What is the rational root theorem formula?

Answer:

Step-by-step explanation

In the first equation

x=17-4y

In the second equation

We clear "x"

y=x-2

x=y+2

We ecuate "x"

x=17-4y=y+2

17-4y=y+2

15=5y

y=3

we substitute to find "x"

x=17-4y=17-4(3)=5

Yes, the isosceles triangles are equal to 180 degrees.

We know that isosceles triangles are triangles which have two equal sides. Since the sides are equal, they subtend equal angles as well.

However, the two equal angles subtended by the equal sides and one more angle which is subtended by the third side of the isosceles triangle all add up to a total of 180 degree as we know that the sum of all the angles of a triangle is always equal to 180 degrees.

Hence we can conclude that the isosceles triangles are also equal to 180 degrees like every other triangle.

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To answer, let's use the exponent rules to solve the power of 1.

Exponents, often known as powers, specify how many times the base number must be multiplied.

Exponent rules are principles that are used to simplify expressions using exponents. These principles are also useful in simplifying formulas with exponents that are decimals, fractions, irrational numbers, or negative integers.

Negative exponents Rule: [tex]a^{-m} = 1/a^m[/tex]

Product Rule: [tex]a^m * a^n = a^{(m+n)}[/tex]

Quotient Rule: [tex]a^m/a^n = a^{(m-n)}[/tex]  

Power of a Power Rule: [tex](a^m)^n = a^{mn}[/tex]

Here, given that, 3 to the power of 1

The number 3¹ may be expressed as 3 to the power of 1, according to the exponent rule.

The base number in this formula is 3, while the power number is 1, and we know that any integer increased to that same power of that one equals the original number.

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Answer:

SB = 4

Step-by-step explanation:

The figure is the intersection of the medians of this triangle. The medians of a triangle bisect the sides of the triangle. The intersection of the medians is called the centroid. In this case, the centroid of this figure would be S.

In fact, the distance from a vertex to the centroid of the triangle is 2/3 of the distance from said vertex to the vertex's opposite side.

Create the equation SB = 2/3(PB).

.....................................SB = 2/3(6)

....................................SB = 12/3

...................................∴SB = 4

Answer:

SB = 4

Step-by-step explanation:

SB = 2/3 BP

SB = 2/3 (6)

SB = 4

Answer: 56 miles per hour

Step-by-step explanation:

45 minutes = 0.75 hour

3 hours and 45 minutes = 3.75 hours

Takes 210 divided by 3.75 = 56 miles per hour

The triangles are congruent if all three sets of comparable sides are present. The side-side-side shortcut is a congruence technique (SSS).

Triangles are considered congruent by SAS if their two sides match up with their corresponding two sides on the other triangle, and if their included angles match up in both triangles.

We can prove two triangles, either by SSS or SAS by simply taking two triangles and checking whether the sides and the angles of the corresponding triangles are congruent or not.

By simply comparing it on the basis of their sides and angles we can easily prove the corresponding triangles by SSS or SAS.

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f(-4) = -18, f(-2) = -10, f(6) = 12 and f(-1) = -6 using the piecewise function.

A function defined by numerous sub-functions, where each sub-function applies to a distinct interval in the domain, is known in mathematics as a piecewise-defined function (also known as a piecewise function, a hybrid function, or definition by cases).  Instead of being a property of the function itself, piecewise definition is a means to express the function.

When the domain may be divided into intervals on which the property holds, the phrase "property holding piecewise for a function" is used, which is separate but related. This is a characteristic of the function itself, as opposed to the idea mentioned above.

f(-4) = 4(-4)-2 = -18  ∵-4≤-1

f(-2) = 4(-2)-2= -10  ∵-2≤-1

f(6) = [tex]\frac{1}{2}*6 + 9 = 12[/tex] ∵6>-1

f(-1) = 4(-1)-2 = -6 ∵-1≤-1

f(-4) = -18, f(-2) = -10, f(6) = 12 and f(-1) = -6 using the piecewise function.

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Answer: 2³

Step-by-step explanation:

    We will use the order of operations to help us solve. This means, in this case, starting with exponents and then multiplying. We will also use the exponent rules.

    Given:

[tex]\displaystyle (2^2)^4\;*\;2^{-5}[/tex]

    Power rule of exponents:

[tex]\displaystyle (2^2)^4\;*\;2^{-5}=(2^{2*4})\;*\;2^{-5}[/tex]

[tex](2^{8})\;*\;2^{-5}[/tex]

    Product rule of exponents:

[tex]\displaystyle (2^{8})\;*\;2^{-5} = (2^{8+-5})= (2^{8-5})[/tex]

[tex](2^{3})[/tex]

      The simplified form of the expression, from the given options, is 2³.

Answer:

Let,

length of rectangle ( L) =9cm

breadth of rectangle (b) =4cm

Area of rectangle=L×b

=9×4

=36cm^2

By combining the mother's as well as father's heights in inches, you may determine the midparental height. For boys, measure 5 inches longer; for girls, measure 5 inches shorter. multiply by two.

However, a number of calculations can offer a reliable approximation of a child's growth. Here is a common illustration:

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Yes , the equation 3x² + 11x + 10 = 0 is a quadratic equation and the roots are x = -5/3 and x = -2

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c = 0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the equation be represented as A

Now , the value of A is

3x² + 11x + 10 = 0   be equation (1)

Now , the equation is of the form ax² + bx + c = 0 , where the value of a = 3 , b = 11 and c = 10

So , the coefficient a is has the variable x² and equation 3x² + 11x + 10 = 0 is a quadratic equation

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

Substituting the values in the equation , we get

x = [ -11 ± √ ( ( 11 )² - 4 ( 3 ) ( 10 ) ) ] / 2 ( 3 )

On simplifying the equation , we get

x = [ -11 ± √ ( 121 - 120 ) ] / 6

x = ( -11 ± 1 ) / 6

So , the two roots of the equations are

x = ( -11 - 1 ) / 6 and

x = ( -11 + 1 ) / 6

x = -2 and

x = -5/3

Therefore , the values of x are -5/3 and -2

Hence , the roots of the quadratic equations are -5/3 and -2

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We may deduce from the contour map that the estimates of the given functions are;

fx(2, 1) = 10

fy(2, 1) = 3

The geographic mapping used as a form of activism against prevailing power systems is known as counter-mapping.

Contour lines are described as the faint lines drawn on a map that link places of equal height above sea level. This indicates that even if you followed a contour line physically, the elevation (height of the land) would stay constant.

According to the contour map, the contour lines indicate that the coordinate (2, 1) in the x-direction has a value of 10.

Therefore;   fx(2, 1) = 10

Using the same idea, we can deduce from the attached contour map that the coordinate (2, 1) in the y-direction will have a value between 0 and 6. Therefore;

Average = (0 + 6) divided by 2 = 3

Thus;   fy(2, 1) = 3

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Step-by-step explanation:

draw a rectangle with width 98 and height 55 there are two of each side, so 98 + 98 + 55 +55 = 306

Answer:

306m

Step-by-step explanation:

You need to find the perimeter of the rectangle. To do that, you just add the side lenghts. So, this is your lawn with the side lengths:

                      55m
           _____________
           |                           |
           |                           |
           |                           |
98m    |                           |     98m
           |                           |
           |                           |
           |                           |
           _____________
                      55m

You just add them together!

55 + 55 + 98 + 98 = 306

so you need 306 meters of fencing

Answer:

first one and second one

Step-by-step explanation:

x + y is lesser or equal to 20

20 being the max amount of hours he can work in one week and x and y being hours he works

second one because they can earn at least 300 dollars, not less than, but x+Y must still be less than 20 though

Answer:

Aisha mix will be more lemony

Step-by-step explanation:

Find Rahul's percentage of the powdered lemon mix by

Finding the total number of cups

14 + 5 = 19 total cups

Then take

5 divided by 19, times 100% = 26.3%

Find Aisha's percentage of the powdered lemon mix by

Finding the total number of cups

11 + 4 = 15 total cups

Then take

4 divided by 15, times 100% = 26.6% or 27%

Answer: Ariana uses 85% drink mix, and Andres uses 90% drink mix. Therefore, Andres's drink will taste more lemony.

Step-by-step explanation:

Ariana uses 17 cups of mix out of the 20 total cups which is 85%

Andres uses 10 cups of mix out of the 11 total cups which is around 90%

Step-by-step explanation:

The three methods to find the mean are arithmetic, geometric and harmonic .

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Parallel lines are two straight lines that never cross. For this to happen, the lines have to have the same slope.

In this case, the equation given is in what's called "slope-intersect" form. The general form of the slope intercept formula is y=mx + b where m is the slope of the line and b is the point on the Y-axis where the line crosses.

The equation given is y=5x+3 and since the 5 is in the place of m from the general equation, 5 is the slope. Since parallel lines have the same slope, 5 is the answer.

Slope-Intercept Form:

When we're given a linear equation we can immediately see if it's in the slope-intercept form if it follows the format  y=mx+b. As long as y does not have a coefficient the slope and y-intercept are the values of m and b.

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The base is the length of one of the triangle's sides, and the height is the distance from that side to the triangle's opposite corner.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.

Here,

The base of the triangle is the length of one of its sides, and the height is the distance from that side to the triangle's opposite corner.

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Hence, the standard deviation of the given data is 7 .

10 28 13 18 29 30 22 23 25 32

Here is the total number of observations n are 10

total= 10 +28+ 13+ 18+ 29+ 30+ 22+ 23+ 25+ 32 = 230

mean  (μ) = total/n

         = 230/10

         = 23

         Xi                 Xi-μ                    (Xi-μ)²

         10           10-23=-13                   169

         28           28-23=5                      25

          13           13-23=-10                   100

          18           18-23=-5                      25

          29           29-23=6                      36

          30          30-23=7                       49

           22         22-23=-1                         1

            23         23-23=0                        0

           25          25-23=2                         4

            32          32-23=9                       81

Use the formula to calculate the standard deviation.

√1/n*∑   (Xi-μ)² =√1/10*490

                        = √49

                         =7

Hence, the standard deviation of the given data is 7 .

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898 integers in that range excluding 100 and 999

There are 900 integers between 100 and 999, inclusive.

Numbers between 999 and 100 inclusive:  999 - 99 = 900

If you want to know the number of integers between 100 and 999, but not including either 100 or 999, then there are 898 integers in that range.

What is an integers number:

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a set of integers that consists of the following:

Positive Numbers: If a number is greater than zero, it is considered positive. For instance, 1, 2, 3, etc.

Negative numbers are those that are less than zero. For instance: 1, 2, 3, etc.

Zero is described as being neither a positive nor a negative number. A whole number, that is.

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The final step is x < 3

What is an inequality?

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

Less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and not equal (≠) are the five inequality symbols.

Given inequality is

-2(5 - 4x) < 6x - 4

The inequality sign is less than.

Applying distributive property on the left side

-10 + 8x < 6x -4

Subtract 6x from both sides

-10 + 8x - 6x < 6x -6x - 4

-10 + 2x < - 4

Add 10 on both sides:

-10 + 2x + 10 < - 4 + 10

2x < 6

Divide both sides by 2:

2x/3 < 6/3

x < 3

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Answer:

Step-by-step explanation:

you can use the zero-product property to find the roots of a factored equation. After you factor a polynomial into its different pieces, you can set each piece equal to zero to solve for the roots with the zero-product property.

We need to draw all sides of the triangle equal in order to make a SSS triangle because we know that the SSS triangle has all 3 sides equal.

Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.

We u can move, flip, twist, and turn these triangles to produce the same effect.

When relocated, they are parallel to one another.

Two triangles are deemed similar by the SSS test for triangle resemblance if their third sides are proportionate to one another.

Therefore, we need to draw all sides of the triangle equal in order to make a SSS triangle because we know that the SSS triangle has all 3 sides equal.

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five plus eight times nine

The value of radius of the merry-go-round will be 6 feet.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

In our daily life, we always see circular objects for example our bike wheel.

The longest line which can be drawn inside the circle will be the diameter.

The perimeter of the circle = 2πr where r is the radius of the circle.

The Merry cover on the round in 3 seconds thus, to cover the 2πr path it takes 3 seconds.

2πr/3 = 12.56

2πr = 37.68

r = 5.996 ≈ 6 feet.

Hence "The value of the radius of the merry-go-round will be 6 feet".

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“6 more than twice m” can be written in the mathematical form as 2m+6.

The question is saying that we have to write “6 more than twice m” as an algebraic expression or into a mathematical expression.

As in the question, it is mentioned that we have to take the number m as a variable.

So, we are going to use this ‘m’ for solving this question.

Let the number be m.

Then, twice of m will be similar to 2 times m or m multiplied by 2.

Therefore, twice m will be 2m.

Now, the question is saying that 6 more than twice m.

“6 more than” means 6 is added to that specific number.

Hence, 6 more than that number which is twice of m will be 2m+6.

Hence, “6 more than twice m” can be written in the mathematical form as 2m+6.

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The x and y intercept of y=3x-15 is X intercept  is 5, Y interceptis -15

To find X intercept substitute y=0

y=0

0=3x-15

3x=15

x=15/3

x=5

X intercept  is 5 line cuts at (5,0)

To find Y intercept substitute x=0

y=3(0)-15

y=-15

Y interceptis -15 line cuts at  (0,-15)

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Using the ratio we know that before the weekend started, she could have won as many as 164 games.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.

A proportion is an equation that sets two ratios at the same value.

For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

So, let n be the number of victories so that:

n/2n = 1/2 and n+3/2n+4 > 503/1000

Now, cross multiply as follows:

1000n + 3000 > 1006n + 2012

n < 988/6 = 164 4/6 = 164 2/3

Therefore, using the ratio we know that before the weekend started, she could have won as many as 164 games.

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Using the concept of percentage, social media budget will cost $425.25

This is the expression of a ratio or fraction in percentage form. This is done by multiplying a ratio by 100.

The original advertising budget is $81,000 and they plan to increase it by 5%.

Let's calculate the 5% increase in the budget.

5% of 81000 =

5 / 100 = x / 81000

0.05 = x / 81000

x = 81000 * 0.05

x = 4050

The budget for next year will 81000 + 4050 = 85050

In the breakdown for the advertising budget, social media budget got 0.5%

Let's find 0.5% of 85050

0.5% * 85050

0.5 / 100 = x / 85050

0.005 = x / 85050

x = 0.005 * 85050

x = 425.25

The social media budget is $425.25

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