Answers
The solutions are: 1 + 6i and 1 - 6i
Explanation:
The general form of the quadratic equation is:
ax² + bx + c = 0
The given equation is:
x² - 2x + 37 = 0
By comparison:
a = 1
b = -2
c = 37
Now, to get the solutions of the equation, we will use the quadratic formula shown in the attached image.
By substitution in this formula, we would find that:
either x = [tex] \frac{2+ \sqrt{(-2)^2-4(1)(37)} }{2(1)} = 1 + 6i[/tex]
or x = [tex] \frac{2- \sqrt{(-2)^2-4(1)(37)} }{2(1)} = 1 - 6i[/tex]
Hope this helps :)
Related Questions
find the lateral area of the prism 3m 6m 3m 6m 15m
Answers
To find the lateral area of a prism, we calculate the combined area of its vertical rectangular faces, excluding the top and bottom faces. This prism has dimensions of 3m x 6m x 15m. It has two pairs of congruent rectangular faces: one pair with dimensions 3m x 15m and the other with dimensions 6m x 15m. The area of each face is determined by multiplying its length by its height. For the first pair of faces, the area is 3m * 15m = 45 square meters each. Similarly, for the second pair, the area is 6m * 15m = 90 square meters each. Adding these areas together (2 * 45 + 2 * 90), we get a lateral area of 270 square meters.
Complete answer;
find the lateral area of the prism 3m 6m 3m 6m 15m
Stefano calculated the mean absolute deviation for the data set 32, 4, 12, 40, 20, and 24. His work is shown below. Step 1: Find the mean. mc006-1.jpg Step 2: Find each absolute deviation. 10, 18, 10, 18, 2, 2 Step 3: Find the mean absolute deviation. mc006-2.jpg What is Stefano’s error? Stefano should have divided by 5 when finding the mean. Stefano found the absolute deviation of 20 incorrectly. Stefano should have divided by 6 when finding the mean absolute deviation. Stefano did not find the correct value for the mean.
Answers
To find the mean, you will find the sum of all the numbers and divide by how many numbers there are.
Mean: 4 + 12 + 20 + 24 + 32 + 40 = 132
132/6 = 22
Mean: 22
To find the mean absolute deviation, you find how far away each of the numbers are from the mean. Find the sum of these and divide by the same number of numbers.
(22 - 4) + (22-12) + (22-20) +(24 - 22) + (32-22) + (40-22)
18 + 10 + 2 + 2 + 10 + 18 = 60
60/6 = 10
The MAD is 10.
I think the correct answer is that Stefano should have divided by 6 when finding the mean absolute deviation.
Answer:
Stefano should have divided by 6 when finding the mean absolute deviation. ed quiz correct
Step-by-step explanation:
The scores of individual students on the act program composite college entrance examination have an approximately normal distribution with mean 18.6 and standard deviation 6.0 and northside high 30 16 years take the test as soon that the scores at this school have the same distribution as national scores what is the probability that a randomly-chosen student has a score of higher than 20 points
Answers
Nico dropped the brand new bottle of dog shampoo and 3 ounces spilled out. He measures 1 1/4 ounces each time he shampoos his dog and the bottle of shampoo originally contained 30 1/2 ounces. Which is the correct equation and value of x, the number of times Nico can bathe his dog using this one bottle?
Answers
Amount of shampoo Nico uses in one bathe for his dog = [tex]1 \frac{1}{4} [/tex]
Since 3 ounces of shampoo is spilled out, the amount of shampoo left in the bottle will be = [tex]27 \frac{1}{2} [/tex]
If Nico can Bathe his dog x times using this bottle, the value of x can be written as:
[tex]x= \frac{27 \frac{1}{2} }{ 1\frac{1}{4} } [/tex]
Using this equation we can find the number of times Nico can use the shampoo to Bathe . The value of x comes out to be 22.
Thus, Nico can Bathe his dog 22 times using the bottle
Nico can bathe his dog 22 times using the one bottle of shampoo.
Explanation:To find the number of times Nico can bathe his dog using the one bottle of shampoo, we need to determine how many times 1 1/4 ounces can fit into the remaining shampoo in the bottle after 3 ounces have spilled out.
First, subtract the spilled amount of 3 ounces from the original amount of shampoo in the bottle, which is 30 1/2 ounces. This gives us 27 1/2 ounces remaining.
Next, divide the remaining amount of shampoo by the amount used per bath (1 1/4 ounces each time).
27 1/2 ounces ÷ 1 1/4 ounces = 22 baths
Therefore, Nico can bathe his dog 22 times using the one bottle of shampoo.
Learn more about Bathing a dog here:https://brainly.com/question/12912769
#SPJ3
Hank delivers packages in his office building. On Tuesday he delivered four more packages than on Monday, and on Wednesday he delivered 6 more packages than on Monday. If he delivered 28 packages all together, how many did he deliver on Monday?
A) 6
B) 10
C) 18
D) 22
Answers
Answer:
a
Step-by-step explanation:
x-5 is less than or equal to 1/3 (9x-6)
Answers
hey can you please help me posted picture of question
Answers
Two
Explanation:
The solution of a system of equations is defined as the values which satisfies both equations.
Graphically, the solutions are represented by the points of intersection between the two equtaions.
In the given graph, we have a circle and a line, we can note that these two intersect in two points.
This means that the system has two solutions
Hope this helps :)
If you need to see up direct deposit which information from your check would you likely need A. Check number B. Memo line C. Numerical amount D. Routing number
Answers
Answer: If you need to see up direct deposit, the information you'd most likely need is your routing number.
Hope this helped you! ♥
State whether the given measurements determine zero, one, or two triangles. B = 86°, b = 21, c = 18
In need of help asap
Answers
Applying the law of sines
b/sin B=c/sin C-----> b*sin C=c*sin B-----> sin C=c*sin B/b
c=18
b=21
B=86°
sin C=18*sin 86/21-----> sin C=0.8550------> C=arc sin(0.8550)
C=58.77°------> C=58.8°
calculate angle A
A+B+C=180--------> A=180-B-C----> A=180-86-58.8----> A=35.2°
b/sin B=a/sin A-------> a=b*sin A/sin B----> a=21*sin 35.2/sin 86
a=12.13-------> a=12
the measure of the first triangle are
a=12
b=21
c=18
A=35.2°
B=86°
C=58.8°
calculate the measures of the second triangle
b=21
c=18
B=86°
C=180-58.8----> C=121.2°
A+B+C=180-----> A=180-86-121.2----> A=-27.2----> It is not possible to build a second triangle
the answer is
it is possible to assemble only a single triangle
a=12
b=21
c=18
A=35.2°
B=86°
C=58.8°
Answer:
one triangle
Step-by-step explanation:
Help see photo attached
Answers
The second statement in the second pair is false, since 0 is not an imaginary number.
what is -1/2x+1=9 with work shown.
Answers
Isabella works at Baker's Book company. If she earned a commission of $63.75 on her sales of $850, what was Isabella's rate of commission?
Answers
7.5% is Isabella's rate of commission.
Use a proportion to convert 18 grams to milligrams. [Hint: 1,000 mg = 1 g.]
Answers
18000=1x
18000mg
[tex] \frac{1g}{1000mg} = \frac{18g}{x} [/tex]
We would then cross-multiply and our answer would be 18,000 milligrams.
0.5 log3 x=2 x = what
Answers
[tex]Domain:x\in\mathbb{R^+}[/tex]
[tex]0.5\log_3x=2\ \ \ |\cdot2\\\\\log_3x=4[/tex]
[tex]Use\ the\ de finition\ of\ the\ logarithm:\\\\\log_ab=c\iff a^c=b[/tex]
[tex]Therefore\ we\ have:\\\\\log_3x=4\iff3^4=x\to x=81[/tex]
Answer: C. 81.
[tex]0.5 log_3 (x) = 2[/tex]
Multiply both sides by 10 to get rid of the decimal:
[tex]10 * 0.5 log_3 (x) = 10 * 2[/tex]
[tex]5 log_3 (x) = 20[/tex]
Divide 5 out
[tex]\frac{5 log_3 x}{5} = \frac{20}{5}[/tex]
[tex]log_3 x = 4[/tex]
Now use the log rule [tex]a = log_b b^a[/tex]
[tex]4 = log_3 (3^4) = log_3 (81)[/tex]
Since we have the same base
[tex]log_3 (x) = log_3 (81)[/tex]
x = 81
a local club is arranging a charter flight to hawaii. the cost of the trip is $574 each for 81 passengers, with a refund of $5 per passenger for each passenger in excess of 81.
find the number of passengers that will maximize the revenue recieved from the flight
also find the maximum revenue.
Answers
The discounted cost is given by,
Cost = 574-5(x-81) = 574-5x + 405 = 979 -5x
Total revenue, R(x) = x(979 - 5x) = 979x - 5x^2
At maximum revenue, dR/dx = 0 => dR/dx = 979 - 10x = 0 =>10x = 979 => x =979/10 = 97.9 ≈ 98 passengers
Therefore,
Revenues, R(97) = 98[574 -5(98-81)] = 98[574-85] = $47,922
15 points!!! GEOMETRY help please!!
Questions attached!
Answers
[tex]\text{If QR is tangent to circle then m}\angle PQR=90^o[/tex]
[tex]\text{We can use the converse of Pythagorean theorem}[/tex]
[tex]8\ and\ 4\sqrt3\\\\check:\ 4^2+(4\sqrt3)^2=8^2\\16+16\cdot3=64\\16+48=64\\64=64\ -O.K.\\\\2\ and\ 4\sqrt2\\\\check:\ 4^2+2^2=(4\sqrt2)^2\\16+4=16\cdot2\\20=32\ -FALSE\\\\3\ and\ 5\\\\check:\ 3^2+4^2=5^2\\9+16=25\\25=25\ -O.K.\\\\2\ and\ 2\sqrt5\\\\check:\ 4^2+2^2=(2\sqrt5)^2\\16+4=4\cdot5\\20=20\ -O.K.\\\\6\ and\ 10\\check:\ 4^2+6^2=10^2\\16+36=100\\52=100\ -FALSE[/tex]
[tex]\text{Answer:}\boxed{8\ and\ 4\sqrt3;\ 3\ and\ 5;\ 2\ and\ 2\sqrt5}[/tex]
10.
[tex]\text{Look at the pictures}[/tex]
[tex]\text{Therefore}\\\\C=2\cdot8+2\cdot16+2\cdot9+2\cdot6=16+32+18+12=78cm[/tex]
[tex]Other\ method:\\C=2\cdot(8+16+6+9)=2\cdot39=78cm[/tex]
Answer:
\text{If QR is tangent to circle then m}\angle PQR=90^o
\text{We can use the converse of Pythagorean theorem}
8\ and\ 4\sqrt3\\\\check:\ 4^2+(4\sqrt3)^2=8^2\\16+16\cdot3=64\\16+48=64\\64=64\ -O.K.\\\\2\ and\ 4\sqrt2\\\\check:\ 4^2+2^2=(4\sqrt2)^2\\16+4=16\cdot2\\20=32\ -FALSE\\\\3\ and\ 5\\\\check:\ 3^2+4^2=5^2\\9+16=25\\25=25\ -O.K.\\\\2\ and\ 2\sqrt5\\\\check:\ 4^2+2^2=(2\sqrt5)^2\\16+4=4\cdot5\\20=20\ -O.K.\\\\6\ and\ 10\\check:\ 4^2+6^2=10^2\\16+36=100\\52=100\ -FALSE
\text{Answer:}\boxed{8\ and\ 4\sqrt3;\ 3\ and\ 5;\ 2\ and\ 2\sqrt5}
10.
\text{Look at the pictures}
\text{Therefore}\\\\C=2\cdot8+2\cdot16+2\cdot9+2\cdot6=16+32+18+12=78cm
Other\ method:\\C=2\cdot(8+16+6+9)=2\cdot39=78cm
Step-by-step explanation:
According to the distributive property, 6(a + b) =
Answers
6a + 6b
Also, whats with the image? Lol.
6 times a = 6a
6 times b = 6b
we don't know what 'a' or 'b' are, so we leave the expressions as is
Therefore, 6*(a+b) = 6a+6b
Solve this system of equations: y = x2 – 3x + 12 y = –2x + 14 1.Isolate one variable in the system of equations, if needed. y = x2 – 3x + 12 y = –2x + 14 2.Use substitution to create a one-variable equation. –2x + 14 = x2 – 3x + 12 3.Solve to determine the unknown variable in the equation. What are the values of x?
Answers
add 2x on both side:
14=x²-x+12
subtract 14 on both side:
x²-x-2=0
factor: (x-2)(x+1)=0
x=2 or x=-1
HOPE THIS HELPS AND PLEASE MARK ME AS BRAINIEST AND ADD ME AS A FRIEND
x^2 - x - 2 =0
x^2 -2x +x -2 = 0
(x-2)(x+1) = 0
x= 2 and x = -1
Hope this will help☺☺
Write out the first four terms of the maclaurin series of f(x) if f(0)=−13,f′(0)=−6,f″(0)=5,f‴(0)=6 f(x) = +⋯
Answers
[tex] -13 - 6x + \frac{5}{2} {x}^{2} + {x}^{3} [/tex]
If the triangle on the grid below is translated by using the (x,y) -> (x+5, y-2) rule, what will be the coordinates of B'?
(–2, 0)
(0, –2)
(5, –7)
(5, –2)
Answers
the coordinates of point B ( -5,0)
the translation has the following rule
(x,y)--------> (x+5, y-2)
so
(-5,0)-----> (-5+5,0-2)-----> (0,-2)
the answer is
(0, –2)
Answer:
[tex]B(-5,0)\rightarrow B'(0,-2)[/tex]
Step-by-step explanation:
From the diagram, B has coordinates [tex](-5,0)[/tex].
We want to find the coordinates of B' after a translation by the rule;
[tex](x,y)\rightarrow(x+5,y-2)[/tex],
We apply the rule to obtain;
[tex]B(-5,0)\rightarrow B'(-5+5,0-2)[/tex],
This implies that;
[tex]B(-5,0)\rightarrow B'(0,-2)[/tex]
Therefore the correct answer is B
You collect old coins. today, you have two coins each of which is valued at $100. one coin is expected to increase in value by 5.2 percent annually while the other coin is expected to increase in value by 5 percent annually. what will be the difference in the value of the two coins 25 years from now?
Answers
write an inequality to represent the situation. the temperature stayed above -15 degrees
Answers
t > -15°
t will represent temperature
t > -15°
Which absolute value statement describes a 40 yard gain in football? A. |40| = 40, B. |-40| = 49, C. -|40| = 40, D. -|40| = 40,
Answers
Answer:
d
Step-by-step explanation:
The digits of a certain three-digit number are consecutive odd numbers. If the sum of the digits is 15, find the number.
Answers
Let the digits of the 3 digit number be [tex] x-2,x,x+2 [/tex]. where [tex] x [/tex] is an integer greater than 1. It is given that the sum of the 3 digits is 15. Hence,
[tex] x-2+x+x+2=15\\
3x=15\\
x=5 [/tex]
Thus the digits are [tex] 3,5,7 [/tex].
Therefore, the number is [tex] 357 [/tex].
We assume that the digits of the number is increasing from the 100th place.
how to get arc length when central angle is 139
Answers
To find the arc length when the central angle is 139 degrees, multiply the fraction of the circle that the angle represents (139/360) by the circle's circumference formula (2πr), where r is the radius.
Explanation:Calculating Arc Length with a Known Central Angle
To calculate the arc length when the central angle is 139 degrees, you need to know the radius of the circle. The arc length, As, is the distance traveled along the circumference of a circle as the radius is rotated through a given angle. Since there are 360 degrees in a full revolution, a central angle of 139 degrees represents a fraction 139/360 of the full circle.
The circumference of the entire circle is given by the formula 2πr, where r is the radius. Therefore, the arc length can be calculated by multiplying the fraction of the circle represented by the angle (in this case, 139/360) by the total circumference. The formula to determine the arc length As is:
As = (139/360) × 2πr
By knowing the radius and the central angle, you can substitute these values into the formula to find the arc length for any circular path.
Nina wants to put color tiles on a square. 3 color tiles fit across the top of the square. How many rows and columns of square will Nina need? How many color tiles will she use in all?
Answers
Total tiles needed = 3 x 3 = 9 tiles.
Answer: 3 rows of 3 tiles. Total of 9 tiles needed.
Nina will need 3 rows and 3 columns of square tiles. She will use 9 color tiles in total to cover the square.
To determine how many rows and columns of square tiles Nina needs, and how many color tiles in total she will use, let's break down the problem step by step:
1. Width and Height of the Square:
Nina can fit 3 color tiles across the top of the square. This implies the width of the square is 3 color tiles.2. Rows and Columns Calculation:
Since the square has 3 tiles across the top, and assuming the square is symmetric (same number of tiles in width and height):
Number of columns(width) = 3 tiles Number of rows (height) = 3 tiles So, Nina will need 3 columns and 3 rows of square tiles.3. Total Number of Color Tiles:
To find out how many color tiles Nina will use in total, calculate the area of the square:
Area of the square = [tex]\( \text{Number of rows} \times \text{Number of columns} \)[/tex]
Area = [tex]\( 3 \times 3 = 9 \)[/tex] color tiles
Therefore:
Nina will need 3 rows and 3 columns of square tiles.
She will use 9 color tiles in total to cover the square.
hey can you please help me posted picture of question
Answers
For first option, the composition will be:
[tex]f(g(x))=2+ \sqrt[3]{2- x^{3} } [/tex]
For second option, the composition will be:
[tex]f(g(x))= \frac{6x-8}{6}+8= \frac{6x-8+48}{6} = \frac{6x-40}{6} [/tex]
For third option, the composition will be:
[tex]f(g(x))= \frac{49}{x+9}-9 [/tex]
For Fourth option, the composition will be:
[tex]f(g(x))=5( \frac{x+11}{5})-11=x+11-11=x [/tex]
So the pair of function given in Fourth option are inverse of each other
what is the last step in planning your budget
Answers
Answer:
review and revisions
Step-by-step explanation:
5n+5=45 what does n =
Answers
Subtract 5 from both sides
5n=40
Divide both sides by 5
n=8
I hope this helps
Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate the current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million. As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%. If P represents the population of each species of insect in millions, and t represents the elapsed time in years, then which of the following systems of equations can be used to determine how long it will be before the populations of the two species are equal?
Answers
Pa = 1.3(1-0.038)^t
while the population Pb of insect B after t years is
Pb = 2.1(1-0.046)^t
We equate the above expressions to find the number of years t it will take the two populations to be equal:
Pa = Pb
1.3(1-0.038)^t = 2.1(1-0.046)^t
1.3(0.962)^t = 2.1(0.954)^t
These are the equations that can be used to determine how long it will be before the populations of the two species are equal.
We can now solve for t:
(0.962)^t / (0.954)^t = 2.1/1.3
(0.962/0.954)^t = 2.1/1.3
After taking the log of both sides of our equation, number of years t is
t = log (2.1/1.3) / log (0.962/0.954)
t = 57 years
Therefore, it will take 57 years for the population of insect A to equal the population of insect B.
y = A * (B) ^ t
Where:
A: initial population.
B: annual exchange rate.
T: Time in years.
Then the equations of the system that must be used to find the time in which both are equal are:
1, 3,00,000 * (1-0,038) ^ t for the type of insect A
2, 1 00 000 * (1-0,046) ^ t for the type of insect B.