To simplify (6 - 4i) - (і +5), you have to apply associative property.
First step is to remove the parenthesis, then you have:
[tex]6\text{ - 4i - i + 5}[/tex]Now collect like terms:
[tex]\begin{gathered} 6\text{ + 5 - 4i - i} \\ =\text{ 11 - 5i} \end{gathered}[/tex]ANSWER:
[tex]11\text{ - 5i}[/tex]Write an equation of the line passing through (4,-2) that is parallel to the line -3x minus 4y =5
Answer:
Step-by-step explanation:
y=4x3
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
First, rearrange -3x - 4y = 5 into y = mx + c form.
-3x - 4y = 5
-4y = 3x + 5
y = -3/4x - 5/4
Since parallel lines have the same gradient, equation of line is y = -3/4x + c.
Substitute (4,-2) into the equation to find c.
-2 = -3/4(4) + c
c = 1
Hence, equation of line is y = -3/4x + 1.
Some help I will mark Brain liest
Answer:
-2.86, -0.37, 0.19, 0.91, 1.46
Step-by-step explanation:
the negatives will always be the least, hope this helps!
Make a table and a graph of y = 4x - 2.
To make the table first replace the given values of x in the equation, operate, and with it, you get their corresponding coordinates in y. Then you have
If x = -2
[tex]\begin{gathered} y=4x-2 \\ y=4(-2)-2 \\ y=-8-2 \\ y=-10 \\ \text{Then you have the ordered pair (-2,-10)} \end{gathered}[/tex]If x = -1
[tex]\begin{gathered} y=4x-2 \\ y=4(-1)-2 \\ y=-4-2 \\ y=-6 \\ \text{Then you have the ordered pair (-1,-6)} \end{gathered}[/tex]If x = 0
[tex]\begin{gathered} y=4x-2 \\ y=4(0)-2 \\ y=0-2 \\ y=-2 \\ \text{Then you have the ordered pair (0,-2)} \end{gathered}[/tex]If x = 1
[tex]\begin{gathered} y=4x-2 \\ y=4(1)-2 \\ y=4-2 \\ y=2 \\ \text{Then you have the ordered pair (1,2)} \end{gathered}[/tex]If x = 2
[tex]\begin{gathered} y=4x-2 \\ y=4(2)-2 \\ y=8-2 \\ y=6 \\ \text{Then you have the ordered pair (2,6)} \end{gathered}[/tex]Finally, the table of the equation
and its corresponding graph will be
Therefore, the correct answer is option A.
How do we do this system of equations?[tex]1. \: \frac{3}{x - 2y} + \frac{2}{2x + y} = 3[/tex]
This system is impossible to solve because we have two uknown values (x,y) and only one equation.
What is 159,100 rounded to nearest thousand
Answer: 159,000
Step-by-step explanation:
The number after the nine (one) is under five, so you keep the number the same instead of rounding up :)
For a normal distribution, it is known that the mean is zero and the standard deviation is 1. Be sure to draw and label a normal distribution for each problem. Find the probability that a z score is between -1.15 and 1.98.
To find the probability between two z-scores on a normal distribution, we can use a z-score table.
A z-score table gives the probability of a data less than the corresponding z-score, like in the picture:
So, if we want the probability between 1.98 and -1.15, we need to do the following:
[tex]P(-1.15However, usually z-score tables go only from z = 0 and above, so we need a way to consult the negative z.Since the normal distribution in symmetric around z = 0, we have that:
[tex]P(z<-1.15)=P(z>1.15)[/tex]And since the whole distribution give a 100% probability, or an area of 1, we have that:
[tex]\begin{gathered} P(z<1.15)+P(z>1.15)=1 \\ P(z>1.15)=1-P\mleft(z<1.15\mright) \end{gathered}[/tex]So, in the end, we have:
[tex]\begin{gathered} P(-1.151.15) \\ P(-1.15So, we can consult the values for the probabilities of z < 1.98 and z < 1.15 on the z-score table:[tex]\begin{gathered} P(z<1.98)\approx0.9761 \\ P(z<1.15)\approx0.8749 \end{gathered}[/tex]So, the total probability is:
[tex]\begin{gathered} P(-1.15So, the probability is approximately 0.8510.Find the value of the following expression: (3^8•2^-5•9^0)^-2•(2^-2/3^3)^4•3^28 Write your answer in simplified form.
Answer:
4
Step-by-step explanation:
Given expression:
[tex](3^{8} \cdot 2^{-5} \cdot 9^{0})^{-2} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
Any number to the power of zero is 1:
[tex]\implies (3^{8} \cdot 2^{-5} \cdot 1)^{-2} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
[tex]\implies (3^{8} \cdot 2^{-5})^{-2} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad (a^b \cdot c^d)^p=a^{bp}\cdot c^{dp}:[/tex]
[tex]\implies 3^{(8 \cdot -2)} \cdot 2^{(-5 \cdot -2)} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \dfrac{\left(2^{-2}\right)^{4} }{\left(3^{3}\right)^{4} } \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \dfrac{2^{(-2 \cdot 4)}}{3^{(3\cdot 4)}} \cdot 3^{28}[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \dfrac{2^{-8}}{3^{12}} \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \dfrac{1}{a^n}=a^{-n}[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot 2^{-8} \cdot 3^{-12} \cdot 3^{28}[/tex]
Gather like terms:
[tex]\implies 2^{10} \cdot 2^{-8} \cdot3^{-16} \cdot 3^{-12} \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies 2^{(10-8)}\cdot3^{(-16-12+28)}[/tex]
[tex]\implies 2^{2}\cdot3^{0}[/tex]
Any number to the power of zero is 1:
[tex]\implies 2^{2}\cdot 1[/tex]
[tex]\implies 2^2[/tex]
Therefore, the solution is:
[tex]\implies 2^2=2 \times 2=4[/tex]
The pentagonal prism below has a cross-sectional area of
27 cm² and a length of 3 cm.
Calculate the volume of the prism.
Give your answer in cm³.
Answer:
81 cm³
Step-by-step explanation:
I will send a picture of the equations because if I type it here it won't make sense.
Hence option A is the correct answer
Write an equation in slope - intercept form for the line that passes through the given paint andis parallel to the given equation.4.(-4, 2), y = -1/2x+ 6
When two equation are parallel it means they have the same slope.
You have the equation:
[tex]y=-\frac{1}{2}x+6[/tex]You can identify the slope(m) as the number next to the x in equation that follow the next form:
[tex]y=mx+b[/tex]Then, the equation parallel to the given equation has an slope of:
m= - 1/2Now, if we have a point of the equation we can find the value of the b (y-intercept) in the slope - intercept form of a lineal equation:
[tex]y=mx+b[/tex]The given point is ( -4 , 2)
You have the next values:
m= - 1/2
y= 2
x= -4
Then we substitute that values:
[tex]2=-\frac{1}{2}(-4)+b[/tex]And clear the b:
[tex]2=\frac{4}{2}+b[/tex][tex]2=2+b[/tex][tex]2-2=2-2+b[/tex][tex]0=b[/tex]Now, we get the value of the slope (m= - 1/2) and the y-intercept (b=0)
We can write the equation in slope - intercept form:
[tex]y=-\frac{1}{2}x+0[/tex]or:
[tex]y=-\frac{1}{2}x[/tex]Find P(z > -0.24)Use the Normal table and give answer using 4 decimal places.
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given z-score
[tex]P(z>-0.24)[/tex]STEP 2: Draw the required region on a graph
STEP 3: Find the probability using the normal distribution tabele
-0.24 = -(0.20 + 0.04)
It can be seen from the table above that the Probability will be the circled portion on the table.
Hence,
[tex]P(z>-0.24)\approx0.5948[/tex]For which of the following intervals does the function (in the image section) have a removable discontinuity?A. [−2.5,−1.5] B. [−1.5,−0.5] C. [−0.5,0.5] D. [0.5,1.5] E. [1.5,2.5]
Given the function below,
[tex]f(x)=\frac{x+2}{x^4-2x^3-x^2+2x}[/tex]Let us now factorize the denominator
[tex]x^4-2x^3-x^2+2x[/tex]First of all, let us factorize x out from the denominator.
[tex]\begin{gathered} x(\frac{x^4}{x}-\frac{2x^3}{x}-\frac{x^2}{x}+\frac{2x}{x}) \\ x(x^3-2x^2-x+2) \end{gathered}[/tex]Therefore, x is a factor of the denominator.
Let us now factorize the remainder
[tex]x^3-2x^2-x+2[/tex]Let us substitute x = 1 into the function to confirm if it is a factor.
[tex]\begin{gathered} x=1 \\ 1^3-2(1)^2-(1)+2 \\ 1-2-1+2=1+2-1-2=3-3=0 \end{gathered}[/tex]Therefore, (x - 1) is a factor.
Let us now divide the function by (x - 1)
[tex]\frac{x^3-2x^2-x+2}{x-1}=\frac{\left(x-2\right)\left(x+1\right)\left(x-1\right)}{x-1}=(x-2)(x+1)[/tex]Hence, the factors of the denominator are,
[tex]x(x-1)(x+1)(x-2)[/tex]Therefore,
[tex]f(x)=\frac{x+2}{x(x-1)(x+1)(x-2)}[/tex]Now, looking at both the numerator and the denominator, we can observe that there is no common factor between the numerator and the denominator.
Hence, there is no removable discontinuity.
Solve for x:1(5x + 12) = 18 (2 points)5
(5x + 12) = 18
Remove the parenthesis from the right hand side:
5x + 12 = 18
Subtract 12 from both sides:
5x + 12 - 12 = 18 - 12
5x = 6
Divide both sides by 5:
5x/5 = 6/5
x = 6/5 = 1.2
⚠ If you are in a rush, only read the bold.
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w/3 as a fraction; w/3 + 14 = 17.6; and how to do it so i know next time
The value of w is 10.8.
what is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
given:
w/3 + 14 = 17.6
Now, solving for w.
Subtract 14 from both side
w/3 + 14 - 14 = 17.6 - 14
w/3 = 3.6
Multiply by 3 both side
w/3 x3 = 3.6 x 3
w= 10.8
Hence, the value of w is 10.8.
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Type the correct answer in each box. Use numerals instead of words.What is the yintercept of this quadratic function?f(3) -52 + 101 - 22).-The y-intercept of function fis (ResetNext
The quadratic function is expressed as
f(x) = - x^2 + 10x - 22
The y intercept is the value of y or f(x) when x = 0
Thus, to find the y intercept, we would substitute x = 0 into the function. Thus, we have
f(0) = - 0^2 + 10 * 0 - 22
f(0) = 0 + 0 - 22
f(0) = - 22
Thus, the y intercept of the function f is (0, - 22)
determine the number of different ways the given number can be written as the sum of 2 primes? 50
the prime numbers smaller than 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
let's find the sums that give us 50:
3+47=50
7+43=50
13+37=50
19+31=50
so the answer is four different ways.
The Busy Bee store bottles fresh jars of honey at a constant rate. In 3 hours, it bottles 36 jars, and in 7 hours, it bottles 84 jars of honey.
Determine the constant of proportionality.
36
12
4
0.08
The constant of proportionality is 12
Number of fresh jars of honey stored by The Busy Bee in 3 hours= 36 jars
Number of fresh jars of honey stored by The Busy Bee in 7 hours= 84 jars
So, In 3 hours = 36 jars
In 1 hour = 36/3 = 12 jars
Similarly, In 7 hours = 84 jars
In 1 hour = 84/7 = 12 jars
So, 12 is the constant number
Let x represent the number of hours and y the total number of jars stored by The Busy Bee after x hours
So, the equation can be formulated as:
y = 12x
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-162) Castel and Sumalee each improved their yards by planting rose bushes and ornamental grass.They bought their supplies from the same store. Castel spent $69 on 5 rose bushes and 8 bunchesof ornamental grass. Sumalee spent $42 on 2 rose bushes and 8 bunches of ornamental grass.What is the cost of one rose bush and the cost of one bunch of ornamental grass?#2
Let 'x' and 'y' be the cost of one rose bush and one bunch of ornamental grass.
Given that Castel paid $69 for 5 rose bushes and 8 bunches of grass,
[tex]5x+8y=69\ldots(1)[/tex]Also, given that Sumalee paid $42 for 2 rose bushed and 8 bunches of grass,
[tex]2x+8y=42\ldots(2)[/tex]Now that we have two equations and two variables. These can be solved using the Elimination Method.
Subtract equation (2) from (1) as follows,
[tex]\begin{gathered} (5x+8y)-(2x+8y)=69-42 \\ 5x+8y-2x-8y=27 \\ 3x+0=27 \\ x=\frac{27}{3} \\ x=9 \end{gathered}[/tex]Substitute this value in (1) and obtain the corresponding y-value,
[tex]\begin{gathered} 5(9)+8y=69 \\ 45+8y=69 \\ 8y=69-45 \\ y=\frac{69-45}{8} \\ y=3 \end{gathered}[/tex]So the simultaneous solution is obtained as,
[tex]\begin{gathered} x=9 \\ y=3 \end{gathered}[/tex]Thus, the cost of one rose bush is $9 and the cost of one bunch of ornamental grass is $3.
Evaluate lc2 + b21, given a = 5, b=-3, and c= -2. A. 13 B. 6 C. 2 D. 10
We have the function:
[tex]|c^2+b^2|[/tex]We then replace the values of b and c, that is:
[tex]|(-2)^2+(-3)^2|=13[/tex]From this expression, we have that the solution is 13.
Julieta has p pennies and n nickels. She has at most $1 worth of coins altogether.
Write this situation as an inequality.
Julieta has at most $1 worth of coins altogether, then the inequality of the given situation is $0.1p + $0.25n ≤ $1.00.
Based on the given conditions,
Julieta has p pennies and n nickels.
He has at most $1 worth of coins altogether.
What is a Inequality :Inequality, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Since p time = $0.1
So n times = $(0.1)n
Since p quarter = $0.25
So n quarters = $(0.25)n
Total of p times and n quarters = $[(0.1)p + (0.25)n]
This total answer has a minimum of $1 worth of mins all to get he.
So,
$[(0.1p + 0.25n)] ≤ 1
Therefore,
Julieta has at most $1 worth of coins altogether, then the inequality of the given situation is $0.1p + $0.25n ≤ $1.00.
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In a survey of 630 randomly selected U.S. companies, 535 reportedthat they performed drug testing on their employees and/or applicantslast year. At the 1% significance level, is there sufficient evidence toconclude that the percentage of U.S. firms that drug-tested last yearexceeds the previous year's figure of 74%? Formulate and carry outthe one-population z-test.Mean = 300Your answer should include:a) a statement of the hypothesesb) the critical value for the testc) the value of the test statisticd) a statement of conclusionTo get you started, here is the null hypothesis:H.p = 0.74
Given the following:
[tex]\begin{gathered} \alpha=0.05 \\ p=0.74 \\ \mu=300 \end{gathered}[/tex]a)
[tex]\begin{gathered} H_0\colon P=0.1 \\ H_1\colon P<0.1 \end{gathered}[/tex][tex]\begin{gathered} z=\frac{\hat{P}-P}{\sqrt[]{\frac{P(1-P)}{\mu}}} \\ \\ =\frac{0.09-0.1}{\sqrt[]{\frac{0.1\mleft(0.9\mright)}{300}}}=-0.58 \end{gathered}[/tex]b) The critical value is -1.645
Also
[tex]\begin{gathered} p<-0.58 \\ =0.28 \end{gathered}[/tex]c) Conclusion:
We fail to reject the test, since there is no enough evidence to conclude that the proportion of wrong tests is less than 10%
Think about what is different here? What makes this a challenge? Can you use skills you already know to figure out the intercepts here?
We are given the following line equation:
[tex]4x+5y=20[/tex]We are asked to determine the x and y-intercepts of the line. To do that, we will convert the given equation into the following form:
[tex]\frac{x}{a}+\frac{y}{b}=1[/tex]Written in that form the value of "a" is the x-intercept and the value of "b" is the y-intercept. Therefore, we need to divide the given equation by 20 in order to get a 1 on the right side:
[tex]\frac{4x}{20}+\frac{5y}{20}=\frac{20}{20}[/tex]Simplifying we get:
[tex]\frac{x}{5}+\frac{y}{4}=1[/tex]Therefore, the y-intercept is 4 and the x-intercept is 5.
INSTRUCTIONS: INSTRUCTIONS: Find the slope of the line and enter it here: 1. Find the slope of the line and enter it here: Find the y-intercept of the line & enter it here: Find the y-intercept of the line the enter it here: Write the equation of the line in form y=mx +b Write the equation of the line in form y=x+h 126 27 17
The slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]from the graph we notice that the line passes through the points (0,2) and (3,0), plugging this values into the equation above we have:
[tex]\begin{gathered} m=\frac{0-2}{3-0} \\ m=-\frac{2}{3} \end{gathered}[/tex]therefore the slope is m=-2/3.
The y intercept is the value of y when x=0; from the graph we conclude that b=2.
The equation of the line is:
[tex]y=-\frac{2}{3}x+2[/tex]Verify algebraically if the function is odd, even, or neither. Need # 6 help
As given by the question
(6)
There are given that the function:
[tex]h(x)=x^9+1[/tex]Now,
For the even:
[tex]h(-x)=h(x)[/tex]So,
From the function
[tex]\begin{gathered} h(x)=x^9+1 \\ h(-x)=(-x)^9+1 \\ =x^9+1 \\ h(-x)\ne h(x) \end{gathered}[/tex]So, the given function is not even.
Then,
For odd:
[tex]\begin{gathered} h(-x)=-h(x) \\ h(-x)=(-x)^9+1 \\ h(-x)=-(x)^9+1 \\ h(-x)\ne-h(x) \end{gathered}[/tex]So, the given function is not odd.
Hence, the given function is neither odd nor even.
Which of the following can be modeled by a linear function?
A taxi driver charges $3.50 per ride and $0.80 per mile driven.
The relationship between the height of a ball after being kicked from the ground and the distance the ball is from the kicker.
The balance in a savings account that acquires 0.7% interest compounded monthly.
The relationship between the time passed and the speed of a car as it slows down for a curve then accelerates back to its regular speed.
Taxi fares start at $3.50 and go up to $0.80 for every mile traveled is an example of a linear equation. Then the correct option is A.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
Taxi fares start at $3.50 and go up to $0.80 for every mile traveled. This relationship is given by the linear equation.
the link between a ball's height after being kicked off the ground and its proximity to the kicker. This relationship is given by the quadratic equation.
The amount in a savings account earns 0.7% interest each month compounded. This relationship is given by the exponential equation.
A car's slowing down for a curve and then reaccelerating to its usual speed. Its links time and speed. This relationship may be given by the linear equation.
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Solving a percent makes your prom using a system of linear equations
Water :60 ounces
Salt solution:60 ounces
Explanation
Step 1
set the equations
Let x represent the amoun of water forthe solution
let y represents the amount of solution ( 40% salt)
so
a)the scientific mixes water with the solution to obtain 120 ounces, so
[tex]x+y=120\Rightarrow equation\left(1\right)[/tex]b)the mixture is 20% salt
so
salt fromwater+salt from solution( 40%) = salt in the solution (20%)
so
[tex]\begin{gathered} 0+0.4y=120*0.2 \\ 0.4y=24 \\ divide\text{ both sides by 0.4} \\ \frac{0.4y}{0.4}=\frac{24}{0.4} \\ y=60 \end{gathered}[/tex]hence, the amount of salt solution is 60 ounces
,now to find x, replace the y value in equation (1)
[tex]\begin{gathered} x+y=120\Rightarrow equation\left(1\right) \\ x+60=120 \\ subtract\text{ 60 in both sides} \\ x+60-60=120-60 \\ x=60 \end{gathered}[/tex]so, water : 60 ounces
therefore, the answer is
Water :60 ounces
Salt solution:60 ounces
I hope this helps you
I've forgotten how to answer questions like this.... Can I get some help with steps please? "Write an Equation of the line passing through the point (3, -5) that is parallel to the line y=5x+7"
If the line is paralell to y = 5x + 7, it will have the same slope, which is 5
The general equation of a line is: y = mx + b
we know that the slope m = 5, and to find b we will use the point (3, -5)
using 3 for x and -5 for y:
y = mx + b
y = 5x + b
-5 = 5(3) + b
-5 = 15 + b
-5 - 15 = b
-20 = b
b = -20
Then the equation is: y = 5x - 20
Answer:
y = 5x - 20
Can someone help to solve question 18 from the picture below.
lim x → 0 (2/x - 2/|x|) does not exist.
We need to find lim x → 0 (2/x - 2/|x|)
lim x → 0 (2/x - 2/|x|) = lim x → 0 (2|x| - 2x / x |x|)
Consider the left hand limit.
lim x → 0^- [(2|x| - 2x) / x |x|]
As the x values approach 0 from the left, the function values decrease without bound.
i.e., the function approaches -∞
Consider the right hand limit.
lim x → 0^+ [(2|x| - 2x) / x |x|]
Consider a table to see the behavior of the function as x approaches 0 from the right.
x f(x)
0.1 0
0.01 0
0.01 0
As the x values approach 0 from right, the function values approach 0.
Thus, the limit of [(2|x| - 2x) / x |x|] as x approaches 0 from the right is 0.
Since the left sided and right sided limits are not equal, the limit does not exist.
Therefore, lim x → 0 (2/x - 2/|x|) does not exist.
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what type of equation will best fit the data below
A quadratic equation
Here, we want to get the type of equation that will fit the given plot
From what we have, the tracing of a line in the direction of the plotted lines will give us a parabola
The parabola represents the plot of a quadratic equation
Hence, the data will be best fit by a quadratic equation
I need help with this problem
