Lauren will reach Andrea after 65 minutes of biking.
What do we mean by mathematical operations?A mathematical function called an operation, also known as an "operand" or "argument," transforms zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.The operations that are most frequently studied are unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, and binary operations (i.e., operations of arity 2), such as addition and multiplication.So, because Lauren is traveling at a speed that is one kilometer per minute slower than Andrea's and vice versa, Andrea's speed is 3/4 km/min and Lauren's is 1/4 km/min.
Thus, Andrea will have biked 3/4 × 5 = 15/4 km in 5 minutes.Lauren will have to bike the following kilometers in total:
20 - 15/4 = 80/4 - 15/4 = 65/4 kmHer speed being 1/4 km/min, the amount of time passed will be:
(65/4)/(1/4) = 65Therefore, Lauren will reach Andrea after 65 minutes of biking.
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It's one more question after this i think guys. Thank for all your help!
30 points
The solution for x in the given expression (7 = 3x/9) is: C. 21.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In this exercise, you're required to describe the steps that should be taken to rearrange and solve for x. Therefore, the appropriate and required steps are listed as follows:
Multiplying both sides by 9, we have:
9 × 7 = 3x/9 × 9
63 = 3x
Dividing both sides by 3, we have:
3x/3 = 63/3
x = 21.
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Question 2 of 10
Which of the following are solutions to the equation below?
Check all that apply.
x² - 6x +9=11
A. x= √√√2 +6
B. x = -√11 +3
C. x = -√2 +6
D. x= √11 +3
E. x=2+√√6
OF. x=2-√6
The solutions of the quadratic equation x² - 6x +9=11 is found to be x = [tex]\sqrt{11} + 3[/tex] or [tex]\sqrt{11}-3[/tex]. So, Option B and D are correct.
What is a quadratic equation?A quadratic equation is ax² + bx + c = 0 . Another name for the terms a, b, and c is quadratic coefficients.
The values of the unknown variable x that fulfill the quadratic equation are the solutions to the problem. Quadratic equations' roots are known as these solutions.
Given equation: x² - 6x +9=11
Subtract 11 on both sides
x² - 6x +9 +(-11) =11 - 11
x² - 6x - 2 = 0
Solving using the quadratic formula,
x = [tex]\frac{-b + \sqrt{b^{2}-4ac } }{2a}[/tex] or [tex]\frac{-b - \sqrt{b^{2}-4ac } }{2a}[/tex]
x = [tex]\frac{6 + \sqrt{-6^{2}-4(-2) } }{2}[/tex] or [tex]\frac{6 - \sqrt{-6^{2}-4(-2) } }{2}[/tex]
x = [tex]\sqrt{11} + 3[/tex] or [tex]\sqrt{11}-3[/tex]
Therefore, the solutions of the quadratic equation x² - 6x +9=11 is found to be x = [tex]\sqrt{11} + 3[/tex] or [tex]\sqrt{11}-3[/tex]. So, Option B and D are correct.
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Nico earns $12.50 per hour as a math tutor. she that the relationship between the amount he earns and the number of hours he tutors is a proportional relationship. then write the equation for the relationship
Answer: [tex]y=12.50x[/tex]
Step-by-step explanation:
Let the number of hours be x and the total earnings in dollars be y. Since the total amount of money earned is the number of hours times the amount earned per hour, the equation is [tex]y=12.50x[/tex].
What is the equation of the line that passes through the point (3,1)(3,1) and has a slope of -4/3
?
i'm going to assume (3,1)(3,1) was a typo.
here is an equation for a line with a slope of (-4/3) that crosses through (3,1)
y = -4/3x + 5;
steps;
1 = -4/3(3)+ b
1 = -4 +b
5 = b
Answer:i'm going to assume (3,1)(3,1) was a typo.
here is an equation for a line with a slope of (-4/3) that crosses through (3,1)
y = -4/3x + 5;
steps;
1 = -4/3(3)+ b
1 = -4 +b
5 = b
Step-by-step explanation:
how to divide 40 by 178
178/40
Answer: 0.224
Step-by-step explanation:
40/178= 0.224
work in the pic
Find the perimeter of this semi-circle with diameter, d = 23cm. Give your answer rounded to 1 DP.
The perimeter of the semi-circle is 59.1 cm
In this question, we have been given the diameter if the semi-circle
d = 23 cm
We need to find the perimeter of the semi-circle.
We know that, the perimeter of the semi-circle of radius 'r' is P = πr + 2r
For diameter d = 23 cm, the radius would be,
r = 11.5 cm
So, the perimeter would be,
P = πr + 2r
P = π × 11.5 + 2 × 11.5
P = (π + 2) × 11.5
P = 59.13 cm
Therefore, the perimeter of the semi-circle is 59.1 cm
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Taylor is struggling with literal equations. She has tried to solve the equation below for several times but still can't get the correct answer. Her steps that she used to solve for m are shown below. In which step is she making an error?
The step 3y = 80v + x is incorrect, as 3y = 80v - x is the correct step by subtraction property of equality.
In this question, we have been given Taylor is solving a literal equation (x + 3y) / 2 = 40v
We have been given her steps that she used to solve for y.
We need to find an error in the steps.
First we solve given literal equation for y.
(x + 3y) / 2 = 40v
x + 3y = 40v × 2 .................(Multiply both the sides by 2)
x + 3y = 80v
x + 3y - x = 80v - x ...................(Subtract x from both the sides)
3y = 80v - x
y = (80v - x)/3 ............(Divide each side by 3)
If we observe Taylor's steps, we can see that there's an error in the step 3y = 80v + x.
Therefore, the step 3y = 80v + x is incorrect, as 3y = 80v - x is the correct step by subtraction property of equality.
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Cual es el volumen de una pirámide triangular que tiene por base 9cm x 8cm y una altura de 16 cm. Aiuda por favor es para mañana
Answer:
Step-by-step explanation:
Así que tienes que multiplicar 8x9x16 y dividir por 2 y luego multiplicar por 4 PUEDE ESTAR EQUIVOCADO ASÍ QUE TEN CUIDADO
Please help with this math problem! Thank you! :D
Answer:
C
Step-by-step explanation:
[tex]\sqrt{2}[/tex] and [tex]\frac{1}{\sqrt{2}}[/tex] are both irrational, but they multiply to 1, which is rational
See below for question
Value of x is 2 and value of k is 0.999.
What is volume?Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. Volume and the notion of length are connected.
Given Data
At t=0, Water Volume is 3,000 Litres
The volume of water in the tank equals t hours later.
As it is also stated, there is x% less water in the tank at the conclusion of every hour than there was at the beginning.
After an hour, the amount of water is equal to 3,000 - = 3,000 - 30 x
Water consumption after two hours = (3,000 - 30 x) - (3,000 - 30 x)
×= (3,000 - 30 x) (3,000 - 30 x)
Also,
= 288120
⇒300000 - 3000 x - 3000 x + 30 x²
= 288120
⇒ 30 x ² - 6,000 x + 11880= 0
When we multiply both sides by 30, we get
⇒ x² - 200 x + 396=0
reducing the quadratic equation to factors
(x -198)(x-2) = 0
x = 198,
x = 2
Which suggests that x = 2 might be the answer to this equation.
Also,
V₁ = 3000- 30(2)
V₁ = 3000 - 60
V₁ = 2940
k = [tex]\frac{2940}{3000}[/tex]
k = 0.999(approximately)
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Solve the equation by extracting the square roots. List both the exact solution and its approximation rounded to two decimal places.
(2x − 1)^2 = 18
The exact solution and its approximation rounded to two decimal places are 2. 6213 and 2. 62 respectively.
What is an algebraic expression?An algebraic expression can be described as a mathematical or arithmetic expressions that is composed of arithmetic terms, factors, constants, variables, and coefficients.
These expressions are also made up of arithmetic operations which includes;
DivisionAdditionParenthesesBracketMultiplicationSubtractionFrom the information given, we have that;
(2x − 1)^2 = 18
Find the square root of both sides, we have;
√(2x − 1)^2 = √18
Note that square root rules out the square, we have;
2x - 1 = 4. 24264
collect like terms
2x = 4. 24264 + 1
2x = 5. 24264
Make 'x' the subject
x = 5. 24264/2
x = 2. 6213
Hence, the value is 2. 6213
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The Sydney Opera House can house no more than 5738 people. Luisa Miller always brings crowds of at least 4,000 people. What is the maximum number of empty seats that might not be filled during her performance?
Answer:
a maximum of 1,738 empty seats
Step-by-step explanation:
5,738 - 4,000 = 1,738
Carpet installers often are paid by the square foot rather than by the hour. If a certain installer is paid $0.50 per square foot, how much would he earn on a day when he installed 896 sq ft of carpet?
Answer:
$44.80
Step-by-step explanation:
Multiply 0.50 by 896.
Aşağıdaki sayı ikililerinden hangisinin en büyük ortak böleni 15 değildir? A) 30 ile 45 C) 60 ile 105 B) 45 ile 75 D) 75 ile 125
Answer:
D 75 and 125
Step-by-step explanation:
cünkü en büyük ortak böleni 25 dir
prove me wrong
h(x)=3x+4 complete the function table help please
The function table should be completed as follows:
x h(x)__
-4 -8
-3 -5
2 10
4 16
5 19
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.
Next, we would evaluate the given function by substituting the value of x as follows:
When x = -4, we have:
Function, h(x) = 3x + 4
Function, h(-4) = 3(-4) + 4
Function, h(-4) = -12 + 4
Function, h(-4) = -8
When x = -3, we have:
Function, h(x) = 3x + 4
Function, h(-3) = 3(-3) + 4
Function, h(-3) = -9 + 4
Function, h(-3) = -5
When x = 2, we have:
Function, h(x) = 3x + 4
Function, h(2) = 3(2) + 4
Function, h(2) = 6 + 4
Function, h(2) = 10
When x = 4, we have:
Function, h(x) = 3x + 4
Function, h(4) = 3(4) + 4
Function, h(4) = 12 + 4
Function, h(4) = 16
When x = 5, we have:
Function, h(x) = 3x + 4
Function, h(5) = 3(5) + 4
Function, h(5) = 15 + 4
Function, h(4) = 19
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(7.98 × 104) + (2.02 x 10-4)
Answer: 846.12
Step-by-step explanation:
In Exercises 6 and 7, use the Law of Detachment to determine what you can
conclude from the given information, if possible.
6. If you eat a healthy breakfast, then you will not be hungry until lunchtime. You
are not hungry until lunchtime.
7. Adjacent angles share one common ray. ∠AOB and ∠ DOB are adjacent angles.
Using the Law of Detachment, the conclusions are given as follows:
6. No conclusion.
7. ∠AOB and ∠ DOB share one common angle.
What is the Law of Detachment?The Law of Detachment is a logic axiom which states that if a conditional and the hypothesis of a statement are true, then the conclusion of the statement is also true.
Supposing a conditional statement p -> q, we have that the hypothesis and the conclusion are defined as follows:
p is the hypothesis.q is the conclusion.For item 6, we have that the statements are given as follows:
Statement p: You eat a healthy breakfast.Statement q: You are not hungry until lunchtime.We have that p->q and q are true, hence no conclusion can be reached from the law of detachment.
For item 7, we have that the statements are given as follows:
Statement p: Adjacent angles.Statement q: Share one common ray.In this case, we have the hypothesis is true, hence the conclusion is that ∠AOB and ∠ DOB share one common angle.
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find the number of calories in a stalk of celery and in a carrot, a carrot hs 13 calories more then a celerystalk, five carrots and 1o celery stalks have only 170 calories
The number of calories in stalk of celerystalk and carrot is found as 20 and 7 respectively.
What is defined as the method of substitution?The algebraic method for solving simultaneous linear equations is the substitution method. The value with one variable through one equation is replaced in the other equation, as the name implies.For the given question;
Let the number of calories present in carrot is 'x'.
Let the number of calorie present in celerystalk is 'y'.
Carrot has 13 more calories than celerystalk.
Thus,
x = y + 13 ......eq 1
Now, 5 carrots and 10 celery stalks have total 170 calories.
The equation becomes.
5x + 10y = 170
Substitute the value of x from eq 1.
5(y + 13) + 10y = 170
Simplify the equation;
5y + 65 + 10y = 170
15y = 105
y = 7 (number of calories in stalk of celerystalk)
Put the value of y in eq 1.
x = y + 13
x = 7 + 13
x = 20 (number of calories in stalk of carrot)
Thus, the number of calories in stalk of celerystalk and carrot is found as 20 and 7 respectively.
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determine if the sequence is arithmetic. if it is find the common difference and the next 3 terms in the sequence 35, 32, 29, 26
Answer:
-3 and 23,20,17
Step-by-step explanation:
35-3=32,32-3=29
1. One of two supplementary angles is four times the other. Find the largest angle.
144 is the largest angle in supplementary angle .
What is an example of a supplementary angle?
Angles that add up to 180 degrees are referred to as supplementary angles. For instance, the sum of angle 130° and angle 50° is 180°, hence they are supplementary angles.The pair of angles known as supplementary angles always add up to 180 degrees. The terms "supplements" for these two viewpoints describe them. The Latin terms "Supplere" and "Plere," which mean "supply" and "fill," respectively, are the source of the English word "supplementary."Let one angle = x
then other angle is four times the other = 4x
x + 4x = 180
5x = 180
x = 180/5
x = 36
smaller angle = 36
largest angle = 4x = 4 * 36 = 144
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15 equals the sum of three and six times a number
Answer: 15 equals the sum of 3 + 6 x 2
Step-by-step explanation: 6x2 is 12 and if you add 3 it is equal to 15, but it is better if you rewrote the equation as 3 + (6x2), that way it is more understandable
Suppose U={1,2,3,4,5,6,7,8} is the universal set and P={2,4,6,8}. Then what is P?
{0,1,3,5,7}
{0,1,3,5,7,9}
{1,3,5,7}
{ }
{ } pls i right,or u can help me out
2/11 multiplied by 7/3
Step-by-step explanation:
14/33.
step 1. in the denominator you find the Lowest commons multiple, since 11 and 3 don't have common multiples, you just do 11 x 3 which is 33. you denomination would be 33
step 2. multiply 2 and 7 which is 14. your answer is 14/33.
Help me solve this!!
Answer:
3.3 x 10^-4
Step-by-step explanation:
It's 3.3 x 10^-4 because 3.3 x 10^-4 would be 0.00033 and 8.0 x 10^0 would be 1 so 0.00033 x 1 = 0.00033. Then when we plug 0.00033 into scientific notation we will get 3.3 x 10^-4
Felipe is having a party. He'll have 4 tables for every 20 guests. Complete the table below showing the number of tables and the number of guests. See the table on the bottom.
( Table: ?, 1 20,4 35,? ?,8 50,?)
Using a proportional relationship, the table relating the number of guests and number of tables is given by the image at the end of the answer.
How to represent a direct proportional relationship?A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality represented by k, according to the equation below:
y = kx.
In the context of the problem, the variables are given as follows:
y: Number of tables.x: Number of guests.He'll have 4 tables for every 20 guests, hence the constant is given as follows:
k = 4/20 = 1/5 = 0.2.
Hence the relation is:
y = 0.2x.
For 1 table, the number of guests is:
0.2x = 1 -> x = 5.
For 8 tables, the number of guests is:
0.2x = 8 -> x = 8/0.2 = 40.
For 35 guests, the number of tables is:
y = 0.2 x 35 = 7.
For 50 guests, the number of tables is:
y = 0.2 x 50 = 10.
The table with these measures is given by the image at the end of the answer.
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is 0.1213141516... a rational number
Answer:
No, because any number than produces and decimal that continuse forever is not rational.
Step-by-step explanation:
Hope it helps! =D
Help please , THANKS!
:DD
Answer:
73°
Step-by-step explanation:
To find ∠QPS, just add ∠1 and∠2
∠QPS = ∠1 + ∠2
= 44° + 29°
= 73°
Answer:
∠QPS = 73°
Step-by-step explanation:
∠1 = 44°
∠2 = 29°
∠QPS = ∠1 + ∠2 = 44° + 29° = 73°
Tell how the Commutative and Associative Properties of Addition can help you evaluate the expression.
The value of the fraction given as - 1 3/4 - (-8 1/3) - (- 4 1/4) will be 10 5/6.
How to calculate the fraction?It should be noted that a fraction is simply used to represent the numbers that aren't whole. The commutative property of addition states that the sum is unaffected by the order of the addends.
According to the associative property of addition, the grouping of integers does not affect the sum.
Based on the information given, the fraction is illustrated as:
= - 1 3/4 - (-8 1/3) - (- 4 1/4)
Note that (-) × (-) = +
Therefore,
= - 1 3/4 - (-8 1/3) - (- 4 1/4)
= - 1 3/4 + 8 1/3 + 4 1/4
The LCM of the denominator is 12
= - 1 9/12 + 8 4/12 + 4 3/12
= 12 7/12 - 1 9/12
= 10 10/12
= 10 5/6
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mike is a good athlete.Mike's father is a good athlete.Mike's sister is a good athlete.Therefore,Mike's son will be a good athlete. (Inductive or Deductive?)
In a particular college class, 60% of the students are female. Of the female students, 75% have long hair. One student is picked randomly in the class. What is the probability that it is a female with long.
There is a 0.75 percent chance that the person is a woman with long hair.
What is probability?Probability can be used to define potential. The occurrence of a random event is the focus of this mathematical field. There is a 0 to 1 value range. The likelihood of anything happening is often referred to as probability. Utilize probability to gauge a situation's likelihood of happening. Numerous factors are difficult to forecast with absolute precision. Using it, we can only speculate on whether or how likely it is that an event will occur. A probability scale with a value of 0 for an impossibility and 1 for a certainty. In a sample space, there is a one probability for every event.
E is the probability of an event . Hence,
P(E) is the ratio of favorable results to all outcomes.
In probability, an event is deemed dependent if it is impacted by other occurrences, and independent if it is wholly unaffected by the occurrence of any other event.
By applying the literature and formulas previously mentioned, we have:
F should signify for the fact that the student is female, and L should stand for the fact that the student has long hair.
P(F)
= 0.60
P(L)
= 0.50
P(F AND L)
= 0.45
P(L|F)
= 0.75
There is a probability of 0.75 that a randomly chosen student has long hair.
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