What is the height, x, of the equilateral triangle?

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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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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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.

∠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:

answers are T,F,T

Step-by-step explanation:

Just had this worksheet

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 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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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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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:

Step-by-step explanation:

Answer:

It depends on what the question is.

Step-by-step explanation:

The factors of the number 36 will be 2, 2, 3, and 3. So, yes, 2 is the factor of 36.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

The number is given below.

⇒ 36

The factor of the number 36 is given below.

36 = 2 x 2 x 3 x 3

The factors of the number 36 will be 2, 2, 3, and 3. So, yes, 2 is the factor of 36.

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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 vertical asymptote of X 4 is x = 4, which means that as x approaches 4, the function approaches infinity.

The vertical asymptote of a function is an x-value at which the function tends to approach infinity. In the case of X 4, the vertical asymptote is x = 4. This means that as x approaches 4, the function X 4 approaches infinity. This can be seen by examining the function. As x approaches 4 from the left, the denominator of X 4 becomes increasingly small while the numerator remains constant. This means that the function's value becomes increasingly large as x approaches 4, eventually resulting in an infinite value. In the same way, as x approaches 4 from the right, the denominator of X 4 becomes increasingly large while the numerator remains constant. This means that the function's value becomes increasingly small, eventually resulting in an infinite value. Thus, the vertical asymptote of X 4 is x = 4.

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Answer:109.4 Fahrenheit

Step-by-step explanation:

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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No, 16 is not a multiple of 3 as they leave some reminder.

Hence, No, 16 is not a multiple of 3 as they leave some reminder.

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Considering the definition of an inequality, the inequality that best represents this scenario is 35x + 60y≥ 7000

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that:

Being:

the inequality that expresses the scenario is

35x + 60y≥ 7000

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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:

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

The claim for the EC sickness benefit are filed at any SSS branch or representative office nearest the member's residence or place of work.

Here we need to find the way to notify SSS for EC sickness benefit.

In order to find the solution, we must know that what is meant by  SSS for EC sickness benefit.

The term  SSS for EC sickness benefit is defined as the  benefits under the EC program may be enjoyed simultaneously with benefits under the social security program effective June 1984.

Based on the definition, we have identified that the notification process is done through  the E-Services tab and click on "Submit SS Sickness Benefit Reimbursement Application (SBRA)."

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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.

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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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

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.

The coefficient of the variable x² in the expression 3x² is 3

Given that,

The expression is 3x²

To find : The coefficient of the variable x² in the expression

Coefficient is the number that is beside the variable in the equation.

The coefficient of x in 3x²  is 3

A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6

As we can see that the term that is in multiplication with x²  is 3.

Hence, the coefficient of x²  in the equation 3x²  is 3.

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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:

1. ∠YZX = 37°

2. ∠YXZ = 53°

3. XZ = 30 meters

Step-by-step explanation:

1. To solve for an unknown angle, we need to utilize the inverse of a trigonometric function.

⭐What are the inverses of the trigonometric functions?

To know which inverse of the trigonometric functions we use, we have to see the type of side lengths we are given (opposite, adjacent, or hypotenuse)

We are given side length XY, which is opposite of ∠YZX, and we are given side length YZ, which is adjacent to ∠YZX. Therefore, we will use [tex]tan^-1 (opposite/adjacent) =[/tex]

Substitute the values we are given into the function:

[tex]tan^-1 (18/24) =[/tex]

Compute this equation using a scientific calculator. I recommend using the Desmos Scientific Calculator:

[tex]= 37[/tex]

∴ ∠YZX = 37°

2. We already know 2 angles (∠YZX = 37°, and ∠ZYX = 90°) Therefore, to find ∠YXZ, we have to utilize the triangle sum theorem.

⭐ What is the triangle sum theorem?

Substitute the angles we know already (∠YZX and ∠ZYX), and solve for ∠YXZ.

[tex]< YZX + < ZYX + < YXZ = 180[/tex]

[tex]37 + 90 + YXZ = 180[/tex]

[tex]127 + YXZ = 180[/tex]

[tex]< YXZ = 53[/tex]

∴ ∠YXZ = 53°

3. We already know 2 side lengths (ZY = 24 meters, and XY = 18). Therefore, to find XZ, we have to utilize the Pythagoras' theorem.

⭐ What is the Pythagoras' theorem?

Substitute the values of the side lengths into the formula:

[tex](XZ)^2 = (XY)^2 + (ZY)^2[/tex]

[tex](XZ)^2 = 18^2 + 24^2[/tex]

Solve for XZ:

[tex](XZ)^2 = 324 + 576[/tex]

[tex](XZ)^2 = 900[/tex]

[tex]\sqrt{(XZ)^2} = \sqrt{900}[/tex]

[tex]XZ = 30[/tex]

∴ XZ = 30 meters