I dont really understand this question, can anyone help me out?

The possible rational roots of x³ - x² - 10x - 8 = 0 are -2, -1, and 4.

In mathematics, a root of an equation is a value of the variable that makes the equation equal to zero.

For example, in the equation x² - 4 = 0, the roots are 2 and -2, because when x = 2 or x = -2, the equation is satisfied (2² - 4 = 0 and (-2)² - 4 = 0). In other words, 2 and -2 are the values of x that "cancel out" the equation.

For a polynomial equation, such as x³ - x² - 10x - 8 = 0, the roots are the values of x that make the polynomial equal to zero. In this case, the roots are the values of x that satisfy the equation x³ - x² - 10x - 8 = 0.

The possible rational roots of x³ - x² - 10x - 8 = 0 are the integers that divide 8 and -8 and are also factors of -1. Since 8 and -8 are divisible by 1, 2, 4, and 8, the possible rational roots of the equation are -1, -2, -4, -8, 1, 2, 4, and 8. But among these, only -2, -1, and 4 makes the equation equal to zero.

Hence, -2, -1, and 4 are the possible rational roots of x³ - x² - 10x - 8 = 0.

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The pair in the solution of the equation -2x + 3y = 6 is (0,2).

The set of all values that, when substituted for unknowns, make an equation true is known as the solution.

A specific location on the graph is the solution of a linear equation in two variables, where ax+by = c, meaning that when the x-coordinate is multiplied by a and the y-coordinate is multiplied by b, the sum of these two values equals c. There are essentially an endless number of solutions to a linear equation with two variables.

Now in the question,

To find the pair of solutions of the equation -2x + 3y = 6, we satisfy all the pairs one by one in the given equation

1. Putting the value of (x, y) as (-3,4) in the equation we get-

-2*-3 +3*4 = 6 ⇒ 18 = 6

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

2. Putting the value of (x, y) as (3,-4) in the equation we get-

-2*3 + 3*-4 = 6 ⇒ -18 = 6

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

3. Putting the value of (x, y) as (0,2) in the equation we get-

-2*0 + 3*2 = 6 ⇒ 6 = 6

Therefore LHS = RHS

Hence it is the solution to the equation.

4. Putting the value of (x, y) as (3,0) in the equation we get-

-2*3 + 3*0 = 6 ⇒ -6 =6

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

Thus (0,2) is the solution of the equation.

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Answer:

u < -5

Step-by-step explanation:

-2u > 10 (Divide both sides by -2)

u > -5 (Change the greater than sign to a less than sign since we divided by a negative number)

Final Answer: u < -5

Answer:

(1/2) (5 - m) or 1/2 * 5 - m or in word form, one half times five minus m

Step-by-step explanation:

Hope it helps! =D

Answer:

y=-8x+9

Step-by-step explanation:

8x+y=9

(subtract 8x  on both sides of the equation)

y=-8x+9

The cost of each of the favors is of $5 and the required equation is 8f+265 = 305

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, A party package costs $265 and covers the entrance fee for guests, a private party room, and an activity guide. Estelle upgraded her package to include a favor for each of her 8 guests, bringing the total to $305.

The addition of 8 favors increase the cost of the party by $40

The equation that can be used to find the number of favors =

8f+265 = 305

Solving for f,

8f = 40

f = 5

Hence, the cost of each of the favors is of $5.

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The inequality is x ≤ 5.09, where x is the number of outfits. Rashon can buy at most 5 outfits while staying within his budget.

To determine the number of biking outfits Rashon can buy while staying within his budget, you can set up an inequality using the information provided.

First, calculate the total cost of the reflectors and gloves:

3 reflectors × $10.78 + $32.64 = $38.34 + $32.64 = $71

Then, subtract the cost of the bicycle, reflectors, and gloves from Rashon's budget: $780 - $481.28 - $71 = $227.72

Now, you can use this remaining amount to determine the number of biking outfits Rashon can buy.

Let x be the number of outfits he can buy

You can set up an inequality as follows:

44.95x ≤ $227.72

Dividing both sides by 44.95:

x ≤ 5.09

However, since the number of outfits is an integer, he can only buy 5 outfits at most.

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Answer:

x = - 1

Step-by-step explanation:

Given:

8(x-10)=-88

Solve:

8(x-10)=-88

Using the distributive property.

How to use distributive property:

Multiply the outside number by the inside parenthesis numbers.

Like this;

8x - 80 = -88

Now add 80 to both sides:

8x - 80+80 = -88+80

8x = -8

Divide both sides by 8:

x = -1

Check:

We can substitute x which is -1 into the equation;

8(-1-10)

8*((-1)-10)

= -88

Hence, x = -1

RevyBreeze

Ordered pairs are also very well known as coordinates.

An ordered pair is a set of two numbers that are used to describe the position of a point on a coordinate plane.

The first number in the ordered pair is called the x-coordinate and the second number is called the y-coordinate. The x and y coordinates represent the horizontal and vertical positions, respectively, of a point on a coordinate plane.

For example, (3,4) is an ordered pair. Here, 3 is the x-coordinate and 4 is the y-coordinate. Point (3,4) is located 3 units to the right of the y-axis and 4 units above the x-axis on a coordinate plane.

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227 18-inch cubes can fit inside the rectangular prism.

You may calculate how many 18-inch cubes can fit within a rectangular prism by dividing the rectangular prism's overall volume by the volume of a single 18-inch cube.

A rectangular prism's volume can be calculated using the formula length x width x height. In this instance, the dimensions are 312 inches long, 212 inches wide, and 3 inches high. As a result, the rectangular prism has a volume of 1,326,720 cubic inches (312 x 212 x 3).

A single 18-inch cube has a volume of 18 x 18 x 18 = 5832 cubic inches.

We divide the volume of the rectangular prism by the volume of a single 18-inch cube to get the number of 18-inch cubes that can fit inside: 1,326,720 / 5832 = 227.

Therefore, the rectangular prism can accommodate 227 18-inch cubes.

Please take note that this is an estimate and that there will not be enough room in the prism to fit 227 cubes exactly.

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So,  the area of the triangle is 12 square inches.

In a two-dimensional plane, the area of a triangle is the region enclosed by it. A triangle, as we all know, is a closed form with three sides and three vertices. Thus, the area of a triangle is the total space filled by the triangle's three sides. The typical formula for calculating the area of a triangle is half of the product of its base and height.

The area of a triangle can be found using the formula: (1/2) * b * h

Given that b = 3 in. and h = 8 in., the area of the triangle would be:

(1/2) * 3 * 8 = (1/2) * 24 = 12 square inches.

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Answer:

1

Step-by-step explanation:

Because the shape divided has to create another shape and for 1 it's an oval at the beginning and then after the lines of symmetry go through its seen as 8 triangles.

Step-by-step explanation:

the point-slope form is

y - y1 = m(x - x1)

m is the slope, (x1, y1) is the given point.

so,

y - -1 = 2(x - 6)

y + 1 = 2(x - 6)

The value of angle D, angle E, angle F are 48° , 84° and 48° respectively

An isosceles triangle is a triangle with two equal sides. In the figure above, the two equal sides have length and the remaining side has length. . This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles.

Since E is not equal to F then we can possibly say F = D since the triangle is an isosceles triangle.

Therefore :

180 = 5x+59 + 2x+38 + 2x + 38

180 = 9x + 135

9x = 180-135

9x = 45

x = 5

therefore angle E = 5×5 + 59 = 25+59 = 84°

angle D = F = 2×5 + 38 = 10 + 38 = 48°

therefore D = 48°, E = 84°, F = 48°

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The perimeter of the rectangle when ℓ = 6.2 units and w = 3.5 units is 9.4 units

The perimeter of a two-dimensional shape is the total length of the outline.

Since the perimeter of a rectangle can be found using the expression 2ℓ+2w

when ℓ=6.2 units and w = 3.5 units, you can get the perimeter by substituting ℓ=6.2 and w = 3.5 into the expression 2ℓ+2w. That is:

perimeter of rectangle = 2ℓ+2w

perimeter of rectangle = 2×6.2 + 2×3.5

perimeter of rectangle = 12.4 + 7

perimeter of rectangle = 19.4 units

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Set each component to 0 and solve for x to discover the roots, or solutions, of the polynomial equation P(x) = 0. Factor the polynomial equation to find the solution. Set each factor to 0. 2x4 = 0 or (x - 6) = 0 or (x + 1) = 0 Determine x.

According to the Fundamental Theorem of Algebra, this 2 n d degree polynomial must have precisely two roots. Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions. In algebra, we utilize integers with definite or fixed values such as 2, 7, 0.068, and so on. In algebra, we employ variables such as x, y, and z in addition to integers. Elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra are all sub-branches of algebra. In algebra, an algebraic expression is composed of integer constants, variables, and the basic arithmetic operations of addition(+), subtraction(-), multiplication(), and division(/). 5x + 6 is an example of an algebraic expression.

Here,

By setting each component to 0 and solving for x, you may obtain the roots, or solutions, of the polynomial equation P(x) = 0. Factor the polynomial equation to solve it. Set each component to zero. 2x4 = 0, (x - 6) = 0, and (x + 1) = 0. Calculate x.

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One of the most effective techniques to recall multiplication tables without just repeating the numbers is by using skip counting.

A sequence is a group of numbers, or "terms," as 2, 5, 8. Some sequences can be made endlessly long by taking advantage of a specific pattern they follow. Add three and use the example of 2,5,8 to continue the series. There are formulas there that demonstrate where to look for words within a sequence. A collection of objects that are in some order is referred to as a sequence informally in mathematics. It has parts, much like a set. The entire, potentially infinite number of ordered objects is referred to as the sequence's length. putting two or more items in a sensible order. Chronological.

given

One of the most effective techniques to recall multiplication tables without just repeating the numbers is by using skip counting.

When counting by skips, you always start with the number you're counting by and keep adding it.

For instance, if you skip count by 2, you would get 2, 4, 6, 8, 10, etc.

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By Pythagoras theorem, The length of MN=5 units and that of LN=4.33 units.

 is the formula for Pythagoras' theorem. The right-angled triangle's longest side, or c, is used in this equation. The hypotenuse is another name for this line. The other two sides of the triangle are shown by letters A and b.

Since, it is a right angle triangle, we can use Pythagoras theorem.

cos 60=base/hypotenuse

1/2=2.5/Hypotenuse

Hypotenuse=2*2.5

Hypotenuse=MN=5 units.

now,

sin 60=perpendicular/hypotenuse

[tex]\sqrt{3}/2=LN/5\\[/tex]

LN=4.33 units.

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Answer:

B' (- 1, - 2 ) , C' (0, - 8 )

Step-by-step explanation:

A (1 , - 4 ) → A' (- 3, - 5 )

1 → - 3 in the x- direction means subtract 4 from the original x- coordinate

- 4 → - 5 in the y- direction means subtract 1 from the original y- coordinate

the translation rule is then

(x, y ) → (x - 4, y - 1 ) , then applying this

B (3, - 1 ) → B' (3 - 4, - 1 - 1 ) → B' (- 1, - 1 )

C (4, - 7 ) → C' (4 - 4, - 7 - 1 ) → C' (0, - 8 )

The equation of line that passes through (6,0) and has a slope of -5/6 is y = (-5/6)x + 5.

The point-slope form is expressed as;

( y - y₁ ) = m( x - x₁ )

Where m is slope, x₁ and y₁ are the coordinates of the point .

Plug the slope m = -5/6 and point (6,0) into point-slope formula and simplify.

( y - y₁ ) = m( x - x₁ )

( y - 0 ) = (-5/6)( x - 6 )

y - 0 = (-5/6)x + (5/6)6

y = (-5/6)x + 5

Therefore, the equation of the line is y = (-5/6)x + 5.

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Answer:

about 91 m high.

Step-by-step explanation:

I have measured them as best I can on my computer screen.

The tower is 14 mm high and the tree is about 91 mm high on the enlarged image.

That makes the tree about 91 m high.

Answer:

A. C. And D.

Step-by-step explanation:

I searched it up for you, cause... I'm not good at this XD. I hope this helps :D

Two triangles are congruent if and only if they have the same shape and size.

What is triangle ?

A triangle in which it is having three sides , three angles and the sum of three angles is always 180 degrees.

So, there are several ways to find out if two triangles are congruent, so we will study the triangles above to find the answers:

Case a. (AAS - Angle, Angle, Side)

AAS stands for "angle, angle, side" and means that we have two triangles where we know two angles and the non-included side are equal. So, for the figure above it is true that:

∠B = ∠E

∠A = ∠D

Case b. We don't have any information about this case that allows us to get a conclusion about congruence. Recall that for congruent triangles you need to compare three elements two by two.

Case c. (SSS - Side, Side, Side)

SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. So, for the figure:

Case d.  We only have two equal elements, but it is necessary to have three elements for comparing them doing the comparison two by two. There is not enough information for getting a conclusion.

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The exact representation of surveying drama club is by second sampling method.

Thus correct option is B .

Given, Selling tickets to the school play .

Systematic random sampling is known to be a type of random sampling technique that needs the selection of samples  using a system of intervals in a specific population.

In Systematic Sampling second sampling method is used. Grounded on the fact that the system of sampling is one that's drawn from the population, it's said to be an effective system of sampling.

Hence option B is correct .

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There have been 3 sides and 3 angles in every triangle, some of which might be the same. The hypotenuse, which is the side that faces the right angle, and the legs, which are the other two sides, are given specific names in the case of a right triangle.

A triangle is a three-sided geometry shape with 3 vertices. The internal angle of the triangle, which is 180 degrees, is built. It means that a triangle's internal angles sum to 180 degrees.

It is the polygon with the fewest sides. Or to put it another way, a triangle is a three-sided, two-dimensional shape whose internal angles are 180°.

Triangles are primarily divided into six varieties based on the angles and side length.

The triangles are further divided based on the angles into:

(1) Acute Angle Triangle

(2) Obtuse Angle Triangle

(3) Right Angle Triangle

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Answer:

a(z+e)

Step-by-step explanation:

(a•z) + (a•e) can be rewritten as:

az + ae

as we can see from the newly created expression, a is the common multiple and we need to add a and z up.

So the answer is

a(z+e)

Answer:

m<y=120

Step-by-step explanation:

m<x=34, m<z=26, = 60.

180-60=120.

angle 3 = 120.

Answer:

D. m<y=120

Step-by-step explanation:

have a good day!

Answer:

Below

Step-by-step explanation:

This is a right traingle with legs 300 and 2250

Tangent = opp leg / adjacent leg

Arc tan (opp / adj) = arctan (300/2250) = 7.6°