To find the equation of a line parallel to the given line, we can use the slope of the given line and the point-slope form of a line. The equation of the line parallel to 7−4x=7y and passing through the point (2,0) is y = (7/4)x - (7/2).
Explanation:To find the equation of a line parallel to the given line, we need to find the slope of the given line first. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Rearranging the given equation, we have y = (7/4)x - 1. Dividing the coefficient of x by the coefficient of y, we find that the slope of the given line is 7/4. Since the line we're looking for is parallel to this line, it will also have a slope of 7/4. Now, we can use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point on the line. Substituting in the values (2, 0) and slope (7/4), we can solve for y to find the equation of the line.
Using the point-slope form, we have y - 0 = (7/4)(x - 2). Simplifying, we get y = (7/4)x - (7/2), which is the equation of the line parallel to the given line and passing through the point (2, 0).
Final answer:
The equation of the line parallel to 7 - 4x = 7y through the point (2, 0) is y = (-4/7)x + 8/7.
Explanation:
To find the equation of a line parallel to the line 7 - 4x = 7y, we need to find the slope of the given line. First, rearrange the equation in the form y = mx + b, where m is the slope. So, 7y = 7 - 4x becomes y = (-4/7)x + 1. The slope of this line is -4/7. Since the line we want is parallel, it will have the same slope.
Next, we have the point (2, 0) through which the line passes. To find the equation, we'll use the point-slope form: y - y1 = m(x - x1). Substituting the given values, we have y - 0 = (-4/7)(x - 2). Simplifying, we get y = (-4/7)x + 8/7.
Therefore, the equation of the line parallel to 7 - 4x = 7y through the point (2, 0) is y = (-4/7)x + 8/7.
A line segment that goes from one side of the circle to the other side of the circle and doesn’t go through the center is
Answer:
A line segment that goes from one side of the circle to the other side of the circle and doesn’t go through the center is called chord of the circle.
Step-by-step explanation:
Consider the provided information.
It is given that the line segment goes from one side of the circle to the other side of the circle and doesn’t go through the center.
Diameter: A line segment goes from one side to another side of a circle passes through the center is called the diameter of the circle.
Chord: A line segment goes from one side to another side of a circle but do not passes through the center is called the chord of the circle.
For better understanding refer the attached figure:
Hence, A line segment that goes from one side of the circle to the other side of the circle and doesn’t go through the center is called chord of the circle.
A man divided $9,000 among his wife, son, and daughter. The wife received twice as much as the daughter, and the son received $1,000 more than the daughter. How much did each receive?
If x is the amount the wife received, then which of the following expressions represents the amount received by the son?
Answer:
Step-by-step explanation:
A man divided $9,000 among his wife, son and daughter.
The wife received twice as much as the daughter.
Let the daughter received d amount.
Then the wife received = 2d
and son received $1,000 more than the daughter.
The son received the amount = 1000+d
So the expression will be = d + 2d +(1000+d) = 9,000
3d + (1000+d) = 9000
4d = 9000 - 1000
4d = 8000
d = [tex]\frac{8000}{4}[/tex]
d = 2000
Daughter received $2,000
Wife received 2d = 2 × 2000 = $4,000
Son received 1000 + d = 1000 + 2000 = $3,000
If x is the amount the wife received, then the expression represents the amount received by the son :
S = 1000 + (x/2)
Which statement is true about whether Z and B are independent events?
Z and B are independent events because P(Z∣B) = P(Z).
Z and B are independent events because P(Z∣B) = P(B).
Z and B are not independent events because P(Z∣B) ≠ P(Z).
Z and B are not independent events because P(Z∣B) ≠ P(B).
Answer:
Z and B are independent events because P(Z∣B) = P(Z).
Step-by-step explanation:
Z and B are independent events
When Z and B are independent events then
P(Z and B) = P(Z) * P(B)
P(Z∣B)= [tex]\frac{P(Z and B)}{P(B)}[/tex]
P(Z∣B)= [tex]\frac{P(Z)*P(B)}{P(B)}[/tex]
We cancel out P(B) on both sides
P(Z|B) = P(Z)
You take a three-question true or false quiz. You guess on all the questions. What is the probability that you will get a perfect score?
The sum of a number and -20 is 40.What is the number?
sum means addition
so x +-20 = 40
x = 40 +20 = 60
x=60
Please explain to me 1) the similarities/differences in the two lines, 2) how are the two graphs related to one another, and 3) how do the equations show this relationship for the following:
if BD is the midsegment and BD is parallel to to AE, then value of AE is
28.
56.
112.
None of the choices are correct.
y varies inversely with x k = 0.6 What is the value of x when y is 0.6? A. x = 0.36 B. x = 1 C. x = 3.6 D. x = 10
Answer:
.
Step-by-step explanation:
.
What is the property of 16+31=31
We have the equation here is
16 + 31 = 31
When we simplify the equation to the understandable form, we move all terms or numbers to right and on left side zero will be left.
0 = 31-16-31
We get, 0 = -16
Now we see that both sides of equations are not equal, it means there is no solution so it is an invalid equation.
The value of a car decreases by 20 percent per year. Mr. Sing purchases a $22,000 automobile. What is the value of the car at the end of the second year?
22,000 - 20% = 17,600
17,600 - 20% = 14,080
$14,080 at the end of the second year .
Which of the following is the radical expression of a to the four ninths power
Answer:
[tex]\sqrt[9]{a^{4}}[/tex]
Step-by-step explanation:
To convert a fraction form into a radical form you need to know that the denominator will be the root index and the numerator will be the exponent into the root. For the case of four ninths:
[tex]a^{\frac{4}{9}} = \sqrt[9]{a^{4}} .[/tex]
You have $5. If candy bars cost $0.75, what is the greatest number of candy bars you can buy
A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)= 120t-16t^2 . What is the maximum height that the ball will reach? Do not round
The answer is: 225.
To find the maximum height that the ball will reach, we need to determine the vertex of the parabola described by the function [tex]\( h(t) = 120t - 16t^2 \)[/tex]. The vertex form of a parabola is[tex]\( h(t) = a(t - h)^2 + k \)[/tex], where [tex]\( (h, k) \)[/tex] is the vertex of the parabola. The value of [tex]\( k \)[/tex] will give us the maximum height.
The given function can be rewritten in the form [tex]\( h(t) = -16(t^2 - \frac{120}{16}t) \)[/tex]. To complete the square, we take the coefficient of [tex]\( t \)[/tex], divide it by 2, and square it. This value is then added and subtracted inside the parentheses:
[tex]\( h(t) = -16(t^2 - \frac{120}{16}t + (\frac{120}{32})^2 - (\frac{120}{32})^2) \)[/tex]
[tex]\( h(t) = -16((t - \frac{120}{32})^2 - (\frac{120}{32})^2) \)[/tex]
Now, we expand the squared term and multiply through by -16:
[tex]\( h(t) = -16(t - \frac{120}{32})^2 + 16(\frac{120}{32})^2 \)[/tex]
[tex]\( h(t) = -16(t - 3.75)^2 + 16(3.75)^2 \)[/tex]
The maximum height [tex]\( k \)[/tex] is the constant term when the equation is in vertex form:
[tex]\( k = 16(3.75)^2 \)[/tex]
[tex]\( k = 16 \times 14.0625 \)[/tex]
[tex]\( k = 225 \)[/tex]
Therefore, the maximum height that the ball will reach is 225 feet.
If a wheel with a radius of 80 inches spins at a rate of 50 revolutions per minute, find the approximate linear velocity in miles per hour.
The probability that an archer hits a target on a given shot is .7 if five shots are fired find the probability that the archer hits the target on three shots out of the five.
The probability that the archer hits the target on exactly three out of five shots is 0.3087, or 30.87%, calculated by using the binomial probability formula.
The probability that an archer hits a target on a given shot is 0.7 and the goal is to calculate the probability that the archer hits the target on exactly three out of five shots. This is a binomial probability problem, as each shot can end in either a success (hitting the target) with a probability of 0.7, or a failure (missing the target) with a probability of 0.3.
To calculate the probability of exactly three successes (hits) out of five, we use the binomial probability formula:
P(X=k) = (n choose k) * (p)^k * (1-p)^(n-k)
Where:
n = total number of trials (5 shots)
k = number of successes (3 hits)
p = probability of success on a single trial (0.7)
Applying the formula, we get:
P(3 hits out of 5) = (5 choose 3) * (0.7)^3 * (0.3)^2
= 10 * (0.343) * (0.09)
= 10 * 0.03087
= 0.3087
Therefore, the probability that the archer hits the target on exactly three out of five shots is 0.3087, or 30.87%.
Find the value of each variable. Please help me!!
What is the value of x in the equation below?
1+2e^x+1=9
Answer:
X = In4-1 C on edge, just took the test
A soccer team is having a car wash.the team spent $55 on supplies.they earned $275 including tips.The teams profit is the amount the team made after paying for supplies.Write a sum of integers that repersents the teams profit.
can someone solve this for me
A wheel makes 5 13/16 revolutions per minute. If it rotates for 76 minutes, how many revolutions does it make?
multiply 5 13/16 by 76
5 13/16 * 76 = 441 3/4 revolutions
If 5(3x-7)=20, then what is 6x-8
5(3x-7) = 20
15x-35 = 20
15x = 55
x = 3.666666
so 6(3.666666) -8 = 13.99999 round to 14
if f(x) = x^2 + 1 and g(x) = x - 4, which value is equivalent to ( f ○ g)
a. 37
b 97
c 126
d 606
(Compostition of Functions)
Chris can be paid in one of two ways. Plan A is a salary of $350 per month, plus a commission of 7% of a sales. pLan B is a salary of $436 per month, plus a commission of 5% of sales. For what amount of sales is Chris better off selecting plan A
Which of the following represents the linear equation 3x =12 - 2y in standard form?
A: y=-2/3x-2
B: y=-2/3x-6
C: y=-3/2x+6
D: y= 2/3x-17/3
A trinomial that contains the variable k the coefficient of the second degree term is 1, the coefficient of the first degree term is -7 and the constant term is -15 how would you write this?
How do you find common factors
To find common factors between numbers, list all factors of each number and identify numbers that are in both lists. When multiplying fractions, multiply numerators and denominators then simplify by common factors. Multiplying both sides by the same factor can help in solving equations with fractions.
Explanation:To find common factors between two or more numbers, you first list out all the factors of each number. Factors are numbers that divide into the original number without leaving a remainder. For instance, if we are looking for common factors of 8 and 12, we list their factors as follows: the factors of 8 are 1, 2, 4, and 8, and the factors of 12 are 1, 2, 3, 4, 6, and 12. After listing out the factors, you look for numbers that appear in both lists. In this example, the common factors of 8 and 12 are 1, 2, and 4.
Another approach mentioned involves multiplying both sides by the same factor to make both sides integers when working with equations. This can be useful when seeking to simplify fractions or solve equations with fractional components.
It is also important to recognize that while multiplying fractions, we multiply the numerators together and the denominators together. Simplifying the result by common factors as needed helps in reducing fractions to their simplest form. For example, if we multiply ½ by ¾, we get a result of ¼ (numerator 1x3=3, denominator 2x4=8) which we can simplify to ¾ by dividing both numerator and denominator by the common factor 3.
Suppose f⃗ (x,y,z)=⟨x,y,4z⟩f→(x,y,z)=⟨x,y,4z⟩. let w be the solid bounded by the paraboloid z=x2+y 2 z=x2+y2 and the plane z=9.z=9. let ss be the closed boundary of ww oriented outward. (a) use the divergence theorem to find the flux of f⃗ f→ through s.
To find the flux of a vector field through a closed boundary using the divergence theorem, calculate the divergence of the vector field and evaluate the triple integral of the divergence over the solid bounded by the boundary. In this case, the flux is 3 times the volume of the solid.
Explanation:The student is asking how to use the divergence theorem to find the flux of a vector field through a closed boundary. In this case, the vector field is defined as f(x, y, z) = ⟨x, y, 4z⟩ and the closed boundary is a solid bounded by the paraboloid z = x^2 + y^2 and the plane z = 9.
To use the divergence theorem, we need to calculate the divergence of the vector field, which is the sum of the partial derivatives of f with respect to each variable. In this case, the divergence is 3.
Then, we can use the divergence theorem to find the flux through the closed boundary by evaluating the triple integral of the divergence over the solid bounded by the paraboloid and the plane. In this case, the flux is 3 times the volume of the solid.
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The flux of [tex]\(\vec{F}\)[/tex] through S is 24π.
To apply the divergence theorem, we first compute the divergence of [tex]\(\vec{F}\)[/tex]:
[tex]\nabla \cdot \vec{F} = \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial y} (y) + \frac{\partial}{\partial z} (4z) = 1 + 1 + 4 = 6.[/tex]
The divergence theorem states that the flux of a vector field through a closed surface is equal to the triple integral of its divergence over the region enclosed by the surface.
Thus, we have:
[tex]\iint_S \vec{F} \cdot d\vec{A} = \iiint_W (\nabla \cdot \vec{F}) \, dV = \iiint_W 6 \, dV[/tex]
The region W is bounded below by the paraboloid [tex]\(z = x^2 + y^2\)[/tex], and above by the plane z = 4.
Converting to cylindrical coordinates, we have:
[tex]\iiint_W 6 \, dV = \int_0^{2\pi} \int_0^2 \int_{r^2}^4 6 \cdot r \, dz \, dr \, d\theta = 24\pi.[/tex]
Adam is going to cook a turkey for 14 people and wants to allow ¾ lb of turkey for each person.
1lb = 450 g
How much would a turkey cost for 14 people?
Paula is given a litre of water during her fitness assessment at the gym she drinks 375 milliliters of water how much is left
in a grocery store steak cost $3.85 per pound if you buy a three pound steak and pay for it with a $20 bill how much change will you get
The change to be recieved is equal to $8.45
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: The price per steak is given as $3.85 per pound.
Thus 3 pound of steak will cost 3×3.85=$11.55
Therefore the change to be recieved is =20-11.55
=$8.45
Hence, The change to be recieved is equal to $8.45
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