in the diagram shown below line A and line B are parallel lines cut by transversal line c. which equation could be used to solve for the value of x.

The factorized form of each expression is given below:

a. (x - 5)(x + 5)

b. (y - 6)(y + 6)

c. (x - 1)(x - 13)

d. (s + 2)(s + 5)

e. (q - 4)(q - 3)

f. (r + 1)(r + 12)

g. (x - 5)(x + 4)

h. (y + 2)(y + 3)

i. (b - 3)(b + 4)

j. (k - 2)(k - 3)

a. x² - 25:

The difference of squares formula is a² - b² = (a - b)(a + b).

Here, a = x, b = 5. So, x² - 25 = (x - 5)(x + 5).

b. y² - 36:

Again, using the difference of squares formula, a = y, b = 6. So, y² - 36 = (y - 6)(y + 6).

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Answer:

A"(-1, -3), B"(-2, -6), C"(1,-7)

Step-by-step explanation:

y= -4 is a horizontal line that cuts y-axis at (0, -4)

A'(-4, -5), B'(-5,-2), C'(-2,-1) are given on thhe graph

first we reflect over the line m, y= -4

A"(-4, -3), B"(-5, -6), C"(-2,-7) because the line m is the bisector of what conects the image and preimage points

second we translate T(3,0) so you add a 3 to the x coordinate of each point

A"(-4+3, -3), B"(-5+3, -6), C"(-2+3,-7)

A"(-1, -3), B"(-2, -6), C"(1,-7)

Answer:

80cubic cm

Step-by-step explanation:

Answer:

22 pounds and 13 ounces

Step-by-step explanation:

I hope this helps!

Answer:

x = -2

y = 4

Step-by-step explanation:

6x-5y=-32

-7x+8y=46

Solve for x in the first equation.

6x = -32 + 5y

x = (-32 + 5y) /6

x = 5/6y - 16/3

Put x as 5/6y - 16/3 in the second equation and solve for y.

-7(5/6y - 16/3) +8y = 46

-35/6y+112/3 +8y = 46

13/6y + 112/3 = 46

13/6y = 46 - 112/3

13/6y = 26/3

y = 26/3 × 6/13

y = 4

Put y as 4 in the first equation and solve for x.

6x-5(4)=-32

6x-20 = -32

6x = -32+20

6x = -12

x = -12/6

x = -2

Answer:

y = 5/4x - 3

Step-by-step explanation:

Answer:

Ans.=250 21/50

Step-by-step explanation:

54.2%=542/100

=271/50

=250 21/50

to get any percent value to a decimal or fraction format, we simply divide it by 100, first off let's make 54.2 to a fraction and then divide by 100.

\(54.\underline{2}\implies \cfrac{542}{1\underline{0}}~\hspace{10em}\cfrac{542}{10}\div 100\implies \cfrac{542}{10}\cdot \cfrac{1}{100}\implies \cfrac{271}{500}\)

Answer:

\(\frac{9\pm\sqrt{61}}{2}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-(-9)\pm\sqrt{(-9)^2-4(1)(5)}}{2(1)}=\frac{9\pm\sqrt{81-20}}{2}\\\\=\frac{9\pm\sqrt{61}}{2}\)

We can expect that 7935 parts would fail to meet a minimum specification limit of 35 lb tensile strength and 2740 parts would have a tensile strength over 48 lb.

We can use the standard normal distribution to solve this problem.

The standard normal distribution has a mean of 0 and a standard deviation of 1. We can convert the normal distribution of the tensile strength to the standard normal distribution using the formula below.z = (x - μ) / σwhere x is the tensile strength, μ is the mean, and σ is the standard deviation.

a) To determine the number of parts that are expected to fail to meet a minimum specification limit of 35 lb tensile strength, we need to find the probability that a part has a tensile strength less than 35 lb. z = (35 - 40) / 5 = -1P(z < -1) = 0.1587

The probability of a part having a tensile strength of less than 35 lb is 0.1587. Therefore, the number of parts expected to fail to meet a minimum specification limit of 35 lb tensile strength is given by: Number of parts = Probability × Total number of parts= 0.1587 × 50,000= 7935b)

(b) To determine the number of parts that have a tensile strength over 48 lb, we need to find the probability that a part has a tensile strength greater than 48 lb. z = (48 - 40) / 5 = 1.6P(z > 1.6) = 0.0548

The probability of a part having a tensile strength greater than 48 lb is 0.0548. Therefore, the number of parts that have a tensile strength over 48 lb is given by: Number of parts = Probability × Total number of parts= 0.0548 × 50,000= 2740

Therefore, we can expect that 7935 parts would fail to meet a minimum specification limit of 35 lb tensile strength and 2740 parts would have a tensile strength over 48 lb.

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Given,

The number of paper clips used for 9 cm paper is 3.

Consider, the number of paper clips used for 15 cm paper,

By proportionality,

Hence, the number of paper clips used for 15 cm of paper is equal to 5.

Answer:

The slope of the line = m = 2

Step-by-step explanation:

Taking two points from the line graph

Determining the slope between (0, 0) and (1, 2)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [2 - 0] / [1 - 0]

               = 2 / 1  

               = 2

Thus, the slope of the line = m = 2

Answer:

not 100 percent sure but i think f

Step-by-step explanation:

Answer:

It will be 40

Step-by-step explanation:

Hope this helped have an amazing day!

The given statement is,

→ if u have 10 and add 20 and add 10.

In mathematical expression,

→ (10 + 20) + 10

→ 30 + 10

→ 40 is the answer.

The median splits the data in the box and whisker plot into two equal halves, with 50% of the data falling below the median and 50% above the median.

In a box and whisker plot, the median is represented by a vertical line or box within the plot. The box represents the interquartile range (IQR), which contains the middle 50% of the data. The lower edge of the box corresponds to the first quartile (Q1), where 25% of the data falls below, and the upper edge of the box corresponds to the third quartile (Q3), where 75% of the data falls below.

The whiskers extend from the box and represent the minimum and maximum values in the dataset, excluding any outliers. The length of the whiskers may vary depending on the range of the data and the presence of outliers.

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Answer:

a) 16.75 cubic inches  

Step-by-step explanation:

Cylindrical mold:  

   V = πr²h

where V is volume, r is radius, and h is height.  

Substituting the known values:

    V = π(2 in)²(4 in)

    V = 16π in³ = 50.26 in³

Spherical mold:

   V = 4πr³/3

Substituting the radius to the equation,

   V = 4π(2 in)³ / 3  

   V = 32π/3 in³ = 33.51 in³

The difference is calculated below:

D = 50.26 in³ - 33.51 in³

D = 16.76 in³

By using the concept of simple interest, it can be calculated that

Brionny has invested £8400.

What is simple interest?

Simple interest is the interest earned on a certain principal at a certain rate over a certain period of time

For the first year-

Principal = £P

Rate = 2%

Time = 1 year

Interest = \(\frac{P \times 2 \times 1}{100}\) =  £\(\frac{P}{50}\)

Amount = £\((P + \frac{P}{50})\)

             = £\((\frac{50P + P}{50})\)

             = £\(\frac{51P}{50}\)

For the Second year:

Principal =  £\(\frac{51P}{50}\)

Rate = 1%

Time = 1 year

Interest = \(\frac{51P \times 1 \times 1}{50 \times 100}\) =  £\(\frac{51P}{5000}\)

Amount = £\((\frac{51P}{50} + \frac{51P}{5000})\)

             = £\((\frac{5100P + 51P}{5000})\)

             = £\(\frac{5151P}{5000}\)

By the problem,

\(\frac{5151P}{5000} = 8653.68\\P = \frac{8653.68 \times 5000}{5100}\\\)

P =  £8400

Brionny has invested £8400.

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The product of numbers is gotten by multiplying the numbers

The product abcd is 0

From the product table, we have:

\(7a * 6 = aaa\)

By trial by error, we set a = 4.

So, we have:

\(74 * 6 = 444\)

The above equation is true,

So, we have:

\(a = 4\)

From the product table, we have the following equations

\(c =a + 6\)

\(a + 6 = d\)

Substitute 4 for a in \(c =a + 6\)

\(c =4 + 6\)

\(c =10\)

c can only take a single digit.

So, we have:

\(c = 0\)

\(a + 6 = d\) becomes

\(1 + a + 6 = d\)

Substitute 4 for a

\(1 + 4 + 6 = d\)

So, we have:

\(11 = d\)

Rewrite as:

\(d = 11\)

d can only take a single digit.

So, we have:

\(d = 1\)

So, the product is:

\(74 * b6 = 7104\)

Divide both sides by 74

\(b6 = 96\)

By comparison:

\(b = 6\)

So, we have:

\(a = 4\)

\(b = 6\)

\(c = 0\)

\(d =1\)

The product becomes

\(abcd =4 * 6 * 0 * 1\)

\(abcd =0\)

Hence, the product abcd is 0

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The probability of either selecting 3 boys and 1 girl or selecting 3 girls and 1 boy from the class is 12/35.

To find the probability, we need to determine the number of favorable outcomes (selecting 3 boys and 1 girl or selecting 3 girls and 1 boy) and divide it by the total number of possible outcomes (selecting any 4 students from the class).

Total number of students in the class = 3 boys + 4 girls = 7 students

Number of ways to select 3 boys and 1 girl:

- Number of ways to select 3 boys from 3 boys = C(3, 3) = 1 way

- Number of ways to select 1 girl from 4 girls = C(4, 1) = 4 ways

- Total number of ways to select 3 boys and 1 girl = 1 * 4 = 4 ways

Number of ways to select 3 girls and 1 boy:

- Number of ways to select 3 girls from 4 girls = C(4, 3) = 4 ways

- Number of ways to select 1 boy from 3 boys = C(3, 1) = 3 ways

- Total number of ways to select 3 girls and 1 boy = 4 * 3 = 12 ways

Total number of possible outcomes = C(7, 4) = 35 ways (selecting any 4 students from 7 students)

Therefore, the probability of either selecting 3 boys and 1 girl or selecting 3 girls and 1 boy is (4 + 12) / 35 = 16/35.

So, the probability is 16/35 that either 3 boys and 1 girl or 3 girls and 1 boy are selected for the special training program in Mathematics.

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The amount of plastic covering needed to cover the window is 25.71.

The window consists of a semi circle and a rectangle. The circumference and the perimeter of the semi circle and a rectangle has to be determined.

Circumference of the semi circle = 1/2πd + d

Where:

π = 3.14

d = diameter = 3

1/2 x 3.14 x 3 + 3 = 7.71

Perimeter of the rectangle = 2(length + width)

2x (6 + 3) = 18

18 + 7.71 = 25.71

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Answer:

x = ± 3\(\sqrt{5}\)

Step-by-step explanation:

x² = 45 ( take the square root of both sides )

x = ± \(\sqrt{45}\) = ± \(\sqrt{9(5)}\) = ± 3\(\sqrt{5}\)

the total parcel size is 88 acres.

Let's denote the total parcel size as X acres.

According to the given information, 1/4 of the land is allocated to shopping, which amounts to 22 acres. Therefore, we can set up the following equation:

(1/4) * X = 22

To find the value of X, we need to solve this equation for X.

Multiplying both sides of the equation by 4, we get:

X = 22 * 4

X = 88

Therefore, the total parcel size is 88 acres.

what is equation?

In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of two sides, known as the left-hand side (LHS) and the right-hand side (RHS), connected by an equals sign (=).

The general form of an equation is:

LHS = RHS

The LHS and RHS can contain variables, constants, mathematical operations (such as addition, subtraction, multiplication, and division), functions, and other mathematical expressions.

The goal when working with equations is to find the values of the variables that satisfy the equation, making both sides equal. This process is often referred to as solving the equation.

For example, the equation "2x + 5 = 13" states that the expression "2x + 5" is equal to 13. To find the value of x that satisfies this equation, we can manipulate the equation to isolate the variable:

2x + 5 - 5 = 13 - 5  (subtract 5 from both sides)

2x = 8

2x/2 = 8/2  (divide both sides by 2)

x = 4

In this case, the value of x that satisfies the equation is 4.

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The total change in the consumed quantity of x₁ as per given price and income  is equal to 213.

x₁ = (21/7)P₁

x₂ = (51/7)P₂

P₁ = 10

P₂ = 5

P₁' = 81

To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',

The difference between the quantities consumed at the original price and the new price.

Let's calculate the quantity consumed at the original price,

x₁ orig

= (21/7)P₁

= (21/7) × 10

= 30

x₂ orig

= (51/7)P₂

= (51/7) × 5

= 36.4286 (approximated to 4 decimal places)

Now, let's calculate the quantity consumed at the new price,

x₁ new

= (21/7)P1'

= (21/7) × 81

= 243

x₂ new

= (51/7)P2

= (51/7) × 5

= 36.4286

The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,

Change in x₁

= x₁ new - x₁ original

= 243 - 30

= 213

Therefore, the total change in the quantity consumed of x₁ is 213.

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The above question is incomplete, the complete question is:

The optimal amount of x1, x2, P1, P2 and income are given by the following:

x1= 21/ 7p1 x2= 51 / 7p2

The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?

Please answer step by step

Answer:

6

Step-by-step explanation:

the number of zeroes is defined by the highest exponent of the variable in the functional expression.

Hey there!

Answer: \( \Rightarrow \sf{\frac{x+3}{x -2}}\)

\( \rightarrow \sf{ \frac{ {x}^{2} + 5x + 6 }{ {x}^{2} - 4 } }\)

\( \rightarrow{ \rm{factorise} \sf{ \frac{ {x}^{2} + 5x + 6 }{ {x}^{2} - 4 } } = \frac{(x + 2)(x + 3)}{ {x}^{2} - 4} = \frac{(x + 2)(x + 3)}{(x + 2)(x - 2)} = \Rightarrow \sf{\frac{x+3}{x -2}}}\)

(a)The equation x - 7 = 2x - 14 + 1 has 7 as a solution (when v = 2) and an extraneous solution of -8.

(b) To have a real number solution, the value of bx + c should be nonzero.

(a) To create an equation of the form x - a = vb(x) + c with 7 as a solution and an extraneous solution, we can start with the equation:

x - 7 = v * (x - 7) + 1

Simplifying this equation, we have:

x - 7 = vx - 7v + 1

Rearranging the terms, we get:

x - vx = 7v - 6

Now, let's assume v = 2. Substituting this value, the equation becomes:

x - 2x = 14 - 6

Simplifying further, we have:

-x = 8

Multiplying both sides by -1, we get:

x = -8

(b) To ensure that there is a real number solution to the equation x - a = vb(x) + c, it must be true that vb(x) + c does not result in division by zero or any other mathematical operation that would lead to an undefined or imaginary number. This implies that bx + c should not be equal to zero, as dividing by zero is undefined.

Therefore, to have a real number solution, the value of bx + c should be nonzero.

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Answer:

x=6

Step-by-step explanation:

Simplifying

x + 15 = 21

Reorder the terms:

15 + x = 21

Solving

15 + x = 21

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-15' to each side of the equation.

15 + -15 + x = 21 + -15

Combine like terms: 15 + -15 = 0

0 + x = 21 + -15

x = 21 + -15

Combine like terms: 21 + -15 = 6

x = 6

Simplifying

x = 6

HOPE THIS HELPS :)

The sum of all the number cards in a deck of 52 playing cards is 36.

A standard deck of playing cards comprises 13 ranks in each of the four French suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠). Each suite has thirteen cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen and king. Thus the entire deck has 52 cards total.

We shall calculate the sum of the number cards as follows;

numbered clubs (♣) = 9 cards

numbered diamonds (♦) = 9 cards

numbered hearts (♥) = 9 cards

numbered spades (♠) = 9 cards

The four suits multiplied by 9;

4 × 9 = 36

Therefore, there are 36 number cards in a deck of cards.

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Answer:

A. 12 + (-9)

Step-by-step explanation:

adding 8 to 4 is 12 and 9 remains as it is.

Answer:

the answer is no solution