define the imaginary unit, i
An imaginary unit, i is a solution to the quadratic equation:
[tex]\text{ x}^2\text{ + 1 = 0}[/tex]Or to simply say,
[tex]i\text{ = }\sqrt[]{-1}[/tex]It can
Find each value if f(x) = 2x - 1 and g(x) = 2 - x2.9. f(0)
ANSWER
f(0) = -1
EXPLANATION
We just have to replace x by 0 into f(x):
[tex]\begin{gathered} f(x)=2x-1 \\ f(0)=2\cdot0-1 \\ f(0)=0-1 \\ f(0)=-1 \end{gathered}[/tex]Help me with this math problem plsWrite the formula for g(x) in terms of f(x)
Given:
Given a graph of f(x) and g(x).
Required:
To write the formula for g(x) in terms of f(x).
Explanation:
The graph of g(x) is 5 units left and 1 units up gfrom the graph of f(x).
Therefore the function g(x) is
[tex]g(x)=f(x+5)+1[/tex]Final Answer:
[tex]g(x)=f(x+5)+1[/tex]Find the area of the rectangle if the length is y + 4 inches and the width is y - 5 inches. Enter your answer as a polynomial in terms of variable y and in standard form, ay2 + by + c.
We have the following:
We have that the area of a rectangle is the following
[tex]\begin{gathered} A=l\cdot w \\ \text{In this case:} \\ l=y+4 \\ w=y-5 \end{gathered}[/tex]replacing:
[tex]\begin{gathered} A=(y+4)(y-5)=y^2-5y+4y-20 \\ A=y^2-y-20 \end{gathered}[/tex]5+3(-2x+1)=16 I need help
Given:
5 + 3(-2x + 1) = 16
Let's solve for x.
• Step 1:
Use distributive property to expand the parenthesis
5 + 3(-2x) + 3(1) = 16
5 - 6x + 3 = 16
• Step 2:
Combine like terms
-6x + 3 + 5 = 16
-6x + 8 = 16
• Step 3:
Subtract 8 from both sides
-6x + 8 - 8 = 16 - 8
-6x = 8
• Step 4:
Divide both sides by -6
[tex]\begin{gathered} \frac{-6x}{-6}=\frac{8}{-6} \\ \\ x=-\frac{4}{3} \end{gathered}[/tex]ANSWER:
[tex]-\frac{4}{3}[/tex]•
Please help me with the question and explain your work! 16 through 19 thank you please please please help
We have the following:
A.
First we find the slope of the line with the following points:
(0, 3) and (5,0)
[tex]m=\frac{0-3}{5-0}=-\frac{3}{5}[/tex]now, for b, with the point (0,3)
[tex]\begin{gathered} 3=-\frac{3}{5}\cdot0+b \\ b=3 \end{gathered}[/tex]The equation is:
[tex]y=-\frac{3}{5}x+3[/tex]B.
The area is:
[tex]\begin{gathered} A=\frac{AC\cdot CB}{2} \\ A=\frac{3\cdot5}{2}=\frac{15}{2} \\ A=7.5 \end{gathered}[/tex]The area is 7.5 square units
for, perimeter:
[tex]\begin{gathered} p=AC+CB+AB \\ AB^2=AC^2+CB^2 \\ AB^2=3^2+5^2=9+25=34 \\ AB=\sqrt[]{34} \\ p=3+5+\sqrt[]{34} \\ p=13.83 \end{gathered}[/tex]The perimeter is 13.83 units
C.
when two lines are perpendicular they fulfill the following
[tex]m_1\cdot m_2=-1[/tex]therefore,
[tex]\begin{gathered} -\frac{3}{5}\cdot m_2=-1 \\ m_2=\frac{5}{3} \end{gathered}[/tex]Therefore, the equation is:
[tex]y=\frac{5}{3}x+3[/tex]A pizza place offers ten different toppings. A special is a pizza with any three different toppings. How many different types of specials are offered?
As given by the question
There are given that the total of 10 different topping
Now,
According to the question:
There is also talk about 3 different pizzas.
So,
The three different toppings from the 10 different toppings:
[tex]10C_3=\frac{10!}{3!(10-3)!}[/tex]Then,
[tex]\begin{gathered} 10C_3=\frac{10!}{3!(10-3)!} \\ 10C_3=\frac{10!}{3!(7)!} \\ 10C_3=\frac{10\times9\times8\times7!}{3!(7)!} \\ 10C_3=\frac{10\times9\times8}{3\times2\times1} \end{gathered}[/tex]Then,
[tex]\begin{gathered} 10C_3=\frac{10\times9\times8}{3\times2\times1} \\ 10C_3=10\times3\times4 \\ 10C_3=120 \end{gathered}[/tex]Hence, 120 different pizzas are possible.
QThe image of point A (3, 4) under translation Tis A' (-1,6). What is the translation rule? worth 50 points guy's can someone please give me an answer really quick please!!!
Here, we want to find the translation rule
Given the lines below, create a line that is parallel, one that is perpendicular, and one that is neither. Y = -6Parallel: Perpendicular: Neither:
Given:
[tex]y=-6[/tex]The slope of the given line is zero.
a) parallel line: Parallel lines have the same slope. Any line whose slope is x=zero will be parallel to line y=-6.
So, one equation can be,
[tex]y=-2[/tex]2) Perpendicular line
Clearly the line y=-6 is the horizontal line having a slope of 0.
So, the line perpendicular to this line will be a verticle line with an undefined slope.
And its equation is of the form x = a.
The equation can be,
[tex]x=2[/tex]c) The lines which are neither parallel nor perpendicular will be just the intersecting lines.
The equation can be,
[tex]y=x+1[/tex]Find the volume of the sphere. Round your answer to the nearest tenth. Use 3.14 for n. A sphere has a radius of 8 centimeters. The volume of the sphere is about cm?.
Find the volume of the sphere. Round your answer to the nearest tenth. Use 3.14 for n. A sphere has a radius of 8 centimeters. The volume of the sphere is about cm?.
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]we have
r=8 cm
pi=3.14
substitute the given values in the formula
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot8^3 \\ V=2,143.6\text{ cm\textasciicircum{}3} \end{gathered}[/tex]answer is
2,143.6 cubic centimetersUse Pascal's Triangle to expand the binomial. (d-3)^6
Using pascal triangle
(d-3)^6
Expoenent 6 has a coeffient of;
1 6 15 20 15 6 1
Hence;
[tex]d^6-6(d)^5(3)+15(d)^4(3)^2-20(d)^3(3)^3+15(d)^2(3)^4-6(d)(3)^5+3^6[/tex]Two things to note here is that;
-There is a minus sign in-between the numbers in the bracket, hence we alternate the sign starting with positive
-secondly as the power of the first variable decreases the power of the second digit increases
We can further simplify;
[tex]d^{6\text{ }}-6d^5(3)+15(d)^4(9)^{}-20d^3(27)+15d^2(81)-6d(243)+729[/tex]We will still simplify to give:
[tex]d^6-18d^5+135d^4-540d^3+1215d^2-1458d\text{ + 729}[/tex]Answer:
The Binomial Theorem Quick Check:
1. [tex]d^6-18d^5+135d^4-540d^3+1215d^2-1458d+729[/tex]
2. [tex]s^5+15s^4v+90s^3v^2+270s^2v^3+405sv^4+243v^5[/tex]
3. [tex]-64b^3[/tex]
100% 3/3
You're Welcome! A brainliest would help me alot. ‿
find an equation of the line having the given slope and containing the given point . Slope -2; through (6,-9) . type answer in slope-intercept form .
Given:
The slope of the line is m = -2.
The line passes throught the point (6,-9).
The objective is to find the equation of line.
Explanation:
Consider the point as,
[tex](x_1,y_1)=(6,-9)[/tex]The general equation to find the equation of line in slope intercept form is,
[tex]y-y_1=m(x-x_1)[/tex]Substitution:
On plugging the given values in the general equation,
[tex]\begin{gathered} y-(-9)=-2(x-6) \\ y+9=-2x+12 \\ y=-2x+12-9 \\ y=-2x+3 \end{gathered}[/tex]Here, slope of the line is -2 and y- intercept is 3.
Hence, the equation of the line in slope intercept form is y = -2x + 3.
20 4/5 whats the decimal number
20 4/5
it means 20 integers and 4/5
4/5 = 0.8
so the number 20 4/5 is equal to 20.8
answer: 20.8
20 7/8 is 20 integers and 7/8
7/8 = 0.875
so 20 7/8 is equal to 20.875
1. Drag the fractions in order from least to greatest value L
Given the fractions 3/4 and 5/16
In order to determine which is less or greater, we need to first express them in percentage as shown;
3/4 = 3/4*100%
3/4 = 3*25 = 75%
5/16 = 5/16 * 100
5/16 = 500/16 = 31.25%
Since 75% is greater than 31.25% hence;
3/4 is greater than 5/16 and the sign that will be in the box will be the greater than sign i.e 3/4>5/16
Strategy: I compared the fraction to the bench mark of >
Suppose Piper eats out twice a week 15% of the time, she eats out once a week 35% of the time, and she does not eat out any time during the week 50% of the time.What is the expected value for the number of times Piper eats out during the week? Round your answer to the nearest hundredth if needed.
Solution
We are given
Probability of eating out twice in a week = 15% = 0.15
Probability of eating out once in a week = 35% = 0.35
Probability of not eating out in a week = 50% = 0.50
Let X be a random variable of the number of times Piper eats out in a week
So we have the table
Note: The Formula For finding the Expected value E(X) is given by
[tex]E(X)=\sum ^{}_{}xp(x)[/tex]Substituting we get
[tex]\begin{gathered} E(X)=0(0.50)+1(0.35)+2(0.15) \\ E(X)=0+0.35+0.30 \\ E(X)=0.65 \end{gathered}[/tex]Therefore, the expected value is
[tex]E(X)=0.65[/tex]what are the coordinates of the library A (3,4)b. (4,3)c..(2,1)d.(1,2
To determine the coordinates of the library, for the x-coordinate, you have to draw a vertical line from the library to the x-axis and read where it intersects the x-axis. And to determine the y-coordinate you have to draw a horizontal line from the position of the library towards the y-axis, and read where the line intersects the y-axis:
The x-coordinate is 4 and the y-coordinate is 3, so the coordinates of the library are (4,3)
Combo 1Combo 2Combo 33 glazed5 glazed4 glazed4 cream filled6 cream filled4 cream filled5 chocolate1 chocolate4 chocolate$38$32$36a)Write a system to represent this situation. Use g for glazed donuts, f for cream filled donuts, and c for chocolate donuts.b)Solve the system ALGEBRAICALLY to find the price of each donuts.
We will use the following variables :
g for glazed
f for cream filled donuts
c for chocolate donuts
So, the equation for combo 1
3 g + 4 f + 5 c = $38
The equation for combo 2:
5 g + 6 f + c = $32
The equation for combo 3:
4 g + 4 f + 4 c = $36
So, the system of equations are:
3 g + 4 f + 5 c = 38 (1)
5 g + 6 f + c = 32 (2)
4 g + 4 f + 4 c = 36 (3)
B) Now, we need to solve the system of equations:
From equation 3:
4 g + 4 f + 4c = 36
divide all terms by 4
So, g + f + c = 9
Solve for c:
c = 9 - g - f
Substitute with the value of c at the equations (1)
At (1):
3 g + 4 f + 5 (9 - g - f) = 38
3g + 4f + 45 - 5g - 5f = 38
-2g - f = 38 - 45
-2g - f = -7
Multiply all terms by -1
2g + f = 7
Solve for f
f = 7 - 2g
Substitute with f at the equation of c
c = 9 - g - (7 - 2g)
c = 9 - g - 7 + 2g
c = g + 2
So, we have reached to :
f = 7 - 2g and c = g + 2
substitute with f and c at the equation (2)
5g + 6f + c = 32
5g + 6 (7 - 2g) + g + 2 = 32
solve for g
5g + 42 - 12 g + g + 2 = 32
5g - 12g + g = 32 - 42 - 2
-6g = -12
Divide both sides by -2
g = -12/-6 = 2
f = 7 - 2g = 7 - 2 * 2 = 7 - 4 = 3
c = g + 2 = 2 + 2 = 4
So, the cost of glazed = $2
The cost of cream filled = $3
The cost of chocolate = $4
Fill in only the blanks. (Whatever that has an answer like the domain don’t do it)only do the empty blanks
From the graph, we can conclude:
[tex]Range\colon(-\infty,1)[/tex]As:
[tex]\begin{gathered} x\to0,f(x)\to-\infty \\ x\to\infty,f(x)\to1 \end{gathered}[/tex]x-intercept:
[tex](1,0)[/tex]Asymptote:
Vertical asymptote:
[tex]x=0[/tex]Horizontal asymptote:
[tex]y=1[/tex]A sofa regularly sells for $600. The sale price is $504.00. Find the percent decrease of the sale price from the regular price
STEP - BY - STEP EXPLANATION
What to find?
Percentage decreaase.
Given:
Original price = $600
new price = $504
Step 1
Recall the formula for percentage decrease.
[tex]\text{ \% decrease=}\frac{decrease}{original\text{ price}}\times100\text{ \%}[/tex]Step 2
Determine the value for the dcerease.
[tex]Decrease=new\text{ price - original price}[/tex][tex]Decrease=504-600=-96[/tex]Step 3
Substitute into the formula and simplify.
[tex]\text{ \% decrease=-}\frac{96}{600}\times100\text{ \%}[/tex][tex]=-16\text{ \%}[/tex]ANSWER
Percent decrease = 16% decrease
please help me ASAP!!!
what 3 1/4 - 1 3/8 equal?
Answer : 1 7/8
Given that: 3 1/4 - 1 3/8
Step 1: Convert the mixed fraction into an improper fraction
3 1/4 = (4 x 3) + 1 / 4
3 1/4 = 12 + 1 / 4
3 1/4 = 13/4
1 3/8 = (8 x 1) + 3 / 8
1 3/8 = 8 + 3 / 8
1 3/8 = 11/8
13/4 - 11/8
The common denominator is 8
2 x 13 - 11 x 1 / 8
26 - 11 / 8
15/8
1 7/8
Therefore, the answer is 1 7/8
IF AB = (2x + 23). BC = (12 + 7x), and CD = 19 - 9x), find AD.
The addition of length of each line segment gives the value of AD.
[tex]\begin{gathered} \text{From the number line, AB+BC+CD=AD} \\ AD=(2x+23)+(12+7x)+(19-9x)=2x+7x-9x+23+12+19=54 \end{gathered}[/tex]The value of AD is 54.
Solve the following system of linear equations by graphing:4x + 4y = 2010x + 2y = 18
one solution: (1, 4)
The equations:
y = -x + 5
y = -5x + 9
Explanation:[tex]\begin{gathered} \text{Given equations:} \\ 4x+4y=20\text{ }\ldots(1) \\ 10x+2y=18\text{ }\ldots(2) \end{gathered}[/tex]To plot the graphs, we can assign values to x. The we get the corresponding values of y for each of the equation.
Rewritting the two equations by making y the subject of formula:
[tex]\begin{gathered} 4x+4y=20 \\ \text{divide through by 4:} \\ x\text{ + y = 5} \\ y\text{ = -x + 5} \end{gathered}[/tex][tex]\begin{gathered} 10x+2y=18 \\ \text{divide through by 2:} \\ 5x\text{ + y = 9} \\ y\text{ = -5x + 9} \end{gathered}[/tex]Plotting the graphs:
The point of intersection of the graphs is the solution.
There is one solution: (1, 4)
5 Three pipes are connected to a water tank. One of the pipes can fill the tank in 30 minutes. The second pipe can fill it in 20 minutes. The third pipe can fill the tank in 40 minutes. How long will it take to fill the tank if all three pipes are opened together? If the slowest pipe is shut off after 3 minutes and the fastest pipe is shut off 3 minutes later, how long will it take the remaining open pipe to finish filling the tank?
Let's call the total volume of the tank as V. The rate each pipe fills the tank is given by the total volume of the tank divided by the amount of time it takes to fill the tank. Let's call the rate of the first pipe as r1, the rate of the second pipe as r2 and the rate of the third pipe as r3.
[tex]\begin{gathered} r_1=\frac{V}{30} \\ r_2=\frac{V}{20} \\ r_3=\frac{V}{40} \end{gathered}[/tex]The product between the rate and the time that has passed will give to us the fraction of the tank that has been filled. When we open the three pipes at once, we sum their rates. When the tank is filled, the product between the rate and the time passed must give the total volume of the tank, therefore, we have the following equation:
[tex]\begin{gathered} (\frac{V}{30}+\frac{V}{20}+\frac{V}{40})t=V \\ \frac{13V}{120}t=V \\ \frac{13}{120}t=1 \\ t=\frac{120}{13} \\ t=9.23076923077... \\ t\approx9.23 \end{gathered}[/tex]It will take approximately 9.23 minutes to fill the tank if all pipes are opened together.
When the three pipes are opened, the fraction that has been filled(let's call it as x) is given by:
[tex]\begin{gathered} (\frac{1}{30}+\frac{1}{20}+\frac{1}{40})\cdot3=x \\ x=\frac{13}{40} \end{gathered}[/tex]Then, the slowest pipe(the third pipe) is closed, then, after 3 more minutes we're going to fill an extra y amount of water, given by:
[tex]\begin{gathered} (\frac{1}{30}+\frac{1}{20})\cdot3=y \\ \frac{1}{10}+\frac{3}{20}=y \\ \frac{5}{20}=y \\ y=\frac{1}{4} \end{gathered}[/tex]Then, after a time t with the first pipe open, we're going to fill the tank(remember that it has been filled already by the amounts x and y, therefore, we must subtract it from the total volume).
[tex]\begin{gathered} \frac{1}{30}\cdot t=1-\frac{13}{40}-\frac{1}{4} \\ \frac{t}{30}=\frac{27}{40}-\frac{10}{40} \\ t=30\cdot\frac{17}{40} \\ t=12.75 \end{gathered}[/tex]If the slowest pipe is shut off after 3 minutes and the fastest pipe is shut off 3 minutes later, it will take 12.75 minutes for the remaining open pipe to finish filling the tank.
Find the value of the ratio using the term sequence 5, 15, 45 , 135, ...
To find the ratio, we just have to divide the second term by the first term.
[tex]\frac{15}{5}=3[/tex]Therefore, the ratio of the sequence is 3.Notice that the given sequence is geometrical because we have to multiply each term with 3 to get each new term.
Can I get help with my math homework I’m struggling with ? 3
Step 1:
The slope intercept form formula is
y = mx + c
m = slope
c = intercept on the y-axis
Final answer
Slope Intercept
Step
Ton graph the function, find both x=intercept and y-intercept
[tex]\begin{gathered} \text{From y = }\frac{3}{2}x\text{ + 1} \\ y-\text{intercept c = 1} \\ \text{Make x subject of the formula} \\ 3x\text{ = 2y - 2} \\ x\text{ = }\frac{2}{3}y\text{ - }\frac{2}{3} \\ x-\text{intercept c = -}\frac{2}{3} \end{gathered}[/tex]Next plot the graph.
Help me solve for equation 6x+3=33
Given:
[tex]6x+3=33[/tex]is given.
Required:
We need to solve this equation.
Explanation:
Here an equation given as
[tex]6x+3=33[/tex]now add both side negative 3 and we get
[tex]\begin{gathered} 6x+3-3=33-3 \\ 6x=30 \end{gathered}[/tex]now multiply both side with inverse 6
[tex]\begin{gathered} \frac{1}{6}*6x=30*\frac{1}{6} \\ x=5 \end{gathered}[/tex]Final answer:
Solution of given equation is
[tex]x=5[/tex]
How much sugar is in a 340 gram mixture if you know the mixture is 50%sugar?
We got 340 gram mixture. The 50% of it is sugar, so:
[tex]\frac{50}{100}\cdot340=170[/tex]Then, there are 170g of sugar.
Given sinx= 5/13 andπ/2 < x < π find the exact value of tan 2x
Given sin(x)=5/13
First, lets find cos(x).
It is known that:
[tex]\begin{gathered} \sin ^2(x)+\cos ^2(x)=1 \\ (\frac{5}{13})^2+\cos ^2(x)=1 \\ \cos ^2(x)=1-\frac{25}{169} \\ \cos ^2(x)=\frac{169-25}{169}=\frac{144}{169} \\ \cos (x)=\pm\sqrt[]{\frac{144}{169}}\text{ = }\frac{\sqrt[]{144}}{\sqrt[]{169}} \\ \cos (x)=\pm\frac{12}{13} \end{gathered}[/tex]Since π/2 < x < π, we are in 2nd quadrant. Then, cos(x) is negative.
[tex]\cos (x)=-\frac{12}{13}[/tex]Since we know the values for sin and cos, we can find tan(x):
[tex]\begin{gathered} \tan (x)=\frac{\sin(x)}{\cos(x)} \\ \tan (x)=\frac{\frac{5}{13}}{-\frac{12}{13}} \\ \tan (x)==-\frac{5}{12} \end{gathered}[/tex]Now, lets work with the expression tan(2x)
It is known that:
[tex]\tan (2x)=\frac{2\tan(x)}{1-\tan^2(x)}[/tex]
Since we know tan(x), we can substitute in the expression above and find the value of tan(2x):
[tex]\begin{gathered} \tan (2x)=\frac{2\tan(x)}{1-\tan^2(x)} \\ \tan (2x)=\frac{2\cdot(-\frac{5}{12}_{})}{1-(-\frac{5}{12})^2} \\ \tan (2x)=\frac{-\frac{10}{12}}{1-\frac{25}{144}}=\frac{-\frac{10}{12}}{\frac{144-25}{144}}=\frac{-\frac{10}{12}}{\frac{119}{144}}=-\frac{10}{12}\cdot\frac{144}{119} \\ \tan (2x)=-\frac{120}{119} \end{gathered}[/tex]Answer: -120/119
what decimals are between 0.82 and 0.83
Answer:
0.82 and 0.83