A line parallel to the line 4x + 7y = 49 - 2x + 4y must have a slope of - 2.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given a line that is 4x + 7y = 49 - 2x + 4y.
7y - 4y = - 2x - 4x + 49.
3y = - 6x + 49.
y = - 2x + 49/3.
Now, lines parallel to each other have the same slope.
Now if we simply the given options none of the lines have a slope of - 2 so none of the given lines are parallel to the line 4x + 7y = 49 - 2x + 4y.
learn more about lines and slopes here :
https://brainly.com/question/3605446
#SPJ1
write an equation of the line perpendicular to -4x+3y=12 and containing the point (6,8)
The equation of the line perpendicular to - 4x + 3y = 12 and containing the point (6,8) is 3x + 4y = 50.
What is a perpendicular line?
Perpendicular lines: A perpendicular line is a straight line that has been put up so that it forms a right angle with another line. The two lines are parallel to one another.
Here,
The slope of ax + by = c is given by m = -a/b
m = -(-4)/3 = 4/3
m = 4/3 for this line.
A perpendicular line will have a slope -1/m = -3/4
The line through (6, 8) with slope -3/4
y = (-3/4)x + b
8 = (-3/4)(6) + b
b = 8 + 9/2 = 25/2
y = (-3/4)x + 25/2
4y = -3x + 50
3x + 4y = 50
Hence, the equation of the line perpendicular to -4x+3y=12 and containing the point (6,8) is 3x+4y = 50.
To learn more about the perpendicular line from the given link
https://brainly.com/question/28028690
#SPJ13
Please help!! 10 points
Answer:
y = - 2x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (4, - 4) ← 2 points on the line
m = [tex]\frac{-4-2}{4-1}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = - 2x + 4 ← equation of line
An expression is shown.
4x+2(9−3x)
Select all that are equivalent to the given expression.
-18x+54
-2(x-9)
-18(x-3)
10x+18
2(5x+9)
-2x+18
Answer:
-2x+18, and -2(x-9)
Step-by-step explanation:
4x+18-6x
4x-6x+18
-2x+18
-2(x-9)
-2x+18
Please help me really fast
The equation of line parallel to the given line is found as y = -6x + 13.
What is meaning of the term parallel slopes?A line's slope is similar to the slopes of adjacent parallel lines, therefore m1 = m2. Additionally, the equations of a parallel line could be determined by applying the formulas; (y−y1)=m(x−x1) ( y − y 1 or by y = mx + c.The equation of the line is-
y = -6x + 1
The second line is parallel to the above line, thus the slopes of both the line are equal.
m1 = m2 = -6
The new line also passes from the point (1, 7)
(x1, y1) = (1,7)
Thus, the equation of the line will be calculated as-
y - y 1 = m2(x - x1)
y - 7 = -6(x - 1)
y - 7 = -6x + 6
y = -6x + 13
Thus, the equation of line parallel to the given line is found as y = -6x + 13.
To know more about the parallel slopes, here
https://brainly.com/question/28427398
#SPJ1
which of the following quantitative research methods uses a relatively small group of people for testing and is most helpful in obtaining data that are representative of the whole population? a.) in-depth interviews b.) secondary data analysis c.) natural experiments d.) random sampling
In-depth interviews are a quantitative research method that uses a relatively small group of people for testing and is most helpful in obtaining data representative of the whole population. The correct option to this question is A.
Although you can use all of these techniques in your comprehensive customer experience management strategy, in-depth interviews can help you gather the information that can give you rich insights into the experiences and preferences of a large sample of your target audience.
An extensive amount of data can be gathered on the behavior, attitude, and perspective of the interviewers through in-depth interviews, a qualitative data collection technique.
Researchers and subjects are free to explore additional topics and alter the course of the interview when necessary during in-depth interviews. It is an independent research methodology that can use a variety of approaches depending on the needs of the study.
For more information on quantitative research methods kindly visit to
https://brainly.com/question/29242901
#SPJ4
Write the equation of the line that passes through the points (8, –1) and (2, –5) in standard form, given that the point-slope form is y + 1 = (x – 8).
x +
y
The equation in standard form is x - y = 9
How to determine the equation in standard form?From the question, we have the following parameters that can be used in our computation:
Points = (8, –1) and (2, –5)
Point-slope form is y + 1 = (x – 8).
Recall that the point-slope form is y + 1 = (x – 8).
So, we have
y + 1 = (x – 8)
Open the brackets
y + 1 = x – 8
Subtract 1 from both sides
y = x - 9
Rewrite as
-x + y = -9
Multiply through by -1
x - y = 9
Hence, the equation is x - y = 9
Read more about linear equations at
https://brainly.com/question/2030026
#SPJ1
Write each ratio as a fraction in simplest form.
11 1/3 out of 50 2/3
Answer:
[tex]\frac{17}{76}[/tex]
Step-by-step explanation:
expressing the ratio in fractional form
[tex]\frac{11\frac{1}{3} }{50\frac{2}{3} }[/tex] ← change mixed number to improper fractions
= [tex]\frac{\frac{34}{3} }{\frac{152}{3} }[/tex] ( multiply numerator and denominator by 3 )
= [tex]\frac{34}{152}[/tex] ( divide numerator and denominator by 2 )
= [tex]\frac{17}{76}[/tex] ← in simplest form
consider the mad statistic. what would happen if you did not take absolute values before calculating the sum of differences between group means? why would this not be a useful calculation without taking absolute values?
This type of calculation will not give the accurate values and hence, it is not useful to do calculation without taking absolute values.
We are asked that, what would happen if you did not take absolute values before calculating the sum of differences between group means.
As, when we calculate the differences between group means then, some of the values may be negative.
When we add those negative values while evaluating the sum then the sum can be less than the absolute and to get over from this type of problem we always take absolute values of the differences between group means and then get the sum.
Also, this type of calculation will not give the accurate values and hence, it is not useful to do calculation without taking absolute values.
Hence, this type of calculation will not give the accurate values and hence, it is not useful to do calculation without taking absolute values.
Learn more about Statistics here https://brainly.com/question/15525560
#SPJ4
What Two numbers multiply to get 20 and add to get 17?
Step-by-step explanation:
x + y = 17
x = 17 - y
xy = 20
(17 - y)y = 20
-y² + 17y = 20
-y² + 17y - 20 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
y = (-17 ± sqrt(17² - 4×-1×-20))/(2×-1) =
= (-17 ± sqrt(289 - 80))/-2 =
= (-17 ± sqrt(209))/-2
y1 = (-17 + sqrt(209))/-2 = 1.271583853...
y2 = (-17 - sqrt(209))/-2 = 15.72841615...
the 2 numbers are
1.271583853...
15.72841615...
eight people are sitting around a circular table, each holding a fair coin. all eight people flip their coins and those who flip heads stand while those who flip tails remain seated. what is the probability that no two adjacent people will stand?
The probability that no two adjacent people will stand is 47/256. This is a problem that represents a combination.
What is combination?A combination is a grouping of items where order does not matter. The formula of combination is
[tex]_{n}C_{r} = \frac{n!} {r! (n-r)!}[/tex]
Where
C = number of combinationsn = number of total itemsr = number of choosing itemsGiven the case eight people sit around a circular table, flip coins, and those who flip heads will stand while those who flip tails will remain seated.
What is the probability that no two adjacent people will stand?
First, we count the total standing arrangements. They will be 2⁸ = 256 arrangements. n(S) = 256.
The number of arrangements according to the number of people standing.
Case 1: 0 people standing = 1 arrangement.
Case 2: 1 people standing = [tex]_{8}C_{1}[/tex] = [tex]\frac{8!} {1! 7!}[/tex] = 8 arrangements.
Case3: 2 people standing = [tex]_{8}C_{2}[/tex] = [tex]\frac{8!} {2! 6!}[/tex] = [tex]\frac{7 \times 8} {2}[/tex] = 28 arrangements, but no two people are next to each other. There are 8 arrangements that two people in this case are standing next to each other. So, it will be 28 - 8 = 20 arrangements.
Case 4: 3 people standing = [tex]_{8}C_{3}[/tex] = [tex]\frac{8!} {3! 5!}[/tex] = [tex]\frac{6 \times 7 \times 8} {6}[/tex] = 56 arrangements. In this case, three people standing are next to each other = [tex]_{8}C_{1}[/tex] = 8 arrangements. Two people standing are next to each other and the third person is not = [tex]_{8}C_{1} \times _{4}C_{1}[/tex] = 8 × 4 = 32. So, it will be 56 - 8 - 32 = 16 arrangements.
Case 5: 4 people standing but no two adjacent people = 2 arrangements.
The number of arrangements that no two adjacent people will stand.
n(A) = 1 + 8 + 20 + 16 + 2 = 47
The probability that no two adjacent people will stand is
P(A) = n(A)/n(S)
P(A) = 47/256
Hence, the probability that no two adjacent people will stand is 47/256.
Learn more about finding probability with combination here:
brainly.com/question/3901018
#SPJ4
Write 8433 in scientific notation.
I know the answer but can someone give me an explanation and steps.
Answer:
8.433 to the power of 4
Step-by-step explanation:
The reason is because the nukber written in scientific notation always has to be between 1-10. It can't be 84.33 or 843.3. The number has to be between 1 and 10.
PLEASE HELP
Write the equation of a line that is perpendicular to y = 5 and that passes through the point
(-7, --5).
The equation of the line that is perpendicular to y = 5 and that passes through the point (-7, -5) is x = -7.
We have to find the equation of a line that is perpendicular to y = 5 and that passes through the point (-7, -5).
y = 5 is a line that is parallel to the x-axis hence, the line perpendicular to it will be parallel to the y-axis.
Also, the line touches (-7,-5) hence, it will touch the line y = 5 at (-7,5).
Hence, the line perpendicular to y = 5 and that passes through the point (-7, -5) is x = -7.
To learn more about equation, here:-
https://brainly.com/question/10413253
#SPJ1
5(x - 3) = - 4(x - 2) + 9x
help meeeeeeeeeeeeeee pleaseee
Answer: See the image below for the table and graph
==========================================================
Explanation:
We replace x with the values mentioned. Do so one at a time to compute the corresponding y value.
For instance, if x = -2, then...
[tex]\text{y} = 2\text{x}^2\\\\\text{y} = 2(-2)^2\\\\\text{y} = 2(4)\\\\\text{y} = 8\\\\[/tex]
If x = -2, then y = 8. This produces the point (-2,8) which is on the parabola.
We'll write "8" without quotes into the box next to x = -2, as shown in the table diagram below.
Repeat for x values x = -1 through x = 2.
Once we determine those point coordinates, we then plot said points to form the parabola shown below. The more points, the better accurate picture you'll have of the curve. I used GeoGebra to make the graph and table. Desmos is another good option which I recommend.
If a person spins a six-space spinner and then flips a coin, describe the sample space of possible outcomes using 1, 2, 3, 4, 5, 6 for the spinner outcomes and H, T for the coin outcomes.
The sample space is S={__}
(Use a comma to separate answers as needed.)
Answer:
Step-by-step explanation:
If one spins a six-space spinner and then flips a coin, then the sample space (S) of possible outcomes using (1, 2, 3, 4, 5, 6) for the spinner outcomes and (H, T) for the coin outcomes will be [S = {(1H), (1T), (2H), (2T), (3H), (3T), (4H), (4T), (5H), (5T), (6H), (6T)}]
As per the question statement, a person spins a six-space spinner and then flips a coin,
And we are required to determine the sample space (S) of possible outcomes using (1, 2, 3, 4, 5, 6) for the spinner outcomes and (H, T) for the coin outcomes.
Now, on spinning a six-space spinner, any one of the 6 faces will come as outcomes, and if these outcomes are denoted by (1, 2, 3, 4, 5, 6).
And after spinning the six-space spinner, if one flips a coin, either of "heads" face or "tails" face will come as outcome, which can be denoted by {H, T}.
Therefore, If one spins a six-space spinner and then flips a coin successively as mentioned above, every possible outcome of the spinner will be accompanied by one of two the possible outcomes the coin. Hence, the sample space (S) of possible outcomes will be [S = {(1H), (1T), (2H), (2T), (3H), (3T), (4H), (4T), (5H), (5T), (6H), (6T)}]
To learn more about Outcomes and Samples Spaces, click on the link below.
https://brainly.com/question/16661472
#SPJ1
Q1 Write a quadratic polynomial
, sum of whose zeroes is 3 and product is -40
The quadratic polynomial for the given conditions of zeros is found as x² - 3x + -40 = 0.
Define the term quadratic polynomial?When a variable term as in polynomial expression has a highest power of 2, the polynomial is said to be quadratic. A second-order polynomial is another name for a quadratic polynomial. A quadratic equation or quadratic function is created if a quadratic polynomial becomes equal to 0. The roots or zeros of both the quadratic equation are the name given to the solutions of this equation.For the stated values,
Sum of zeroes is 3 and product is -40
Use formula,
x² - x (sum of zeros) + (product of zeros) = 0.
Put the values.
x² - x (3) + (-40) = 0.
x² - 3x + -40 = 0.
Thus, the quadratic polynomial for the given conditions of zeros is found as x² - 3x + -40 = 0.
To know more about the quadratic polynomial, here
https://brainly.com/question/17489661
#SPJ4
The side lengths of triangle ABC are written in terms of
the variable p, where p > 3.
A
p+4
C
4p-1
3p
B
Which is correct regarding the angles of the triangle?
Om/A> m2C> mzB
OmZB> mzA> mZC
Omzc>m mZB
O mzC> m2B> MZA
m∠C > m∠A > m∠B is correct regarding the angles of the triangle ABC.
What is the angle of the triangle?
While the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it, the interior angles of a triangle always add up to 180°.
Here, we have
In Δ ABC, the side lengths of triangle ABC are written in terms of the variable p, where p ≥ 3.
AB=4p-1 , AC=p+4 , BC=3p
where p+4 < 3p [as p≥3]
3p < 4p-1 [as p≥3]
⇒ 4p-1> 3p > p+4
⇒AB > BC > AC
Angle opposite to AB, BC, and AC is m∠C,m∠A, and m∠B.
m∠C > m∠B > m∠A [∵Angle opposite to greater side is greater]
Hence, mC > mA > m∠B is correct regarding the angles of the triangle ABC.
To learn more about the angles of the triangle from the given link
https://brainly.com/question/20126678
#SPJ13
(100 POINTS) HELP ASAP
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents.
y to the three fourths power, all over y to the one half power
the eighth root of y to the third power
the square root of y to the three fourths power
the fourth root of y
the square root of y
Answer:
[tex]^4\sqrt{2}[/tex]
Answer: Option C
Step-by-step explanation: just took the test.
When nineteen is subtracted
from three time a
number "X", the result is 110. Translate and find
the number.
Answer: x=43
Step-by-step explanation:
3x-19=110
3x-19+19=110+19
3x=129
3x/3=129/3
x=43
When f(x) equals X -7/2, what is the value of (F•F^-1) (3)
The value of [tex]f.f^{-1}(x)[/tex] is 3 from the given function.
The given function is f(x)=x-7/2.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The inverse of the given function is
y=x-7/2
Replace y with x and x with y, we get
x=y-7/2
y=x+7/2
[tex]f^{-1}(x)[/tex]=x+7/2
When x=3
[tex]f^{-1}(3)=3+7/2[/tex]
=6.5
f(6.5)=6.5-7/2
=6.5-3.5
=3
Therefore, the value of [tex]f.f^{-1}(x)[/tex] is 3 from the given function.
To learn more about the function visit:
https://brainly.com/question/28303908.
#SPJ1
Zyndy is twice the age of Vyndel. The sum of their age is twenty-one. Determine their ages.
Pa sagot po pls pasahan na po namin bukas :
Answer:
Zyndy is 14, Vyndel is 7.
Step-by-step explanation:
Let Zyndy's age be represented by 'z', and Vyndel's age be represented by 'v'.
Zyndy is twice the age of Vyndel, so z=2v
The sum of their age is twenty-one, so z+v=21
Sub the first equation above into the second to get:
2v+v=21
3v=21
v=7
Knowing v=7, we can say z=2(v)=14.
What is the perimeter of pentagon ABCDE with the given vertices?
A (4,2)
B(4, 10)
C (7, 10)
D (15, 4)
E (7, - 2)
Answer:
36
Step-by-step explanation:
The perimeter of ABCDE is equal to AB + BC + CD + DE + AE.
AB = 10 - 2 = 8 (The x values of A and B are the same, therefore the distance between them is the difference between their y values.)
BC = 7 - 4 = 3 (The y values of B and C are the same, therefore the distance between them is the difference between their x values.)
CD = [tex]\sqrt{(X_D - X_C)^2 + (Y_D - Y_c)^2} = \sqrt{(15 - 7)^2 + (4 - 10)^2} = \sqrt{8^2 + (-6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10[/tex]
DE = [tex]\sqrt{(X_E - X_D)^2 + (Y_E - Y_D)^2} = \sqrt{(7 - 15)^2 + (-2 - 4)^2} = \sqrt{(-8)^2 + (-6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10[/tex]
AE =
[tex]\sqrt{(X_E - X_A)^2 + (Y_E - Y_A)^2} = \sqrt{(7 - 4)^2 + (-2 - 2)^2} = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5[/tex]
[tex]\Delta \text{ABCDE} = \text{AB} + \text{BC} + \text{CD} + \text{DE} + \text{AE} = 8 + 3 + 10 + 10 + 5 = 36[/tex]
Which statement best analyzes the role this event plays in the plot?
In "The Necklace" Mathilde realizes too late that the necklace is a fake.
The statement that best analyzes the role this event plays in The Necklace plot is A. It leads to the resolution where Mathilde learns (a little too late) a lesson about the downfall that can come from vanity and greed.
How to illustrate the information?There are both planned and unplanned events, and the start and end times may be noted. Event types include accidents, celebrations, natural disasters, and rallies. The event is the occurrence of the event.
Loisel is well-liked and adored by all. As she walks away, she searches for the pendant and discovers it has gone missing. After days of searching, she and her husband decide to replace it with something similar. It takes her ten decades to pay for the successor, which costs the same as your salary.
In this case, it best analyzes the role this event plays in leading to the resolution where Mathilde learns a lesson about the downfall that can come from vanity and greed The plot of The Necklace.
Therefore, the correct option is A.
Learn more about the necklace on:
https://brainly.com/question/18922838
#SPJ1
Complete question
Which statement best analyzes the role this event plays in The Necklace plot?
“Oh, my poor Mathilde! Why, my necklace was paste! It was worth at most only five hundred francs!”
It leads to the resolution where Mathilde learns (a little too late) a lesson about the downfall that can come from vanity and greed.
It is the climax of the story since the reader is most excited at this point.
It serves as a complicating incident because Mathilde will have to suffer the consequences of her actions.
It serves as the falling action because it shows that Mathilde will have to get used to her place in life.
-4 + (-1) - (-3)
Need HELP
Answer: The answer is -2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
-4 + (-1) - (-3) Distribute the + and - since they are outside the parenthesis
-4 - 1 + 3 Subtract 1 to -4
-5 +3 Add 3 to -5
-2
HELP MEEE PLEASEEEE
Answer:
5.8 cm
Step-by-step explanation:
the Pythagorean theorem states that a^2=b^2+c^2, where a is the hypotenuse, and b and c are the legs. Plugging in your values, we get:
4^2 + 4.2^2 = a^2
Simplify: 16 + 17.64=a^2
Simplify again: 33.64 = a^2
Square root both sides: 5.8 = a
According to a report for veterinarians in the united states, 36. 5 percent of households in the united states own dogs and 30. 4 percent of households in the united states own cats. If one household in the united states is selected at random, what is the probability that the selected household will own a dog or a cat?.
The probability of the selected household will own a dog or a cat can't be determined because there is not enough information to determine the probability
How to calculate probility?Probability is counted by dividing the event number with the total number of outcomes. In this case, the probability of the selected household will own a dog or a cat will have a formula like this:
P(A ∨ B)=P(A)+P(B)+P(A ∧ B)
Annotation:
P(A ∨ B) = probability own a dog or a cat
P(A) = probability own a dog
P(B) = probability own a cat
P(A ∧ B) = probability own a dog and a cat.
Based on question, we cant find value of the probability own a dog and a cat. Therefore, the best answer for this question there is not enough information to determine the probability
Learn more about probability https://brainly.com/question/24756209
#SPJ4
60+16=x-16+16 x=? This math book hates me
Answer: 76
Step-by-step explanation: simplify equation
60+16=x-16+16 (cancel out 16 and add 60+16)
76=x
60+16=x-16+16
76=x
x=76
0 . 476 × 10 to the 1st power
Answer:
4.76
Step-by-step explanation:
had this on a test today!
The president of the Huerta Middle School science club suggested a field trip to the local
aquarium. Tickets will cost $21.25 for the club adviser and $14.75 for each student who
goes.
Write an equation showing how the total cost, y, depends on the number of students going,
X.
Do not include dollar signs in the equation.
►
y =
The equation that shows the total cost, depends on the number of students going is y = 21.25 + 14.75x
Equation:
An equation is made up of two expressions connected by an equal sign.
For example, y = 3x + 6 is an equation.
Given,
The president of the Huerta Middle School science club suggested a field trip to the local aquarium. Tickets will cost $21.25 for the club adviser and $14.75 for each student who goes.
Here we need to find the equation that shows the total cost depends on the number of students.
Let us consider x be the number of students and y be the cost for x number of students.
Here we know that, there is one club advisor whose ticket cost is $21.25 and the cost per student is $14.75.
So, based on these details, the equation for the total cost is calculated as,
=> y = 21.25 + 14.75x
To know more about Equation here.
https://brainly.com/question/10413253
#SPJ1
A triangle has vertices A(−1,2)
, B(2,5)
, and C(3,−4)
. If the image resulting from a rotation has vertices A'(−2,−1)
, B'(−5,2)
, and C'(4,3)
, write the rule that describes the rotation:
Answer: [tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]
90 degree counter-clockwise rotation around the origin.
===================================================
Explanation:
Focus on A(-1,2) and A'(-2,-1)
The coordinates of point A have swapped to go from "-1,2" to "2,-1". Then we stick a negative in front of the new x coordinate to get "-2,-1"
In other words, we've gone from (x,y) to (y,x) to (-y,x)
Representing this with arrows looks like:
[tex]\left(\text{x}, \text{y}\right) \to \left(\text{y}, \text{x}\right) \to\left(-\text{y}, \text{x}\right)[/tex]
or in short
[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]
which represents a 90 degree counter-clockwise rotation around the origin.
-----------------------------------
Let's see if this rule works with point B(2,5). We should rotate to B'(-5,2)
[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(2,5\right) \to \left(-5, 2\right)[/tex]
Sure enough, it works for point B.
Lastly, let's check if it works for point C.
We should go from C(3,-4) to C'(4,3).
[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(3,-4\right) \to \left(-(-4), 3\right)\\\\\left(3,-4\right) \to \left(4, 3\right)\\\\[/tex]
All points have been confirmed.
