4.What is the equation in point-slope form of the line passing through (3, 6) and (−2, 1)? (5 points)


a
y + 6 = 1(x + 3)

b
y + 1 = −1(x + 2)

c
y − 6 = −1(x + 3)

d
y − 6 = 1(x − 3)

There are 2 perfect squares that are two-digit and divisible by 3.

To find the two-digit perfect squares that are divisible by 3, we can start by finding all the two-digit perfect squares and then check which ones are divisible by 3. The two-digit perfect squares are:

4: 16

5: 25

6: 36

7: 49

8: 64

9: 81

Now we can check which of these numbers are divisible by 3:

16: not divisible

25: not divisible

36: divisible

49: not divisible

64: not divisible

81: divisible

Thus, there are two two-digit perfect squares that are divisible by 3: 36 and 81.

So, the answer is 2.

Additive inverse of 2 is -2.

Multiplicative Inverse of 2 is 1/2.

To produce a result equal to 0, add the original number and the additive inverse by simply reversing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.

A multiplicative inverse or reciprocal for a number x is a number that, when multiplied by x, produces the multiplicative identity, or 1. It is represented by 1/x or x/1. A fraction a/b has a multiplicative inverse of b/a. Divide 1 by the real number to obtain the multiplicative inverse of the number.

A function that "undoes" another function is called an inverse. In other words, if f(x) generates y, then y entered into the inverse of f creates x. An invertible function is one that has an inverse, and the inverse is indicated by the symbol [tex]f^{-1}[/tex].

Additive inverse of 2 is -2.

Multiplicative Inverse of 2 is 1/2.

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Answer:

It depends on what the question is.

Step-by-step explanation:

5x-y+8=0  is the equation of a line having a slope of 5 and whose y-intercept is 8.

The value of the steep slopes or the direction of a line in a coordinate plane is known to as the slope of a line, also known as the gradient.

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. Mostly on y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

given information like Slope=m=5 and Y intercept equals c=8,

A line's equation is y=mx+c.

As a result of the information provided, the equation for a line is y=5x+8.

A line must have the equation 5x-y+8=0.

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Answer:

  undefined

Step-by-step explanation:

You want the slope of the line through points (-1, 1) and (-1, 4).

The two points lie on the vertical line x = -1. A vertical line has undefined slope.

The slope of the line is undefined.

__

Additional comment

The slope is the ratio of rise to run. For a vertical line, the "run" is zero for any chosen "rise." Division by zero gives an undefined result.

X= (any number that isn't 0)

so X=1 X=2 x=3 those would all work

the x intercept is when any point on the x axis is intercepted, and any line with a slope that isn't 0 will always intersect that point. So you need to have X= something so that it will stay parallel to the X axis, but never intersect.

Each side of the fountain is 5 units .

Given :

All the sides of the hexagon are equal.

Vertices of the fountain are :

( 10.5 , 8 ), ( 14.5 , 5 ), ( 10.5, 2 ), ( 5.5, 2 ), ( 1.5, 5 ), and ( 5.5, 8 ).

we know that ,

Distance = √( x2 - x1 )^2 + ( y2 - y1 )^2

= √( 14.5 - 10.5 )^2 + ( 5 - 8 ) ^2

= √4^2 + 3^2

= √ 16 + 9

= √25

= 5 units

we know that all the sides of the hexagon are equal so the length of each side of hexagon or fountain is 5 units .

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The equation x² + 3x - 3 = 0 has the sum of its roots as 3. This can be found by using the quadratic formula, which gives us two roots x1 and x2. Their sum is x1 + x2 = 3, which is the sum of the roots of the equation.

The correct answer is B: x² + 3x - 3 = 0

The equation has the form of ax² + bx + c = 0.

a = 1, b = 3, c = -3

The sum of the roots can be found using the quadratic formula:

x = (-b ± √(b² - 4ac))/2a

x = (-3 ± √(9 - 4*1*(-3))/(2*1)

x = (-3 ± √15)/2

x = (-3 ± 3√5)/2

x1 = (3 - 3√5)/2

x2 = (3 + 3√5)/2

The sum of the roots is x1 + x2 = 3.

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The ball is hits the ground after 3.4 seconds it strike s

From the question, we have the following parameters that can be used in our computation:

h(t)=-18t^2+60t+4.

Rewrite as

h(t) = -18t² + 60t + 4

When the ball hits the ground, we have

h(t) = 0

So, the equation becomes

-18t² + 60t + 4 = 0

Divide through by 2

-9t² + 30t + 2 = 0

So, we have

9t² - 30t - 2 = 0

Using a graphing tool, we have

t = 3.4

Hence, the time is 3.4 seconds

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The value of the function (f - g)(x) would be [tex](f-g)(x)=x^2-11x+4[/tex].

Option (A) is correct.

What are composite functions?

A composite function is generally a function that is written inside another function. The composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.'

Given:

                [tex]f(x)=4x^2-5x\\\\g(x)=3x^2+6x-4[/tex]

Now by using the definition of composite functions we can write,

      [tex](f-g)(x)=f(x)-g(x)\\\\(f-g)(x)=4x^2-5x-(3x^2+6x-4)\\\\(f-g)(x)=4x^2-5x-3x^2-6x+4\\\\(f-g)(x)=x^2-11x+4[/tex]

Hence, the value of the function (f - g)(x) would be [tex](f-g)(x)=x^2-11x+4[/tex].

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Answer:

10 + 2z

Step-by-step explanation:

2( 5+z)

10 + 2z

Answer:

To determine Beau's front-end ratio, you need to calculate the percentage of his monthly income that will be taken up by his mortgage, homeowner's insurance, property taxes, credit card payment, and car payment.

First, add up all of Beau's monthly expenses: $1,025 (mortgage) + $635 (homeowner's insurance) / 6 (months in a half year) + $4,785 (property taxes) / 12 (months in a year) + $2,000 (credit card payment) + $250 (car payment) = $3,715.83.

Next, divide this total by Beau's monthly income: $3,715.83 / ($89,750 / 12) = $3,715.83 / $7,479.17 = 0.49, or approximately 49%.

Since this ratio is expressed as a percentage, the final answer is 49%. Therefore, the correct answer is (d) 24%.

The parabola Refer the attached figure, x- intercepts are (4,0) and (-2,0)

Quadratic function = f(x) = 2x²-4x-16.

To find: The graph of the quadratic function using parabola tool?

First we find the vertex form of the equation.

f(x) = 2x²-4x-16

Where, a=2 ,b=-4 , c=-16

Vertex is V,

             [tex]v=\frac{-b}{2a} , f(\frac{-b}{2a})\\\\\frac{-b}{2a} = \frac{4}{4} =1\\\\f(\frac{-b}{2a})=f(1)\\\\=-10[/tex]

So, The vertex of the equation is (1,-10).

Now, we find y- intercept by putting x=0 in the equation

            [tex]y=2(0)^{2} -4(0)-16\\\\y=-16[/tex]

y- intercept (0,-16)

Now, we find x- intercept by putting y=0 in the equation.

           [tex]2x^{2} -4x-16=0\\\\x^{2} -2x-8=0\\\\x^{2} -4x+2x-8=0\\\\x=4 \ and \ x=-2[/tex]

x- intercepts are (4,0) and (-2,0)

Placing all the points and plot a graph.

Refer the attached figure below.

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Answer: If Debra, the mirror, and the bottom of the tree are points on the ground all on one line, then the two right triangles are these: LEFT: y and 33 as the legs and unknown hypotenuse. RIGHT: 6 and 9.7 as legs and unknown hypotenuse. The two angles at the mirror are of same measure; that is, the 33 and the hypotenuse of a LEFT triangle makes same angle measure as the 9.7 and the hypotenuse of the RIGHT triangle.

Note, these are two SIMILAR triangles.

y/33 = 6/9.7

In addition,  Y = 20.4

highlight%28y=20.4%29

Step-by-step explanation:

Answer:

  order of operations

Step-by-step explanation:

You want to know why -4² = -16 and (-4)² =16.

The calculator properly applied the order of operations to -4². In evaluating, this expression, the exponentiation operation is performed first. That means this is evaluated as ...

  -4² = -(4×4) = -16

When the parentheses include the minus sign, as in the second expression, the squaring operation is applied to -4, not to 4:

  (-4)² = (-4)×(-4) = 16

Answer:109.4 Fahrenheit

Step-by-step explanation:

I don't see the picture. Can you send it in the message.

The statement as an inequality expression is 12.75 < 7x

From the question, we have the following statement that can be used in our computation:

12 and 3/4 less than the product of 7 and a number x

Express the numbers as fractions

So, we have the following representation

12 + 3/4 less than the product of 7 and a number x

Introduce the inequality symbols

So, we have

12 + 3/4 < the product of 7 and a number x

Next, we have

12 + 3/4 < 7x

Express as decimal

12.75 < 7x

hence, the expression is 12.75 < 7x

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∠ABP = ∠CBP (By angle bisector).∠PXB = ∠PYB (All right angles are congruent).BP = BP (Common side).ΔBXP = ΔBYP (By ASA rule).PX = PY (corresponding sides of congruent triangles are the same).

If two figures are exactly the same in sense of their length side all things then they will be congruent.

In other meaning, if you can copy a figure then that copy and the original figure will be congruent.

As per the given two bisectors' angle.

∠ABP = ∠CBP (By angle bisector)

∠PXB = ∠PYB (All right angles are congruent).

BP = BP (Common side)

ΔBXP = ΔBYP (By ASA rule)

PX = PY (corresponding sides of congruent triangles are the same)

Hence "∠ABP Equals ∠CBP (By angle bisector). ∠PXB = ∠PYB (All right angles are congruent). BP = BP (Common side) (Common side). ΔBXP = ΔBYP (By ASA rule). PX = PY (matching sides of congruent triangles are the same) (corresponding sides of congruent triangles are the same).".

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Answer:

1/2

Step-by-step explanation:

do trust me on this one if you dare go head

Answer: 1/2

Step-by-step explanation:

Do the rise over run strategy, go up 1 and then right 2

Answer:

Step-by-step explanation:

The coordinates of point A are (23/5, 44/5).

A line segment is a section of a straight line that is enclosed by two clearly defined endpoints and contains every point on line b within.

Given:

The ratio = 2:3

P is (1,4) and H is (19,28)

Calculate the mid-point coordinates as shown below,

E = (1 + 19 / 2), (28 + 4 / 2)

E = (10, 16)

Calculate the coordinates of point A,

A = (2 × 10 + 3 × 1 / 2+3) , (16 × 2+ 4 × 3 / 2+3)

A = (23/5, 44/5)

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Figure PQRS may be mapped onto image P'Q'R'S using only one transformation, which is a reflection.

There are four different ways to change a point, line, or geometric figure, and each one has an impact on the object's shape and/or placement. Pre-Image is the shape of the item before transformation, and image is the position and final shape of the object after transformation.

As a result, the coordinates for the figure PQRS are P(2,2) Q(5,2) R(5,6) and S(2,6), whereas those for the picture P'Q'R'S' are P(-6,2) Q(3,2) R(3,6) and S' (-6,6).

Reflection is a sort of transformation that flips a shape along a mirror line, also known as a line of reflection, such that each point is at the same distance from the mirror line as its mirrored point.

The y-axis reflects the PQRS figure, which is then translated left to 1 unit.

As a result, one transformation can reflect picture P'Q'R'S onto figure PQRS.

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The number of roots of a polynomial is always less than or equal to the degree of the polynomial because the degree of f(x) is the sum of the degrees of the factors

The number of roots of a polynomial is equal to the number of values of x that make the polynomial equal to zero.

The degree of a polynomial is the highest exponent of the variable in the polynomial. For example, the polynomial x² + 3x + 2 has a degree of 2, because the highest exponent of x is 2.

It can be shown mathematically that the number of roots of a polynomial is always less than or equal to the degree of the polynomial. This is known as the Fundamental Theorem of Algebra.

Since each of the factors has a degree of 1, the degree of f(x) is the sum of the degrees of the factors, which is equal to 3.

Therefore, the number of roots of a polynomial is always less than or equal to the degree of the polynomial.

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Two figures are similar by transformations if they have the same shape, but are either rotated, reflected, translated, or enlarged/reduced. They must also have corresponding angles of the same degree and corresponding sides of the same length (or in the case of enlargement/reduction, in the same ratio).

Four distinct approaches to modify the position and/or shape of a point, line, or geometric figure are collectively referred to as transformations. The Pre-Image of the object is its initial shape, while the Image, after transformation, is the final shape and location of the thing.

A drastic change in shape or appearance is called a transformation. An crucial occasion, such as receiving your driver's license, enrolling in college, or getting married, might change the course of your life. Extreme, dramatic change is what we refer to as transformation.

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Answer:

Rhombus

Step-by-step explanation:

A rhombus is a type of quadrilateral in which all four sides are of equal length. Also, the diagonals are perpendicular to one another and bisect each other too.

On observing the provided question, we can say that - In Korea, 10th grade is = 16 or 17 year old ,  11th grade is = 17 or 18 and  12th grade is = 18 or 19.

Grading may be done using letters, numbers, percentages, points, or descriptions. The most prevalent grades are in the form of letters, and they usually correspond to a variety of percentages or points. Many people consider "A" and "B" grades to be "good." D and F grades are referred to as "poor grades." Commonly regarded as average is a "C."

We can say that

In Korea,

10th gradis = 16 or 17 year old ,

11th grade is = 17 or 18 and  12th grade is = 18 or 19.

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The equation of a line that is parallel to y= 1/2 − 5 and passes through the point (-4, 1) will be y = (1/2)x + 3.

Let the condition of the line be hatchet + by + c = 0. Then, at that point, the condition of the equal line that is lined up with the line hatchet + by + c = 0 is given as hatchet + by + d = 0.

The equation of the line is given below.

y = (1/2)x - 5

The equation of the parallel line to the given line is written as,

y = (1/2)x + d

The equation of the line passing through (-4, 1), then we have

1 = (1/2) × (-4) + d

1 = - 2 + d

d = 3

The condition of a line that is lined up with y= 1/2 − 5 and goes through the point (- 4, 1) will be y = (1/2)x + 3.

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Answer:

y=1/4x-5

Step-by-step explanation:

y=mx+b is slope intercept form

m is slope

b is y intercept

we know m is 1/4 so we fill it in

y=1/4x+b

fill is the coordinates to find b

-3=1/4(8)+b

-3=2+b

-2. -2

-5=b

place b in

y=1/4x-5

hopes this helps

Answer:y=1/4x-5

Step-by-step explanation:

Your point was (8,-3) and your rise is 1 and your run is 4 so if you want to get from 0 to 8 and count by 4 you need to move twice, and if you established that you will move twice then you need a number that you add 2 to that will give you -3. And that number is -5 so your y-intercept is

Answer:

answers are T,F,T

Step-by-step explanation:

Just had this worksheet