The correct option are a. [tex]\(x = -3 + 3i\)[/tex] and b. [tex]\(x = -3 - 3i\)[/tex].The solutions are complex numbers [tex]\(x = -3 + 3i\)[/tex] and [tex]\(x = -3 - 3i\)[/tex].
To find the solution of the quadratic equation [tex]\(x^2 + 6x = -18\)[/tex], we need to solve it for [tex]x[/tex].
Starting with the given equation:
[tex]\[x^2 + 6x = -18\][/tex]
Rearranging it to the standard form of a quadratic equation:
[tex]\[x^2 + 6x + 18 = 0\][/tex]
Now, to find the solutions, we can use the quadratic formula:
[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]
where [tex]\(a = 1\), \(b = 6\)[/tex], and [tex]\(c = 18\).[/tex]
Substituting the values:
[tex]\[x = \frac{{-6 \pm \sqrt{{6^2 - 4 \cdot 1 \cdot 18}}}}{{2 \cdot 1}}\]\[x = \frac{{-6 \pm \sqrt{{36 - 72}}}}{2}\]\[x = \frac{{-6 \pm \sqrt{{-36}}}}{2}\]\[x = \frac{{-6 \pm 6i}}{{2}}\]\[x = -3 \pm 3i\][/tex]
So, the solutions are complex numbers [tex]\(x = -3 + 3i\)[/tex] and [tex]\(x = -3 - 3i\)[/tex].
The complete question is:
Which of the following is a solution of [tex]\(x^2 + 6x = -18\)[/tex]?
a) [tex]\(x = -3 + 3i\)[/tex]
b) [tex]\(x = -3 - 3i\)[/tex]
c) [tex]\(x = -3\)[/tex]
d) [tex]\(x = 3\)[/tex]
2. Find the area of the regular polygon. Give the answer to the nearest tenth. Hexagon with a radius of 5 in.
A. 65.0 in.^2
B. 129.9 in.^2
C. 259.8^2
D. 53.0^2
3. Divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of length 2.75 miles and 1.32 miles. The angle between the sides of the triangle is 35°. To the nearest hundredth, find the search area.
A. 2.08 mi.^2
B. 2.97 mi.^2
C. 1.49 mi.^2
D. 1.04 mi.^2
Answer: The correct options are (2). A, (3). A.
Step-by-step explanation: The calculations are as follows:
(1) We are to given the area of a regular hexagon with radius 5 in.
The AREA of a regular hexagon with side 'a' units is given by
[tex]A=\dfrac{3\sqrt3}{2}a^2.[/tex]
We know that the radius of a regular hexagon is equal to the length of each side, so we have
a = 5 in.
Therefore, the area of the hexagon will be
[tex]A=\dfrac{3\sqrt3}{2}\times 5^2=1.5\times 1.732\times 25=64.95\sim 65~\textup{in}^2.[/tex]
Thus, (A) is the correct option.
(2) Given that two adjacent sides of the triangle measure 1.32 miles and 2.75 miles.
The angle lying between the two sides measure 35°.
we are to find the area of the triangle.
We know that the area of a triangle with two adjacent sides of measure 'a' and 'b' units and 'β' be the measure of the angle lying between them is given by
[tex]A=\dfrac{1}{2}ab\sin \beta.[/tex]
Here, a = 2.75 miles, b = 1.32 miles and β = 35°.
Therefore, the total search area, in the form of triangle is given by
[tex]A=\dfrac{1}{2}\times 2.75\times 1.32\times \sin 35^\circ=1.815\times 0.5735=2.08~\textup{mi}^2.[/tex]
Thus, the correct option is (A) 2.08 mi².
Hence, the correct options are (2). A, (3). A.
True or False ? explain your answer
18.csc^{-1} (csc(-\frac{\pi}{4} )) = -\frac{\pi}{4}
19.sec(sec^{-1} (\sqrt{3} ))=\sqrt{3}
Which expression is equivalent to x+2+ [4x - x2+6x+8\x+4]
If the area of a circle below is 18ft, what is the area of the shaded sector?
Answer: It’s definitely 4.5, so D! Hope this helps someone! :>
Danny decided to invest his $500 tax refund rather than spending it. He found a bank that would pay him 4% interest, compounded quarterly. If he deposits the entire $500 and does not deposit or withdraw any other amount, how long will it take him to double his money in the account? Round your answer to the nearest tenth of a year. It will take Answer years for his investment to double.
Need help on this!!!
What is the domain of the function
Algebra question ( Matrices and Determinants ) 20 points
Answer:
.
Step-by-step explanation:
What is the selling price of an item if the original cost is $784.50 and the mark up on the item is 6.5 percent?
from my calculations it should be $835.49
Answer:
30
Step-by-step explanation:
Kendra has a painting canvas that is 20 inches wide by 37 inches high. She painted a red rose, which covered 50% of the canvas.
What was the area of the canvas which was covered by the red rose?
The area of the canvas covered by the red rose is 370 square inches, calculated by multiplying the width and height of the canvas to find the total area and then taking 50% of that area.
The task is to calculate the area of a canvas that was covered by a red rose painting, which took up 50% of the total canvas area. To find the area covered by the red rose, we first need to calculate the total area of the canvas. The total area (A) of a rectangle is calculated by multiplying its width (W) by its height (H), which gives us the formula:
A = W x H
In this case, Kendra's canvas is 20 inches wide and 37 inches high. Using the formula:
A = 20 inches x 37 inches = 740 square inches
Now, since the red rose covers 50% of the canvas, we simply take 50% of the total area to find the area covered by the red rose:
Area covered by the red rose = 50% of 740 square inches = 0.50 x 740 square inches = 370 square inches
Therefore, the area of the canvas covered by the red rose is 370 square inches.
Jake rented a kayak at $26 for 3 hours. If he rents the same kayak for 5 hours, he has to pay a tota rent of $42. Write an equation in the standard form to represent the total rent (y) that Jake has to pay for renting the kayak for X hours
You spin a spinner 48 times. Out of the 48 trials, the pointer lands 6 times on section two. What is the experimental probability of the pointer landing on section two?
1/3
1/27
1/8
1/7
Answer:
1/8
Step-by-step explanation:
what expression is equivalent to \root(4)(x^(10))
The equivalent expression to \(\root(4)(x^{10})\) is \(x^{\frac{5}{2}}\), which is obtained by realizing that the fourth root of a number can be expressed as raising that number to the 1/4 power and then applying exponent multiplication.
Explanation:To find an expression equivalent to \(\root(4)(x^{10})\), we need to apply the laws of exponents for roots and powers. The fourth root of a number is the same as raising that number to the 1/4 power, and we know from the properties of exponents that when we raise a power to another power, we multiply the exponents. Therefore:
\(\root(4)(x^{10}) = x^{\frac{10}{4}} = x^{\frac{5}{2}}\)
Thus, the equivalent expression is \(x^{\frac{5}{2}}\).
Which point is an x-intercept of the quadratic function f(x) = (x – 8)(x + 9)? (0,8) (0,–8) (9,0) (–9,0)
Tony makes an hourly salary of 15.40 for 40 Regular hours of work. For any time work beyond 40 hours, he is paid at a rate of time and a half per hour. Last week, Tony worked 46 hours. Find each of the following for this period.
Tony's total earnings for the week are $754.60, which includes his regular pay for 40 hours at an hourly rate of $15.40 and overtime pay for 6 extra hours at a rate of time and a half.
Explanation:The subject of this question is Mathematics, specifically, it involves calculations relating to wage and overtime pay.
Calculating Regular and Overtime Pay
Tony earns an hourly wage of $15.40 for regular hours and is paid at a time and a half rate for any hours worked beyond 40 hours. Since he worked 46 hours last week, we can calculate his earnings as follows:
Calculate regular pay for 40 hours: 40 hours × $15.40 = $616.00.
Calculate the overtime pay rate: $15.40 × 1.5 = $23.10 per hour.
Calculate overtime pay for 6 hours: 6 hours × $23.10 = $138.60.
Add regular pay and overtime pay to get total earnings: $616.00 + $138.60 = $754.60.
Therefore, Tony's total earnings for the week, including overtime, are $754.60.
you are purchasing a house 12 years from now the estimated purchase price is 171,600.00 you want to make a 20%down payment how much do you have to save per month to reach your goal
Each of the walls of a room with square dimensions has been built with two pieces of sheetrock, a smaller one and a larger one. the length of all the smaller ones is the same and is stored in the variable small. similarly, the length of all the larger ones is the same and is stored in the variable large. write a single expression whose value is the total area of this room. do not use the pow function. submit
Suppose you cut a small square from a square of fabric as shown in the diagram. Write an expression for the remaining shaded area. Factor the expression. Type your answer below.
Which expression is equivalent to 17s-10+3(2s+1)?
A.23s-9
B.23s-7
C.11s-7
D.11s-9
The product of two consecutive integers is 156. what are the integers?" what type of equation should she create to solve this problem?
Answer:
12 and 13 or
- 13 and - 12
A quadratic equation r² + r - 156 = 0
Step-by-step explanation:
Let the first number be r, it means that the second will be r + 1.Given that the product of two consecutive integers is 156. we may interpret that to mean that
r(r + 1) = 156
r² + r - 156 = 0
r² + 13r - 12r -156 = 0
(r + 13)(r - 12) = 0
r = -13 0r 12
if r = -13, r + 1 = -12
If r = 12, r + 1 = 13
Pamela drove her car 99 kilometers and used 9 liters of fuel. She wants to know how many kilometers shee can drive with 12 liters of fuel. How many kilometers can Pamela drive with 12 liters of fuel?
Answer:
132 km
Step-by-step explanation:
1. she can drive 99 km (kilometers) with 9 liters of fuel, 99/9 is 11
2. if she wants to find out how many kilometers she can drive with 12 liters of fuel, then just multiply 12x11 which is 132
Use the distance formula to find the distance between (−8, 2.5) and (0, −4.5). 1. Substitute coordinates: 2. Simplify parentheses: 3. Evaluate powers: 4. Simplify. What is the distance between (–8, 2.5) and (0, –4.5)? Round to the nearest hundredth. d ≈
We have to use the distance formula to find the distance between (−8, 2.5) and (0, −4.5).
The distance formula states:
" For the given points [tex] A(x_{1},y_{1}) [/tex] and[tex] B(x_{2},y_{2}) [/tex], the distance between A and B is given as:
AB = [tex] \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}} [/tex]
We have to find distance between (−8, 2.5) and (0, −4.5). So, [tex] x_{1}= -8, y_{1}= 2.5 , x_{2}=0 , y_{2}=-4.5 [/tex]
AB = [tex] \sqrt{(0+8)^{2}+(-4.5-2.5)^{2}} [/tex]
AB = [tex] \sqrt{64+49} [/tex]
AB = [tex] \sqrt{113} [/tex]
AB = 10.630 units
By rounding to the nearest hundredth, we get
Distance between A and B = 10.63 units.
A ________________ event has a 100% chance of occurring. Example: Picking a red ball from a bag of only red balls.
We have been given that probability of the even is 100%. In other words we can say that the probability is 1. It means that the event will certainly occur.
Now, we know that the highest value of probability is 1 and lower value is 0.
Mathematically, we can represents it as
[tex]0\leq P(E)\leq 1[/tex]
If the probability is 0 then the event will never occur.
And if the probability is 1 then event will definitely occur.
Therefore, A certain event has a 100% chance of occurring.
A surveying instrument aimed at a location can “shoot” the distance to the location, giving the surveyor a measurement. A surveyor used such an instrument to record the distance to a point on a tree 60 m from his position. After rotating his surveying instrument 57° to the left, he measured the distance from his same position to a fence post 35 m away.
a.) Draw the diagram and label the tree as point T, the surveyor as point S, and the fence post as point F.
b.) Determine the distance between the point on the tree and the fence post. (Show
the appropriate formula, substitutions, and work. Give the distance to the nearest tenth of
a meter.)
c.) Use the Law of Sines to find the measure of T. (Show the appropriate formula, substitutions, and work. Give the measure of T to the nearest degree.)
d.) Find mF
Please Help Me :(
what is 68 less than 5 times a number is equal to the number?
The number here is will be represented as under -
Let the number be x.
Thus, the 5 times the number will be = 5x.
Now, it says, the number is 68 less than 5 times a number.
The equation so formed will be -
5x - 68 = x
4x = 68
x = 68.
Thus, the number will be 17.
Let us re-check the number,
(5 × 17) - 68 = 17
85 - 68 = 17
17 = 17. Thus, the number will be 17.
Find the probability for the experiment of tossing a six-sided die twice. the sum is less than 7
Final answer:
The probability of getting a sum less than 7 when rolling a six-sided die twice is 5/12. There are 15 possible outcomes where the sum is less than 7 out of 36 total outcomes.
Explanation:
The question asks for the probability that the sum of the numbers shown by rolling a six-sided die twice is less than 7. To find this probability, we need to consider all the possible outcomes of rolling two dice.
Each die has 6 faces, so when you roll two dice, there are a total of 6 x 6 = 36 possible outcomes. To get the sum less than 7, we can have the following combinations:
(1,1) Sum = 2
(1,2) Sum = 3
(2,1) Sum = 3
(1,3) Sum = 4
(2,2) Sum = 4
(3,1) Sum = 4
(1,4) Sum = 5
(2,3) Sum = 5
(3,2) Sum = 5
(4,1) Sum = 5
(1,5) Sum = 6
(2,4) Sum = 6
(3,3) Sum = 6
(4,2) Sum = 6
(5,1) Sum = 6
Adding up the number of outcomes, there are 15 possibilities where the sum is less than 7. Therefore, the probability is 15 out of 36. This simplifies to 5/12 when reduced to its simplest form.
So, the probability of getting a sum less than 7 when rolling a six-sided die twice is 5/12.
Anyone know the answer?
Find a polynomial with integer coefficients that satisfies the given conditions degree 3 with roots 9 2 and 0
What is the equation of a parabola with a focus (-2,4) and directrix y = 0?
The equation of the parabola with focus (-2,4) and directrix y = 0 is (x + 2) = 8(y - 2). This is derived by finding the vertex and applying the general equation for a vertically oriented parabola.
To find the equation of a parabola with a given focus and directrix, we use the definition that a parabola is the set of all points that are equidistant from the focus and the directrix. In this case, the focus is at (-2,4) and the directrix is y = 0. The vertex of the parabola will thus be halfway between the focus and the directrix, which means it will lie on the line y = 2 (since the focus has a y-coordinate of 4 and the directrix is at y = 0).
The standard form equation of a vertically oriented parabola with its vertex at the origin is x = 4py, where p is the distance from the vertex to the focus (or to the directrix). For a parabola that is shifted to have a vertex not at the origin, the equation is (x-h)² = 4p(y-k) where (h,k) is the vertex.
In this scenario, because the vertex is not at the origin and the parabola opens upwards (since the directrix is below the focus), we'll adjust the standard form equation to take these factors into account. The vertex (h,k) is (-2,2), the focus is (-2,4), thus p = 2. Therefore, the equation is (x + 2)² = 4*2*(y - 2)
Lisa swims laps during swim practice. Her coach tells her to swim a certain number of meters (total) each week. Here's a formula for this scenario:
p= t/n
t= total number of meters
p= length of a lap (in meters)
n= number of laps Lisa swims
Lisa wants to know how many laps she must swim to meet her goal. Rewrite the formula to determine the number of laps (not a multiple choice, you don't have to show work) someone please help!
Answer:
formula = n = t / p
Step-by-step explanation: