Two perpendicular lines have opposite y-intercepts. The equation of one of these lines is y = mx + b. Express the x-coordinate of the intersection point of the lines in terms of m and b.

Hello!

Given the function, f(x) = 5x, find the equation where the function f, is reflected over the x-axis.

There are two types of reflections. One reflection is over the x-axis (the most common) and over the y-axis.

Say for example, we are given the point (x, y), and we want to reflect it over the x-axis. If the point (x, y) is reflected over the x-axis, then the point is (x, -y). Why? It's because y-values above the x-axis are POSITIVE while x-values below are NEGATIVE.

So, an equation to show this is: y = -f(x).

To find it, we multiply the entire function, which is f(x), by a negative. Since f(x) = 5x, the transformed function is f(x) = -5x.

Therefore, the function rule for the function shown is -f(x).

The function rule for the function f(x) = 5x reflected over the x-axis is -f(x) = -5x. This is due to the reversal of the y-values when reflecting a function over the x-axis.

In Mathematics, when we reflect a function over the x-axis, it simply means reversing the signs of the y-values. For this given function f(x) = 5x, its reflection would get the y-values inverted, which would convert the positive to negative (or vice versa). Taking this into account, the function reflecting in the x-axis would be -f(x) = -5x.

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The closet area is 1/9 of the bedroom area, so is (1/9)·(90 ft²) = 10 ft².

The width of the closet multiplied by the length is the area.

... length×(2 ft) = 10 ft²

... length = (10 ft²)/(2 ft) = 5 ft

The length of Jackson's closet is 5 ft.

Answer:

B. 120

Step-by-step explanation:

2cos x + 1 = 0

2 cos x = -1

cos x = -1/2

x = cos^1(-1/2)

(cos inverse (-1/2))

x = 120°

Drop all the minus signs (change them to +) to get your answers:

37, 2.987, 54, 2/3, 45

Hi ArbogastMadyson,

Which type of triangle is shown here?

There are 6 types of triangle:

Since your triangle contains length in inches not degrees we will not use the 1st, 5th, and 6th clssifications.

Scalene Triangle - 3 unequal sides

Isosceles Triangle - 2 equal sides, 1 unequal,

Equilateral Triangle - 3 Equal Sides

In your image all 3 lengths are different.

Answer - Scalene Triangle

It would of been easier to search the definition of the answers up.

the point was reflected over the x- axis

note that for reflection in the x- axis

a point (x, y ) → (x, - y )

the x-coordinate remains unchanged while the y- coordinate of the image is the negative of the original y- coordinate

Answer:

Option B and C are correct.

Step-by-step explanation:

It is given that A point located at (1, 6) undergoes a transformation. Its image is at (1, -6).

[tex]P(1,6)\rightarrow P'(1,-6)[/tex]

If the point was reflected over the y-axis, then

[tex]P(x,y)\rightarrow P'(-x,y)[/tex]

[tex]P(1,6)\rightarrow P'(-1,6)\neq P'(1,-6)[/tex]

If the point was translated down 12 units, then

[tex]P(x,y)\rightarrow P'(x,y-12)[/tex]

[tex]P(1,6)\rightarrow P'(1,6-12)=P'(1,-6)[/tex]

If he point was reflected over the x-axis, then

[tex]P(x,y)\rightarrow P'(x,-y)[/tex]

[tex]P(1,6)\rightarrow P'(1,-6)[/tex]

If he point was translated up 12 units, then

[tex]P(x,y)\rightarrow P'(x,y-+12)[/tex]

[tex]P(1,6)\rightarrow P'(1,6+12)=P'(1,18)\neq P'(1,-6)[/tex]

Hence, the correct options are B and C.

Answer:

Erica

Step-by-step explanation:

Two lines with the same (defined) slope will only have infinite solutions if their y-intercepts are the same. Otherwise, the number of solutions (points on both lines) is zero.

Since the 2 lines have the same slope, then the lines are parallel and never intersect. Thus there is no solution to the system of equations

Neither Jake nor Erica are correct.

given a linear equation in slope- intercept form y = mx + c

where m is the slope and c the y -intercept

the slope of a line perpendicular to it is - [tex]\frac{1}{m}[/tex]

If equation is y = 2x + 3 ( with slope m = 2 )

then the perpendicular slope = - [tex]\frac{1}{2}[/tex]

- 3, - 9.6 and - 22.8

to generate the first, fourth and tenth term substitute n = 1, 4, 10 into the rule

a(1) = - 3 + 0 = - 3

a(4) = - 3 - 6.6 = - 9.6

a(10) = - 3 - 19.8 = - 22.8

If you actually do what the problem statement tells you to do, the answer falls into your lap.

The attachment shows the triangle reflected across the y-axis (blue), then across the x-axis (red). The red triangle is clearly equivalent to the original being rotated 180° about the origin.

The appropriate choice is ...

... a 180° rotation about the origin

_____

Algebraically, reflection across the y-axis negates the x-coordinate:

... (x, y) ⇒ (-x, y)

and reflection across the x-axis negates the y-coordinate:

... (x, y) ⇒ (x, -y)

Then, reflection across first one axis then the other will result in both coordinates being negated:

... (x, y) ⇒ (-x, -y)

This is precisely what happens when a figure is rotated 180° about the origin.

Answer:

A 180 rotation about the origin

The median on any box plot is the little dot in the middle of the box so the answer is C)42. So where the line is in the middle of the box it is always going to be the median. The median is in the middle. You can also remember it like this Hey Diddle diddle the medians the middle you add and divide for the mean and the mode is the most.

Answer:  

B) 38  

Step-by-step explanation:

38 is the first (lower) quartile of the box-and-whisker plot.

The answer would be A because the distance from 8 to 0 is 8 and the distance from 0 to -12 is 12 so 8+12 is 20

Adam will be 14, and it is 8 more than 6.

We have given that,

Adam is three years younger than twice bobs age. in 5 years Adams's age will be 8 years more than bobs age.

We have to determine the what are their 2 ages.

The age of majority is the age when children legally become adults.

Adam is 9 years old and Bob is 6.

Twice Bob’s age is 12, and three years younger than that is 9.

If Adam is 9 now then in five years, Adam will be 14, which is 8 more than 6.

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y + 3 = [tex]\frac{2}{3}[/tex] (x - 5)

the equation of a line in point- slope form is

y - b = m ( x - a )

where m is the slope and (a, b) a point on the line

here m =[tex]\frac{2}{3}[/tex] and (a,b) = (5 , - 3 )

y + 3 = [tex]\frac{2}{3}[/tex] (x - 5 ) ← in point-slope form

The equation of the line that passes through the point (5, -3) and has a slope of 2/3 is y = 2/3x - 19/3, using the point-slope form for the equation of a line.

The line that you're looking for can be represented using the point-slope form of a linear equation. This form is written as y - y1 = m(x - x1), where (x1, y1) are the coordinates of a point on the line and 'm' is the slope of the line. For a line that passes through the point (5, -3) and has a slope of 2/3, you replace x1 with 5, y1 with -3, and m with 2/3. So, the equation of the line becomes y - (-3) = 2/3(x - 5), which simplifies to y + 3 = 2/3x - 10/3. Further simplifying, we get y = 2/3x - 10/3 - 3, or y = 2/3x - 19/3.

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The median is the middle number in order of the set of values:

2, 4, 8, 10, 12

8 is the median in the set of values!

Answer:

its 8

Step-by-step explanation:

No

Lines k and n are perpendicular

The slope of line k is -6

Fact: The product of slopes of two perpendicular lines = -1

So the slope of line n = -1 ÷ -6 = 1/6

The correct choice is 'D.'

If lines k and n are Slopes of Perpendicular Lines k is -6, then the slope of the perpendicular line n is 1/6.

In the study of Mathematics, especially when dealing with Geometry and Algebra, understanding the relationship between lines can be critical.

This particular question asks about perpendicular lines and their slopes. If lines k and n are perpendicular, knowing the slope of one can help deduce the slope of the other.

As per the properties of perpendicular lines, the product of their slopes is -1.

In the case where the slope of line k is -6, the slope of the perpendicular line n would be the Positive reciprocal, which is simply flipping the fraction and changing the sign.

Hence, the slope of line n would be 1/6.

So, ultimately the answer is Option d: 1/6, which is the slope of line n that is perpendicular to line k with a slope of -6.

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Answer:

Yes. (See below for explanation.)

Step-by-step explanation:

The number of servings is found by dividing the quantity available by the size of a serving. The quantity of punch is the sum of the quantities of the juices that go into the punch. The serving size of 3/4 cup is the same as 6 ounces, since a cup is 8 ounces. (3/4 × 8 oz = 6 oz)

The quantity available is (64 oz + 28 oz + 76 oz). The serving size is 6 oz. Since the units of numerator and denominator are the same, they cancel, leaving ...

... number of servings = (quantity available)/(serving size)

... = (64 +28 +76)/6 . . . . as shown in the problem statement

_____

It might not be obvious that the above ratio gives the number of servings. However, if you look at the real units, you see how it happens.

[tex]\dfrac{oz}{(\frac{oz}{serving})}= oz\dfrac{serving}{oz}=\dfrac{oz}{oz}serving=serving[/tex]

Try this option (answers: 5.53 and 3.22)

Answer:

The correct answer is that the function starts high and ends low.

Step-by-step explanation:

First we need to check for the highest power in a term. Since it is 5, which is an odd number, we know that they start and end in different places.

Next, we determine where it finishes based on the coefficient of that term, which is -1. Since it is negative, we know it finishes down. Since they are different, this means it starts up

Answer:

A ) The graph of the function start high and ends low .

Step-by-step explanation:

Given  : f(x) = [tex]-x^{5} +x^{2} -x[/tex].

To find : Describe the end behavior of the following function.

Solution : We have given function

f(x) = [tex]-x^{5} +x^{2} -x[/tex].

We can see the Degree = 5  ( Odd) ,  Leading coefficient = negative  .

By the End Behavior Rule  : If  the degree odd and leading coefficient is negative then the left side of graph would be up and right would be down.

Therefore, A ) The graph of the function start high and ends low .

In the attachment, the original parallelogram is shown in red. Its image is shown in blue. The purple parallelogram is the original reflected across the y-axis. You can see that it becomes the blue parallelogram if rotated 90° clockwise around the origin.

The appropriate choice is ...

... a reflection over the y-axis and then a 90 degree clockwise rotation about the origin

Answer:

B. a reflection over the y-axis and then a 90degree clockwise rotation about the origin

Step-by-step explanation:

I just did it, and all was well! :) :) :)

Short answer: you don't.

The linear term in the numerator of the integral means the form shown is not applicable. Rather, you perform the integration using partial fraction expansion.

[tex]\displaystyle\int{\frac{5x+1}{25x^2+60x-13}}\,dx=\int{\frac{5x+1}{(5x-1)(5x+13)}}\,dx\\\\=\frac{1}{35}\int{\frac{5}{5x-1}}\,dx+\frac{6}{35}\int{\frac{5}{5x+13}}\,dx[/tex]

The integral is ...

... (1/35)ln|5x-1| +(6/35)ln|5x+13| +C

_____

If the numerator of your integral were a constant, then the fractions multiplying the separate partial fraction integrals would have the same magnitude and opposite signs. You would end with the difference of logarithms, which could be expressed as the log of a ratio as shown in your problem statement.

First you had to switch sides of equation form.

[tex]\frac{x}{100}= \frac{7}{10}[/tex]

Then you multiply by one-hundred from both sides of equation form.

[tex]\frac{x}{100}*100= \frac{7}{10}*100[/tex]

And finally, simplify by equation.

[tex]\frac{x}{100}*100=x[/tex]

[tex]\frac{7}{10}*100=70[/tex]

[tex]70*1=70[/tex]

[tex]x=70[/tex]

Final answer: [tex]\boxed{x=70}[/tex]

[tex]70/10=7[/tex]

[tex]70/7=10[/tex]

[tex]10*7=70[/tex]

[tex]7*10=70[/tex]

Hope this helps!

And thank you for posting your question at here on brainly, and have a great day.

-Charlie

x = 70

given [tex]\frac{7}{10}[/tex] = [tex]\frac{x}{100}[/tex] ( cross-multiply )

10x = 7 × 100 = 700 ( divide both sides by 10 )

x = [tex]\frac{700}{10}[/tex] = 70

The only factorial expression that is shown properly evaluated is that of selection A.

_____

If you number the terms starting from 0 on the left, you find that 20 is term #3 on the row that has 6 as term #1. In combination notation, this would be

... 6C3 or C(6, 3)

It is computed as

... 6!/(3!·(6-3)!) = 6·5·4/(3·2·1) = 20

ANSWER

The number that fills in the blanks is 1

EXPLANATION

Two numbers are relatively prime if they have no common factor greater than 1.

For exam 12 and 17 have no common factor greater than 1.

This is equivalent to saying that the greatest common divisor (GCD) of the two numbers is 1.

[tex]gcd(12,17)=1[/tex]

This means that [tex]12[/tex] and [tex]17[/tex] are relatively prime.

But

[tex]gcd(12,16)=4[/tex]. This means 12 and 16 are not relatively prime or coprime

B

the average temperature rose by + 5°

this years average = - 19 + 5 = - 14°

we have

[tex]f(x)=\frac{1}{2}x+2[/tex]

To graph the line find the x and y intercepts

we know that

The x-intercept is the value of x when the value of y is equal to zero

The y-intercept is the value of y when the value of x is equal to zero

so

Find the y-intercept

For [tex]x=0[/tex]

[tex]f(0)=\frac{1}{2}*0+2=2[/tex]

the y-intercept is the point [tex](0,2)[/tex]

Find the x-intercept

For [tex]y=0[/tex]

[tex]0=\frac{1}{2}x+2\\x=-4[/tex]

the y-intercept is the point [tex](-4,0)[/tex]

Using a graphing tool

Plot the points to graph the line

therefore

the answer in the attached figure

The graph of the linear function f(x) = 12x + 2 is attached below

The graph of a linear equation is a straight line when plotted on a coordinate plane. A linear equation can be written in the form:

y = mx + b

Where:

"y" represents the dependent variable (usually plotted on the vertical axis).

"x" represents the independent variable (usually plotted on the horizontal axis).

"m" is the slope of the line, which determines its steepness.

"b" is the y-intercept, which is the point where the line crosses the y-axis.

The graph of the linear equation f(x) = 12x + 2 is attached below;

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Answer: The answer is 40

Step-by-step explanation: