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2 years ago

Write the equation of the line that is parallel to the line y=-7/4x-2 through the point (4,2)! Help please

1 answer:

6 0

as you already know, the equation y=-7/4x-2, is already in slope-intercept form and thus its slope is the coefficient of the "x", namely -7/4.

parallel lines have the same exact slope, so a parallel line to this one will also have a slope of -7/4, and it passes through 4,2,

$\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad \qquad \qquad slope = m\implies -\cfrac{7}{4} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-2=-\cfrac{7}{4}(x-4) \\\\\\ y-2=-\cfrac{7}{4}x+7\implies y=-\cfrac{7}{4}x+9$

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Your new flashlight uses a parabolic mirror which can be modeled by the equation (x – 2)² = 5(y + 1), where x and y are measured

Ksju [112]

The given equation is
(x - 2)² = 5(y + 1).

The given equation for the parabola is in the standard form
(x - h)² = 4p(y - k)
where
h = 2
4p = 5, so that p = 5/4
k = -1

The vertex is at
(h,k) or (2, -1)

The focus is located at
(h, k + p) or (2, -1 + 5/4) = (2, 1/4)

We should place the bulb at p = 5/4 from the vertex.

Answer: 1 1/4 or 1.25 cm

6 0

2 years ago

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Think about the commutative property of real number operations as it applies to addition and subtraction of functions how do you

kati45 [8]

The question does not make sense.
The commutative property applies to addition and multiplication, not addition and subtraction.
The commutative property does not apply to subtraction or division because in those operations, the order of the numbers makes a difference, whereas in addition and subtraction the order does not make a difference.

For example:

Addition
5 + 4 = 9
4 + 5 = 9
5 + 4 = 4 + 5
Changing the order of the 4 and the 5 gives the same answer.
The commutative property does apply to addition.

Multiplication
5 * 4 = 20
4 * 5 = 20
5 * 4 = 4 * 5
Changing the order of the 4 and the 5 gives the same answer.
The commutative property does apply to multiplication.

Subtraction
5 - 4 = 1
4 - 5 = -1
5 - 4 is not equal to 4 - 5
Changing the order of the 4 and the 5 gives a different answer.
The commutative property does not apply to subtraction.

Division
5/4 = 1.25
4/5 = 0.8
1.25 is not equal to 0.8.
Changing the order of the 4 and the 5 gives a different answer.
The commutative property does not apply to division.

8 0

2 years ago

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One semester in a chemistry class, 14 students failed due to poor attendance, 23 failed due to not studying, 15 failed because t

BlackZzzverrR [31]

Answer:

(a) 16 students failed for exactly two of the three reasons.

(b) 7 students failed because of poor attendance and not studying but not because of not turning in assignments.

(c) 14 students failed because of exactly one of the three reasons.

(d) 3 students failed because of poor attendance and not turning in assignments but not because of not studying.

Step-by-step explanation:

We are given that one semester in a chemistry class, 14 students failed due to poor attendance, 23 failed due to not studying, 15 failed because they did not turn in assignments, 9 failed because of poor attendance and not studying, 8 failed because of not studying and not turning in assignments, 5 failed because of poor attendance and not turning in assignments, and 2 failed because of all three of these reasons.

As shown in the diagram attached below, a Venn diagram represents the situation given in the question;

In the diagram below, 2 in represents purple color represents the number of students failed because of all three of these reasons.

7 represents the number of students who failed because of poor attendance and not studying but not due to not turning in assignments.

6 represents the number of students who failed because of not studying and not turning in assignments but not due to poor attendance.

3 represents the number of students who failed because of poor attendance and not turning in assignments but not due to not studying.

2 in red color represents the number of students who failed only due to poor attendance.

8 in red color represents the number of students who failed only due to not studying.

4 in red color represents the number of students who failed only due to not turning in assignments.

(a) The number of students who failed because of exactly two of the three reasons = 7 + 6 + 3 = 16 students.

(b) The number of students who failed because of poor attendance and not studying but not because of not turning in assignments = 9 - 2 = 7 students.

(c) The number of students who failed because of exactly one of the three reasons = 2 + 8 + 4 = 14 students.

(d) The number of students who failed because of poor attendance and not turning in assignments but not because of not studying = 5 - 2 = 3 students.

7 0

2 years ago

4.5x-7=20 i need help whats the answer

Dmitry [639]

Your answer will be 6.

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2 years ago

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A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is

anzhelika [568]

You need to solve for one variable in equation 1 and substitute it in equation 2 to solve.

Equation 1: x+y=24
x= number of 3 pt questions
y= number of 5 pt questions
24= Total number of questions

Equation 2: 3x+5y=100
100= Total point value possible on test
3x= point value of 3 pt questions
5y= point value of 5 pt questions

x+y=24
Subtract y from both sides
x=24-y

Substitute in equation 2:
3x+5y=100
3(24-y) +5y=100
72-3y+5y=100
72+2y=100
Subtract 72 from both sides
2y=28
Divide both sides by 2
y=14

Substitute y=14 back in to solve for x:
3x+5y=100
3x+5(14)=100
3x+70=100
Subtract 70 from both sides
3x=30
Divide both sides by 3
x=10

So there are 10 three point questions
There are 14 five point questions.

Hope this helped! :)

6 0

2 years ago

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