The interval notation for the set {x ∈ Z : −1 ≤ x < 43} is [-1, 43).
An "interval" in mathematics refers to a set of numbers between two given endpoints, where the endpoints can be included or excluded from the set, depending on the specific interval notation being used.
In the case of the set {x ∈ Z : −1 ≤ x < 43}, we are looking at all integers (x ∈ Z) that satisfy the inequality −1 ≤ x < 43.
This means that we are looking at all integers greater than or equal to −1 and less than 43.
Here we need to express this set in interval notation, we have to decide whether or not to include the endpoints −1 and 43.
Since the inequality symbol used is "<" for 43, we will exclude 43 from the set and use a parenthesis around 43 in the interval notation to indicate that it is not included in the set.
Therefore it can be written as, [-1, 43).
To know more about interval notation here,
https://brainly.com/question/29531272
#SPJ4
estimate the sum of 9/10 and 5/6
The sum of 9/10 and 5/6 is 26/15.
The sum of two fractions can be calculated only if the denominator (the bottom number) is the same. Here, in 9/10, 10 is the denominator and in 5/6, 6 is the denominator. To equate two denominators LCM(least common multiple) should be done.
LCM of 10 and 6 is 30.
To convert is to multiply each by the bottom number of the other over the other
9/10 + 5/6
= 9/10×3/3 + 5/6×6/6
=27/30 + 25/30
=52/30
=26/15 or 1 11/15
Therefore, the sum of 9/10 and 5/6 is 26/15 or 1 11/15.
To know more about fractions,
https://brainly.com/question/78672
The sum of 9/10 and 5/6 equals 26/15.
Only if the denominator (the bottom number) is the same can two fractions' total be calculated. In this case, the denominator in 9/10 is 10 and in 5/6 is 6. The LCM (least common multiple) method should be used to equate two denominators.
30 is the LCM of 10 and 6.:
By multiplying each by the bottom number of the other over the other, you may convert.
9/10 + 5/6
= 9/10×3/3 + 5/6×6/6
=27/30 + 25/30
=52/30
=26/15 or 1 11/15
As a result, 9/10 plus 5/6 equals 26/15.
Learn more about fractions on:
https://brainly.com/question/17220365
Reflect the endpoint of a line segment (-5, 10) across the x-axis. What is the result?
The result after the endpoint of a line segment is reflected is (-5. -10)
How to detemrine the result of the transformationFrom the question, we have the following parameters that can be used in our computation:
Point = (-5, 10)
The reflection rule is given as
Reflection across the x-axis
Mathematically, this is represented as
(x, y) = (x, -y)
So, we have
Image = (-5, -10)
Hence, the image is (-5, -10)
Read more about transformation at
https://brainly.com/question/27224272
#SPJ1
In baseball, a player's slugging ratio is (s + 2d + 3t + 4h)/b, where:s = number of singlesd = number of doublest = number of triplesh = number of home runsb = times at batLucase came to bat 35 times during the season and hit 18 singles, 2 doubles, 0 triples, and 1 home run. What is Lucas's slugging ratio, rounded to the nearest thousandth?: *A) 0.714B) 0.829C) 0.629D) 0.743
Lucas's slugging ratio, rounded to the nearest thousandth is 0.743.
Therefore the answer is D) 0.743.
To find Lucas's slugging ratio, we first need to calculate the numerator of the equation:
number of singles, s = 18 singles
number of doubles, d = 2 doubles
number of triples, t = 0 triples
number of home runs, h = 1 home run
numerator = (s + 2d + 3t + 4h) = (18 + 2 * 2 + 3 * 0 + 4 * 1) = 26
denominator = b = 35 times at bat
Lucas's slugging ratio is numerator / b
= 26 / 35
= 0.743
To know more on ratio
https://brainly.com/question/13419413
#SPJ4
Hector pent $38. 45 for 2DVD the ale tax wa $2. 85, and he didn't have a coupon. Each DVD cot the ame amount. How much would each DVD cot?
Each DVD cost is $17.80
This is a simple equation
From the question we have the following information :
1. Total spent for 2 dvd ( before tax ) = $17.80
2. Sales Tax for those spending = $2.85
Let's call the cost of each DVD "x".
The total cost of both DVDs would be 2x.
We know that the total cost of both DVDs and the sales tax was $38.45, so we can set up an equation:
2x + $2.85 = $38.45
Solving for x:
2x = $38.45 - $2.85 = $35.60
x = $35.60 / 2 = $17.80
Hence from explanation above, each DVD cost $17.80.
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
how many arrangements of the letters mathematics are there if h must imme- diately follow one of the ts, and e does not immediately follow h?
There are 3,265,920 arrangements of the letters in mathematics.
Consider T+H together which is easy to solve, and also consider the “TH” as one letter. There are two Ts in maThemaTics, and they can be together as TH or HT.
so there are actually 2*2=4 ways to build the TH itself. Now just plug a short hold on the “not followed by the h” and let us know how many ways to build it with just the TH restriction.
So with TH together, we can construct 10 letters in the word, two As, two Ms, and 1 as each of the remaining 6 letters. So it means there are
10!2!2!(1!)6=10!2!2!=36288004=907200
Now there are 4 ways to construct the TH, so 907200∗4=3,628,800.
To then add the “not followed by h” restriction, we should first determine all of the combinations where you have “THE” or “HTE” in the word. There are 4 ways to construct this letter grouping.
Then we have the remaining 9 letters in the word, two As, two Ms, and 1 of each of the remaining 5 letters.
So there are 4∗9!2!2!(1!)5=4∗9!4=3628802=362,880 ways to construct the word where you force THE/HTE together.
Finally, subtract the arrangements we have THE/HTE in the word from the arrangements where you just have TH/HT in order to get the arrangements that have TH/HT that is not immediately followed by h. 3,628,800–362,880=3,265,920.
Therefore, there are 3,265,920 arrangements.
To know more about combinations :
https://brainly.com/question/4658834
#SPJ4
.
A thin wire of linear charge density ????λ is bent in the form of a triangle "ABC" and an imaginary cube of side 'a' is taken with vertex "A" at the centre of the top face and vetices B, C at the opposite edge centre of the bottom face.The total electric flux linked with the cube is
The total electric flux linked with the cube is .
Electric flux is a characteristic of an electric field and refers to the quantity of electric lines of force (or electric field lines) that span a given area. This hypothesis states that electric field lines have positive electric charges at the beginning and negative electric charges at the end. Field lines pointing toward a closed surface are deemed negative, whereas those pointing away from it are deemed positive.
The electric field inside a charged conductor is zero, and since the wire is a conductor, the electric field inside the cube is zero.
Hence, the total electric flux linked with the cube is also zero.
To learn more about flux here:
https://brainly.com/question/29665619
#SPJ4
dentifying a Constant of Proportionality
onsider the equation y = 4.2x and the table below that
presents this relationship.
x
0
2
4
6
Y
0
8.4
16.8
25.2
The coefficient of the equation or constant of
proportionality is
Answer:
Step-by-step explanatio
23.2
Suppose that a colony of Jeevesium beetles grows exponentially with doubling time 9 years. How many years does it take for the colony to triple in size? (Give the answer as a decimal number with no units. Round to three decimal places.)
The population of Jeevesium beetles is tripled in a time of approximately 14.265 years.
How to predict the population of a colony of Jeevesium beetles
The statement indicated that a colony of Jeevesium beetles double its population every 9 years and we are required to find the number of years such that the population is tripled, the prediction model for population growth is shown below:
[tex]p(t) = p_{o}\cdot 2^{\frac{t}{9}}[/tex]
Where:
p₀ - Initial populationp(t) - Current populationt - Time, in yearsIf we know that p(t) / p₀ = 3, then the time needed for the colony of Jeeversium beetles is:
[tex]3 = 2^{t / 9}[/tex]
㏒₂ 3 = t / 9
t = 9 · ㏒₂ 3
t ≈ 14.265
To learn more on doubling times: https://brainly.com/question/30396066
#SPJ1
A rectangular lawn measures 10 m by 5 m. A uniform border of flowers is to be planted along two adjacent sides of the lawn. If the flowers that have been purchased will cover an area of 150 m^2, how wide is the border?
The border must have a width of 10 meters.
How wide is the border?We first have a rectangular lawn of 10m by 5m, so if we have a border with a width of x meters, the area of the border is given by:
A = 10m*x + 5m*x
Where we compute the area in that way because the flowers will be only on two adjacent sides of the rectangle.
And the area is 150 m^2, then we will get:
150m^2 = 10m*x + 5m*x
150m^2 = 15m*x
150m^2/15m = x
10m = x
The border has a width of 10 meters.
Learn more about areas at:
https://brainly.com/question/24487155
#SPJ1
The membership at Gym A costs $20 to join for 1 month plus $3 per visit. The membership at Gym B costs a flat rate of $40 for 1 month.
If you join Gym A, it will cost $20 to join for 1 month plus $3 per visit. If you visit the gym x times, your total cost will be 20 + 3x dollars.
If you join Gym B, it will cost a flat rate of $40 for 1 month.
To determine which membership is more cost-effective, you would need to compare the costs for different number of visits. For example, if you plan to visit Gym A 10 times in a month, your total cost would be 20 + 3(10) = $50. If you plan to visit Gym B only 2 times in a month, membership B is more cost-effective. If you plan to visit more than 13 times, membership A is more cost-effective.
It would be helpful to make a table with different number of visits to compare the cost of both gym memberships.
An isosceles triangle has base angles that each measure 64°. Which equation can be used to find n, the measure of the third angle of this isosceles triangle in degrees?
Answer:
Below
Step-by-step explanation:
The interior three angles of a triangle sum to 180°
you know tow of them are 64 degrees
so the third one is 180 - 64 - 64 or 180 °- 128°
Help me understand how to do it so I can pass?
Answer: Hi there! X = 7 would be your answer
Step-by-step explanation:
Simplify both sides of the equation.
2(3x − 6) = 3(x + 3)
(2) (3x) + (2) (−6)= (3) (x) + (3) (3)
6x + −12 = 3x + 9
6x − 12 = 3x + 9
Subtract 3x from both sides.
6x − 12−3x = 3x + 9−3x
3x − 12 = 9
Add 12 to both sides.
3x − 12+12 = 9+12
3x=21
Divide both sides by 3.
3x/3=21/3
x=7
I hope this helps!!
[tex] \: [/tex]
[tex] \frak{6x - 12 = 3x + 9}[/tex][tex] \: [/tex]
[tex] \frak{6x - 3x = 9 + 12}[/tex][tex] \: [/tex]
[tex] \frak{3x = 21}[/tex][tex] \: [/tex]
[tex] \frak{x = \cancel\frac{21}{3} }[/tex][tex] \: [/tex]
[tex] \underline{ \boxed{ \bold{ \frak{{ \red{x = 7}}}} }}[/tex][tex] \: [/tex]
hope it helps!:)
someone help please. i need to turn this in tomorrow. Question is in the picture!
Answer:
0.35 mL
Step-by-step explanation:
There are 1000 mL in 1 Liter. 350 of 1000 is 0.35
You and your friend each deposit $50 in separate savings accounts. Your account earns 2% simple annual interest. Your friend’s account earns 6% simple annual interest. How long does it take for you to earn $12 in interest? How long does it take for your friend to earn $12 in interest?
I earn $12 in interest after 12 years while my friend earns the same amount in 4 years.
What Is Simple Interest?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.
Given here: My principal = $50 and friend's =$50 also friend's account earns 6% annual interest rate
As per question we get
let the time taken to earn $12 interest rate be t then
12=50×2×t /100
t=12 years
while for my friend
12=50×6×t /100
3t=12
t=4 years
Hence, I earn $12 in interest after 12 years while my friend earns the same amount in 4 years.
Learn more about simple interest here:
https://brainly.com/question/25845758
#SPJ1
M. Houton’ fifth grade cla of 20 tudent i going to a mueum the cla raie $128 for the trip. Tranportation to the mueum cot $5 for each tudent. The mueum ell mall foil for $4 each. How many foil can the tudent buy with the money they have left?
With the money they have left, the students in M. Houton's fifth grade class of 20 students can buy 32 foils.
This is calculated by subtracting the cost of the transportation from the total amount raised ($128 - $5*20 = $28) and then dividing that amount by the cost of each foil ($4). Therefore, the students can buy $28 / $4 = 32 foils.
To calculate how many foils the students in M. Houton's fifth grade class of 20 students can buy with the money they have left, you must subtract the cost of their transportation from the total amount raised ($128 - $5*20 = $28).
Then, divide the remaining amount by the cost of each foil ($4) to get the number of foils they can buy with the money they have left ($28 / $4 = 32 foils).
Learn more about mathematics:
https://brainly.com/question/26310043
#SPJ4
BROO HELP PLEASE THANK YOUUU
We will multiply the first 7×1 =7. Option A is the correct option.
What is a table?
An array displaying the outcomes of multiplying two numbers.
The results are displayed where a row and a column converge. One number runs along a row, the other down a column.
Information is organized in rows and columns, such as numbers and descriptions.
This table lists the sports that people participate in.
The table for 7:
7×1 = 7
7×2 = 14
7×3 = 21
7×4 = 28
7×5 = 35
7×6 = 42
7×7 = 49
7×8 = 56
7×9 = 63
7×10 = 70
According to the table, we first multiply 7×1 then 7×2.
Thus 7×1 =7 is the correct answer.
To learn more about multiplication, click on the below link:
https://brainly.com/question/3730340
#SPJ1
Suppose ln x-ln y=y-4 , where y is a differentiable function of x and y=4 when x=4 . What is the value of dy/dx when x=4 ?
Answer:
When x=4, ln x-ln y=y-4, so ln 4-ln 4=4-4, which is true. Therefore, when x=4, y=4, and dy/dx=0.
Step-by-step explanation:
So, when x = 4, the value of the differentiable function dy/dx is 0.
What is differentiable function?A differentiable function of one real variable is one that has a derivative at each point in its domain. In other words, a differentiable function's graph has a non-vertical tangent line at each interior point in its domain.
Here,
Given the equation ln x - ln y = y - 4, we can rearrange it to get ln(x/y) = y - 4. Taking the derivative of both sides with respect to x using the chain rule:
d/dx (ln(x/y)) = d/dx (y - 4)
(1/x) (dx/dx) - (1/y) (dy/dx) = dy/dx
dy/dx = (1/y) (dx/dx) + (1/x) (dy/dx) = (1/y) + (1/x) (dy/dx)
Rearranging and solving for dy/dx:
(x/y) (dy/dx) = (1/y) - (1/x)
dy/dx = (x/y^2) (1/x - 1/y) = (x/y^2) (1/x - 1/y)
We can substitute x = 4 and y = 4 into the expression to find the value of dy/dx when x = 4:
dy/dx = (4/16) (1/4 - 1/4) = 0
So, the value of differentiable function dy/dx when x = 4 is 0.
To know more about differentiable function,
https://brainly.com/question/30079101
#SPJ4
Provide the answer to question number 5
The function value that us greater is with estimated value of 96
How to find the estimated value?The estimated value is the value read from the graph which gives the accumulated value for each of the line
The first line gives an estimated value of
10+14+18+19+28 = 89
The second graph gives gives an estimated value of
17+18+19+20+22 = 96
Therefore comparing the two graphs, the one with 96 has the greater value
Learn more about a graph on https://brainly.com/question/17267403
#SPJ1
I REALLY NEED THIS ANSWERED
Brenda invests $4,848 in a savings account with an interest rate compounded semiannually. If the account balance after 6 years is $6,520.02, what is the interest rate?
(Hint: SADMEP-Do not round calculations until the final answer.)
Round your answer to the nearest percent. ( Two decimal places or a whole number percentage)
The interest rate is -17.72%
What is the interest rate?
The proportion of a loan that is charged as interest to the borrower is typically expressed as an annual percentage of the loan outstanding.
The formula for finding the interest rate is:
A = P * (1 + r/n)^(nt)
Where A is the end balance, P is the starting principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.
Since the interest rate is compounded semi-annually, n = 2. And the starting principal is $4,848, t = 6 years. So the equation becomes:
$6,520.02 = $4,848 * (1 + r/2)^(2 * 6)
Now we'll isolate r by taking the natural logarithm of both sides:
ln(6520.02 / 4848) = ln((1 + r/2)^(2 * 6))
ln(6520.02 / 4848) = 12 * ln(1 + r/2)
Now we'll solve for r by dividing both sides by 12 and taking the exponential of the result:
r/2 = (ln(6520.02 / 4848) / 12)^(1/12) - 1
r = 2 * ((ln(6520.02 / 4848) / 12)^(1/12) - 1)
Finally, we'll convert the interest rate to a percentage by multiplying by 100:
r = (2 * ((ln(6520.02 / 4848) / 12)^(1/12) - 1)) * 100%
= (2 * ((ln(1.34814) / 12)^(1/12) - 1)) * 100%
= (2 * (0.113774 - 1)) * 100%
= (2 * -0.886226) * 100%
= -17.72452%
hence, the interest rate is -17.72%
To learn more about the interest rate visit,
https://brainly.com/question/25720319
#SPJ1
i need help and i need it ASAP
The requried simplified value of the given exponential expression is 1.
what is an exponential function?The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here,
F = [25x²y¹⁴w³]⁰
Since a⁰ = 1
F = 1
Thus, the requried simplified value of the given exponential expression is 1.
Learn more about exponential function here:
brainly.com/question/15352175
#SPJ1
A swim instructor would like to test the effect of a new swim technique versus the standard technique for a group of 25 competitive swimmers.
The swim instructor divides the students by class (junior or senior), and then randomly allocates half of the 14 juniors and 5 of the 11 seniors to receive instruction on the new technique.
During swim practice, the instructor times the juniors as they race against each other to see if those who learned the new technique outperform their peers. The instructor does the same for the seniors.
At the end of practice, the instructor compares the average swim time for both juniors and seniors among those who did and did not use the new technique.
What type of experimental design did the instructor use?
A) matched pairs experimental design
B) completely randomized experimental design
C) randomized block experimental design
D) none (observational study only)
C) randomized block experimental design.
What type of experimental design did the instructor use?The swim instructor used a randomized block experimental design for their experiment.This type of experimental design involves dividing the participants into groups (in this case, juniors and seniors) and then randomly allocating half of each group to receive instruction on the new technique.This helps to control for any potential confounding variables, such as age, that could affect the results of the experiment.By comparing the average swim time for both juniors and seniors among those who did and did not use the new technique, the instructor can determine if the new technique has an effect on swim performance.This type of experimental design is often used when the experimenter wants to compare the effects of a treatment or intervention between two or more groups with similar characteristics.To learn more about experimental design refer to:
https://brainly.com/question/17280313
#SPJ1
Answer:c
Step-by-step explanation:
4. in a box are 7 red balls and 8 blue balls. from this box are drawn 4 balls and placed in a second box. then, one ball is drawn from the second box. what is the probability the ball drawn from the second box is red?
The probability the ball drawn from the second box is red, is 17/56.
In a box are 7 red balls and 8 blue balls.
From this box are drawn 4 balls and placed in a second box.
We have to determine the probability the ball drawn from the second box is red.
The total number of balls = Red Balls + Blue Balls
The total number of balls = 7 + 8
The total number of balls = 15
The number of balls placed in second balls = 4
The number of combination of balls in box 2.
BBBB, BBBR, BBRR and BRRR
Then, one ball is drawn from the second box.
The probability the ball drawn from the second box is red.
P(Ball is red in the second box) = P(BBBB) + P(BBBR) + P(BBRR) + P(BRRR)
P(Ball is red in the second box) = [tex]\frac{^{5}C_{4}}{^{8}C_{0}}(0)+\left(\frac{^{5}C_{3}\times ^{3}C_{1}}{^{8}C_{4}}\right)\times\frac{^{1}C_{1}}{^{4}C_{1}}+\left(\frac{^{5}C_{2}\times ^{3}C_{2}}{^{8}C_{4}}\right)\times\frac{^{2}C_{1}}{^{4}C_{1}}+\left(\frac{^{5}C_{1}\times ^{3}C_{3}}{^{8}C_{4}}\right)\times\frac{^{3}C_{1}}{^{4}C_{1}}[/tex]
P(Ball is red in the second box) = [tex]0+\left(\frac{30}{70}\times\frac{1}{4}\right)+\left(\frac{30}{80}\times\frac{1}{2}\right)+\left(\frac{5}{70}\times\frac{3}{4}\right)[/tex]
P(Ball is red in the second box) = 3/48 + 3/16 + 3/56
P(Ball is red in the second box) = (21 + 63 + 18)/336
P(Ball is red in the second box) = 102/336
P(Ball is red in the second box) = 17/56
To learn more about probability link is here
brainly.com/question/9344931
#SPJ4
Which of these groups of values plugged into the TVM Solver of a graphing
calculator will return the same value for PV as the expression
($415)((1+0.003) 24-1)
(0.003)(1+0.003) 24
A. N=2; 1%-3.6; PV = ; PMT=-415; FV=0; P/Y=12; C/Y=12; PMT:END
B. N=24; 1%-0.3; PV = ; PMT=-415; FV=0; P/Y=12; C/Y=12; PMT:END
C. N=24; 1%-3.6; PV =; PMT=-415; FV=0; P/Y=12; C/Y=12; PMT:END
D. N=2; 1%-0.3; PV =; PMT=-415; FV=0; P/Y=12; C/Y=12; PMT:END
D. N = 24, I% = 3.6, PV =, PMT = -415, FV = 0, P/Y = 12, C/Y = 12, and PMT:END are the values in the group that would provide the same result as the given equation.
What in math is PV?The present value of a sum of money is its current value. For instance, the present value is what $110 is currently worth if you are promised $110 in a year.
In the TVM solver, we have;
I = The annual percentage rate
N = n × t
t = The number of years
PV = Present value
PMT = Payment
P/Y = Payments made annually = n
C/Y equals the number of compounding periods in a year.
The following is how the monthly payment formula is stated.
M = P(r/n)(1+r/n)ⁿˣⁿ/(1+r/n)ⁿˣⁿ-1
which gives,
P = M [(1+r/n)ⁿˣⁿ-1] / (r/n)(1+r/n)ⁿˣⁿ
Therefore, we get:
where:
M = PMT = -415
P = PV
r = I
P/Y = n = 12
Therefore,
0.003 = I/12
I = 0.003 × 12 = 0.036 = 3.6%
N = n×t = 24
P = (415)[(1+I/12)²⁴- 1] /(I/12)(1+I/12)²⁴
= ( 415) [(1+0.003)²⁴ - 1] / (0.003)(1+0.003)²⁴ = ?
The present value, PV, is the equation's value.
We have FV = 0 when payments are paid based on the PV.
The set of values with the same value as ($415)(1+0.003)24 - 1 / (0.003)(1+0,003)
24 has the following values when entered into a calculator's TVM solver: D. N = 24, I% = 3.6, PV =, PMT = -415, FV = 0 and PMT:END.
To know more about Present value solver visit:-
https://brainly.com/question/25781865
#SPJ1
Determine the truth value of the following statements if the universe of discourse of each variable is the set of real numbers.
1. ∃x(x2=−1)∃x(x2=−1)
2. ∃x∀y≠0(xy=1)∃x∀y≠0(xy=1)
3. ∀x∃y(x2=y)∀x∃y(x2=y)
4. ∃x∃y(x+y≠y+x)∃x∃y(x+y≠y+x)
5. ∃x∀y(xy=0)∃x∀y(xy=0)
6. ∀x∃y(x=y2)∀x∃y(x=y2)
7. ∀x∀y∃z(z=x+y2)∀x∀y∃z(z=x+y2)
8. ∀x≠0∃y(xy=1)∀x≠0∃y(xy=1)
9. ∃x(x2=2)∃x(x2=2)
10. ∀x∃y(x+y=1)∀x∃y(x+y=1)
11. ∃x∃y((x+2y=2)∧(2x+4y=5))∃x∃y((x+2y=2)∧(2x+4y=5))
12. ∀x∃y((x+y=2)∧(2x−y=1))
The truth value of the given statements if the universe of discourse of each variable is the set of real numbers are 1. false, 2. false, 3. true, 4. false, 5. false, 6. false, 7. true, 8. true, 9. false, 10. true, 11. true, and 12. true.
1. False. There is no real number x such that x^2 = -1.
2. False. For any x in the real numbers, there exists a y such that xy ≠ 1. For example, if x ≠ 0, then y = 1/x will satisfy xy ≠ 1.
3. True. For any real number x, the real number y = x^2 satisfies the equation x^2 = y.
4. False. For any x and y in the real numbers, x + y = y + x.
5. False. For any x in the real numbers, there exists a y such that xy ≠ 0. For example, if x ≠ 0, then y = 1/x will satisfy xy ≠ 0.
6. False. There is no real number y such that y^2 = -1.
7. True. For any x and y in the real numbers, the real number z = x + y^2 satisfies the equation z = x + y^2.
8. True. For any x ≠ 0 in the real numbers, the real number y = 1/x satisfies the equation xy = 1.
9. False. There is no real number x such that x^2 = 2.
10. True. For any x in the real numbers, the real number y = 1 - x satisfies the equation x + y = 1.
11. True. The solution to the system of equations x + 2y = 2 and 2x + 4y = 5 is x = -1 and y = 3.
12. True. For any x in the real numbers, the real number y = (1 - x)/2 satisfies the equation (x + y = 2) and (2x - y = 1).
To know more about real numbers, here
https://brainly.com/question/2742555
#SPJ4
The function g is defined by the following rule. g(x) = 2x + 5 Complete the function table.
Step-by-step explanation:
The function g is defined by the rule g(x) = 2x + 5. To complete the function table, we need to substitute different values of x into the function and find the corresponding output values.
Table:
⬇️
x g(x)
1 2*1 + 5 = 7
2 2*2 + 5 = 9
3 2*3 + 5 = 11
4 2*4 + 5 = 13
5 2*5 + 5 = 15
And so on, for any value of x you can substitute it into the function g(x) = 2x + 5 and you will get the result.
FIND AREA PLS HELP ASAP!!!
Area of a rhombus is half the product of its diagonals:
A = d₁d₂/2A = (3+3)(9+9)/2 = 54 units²Question 6Area of a trapezoid is the product of the height and half the sum of its bases:
A = (b₁ + b₂)h/2A = (17 + 29)*5/2 = 115 units²emily convinced her mom to buy a giant box of her favorite cereal. her mom doesn't think the box will fit on their shelf. the volume of the box is 10 , 000 10,00010, comma, 000 cm 3 3 cubed. the base of the box is 25 2525 cm by 10 1010 cm. how tall is the box of cereal?
an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is t minimize the time it takes to travel from $a$ to $b$?
Select the correct answer.
The zeros of a quadratic function are 6 and -4. Which of these choices could be the function?
A.
f(x) = (x − 6)(x + 4)
B.
f(x) = (x + 6)(x + 4)
C.
f(x) = (x − 6)(x − 4)
D.
f(x) = (x + 6)(x − 4)
The function corresponding to zeroes 6 and -4 is f(x)=(x-6)(x+4) i.e. A.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
Now ,
We can find function for zeroes 6 and -4 by putting f(x)=0
Therefore,
(x-6)(x+4)=0
x-6=0 and x+4=0
Hence,
x=6,-4
The function corresponding to zeroes 6 and -4 is f(x)=(x-6)(x+4).
To know more about functions visit the link
https://brainly.com/question/12431044?referrer=searchResults
#SPJ1
if f(x) = 7x2 − x3, what is the rate of change of f '(x) at (2, 20)?
The rate of change of f '(x) at (2, 20) is -52
We are given f(x) = 7x² − x³ and are asked to find the rate of change of f'(x) at (2, 20)
We can use the slope formula to find the average rate of change:
m = y2-y1/x2-x1
Here we need to find
Rate of change = f'(x2) - f'(x1) / x2 - x1
and here x1 = 2 and x2 = 20
First, we need to find f'(x)
f'(x) = 14x - 3x²
f'(x1) = f'(2) = 16
f'(x2) = f'(20) = -920
So, Rate of change = f'(x2) - f'(x1) / x2 - x1 = (-920 - 16)(20 - 2)
= -52
To learn more about rate of change here:
brainly.com/question/29518179
#SPJ4
Can a triangle be formed with ide length 3 inche, 3 inche and 5 inche? why or why not?
Yes, a triangle can be formed with side lengths of 3 inches, 3 inches, and 5 inches.
A triangle can be formed if and only if the sum of the lengths of any two sides is greater than the length of the third side. In this case, the sum of the lengths of sides 3 inches and 3 inches (6 inches) is greater than the length of the third side (5 inches), so a triangle can be formed.
In summary, a triangle can be formed with side lengths 3 inches, 3 inches, and 5 inches because the sum of the lengths of any two sides is greater than the length of the third side.
Learn more about Triangles here:
https://brainly.com/question/17335144
#SPJ4
