The solution to the expression (12-√-8)/2 as a complex number is 6 - i√2.
What is expression?
In mathematics, an expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, division, exponents, and roots.
The expression (12-√-8)/2 involves a square root of a negative number, which cannot be represented by a real number. Therefore, we need to extend the real numbers to the complex numbers to solve this expression.
To evaluate the square root of a negative number, we can use the imaginary unit, denoted by i, which is defined as the square root of -1. Then, we have:
√-8 = √(8) √(-1) = 2i√2
Substituting this value back into the original expression, we get:
(12-√-8)/2 = (12 - 2i√2)/2
Simplifying the expression by dividing both the numerator and denominator by 2, we get:
(12 - 2i√2)/2 = 6 - i√2
Therefore, the solution to the expression (12-√-8)/2 as a complex number is 6 - i√2.
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Graph the line with the equation y = - 3/5x - 3
we have
y = - 3/5x - 3
To graph the line we need at least two points
so
Find the intercepts
step 1
Find the y-intercept (value of y when the value of x is zero)
For x=0
y=-(3/5)*(0)-3
y=-3
the y intercept is the point (0,-3)
step 2
Find the x-intercept (value of x when the value of y is zero)
For y=0
0=-(3/5)x-3
(3/5)x=-3
x=-5
so
the x-intercept is the point (-5,0)
step 3
Graph the line
Plot the intercepts and join them to draw the line
using a graphing tool
see the attached figure
please wait a minute
Answer:
Step-by-step explanation:
y=−
5
3x
−3
2 Add 33 to both sides.
y+3=-\frac{3x}{5}
y+3=−
5
3x
3 Multiply both sides by 55.
(y+3)\times 5=-3x
(y+3)×5=−3x
4 Regroup terms.
5(y+3)=-3x
5(y+3)=−3x
5 Divide both sides by -3−3.
-\frac{5(y+3)}{3}=x
−
3
5(y+3)
=x
6 Switch sides.
x=-\frac{5(y+3)}{3}
x=−
3
5(y+3)
Alejandro has a computer support business. He estimates that the cost to run his business can be represented by X = 48 x + 500, where x is the number of customers. He also estimates that his income can be represented by R = 65 x - 145. How many customers he will need in order to break even?
If Alejandro has a computer support business. The number of customers he will need in order to break even is 38 customers.
How to find the number of customers to break even?Given data:
Cost of business = 48 x + 500
Income = R = 65 x - 145
Let x is the number of customers. He
Income equation
R= 65x- 145
Substitute 48x + 500 for y
48x + 500 = 65x -145
Substract 48x from both side
500 = 17x - 145
Add 145 to each side
645 = 17x
Divide both side by 17x
x =645 /17
x = 37.9
x = 38 customers (Approximately)
Therefore the number or customers is 38 customers.
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Can someone please help me?
The hardware store is 3 miles from Chris's house. How many feet would he have to go if he were walking toward the ? hardware store?
Answer:
First you need to know how many feet are in a mile (5280 ft) and so you would multiply this by 3 and to show your work because teachers need that now sadly you do this
[tex]3x5280=[/tex]
15820
:)
Nov 03, 2:56:13 PM
Find the Area of the figure below, composed of a rectangle with two semicircles
removed. Round to the nearest tenths place.
Answer:
10
D(
PLEASE HELP 30 POINTS !!!!!!!!!!!!
Answer:
31.7 units²
Step-by-step explanation:
Since the two semicircles have the same radius, they have the same combined area as a full circle.
Rectangle: length 10; width 6
Circle: diameter 6; radius 3
area = area of rectangle - area of circle
area = LW - πr²
area = 10 × 6 - 3.14159 × 3²
area = 60 - 28.27431
area = 31.72569
Answer: 31.7 units²
Select the correct
symbol to make 22/7 √17 a true statement
Options: <, >, or =
Among the given numbers, [tex]\sqrt{17} > \frac{22}{7}[/tex]
We have two numbers, which are 22/7 and [tex]\sqrt{17}[/tex]
Both of the numbers are irrational numbers, they are nonrepeating and nonterminating.
A fraction written in a particular way is called decimal form.
Now, evaluating both the given numbers in decimal form, we get,
22/7 = 3.14
and [tex]\sqrt{17} = 4.12[/tex]
Now, Clearly, 4.12 > 3.14
Thus, [tex]\sqrt{17} > \frac{22}{7}[/tex]
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Deshawn and lee have 64 shirts altogether. Lee has 18 fewer shirts than deshawn.
Answer: The answer is 64-18 so its 46 hope i helped
Step-by-step explanation:
64-18
Lena uses 2 cups of flour for a batch of cookies, 2 1/2 cups for loaf of bread, and 1/2 cups for dusting her workbench. Let c be the number of cookie batches and b be the number of bread loaves Lena makes. Which of the following expressions could represent how much flour she uses?
The expression that could represent how much flour Lena uses for baking cookies and bread is 2c + 2 1/2b + 1/2.
What is an algebraic expression?
An algebraic expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.
For example 2x + 4, 58m + 2n, 100p + 3q + r.
According to the given question:
(Question with options is attached below)
Let c be the number of cookie batches and b be the number of bread loaves Lena makes.
Lena makes 2 cups of flour for a batch of cookies
∴ Flour used to make cookie batches = 2c
She uses 2 1/2 cups for loaf of bread
∴ Flour used for bread loaves = 2 1/2 b
Ans 1/2 cup flour is used for dusting workbench
Hence expression for the amount of flour used is sum of flour used for making batches of cookies, bread loaves and for dusting.
The expression is 2c + 2 1/2b + 1/2
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Express the integral as a limit of Riemann sums using right endpoints. Do not evaluate the limit.
Answer:
23,207/210
Step-by-step explanation:
[tex]\int\limits^7_4 {x^{2}+\frac{1}{x} } \, dx \\[/tex]
Right endpoints start at 7
It doesn't say how many so I will assume there are 3.
7, 6, 5
Plug in those values into the integrand:
7^2+ 1/7=
49+1/7
6^2+1/6=
36+1/6
5^2+1/5=
25+1/5
1(49+1/7+36+1/6+25+1/5)
110+1/7+1/6+1/5 The least common factor of 7,6,5 is 210
[tex]110 + \frac{30+35+42}{210} \\110 + \frac{107}{210} \\\frac{23,100+107}{210} \\\\\frac{23,207}{210} \\[/tex]
Match the cards that have equivalent expressions. WILL GIVE BRAINLIEST!!!
Answer:
• 5x + 20 = 5(x + 4)
• 5(2x + 8) = 10x + 40
,• 5(x + 8) = 5x + 5.8
A contractor bought 8.2 ft² of sheet metal. He has used 4.9 ft² so far and has $52.80 worth of sheet metal remaining. The
equation 8.2x -4.9x = 52.8 represents how much sheet metal is remaining and the cost of the remaining amount. How much
does sheet metal cost per square foot?
Sheet metal costs : per square foot.
1
The cost of the sheet metal per square foot is $30.
The first step is to determine the square feet that the contractor used. This can be determined by subtracting the square feet of sheet she bought from the sheet metal she has used so far.
Sheet metal used = 8.2 - 2.1 = 6.1 square feet.
This means that 6.1 square feet costs $183.
The second step is to determine the cost of one square feet of sheet metal. This can be determined by dividing $183 by 6.1
$183 / 6.1 = $30
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Use the graph to answer the question.The vector u is graphed. Which of the vectors below would be orthogonal to vector u?
We can find the orthogonal vector when we use the dot product.
Then, the result must be equal to zero.
The vector u is given by coordinates <-7,-4>
Then, we need to find a vector in which their dor product will be equal to zero:
<-7,-4>*<1/7,-1/4> =-7*1/7 +(-4)*-1/4 = -1+1 =0
Therefore, the orthogonal vector is <1/7,-1/4>
The correct answer is option B
Answer:
Step-by-step explanation:
1.c
2.c
3.a
4.d
5.d
6.c
7. they are equal
8 A.a
8 B.d
9 A. c
9 B. b
10 A.c
10 B. b
11.b
12.d
13.b
14.b
15. a
16.d
17.c
18. 26.56 degrees
A pack of paper costs $3.79, including tax. Mr. Valentino wants to purchase packs of paper for his class and has a $15 budget. Write and solve an inequality to solve for the number of packs of paper Mr. Valentino can purchase,
Explanation
Let the unknown pack of books x. Therefore;
[tex]3.79x\leq15[/tex]Hence;
[tex]\begin{gathered} 3.79x\leq15 \\ x\leq\frac{15}{3.79} \\ x\le\:3.95778 \end{gathered}[/tex]Answer: Mr Valentino can buy approximately 3 packs
For the spring picnic, Mr. Jones served 85 hot dogs to 50 people. Mr. Jones expects 68 people at the fall picnic. Which proportion could be used to find how many hot dogs Mr. Jones needs for the fall picnic?
If Mr. Jones served 85 hot dogs to 50 people the proportion of hot dogs is:
[tex]\frac{85}{50}\text{ hot dogs/person}[/tex]If he expects 68 people at the fall picnic, the amount of hot dogs he will need is the number of people multiplied by this proportion:
[tex]\text{hot dogs = 68p }\cdot\frac{85}{50}\text{ hot dogs/p}[/tex]Answer
The proportion that could be used to find how many hot dogs Mr. Jones will need for the fall picnic is 85/50
He will need 115.6 hot dogs (since the number of hot dogs is a whole number, He will have to buy 116 hot dogs)
football field is 300 ft long and 160 ft wide , to nearest hundredth, how many acres in football field
Find the slope of any line parallel to the line through (6, 2) and (-6, 3).Slope=
Parallel lines will have the same slope.
Then we can calculate the slope for this line and it will be the same for all its parallel lines.
Given two points (x1,y1) = (6,2) and (x2,y2) = (-6,3) we can calculate the slope m as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-2}{-6-6}=\frac{1}{-12}=-\frac{1}{12}[/tex]The slope for this line and all its parallels is m = -1/12.
Answer: -1/12
is y= -4 a linear equation?
Answer:
Yes
Step-by-step explanation:
Answer: yes it is linear
Step-by-step explanation: linear line is a straight line and y=-4 is 1 line so it is linear
What equation is graphed in this figure? y+2=(x - 2) y+1=(x − 3) y -4 = (x+2)y-3 =3/2 (x+1)
the Answer:is y=-3x+1 so it would b c:)
I need help with my math
The equation of a line is the form of
[tex]\begin{gathered} y\text{ = mx +c} \\ \text{where} \\ m\text{ = slope} \\ \text{and} \\ c\text{ = y-intercept} \end{gathered}[/tex]The equation of the line was, however, given as
[tex]5x-3y\text{ = (-9)}[/tex]To rewrite this equation in slope-intercept form, we must first find the slope and y-intercept from the equation by rearranging it
[tex]\begin{gathered} 5x+9=3y \\ 3y\text{ = 5x+9} \\ \frac{3y}{3\text{ }}=\frac{5x}{3}+\frac{9}{3} \\ y\text{ = }\frac{5}{3}x+3 \\ \text{From here the slope, m =}\frac{5}{3} \\ \text{and } \\ \text{the y-intercept, c = 3} \end{gathered}[/tex]Hence the required equation is y =(5/3)x +3. The answer is the third option
find the slope and y intercept of the line.y= -3/4x+1
Explanation
we can easily solve this by checking the equation
[tex]y=-\frac{3}{4}x+1[/tex]It is writen in slope- y intercept fom
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope} \\ \text{and b is the y-intercept} \end{gathered}[/tex]hence
[tex]\begin{gathered} y=-\frac{3}{4}x+1\Rightarrow y=mx+b \\ \text{ therefore} \\ m=\text{slope}=-\frac{3}{4} \\ b=y-\text{Intercept}=1 \end{gathered}[/tex]I hope this helps you
Write the equation of the line that it is perpendicular to [tex]y = 7x - 3[/tex]and passes through the origin
Answer
The equation of the line is
y = (-x/7)
We can cross multiply and write it in the form of
7y = -x
OR
x + 7y = 0
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
The relationship between the slopes of two lines that are perpendicular to each other is
m₁m₂ = -1
m₁ = Slope of line 1
m₂ = Slope of line 2
For the given equation, if we compare its equation with y = mx + b,
y = 7x - 3
y = mx + b
m = 7, b = -3
We can now find the slope of the line we want.
m₁m₂ = -1
m₁ = 7
m₂ = ?
m₁m₂ = -1
(7)m₂ = -1
7m₂ = -1
Divide both sides by 7
(7m₂/7) = (-1/7)
m₂ = (-1/7)
Then we can find the equation of the line we want.
For that line,
m = slope = (-1/7)
b = y-intercept (where the line crosses the y-axis) = 0
This is obtained from the point given that the line passes through the origin, (0, 0)
So, we can write y = mx + b
y = (-1/7)x + 0
y = (-x/7)
We can cross multiply and write it in the form of
7y = -x
OR
x + 7y = 0
Hope this Helps!!!
what is the value of y in the triangle at the right? (sorry the picture is a little blurry)
Answer:
To find the length y from the given right anled triangle.
Since the given triangle is right anled triangle,
we have the following,
[tex]\sin \theta=\frac{opposite\text{ side}}{hypotenuse}[/tex]Let,
hypotenuse =14
opposite side=y
Substitute the values we get,
[tex]\sin 30\degree=\frac{y}{14}[/tex]we know that, sin 30=1/2
Using this we get,
[tex]\frac{1}{2}=\frac{y}{14}[/tex][tex]y=\frac{14}{2}[/tex][tex]y=7[/tex]Answer is: option D: 7
identify which are functions (2, 3) , (2,4), (3,6)
ok
Could you send me all the options?
A function is a relationship between two magnitudes (x, y). In which, each value of the first corresponds to a single value of the second
Write and solve an equality to find the values of x for which the perimeter of the rectangle is less than 128
The value of x for which the perimeter of the rectangle is less than 128 is x < 30.
How to find the perimeter of a rectangle?The perimeter of a rectangle is the sum of the whole sides of a rectangle. Recall a rectangle is a quadrilateral with opposite sides equal to each other and opposite side parallel to each other.
Therefore, the perimeter of the rectangle is less than 128.
Hence,
perimeter of a rectangle = 2(l + w)
perimeter of a rectangle = 2l + 2w
where
l = side lengthw = widthTherefore,
2(x + 4) + 2x < 128
2x + 8 + 2x < 128
4x + 8 < 128
4x < 128 - 8
4x < 120
Therefore,
x < 30
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A scuba diver descends below the surface of a lake at a rate of 12 feet per minute. What is the depth of the diver after 4 minutes?
The depth of the diver after 4 minutes when a scuba diver descends below the surface of a lake at a rate of 12 feet per minute is 48 feet.
What is a rate?The concept that is used in the solution is the concept of rate in mathematics. A rate can be described as a special ratio having two terms that are in different units.
The rate that is been given is 12 feet per minute which implies that 12 feet will operate at the time of 1 minute. Then we were now given the depth of the diver after 4 minutes, using the given rate, then ;
12feet = 1mins
X feet = 4mins
where X is the depth of the diver after 4 minutes then we can cross multiply,
X= (4mins *12feet) / 1mins
= 48feets.
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3. If the length of a rectangular garden is 2 feet less than the length of a house and the
width of the garden is 5 feet less than half the length of the house, what is the
expression for the area of the garden?
A. 0.5x² - 6x + 10
B. 0.5x²+6x-7
C. 0.5x+10
D. 1.5x² - 6x + 10
E. 1.5x²-6x + 10
Answer:
A. 0.5x² - 6x + 10
hope you get a point
Graph the image of this figure after a dilation with a scale factor of centered at the origin.
Use the polygon tool to graph the dilated figure.
Answer:the real answer is (-2,1), (-1,4), (1,2)
Step-by-step explanation:
pls mark brainliest
A worn, poorly set-up machine is observed to produce components whose length x follows a normal distribution with a mean equal to 14 centimeters and a variance equal to 9. Determine the probability that a component is at least 10 centimeters long. Round your answer to four decimal places.
80.64% probability that a component is at least 10 centimeters long.
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation , the z-score of a measure X is given by:
Z = x - μ / σ
Z-scores are used to measure how far a measure is from the mean. We find the p-value associated with this Z-score by looking at the z-score table after finding the Z-score. The p-value represents the probability that the measure is smaller than X, which is the percentile of X. The probability of the measure being greater than X is calculated by subtracting 1 from the pvalue.
μ = 14
Variance is 9.
The standard deviation is the square root of the variance.
So,
σ = √9 = 3
This is the pvalue of Z when X = 10
z = 10 - 14/3
z = -1.3
z = -1.3 has a p value of0.1936
1-0.1936 = 0.8064
80.64% probability that a component is at least 10 centimeters long.
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Answer:
0.7475
Step-by-step explanation:
The mean is μ=14, and the standard deviation is σ=9‾√=3.Open Excel. Click on an empty cell. Type =NORMDIST(12,14,3,1) and press ENTER.The probability, rounded to four decimal places, is P(X<12)≈0.2525.The desired probability is P(X≥12), so subtract from 1 to get P(X≥12)=1−0.2525=0.7475
answer to this problem
Answer:
Step-by-step explanation:
decrese by 10
A cat of mass 4kg jumps on a dining table of mass 28kg. As the cat walks around on the table, what is the average force that the table applies to the cat? (gravity is 10 meters per second-squared)
*
1 point
7N
280N
.4N
40N
2.8N
The average force that the table applies to the cat is 40N, by using newton's law.
What is the meaning of acceleration?
Acceleration: the rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting.
Given that the mass of the cat is 4 kg. The gravity is 10 meters per second-squared.
Force is the product mass and acceleration.
Mass = 4 kg
Acceleration = 10 ms⁻².
The force that the table applies to the cat is (4 kg × 10 ms⁻²) = 40 N.
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