in how many ways can 10 balls be selected if at least one red ball, at least two blue balls, and at least three green balls must be selected?

The  △ABC and △DEF are congruent by SAS if  BC = EF. Hence option D is the correct option.

What are congruent triangles?

If all three corresponding sides are equal and all three corresponding angles are identical in measure, two triangles are said to be congruent. These triangles can be moved, rotated, flipped, and turned to look exactly the same. They coincide if they are relocated. ' is the symbol of congruence.

Given that in △ABC and △DE:

AB = DE

∠A ≅ ∠D

SAS rule: Two triangles are congruent if two sides and an included angle of one triangle are equivalent to two sides and an included angle of the second triangle.

The opposite side of ∠A is BC and the opposite side ∠D is EF.

Thus the additional information, that is needed is BC = EF.

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The slope-intercept form of the line equation 2x+ y = 10 is y = -2x + 10

There are three type of the equation of line:

- slope-intercept form.

The equation of line is: y = mx + b

Where:

m = slope

b = y-intercept

- point-slope form

The equation of line is: y - y₁ = m(x - x₁)

Where:

m = slope

(x₁,y₁)  = a point on the line

- standard form
Ax + By + C = 0

Where A, B, C are constant

The given equation is: 2x+ y = 10

we will convert it into  slope-intercept form  y = mx + b

Subtract both sides by 2x:

2x+ y -2x = 10 -2x

y = -2x + 10

Hence, the slope-intercept form is y = -2x + 10

There was a typo in your question, most probably your question was:

What is the slope-intercept form of the equation 2x+ y = 10?

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equation for a tractrix, hence it proves that the trace of the tractrix is given as (t, t tan t).

The trace of the tractrix is given as:

Trace = (x, y) = (t, t tan t)

To show that the trace is that of a tractrix, we will use the equation for a tractrix, which is given as:

x = t – t tanh t

where t is the angle that the y-axis makes with the vector.

Substituting the value of x in the trace equation, we get:

t – t tanh t = t

Simplifying the equation, we get:

t tanh t = 0

This is the equation for a tractrix, hence it proves that the trace of the tractrix is given as (t, t tan t).

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The statement 115 < -225 because 115 is located to the right of -225 on the number line is not true.

The horizontal straight lines in mathematics known as number lines are where integers are arranged in equal intervals. A number line can be used to represent every number in a sequence. This line continues forever at both ends.

On a number line as we go from left to right the numbers increase. For the given numbers, 115 > -135> -225 as 115 is located on the right of the number line.

Hence, statement one 115 < -225 because 115 is located to the right of -225 on the number line is not true.

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h = kv is the formula connecting the height reached and the initial velocity

A variation is a relation between a set of values of one variable and a set of values of other variables.

From the information, the stone is thrown upwards, the height, h, it reaches is proportional to the square of the initial velocity, v.

Since the height, h is proportional to the square of the initial velocity, v.

We can write the formula as follows:

h α v

h = kv   (where k is constant of proportionality)

Therefore, the formula connecting the height reached and the initial velocity is h = kv  

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The equation to calculate slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁).

Here,

m = the line's slope

x1 is equal to the initial point's x-coordinate.

y1 is the first point's y-coordinate.

x2 is equal to the second point's x-coordinate.

The second point's x-coordinate is equal to y2.

It only takes applying the slope formula rise/run to find the slope between two places. With various forms of information about the line available, various formulas can be used to determine the slope. Particularly when two points on the line are given, the formula for finding the slope from two points is utilized.

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The measure of congruent angles X and Y of the hexagon are 135.

let the measure of the congruent angles of  X and Y be a

Then by the angle sum property of a hexagon sum of all the angle will be

U +V +W +X +Y +Z = 720

then 100 + 110+ 149 + 91 + a + a =720

2a = 720 - 450

2a = 270

Then a = 135

Hence the congruent angles X and Y are 135.

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Answer

0^0 =1

or

0^0 can be undefined.

The optimal values of x and y to maximize the profit are 10 and 10, respectively, and the maximum profit is $200.

Let X and Y represent the number of units of product A and B that we want to produce. We want to maximize the profit, so our objective function is:

Profit = 10x + 15y

The constraints are:

X + Y ≤ 20

2X + Y ≤ 30

X ≥ 0, Y ≥ 0

To find the optimal values of x and y, we must first solve the system of equations. By subtracting the first equation from the second equation, we get:

X = 10

Substituting this value into the first equation, we get:

Y = 10

Now that we have found the values of x and y, we can plug them into the objective function to find the maximum profit:

Profit = 10(10) + 15(10) = 200

Therefore, the optimal values of x and y to maximize the profit are 10 and 10, respectively, and the maximum profit is $200.

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Answer:

Step-by-step explanation:

The prime multiples of 4 are 2*2 or 2^2.

Answer: 0.125 Miles

Step-by-step explanation:

X+2.25 +2.125 = 4.5
X+4.375 =4.5
4.5-4.375= X = 0.125

The two plans will cost the same when Lucy has driven average speed 550miles. ($55 + $0.50 x 550)= $330

Divide the overall distance traveled by the time period to find the average speed. An someone traveling at an average speed of 40 miles divided by 40 minutes, or 1 mile per minute, would be driving 20 miles north and then 20 miles south to arrive at the same location (60 mph)

The overall distance traveled by an object over the total amount of time is the thing's average speed. The average speed v of an object during a motion that covers a total distance of d and a total duration of t can be estimated using the formula v = d t.

(0.6*550)=$330

The difference between both the trip rate is .10$

and the difference between initial fee is 55$

so after 1 mile the difference is .10$

the 55$can be earn after

55*10=550 mile.

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200

Portions of quantities can be represented as percentages and decimals, which can help solve different types of questions.

Multiplying Decimals

To find any percent of a quantity, you can multiply the quantity by the percentage as a decimal. We can convert percentages to decimals easily. By moving the decimal point 2 places to the left, we can change 40% into a decimal. So, 40% is equal to 0.4. Now, multiply this by 500.

So, Leo has put together 200 pieces.

Multiples of 10

Since 40% is a multiple of 10, we can solve using another method. It is easy to find 10% of any quantity, just move the decimal point 1 place to the left. So, 10% of 500 is 50.

Then, since 40 is 4 times 10, we can say that 40% of 500 is 4 times 10% of 500.

This proves that Leo has done 200 pieces.

Number of cups of flour required to make the same recipe for 3 cups of almond as per the given relation is equal to 7.5 cups of flour.

As given in the question,

For the given recipe cups of flour and cups of almond given is :

2 cups of almond used for 5 cups of flour

The relation is written in the form of expression :

2 cups of almond = 5 cups of flour

⇒ 1 cups of almond = ( 5 / 2 ) cups of flour

⇒ 3 cups of almond =  [ ( 5 / 2 ) × 3 ] cups of flour

⇒ 3 cups of almond =  ( 15 / 2 ) cups of flour

⇒ 3 cups of almond = 7.5 cups of flour

Therefore, the cups of flour required for 3 cups of almond is equal to 7.5 cups of flour.

The above question is incomplete , the complete question is :

A recipe call for 2 cup of almond for 5 cup of flour. Using the same recipe, how many cup of flour will you need for 3 cup of almond?

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0 is not a prime number. A prime number is defined as a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. If we look at 0 it does not meet this requirement it means it cannot be a prime number.

0 does not meet this definition because it is not greater than 1 and it does have positive integer divisors other than 1 and itself (for example, it is divisible by 2, 4, and so on). Additionally, the concept of prime numbers is defined only for positive integers, 0 is not positive.

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The type of function that represents function g(x) is given as follows:

Logarithmic.

To define the function in this problem, we must observe a pattern with the inputs and the outputs.

The input and output pairs are given as follows:

From the pattern, we can see that each output is obtained as the power of 3 to which the input is elevated.

This means that the function is a logarithmic function, more specifically the logarithm of base 3 of x.

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Answer:

Correct options are B) and C)

Step-by-step explanation:

The given equation is 2x+y=10.

Clearly, x=3 and y=4 satisfy this equation.

Therefore , x=3 and y=4 is one of the solution of given equation.

Answer: 24

Step-by-step explanation:

The two triangles IFE and IHG are similar(AA Similarity).

The ratio of line IH : IF = EF : GH = 5 : 12

Therefore, 1.4x + 3 : 6.1x-6.5 = 5:12

Solve this ratio, and you'll get

16.8x+36 = 30.5x-32.5

13.7x = 68.5

x = 5

X is 5, so using X, we can find the length of HI.

30.5-6.5 = 24

Therefore, the answer is 24.

The equation connecting h and v is h = 56/v and the value of h when v = 5 is 11.2

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

Variation = inverse variation

h = 8, v = 7

An inverse variation is represented as

k = vh

Where k is the constant of proportion

Substitute the known values in the above equation, so, we have the following representation

k = 7 * 8

Evaluate

k = 56

So, we have the following representation

vh = 56

Make h the subject

h = 56/v

Substitute the known values in the above equation, so, we have the following representation

h = 56/5

Evaluate

h = 11.2

Hence, the solution is 11.2

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To determine the limit of f(x) as x approaches -7, we need to analyze the behavior of the function as x gets closer and closer to -7.

Since f(x) is defined differently for x < 7 and x >=7, we need to look at both cases separately.

For x < 7, f(x) = -3x + 0

For x >= 7, f(x) = 5x + 1

If we substitute x = -7 into the first equation, we get f(-7) = -3(-7) + 0 = 21

If we substitute x = -7 into the second equation, we get f(-7) = 5(-7) + 1 = -36

We can see that the function is defined differently for x < 7 and x >=7, and it does not have the same value when x = -7.

Therefore, the limit of f(x) as x approaches -7 does not exist (DNE).

A graph of f(x) with two different lines for x<7 and x>=7, one with slope -3 and y-intercept 0, the other with slope 5 and y-intercept 1. The two lines do not intersect at x = -7, this illustrates the DNE limit.

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The value of function f+g(x) will be -5^x-3x-6 i.e. C.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

Given function are f(x)=-5^x-4

anf g(x)=-3x-2

so f+g(x) will be f(x)+g(x)

f+g(x)=-5^x-4-3x-2

=-5^x-3x-6

Hence,

           The value of function f+g(x) will be the polynomial -5^x-3x-6.

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Difference in the weekly earnings of Dana and Monique is $127.5.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Dana :

Number of days Dana grooms dogs = 4 days a week

Number of dogs Dana grooms in a day = 15 dogs

Number of dogs Dana grooms in a week = 15 × 4 = 60 dogs

Earning of Dana per dog = $12.75

Earnings of Dana in a week = 60 × $12.75 = $765

Monique :

Number of days Monique grooms dogs = 5 days a week

Number of dogs Monique grooms in a day = 10 dogs

Number of dogs Monique grooms in a week = 10 × 5 = 50 dogs

Earning of Monique per dog = $12.75

Earnings of Monique in a week = 50 × $12.75 = $637.5

Difference in their earnings = $765 - $637.5 = $127.5

Hence there is a difference of $127.5 in their earnings.

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The value of m in the equation is 35

Index is the power or exponent which is raised to a number or a variable e.g. in number 3⁵, 5 is the index of 3. The 3 is called the base. The plural form of index is indices.

Product law: To multiply two variables or numbers with the same base, we need to add their powers and raise them to that base":  P⁴ + P⁶ = P¹⁰

[tex](x^{m})^{3}[/tex] = (x¹³)⁵ × (x⁻⁸)⁻⁵

[tex](x^{m})^{3}[/tex] =  x⁶⁵ × x⁴⁰

[tex](x^{m})^{3}[/tex] = x⁶⁵⁺⁴⁰

[tex](x^{m})^{3}[/tex] = x¹⁰⁵

[tex](x^{m})^{3}[/tex] =  (x³⁵)³

Comparing both sides of the equation, m = 35

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the values of x will be:

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

Given, Two functions, " x ÷ 5/6 = 1 and 4/5" and " x ÷ 2 and 1/10 = 1 and 2/3"

For  x ÷ 5/6 = 1 and 4/5

Simplifying the value,

x ÷ 5/6 = 1 4/5

x ÷ 5/6 = 9/5

x ÷ 5/6 = 9/5

Cross multiply

x = 9/5 * 5/6

x = 1.5

For  x ÷ 2 and 1/10 = 1 and 2/3

Simplifying the value,

x ÷ 2 1/10 = 1 2/3

x ÷21/10 = 5/3

x = 3.5

Therefore, the values of x will be:

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Answer:

x = 3 and y = 0     or  (3, 0)

Step-by-step explanation:

First, you use the first equation to find what y equals.

3x + y = 9

y = 9 - 3x

Next, you plug in y to the second equation.

2x - y = 6

2x - (9 - 3x) = 6

2x - 9 + 3x = 6

5x - 9 = 6

5x = 15

x = 3

Then, you plug in x in the first equation.

3x + y = 9

3(3) + y = 9

9 + y = 9

y = 0

Answer:

For me, it always helps to break down equations like this. Divide it up into two separate parts.

4^2*4^2=x

4^2=16

Replace both 4^2 with 16

16*16=256

The coordinates of the points after dilation is D'(-5/3,1),  E'(1,-2/3), F'(5/3,-1), and C'(-1,-4/3)

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.

Given that the scale factor is 1/3. The coordinates of the points after dilation is,

D(-5,3) = D'(-5/3,1)

E(3,-2) = E'(1,-2/3)

F(5,-3) = F'(5/3,-1)

C(-3,-4) = C'(-1,-4/3)

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[tex]x=\cfrac{cos(2y)}{e^y}\hspace{5em}x\left( \frac{\pi }{8} \right)=\cfrac{1}{e^{\frac{\pi }{8}}\sqrt{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{dx}{dy}\implies \stackrel{quotient~rule}{\cfrac{-2sin(2y)e^y-cos(2y)e^y}{(e^y)^2}}\implies \cfrac{-2sin(2y)-cos(2y)}{e^y} \\\\[-0.35em] ~\dotfill\\\\ \left. \cfrac{dx}{dy} \right|_{y=\frac{\pi }{8}}\implies \cfrac{-2sin(\frac{\pi }{4})-cos(\frac{\pi }{4})}{e^y}\implies \cfrac{-3}{e^{\frac{\pi }{8}}\sqrt{2}}\impliedby m[/tex]

now, since we have the value of "x" at π/8 and we know that at that point y = π/8, and we also have the slope at π/8, let's plug all those fellows in the point-slope formula

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\cfrac{\pi }{8}~~ = ~~\cfrac{-3}{e^{\frac{\pi }{8}}\sqrt{2}}\left(x-\cfrac{1}{e^{\frac{\pi }{8}}\sqrt{2}} \right)[/tex]

[tex]y-\cfrac{\pi }{8}~~ = ~~\cfrac{-3}{e^{\frac{\pi }{8}}\sqrt{2}}x+\cfrac{3}{2e^{\frac{\pi }{4}}} \implies \boxed{\cfrac{3}{e^{\frac{\pi }{8}}\sqrt{2}} {\Large \begin{array}{llll} x \end{array}} + {\Large \begin{array}{llll} y \end{array}}-\cfrac{\pi }{8}-\cfrac{3}{2e^{\frac{\pi }{4}}}~~ = ~~0}[/tex]

Let's call Mindy's height "M". According to the problem, we know that:

Camille's height = 66 inches

Camille's height = 2 * Mindy's height - 20 inches

We can substitute the first equation into the second equation to solve for Mindy's height:

66 inches = 2 * M - 20 inches

We can add 20 inches to both sides of the equation to get:

66 inches + 20 inches = 2 * M

This gives us:

86 inches = 2 * M

To find Mindy's height, we can divide both sides of the equation by 2:

M = 86 inches / 2

So Mindy is 43 inches tall.

Answer:

Mindy is  46 inches

Step-by-step explanation:

Let m = Mindy's height

66 = 2m - 20  Add 20 to both sides

66 + 20 = 2m - 20 + 20

86 = 2m  Divide both sides by 2

[tex]\frac{86}{2}[/tex] = [tex]\frac{2m}{2}[/tex]

46 = m