When taking the square root of both sides of this equation, the square roots may depend upon equation.
Let, the equation be:
x² = 4
May be the Equation has two solutions:
x = ±√4 = ±2
Equations involving distances, such as those obtained when using the Pythagorean theorem, have solutions. Negative solutions are irrelevant because there are no negative distances.
c² = a² + b²
⇒ c = √(a² + b²) .
Generally these are considered irrelevant as they are useless. Mathematically, negative time values work in the equation, but have no real interpretation.
Expressions such as:
x⁶ = 4
This, has 2 real and 4 complex solutions.
Again,
x³ = ±2 . after rooting both sides
The two real solutions are :
x = ±∛2
Learn more about Square Root:
https://brainly.com/question/3120622
#SPJ4
What is the max value of e?
The maximum value of e is equal to 2.718.
e
The number e, also known as Euler's number, is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of the natural logarithms. It is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series.
The number e itself also has applications in probability theory, in a way that is not obviously related to exponential growth
Learn more about euler constant here :-
https://brainly.com/question/22244082
#SPJ4
Find the dimensions of a rectangle with perimeter 100 m whose area is as large as possible.
The dimensions of the rectangle is 25m × 25m.
How do you find the dimension of a rectangle?
Two dimensions make up a rectangle: the length and, perpendicular to that, the breadth.
What are the three dimensions of a rectangle?
The three dimensions of a three-dimensional shape are length, width, and depth.
It is given that
Perimeter of the rectangle = 100m
Area is as large as possible if both the values are the same number.
The measurements must be equivalent for the rectangle to attain its maximum area.
Consider the dimensions as x
So perimeter can be written as
2 (x + x) = 100
2 (2x) = 100
By additional computation
4x = 100
Divide both sides by 4
x = 25
Therefore, the dimensions of a rectangle is 25m × 25m.
To learn more about dimension of a rectangle visit:
https://brainly.com/question/15225905
#SPJ4
evaluate a 3 - b 2 if a = 3 and b = 6
Answer:
3a - 2b = -3
Step-by-step explanation:
= (3) (3) - (6) (2)
= 9 - 12
= -3
Answer:
Step-by-step explanation:
3(3)- (6)2
9-12
-3
Solve the following system of equations graphically after graphing be sure to label each line with its equation
Answer:
Step-by-step explanation:
A system of equation can be solved in several ways, which includes the use of graphs
The solution to the system of linear equations is (3,2)
The system of equations is given as:
See attachment for the graphs of and .
From the attachment, the point of intersection of the lines of both equations is (3,2)
Hence, the solution to the system of linear equations is (3,2)
Read more about system of equations at:
brainly.com/question/14323743
The Student Council sold the following items at the home football game.
If i stands for income and e stands for expenses, what is the formula for p, profits?
The formula for profit is:
P = I - E
Where,
Income = I
Expenses = E
Profit = P
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Income = I
Expenses = E
Profit = P
Now,
Profit = Income - Expenses.
P = I - E
Thus,
The formula for profit is:
P = I - E
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
Which are necessary conditions to apply the sas triangle congruence theorem? select all that apply.
Answer:
For two triangles to be congruent, SAS theorem requires two sides and the included angle of the first triangle to be congruent to the corresponding two sides and included angle of the second triangle. If the congruent angles are not between the corresponding congruent sides, then such triangles could be different.
hope that helps
Step-by-step explanation:
i need help please answer correctly
6. Applying the inscribed angle theorem, x = 33
7. m<ABP = 90°.
m<APB = 48°
What is the Tangent Theorem?The tangent theorem states that the tangent of a circle is perpendicular to the radius of that circle and therefore forms a right angle at the point of tangency.
What is the Inscribed Angle Theorem?An inscribed angle has a measure that is half the measure of the intercepted arc, according to the inscribed angle theorem.
Therefore:
Question 6:
Based on the inscribed angle theorem,
Measure of arc AB = 2(x + 3) = 2x + 6
108 + 2x + 6 = 180 [semicircle]
Solve for x
114 + 2x = 180
2x = 180 - 114
2x = 66
x = 33
Question 7:
Given that line PB is tangent to circle A, therefore, based on the tangent theorem, the measure of angle ABP = 90°.
m<APB = 180 - 90 - 42
m<APB = 48°
Learn more about the tangent theorem on:
https://brainly.com/question/9892082
#SPJ1
If you start with 1 and repeatedly multiply by 1/2, will you reach 0? Explain why or why not.
Answer:
nope
Step-by-step explanation:
1 multiplied by 1/2 just equals 1/2 since it's being multiplied by one, it wouldn't matter if you kept multiplying 1/2 either because the numerator will stay the same regardless, and the denominator just gets bigger and bigger since you're multiplying by two. if the numerator wasn't 1 then I'm sure there's a possibility, but in this scenario, it's not.
Answer: You will reach 0
Step-by-step explanation:
Yes, if you start with 1 and repeatedly multiply by 1/2, you will reach 0.
To see why this is the case, let's consider the following sequence of numbers:
1 * (1/2) = 0.5
0.5 * (1/2) = 0.25
0.25 * (1/2) = 0.125
0.125 * (1/2) = 0.0625
0.0625 * (1/2) = 0.03125
As you can see, each time we multiply by 1/2, the result is half of the previous number. Because any number multiplied by 0 is 0, we will eventually reach 0 if we keep multiplying by 1/2.
Therefore, if you start with 1 and repeatedly multiply by 1/2, you will reach 0.
suppose a 90% confidence interval for the population mean resulted in an upper limit of $658 and a lower limit of $273. what is the correct interpretation of this confidence interval? question 5 options: 1) we are 90% confident the population mean is in this interval. 2) there is a .90 probability the population mean is in this interval. 3) we are 90% confident the population proportion is in this interval. 4) there is a .90 probability the sample mean is in this interval.
The correct interpretation of this confidence interval is that "we are 90% confident the population mean is in this interval." This means that if we were to repeat the sampling process many times, we would expect that 90% of the resulting confidence intervals would contain the true population mean.
A cookie recipe uses 1/2 teaspoon of vanilla with 3/4 cup of flour. How
much vanilla should be used with five cups of flour?
What does 1.022 represent in the expression?
Because b > 1, the correct response in this situation would be: "1.022 is the growth factor for the GDP since 1950, and the GDP increases by a factor of 1.022 every year."
In this instance, we're assuming that we can use the following function to simulate the US GDP, or gross domestic product, in dollars:
[tex]GDP = 11(1.0220)^{t}[/tex]
We can also see that the exponential model formula given by: governs this formula.
[tex]GDP = 11(1.0220)^{t[/tex]
Where a denotes the starting sum, b the model's growth/decay rate, and t is the number of years since 1950.
The value of b in this instance is provided by:
b = 1.022
And when we calculated r as the growth rate, we obtained:
1.022 = 1 + r
r = 1.022 - 1
r = 0.022
Because b > 1, the correct response in this situation would be: "1.022 is the growth factor for the GDP since 1950, and the GDP increases by a factor of 1.022 every year."
To know more about GDP
https://brainly.com/question/15682765
#SPJ1
What will be the y-coordinates of L’ if AL is dilated by a factor of 2/5 centered at the origin?
A 16/5
B 4/5
C 2
D 34/5
By means of rigid transformation, the point L' has a y-coordinate equal to 4 / 5.
What are the coordinates of a point by transformation rules?
Herein we find a representation of a line segment on a Cartesian plane, from which we must determine the coordinates of the image of one of its ends (point L' is the image of point L) by means of the following transformation rule, a dilation centered at the origin:
L'(x, y) = k · L(x, y)
Where:
k - Scale factorL(x, y) - Original pointL'(x, y) - Resulting pointIf we know that L(x, y) = (10, 2) and k = 2 / 5, then the coordinates of the point L' are:
L'(x, y) = (2 / 5) · (10, 2)
L'(x, y) = (4, 4 / 5)
The y-coordinate of point L' is 4 / 5.
To learn more on transformation rules: https://brainly.com/question/21298384
#SPJ1
Help Please This is hard
Answer: 63
Step-by-step explanation:
Let's start with what we know. A straight line measures an angle of 180. So, at point m, we have one degree measuring 118. We do:
180 - 118 = 62
So, 62, is the angle in the corner.
We also know that the sum of the angles in a triangle = 180 so:
10x - 2 + 62 = 180
10x + 60 = 180
10x = 120
x = 12
So angle K is 63.
(Hope this is correct)
help help help help help help help
Answer: the data suggests that playing video games has a negative effect on academics. I think this because the more time spent playing video games the less time spent doing homework
if the work remaining is greater than the time remaining, the critical ratio (cr) will be group of answer choices less than one. greater than one. none of these answer choices is correct. equal to one.
The critical ratio (cr) will be less than one if the amount of work left is larger than the amount of time left.
In a work center, the critical ratio is a rule of thumb used to prioritize jobs that need to be processed (CR). The remaining shop time is divided by the equation (due date - today's date), and the result is the CR priority index number. When sequencing according to these criteria, the job with the lowest CR is put on the schedule first. a dispatching rule that generates a priority index number by dividing the amount of time remaining before the deadline by the estimated amount of time required to accomplish the job. Ratios below 1.0 are frequently thought of as being behind schedule, whereas ratios over 1.0 are thought of as being ahead of time. Critical ratio (CR) = CPI x SPI
To read more about critical ratio, visit https://brainly.com/question/29574348
#SPJ4
The sum of two numbers is 34 and the difference is 10. What are the numbers?
Answer:
22 and 12! i think unless i misunderstood the question
Step-by-step explanation:
for a given arithmetic sequence, the first term a1 is equal to 28 and the 93r term is equal to -432 find the value of the 33rd term a33
The 33rd term of the given Arithmetic progression will be -132.
What is an Arithmetic progression?
A series of numbers is called a "arithmetic progression" (AP) when any two subsequent numbers have a constant difference. Arithmetic Sequence is another name for it.
Given, first term= a1= 28
and, a93 = -432
we know that, a93 = -432
a + 92d = -432 (where d is the common difference)
28 + 92d = -432
92d = -432-28
= -460
d = -460/92 = -5.
Now, we can find the a33,
a33 = a + 32d
= 28 + (32× -5)
= 28-160
= -132.
Learn more about Arithmetic progression from the link given below:
https://brainly.com/question/6561461
#SPJ4
Abigail owns a food truck that sells tacos and burritos. She only has enough supplies
to make 130 tacos or burritos. She sells each taco for $3 and each burrito for $6.
Abigail must sell no less than $600 worth of tacos and burritos each day. If x
represents the number of tacos sold and y represents the number of burritos sold,
write and solve a system of inequalities graphically and determine one possible
solution.
Answer:
Inequality 1: x + y ≤ 1.50
Inequality 2: 4x + 6.5y ≥ 780
So, the possible solution can be x = 20, y = 1.20
(1) The inequalities can be written as:-
Inequality 1: x + y ≤ 1.50
Inequality 2: 4x + 6.5y ≥ 780
(2) The possible solution for the value of x and y can be x = 0.30, y = 1.20.
What is inequality?The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.
Given that Abigail owns a food truck that sells tacos and burritos. She only has enough supplies to make 130 tacos or burritos. She sells each taco for $3 and each burrito for $6. Abigail must sell no less than $600 worth of tacos and burritos each day.
The inequalities can be written as:-
Inequality 1: x + y ≤ 1.50
Inequality 2: 4x + 6.5y ≥ 780
The two inequalities can be solved as:-
x + y = 1.50 or x= 1.50 - y
4x + 6.5y = 780
4( 1.5 - y ) + 6.5y = 780
6 - 4y + 6.5y = 780
y = 1.20
The value of x will be,
x= 1.50 - y
x= 1.50 - 1.2
x = 0.30
To know more about inequality follow
https://brainly.com/question/24372553
#SPJ2
What is the slope of a line perpendicular to the line whose equation is 3x+3y=18. Fully simplify your answer.
The slope of a line is -1
What is a line ?
A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.
A line is a perfectly straight, one-dimensional shape that extends infinitely in both directions and has no thickness. In order to stress that a line has no "wiggles" anywhere along its length, it is occasionally referred to as a straight line or, more formally, a right line (Casey 1893).
y = mx + c
Subtract 3x from both sides of the equation
3y = 18 - 3x
dividing by 3
y = 6 - x
re-ordering we get y = -x + 6
using slope-intercept form ,
the slope m = -1
To learn more about a line from the given link
https://brainly.com/question/18831322
#SPJ1
at the 0.01 significance level, do women save more money than men? what is the value of the test statistic for this hypothesis test?
Both means are approximately equal at 1% level of significance.
What is significance level?
A finding has statistical significance in statistical hypothesis testing when it is highly unlikely to have happened given the null hypothesis.
H0: Mean of mean = mean of women
Ha: means of men < mean of women
(Left tailed test)
Since population std deviation is known but sample sizes are small t test is used.
The mean of Men minus Women equals -5.00
standard error of difference = 2.201
t = 2.2721
df = 53
p value= 0.0136
since p >0.01 at 1% significance level we fail to reject H0.
Both means are approximately equal at 1% level of significance.
To know more about significance level visit,
https://brainly.com/question/14363703
#SPJ4
Question 8 pls help!!!!!!!
Answer:
since the arcs are made on top and bottom of the line ,so by joining both the points of intersection of the arc we get a perpendicular bisector of the line
therefore , it is option d) the perpendicular bisectorof line MN
It takes Cathy ½ hour to hike 2 ¼ miles.
a) What is her rate, in miles per hour?
b) At this rate, how far will she hike in 2 hours?
Answer: a= 4.5 miles per hour
b= 9 miles
A. 1/2 x 2 = 1 hour so 2 1/4 x 2 = 4.5 miles
B. 1/2 and hour x 4 = 2 hours so 2 1/4 miles x 4 = 9 miles
4. How high must an individual score on the GMAT in order to score in the
highest 5%? (Round to the nearest whole number)
The scores needed in order to score in the highest 5% of the GMAT are given as follows:
At least 711.
How to obtain the score using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation of GMAT scores are given as follows:
µ = 527, σ = 112.
The highest 5% of scores are composed by scores of the 95th percentile and above, hence the minimum score is X when Z = 1.645.
Then:
1.645 = (X - 527)/112
X - 527 = 1.645 x 112
X = 711.
Missing InformationThe mean and the standard deviation of scores are given as follows:
µ = 527, σ = 112.
More can be learned about the normal distribution at https://brainly.com/question/25800303
#SPJ1
a group spends $277.50 to rent 15 tubes for a float down the ichetucknee river. how many of each type of tube does the group rent?
Each tube costs $15.17 to the group of friends when they rent 15 tubes for floating down near the Ichetucknee River. The procedure is as follows:
Given, the cost of each tube; 15 tubes would cost $277.50 to rent.
1 dollar equals 100 cents. Along these lines, $227= 22700 penniesConsequently,
the cost of 15 tubes be = (22700+50)cents=22750 pennies
The expense of one tube= (22750/15)cents
=1516.7 pennies
= $15.17
The expense split technique is a method used to distribute the cost of a shared expense among a group of individuals. It involves dividing the total cost of the expense by the number of people in the group to calculate each person's share of the cost.
Learn more about Expense Split here:
https://brainly.com/question/4280136
#SPJ4
can someone pls help me with exercise 7 in algebra
Answer: Ok so the slope is always going to be m and the y intercept will be the b.
Step-by-step explanation: For example the slope form in y=mx+b. Whatever is in that b spot is going to be the y-intercept. So for number one on exercise 7 the slope will be 2/3 and the y- intercept will be -4. Same for number 2 remember take your time and know that m is the slope and b is your y-intercept. I really hope this helps you.
Which of the following values are solutions to the inequality - 8 - 4x > 1?
I.-10 II. -1 III. 6
The solution of the linear inequation -8 - 4x > 1 is x < [tex]-\frac{9}{4}[/tex]
-10 satisfies the given linear inequation
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, ≥, ≤
A one degree inequation is known as linear inequation.
The given linear inequation is
-8 - 4x > 1
Now,
-8 - 4x > 1
-4x > 1 + 8
-4x > 9
x < [tex]-\frac{9}{4}[/tex]
-10 satisfies the given linear inequation
To learn more about linear inequation, refer to the link-
https://brainly.com/question/24372553
#SPJ1
For Daniela’s bicycle business the ne profit (in dollars) for renting b bicycles is: P(b)=25b+7. If Daniela rents 6 bicycles, what is her profit
By using the concept of profit, it can be calculated that-, Profit for renting 6 bicycles = $157
What is profit?
Profit is a financial gain earned when the revenue from a business activity exceeds the expenses associated with it. This gain is usually measured in monetary terms, but it could also be measured in terms of goods or services. Profit is the main reason why businesses exist and it can be used to reinvest in the business, pay shareholders, purchase new assets, or do other things. Profit is the lifeblood of any business and it is essential for sustaining and growing its operations.
For Daniela’s bicycle business the net profit (in dollars) for renting b bicycles is: P(b)=25b+7.
Number of bicycles Daniela rented = 6
So Profit for renting 6 bicycles = $([tex]25 \times 6 + 7[/tex]) = $157
To learn more about profit, refer to the link-
https://brainly.com/question/19104371
#SPJ1
Help me in this plis
Answer:
PROBALLY, A
Step-by-step explanation:
Not entirely sure but translating up 7 units from 5 would be 3x-12
It rained 1.5 inches in Drake City yesterday. The meteorologist's rainfall prediction was 20% less than that. How much rainfall did the meteorologist predict?
Answer:
Step-by-step explanation
To find the amount of rain the meteorologist predicted, start by listing the key information from the problem.
The actual amount of rain was 1.5 inches.
The meteorologist's prediction was 20% less than that. This is the percent error.
First, find the amount of error. It is 20% of the actual amount of rain.
0.21.5=0.3
So, the amount of error in the meteorologist's prediction is 0.3 inches. Since the predicted amount was less than the actual amount, subtract 0.3 from the actual amount of rain.
1.5–0.3=1.2
The meteorologist predicted 1.2 inches of rainfall.
You could also find the meteorologist's rainfall prediction by finding 80% of the actual amount of rain.
0.81.5=1.2
The amount of rainfall the meteorologist predict is 1.2 inches
How to determine how much rainfall the meteorologist predict?From the question, we have the following parameters that can be used in our computation:
Amount of rainfall = 1.5 inches
Prediction = 20% less than the amount of rainfall
These parameters imply that:
Prediction = Amount of rainfall * (1 - Percentage less)
Substitute the known values in the above equation, so, we have the following representation
Prediction = 1.5 * (1 - 20%)
Evaluate
Prediction = 1.2
Hence, the prediction is 1.2 inches
Read more about proportion at
https://brainly.com/question/870035
#SPJ1
You earn 1,166 gro taxable income every week, and have claimed no exemption. Auming that you have no other ource of income, what i the amount of income tax withheld each week
The amount of income tax withheld each week is $350.
In the question ,
it is given that ,
the total gross taxable income every week is = $1166 ,
we know that the percent tax is = 30% ,
and their is no other source of income
So the income tax will be = 30% of total gross taxable income .
Substituting the value of gross taxable income ,
we get ,
income tax = 30% × 1166
= 0.30 × 1166 ...because 30% = 0.30
Simplifying further ,
we get ,
= 349.8
≈ 350
Therefore , amount of income tax withheld is $350 .
The given question is incomplete , the complete question is
You earn $1,166 gross taxable income every week, and have claimed no exemption. Assuming that you have no other source of income, what is the amount of income tax withheld each week ?
Learn more about Income Tax here
https://brainly.com/question/11758414
#SPJ4