sylvie finds the solution by graphing y=2/3x+1 and y=-2/3x-1
which graph shows the solution to sylvies system of equations?
we have
[tex] y=\frac{2}{3} x+1 [/tex] ----------> equation [tex] 1 [/tex]
[tex] y=-\frac{2}{3} x-1 [/tex] ----------> equation [tex] 2 [/tex]
using a graph tool
we know that
the intersection point of both lines is the solution of the system
so
the solution is the point [tex] (-1.5,0) [/tex]
see the attached figure
therefore
the answer is
The solution of the system is the point [tex] (-1.5,0) [/tex]
The graph in the attached figure
How do you write 1/5 as a percentage and a decimal?
1. Solve for x. Show your work.
2x-1/2=3-x
39/4 as a mixed number
Answer is provided in the image attached.
A building has a ramp to its front doors to accommodate the handicapped. If the distance from the building to the end of the ramp is 17 feet and the height from the ground to the front doors is 7 feet, how long is the ramp? (Round to the nearest tenth.)
Answer:
18.4 ft
Step-by-step explanation:
Use Pythagorean Theorem: a^2+b^2=c^2
17^2+7^2=c^2
sqrt 338=sqrt c^2
(sqrt and power 2 cancel)
sqrt 338=c
sqrt 338= 18.4 ft
Which of the following is a polynomial with roots 4,6, and -7?
Answer:
P(x)= x³ - 3 x² - 46 x +168
Step-by-step explanation:
given roots of the polynomial are given as (4,6, -7)
hence the polynomial will be equal to
P(x) = (x-4) (x-6) (x+7)
P(x) = (x-4) (x²+7 x -6 x -42)
P(x) = (x-4) (x²+x -42)
P(x) = x³ + x²-42 x -4 x² -4 x +168
P(x) = x³ - 3 x² - 46 x +168
hence, the required polynomial is P(x) = x³ - 3 x² - 46 x +168
a rectangle has a width that is 7 centimeters less than its length, and it's area is 330 square centimeters. what are the dimensions?
length = _____ centimeters
width = _____ centimeters
Answer:
A rectangle has a width that is 7 centimeters less than its length, and its area is 330 square centimeters. What are the dimensions of the rectangle?
length =
22
centimeters
width =
15
centimeters
24 is what percent of 32?
write the proportion too please! ...?
Tickets for a school play cost $7 and $10 for the adults. The equation 7x+10y=80 represents the number of students(x) and the number of adults(y) who can attend the play for $80. If no students attend, how many adults can see the play for $80?
If no students attend the play, then 8 adults can see the play for $80.
Explanation:The subject of this question is Mathematics, specifically linear equations. The scenario presented involves ticket sales for a school play with different ticket prices for students and adults. $7 is the price for a student ticket and $10 is for an adult ticket. The given equation 7x+10y=80 represents the total sum of $80 that needs to be reached with a combination of student tickets (x) and adult tickets (y).
If no students attend, x in the equation is 0, so we have 10y = 80. To find the number of adults (y) that can attend the play for $80, we need to solve this equation for y. So, y = 80 / 10. Therefore, y = 8, meaning 8 adults can attend the play for $80 when no students attend.
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If a die is rolled 1 time find the probability of getting a number less than 6
The angle of depression from the top of a 150 m high cliff to a boat at sea is 7 degrees. How much closer to the cliff must the boat move for the angle of depression to become 19 degrees ...?
(4n^2 3n) (2n^3-4) (3n^2-2n) ?
Which number is a solution of the inequality?
y>1.9
(A) -9
(B) -2
(C) 2
(D) 1.9
The correct option is option C that is the solution of the inequality is 2.
What are inequalities ?
When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.
It is given that an inequality is given y > 1.9. Here , y is a number which can be anything greater than 1.9.
Let's check which of the given options is a solution for the given inequality.
A)
-9 is a negative number whereas 1.9 is a positive number , so - 9 is not a solution to given inequality.
B)
-2 is also less than 1.9 , so this also not a solution to given inequality.
C)
2 is greater than 1.9 and it is a suitable solution to the given inequality. So , 2 is a solution of given inequality.
D)
As per the question value of y should be greater than 1.9 and not equal to 1.9 . So , this is also not a solution to given inequality.
Therefore , the correct option is option C that is the solution of the inequality is 2.
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The quotient of a number and - 2/3 is -9/10.
What is the number?
1 7/10
3/5
20/27
29/30
Answer:
3/5
Step-by-step explanation:
i am doing the same thing right now and got it right
An unconditional acceptance into a graduate program at a university will be given to students whose GMAT score plus 400 times the undergraduate grade point average is at least 1800. Robbin's GMAT score was 800. What must her grade point average be in order to be unconditionally accepted into the program?
Robbin needs a GPA of at least 2.5 to be unconditionally accepted into the graduate program.
To determine the undergraduate grade point average (GPA) Robbin must have to be unconditionally accepted into the program, we can set up an equation based on the information given. The criterion for acceptance is that the GMAT score plus 400 times the GPA must be at least 1800. Robbin's GMAT score is 800, so we can use the following equation:
800 + 400(GPA) ≥ 1800
We can then isolate the GPA:
400(GPA) ≥ 1800 - 800
400(GPA) ≥ 1000
GPA ≥ 1000 / 400
GPA ≥ 2.5
What is 1 third of 48?
Explain why the vertical line test is used to determine if a graph represents a function.
PLEASE HELP ANYTHING WILL HELP!!!!!!!!!!!!
When a vertical line passes through the graph of a function, it will intersect the graph at only one point. More than one point on any given vertical line means that the same x is being paired with 2 different y's and that make the graph not a function.
Please rate and thank : )
And btw copying and pasting is plagiarism
Which best describes the meaning of the term theorem? A.A statement that is easily deduced from a proven theorem B.A conclusion proved by deductive reasoning C.A conjecture based on inductive reasoning D.A statement explaining the meaning of a geometric term
HELPPP!!
Find the dimensions of a box with a square base with
(a) volume 12 and the minimal surface area
(b) surface area 20 and minimal volume ...?
The dimensions of the box for minimal surface area when volume is 12 are both the cube root of 3. When surface area is 20 for minimal volume, the dimensions are sqrt(5) for the base and (15 / (4*sqrt(5))) for the height.
Explanation:The concept in this problem is about minimizing surface area and volume with relation to the dimensions of a box.
Let's consider a box with a square base of side 'x' and height 'h'. For part (a), the volume V of a box is given by V = x^2 * h which implies h = V / (x^2).
Substituting V = 12, we get h = 12/x^2. The surface area S of a box is given by S = x^2 + 4xh.
Substituting the value of h in the surface area equation, we have S = x^2 + 48/x.
To find the minimum surface area, we differentiate the above with respect to 'x' and set it equal to 0, which gives the dimensions of the box to be x = h = cube root of 3.
For part (b), the surface area S is given to be 20. So, S = x^2 + 4xh implies 4xh = 20 - x^2. The volume of the box is V = x^2 * h = (20 - x^2) / 4.
To minimize the volume, we differentiate V with respect to 'x' and set it to 0. That gives us the value of 'x' to be sqrt(5), and 'h' to be (20 - 5) / (4*sqrt(5))
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Simplify the expression.
4 × 22 + 4 ÷ 4 - (1 + 4)
A. 12
B. 22
C. 20
D. 15
In quadrilateral ABCD, diagonals AC and BD bisect one another:
What statement is used to prove that quadrilateral ABCD is a parallelogram?
Angles ABC and BCD are congruent.
Sides AB and BC are congruent.
Triangles BPA and DPC are congruent.
Triangles BCP and CDP are congruent.
Answer:
(C) Triangles BPA and DPC are congruent.
Step-by-step explanation:
It is given that In quadrilateral ABCD, diagonals AC and BD bisect one another.
We have to prove that quadrilateral ABCD is a parallelogram.
(A) The given statement is:
Angles ABC and BCD are congruent
The above statement is not correct because these angles forms the corresponding angle pair and thus are not congruent.
Hence, this option is not correct.
(B) The given statement is:
Sides AB and BC are congruent.
The above statement is not correct because the given sides are formed by the same vertex and thus cannot be equal.
Hence, this option is not correct.
(C) The given statement is:
Triangles BPA and DPC are congruent.
The above statement is correct because the given triangles are congruent by the SAS rule of congruency.
Hence, this option is correct.
(D) The given statement is:
Triangles BCP and CDP are congruent.
the above statement is not correct because the given triangles cannot be congruent using any rule of congruency,
Hence, this option is not correct.
Check answer please, will upvote!
Evaluate the function rule for the given value.
y = 4 • 2x for x = –6
Is it -48?
Hey there!
[tex]\bold{y=4\bullet2x;x=-6}[/tex]If we found the value of "[tex]\bold{x}[/tex]" then plug it into the equation[tex]\bold{y=4\times2(-6)}[/tex][tex]\bold{2\times(-6)=-12}[/tex][tex]\bold{4\times-12=-48}[/tex][tex]\bold{-48=-48}[/tex] [tex]\checkmark[/tex][tex]\boxed{\boxed{\bold{Answer:Yes}}}[/tex]Good luck on your assignment and enjoy your day!
~[tex]\frak{LoveYourselfFirst:)}[/tex]
f(x)=128(0.5)^x
(0, 1)
(1, 64)
(3, 16)
(8, 0.5)
How many window coverings are necessary to span 50 windows if each window covering is 15 windows long?
To find out how many 15-window coverings are needed for 50 windows, divide 50 by 15, which gives approximately 3.33. Rounding up because we can't have partial window coverings, we will need 4 coverings.
Explanation:The question asks: How many window coverings are necessary to span 50 windows if each window covering is 15 windows long?
To answer this question, we can do a simple division. We divide the total number of windows (50) by the length of each window covering (15).
So, we have 50 ÷ 15 which equals approximately 3.33. However, since we cannot have a fraction of a window covering, we need to round this number up. Therefore, we would need 4 window coverings to span 50 windows.
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lim h--> 0
(sin (pi/6+h) - sin pi/6)/ h ...?
The limit does not exist for this expression.
To evaluate the limit as h approaches 0 of (sin(pi/6 + h) - sin(pi/6))/h, we can use the limit definition of the derivative of sin(x).
The derivative of sin(x) is cos(x), so we can rewrite the expression as:
lim h->0 (cos(pi/6 + h) - cos(pi/6))/h
Now, we can use the limit definition of the derivative to evaluate this limit. The derivative of cos(x) is -sin(x), so we have:
lim h->0 (-sin(pi/6 + h))/h
Now, let's substitute h = 0 into the expression:
(-sin(pi/6 + 0))/0
Since sin(pi/6) = 1/2, we have:
(-1/2)/0
However, division by zero is undefined. Therefore, the limit does not exist for this expression.
Numbers 1 - 10 are written on cards and placed in a bag. Find the probability of choosing a number greater than 5 or choosing an odd number. ...?
The probability of selecting a card greater than 5 or an odd number from a bag of cards numbered 1 to 10 is 0.8 or 80%.
Explanation:The question asks for the probability of choosing a number greater than 5 or an odd number from a bag containing numbered cards from 1 to 10. To solve this, we should consider that numbers greater than 5 are 6, 7, 8, 9, and 10. There are 5 odd numbers in the set: 1, 3, 5, 7, and 9. The number 7 and 9 are both greater than 5 and odd, so they are counted only once when combining the two groups.
First, let's count the total unique outcomes that either meet the criterion of being greater than 5 or being odd: 6, 7, 8, 9, 10, 1, 3, 5 (7 and 9 are already counted). There are 8 such numbers.
The total number of possible outcomes is 10, as there are 10 cards. The probability is the number of favorable outcomes divided by the total number of possible outcomes: P = favorable outcomes / total outcomes = 8/10 = 0.8 or 80%.
Suppose a car manufacturer believes its windscreen wipers will last on average for three years on their cars if driven by a typical driver in the province. Moreover, the manufacturer believes the lifetime of the wipers under such conditions is Normally distributed with a standard deviation of two years. Find the probability that, if on a car driven by a typical driver, a windscreen wiper lasts for a time that is not within 1.7 years of the mean lifetime.
The probability is:?
To calculate the probability that a windscreen wiper lasts for a time not within 1.7 years of the mean, one must find the corresponding z-scores and use a standard normal distribution table. The probability is approximately 39.58%.
Explanation:To find the probability that a windscreen wiper lasts for a time that is not within 1.7 years of the mean lifetime of three years, we can use the properties of the normal distribution. We are given a mean (μ) of 3 years and a standard deviation (σ) of 2 years. We are interested in the probability that a wiper lasts less than 1.3 years (3 - 1.7) or more than 4.7 years (3 + 1.7).
First, we need to calculate the z-scores for 1.3 and 4.7 years:
Z1 = (1.3 - 3) / 2 = -0.85
Z2 = (4.7 - 3) / 2 = 0.85
Using a standard normal distribution table or a calculator, we find the probabilities corresponding to these z-scores. The probability of a wiper lasting less than 1.3 years is P(Z < -0.85), and the probability of lasting more than 4.7 years is P(Z > 0.85).
Since the normal distribution is symmetric, P(Z < -0.85) is equal to P(Z > 0.85). Thus, we only need to calculate one of these probabilities and double it to find the total probability. Let's say P(Z > 0.85) = p, then the total probability is 2p.
Assuming P(Z > 0.85) = 0.1979 (from standard normal distribution tables), the total probability is:
Probability = 2 * 0.1979 = 0.3958
Therefore, the probability that a windscreen wiper lasts for a time not within 1.7 years of the mean lifetime is approximately 0.3958 or 39.58%.
Final answer:
By standardizing the values and using a standard normal distribution table, we can find the probability to be approximately 0.7422 or 74.22%.
Explanation:
To solve this problem, we can use the normal distribution. Given that the mean lifetime of the windscreen wipers is 3 years with a standard deviation of 2 years, we want to find the probability that the wiper lasts for a time that is not within 1.7 years of the mean lifetime.
First, we need to standardize the values by calculating the z-scores.
The z-score formula is (x - mean) / standard deviation. In this case, we have x = 1.7, mean = 3, and standard deviation = 2.
Plugging in these values, we get a z-score of -0.65.
Using a standard normal distribution table or calculator, we can find the probability corresponding to a z-score of -0.65.
The area under the curve to the left of -0.65 is approximately 0.2578. Since we want the probability that the wiper lasts for a time that is not within 1.7 years of the mean, we subtract this probability from 1.
Therefore, the probability is approximately 1 - 0.2578 = 0.7422, or 74.22%.
Benton has an extension ladder than can only be used at a length of 10 feet, 15 feet, or 20 feet. He places the base of the ladder 6 feet from the wall and needs the top of the ladder to reach 8 feet.
Which ladder length would Benton need to use to reach this height on the wall?
A. 10 feet
B. 15 feet
C. None of these ladder lengths would reach this height.
Final answer:
To reach a height of 8 feet on the wall, Benton would need to use a ladder length of approximately 4.8 feet.
Explanation:
To determine which ladder length Benton would need to use to reach the desired height of 8 feet on the wall, we can use the concept of similar triangles. The distance from the base of the ladder to the wall is 6 feet and the height Benton wants to reach on the wall is 8 feet. Let x represent the length of the ladder needed. Using the properties of similar triangles, we can set up the following proportion:
(x)/(6) = (8)/(10)
Cross multiplying gives us:
x = (6 * 8) / 10 = 4.8
Therefore, Benton would need to use a ladder length of approximately 4.8 feet to reach a height of 8 feet on the wall. Since this length is not among the options provided, the correct answer is C. None of these ladder lengths would reach this height.
Determine whether the sequence:
ln(2n^2 +1) - ln(n^2 +1)
converges or diverges. If the sequence converges, find the limit.
Final answer:
The sequence ln(2n² +1) - ln(n² +1) simplifies to ln[(2n² + 1)/(n² + 1)]. As n approaches infinity, the sequence converges and the limit is ln(2).
Explanation:
To determine whether the sequence ln(2n² +1) - ln(n² +1) converges or diverges, we can use the properties of logarithms and limits.
First, we rewrite the expression using the property of logarithms that ln(a) - ln(b) = ln(a/b).
Our sequence then becomes ln[(2n² + 1)/(n² + 1)]
As n approaches infinity, the terms 2n² and n² dominate the behavior of the sequence.
Thus, the sequence can be approximated by ln(2n²/n²), which simplifies to ln(2).
Since ln(2) is a constant, we can conclude that the sequence converges and the limit is ln(2).
The soccer team voted on what they wanted to eat. there are 20 members on the team. six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs. which ratio represents the number of votes for hot dogs to chicken
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
The ratio is hot dogs to chicken the chicken isten tho to find the hot dogs first you do
10+6=16
So it says 20 members so then you needa see how much would equal the amont 20 obviously 4 so the hot dogs equal to 4 so the ratio is 4:10
Answer:
2/5
Step-by-step explanation:
just did it and it is correct