Answer:
- i
Step-by-step explanation:
i = √( - 1) ;
i³ = (√( - 1))(√( - 1))(√( - 1)) = - 1 (i) = - i
How do I solve this problem and check all the solutions?
Answer:
x-5=sqrt(2x+5)
then square both sides
x2-10x+25=2x+5
x2-8x+20=0
rest is trivial
Step-by-step explanation:
Answer:
x = 10
Step-by-step explanation:
Given
x - [tex]\sqrt{2x+5}[/tex] = 5 ( subtract x from both sides )
- [tex]\sqrt{2x+5}[/tex] = 5 - x ( divide all terms by - 1 )
[tex]\sqrt{2x+5}[/tex] = x - 5 ( square both sides )
2x + 5 = (x - 5)²
2x + 5 = x² - 10x + 25 ( subtract 2x + 5 from both sides )
0 = x² - 12x + 20 ← in standard form
0 = (x - 2)(x - 10) ← in factored form
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x - 10 = 0 ⇒ x = 10
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are the solutions
x = 2
2 - [tex]\sqrt{4+5}[/tex] = 2 - [tex]\sqrt{9}[/tex] = 2 - 3 = - 1 ≠ 5
Thus x = 2 is an extraneous solution
x = 10
10 - [tex]\sqrt{20+5}[/tex] = 10 - [tex]\sqrt{25}[/tex] = 10 - 5 = 5 = right side
Thus x = 10 is the solution
A little girl counts using the fingers of her left hand as follows: She starts by calling her thumb 1, the first finger 2, middle finder 3, ring finger 4, and little finger 5. Then she reverses direction, calling the ring finger 6, middle finger 7, first finger 8 and thumb 9, after which she calls her first finger 10 and so on. If she continues to count in this manner, on which finger will she stop?
a) What if the girl counts from 1 to 10?
b) What if the girl counts from 1 to 100?
c) What if the girl counts from 1 to 1000?
Answer:
(a) Index finger
(b) Ring finger
(c) Index finger
Step-by-step explanation:
Taking thumb as standard for the question.
Thumb series 1 , 9 , 17 ,25, 33......
general term for this
a(n) = 1 + (n-1)8
= 1 + 8n -8
= 8n -7
(a) For 1 to 10
8n -7 = 10
8n = 16+1 (remainder)
so the thumb is for 9 and the next is index finger.
10th = index finger.
(b) for 1 to 100
8n - 7 = 100
8n= 107
107 = 13x 8 + 3(remainder)
so the third finger from thumb is Ring finger
100th = Ring finger
(c) 8n - 7 = 1000
8n = 1007
1007= 125x8 +7 (remainder)
so the 7th finger next to thumb is Index finger
1000th = index finger
Function or not a Function?
A piece of candy corn is in the
shape of a cone.
The height of
the candy corn is 4 centimeters
and the diameter is 2
centimeters.
Find the volume.
Can someone help me out with this please!
What is the domain and range of the function: y= 10(4) + 100
Domain: ____
Range: ____
giving brainly
what is the equation of the line in slope intercept form
Answer:
y=-4/3x-60
Step-by-step explanation:
Answer:
y=-4/3x-60
Step-by-step explanation:
The line intercepts -60 and the slope by using a slope triangle, for y it was from -20 to 20 so 40 units difference, and for x it was -30 to -60 so 30 unit difference. 40/-30 simplified = -4/3
What is the equation of the line in slope-intercept form that is perpendicular to the line y = -x-2 and passes
through the point (-12, 10)?
O y=-x-6
O y=-x + 6
Oy= x + 26
O y = x + 10
The equation of the line that is perpendicular to y = -x - 2 and passes through the point (-12, 10) is y = x + 22 in slope-intercept form.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The given line has a slope of -1, since it is in the form y = mx + b, where m is the slope, and in this case, m = -1.
To find the equation of the line that is perpendicular to this line,
We need to use the fact that the product of the slopes of two perpendicular lines is -1.
Let the slope of the perpendicular line be m'.
Then:
-1 x m' = -1
m' = 1
So the slope of the perpendicular line is 1.
We also know that the perpendicular line passes through the point (-12, 10).
Using the point-slope form of the equation of a line, we have:
y - y(1) = m' (x - x(1))
Substituting m' = 1 and (x(1), y(1)) = (-12, 10),
We get:
y - 10 = 1 (x + 12)
Simplifying this equation gives:
y = x + 22
Thus,
The equation of the line that is perpendicular to y = -x - 2 and passes through the point (-12, 10) is y = x + 22 in slope-intercept form.
Learn more about equation of a line here:
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PLEASE HELP! Ann needs to buy plastic forks. Brand A has a box of 25 forks for $2.12. Brand B has a box of 72 forks for $5.09 .
Find the unit price for each brand. Then state which brand is the better buy based on the unit price.
Round your answers to the nearest cent. And thank you if you answer this I really need the answer.
Answer:
To find the price per spoon of brand A, divide the cost by the amount of spoons:
1.99 / 25 = 0.0796
Repeat this process for brand B:
3.89 / 42 = 0.0926
Brand A, at $0.08 a unit, is the better buy of brands A and B.
ΔABC is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in the image ΔA′B′C′. If A = (2, 2), B = (4, 3), and C = (6, 3), what is the length of ?
Answer:
Fourth option is correct. The length of B'C' is 1 unit.
Step-by-step explanation:
The vertices of triangle ABC are A = (2, 2), B = (4, 3), and C = (6, 3).
Distance formula:
The length of BC is 2 units.
It is given that ΔABC is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in the image ΔA′B′C′.
It means the ΔABC and ΔA′B′C′ are similar and corresponding sides of ΔA′B′C′ and ΔABC are proportional.
The scale factor is 0.5.
Therefore the length of B'C' is 1 unit and fourth option is correct
Answer:
D= 1 unit
Step-by-step explanation:
Which system is equivalent to StartLayout Enlarged left-brace 1st Row 3 x squared minus 4 y squared = 25 2nd row negative 6 x squared minus 2 y squared = 11 EndLayout
Answer:
second option :)
Step-by-step explanation:
Answer:
B.
StartLayout Enlarged left-brace 1st Row 3 x squared minus 4 y squared = 25 2nd row negative 12 x squared + 4 y squared = 22 EndLayout
Step-by-step explanation:
what is the range of the function f(x)=-8x+13 when the domain is (-2,0,3)?
Answer:
The complete set of domain (x) and range values (y) is given by:
x y
-2 39
0 13
3 11
Step-by-step explanation:
Considering the function
[tex]f(x)=-8x+13[/tex]
As we know that the range of a function consists of the entire set of all possible resulting values of the dependent variable commanly called y or f(x), once we have substituted the domain.
Now
As the x values are -2, 0, and 3. So, the domain interval is (-2,0,3).Putting x = -2 in f(x) to determine the range for the value x = -2
[tex]f(x)=-8x+13[/tex]
[tex]f(-2)=-8(-2)+13=16+13=39[/tex]
Putting x = 0 in f(x) determine the range for the value x = 0
[tex]f(x)=-8x+13[/tex]
[tex]f(0)=-8(0)+13=0+13=13[/tex]
Putting x = 0 in f(x) determine the range for the value x = 3
[tex]f(x)=-8x+13[/tex]
[tex]f(3)=-8(3)+13=-24+13=11[/tex]
Therefore, the complete set of domain (x) and range values (y) is given by:
x y
-2 39
0 13
3 11
A litter of puppies had 2 white puppies and 5 brown puppies. What percent of white puppies are in the litter? Round to the nearest whole number
Answer:
29%
Step-by-step explanation:
0.28571428571 as an approximate percent is 29%. There are 2 white puppies and 7 total puppies(2 white + 5 brown)
Hope this helps!
Answer:
29%
Step-by-step explanation:
0.28571428571 is the original number which makes 29%
Hope this helps! Have a great day :)
Marking brainless!!!
Answer:
A
Step-by-step explanation:
gordon types 1800 words in 25 minutes. word per minute
Answer:
72
Step-by-step explanation:
words per minutes= 1800÷25=72
Can someone help me solve this equation? x2 + x - 30 = 0
Answer:
x = 10
Step-by-step explanation:
x x 2 + x - 30 = 0 use the commutative property to reorder the terms
2x + x - 30 = 0 collect like terms
3x - 30 = 0 move constant to the right hand side and change its sign
3x = 30 divide both sides of the equation by 3
x = 10
what is 2 1/9 x 1 1/2
Answer:
3.16
Step-by-step explanation:
Hope this helps!
Name the coefficients in a +2a+3a-4a
Answer:
2,3,4
Step-by-step explanation: there next to veribuls
Help I need an answer as soon as possible
Answer:
charlie is the one,im pretty sure
Which statements can be used to justify the fact that two right angles are supplementary? Select two options.
A right angle measures 90°.
If two angles are complementary, the sum of the angles is 90°.
If two angles are supplementary, the sum of the angles is 180°.
A complementary angle is one-half the measure of a supplementary angle.
A supplementary angle is twice the measure of a complementary angle.
Answer:
Which statements can be used to justify the fact that two right angles are supplementary? Select two options.
* A right angle measures 90°.
If two angles are complementary, the sum of the angles is 90°.
* If two angles are supplementary, the sum of the angles is 180°.
A complementary angle is one-half the measure of a supplementary angle.
A supplementary angle is twice the measure of a complementary angle.
Step-by-step explanation:
(A) and (C)
A right angle measures 90°, hence the sum of two right angles is 180° (supplementary)
AnglesAn angle is formed when two lines intersect each other. Two angles are said to be supplementary if their measures add up to 180 degrees while Two angles are called complementary if their measures add up to 90 degrees.
To justify the fact that two right angles are supplementary. Firstly a right angle measures 90°, hence the sum of two right angles is 180° (supplementary)
Find out more on Angles at: https://brainly.com/question/25770607
A store sells 3 cans of beans for $9. What is the price of 7 cans of beans?
Answer:
21
Step-by-step explanation:
because you divide 9 byy 3 and you get 3 so then you do 7 x 3 7x3 is 21
I need help with this equation
Answer:
Here:)
Step-by-step explanation:
x= -8
Answer: x = -8
Step-by-step explanation:
8x = 4x - 32
subtract 4x from both sides
4x = -32
divide by 4 on both sides
x = -8
:)
pls help quickly thank you
Answer: $637
Step-by-step explanation:
At a high school football game, admission is $5 for students and $10 for non-students. There were 500 people at the first game, and the school made $4,000 from admissions. In this activity, you will find the number of students and non-students at the game.
Please write the two equations algebraically and then solve :)
Answer:x = 200 students
y = 300 non-students
Step-by-step explanation:
5x + 10y = 4000
x + y = 500
Set y = 500-x
5x + 10(500-x) = 4000
5x + 5000-10x
-5x + 5000 = 4000
-5x = -1000
x = 200 students
y = 300 non-students
Let's double checks
5(200) + 10(300)
1000 + 3000 = 4000
As an estimation we are told 5 miles is 8 km.
Convert 60 km to miles.
Answer:
37.5 miles
Step-by-step explanation:
We can find the rate of conversion by dividing kilometers by miles. 5÷8=1.6, so 1.6 km = 1 mile. Now we can divide 60 by 1.6 to find miles.
[tex]60/1.6=37.5[/tex]
Hope this helped!
Answer:
96 km
Step-by-step explanation:
I try it its 96 km
Trust me
A $ 4.00 sales tax is charged for a $ 50.00 purchase . At this rate, what is the sales tax for a 1200.00 purchase
Sales tax for the purchase of $50 is $4
Therefore, x% of 50 = 4
(x%) 50 = 4
x/100 x 50 = 4
x/2 = 4
x = 4 x 2
x = 8
Therfore, there is a 8% sales tax on the purchase.
Sales tax on the purchase of $1200 = 8% of 1200
= 8/100 x 1200
= 8 x 12
= 96
A $96.00 sales tax is charged on a purchase of $1200.00
Solve for x.
x/3+y=2x+19
Answer:
The answer is [attached photo].
Hope this helps and if you could mark this as brainliest. Thanks!
Answer:
(3+y)-19=x
Step-by-step explanation:
x/3+y=2x+19
=3+y=2x-x+19
(3+y)-19=x
A bread recipe calls for 2 cups of wheat flour and 3 1/4 cups of white flour. How much flour does the recipe call for altogether?
Answer:
Step-by-step explanation:
2+3.25=5.25 or 5 1/4 cups of flour total
Find the equation of the line shown.
Answer:
I think that it is y= -2x +9
Step-by-step explanation:
I am sure about the slope but the y-intercept (9) might be wrong.
the slope of the line that goes through the points (2,4) and (7,8)
Mark bought gifts for his friends, and each gift cost $9. Let y represent the total cost and x represent the number of gifts. Write an equation to represent the proportional relationship between the total cost and the number of gifts he bought.
Answer:
y = 9x
Step-by-step explanation:
You can set up linear equations like this: y = mx + b, where m is the slope or rate, and b is the y-intercept.
9 would be the slope, since he has to pay $9 per gift.
The y-intercept is when x = 0, but if he doesn't buy any gifts, he won't have to pay anything, so b = 0. You don't have to include it since it's 0.
So, it's just y = 9x
Hope that helps! :D
Answer:
easy
Step-by-step explanation: