- i + 3) - 3(6 - 21) ← distribute both parenthesis
= - 4i² + 12i - 18 + 6i
= - 4(- 1) - 18 + 18i
= 4 - 18 + 18i
= - 14 + 18i
The indicated operation of 4i(-i + 3) - 3(6 - 2i) in the form a + bi is -14 + 18i.
To perform the indicated operation and write the result in the form a + bi, we have to distribute and combine like terms carefully.
Starting with 4i(-i + 3), we distribute 4i:
4i * (-i) = -4i^2 = 4 (since i^2 = -1)
4i * 3 = 12i
This gives us 4 + 12i.
Now addressing the second part, -3(6 - 2i), we also distribute:
-3 * 6 = -18
-3 * (-2i) = 6i
This results in -18 + 6i.
Combining both parts (4 + 12i and -18 + 6i):
(4 + 12i) + (-18 + 6i) = (4 - 18) + (12i + 6i)
= -14 + 18i
Share 160 sweets in the ratio 8:12
let's divide the whole by the sum of its ratios, namely let's 160 ÷ (8+12), and then distribute accordingly.
[tex]\bf \textit{160 at 8:12 ratio}\qquad \qquad \cfrac{8\cdot \frac{160}{8+12}}{12\cdot \frac{160}{8+12}}\implies \cfrac{8(8)}{12(8)}\implies \cfrac{64}{96}[/tex]
Solving the elimination method what is 3x-y=9 2x-y=7
Answer:
x = 2 , y = -3
Step-by-step explanation by elimination:
Solve the following system:
{3 x - y = 9 | (equation 1)
2 x - y = 7 | (equation 2)
Subtract 2/3 × (equation 1) from equation 2:
{3 x - y = 9 | (equation 1)
0 x - y/3 = 1 | (equation 2)
Multiply equation 2 by 3:
{3 x - y = 9 | (equation 1)
0 x - y = 3 | (equation 2)
Multiply equation 2 by -1:
{3 x - y = 9 | (equation 1)
0 x+y = -3 | (equation 2)
Add equation 2 to equation 1:
{3 x+0 y = 6 | (equation 1)
0 x+y = -3 | (equation 2)
Divide equation 1 by 3:
{x+0 y = 2 | (equation 1)
0 x+y = -3 | (equation 2)
Collect results:
Answer: {x = 2 , y = -3
Answer:
x=2 y=7.
Step-by-step explanation:
3x-y=9
-2x+y=7
x=2
2(2)+y=7
4+y=7
-4. -4
y=7
Zara is six months into her first job, and she’s also attending community college. She is planning to start saving a portion of her paycheck and has created a monthly budget to track her spending. Which budget item should Zara reduce to increase her savings?
Answer:
B.Dining out
Step-by-step explanation:
I hope the below question is the full one that you want to ask
Select the correct answer. Zara is six months into her first job, and she’s also attending community college. She is planning to start saving a portion of her paycheck and has created a monthly budget to track her spending. Which budget item should Zara reduce to increase her savings? A. college tuition B. dining out C. rent D. utility bills
I think it is B: dinning out.
Because A C D are fixed cost, she could not adjust or change by herself. She can only save money when she cooks, do not need to go out for food.
Sarah has a bag of 50 skittles, some are red and some are yellow. Sarah randomly pulls a skittle out of the bag and records it, and returns it back to he bag.so far she has recorded 8 reds and 12 yellows.based on these results what is the MOST likely numbers of reds in the bag?
Answer:
20
Step-by-step explanation:
Assume n is the number of times she pick a skittle out of the bag
The probability she pick out red : 8/n
The probability she pick out yellow : 12/n
=> The ratio of red and yellow skittle : 8/n : 12/n = 8/12 = 2/3, means every 2 red skittles we have 3 yellow ones.
But we have 50 skittles, so the likely numbers of reds in the bag is = 2*[tex]\frac{50}{5}[/tex] = 20
How should the decimal point in 52.48 be moved to determine the product 52.48×105 ?
Answer:
5 spaces to the right because there are 5 terminating zeros in 10^5. This is because 10^5 = 100000, which has 5 terminating (ending) zeros.
Hope this helps.
Final answer:
To multiply 52.48 by 10⁵, move the decimal point five places to the right, resulting in a final product of 5248000.
Explanation:
To determine the product of 52.48×10⁵, you should move the decimal point in 52.48 a certain number of places to the right. Since we are multiplying by 105, which is the same as 10 to the power of five, we have five zeros after the 1 in 10 to the power of 5. Therefore, we move the decimal point five places to the right. Sometimes we may not have enough digits, and in such a case, we add zeros as placeholders.
Performing this movement with our number 52.48 gives us:
52.48 (original number)
524.8 (after moving 1 place)
5248 (after moving 2 places)
52480 (after moving 3 places)
524800 (after moving 4 places)
5248000 (after moving 5 places)
Therefore, the product of 52.48 and 10 to the power of 5 is 5248000.
Distrubite and Combine like terms
4(2a-5b-7)-3(2a+3b+5)
Answer:
2a-29b-43 pls give me brainlist because my answer is the best
Step-by-step explanation:
8a-20b-28-6a-9b-15
2a-29b-43
In factored form, y = a (x - p) (x – q) we are able to see what important
point(s)?
[tex]y= a(x-p)(x-q)[/tex]
Answer:
The x-intercepts
[tex]y[/tex] can only be [tex]0[/tex], if either [tex]x=p[/tex], or [tex]x=q[/tex]...
so, the parabola must have the points [tex]\left(p,0\right)[/tex] and [tex]\left(q,0\right)[/tex]
Find the product of 3 2/3 as a mixed number
Answer:
11/3
Step-by-step explanation:
Theo started to solve the quadratic equation
Answer:
[tex]x + 2 = \pm2[/tex]
Step-by-step explanation:
After Theo added to both sides of:
[tex] {(x + 2)}^{2} - 9 = - 5[/tex]
He got;
[tex]{(x + 2)}^{2} = 4[/tex]
Next he took the square root of both sides to get;
[tex]x + 2 = \pm \sqrt{4} [/tex]
When Theo simplifies, he will obtain:
[tex]x + 2 = \pm2[/tex]
Therefore the second option is correct.
Solve the equation. Then check your solution
Please select the best answer from the choices provided
Answer:
D. [tex]- \frac{13}{35}[/tex]
Step-by-step explanation:
[tex]\frac{4}{5} + x = \frac{3}{7} \\\\x = \frac{3}{7} - \frac{4}{5} \\\\x = \frac{15 - 28}{35} = -\frac{13}{35}[/tex]
HELP!!!! WILL MARK BRAINLEST IF CORRECT!
How is the distributive property used when finding the product of two polynomials? How are polynomials closed under multiplication?
Answer:
Multiplying polynomials is a bit more challenging than adding and subtracting polynomials. We must use the distributive property to multiply each term in the first polynomial by each term in the second polynomial. We then combine like terms. We can also use a shortcut called the FOIL method when multiplying binomials. Certain special products follow patterns that we can memorize and use instead of multiplying the polynomials by hand each time. We will look at a variety of ways to multiply polynomials.
(-2h3n2)(-5h2n2)
How
Answer: 9h x 8n^2
we rearrange this underneath the question (-5h-2h) (2nx3n)(2+2) or if 2^2 see explanation. It must therefore be 7h6n4
Step-by-step explanation:
if its ^2 )(power2) then the second reasonable answer is (7h-2h)(2n^2 x 2n^2)=9h x 4n^2 x4n^2 =9h 8n^2 or 17hn^2 but i leave as 9h 8n^2
You can expand only if multiplying 9hx4 for example but not combine the letters. The questions that ask you to mix are much different to this. but if you want to add them 9h+8n^2 =17hn^2
Which graph represents the solution to the inequality 11 Less-than-or-equal-to y - 43?
A number line going from 50 to 60. A solid circle is at 54. Everything to the left of the circle is shaded.
A number line going from 50 to 60. A solid circle is at 54. Everything to the right of the circle is shaded.
A number line going from negative 35 to negative 25. A solid circle is at negative 32. Everything to the left of the circle is shaded.
A number line going from negative 35 to negative 25. A solid circle is at negative 32. Everything to the right of the circle is shaded.
11 <= y -43
Solve for y:
First rewrite so y is on the left side:
Y-43 >= 11
Add 43 to both sides:
Y >=54
Since 54 is included in the answer it would be a solid dot on 54 and the shaded area would cover all numbers greater than 54.
The answer Is:
A number line going from 50 to 60. A solid circle is at 54. Everything to the right of the circle is shaded.
Answer:
B. second choice
Step-by-step explanation:
I answered the question on Edge and got it right.
142% as a mixed numer in simplest form
Answer:
71/50 hope this helped
Step-by-step explanation:
Answer:
[tex]1\frac{21}{50}[/tex]
Step-by-step explanation:
[tex]142\% = \frac{142}{100} = 1\frac{42}{100} = 1\frac{21}{50}[/tex]
142% = 1.42
Divide 3x^3 - 2x^2 - 61x - 20 by x - 5.
3x^2 + 13x + 4
3x^2 - 13x + 4
3x^2 - 17x + 24 R 100
3x^2 + 17x - 24 R 100
Answer:
3x² + 13x + 4
Step-by-step explanation:
3x³ - 2x² - 61x - 20
3x³ - 15x² + 13x² - 65x + 4x - 20
[3x²(x - 5) + 13x(x - 5) + 4(x - 5)]/(x-5)
3x² + 13x + 4
Find the area of the sector with a central angle of 60° and a radius of 5 inches. Round to the nearest tenth.
Answer:
15.4 inches square
Step-by-step explanation:
Formula for finding the sector of a circle is:
[tex]A = \frac{\theta°}{360°} \times \pi {r}^{2} [/tex]
Given that,
[tex]{\theta} = {60}^{0} [/tex]
r= 5 inches
Take;
[tex]\pi = 3.14[/tex]
By substitution,
[tex]A = \frac{60°}{360°} \times 3.14 \times {5}^{2} [/tex]
A =15.4 inches square
If Bart has 20$ and Andy took $19.65 how much does Bart have
Answer:
well bart has 20.00
andy took 19.65
Step-by-step explanation:
subtract [tex]20.00\\-19.65\\\\_______\\0.35[/tex]
your answer should be 0.35
Bart had $20, and Andy took $19.65. Bart will have $0.35 remaining.
Start with Bart's initial amount: $20
Subtract the amount Andy took:
$20 - $19.65 = $0.35
Therefore, Bart will have $0.35 remaining.
Help, ill give brainliest
Answer:
its been awhile so i aint even going to try
Step-by-step explanation:
laskjdflaksjfasldkjfa;sldfjkal;kdfjasl;kfjasl;dkfj
The legs of a right triangle measure 4 and 6 inches. The area of the triangle is
5 in.2
24 in.?
12 in.2
Answer:
12
Step-by-step explanation:
The area of a right triangle is base1 * base2 *.5
This means the area is 4*6*.5 = 12
Solve the following system of equations. Enter the y-coordinate of the
solution. Round your answer to the nearest tenth.
5x+2y=7
- 2x + 6v=9
Y= 1.3 (Rounded to nearest tenth) x = 0.7 (rounded to the nearest tenth)
Step-by-step explanation:
You can solve this using substitution or elimination.
I used elimination.
-3(5x+2y =7) <---- On this step I used multiplicitive property of equality and multiplied everything by -3.
-15-6y=-21
-2x+6y=9
+_____________________
Add these and we get -17x=12
We divide by -17 and we get that x= 12/-17
Substitute this back into the original equation and we get that y=1.3 (rounded)
Answer:x=0.95
Y=1.12
Step-by-step explanation:
5x+2y=7...(1)
-2x+6y=9..(2)
Multiply (1) by -2
-10x-4y=7...(3)
Multiply (2) by 5
-10x+30y=45..(4)
Substrate (3) from (4)
34y=38
Y=38/34
Y=1.12
Substitute y=1.12 to(1)
5x+2(1.12)=7
5x+2.24=7
5x=7-2.24
5x=4.76
X=4.76/5
X=0.95
Formative exit ticket #2
Venus is approximately 67,000,000 miles from the Sun. Earth is approximately
26,000,000 miles from Venus. Approximately how many miles is Earth from the
Sun?
Answer:
92.768 million mi
Step-by-step explanation:
Answer:
Approximately 93 million.
Step-by-step explanation:
If Venus is 67 million miles from the sun, and Earth is 26 million miles from Venus, then you would need to add the distance from Earth to Venus to the distance from the sun to Venus
67,000,000 + 26,000,000 = 93,000,000
what is the value of z?
Polk Fitness sells gym passes in packs of 3. A competing gym, Benton Wellness, sells gym
passes in sets of 7. If both sold the same number of gym passes last month, what is the
smallest number of passes each could have sold?
undo the subtraction of x-2=6
Answer:
x = 8
Step-by-step explanation:
I am assuming that you want to solve for x.
Note the equal sign, what you do to one side, you do to the opposite side. Isolate the variable, x. Add 2 to both sides:
x - 2 (+2) = 6 (+2)
x = 6 + 2
x = 8
x = 8 is your answer.
~
Which is more work, pushing with 115 N over 15 m or lifting 20 kg 10 m?
Answer: THEY ARE THE SAME
Step-by-step explanation:
Therefore, lifting 20 kg 10 m requires more work than pushing with 115 N over 15 m.
Note: It's important to mention that the unit of work is the Joule (J), where 1 Joule is equal to 1 N·m. So, in both cases, the units of work are in Joules.
The perimeter of a triangle is 65 meters. The second side is 5 meters less than the first side The third side is 7
meters more than the first side. What is the length of each side?
Answer:
The length of each side is 31.5m, 26.5m, 7m
Step-by-step explanation:
Let the length of the first side of the triangle be x meters.
Then, the second side is x-5 meters.
The third side is given as 7 meters.
The perimeter is 65 meters
This gives us the equation:
[tex]65 = x + x - 5 + 7[/tex]
[tex]65 - 7 + 5 = x + x[/tex]
[tex]63 = 2x[/tex]
[tex]x = \frac{63}{2} = 31.5[/tex]
The length of each side is 31.5m, 26.5m, 7m
how many 8 oz bags of trail mix can be filled from a 10 pound bag of trail mix?
Answer:
20 bags
Step-by-step explanation:
Write the equation that describes the sequence 20, 28, 36, 44,...
Equation is a(n) = 12 + 8n
Step-by-step explanation:
Step 1: This is an Arithmetic Sequence with first term (a) = 20 and common difference (n) = 28 - 20 = 8. Find the equation using the expression for nth term.a(n) = a + (n -1)d
a(n) = 20 + (n - 1)8
= 20 + 8n - 8
= 12 + 8n
∴ Equation is a(n) = 12 + 8n
Answer:
12+8n
Step-by-step explanation:
This is sequence and series
Using the formula,a+(n-1)d
a means the first number
n means the number of progression
d means the difference
a=20
n=?
d=8
Apply the formula
=20+(n-1)8
=20+(8n-8)
=20+8n-8
=20-8+8n
=12+8n
The arithmetic equation is 12+8n
Here's some EZ Points
Answer:
ye thats cool
Step-by-step explanation:
i just did
Answer:
its the 3rd image
Step-by-step explanation:
Heeelllllkkpppp meeee
Answer:
it is 2
Step-by-step explanation:
corona is a beer virus so drink lots of it
Answer:
y = 1/3 +2
Step-by-step explanation: