Remember that a function is a relation between two sets of numbers where the first set is called domain, and the second set is called range.
The main characteristic that defines a function is that a domain element can be associated with only one element of the range set. In other words, one input value cannot have two different output values.
Therefore, the right answer is the third choice
[tex]\left\lbrace (-1,3\right)(0,4)(1,14)(5,6)(7,2)\}[/tex]Because this represents a function and its inverse also represents a function, that is, it's inverse have the characteristic of a function. The following set represents the inverse
[tex]\left\lbrace (3,-1\right)(4,0)(14,1)(6,5)(2,7)\}[/tex]As you can observe, this inverse set also follows the function definition, because every single input is associated with only one output.
The first part of the function rule for the values in the table below is Y equals X over two. What is the complete function rule?
Given:
The tabular representation having different values of x and y.
Required:
The relation between x and y.
Explanation:
When x = 6 and y = 2,
[tex]y\text{ = }\frac{6}{2}\text{ = 3 }\Rightarrow\text{ 3 - 1 = 2 = x}[/tex]When x = 8 and y = 3,
[tex]y\text{ = }\frac{8}{2}\text{ = 4 }\Rightarrow\text{ 4-1 = 3}[/tex]When x = 10 and y = 4,
[tex]undefined[/tex]What is the digit in the units place of the sum of 1^1+ 2^2+ 3^3+ 4^4 +.....+ 99^99 + 100^100?
Let us write down first few factors
1^1 = 1
2^2 = 4
3^3 = 27
4^4 = 256
5^5 = 3125
6^6 = 46656
.
.
.
100^100 = ... finish in zero
The last two digits in the sum would be 20
The digit in the unit would be 0
Solve the quadratic equation x2 − 6x + 13 = 0 using the quadratic formula. What is the solution when expressed in the form a ± bi, where a and b are real numbers?
The given quadratic equation is:
[tex]x^2-6x+13=0[/tex]The quadratic formula is given by the equation:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac^{}}}{2a}[/tex]From the given quadratic equation;
[tex]a=1;b=-6\text{ and c=13}[/tex]Thus, we have:
[tex]x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(1)(13)}}{2(1)}[/tex][tex]\begin{gathered} x=\frac{6\pm\sqrt[]{36-52}}{2} \\ x=\frac{6\pm\sqrt[]{-16}}{2} \\ In\text{ complex form, the }\sqrt[]{-16}=4i \\ \text{Thus, we have:} \\ x=\frac{6\pm4i}{2} \\ x=\frac{6}{2}\pm\frac{4i}{2} \\ x=3\pm2i \end{gathered}[/tex]Hence, the correct option is Option A
Dunoga cycled 15.26 kilometres and then ran 740 metres. What was the total distance he covered in kilometres?
Answer:16 Kilometers
Step-by-step explanation:15.26km+.74km
Dunoga covered a distance of 16 km in total.
What is unit conversion?A unit conversion expresses the same property as a different unit of measurement.
For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.
Given that, Dunoga cycled 15.26 kilometers and then ran 740 meters. We need to find the distance he covered in kilometers,
To find the total distance, we will add the distance he covered by cycle and by running,
But the units of both the distances are not same and to add we need to convert the units,
Since, the answer required in kilometers, so we will convert meter into kilometers,
1 km = 1000 m
Therefore,
740 m = 740 / 1000 = 0.74 km
Therefore, the distance he covered in kilometers = 0.74+15.26
= 16 km
Hence, Dunoga covered a distance of 16 km in total.
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it says i need to find the shortest distance between the point and the line for geometry honors, how would i figure it out
The given line equation is,
[tex]3x-y=-6[/tex]The given point is ,
[tex](5,1)[/tex]The graph will look like this,
let us rewrite the line equtaion as ,
[tex]3x-y+6=0[/tex]now, let us compare with the general equation of line,
[tex]Ax+By+C=0[/tex]then, A= 3,B=-1 and c= 6.
let us use the formula,
[tex]\begin{gathered} d=\frac{|Ax+By+c|}{\sqrt[]{A^2+B^2}} \\ d=\frac{|3\times5+(-1)\times1+6|}{\sqrt[\square]{3^2+(-1)^2}} \\ d=\frac{|15-1+6|}{\sqrt[\square]{9+1}} \\ d=\frac{20}{\sqrt[\square]{10}} \\ d=6.32 \end{gathered}[/tex]The shortest distance is 6.32 .
Real number between 0 and 6 will be picked according to the probability distribution shown in the figure. Regions under the curve are liable with A, B, C, and D. The area of each is shown in the table. Use the figure and table to answer the parts
Part A
The probability that a real number between 1 and 4 is picked
P=PB+PC
P=0.15+0.50
P=0.65Part B
The probability that a real number between 2 and 6 is picked
P=PC+PD
P=0.50+0.30
P=0.80Explain why the product of 20 x 30 is equal to 600.
BIU
Answer:
600
Step-by-step explanation:
2 X 3 = 6
20 has one 0
30 has one 0
one 0 and one 0 is two 0s
6 plus two 0s = 600
The midpoint of AB is M(7,-2). If the coordinates of A are (8,3), what are thecoordinates of B ?
The coordinates are ordered pairs with the x value listed first.
The change in x position is, 8-7=1
The change in y position is, 3-(-2)=5
Since the midpoint is halfway between A and B, the change will stay the same,
So, for B,
x is 7-1=6
y is -2-5=-7
The coordinnates of B is (6,-7)
How many values does the expression 6+ (7 + 3)² have? Write down the values.
Answer:
3
Step-by-step explanation:
6
7
3
The values are the number that compose the expression
top question says: Triangle ABC can be taken to triangle A'B'C' using rigid motions and a dilation. help me pls
If triangle ABC can be taken to triangle A'B'C', it means that they are similar triangles. If tow triangles are similar, it means that the ratio of their corresponding sides are equal. Thus, we have
A'B'/AB = B'C'/BC = A'C'/AC
Thus, looking at the options, the true equations are
A) A'C'/B'A' = AC/BA
D) CA/C'A' = CB/C'B'
E) A'B'/AB = C'B'/CB
If we look at these options the ratios are always the same
QUESTION IS IN IMAGE!!! DONT NEED TO SHOW WORK JUST NEED ANSWER!!!!!
Since P is the center of the circle, then the segments PS and PQ are both radii of the circle and have the same measure. Then, the triangle PQS is an isosceles triangle, then, the measures of the angles PQS and QSP must be the same.
Since the sum of the internal angles of a triangle must be equal to 180º, then:
[tex]\begin{gathered} m\angle PQS+m\angle QSP+m\angle SPQ=180º \\ \Rightarrow m\angle PQS+m\angle PQS+113º=180º \\ \Rightarrow2m\angle PQS=180º-113º \\ \Rightarrow2m\angle PQS=67º \\ \Rightarrow m\angle PQS=\frac{67º}{2} \\ \Rightarrow m\angle PQS=33.5º \end{gathered}[/tex]The measure of RQS is the same as the measure of PQS.
Therefore, the answer is:
[tex]m\angle RQS=33.5º[/tex]solve the equation and check the solution:7x - 7 = 13 + 12x
we have the equation
7x - 7 = 13 + 12x
solve for x
Group terms
12x-7x=-7-13
Combine like terms
5x=-20
x=-20/5
x=-4Verify
substitute the value of x=-4 in the original expression
7(-4)-7=13+12(-4)
-28-7=13-48
-35=-35 -------> is ok
on the coordinate plane below
As we can see by the picture below, the school is on the point (5, -2).
This season, the probability that the Yankees will win a game is 0.59 and theprobability that the Yankees will score 5 or more runs in a game is 0.43. Theprobability that the Yankees lose and score fewer than 5 runs is 0.3. What is theprobability that the Yankees win and score 5 or more runs? Round your answer to thenearest thousandth.
From the information given we conclude that the probability that the Yankees win and score 5 or more scores is 0.43
It is because of the description given in the problem.
Give two examples when you would need to know the perimeter and two examples of when you would need to know the area.
Perimeter is the distance around a figure. The instances where we need to find perimeter include
1) The total length of the boundary of a marked field. This would involve adding the distance around it. Both the curved and straight paths
2) The length of barbed wire to be placed on a fence would require us to find the distance round the fence
The area of a shape is the space enclosed within the perimeter of the shape. The instances where we need to find area include
1) The area of a wall is calculated to determine how much paint is needed to paint it. The paint is used per square unit.
2) The area of a field is calculated to determine the cost of mowing it since the cost is calculated per unit square
A new born child receives a $8,000 gift toward a college education from her grandparents. How much will the $8,000 be worth in 17 years if it is invested at 72% compounded quarterly?It will be worth $(Round to the nearest cent)
The money will be worth $618111016.19 at the end of 17 years
Explanation:Initial amount received, P = $3000
Interest rate, r = 72%
r = 72/100
r = 0.72
Number of times compounded in a year, n = 4
Time, t = 17 years
Amount after 17 years will be calculated as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Substitute P = 8000, r = 0.72, n = 4, and t = 17 into the formula above
[tex]A=8000(1+\frac{0.72}{4})^{4(17)}[/tex][tex]\begin{gathered} A=8000(1+0.18)^{68} \\ A=8000(1.18)^{68} \end{gathered}[/tex]A = $618111016.19
The money will be worth $618111016.19 at the end of 17 years
Find the set An B.
U = {1, 2, 3, 4, 5, 6, 7, 8)
A = {1, 2, 3, 4)
B = {1, 2, 6}
Step-by-step explanation:
I assume A n B means the intersection of the sets A and B.
that means all the elements that are in A and in B.
that is the set {1, 2}
For the point P(24,14) and Q(31,17), find the distance d(P,Q) and the coordinates of the midpoint M of the segment PQ.
STEP 1
Identify what is given and establish what is required.
We are given the coordinates of two points P and Q on the cartesian and are asked to find their midpoint M assuming a straight line is drawn from P and Q
Midpoint between two points is given as:
[tex]\begin{gathered} M=\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2_{}}{2} \\ \text{Where} \\ x_1,y_{1\text{ }}are\text{ the coordinates of point 1} \\ x_2,y_{2\text{ }}are\text{ the coordinates of point }2 \end{gathered}[/tex]STEP 2
Employ formula while putting the appropriate variables.
We select point P as our point 1 as in the formulae and
We select point Q as our point 2 as in the formulae
This gives us:
[tex]\begin{gathered} M=\frac{24+31}{2},\frac{14+17}{2} \\ M=\frac{55}{2},\frac{31}{2} \\ M=27.5,15.5 \end{gathered}[/tex]Therefore, our midpoint M is(27.5, 15.5)
(3x10⁴) (2x10⁵)Find the answer by simplifying
The given expression (3x10⁴) (2x10⁵)
we seperate the terms and collect like terms:
[tex]\begin{gathered} \mleft(3\times10^{4}\mright)(2\times10^{5})\text{ = 3}\times10^{4}\times2\times10^{5} \\ =\text{ 3}\times2\times10^{4}\times10^{5} \end{gathered}[/tex]When multiplying exponent (power) of the same base, the exponenet of the two numbers (base) are added together.
[tex]\begin{gathered} \text{Base = 10 , exponent = 4 and 5} \\ =3\times2\times10^{4+5} \\ =\text{ 6}\times10^9 \end{gathered}[/tex]
Shawn pays a rate of 35.55 mills in property tax on a home with an assessed value of $63,500. What is his property tax?
Answer:
$2257.425
Explanation:
A rate of 35.55 mills means that they have to pay 35.55 per each $1000 in the assessed value. If the assessed value is 63,500, we can calculate his property tax as
[tex]63,500\times\frac{35.55}{1000}=2257.425[/tex]Therefore, the answer is $2257.425
Factor completely: 3x'2 + 6x + 3a. (3x + 1) (x + 6)b. (3x + 3) (x + 1)c. 3(x + 1)'2d. 3(x + 1) (x-1)the 2s with the commas are exponents
3x^2 + 6x + 3
a= 3
b= 6
c = 3
Find the product of a and c
3x3 = 9
Now, find a product that equal 3x3 and equals be when added
b= 6
3+3 = 6
3x3= 9
Rewrite the expression with the new numbers taking the middle place:
3x^2 +3 x+ 3x +3
Isolate terms and factor out the greatest common factor:
(3x^2 +3 x) + (3x +3)
3x ( x+1) + 3 (x+1)
Factor out x+1 and rewrite:
(3x+3) (x+1)
Carly actions by-40; + 2) - 107j+2=-40 Step 1Tj = -42 Step 2j=-6 Step 3--Step 1Step 2Step 3Carly did not make a
Carly made a mistake in step 1 because she divided by -4 on the left side but multiplied by -4 on the right side.
On step 1 carly's equation should look like this
[tex]7j+2=-\frac{10}{4}[/tex]If I complete this review, then I will do well on the test. If I do well on the test. If I do well on the test, then I will get an “A” on my progress report. Make a conclusion using the law of syllogism
Law of syllogism:
If p, then q
If q, then r
Conclude:
If p, then r
Given situation:
p: complete this review
q: do well on the test
r: get an “A” on my progress report
If p, then q: If I complete this review, then I will do well on the test
If q, then r: If I do well on the test, then I will get an “A” on my progress report
Conclusion:
If p, then r: If I complete this review, then I will get an “A” on my progress report
Please give me the answers asap the time is running down
Explanation
Given the question
[tex]|x|<13[/tex]To get the values of x, we will consider two possibilities which are:
[tex]\begin{gathered} x\text{ being positive},\text{ so that} \\ x<13 \end{gathered}[/tex]And
[tex]\begin{gathered} x\text{ being negative} \\ -x<13 \\ x>-13 \end{gathered}[/tex]Therefore, the value of x is
[tex]\begin{bmatrix}\mathrm{Solution\colon}\: & \: -13So the correct option is
[tex]\begin{bmatrix}\mathrm{Solution\colon}\mleft\lbrace x|\: \mright? & \: -13Option A is correctThe first option is correct
The graphs of the functions g and h are shown below. For each graph, find the absolute maximum and absolute minimum. If no such value exists, click on "None".
Assume that the dashed line shown is a vertical asymptote that the graph does not cross.
For the graph g, the absolute maximum is 2 and the absolute minimum is -4.
Similarly, for graph h, the absolute maximum is 3 and the absolute minimum is -5.
Absolute Maximum of a Graph:
The absolute maximum of a graph is the point on the graph with the highest y-value. There can only be one absolute maximum of a graph.
Absolute Minimum of a Graph:
The absolute minimum of a graph is the point on the graph with the lowest y-value. There can only be one absolute minimum of a graph.
Given,
Here we have the two graph called g and h.
Now, we need to find the absolute maximum and minimum from it.
AS per the given definition, we know that,
For graph g,
The absolute maximum is 2 and the absolute minimum is -4.
Similarly, for graph h, the absolute maximum is 3 and the absolute minimum is -5.
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Daylyn wants to win headphones . In addition to his grandmother and uncle, some friends of his agree that each one will give him a $5 donation . Some other friends agree that each one will pay him $0.25 for every correct answer. The number of friends who donate $ 5 to Daylyn is 3 times the number who pays him for correct answers. Write and solve an equation to find the number of friends who must pay him $0.25 for each correct answer in order for Daylyn to meet his goal
Let
x ------> number of friends of his agree that each one will give him a $5 donation
y -----> the number of friends who must pay him $0.25 for each correct answer
so
to win headphones-------> $350
we have that
x=3y -------> equation A
5x+0.25y=350 -------> equation B
substitute equation A in equation B
5(3y)+0.25y=350
solve for y
15y+o.25y=350
15.25y=350
y=22.95
therefore
the answer is 23 friends who must pay him $0.25 for each correct answerFind the equation in standard form of lines P that are A) parallel to and B) perpendicular to line L P(1,2); L: 3x-2y=1P(8,7);L: y= -4
To find if two lines are parallel, the slope must be the same.
so m=m
for P(1,2); L: 3x-2y=1
First, solve the equation for y:
3x-2y=1
Subtract both sides by 3x
3x-2y=1
3x-3x-2y =1-3x
-2y=1-3x
Now, divide both sides by -2y
-2y/-2 = 1-3x
y =1/-2 +3x/2
The parallel line using the point P(1,2)
y-y1 =m(x-x1)
Replace the values and solve for y.
y-2=3x/2 -1
y=3x/2+2
So the parallel lines is y=3x/2+2
To find a perpendicular line, when you multiply the slopes the result must be equal to -1.
So:
m1*m2 = -1
Replace m1=3/2
m1*m2 = -1
3x/2* m2 = -1
m2 = -1/(3x/2)
m2 = -2/3
To find the line use:
y-y1 =m(x-x1)
y-2=-2/3(x-1)
y-2=-2x/3 +2/3
y= -2x/3 +8/3
So y= -2x/3 +8/3 is the perpendicular line.
Newton's law of cooling is T = A * e ^ (- d * t) + C where is the temperature of the object at time and C is the constant temperature of the surrounding mediumSuppose that the room temperature is 71^ + and the temperature of a cup of tea 160when it is placed on the table. How long will it take for the tea to cool to 120 degrees for k = 0.0595943 Round your answer to two decimal places.
Solution
Given
[tex]\begin{gathered} T=Ae^{-kt}+C\text{ --------\lparen1\rparen} \\ \\ C=71 \\ \\ A=160-71 \\ \\ T=120 \\ \\ k=0.0595943 \end{gathered}[/tex]To find the time, we nee to substitute the C, A, T, and k in (1) and then determine (t
[tex]\begin{gathered} 120=(160-71)e^{-0.0595943t}+71 \\ \\ \Rightarrow\frac{120-71}{160-71}=e^{-0.0595943t} \\ \\ \Rightarrow\frac{49}{89}=e^{-0.0595943t} \\ \\ \Rightarrow-0.0595943t=\ln(\frac{49}{89}) \\ \\ \Rightarrow t=\frac{1}{-0.0595943}\ln(\frac{49}{89})=10.01456\text{ s} \end{gathered}[/tex][tex]t=\frac{10.01465}{60}\text{ mins}=0.17\text{ mins}[/tex]what is 5x6 I need help
Thus, the required solution is 30.
Answer: 30
Step-by-step explanation: 30
Solve the inequality 8y- 5 < 3
Solve the inequality as you do with equations.
[tex]\begin{gathered} 8y-5<3 \\ 8y<3+5 \\ y<\frac{8}{8} \\ y<1 \end{gathered}[/tex]y is less than 1.
The graph of the solution is: