Answer:
Step-by-step explanation:
In a physical change the appearance or form of the matter changes but the kind of matter in the substance does not. However in a chemical change, the kind of matter changes and at least one new substance with new properties is formed.
If A={a,c} and B={d,g,w} then complete the Following:a. Find AxBb. Find n(AxB)c. write a multiplication equation involving numerals related to the parts in (a) and (b)...a. AxB = {____} Type an ordered pair. Use commas to separate answers as needed
Given the two sets:
[tex]\begin{gathered} A=\mleft\lbrace a,c\mright\rbrace \\ B=\mleft\lbrace d,g,w\mright\rbrace \end{gathered}[/tex]we can write the product set of A and B in the following form:
[tex]AxB=\mleft\lbrace(a,d\mright),(a,g),(a,w),(c,d),(c,g),(c,w)\}[/tex]next, we have that the number of elements in A is 2 and the number of elements in B is 3, then, we have:
[tex]n(AxB)=2\cdot3=6[/tex]finally, the equation that involves the numerals of the previous parts is:
[tex]n(AxB)=n(A)\cdot n(B)[/tex]where n(A) and n(B) represents the number of elements in A and B respectively.
Find the missing number to make the fractions equivalent. 3/4 = 9/?
We have the following:
[tex]\frac{3}{4}=\frac{9}{x}[/tex]solving:
[tex]\begin{gathered} x=\frac{9\cdot4}{3} \\ x=12 \end{gathered}[/tex]Therefore, the answer is [B] 12
Can someone explain how I would know the difference between a 2:7 ratio and 7:2 ratio when a point partitions the line? Thank you!
Solution
For this case we can do the following:
We can understand 7/2 as the reciprocal of 2/7 and we can create the following diagram
3x - 4y = 65x + 8y = -1
Use U-Subscription to solve the following polynomial. Compare the imaginary roots to the code breaker guide. Hi this is a project and this is one of the questions, I have the guide so ignore the code piece part.
We will substitute the variable x with the variable u using the following relation:
[tex]u=x^2[/tex]Then, we can convert the polynomial as:
[tex]4x^4+2x^2-12=4u^2+2u-12[/tex]We can use the quadratic equation to calculate the roots of u:
[tex]\begin{gathered} u=\frac{-2\pm\sqrt[]{2^2-4\cdot4\cdot(-12)}}{2\cdot4} \\ u=\frac{-2\pm\sqrt[]{4+192}}{8} \\ u=\frac{-2\pm\sqrt[]{196}}{8} \\ u=\frac{-2\pm14}{8} \\ u_1=\frac{-2-14}{8}=-\frac{16}{8}=-2 \\ u_2=\frac{-2+14}{8}=\frac{12}{8}=1.5 \end{gathered}[/tex]We have the root for u: u = -2 and u = 1.5.
As u = x², we have two roots of x for each root of u.
For u = -2, we will have two imaginary roots for x:
[tex]\begin{gathered} u=-2 \\ x^2=-2 \\ x=\pm\sqrt[]{-2} \\ x=\pm\sqrt[]{2}\cdot\sqrt[]{-1} \\ x=\pm\sqrt[]{2}i \end{gathered}[/tex]For u = 1.5, we will have two real roots:
[tex]\begin{gathered} u=1.5 \\ x^2=1.5 \\ x=\pm\sqrt[]{1.5} \end{gathered}[/tex]Then, for x, we have two imaginary roots: x = -√2i and x = √2i, and two real roots: x = -√1.5 and x = √1.5.
Answer:
Let u = x²
Equation using u: 4u² + 2u - 12
Solve for u: u = -2 and u = 1.5
Solve for x: x = -√2i, x = √2i, x = -√1.5 and x = √1.5
Imaginary roots: x = -√2i and x = √2i
Real roots: x = -√1.5 and x = √1.5
For one of the meals eaten duringthe field trip to Williamsburg, VA,WHMS will be charged $115.50 foradults to eat and $712.50 forstudents to eat WHMS will leave a10% tip. How much money willWHMS leave for the tip
The total amount the WHMS would be charged for adults and students to eat is
115.5 + 712.5 = $828
We were told that WHMS will leave a 10% tip. Recall that percentage is expressed in terms of 100. This means that the amount of money that WHMS will leave for the tip is
10/100 * 828 = $82.8
WHMS would leave $82.8 for the tip
Solve for x(2x+3)(3x-2)=(3x+3)(2x-2)
To solve for x, we need to apply distributive property as:
[tex]\begin{gathered} \left(2x+3\right)\left(3x-2\right)=\left(3x+3\right)\left(2x-2\right) \\ 2x\cdot3x+2x\cdot(-2)+3\cdot3x+3\cdot(-2)=3x\cdot2x+3x(-2)+3\cdot2x+3\cdot(-2) \\ 6x^2-4x+9x-6=6x^2-6x+6x-6 \\ 6x^2+5x-6=6x^2-6 \\ 6x^2+5x-6+6=6x^2-6+6 \\ 6x^2+5x=6x^2 \\ 6x^2+5x-6x^2=6x^2-6x^2 \\ 5x=0 \\ x=0 \end{gathered}[/tex]Answer: x = 0
Assume that Jim Bruce and Valerie are 3 of the 17 members of the class, and that of the class members will be chosen randomly to deliver their reports during the next class meeting. What is the probability that Jim Bruce and Valerie are selected in that order?
The probability that Jim, Bruce and Valerie are selected in that order is P = 1/680
Given,
Number of students in a class = 17
Jim, Bruce and Valerie are 3 of the 17.
Three of students from the class are randomly chosen to deliver their reports during the next class meet.
We have to find the probability that Jim, Bruce and Valerie are selected in that order;
Here,
The total number of possible selection;
S = ⁿCr
Where, n = 17 and r = 3
Then,
S = ¹⁷C₃
S = 17! / 14! x 3!
S = 680
Therefore,
The probability that Jim, Bruce and Valerie are selected in that order is P = 1/680
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A music club charges an initial joining fee of $24.00. The cost per CD is $8.50. The graph shows the cost of belonging to the club as a function of CDs purchased. How will the graph change if the cost per CD goes up by $1.00.? (The new function is shown by the dotted line.)
Given the function with a graph that shows the cost of belonging to the club as a function of CDs purchased
linear function with the form
[tex]y=x[/tex]since the new graph has a new cd cost up by $1.00
then the new line is
Correct answer
Option C
Describe and justify the methods you used to solve the quadratic equations in parts A and B.
We know that give any pair of real numbers A and B, the following statement will be true:
[tex]A\cdot B=0[/tex]if, and only if
[tex]\begin{gathered} A=0 \\ or \\ B=0 \end{gathered}[/tex]Now, if we factor a quadratic equation into two factors A and B, and use the fact we've just mentioned, we can then equal each factor to zero, solve for x and get the solutions to said quadratic equation.
Here is a right triangle with a missing side length what is the missing side length
Right Triangles
A right triangle is recognized because it has an interior angle of 90°.
In right triangles, the Pythagora's Theorem is satisfied.
Being a and b the shorter sides (also called legs) of the triangle, and c the longer side (called hypotenuse), then:
[tex]c^2=a^2+b^2[/tex]The triangle shown in the image has the two legs of values a=15 and b=8. The hypotenuse is c=x, thus:
[tex]x^2=15^2+8^2[/tex]Operating:
[tex]x^2=225+64=289[/tex]Solving for x:
[tex]x=\sqrt[]{289}=17[/tex]x = 17
How do I Graph the line with the given slope m and y-intercept b.
M=-4/3,b=2
Irlene has just returned from a business trip in Britain with £200 of uncashed traveller's cheques. How much would she receive from the bank when she converts the currency back to Canadian dollars, assuming that the bank offers an exchange rate of C$1.00 = £0.5544 and charges a 0.65% fee to convert the traveller's cheques to Canadian funds? For full marks your answer(s) should be rounded to the nearest cent.
The converted money in Canadian dollars is $111.6.
Given that, Irlene has just returned from a business trip in Britain with £200 of uncashed traveler's cheques.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the converted Canadian dollars be x.
x = 200 × 0.5544 + 0.65% of 200 × 0.5544
= 110.88 + 0.0065 × 110.88
= 111.60072
≈ 111.6
Therefore, the converted money in Canadian dollars is $111.6.
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For which values of A, B, and C will Ax + By = C be a horizontal line through the point (−4, 2)?
The set of values {A = 0, B = 1, and C = 2} to have a completely horizontal line.
What is a horizontal line?A horizontal line is defined as a line with slope m = 0 that is parallel to the x-axis.
A horizontal line across (-4,2) informs us of two things.
A horizontal line with slope m = 0 is parallel to the x-axis.
The line crosses the point (-4,2).
Ax + By = C has m = B/A = 0 slope and intersects point (-4,2).
Then, B = A×0 indicates that any constant A will work, and the Ax term disappears.
Ax + By = C then becomes y = C. To find C, use the point (-4,2).
⇒ C = 2
This line's equation is y = 2, and any point (x,2) matches the equation.
Therefore, the set of values {A = 0, B = 1, and C = 2} to have a completely horizontal line.
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Answer:
Step-by-step explanation:
17
From least to greatest. -1.4-1.02 -1.20
We could put these values in the number line:
Therefore, the order of the numbers from least to greatest is:
-1.4 , -1.20 , -1.02
The least number between all the options given is -1.4 because if you see, all numbers are negative, so, when a negative number is greater, as the amount after the negative sign becomes greater, the number is going to be least. That's the reason of the order.
Sydney is making bracelets, 3 bracelets require 21 beads. The number of braclets varies directly with the number of beads.
Write an equation in the form of y = ax then find the amount o
beads needed for 32 bracelets.
Step-by-step explanation:
"varies DIRECTLY with" means there is an y = ax relationship.
y = number of bracelets
x = number of beads
3 = a×21
a = 3/21 = 1/7
now, when we have 32 bracelets
32 = 1/7 × x
32×7 = x = 224
224 beads are needed for 32 bracelets.
Pattern Exercise Mins Components Fitnes 0 5 1 9 2 25 3 89 4 ? What do you notice about the pattern of components from minute to minute? 2. State the value for the question mark. I E O BI
We can calculate how much each component increases, this is shown in the following image:
So we can see that the pattern in which the components increase from minute to mites is that starts by adding 4, then they add 4x4=16, then they add 16x4=64, and so on:
So the rule is that the next increase is the previous increase multiplied by 4.
Thus, the next increase in components (the question mark) should be:
The previous one +256, which gives:
[tex]?=89+256=345[/tex]Answer: 345
what is the length of the dominant line in the time graph below? l leave your answer in simplest radical form.
Let's first calculate the lenght of the side of the rectangle.
[tex]l=\sqrt[]{8^2+5^2}=\sqrt[]{64+25}=\sqrt[]{89}[/tex]so we get that the dotted line is:
[tex]d=\sqrt[]{2^2+89}=\sqrt[]{93}[/tex]so the answer is square root of 93
factor completely5r^3-10r^2+3r-6
You have the following polynomial:
5r³ - 10r² + 3r - 6
In order to factorize the given polynomial, use synthetic division:
5 -10 3 -6 | 2
10 0 6
5 0 3 0
The remainder is zero in the previous division, then, r - 2 is a factor of the given polynomial, the other factor is formed with the coefficients of the division, just as follow:
5r³ - 10r² + 3r - 6 = (r - 2)(5r² + 3)
Hence, the factor are (r - 2)(5r² + 3)
Answer:(r-2) x (5r^2+3)
Step-by-step explanation:
. Identify the difference. -2-(-6)
In this case,
This difference is made this way:
-2 - (-6) =
-2 +6 = 4
So there we have this identity. The minus before the parentheses turns the minus into plus sign.
HELP ASAP!!!
Find the square of 1-4i.
ANSAWER:
−15+8i
Explanation:
First, you can expand the square of the bynomial:
Solve the following system of linear equations using elimination.
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
By applying the elimination method, the solutions to this system of three linear equations include the following:
x = 2.y = -2.z = 0.How to solve these system of linear equations?In order to determine the solutions to a system of three linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.
Given the following system of linear equations:
x – y - 3z = 4 .........equation 1.
2x + 3y – 3z = -2 .........equation 2.
x + 3y – 2z = -4 .........equation 3.
From equation 1 and equation 3, we would eliminate x as follows:
x – y - 3z = 4
x + 3y – 2z = -4
-4y - z = 8 .........equation 4.
Next, we would pick a different pair of linear equations to eliminate x:
(x – y - 3z = 4) × 2 ⇒ 2x - 2y - 6z = 8
2x - 2y - 6z = 8
2x + 3y - 3z = -2
-5y - 3z = 10 ........equation 5.
From equation 4 and equation 5, we would eliminate z to get the value of y:
(-4y - z = 8) × 3 ⇒ -12y - 3z = 24
-12y - 3z = 24
-5y - 3z = 10
-7y = 14
y = 14/7
y = -2.
For the value of z, we have:
-4y - z = 8
z = -4y - 8
z = -4(-2) - 8
z = 8 - 8
z = 0
For the value of x, we have:
x – y - 3z = 4
x = 4 + y + 3z
x = 4 - 2 + 3(0)
x = 2
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The length of each side of a square is extended 5 in. The area of the resulting square is 64 in,2 Find the length of a side of the
original square.
Answer: i donno
Step-by-step explanation:
ask Professor Ahmad Shaoki
express the fuction graphed on the axes below as a piecewise function
Concept
Find the equation of line for the second line.
x1 = -2 y1 = 1
x2 = -4 y2 = 2
Next, apply equation of a line formula
[tex]\begin{gathered} \frac{y-y_1}{x-x_1\text{ }}\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \frac{y\text{ - 1}}{x\text{ + 2}}\text{ = }\frac{2\text{ - 1}}{-4\text{ + 2}} \\ \frac{y\text{ - 1}}{x\text{ + 2}}\text{ = }\frac{1}{-2} \\ -2(y\text{ - 1) = 1(x + 2)} \\ -2y\text{ + 2 = x + 2} \\ -2y\text{ = x} \\ y\text{ = }\frac{-1}{2}x \end{gathered}[/tex]Final answer
The graphed as a piecewise function is given below
For what values of b will F(x) = logb x be a decreasing function?A.0 < b < 1B.0 > b > -1C.b > 0D.b < 0
Given:
There is a function given as below
[tex]F(x)=\log_bx[/tex]Required:
For what value of b the given function in decreasing
Explanation:
The given function is logarithm function
also written as
[tex]F(x)=\frac{log\text{ x}}{log\text{ b}}[/tex]The base b is determines that if the function is increasing or decreasing
here
for
[tex]0the given function is decreasingfor
[tex]b>1[/tex]the given function is increasing
Final answer:
[tex]0
the first yr a community college offered a Certificate in data management , 12 people earned the certificate. the next year 17 people earned the certificate. what was the percent increase in the # of people earning the certificate?
we make an expression
[tex]12\times x=17[/tex]we know that if we multiply to twelve by the ratio of increase we will obtain 17
now solve for x that is the ratio
[tex]x=\frac{17}{12}=1.42[/tex]multiply by 100 to obtain a percentage
[tex]1.42\times100=142[/tex]the percentage is 142%
Tents-R-Us makes and sells tents. Tents-R-Us' motto is“Keep It Simple.” The company decides to makes justthree sizes of tents: the Mini, the Twin, and theFamily-Size. All the tents they make have equilateraltriangular ends as shown at right.1. For the Twin, each edge of the triangle will be 8 ft. Find the heightof the tent at the center, correct to the nearest inch. One way to findthis height is to make an accurate scale drawing and measure.
The company decides to make just three sizes of tents: the Mini, the Twin, and the Family-Size.
The shape of these tents is an equilateral triangle.
Part 1:
For the Twin, each edge of the triangle will be 8 ft.
The height of the tent is given by
[tex]h=a\cdot\frac{\sqrt[]{3}}{2}[/tex]Where a is the length of the edge of the triangle.
Since we are given that a = 8 ft
[tex]\begin{gathered} h=a\cdot\frac{\sqrt[]{3}}{2} \\ h=8\cdot\frac{\sqrt[]{3}}{2} \\ h=4\sqrt[]{3} \\ h=6.9\: ft \end{gathered}[/tex]Therefore, the height of the Twin tent at the center is 6.9 ft
Part 2:
The Mini tent will have edges 5 ft long.
The height of the tent is given by
[tex]h=a\cdot\frac{\sqrt[]{3}}{2}[/tex]Where a is the length of the edge of the triangle.
Since we are given that a = 5 ft
[tex]\begin{gathered} h=a\cdot\frac{\sqrt[]{3}}{2} \\ h=5\cdot\frac{\sqrt[]{3}}{2} \\ h=4.3\: ft \end{gathered}[/tex]Therefore, the height of the Mini tent at the center is 4.3 ft
Part 3:
The Family-Size tent will have a height of 10 ft at the center.
Recall that the height of the tent is given by
[tex]h=a\cdot\frac{\sqrt[]{3}}{2}[/tex]Re-writing the formula for edge (a)
[tex]a=h\cdot\frac{2}{\sqrt[]{3}}[/tex]Since we are given that h = 10 ft
[tex]\begin{gathered} a=h\cdot\frac{2}{\sqrt[]{3}} \\ a=10\cdot\frac{2}{\sqrt[]{3}} \\ a=\frac{20}{\sqrt[]{3}} \\ a=11.6\: ft \end{gathered}[/tex]Therefore, the length of edges of the Family-Size tent is 11.6 ft
A rectangle is 2 4/5 meters wide and 3 1/2 meters
long. What is its area?
Answer: Area = l × w
= 3.5 × 2.8
= 9.8 meters2
Step-by-step explanation:
I need help with this practice problem Having a tough time solving properly
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
r = 7 sin (2θ)
Step 02:
polar equation:
r = 7 sin (2θ):
r = a sin nθ
n odd ==> n petals
n even ===> 2n petals
n = 2 ===> 2*2 petals = 4 petals
graph:
length of the petals:
r = 7 sin (2θ)
θ = 45°
r = 7 sin (2*45°) = 4.95
The answer is:
4.95
Simplify the expression by combing like terms.21v + 8 - 12v - 7 + 3t - t
We need to simplify the like terms.
"The like terms are whose with the same variable and exponent"
Therefore, the like terms are:
21v - 12v = 9v
8 - 7 = 1
3t - t = 2t
Now, the result is :
9v + 2t + 1
Hence, the correct answer is option D.
