Answers
First, we know that a possible equation of L2 is y=1, then c=-1 => -y=-1 or y=1.
Of course, c could be just any negative number so that L2 lies above the x-axis.
=> c<0 ..........................................(III) is true
Next, we note that L1 has a negative intercept, that meant that when x=0, y<0. Go back to the original equation
ax+by=-1 => when x=0, by=-1, so b>0 in order for y to be negative. So
b>0.
We already know that c<0, so
b>c .....................................................................(II) is true
Further, we note that L2 has a negative slope. From the definition of slope, m, where m=-a/b
=>
m=-a/b<0 => a/b>0.
We already know that b>0, so for a/b>0, a>0. Therefore
a>0 ...................................................................(I) is true
So we have established the truth values of (I), (II) and (III).
It will be up to you to select the answer choices.
Do check and understand all the arguments. If in doubt, please post your queries.
Related Questions
1. You are visiting Baltimore, MD and a taxi company charges a flat fee of $3.00 for using the taxi and $0.75 per mile.
A. Write an equation that you could use to find the cost of the taxi ride in Baltimore, MD. Let x represent the number of. miles and y represent the total cost.
B. How much would a taxi ride for 8 miles cost?
C. If a taxi ride cost $15, how many miles did the taxi travel?
Answers
B) $9.00
C) 16 miles
hope that helps
Answers to all parts are as follows -
The equation to find the cost will be y(x) = 0.75x + 3 For 8 miles of travel, the total cost would be $9.For a total fare of $15, we can ride for 16 miles.What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is taxi company charges a flat fee of $3.00 for using the taxi and $0.75 per mile.
PART - A
Assume that [x] represent the number of miles and [y] represent the total cost. Therefore, the equation that you could use to find the cost of the taxi ride in Baltimore can be written as-
y(x) = 0.75x + 3
or
y(x) = 3x/4 + 3
PART - B
For [x] = 8 miles, the total cost will be -
y(8) = (3 x 8)/4 + 3
y(8) = 6 + 3
y(8) = 9
For 8 miles of travel, the total cost would be $9.
PART - C
For a total fare of $15 -
15 = 3x/4 + 3
12 = 3x/4
x = (12 x 4)/3
x = 16
For a total fare of $15, we can ride for 16 miles.
Therefore -
The equation to find the cost will be y(x) = 0.75x + 3 For 8 miles of travel, the total cost would be $9.For a total fare of $15, we can ride for 16 miles.To solve more questions on equation modelling, visit the link below-
https://brainly.com/question/14516577
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Find the value of z such that 0.96420.9642 of the area lies between −z−z and z. round your answer to two decimal places.
Answers
P(z)-P(-z)=0.9642=1-2P(-z) => P(-z)=(1-0.9642)/2=0.0179
=>
-z=-2.099192
=> z=2.099192
Check:
P(2.099192)-P(-2.099192)=0.9642 ok
Final answer:
The value of z where 0.9642 of the area lies between -z and z is found by looking up the area 0.4821 (half of 0.9642) in a Z-table or using the invNorm function with 0.4821 on a normal distribution calculator. This will provide the z-score to be rounded to two decimal places.
Explanation:
You are looking for the value of z such that 0.9642 of the area under the normal distribution curve lies between −z and z. To find this, you'll need to use the properties of the standard normal distribution, commonly represented by a Z-table.
For a symmetrical distribution, half of the area you are interested in would be to the left of 0 and half to the right. Since 0.9642 is the total area between −z and z, we need to find the z-score that corresponds to half of this area from the mean to one end. Specifically, you're looking for the z-score where the area to the left is 0.4821 (0.9642 divided by 2).
Using a Z-table or an inverse normal function on a calculator, you can find the z-score that corresponds to an area of 0.4821. If you're using a Z-table, look up the closest area in the body of the table and find the corresponding Z-score. If you're calculating it (such as with the invNorm function on a calculator like the TI-83 or 84), input the left-tail area. The answer should be rounded to two decimal places.
The calculation would be something similar to invNorm(0.4821, 0, 1), where 0 and 1 are the mean and standard deviation of the standard normal distribution, respectively.
If z represents the variable of the standard normal distribution curve N(0,1), which is symmetrical about z=0, then we look for
P(z)-P(-z)=0.9642=1-2P(-z) => P(-z)=(1-0.9642)/2=0.0179
=>
-z=-2.099192
=> z=2.099192
Check:
P(2.099192)-P(-2.099192)=0.9642
You flip a coin 10 times. Knowing that the event satisfies the requirements for a binomial distribution, find the probability that exactly 7 of the outcomes are heads.
Answers
p=0.50
n=20
The number of successes, x, is then given by[tex]P(x)=C(n,x)p^x(1-p)^{n-x}[/tex]where[tex]C(n,x)=\frac{n!}{x!(n-x)!}[/tex]
For x=7,
[tex]P(x)=C(n,x)p^x(1-p)^{n-x}[/tex]
[tex]P(7)=C(n,x)p^x(1-p)^{n-x}[/tex]
[tex]=C(20,7)0.5^7(0.5)^{20-7}[/tex]
[tex]=C(20,7)0.5^{20}[/tex]
[tex]=\frac{77520}{1048576}[/tex]
[tex]=\frac{4845}{65536}[/tex]
[tex]=0.07393[/tex] to 5 places of decimal
Ans. the probability is 0.07393 to 5 places of decimal.
Answer:
0.1172
Step-by-step explanation:
The formula for the probability in a binomial distribution (n trials, r successes) is
[tex]\binom{n}{r}(p)^r(1-p)^{n-r}[/tex] where p is the probability of success.
For flipping a coin, the probability of success, p, is 0.5.
The number of trials, n, is 10. The number of successes, r, is 7. This gives us
[tex]\binom{10}{7}(0.5)^7(1-0.5)^{10-7}\\\\\binom{10}{7}(0.5)^7(0.5)^3=0.1171875 \approx 0.1172[/tex]
The table below shows a baseball player’s batting average batting left and right versus left- and right-handed pitches Left-handed pitchers Right-handed pitchers Bats left 0.285 0.175 Bats right 0.215 0.250 Assume these numbers are the probabilities that he will get a hit during an “at bat.” On average, when he bats left 100 times, how many more hits will he get when he faces left-handed pitchers as opposed to right-handed pitchers? 1 2 11 22
Answers
Answer:
C. 11 is the correct answer
Step-by-step explanation:
The table representing the probabilities of player's batting average is,
Left-Handed pitchers Right-Handed pitchers
Bats Left 0.285 0.175
Bats Right 0.215 0.250
So, when the players bats left 100 times,
The probability of hits he gets when faced by left-handed pitchers = 0.285 × 100 = 28.5
The probability of hits he gets when faced by right-handed pitchers = 0.175 × 100 = 17.5
Thus, the difference in the hits = 28.5 - 17.5 = 11
Hence, the player will get 11 more hits t when he faces left-handed pitchers as opposed to right-handed pitchers.
Sabah has $450 to pay for college textbooks. She expects to pay about $75 per book. Her friend told her that 4 of them can be checked out of the library for free.
Complete the equation below to find the total number of books that Sabah can get for her classes. Use b to represent the total books.
Answers
PLEASE SHOW ALL WORK!!!
The base of a triangle measures (8x + 2) units and the height measures (4x − 5) units.
Part A: What is the expression that represents the area of the triangle? Show your work to receive full credit. (4 points) Hint: Area = 0.5bh
Part B: What are the degree and classification of the expression obtained in Part A? (3 points)
Part C: How does Part A demonstrate the closure property for polynomials? (3 points)
Answers
[tex]A=0.5(8x+2)(4x-5)[/tex]
[tex]A=0.5(32 x^{2} -40x+8x-10)[/tex]
[tex]A=0.5(32 x^{2} -32x-10)[/tex]
[tex]A=16 x^{2} -16x-5[/tex]
Now the only thing left is factor the quadratic polynomial:
[tex]A=(4x+1)(4x-5)[/tex]
W can conclude that the area of our triangle is [tex]A=(4x+1)(4x-5)[/tex]
Part B: Our polynomial has three terms, so is a trinomial; also, our polynoal only has one variable, [tex]x[/tex], and the largest exponent of that variable is 2; therefore is a degree 2 polynomial. In summary, we have a trinomial of degree 2.
Part C: Part A demonstrate the closure property of polynomials because after multiplying tow polynomials we obtained another polynomial.
Part A:
As given,
Base of the triangle = 8x + 2 units
Height of the triangle = 4x − 5 units
Formula to find area of a triangle = [tex]\frac{base * height}{2}[/tex]
= 0.5bh
we have been given base and height, so the area becomes,
area = [tex]\frac{(8x+2)(4x-5)}{2}[/tex]
area = 0.5(8x+2)(4x-5)
= 0.5(32x²-32x-10)
= 16x²-16-5
after factoring it, we get
area = (4x-5)(4x+1) units.
Part B:
It is a degree 2 polynomial as the polynomial has one variable that is x, and the largest exponent of that variable is 2.
Part C:
Part A demonstrates the closure property of polynomials because after multiplying two polynomials we get another polynomial.
Answer step by step
1.Avas school took a field trip. A total of 32 vehicles were needed for the trip.Some students took the bus, and some students car-pooled. There are 27 people on each bus and 3 people on each car. 408 people altogether attended the trip. How many buses and cars were needed for the trip?
Answers
1. suppose, that number of cars is 'x', numbers of buses is 'y'.
2. according to the condition 'a total of 32', it means that x+y=32. This is the 1st equation.
3. according to the condition in one car are 3x persons, in one bus are 27y persons, and totaly 3x+27y=408 people. This is the 2d equation.
4. if to solve the system of two equations:
[tex] \left \{ {{x+y=32} \atop {3x+27y=408}} \right. \ =\ \textgreater \ \ \left \{ {{x=19 (cars)} \atop {y=13(buses)}} \right. [/tex]
Answer: 13 - b., 19 - c.
A company sells boxes that are 2 3/8 feet high, 3 5/8 feet long, and 1 7/8 feet wide. John has a storage room that is 8 feet wide, 10 feet deep, and 12 feet high. You may rotate the boxes so that the width and length are interchanged, but the boxes may not be laid on their sides. a. What is the maximum number of boxes that he may stack on top of one another? b. How much room will there be left between the top of the stack of boxes and the ceiling?
Answers
The maximum height of a stack of boxes is 5 boxes.
b) (1/19)*(2 3/8 ft) = 1/8 ft is the room left at the top of the stack.
Find the 29th term of the following sequence. 19.5, 19.9, 20.3, 20.7, . . .
Answers
the nth value is given by:
nth=a+(n-1)d
where:
a=first term
d=common difference
n=number of terms
From the series:
19.5, 19.9, 20.3, 20.7,.....
a=19.5
d=0.4
n=29
thus
29th=19.5+(29-1)0.4
29th=30.7
find the surface area of the composite solid round your answer to the nearest tenth and explain your answer
Answers
Volume of the cone is 13.1
Volume of the cylinder is 18.9
Now, you just subtract two of the flat circular surfaces, because the two shapes are attached, therefore those parts are not surface area. And there is your answer.
Write the expression to find the surface area
sa = lateral side of cone + lateral side of cylinder + circle
sa = (π × r × s) + (2 × π × r × t) + (π × r²)
Input the numbers
sa = (π × 1 × 3) + (2 × π × 1 × 2) + (π × 1²)
sa = 3π + 4π + π
sa = 8π
sa = 8 × 3.14
sa = 25.12
to the nearest tenth
sa = 25.1
The surface area of the composite solid round is 25.1 m²
Find the slope of the line that contains the points named. A(3, 2), B(7, 8)
Answers
[tex]slope= \frac{ y_{1} - y_{2} }{ x_{1} - x_{2} } [/tex]
Plug in the data we know.
[tex]slope= \frac{ y_{1} - y_{2} }{ x_{1} - x_{2} } = \frac{2-8}{3-7} = \frac{-6}{-4}= \frac{6}{4} = 1.5 [/tex]
Answer:
3/2
Step-by-step explanation:
To find the slope of the line that contains the points A(3, 2) and B(7, 8), we can use the formula for slope:
slope = (change in y) / (change in x)
Let's calculate the values:
Change in y = 8 - 2 = 6
Change in x = 7 - 3 = 4
Now, we can find the slope:
slope = 6 / 4 = 3/2
Therefore, the slope of the line that contains the points A(3, 2) and B(7, 8) is 3/2.
What happens when year on year percent change goes below 0%?
Answers
Suppose that you invest 5873 in an account that earns an interest rate of 4.4% compounded monthly determine the accumulated balance after 7 years
Answers
interest rate, i = 4.4%/12 = 0.044/12 per month
Number of periods, n = 7*12 = 84 months.
Future value
[tex]F=P(1+i)^n[/tex]
[tex]=5873(1+0.044/12)^{84}[/tex]
[tex]=7986.90[/tex] to the nearest cent
(Will give Brainliest/5 stars for correct answer)
Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.
B = 46°, a = 12, b = 11
A) A = 38.3°, C = 95.7°, c = 8; A = 141.7°, C = 84.3°, c = 8
B) A = 51.7°, C = 82.3°, c = 8; A = 128.3°, C = 5.7°, c = 8
C) A = 38.3°, C = 95.7°, c = 15.2; A = 141.7°, C = 84.3°, c = 15.2
D) A = 51.7°, C = 82.3°, c = 15.2; A = 128.3°, C = 5.7°, c = 1.5
Answers
The part of interest is the law of sines tells you
.. A = arcsin((12/11)*sin(46°)) = 51.7° . . . or . . . 180°-51.7° = 128.3°
.. c = 11*sin(82.3°)/sin(46°) ≈ 15.2 . . . or . . . sin(5.7°)/sin(46°) ≈ 1.5
Selection D is appropriate.
What are 3 consecutive integers that have a sum of 234?
Answers
1. three consecutive integers are: x, x+1 and x+2, the sum is 234.
Equation x+x+1+x+2=234; ⇔ x=77.
2. x=77, x+1=78; x+2=79.
Answer: 77,78,79.
help me plssssssssssssssssssssssssssssssssssssssss
Answers
Let
x = gallons of water to be added
For the 10% solution we have:
0.1 * 8 = 0.8
Then, for 5% we have:
(0.8 / x + 8) = 0.05
Rewriting:
(0.8 / x + 8) = (5/100)
Answer:
An equation can be used to find x, the humber of gallons of water he should add is:
(0.8 / x + 8) = (5/100)
The Symmetric Property of Congruence allows you to say that if ∠LMN ≅ ∠NSP, then ∠NSP ≅ _____.
Answers
The Symmetric Property of Congruence states that If angle A is equivalent to angle B then the angle B will also be equivalent to angle A .
In the problem it is given that ∠LMN ≅ ∠NSP
So, as per the Symmetric Property of Congruence ∠NSP ≅ ∠LMP
The Symmetric Property of Congruence allows you to say that if ∠LMN ≅ ∠NSP, then ∠NSP ≅ ∠LMN.
Hope this helps..!!
Thank you :)
The correct completion of the statement using the Symmetric Property of Congruence is: If [tex]\( \angle LMN \cong \angle NSP \)[/tex], then [tex]\( \angle NSP \cong \angle LMN \)[/tex].
The Symmetric Property of Congruence states that if two angles are congruent, then the second angle is also congruent to the first. In other words, the order in which the angles are listed does not affect the congruence. Therefore, if [tex]\( \angle LMN \)[/tex] is congruent to [tex]\( \angle NSP \)[/tex], it follows that[tex]\( \angle NSP \)[/tex] is congruent to [tex]\( \angle LMN \)[/tex]. This property is a fundamental aspect of geometry that allows us to reverse the order of the angles in a congruence statement without changing the meaning of the statement.
The tax revenue that a small city receives increases by 3.5% per year. in 1990, the city received $250,000 in tax revenue. Determine the tax revenue in 1995 and in 2006.
Answers
1995: $296,921.58
2006: $433,496.51
To find the tax revenue in 1995 and 2006 for a city with an annual increase of 3.5%, we use the formula for exponential growth. The revenue in 1995 is calculated to be $296,923, and for 2006, it is calculated to be $438,995.
Explanation:The tax revenue that a small city receives increases by 3.5% per year. To calculate the tax revenue for the years 1995 and 2006, we can use the formula for exponential growth: Final Amount = Initial Amount * (1 + Growth Rate)Number of Years.
For 1995, which is 5 years after 1990, the calculation would be:
Revenue in 1995 = $250,000 * (1 + 0.035)5
Revenue in 1995 = $250,000 * (1.035)5
Revenue in 1995 = $250,000 * 1.18769
Revenue in 1995 = $296,923
Similarly, for 2006, which is 16 years after 1990, the calculation would be:
Revenue in 2006 = $250,000 * (1 + 0.035)16
Revenue in 2006 = $250,000 * (1.035)16
Revenue in 2006 = $250,000 * 1.75598
Revenue in 2006 = $438,995
Find the length of the chord of a circle of radius 100 feet subtended by an angle of 75◦ ?
Answers
Chord lenght=2rSin(A/2)
2. Let's convert the angle from degrees to radians:
75°π/180°=5π/12
3. So, you have:
r: It is the radius of the circle (r=100 feet).
Sin: It is the sine function.
A: It is the angle subtended at the center by the chord (A=5π/12).
4. When you substitute these values into the formula (Chord lenght=2rSin(A/2)), you obtain the chord lenght:
Chord lenght=2rSin(A/2)
Chord lenght=2(200 feet)(Sin(5π/12/2))
5. Therefore lenght of the chord is:
Chord lenght=18.2706 feet
6 + w = -8. What is w?
Answers
w = -14
Happy to help and just let me know if ya need extra help.
~Brooke❤️
The answer would w = -14 because you take -8 and switch the sign to positive +8 and add 6, so 8 + 6 = 14 then you take 14 and make it a negative number and putting it in the place of w, therefore 6 + (-14) = -8
At southern states university (ssu) there are 399 students taking finite mathematics or statistics. 238 are taking finite mathematics, 184 are taking statistics, and 23 are taking both finite mathematics and statistics. how many are taking finite mathematics but not statistics?
Answers
We know that a total of 238 students are taking finite mathematics; this includes the 23 that are taking both. We subtract these to calculate just finite mathematics:
238 - 23 = 215 taking just finite mathematics.
37.5 x 10 to the negative 6 in scientific notation?
Answers
Eloise is investing in a retirement account. She plans on adding an additional $50 at the end of every year and the expected monthly rate of return is 3% of the amount invested, calculated at the end of the month. If she starts with $1000 in the account find an equation that models the amount of money in the account each month for the first year.
Answers
F=P(1+i)^n
where
P=amount of deposit (made at the beginning of the first period)
i=monthly interest, APR/12 = 3%/12 =0.0025
n=number of periods (month)
For example, the future value for the 6th month is
F(6)=1000(1.0025^6)=1015.09 (to the nearest cent)
Here is a schedule of the values,
i=month
F(i) = value at the end of month i.
i F(i)
0 1000.0
1 1002.5
2 1005.01
3 1007.52
4 1010.04
5 1012.56
6 1015.09
7 1017.63
8 1020.18
9 1022.73
10 1025.28
11 1027.85
12 1030.42 + $50 deposit = 1050.42
All values are rounded to the nearest cent.
The simplified answer is y = 1000(1.03)x.
use the proportion to convert millimeters to centimeters. 10mm/1cm=47mm/x
Answers
- 1 centimeter=10 milimeters.
- The milimeter is defined as a unit of lenght and its symbol is "mm".
1. If you want to convert 47 milimeters to centimeters by using proportions, you have:
10 mm/1 cm=47mm/x
2. Then, you only have to clear the "x":
(10 mm)x=(47mm)(1 cm)
x=(47 mm)(1 cm)/10 mm
3. Therefore, the result is:
x=4.7 centimeters
solve for y: when 3x + 2x+3y =180
Answers
that's your answer!
Can someone please answers these questions
Answers
1) rule for n-angle is: S=180°(n-2), where n - number of the sides. S₁₅=180*13=2340°;
2) S₂₅=180*23=4140°;
4) this is deltoid;
5) this is paralelogram;
6) x=130°; y=50°;
10) x=90°; y=30° (it is deltoid);
12) not enough info for parallelogram (the same for deltoid);
14) it is enough: according to a property of a parallelogram (it means that a square and rombus are parallelograms);
15) it is enough according to the properties of parallelograms;
16) x=2; y=1;
18) poit S(0;0); point T(b+c;d). The coordinates of the midpoint are (0.5b+0.5c;0.5d); slope=arctg(d/(b+c)).
Write a function numberofpennies() that returns the total number of pennies given a number of dollars and (optionally) a number of pennies. ex: 5 dollars and 6 pennies returns 506.
Answers
The general idea should be the same. Since 1 dollar = 100 pennies, we should write something like...
Java:
public static double numberofpennies(double dollars, double penny) {
double sum = 0;
// The amount of pennies that dollar represents
double converted = dollars * 100.0;
sum = converted + penny;
return sum;
}
Note: You should probably place this question under the category computer and technology instead of math. Also, this is just an example of what you could possibly write. What parameters you are allowed to use, what type (double? int? etc?) of pennies are you allowed to return, etc. depends on how you write it.
The numberofpennies() function calculates the total number of pennies by converting dollars to pennies and adding any additional pennies. It multiplies the number of dollars by 100 and adds the extra pennies to find the total.
Explanation:Function to Calculate Total Number of Pennies
The function numberofpennies() is used to calculate the total number of pennies for a given amount of dollars and optionally, additional pennies. To do this, it converts the dollars into pennies and then adds the additional pennies if they are provided.
Example Function in Python
Here is an example of how one might write the numberofpennies() function in Python:
def numberofpennies(dollars, extra_pennies=0):return (dollars * 100) + extra_pennies
# Example usage:
total_pennies = numberofpennies(5, 6)
print(total_pennies) # This would print 506
In this example, the function takes two arguments: dollars, which is a mandatory argument representing the number of dollars, and extra_pennies, which is an optional argument representing additional pennies. The function then returns the total number of pennies by multiplying the number of dollars by 100 and then adding the extra pennies if any.
what values of x make the two expressions below equal? (x+3)(x+8)/5(x+8) = x+3/5
a. all real numbers except -8
b. all real numbers except -3
c. all real numbers
d. all real numbers except -8 and -3
Answers
[tex] \frac{(x+3)(x+8)}{5(x+8)} = \frac{x+3}{5}[/tex]
I will asume that second exressin is [tex]\frac{(x+3)}{5}[/tex]. Then the answer would be all number, because those two expressions are identical.
If we look at the expression you wrote in the question [tex]x+3/5[/tex], you can see that there are no numbers for which these two would be equal.
So the final answer is C.
Chapter 5 lesson 5.1 2nd grade
Answers
Answer:
What is the question?yea
Step-by-step explanation:
Your friend asks you to help him with his snow shoveling business and will pay you 3 3 pennies for the first job. You agree to help if he triples your payment for each job completed. After 2 2 shoveling jobs, you will receive 9 9 pennies, and after 3 3 shoveling jobs, you will receive 27 27 pennies. What is the exponent?
Answers
This is how it would look
3^1 (the "^" means 'to the power of')
3^2
3^3
3^1= 3
3^2=9
3^3=27