Answer:
[tex]\large\boxed{\sqrt{-2}+\sqrt{-18}=4\sqrt2\ i}[/tex]
Step-by-step explanation:
[tex]\sqrt{-1}=i\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\===================\\\\\sqrt{-2}+\sqrt{-18}=\sqrt{(2)(-1)}+\sqrt{(9)(2)(-1)}\\\\=\sqrt2\cdot\sqrt{-1}+\sqrt9\cdot\sqrt2\cdot\sqrt{-1}\\\\=\sqrt2\cdot i+3\cdot\sqrt2\cdot i\\\\=i\sqrt2+3i\sqrt2=4i\sqrt2[/tex]
The sum of √-2 and √-18 is 4√2i.
What is the square root of -1?The square root of -1 is an imaginary number which is represented by i.
√-1=i
Here we have to calculate √-2+√-18
√-2+√-18
=√(-1).2+√(-1).18
=√(-1).√2+√(-1).√18
=i√2+i√18 (as √-1=i where i is imaginary number)
But √18=√(9*2)=√9*√2=3√2
(as √(ab)=√a.√b)
=i√2+i3√2
=√2(i+3i)
=√2*4i
=4√2i
Therefore the sum of √-2 and √-18 is 4√2i.
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On a map 1/8 of an inch stands for 24 miles. On this map two cities are 2.5 inches apart. What is the actual distance between cities
Answer:
The actual distance between the cities is 480 miles.
Step-by-step explanation:
2.5 inches is 20/8 inches, multiply 20 by 24 miles which gives you 480.
Answer:
480 miles.
Step-by-step explanation:
By proportion the actual distance is
(2.5 / 1/8) * 24
= (2.5 / 0.125) * 24
= 20 * 24
= 480 miles.
What is the solution to this equation?
x + 4(x + 5) = 40
O A. x= 12
O B. x = 7
O c. x= 9
O D. x= 4
Solve -5x=30 (5points)
6
-6
25
35
Answer: -6
Step-by-step explanation:
-5x = 30
x = 30/-5
x = -6
Hope it helped!
The quotient of three times a number and 4 is at least -16
Quotient is division,
Writing the equation out you get:
3x/4 ≥ -16
Now we can solve by x.
First multiply both sides by 4:
3x ≥ -64
Now divide both sides by 3:
x ≥ -64/3
A polynomial has been factored below, but some constants are missing.
3x^3+6x^2-24x=ax(x+b)(x+c)
What are the missing values of a,b, and c
Answer:
a=3 b=-2 c=4
Step-by-step explanation:
Select the graph for the solution of the open sentence. Click until the correct graph appears. |x| > 4
Answer:
***********o o**************
<----------(-4)--------(-2)--------(0)--------(-2)----------(4)-------------->
x>4 or x<-4
Step-by-step explanation:
You are looking for numbers that give you a distance, x, greater than 4 from 0. That wouldn't be anything between -4 and 4 because these would all give you a distance less than 4 from 0. So the answer would be to shade everything greater than 4 while also shading everything less than -4.
Here is a number line <-----|-----|-----|-----|-----|-----|-----|-----|-->
-6 -4 -2 0 2 4 6 8
Let's think about this more which of these numbers on this number line would satisfy |x|>4?
Numbers inside the numbers -4 and 4.
Or the numbers on the outside.
Let's try the inside numbers:
-2,02
|-2|>4
2>4 is false which means -2 doesn't satisfy |x|>4
|0|>4
0>4 is false which means 0 doesn't satisfy |x|>4
|2|>4
2>4 is false which means 2 doesn't satisfy |x|>4
We could also try -4 and 4... but these will both give you a distance equal to 4 from 0. And we are looking for greater than.
|-4|>4
4>4 is false which mean -4 doesn't satisfy |x|>4
|4|>4
4>4 is false which means 4 doesn't satisfy |x|>4
Now let's try the numbers on the outside:
-6,6,8
|-6|>4
6>4 is true so -6 does satisfy |x|>4
|6|>4
6>4 is true so 6 does satisfy |x|>4
|8|>4
8>4 is true so 8 does satisfy |x|>4
So what I'm trying to do is convince you more that the only numbers that would satisfy |x|>4 are numbers outside the interval from -4 to 4.
So x>4 or x<-4.
On a number line the solution would look like this:
***********o o**************
<----------(-4)--------(-2)--------(0)--------(-2)----------(4)-------------->
We have holes at -4 and 4 to mean we do not include those numbers. We would have if the inequality read [tex]|x| \ge 4[/tex]. The line underneath this inequality means to include or equals. We do not want to include; we did not have the equal sign. The only difference between the two solutions would be to fill the holes if you [tex]|x| \ge 4[/tex].
***********o o**************
<----------(-4)--------(-2)--------(0)--------(-2)----------(4)-------------->
The compound probability of two events, E and F, is ; the probability of E is and of F is . In two or more complete sentences, explain why E and F are not independent.
Answer:
Events E and F are not independent if the probability of event E occurring is affecting the probability of event F occurring.
Step-by-step explanation:
Two events are independent when the probability of one event occurring has no connection with that of the other event.
Example, when you toss a coin and roll a six sided die, the probability of getting a head or a tail has no connection with the probability of getting any number face.A real life example will be the probability going to the mall and owning a cat at home.These two have no influence on one another.
Mathematically independent events can be calculated as;
P(E∩F)=P(E)-P(F)
Find distance in units from Point A (4,2) to Point B (-3,2)?
Answer:
using distance formula or graphing you can find your answer
Step-by-step explanation:
(7,0) from 4 to -3 is -7. Take the absolute vale of -7 and you get 7.
Hope i helped :)
Answer:
Distance from A to B = 7 units
Step-by-step explanation:
We are given the following two points and we are to find the distance between them:
A (4,2)
B (-3,2)
We will be using the distance formula for this:
Distance = [tex] \sqrt { ( x _ 2 - x _1)^ 2 + ( y _ 2 - y _ 1 ) ^ 2 } [/tex]
AB = [tex]\sqrt{(-3-4)^2+(2-2)^2} = \sqrt{49}[/tex] = 7 units
(- 7x + 1) - (4x - 5)
Answer:-11x+6
Step-by-step explanation:
(-7x+1)-(4x-5)
collect the like terms and then calculate the sum
-7x+1-4x+5
-11x+1+5
-11x+6
Answer:
-11x +6
Step-by-step explanation:
(- 7x + 1) - (4x - 5)
Distribute the minus sign
(- 7x + 1) - 4x + 5
Combine like terms
-11x +6
Your friend has 100$ when he goes to the fair and 20$ on food. Rides at the fair cost $2 per ride. Which function can be used to determine how much he has left after X rides
Bryan is getting trained and licensed to be a truck driver. He only has $350 in his bank account. The training is free but gas costs 13 cents per mile. Write an equation where a is the amount of money in Bryan's bank account and m is the number of miles he travels.
A. a=0.13m−350
B. a=350−13m
C. a=13m−350
D. a=350−0.13m
Answer:
D
Step-by-step explanation:
a= 350 minus every 13 cents per mile
What is .7995 rounded to the nearest cent?
Answer:
.7995 rounded to the nearest cent is 0.80 cents
Answer:
.7995 rounded to the nearest cent is .80.
Step-by-step explanation:
Rounding with numbers higher than 4 makes them round up, lower than 5 makes them round down.
The original price of a game system was reduced by $99.
If p = the game system's original price in dollars, which algebraic expression
represents the reduced price?
Final answer:
The algebraic expression for the reduced price of the game system is p - $99, where p represents the original price in dollars.
Explanation:
To express the reduced price of the game system algebraically, we start with the original price, represented by the variable ( p ), and subtract the reduction amount of $99. Mathematically, this can be represented as p - $99.
This expression signifies that we are taking the original price ( p ) and reducing it by $99 to find the new price after the discount. It's essential to understand that algebraic expressions provide a concise and general way to represent mathematical relationships.
In this case, the expression p - $99 encapsulates the idea of reducing the original price by $99, allowing us to calculate the reduced price for any given original price represented by the variable ( p ). This algebraic representation is flexible and can be applied to various scenarios involving discounts or reductions.
The variable z is directly proportional to x. When x is 15, z has the value 165. What is the value of z when x = 25?
Answer:
z=275
Step-by-step explanation:
it has a ratio 1:11
that must be it
Answer:
275
Step-by-step explanation:
z is directly proportional to x:
z = kx
When x is 15, z is 165.
165 = k × 15
k = 11
When x = 25:
z = 11 × 25
z = 275
what is the ratio of 8 to 8
Answer:
1 to 1
Step-by-step explanation:
8 to 8 = 8:8 = 8/8
You can treat a ratio as a fraction. Reduce the fraction 8/8 by dividing the numerator and denominator by 8.
8/8 = 1/1
8 to 8 = 1 to 1
Answer:
1:1
Step-by-step explanation:
A ratio says that "for every _ of this quantity, you have _ of another quantity". This is just saying for every 8 of one thing, you have 8 of another. And then you can simplify, just like a fraction.
What are the solutions of 3x^2 - x +7 =0?
Answer: Option A
[tex]x=\frac{1+\sqrt{83}i}{6}[/tex] or [tex]x=\frac{1-\sqrt{83}i}{6}[/tex]
Step-by-step explanation:
Use the quadratic formula to find the zeros of the function.
For a function of the form
[tex]ax ^ 2 + bx + c = 0[/tex]
The quadratic formula is:
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
In this case the function is:
[tex]3x^2-x+7=0[/tex]
So
[tex]a=3\\b=-1\\c=7[/tex]
Then using the quadratic formula we have that:
[tex]x=\frac{-(-1)\±\sqrt{(-1)^2-4(3)(7)}}{2(3)}[/tex]
[tex]x=\frac{1\±\sqrt{1-84}}{6}[/tex]
[tex]x=\frac{1\±\sqrt{-83}}{6}[/tex]
Remember that [tex]\sqrt{-1}=i[/tex]
[tex]x=\frac{1\±\sqrt{83}*\sqrt{-1}}{6}[/tex]
[tex]x=\frac{1\±\sqrt{83}i}{6}[/tex]
[tex]x=\frac{1+\sqrt{83}i}{6}[/tex] or [tex]x=\frac{1-\sqrt{83}i}{6}[/tex]
Final answer:
The solutions to the equation 3x² - x + 7 = 0 are complex numbers. Using the quadratic formula, we find the solutions to be x = (1 + i√83) / 6 and x = (1 - i√83) / 6.
Explanation:
The solutions of the quadratic equation 3x² - x + 7 = 0 cannot be real numbers because the discriminant (b² - 4ac), in this case, is negative ((-1)² - 4(3)(7) = 1 - 84 = -83). Therefore, we need to use the quadratic formula to find the complex solutions. This formula is given by x = (-b ± √(b² - 4ac)) / (2a). By substituting the values from the equation into the quadratic formula, we obtain the complex solutions.
Quadratic formula application:
x = (-(-1) ± √((-1)² - 4(3)(7))) / (2(3))
x = (1 ± √(-83)) / 6
Therefore, the two complex solutions are x = (1 + i√83) / 6 and x = (1 - i√83) / 6, where i is the imaginary unit.
To confirm these answers, we can substitute each value back into the original equation and verify by simplification that each results in an identity.
HELP ASAP! I don’t under stand this.
Answer:
8/17
Step-by-step explanation:
Since this is a right triangle, we can use the trigonometric identities
sin Y = opposite side/ hypotenuse
= 16/34
Dividing the top and bottom by 2
= 8/17
which of the segments below is a secant
Answer:
B
Step-by-step explanation:
A secant is a line which intersects a circle at 2 points
From the diagram this is XY → B
The correct option is option B: The line segment XY is a secant.
What is secant?Line segment which intersects the circle at two points is called secant.
We are given circle with center at O.
From the options,
1. Line UZ :
UZ intersects the circle at one point. So it can't be secant.
2. Line XY:
XY intersects the circle at TWO points. So it is a secant.
3. Line XO :
XO intersects the circle at one point. So it can't be secant.
Therefore the line segment XY is a secant.
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The function f(x) = 10(5)x represents the growth of a lizard population every year in a remote desert. Crista wants to manipulate the formula to an equivalent form that calculates every half-year, not every year. Which function is correct for Crista's purposes? (1 point)
f(x) = 10(52) the x over 2 power
f(x) = ten halves (5)x
f(x) = 10(5)x
f(x) = 10( 5 to the one half power )2x
Answer:
[tex]f(x)=10(5^{2})^{\frac{x}{2}}[/tex] (first option)
Step-by-step explanation:
we have
[tex]f(x)=10(5)^{x}[/tex]
where
x ----> is the time in years
we know that
Crista wants to manipulate the formula to an equivalent form that calculates every half-year
The exponent will be
x/2 -----> the time every half year
To find an equivalent form
[tex]f(x)=10(5^{a})^{\frac{x}{2}}[/tex]
[tex]10(5)^{x}=10(5^{a})^{\frac{x}{2}}[/tex]
[tex]10(5)^{x}=10(5)^{a\frac{x}{2}}[/tex]
so
[tex]x={a\frac{x}{2}}[/tex]
[tex]a=2[/tex]
The equivalent form is
[tex]f(x)=10(5^{2})^{\frac{x}{2}}[/tex]
what is the solution of sqrt(x+2) -15=-3
Answer:
x = 142
Step-by-step explanation:
We are given the following expression for which we are to find the solution:
[tex] \sqrt { x + 2 } - 1 5 = - 3 [/tex]
Rearranging the equation to get:
[tex] \ sqrt { x + 2 } = - 3 + 1 5 [/tex]
Taking square root on both sides of the equation to get:
[tex](\sqrt{x+2} )^2=(12)^2[/tex]
[tex]x+2=144[/tex]
x = 142
[tex]\displaystyle\\\sqrt{x+2}-15=-3\\\\\sqrt{x+2}=-3+15\\\\\sqrt{x+2}=12~~\Big|~^2\\\\x+2=144\\\\x=144-2\\\\\boxed{x=142}[/tex]
.
A ski club charges a $45 membership fee plus $18 to rent ski equipment per day. Which of the following equation can be used to find the total cost of membership at the club, when renting equipment for X days?
Answer:
[tex]y = 18x + 45[/tex]
Step-by-step explanation:
You can use a linear equation of the form
[tex]y = mx + b[/tex] to represent the situation.
where b is the constant amount represented by the intercept with the y-axis, in this case b e is the cost of membership.
m is the slope, and in this case it is the cost per day of renting a team for x days.
y is the total cost of membership at the club, when renting equipment for X days
So the linear equation is:
[tex]y = 18x + 45[/tex]
slope intercept form of equation of a line that passes through (-3,8) y=-2/3x+6 what is the point slope equation for this line???
Answer:
[tex]\large\boxed{y-8=-\dfrac{2}{3}(x+3)}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
We have the equation of a line in the slope-intercept form
[tex]y=-\dfrac{2}{3}x+6\Rightarrow m=-\dfrac{2}{3}[/tex]
and the point (-3, 8).
Substitute:
[tex]y-8=-\dfrac{2}{3}(x-(-3))\\\\y-8=-\dfrac{2}{3}(x+3)[/tex]
Classify the isometry.
a) glide reflection
b) reflection
c) rotation
d) translation
Answer:
A. glide reflection
Step-by-step explanation:
This is a glide reflection since the figure has been both reflected over a line and transported downwards.
Answer:
a) glide reflection
Step-by-step explanation:
An isometry is a transformation of a figure in the plane that preserves lenght, it could be reflections, rotations, or translations, in the figure you can se what is called a glide reflection, which is a reflection of the figure over a line, and then a translation of the same figure.
Which of the following inequalities matches the graph?
A.3x - 2y \geqslant 4
B.3x - 4y \leqslant 2
C.3x - 2y \leqslant 4
D.the correct inequality is not listed
Answer:
C.Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have the points (0, -2) and (6, 7).
(0, -2) → b = -2
Calculate the slope:
[tex]m=\dfrac{7-(-2)}{6-0}=\dfrac{9}{6}=\dfrac{9:3}{6:3}=\dfrac{3}{2}[/tex]
Put the value of b and m to the equation of the line in the slope-intercept form:
[tex]y=\dfrac{3}{2}x-2[/tex]
=====================================
<, > - dotted line
≤, ≥ - solid line
<, ≤ - shaded region below the line
>, ≥ - shaded region above the line
======================================
We have the soli line (≤ or ≥).
Shaded region is above the line (> or ≥)
Therefore we have the answer: [tex]y\geq\dfrac{3}{2}x-2[/tex]
Convert to the standard form: [tex]Ax+By=C[/tex]
[tex]y\geq\dfrac{3}{2}x-2[/tex] multiply both sides by 2
[tex]2y\geq3x-4[/tex] subtract 3x from both sides
[tex]-3x+2y\geq-4[/tex] change the signs
[tex]3x-2yleq4[/tex]
what number should be added to both sides of the equation to complete the square
xsquared2-10x=7
Answer:
subtract 2 from each side and o think u decide the last two numbers
Answer:
Step-by-step explanation:2-10x=7
First you have to subtract you 2 on both sides so it would 7-2= 5
You are left with -10x =5
Then you divide your -10x by -10 to get rid of your x
Last you divide 5/-10
Find three rational numbers between -2 and 1 ?
Answer:
-19/10,-18/10,-17/10
Step-by-step explanation:
multiply the both numbers up and down by 10.
then find the numbers
Answer:-1, 0, -1.33
Step-by-step explanation: Rational numbers include those with repeating decimals, natural, counting, etc.
There are 42 boys and 48 girls in the sixth grade and each student must be assigned a homeroom. Each homeroom should have the same number of boys and the same number of girls.
What is the greatest possible number of sixth-grade homerooms?
A
8
B
6
C
4
The most significant number of homerooms that can be created with an equal number of boys and girls in each is 6.
Explanation:To answer this question, we need to find the greatest common divisor (GCD) for the number of boys and girls. The GCD is the most significant number that can divide both numbers equally. The GCD of 42 (number of boys) and 48 (number of girls) is 6.
Therefore, the sixth grade's most significant possible number of homerooms would be 6, with each homeroom having seven boys and eight girls.
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18 divided 5236
[tex]18 \sqrt{5236} [/tex]
A triangle has two sides of lengths 4 and 5. What value could the length of the third side be?
Answer:
2, 3, 4, 5, 6, 7 or 8.
Step-by-step explanation:
We know that the sum of two sides on a triangle should ALWAYS be greater than the third side. Then we have:
5-4 < x < 5 + 4
1 < x < 9
Therefore, the lenght of the third side could be any number between 1 and 9. If the lenght of the third side is an integrer, then the lenght could be:
2, 3, 4, 5, 6, 7 or 8.
Answer:
The length of the third side could be all real numbers greater than 1 unit and less than 9 units
Step-by-step explanation:
we know that
The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
so
Applying the triangle inequality theorem
Let
x ----> the length of the third side
1) 4+5 > x
9 > x
Rewrite
x < 9 units
2) 4+x > 5
x > 5-4
x > 1 units
therefore
The solution for the third side is the interval -----> (1,9)
All real numbers greater than 1 unit and less than 9 units
therefore
The length of the third side could be all real numbers greater than 1 unit and less than 9 units
Consider the polynomial:
x/4 -2x^5 +x^3/2+1
Which polynomial represents the standard form of the original polynomial?
A. x^3/2– 2x5 +x/4 + 1
B.–2x5 +x^3/2 +x/4 + 1
C.–2x5 +x/4 + x^3/2 + 1
D.1 – 2x5 + x^3/2 + x/4
Answer:
Step-by-step explanation:
Remember that polynomials involve ONLY integer powers of x. x^(3/2) does not satisfy that criterion.
Answer: OPTION B.
Step-by-step explanation:
In order to write a polynomial in Standard form you must arrange the terms by decreasing order of degree.
Then, given the polynomial:
[tex]\frac{x}{4} -2x^5 +\frac{x^3}{2}+1[/tex]
You must observe the exponent of each term of the polynomial and then arrange them from highest degree to lowest degree. Then, this polynomial written in Standard form is:
[tex]-2x^5 +\frac{x^3}{2}+\frac{x}{4}+1[/tex]