The solutions are:
[tex]x =3+2\sqrt{3}i\\\\\:x=3-2\sqrt{3}i[/tex]
Solution:
[tex]f(x) = x^2 - 6x + 21[/tex]
We have to find solutions when f(x) = 0
[tex]x^2 - 6x + 21 = 0[/tex]
Solve by quadratic formula
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=-6,\:c=21\\\\x=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:21}}{2\cdot \:1}[/tex]
[tex]x = \frac{6 \pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:21}}{2\cdot \:1}\\\\Simplify\\\\x = \frac{6 \pm \sqrt{36 - 84}}{2}\\\\x = \frac{6 \pm \sqrt{-48}}{2}\\\\x = \frac{6 \pm i \sqrt{48}}{2}\\\\simplify\\\\x = \frac{6 \pm 4\sqrt{3}i}{2}\\[/tex]
[tex]x = 3 \pm 2 \sqrt{3} i[/tex]
We have two solutions:
[tex]x = 3 + 2 \sqrt{3} i\\\\x = 3 - 2 \sqrt{3} i[/tex]
Thus the solutions are:
[tex]x =3+2\sqrt{3}i\\\\\:x=3-2\sqrt{3}i[/tex]
Which of the following is the solution to the compound inequality below? 5+ x >3 or 6x +1 <-29
The solution to the compound inequality is x > -2 and x < -5, or (-∞, -5) ∪ (-2, ∞).
Explanation:To find the solution to the compound inequality, we need to solve the individual inequalities separately and then find the intersection of their solution sets.
First, solve the inequality 5 + x > 3:The solution to the compound inequality is the intersection of the solution sets of the individual inequalities, so the solution is x > -2 and x < -5. To express this in interval notation, we write (-∞, -5) ∪ (-2, ∞).
Learn more about Compound inequality here:https://brainly.com/question/20296065
#SPJ12
Jill drove the 200 miles to Cincinnati at an average speed of 10 miles per hour faster than her usual average speed. If she completed the trip in 1 hour less than usual, what is her usual driving speed, in miles per hour
Let [tex]v[/tex] be the usual speed, and [tex]t[/tex] be the usual time.
Following the equation [tex]s=vt[/tex], where s is the space, v is the velocity and t is time, we know that usually we have
[tex]200=vt[/tex]
But this time we were 10mph faster and it took one hour less, so we have
[tex]200=(v+10)(t-1)[/tex]
Since both right hand sides equal 200, they must equal each other:
[tex]vt=(v+10)(t-1)=vt+10t-v-10 \iff 10t-v-10=0 \iff v=10t-10[/tex]
Plug this value in the first equation and we have
[tex]200=vt=(10t-10)t \iff 10t^2-10t-200=0[/tex]
This equation has solutions [tex]t=-4,\quad t=5[/tex]. We can only accept positive solutions, so we have t=5. We finally deduce, again from the first equation,
[tex]200=5v \iff v=\dfrac{200}{5}=40[/tex]
Solve y = 1/-25 x 8 + 175
Answer:
174.68
Step-by-step explanation:
Use PEMDAS. First, multiply 1/-25 by 8. (-8/25 or-.32)
Then, add 175 and y should= 174.68.
write an expression that represents the edge length of jewelry box
Answer:
The cubed-root of v (/v)
Step-by-step explanation:
Like your work on the second question illustrated, the cubed root of v (which is 216) is your expression for the edge length of the box in inches.
Hope this helps!
Step-by-step explanation:
Part A
Since volume of jewelry box is v cubic inches
Therefore,
Answer: Length of edge = v inches
Part B
Answer: 6 inches
4x+6=2x+10 find value of x makes equation true
Answer:
x = 2
Step-by-step explanation:
[tex]4x + 6 = 2x + 10 \\ \\ 4x - 2x = 10 - 6 \\ \\ 2x = 4 \\ \\ x = \frac{4}{2} \\ \\ x = 2[/tex]
Find the sum or difference. Write your answer in the simplest form. 5 1/3 + 6 1/6
Answer:
The answer for addition one is 11 1/2. The answer for subtraction would be -5/6.
Hope this helps. Can I please get brainliest if possible?
The answer you are looking for is 11 and 1/2.
To find this answer, you must first add the fractions together. Before you do so, you must make sure they have a common denominator. So, multiply 1/3 by 2/2 to get 2/6. Now, add 2/6 and 1/6 to get 3/6. 3/6 simplified (divided by 3/3) is 1/2.
Next, add the whole numbers. 5 + 6 is 11. Thus making your final answer 11 and 1/2.
I hope this helps!
The sum of six different natural numbers is 22. Find these numbers.
Answer:
1,2,3,4,5,7
Step-by-step explanation:
1+2+3+4+5+7 = 22
Final answer:
Six different natural numbers that add up to 22 are 1, 2, 3, 4, 5, and 7. The process involved starting with the smallest natural numbers and then incrementally adjusting the sequence to arrive at the sum of 22.
Explanation:
The question asks to find six different natural numbers whose sum equals to 22. We can begin with the smallest natural numbers, knowing that 1 cannot be included because the sum of the next five natural numbers (2, 3, 4, 5, and 6) already exceeds 22. If we start with 2 and follow with the next smallest numbers (3, 4, 5, and 6), the sum would be 20, which is close but not quite the target sum. To reach the sum of 22, we need to replace one of these numbers with a slightly larger number while still maintaining the rule that every number must be different.
Let's replace the 6 with a 7, so our numbers are now 2, 3, 4, 5, and 7. If we sum these up (2 + 3 + 4 + 5 + 7), we get 21. We need to add one more number to reach 22. The smallest number we haven't used yet is 1, but adding 1 to our sequence would require us to adjust another number as follows: 1, 2, 3, 4, 5, and 7 add up to 22. Therefore, the six different natural numbers whose sum is 22 are 1, 2, 3, 4, 5, and 7.
Write a polynomial function, with 5 zeros, with one zero with a multiplicity of 3, and one zero with a multiplicity of 2
Answer:
[tex](x-a)^{2} (x-b)^{3}[/tex]
Step-by-step explanation:
This is an openended question, but the anwer would be the following (where a and b are different real numbers)
[tex](x-a)^{2} (x-b)^{3}[/tex]
This would make the roots a (multiplicity of 2) and b (multipicity of 3).
Which of the following terms describes the measure indicated by the black
arrow below?
A. Mean
0
B. Minimum
O
C. Median
D. Range
Answer:
Median :)
Step-by-step explanation:
The term that describes the measure indicated by the black arrow below is option (C) median is the correct answer.
What is median?
The median is the middle value when a data set is ordered from least to greatest. Median is a measure of central tendency which gives the value of the middle-most observation in the data.
For the given situation,
The diagram shows the graph of data plotted in the plane.
In the graph, the black arrow is drawn in the middle of the data set.
The right side of the data is symmetric to the left side of the data.
Thus the arrow gives the value of the middle-most observation in the data.
Hence we can conclude that the term that describes the measure indicated by the black arrow below is option (C) median is the correct answer.
Learn more about median here
https://brainly.com/question/21396105
#SPJ3
In the diagram, shown below:
If ∠ABC = 63° and ∠BCA = 54° , then what is ∠DAB?
Answer:
DAB is 117.
Step-by-step explanation:
You can solve 2 ways, either by adding the opposite angles together or by finding the 3rd angle of the triangle and using linear pair.
First Method: 63 + 54 = 117
Second Method:
180 - 63 - 54 = 63 (All triangles = 180)
180 - 63 = 117 (All linear pairs = 180)
Solve for the equation for x: 4.5x-2.3=6.7
Step-by-step explanation:
4.5x-2.3=6.7 (add 2.3 so no number in the equation)
6.7+2.3 is 9
4.5x=9 (divide by 4.5 as it's 9 is divisible by 4.5
9/4.5 is 2
X=2
put it back into the equation
4.5*2 is 9
9-2.3 is 6.7
Therefore X=2
Answer:
x = 2
Step-by-step explanation:
Add 2.3 to both sides. We get:
4.5x = 6.7 + 2.3 = 9
If 4.5x = 9, then x = 2
What is a muscle verb??
Definition of muscle (Entry 2 of 2) transitive verb. : to move or force by or as if by muscular effort muscled him out of office. intransitive verb. : to make one's way by brute strength or by force.
Answer: move (an object) in a particular direction by using one's physical strength. -angie:) . pls mark me brainliest! have a nice day!
Step-by-step explanation: pls trust me
Which statements are true?
Select each correct answer.
a. 30x4−12x3=6x3(5x−2)
b. 4x2+10x=2x(2x+5)
c. 100x3+5=5x3(20x+1)
d. 8x3−6x=2x3(4−3x3)
Answer:
30x^4−12x^3=6x^3(5x−2) = True
4x^2+10x=2x(2x+5) = True
100x^3+5=5x^3(20x+1) = False
8x^3−6x=2x^3(4−3x3) = False
Step-by-step explanation:
The statements which are true are 30x4−12x3=6x3(5x−2) , 4x2+10x=2x(2x+5) and 100x3+5=5x3(20x+1)
To determine which of the statements are true, we can simplify each equation and compare.
Option a :
30x4−12x3=6x3(5x−2): Factoring out the common term we can see this equation is true.
Option b:
4x2+10x=2x(2x+5): After simplifying both sides we find that 2x(2x + 5) = 4x2 + 10x, so statement (b) is true.
Option c:
100x3+5=5x3(20x+1): Attempt to simplify this equation as 5x3(20x + 1). Since this simplification holds, statement (c) is also true.
Option d:
8x3−6x=2x3(4−3x3): Simplifying the right side does not give us the left side; thus, statement (d) is false. The correct form would be 2x(4x2 - 3), assuming a typo in exponent notation.
Triangle XYZ is similar to triangle ABC. SOLVE FOR K.
Answer:
k=13.5
Step-by-step explanation:
Ⓗⓘ ⓣⓗⓔⓡⓔ
Well we know there is a scale factor of 3 for the first triangle to the second.
4.5 to k
3 to 9
4 to 12
Hence, all we need to do it 4.5*3=k
4.5*3=13.5
k=13.5
(っ◔◡◔)っ ♥ Hope this helped, have a great day! ♥
˜”*°•.˜”*°• ~Star •°*”˜.•°*”˜
Answer:
13.5
Step-by-step explanation:
Because they are similar you can create a ratio problem
4.5/k = 3/9
3k = 40.5
k = 13.5
You have 20 quarters. You find 40% more quarters in your room. Then you go shopping and spend 50% of the total number of quarters. Write a expression that represents the total number of quarters you take with you when you go shopping. How much money do you have left
Answer:
a) 28 quarters
b) 14 quarters
Step-by-step explanation:
We are given the following in the question:
Number of quarters = 20 quarters
Number of quarters in room = 40%
Total number of quarter in room =
[tex]=40\%\times (20)\\\\=\dfrac{40}{100}\times 20\\\\=8[/tex]
Thus, the total quarters taken to shopping =
[tex]=20 +40\%\times (20)\\\\=20+8\\=28[/tex]
Thus, 28 quarters were taken to shopping.
Quarter spent on shopping = 50%
Total number of quarter spent in shopping =
[tex]=50\%\times (28)\\\\=\dfrac{50}{100}\times 28\\\\=14[/tex]
Money left =
Money taken for shopping - Money spent
[tex]= 28-14\\=14[/tex]
Thus, we are left with 14 quarters after shopping.
2/3=n/12
solve the proportion
Answer: [tex]n=8[/tex]
Cross-multiply
[tex]2/3=n/12[/tex]
[tex](2)*(12)=n*(3)[/tex]
[tex]24=3n[/tex]
Flip the equation
[tex]24=3n---->3n=24[/tex]
Divide both sides by 3
[tex]3n/3=24/3[/tex]
[tex]24/3=8----> n=8[/tex]
Final answer:
To solve the proportion 2/3 = n/12, cross multiply to get 2×12 = 3×n. Simplify the equation to 24 = 3×n, and divide both sides by 3 to get n = 8.
Explanation:
To solve the proportion 2/3 = n/12, you begin by cross multiplying to find the value of n. This means you multiply 2 by 12 and 3 by n. The equation now looks like this: 2×12 = 3×n.
Next, simplify the left side of the equation, which results in 24 = 3×n.
Finally, solve for n by dividing both sides of the equation by 3, leading to n = 8.
This method of cross multiplication and division is a common technique used to solve proportions and find missing values in ratios.
A mother gives birth to a 9 pound baby. Every 4 months, the baby gains 2 pounds.
If x is the age of the baby in months, then y is the weight of the baby in pounds.
Find an equation of a line in the form y = mx + b that describes the baby's weight.
Answer:
y=2/4x+9
Step-by-step explanation:
Let event A = the place is a city let B = the place is in North America what is P(A and B)
A. 5/7
B. 3/7
C.4/7
D.2/7
Answer:
D. 2/7
Step-by-step explanation:
We assume that the intention is that one of the places is chosen at random from the list of 7 places.
2 of those are cities in North America, so the probability that a place randomly chosen from this list is a city in North America is ...
P(A & B) = 2/7
Answer: 4/7
Step-by-step explanation:
Tom rented a truck for one day. There was a base fee of 19.95 , and there was an additional charge of 85 cents for each mile driven. Tom had to pay 216.30 when he returned the truck. For how many miles did he drive the truck?
Answer:
231 miles.
Step-by-step explanation:
Tom rented a truck with a base fee of 19.95. You will subtract this from the total since you just want to get the mileage.
Tom is getting charged .85 cents per mile driven.
Tom payed 216.30 subtotal minus the 19.95 base fee since we are trying to only see how many miles he drove.
(216.30-19.95=196.35) This will be total for each mile. All we need to do is divide to get the total of miles
(196.35÷.85= 231)
231 is the number of miles Tom drove.
given f(x) = 5x-1....what is f(-2) ?
Answer: -11
Step-by-step explanation:
f(-2)=5(-2)-1
f(-2)= -10-1
f(-2)= -11
Answer:
f(-2) = -11
Step-by-step explanation:
x = -2
plug in -2 for x in the given equation:
f(x) = 5x - 1
f(-2) = 5(-2) - 1
Simplify. Remember to follow PEMDAS. First, multiply, then subtract:
5(-2) = 5 * -2 = -10
-10 - 1 = -11
f(-2) = -11.
~
A store has 500 winter coats. 35% are wool and 1/4 are nylon. How many coats are either wool or nylon?
Answer:
60%
Step-by-step explanation:
P(A or B) = P(A) + P(B)
175/500 are wool and 125/500 are nylon
Add them to get 300/500 or 3/5 or 60%
There are 300 coats that are either wool or nylon.
A store has 500 winter coats. 35% are wool, and 1/4 are nylon.
To find the number of coats that are either wool or nylon, we add the number of wool coats and nylon coats.
First, calculate the number of wool coats: 500 coats * 35% = 0.35 * 500 = 175 wool coats.
Then, calculate the number of nylon coats: 500 coats * 1/4 = 500 * 1/4 = 125 nylon coats.
Finally, add the number of wool and nylon coats to find the total number of coats that are either wool or nylon: 175 wool coats + 125 nylon coats = 300 coats.
Which expression is equivalent to (3x^2)^3
Answer:
27x^6
Step-by-step explanation:
(3x^2)^3=
3^3(x^2)^3=
27x^6
Final answer:
The expression equivalent to (3x²)³ simplifies to 27x⁶, by cubing the coefficient and multiplying the exponent by 3.
Explanation:
The expression equivalent to (3x²)³ is found by cubing the digit term and multiplying the exponent by 3. When we cube 3, we get 3 x 3 x 3 which equals 27. Then, we apply the cubing to the variable term x², by multiplying the exponent 2 by 3, giving us x²ˣ³ or x⁶. Thus, the expression simplifies to 27x⁶.
Let f(x)= x2 - 14 and g(x) = 6-X.
Find (fq)(7).
Answer:
[tex](fg)(7) = - 35[/tex]
Step-by-step explanation:
The given functions are:
[tex]f(x) = {x}^{2} - 14[/tex]
and
[tex]g(x) = 6 - x[/tex]
We want to to find
[tex](fg)(7)[/tex]
Note that:
[tex](fg)(x) = f(x) \times g(x)[/tex]
We substitute the functions to obtain:
[tex](fg)(x) = ( {x}^{2} -1 4 ) \times (6 - x)[/tex]
We now substitute x=7, to get:
[tex](fg)(7) = ( {7}^{2} -1 4 ) \times (6 - 7)[/tex]
This implies that
[tex](fg)(7) =( 49-1 4 ) \times (6 - 7)[/tex]
[tex](fg)(7) = 35 \times - 1 = - 35[/tex]
Somebody please help meeeee
Step-by-step explanation:
[tex] \frac{2 + 3i}{4 - 5i} [/tex]
[tex] \frac{(2 + 3i)(4 + 5i)}{(4 - 5i)(4 + 5i)} [/tex]
[tex] \frac{8 + 10i + 12i + 15 {i}^{2} }{16 - 25 {i}^{2} } [/tex]
[tex] \frac{8 + 22i + 15( -1 )}{16 - 25 ( - 1)} [/tex]
[tex] \frac{8 - 15 + 22i}{16 + 25} [/tex]
[tex] \frac{ - 7 + 22i}{41} [/tex]
So, a= -7
b= 22
c= 41
Jacob copies 30% of a document. He copies 8 pages. Write the number of pages in the
document.
Answer:
27
Step-by-step explanation:
Number of documentsjacob copies 30% of a document which is 8 pages
we can solve this using cross multiplication
30 % : 8
100% : x
30%x = 100%*8
30% x = 8
x = 8/ 30%
x = 26.667
to 2sf
number of pages in the documents 27Solve the inequality.
7- 9x4 - 11x
Answer:
-11x-29
Step-by-step explanation:
£2300 is invested for 4 years at 5% per year simple interest. Work out the total interest
Answer: £460
Step-by-step explanation:
Use this formula to find the total interest [tex]I=\frac{P*R*T}{100}[/tex]
I stands for interest, P is principal, R is rate, and T is time.
Principle = £2300
Rate = 5%
Time = 4 years
[tex]\frac{2,300*5*4}{100} =\frac{46,000}{100} =460[/tex]
Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! :-)
- Cutiepatutie ☺❀❤
Answer:
£460
Step-by-step explanation:
Simple interest =PRT/100
Where P = principal
R= rate
T = Time
Given
P= £2300
T= 4yrs
R = 5%
Interest = 2300 x 5 x 4/100
Multiply through
Interest = 46000/100
Interest = £460
ILL GIVE BRAINILIST!!! reasoning plz!
Answer:
4th parallelogram is correct
Step-by-step explanation:
you can find this answer by making use of ratios
the angles (112 ) should remain the same hence :
the second and third answer are incorrect
now lets look at the 1st and 4 th answer
IST paralleogramthe diagonal is 4.8 and horizontal is 6
now compare to the original by using ratios.. the ratios for both diagonal and horizontal should be the same for it to be correct
diagonal ratio = 5.8/4.8 = 1.21
horizontal ratio = 8/6= 1.33
both ratios are not the same hence INCORRECT
4TH parallelogramthe diagonal is 2.9 and horizontal is 4
now compare to the original by using ratios.. the ratios for both diagonal and horizontal should be the same for it to be correct
diagonal ratio = 5.8/2.9 = 2
horizontal ratio = 8/4 = 2
both ratios are the same. hence CORRECT
4TH parallelogram is correctA person buys 3 shirts for 42.00 how much would 8 shirts costs at that same price
Answer:
$112
Step-by-step explanation:
9. John is painting a box that is shaped like a cube. One-eighth of a bottle of paint covers of one face of the box. How many bottles of paint will John need to paint the entire box?
Final answer:
John will need 4.5 bottles of paint to cover the entire cube, with one-eighth of a bottle covering one-sixth of one face and a cube having 6 faces.
Explanation:
The question asks how many bottles of paint John will need to paint the entire cube. If one-eighth of a bottle covers one-sixth of one face, then to cover the whole face, John would need 6 times the amount of paint for one-sixth of the face, which is 6 x 1/8 = 3/4 of a bottle. Since a cube has 6 faces, he will need 6 times 3/4 bottles to paint the entire cube. Therefore, John will need 4.5 bottles to paint the entire cube, as each face requires 3/4 of a bottle and there are 6 faces.