what is the change of rate for 3x - 5y = 20

Answer:

x = 3

Step-by-step explanation:

2(4 + 3x) + 6 = 32 ( subtract 6 from both sides )

2(4 + 3x) = 26 ( divide both sides by 2 )

4 + 3x = 13 ( subtract 4 from both sides )

3x = 9 ( divide both sides by 3 )

x = 3

As a check

substitute x = 3 into the left side of the equation and if value obtained is equal to the right side (32) then it is a solution to the equation.

2(4 + 3(3)) + 6

= 2(4 + 9) + 6

= 2(13) + 6

= 26 + 6

= 32

left side = right side

then x = 3 is the solution to the equation

Answer:

\( \sf \: x = 3\)

Step-by-step explanation:

\( \sf \rightarrow \: 2(4 + 3x) + 6 = 32\)

Apply the distributive property

\( \sf \rightarrow8 + 6x + 6 = 32\)

Combine like terms

\( \sf \rightarrow 14 + 6x = 32\)

Rearrange variables to the left side of the equation

\( \sf \rightarrow 6x = 32 - 14\)

Calculate

\( \sf \rightarrow 6x = 18\)

Divide both sides by the coefficient of 6

\( \sf \rightarrow \frac{6x}{6} = \frac{18}{6} \)

Calculate

\( \sf \rightarrow x = \frac{18}{6} \)

\( \sf \rightarrow \: x = 3\)

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Answer:

<Q, <R, <P

Step-by-step explanation:

The measures of the angles are in the same order of size as the length of the opposite side.

shortest side: RP = 2; opposite angle: Q

middle side: PQ = 5; opposite angle: R

longest side: QR = 6; opposite angle: P

Answer: <Q, <R, <P

Biggest angle has biggest side and vice versa.

Orde of sides

Order of angles

There are 87 possible outcomes that contain at least three heads when a coin is flipped 9 times.

When a coin is flipped nine times, there are 512 possible outcomes, or 29. Using the equation:

P (At least one head) = 1 - 0.5n,

where n is the total number of flips, we can determine the number of outcomes that contain at least three heads.

Therefore, P (At least three heads) = 1 - P (No heads) - P (One head) - P (Two heads)

= 1 - (0.5)⁹ - 9(0.5)⁹ + 36(0.5)⁹

= 0.1718751.

The formula used to calculate the number of possible outcomes that contain at least three heads is C(9,3) + C(9,4) + C(9,5) + C(9,6) + C(9,7) + C(9,8) + C(9,9),

where C(n,r) denotes the variety of options for selecting item(s) r from a set of item(s) n.

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Answer:

A

Step-by-step explanation:

5/8=0.625

0.42=0.42^2

An articulated ladder should be utilized in a stepladder design for working on stairs. This structure is especially built for stairway safety and stability, with movable legs that can be placed to different heights to suit uneven stairs and give a level area for standing.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. The area of a planar figure is the space contained by its border. The number of unit squares that cover the surface of a closed form is the figure's area. The area is the region defined by an object's form.

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2. EFGH is a parallelogram. 3. EFGH is a rectangle.4. EFGH is not a square.5. the length of EF is √(2.25+2.25) = √(9) = 3.

A quadrilateral is a polygon with four sides and four vertices. It is a 2-dimensional shape that can be either convex or concave. The sum of the interior angles of a quadrilateral is always equal to 360 degrees.

There are many types of quadrilaterals, including rectangles, squares, parallelograms, trapezoids, and rhombuses. Each type of quadrilateral has its own unique properties and characteristics.

2. To determine if Quadrilateral EFGH is a parallelogram, we need to check if opposite sides are parallel. We can calculate the slope of each side using the coordinates:

EF: slope = (6-3)/(0-2) = -3/2

FG: slope = (-4-6)/(3-0) = -10/3

GH: slope = (-1+4)/(-1-3) = -3/4

HE: slope = (3-(-1))/(2-(-1)) = 4/3

We can see that opposite sides EF and GH have the same slope, and opposite sides FG and HE have the same slope. Therefore, EFGH is a parallelogram.

3. To determine if Quadrilateral EFGH is a rectangle, we need to check if all angles are right angles. We can calculate the slope of each side using the coordinates and use the fact that perpendicular lines have negative reciprocal slopes:

EF: slope = -3/2, so a line perpendicular to EF has slope 2/3

FG: slope = -10/3, so a line perpendicular to FG has slope 3/10

GH: slope = -3/4, so a line perpendicular to GH has slope 4/3

HE: slope = 4/3, so a line perpendicular to HE has slope -3/4

We can see that the lines perpendicular to EF and GH have the same slope, and the lines perpendicular to FG and HE have the same slope. Therefore, all angles of EFGH are right angles, and EFGH is a rectangle.

4. To classify EFGH as a square, we need to check if it is both a parallelogram and a rectangle, and if all sides are congruent. We have already established that EFGH is a parallelogram and a rectangle. To check if all sides are congruent, we can calculate the distance between each pair of opposite vertices:

EF: distance = √((0-2)² + (6-3)²) = √(10)

FG: distance = √((3-0)² + (-4-6)²) = 5√(2)

GH: distance = √((-1-3)² + (-1+4)²) = 5

HE: distance = √((2-(-1))² + (3-(-1))²) = √(29)

We can see that all four sides have different lengths, so EFGH is not a square.

5. To draw a right triangle EFR with hypotenuse EF, we need to find the coordinates of R. We can use the midpoint formula to find the midpoint of EF:

Midpoint of EF = ((2+0)/2, (3+6)/2) = (1, 4.5)

We can then use the distance formula to find the length of ER and RF:

ER = √((1-2)² + (4.5-3)²) = √(2.25) = 1.5

RF = √((1-0)² + (4.5-6)²) = √(2.25) = 1.5

Therefore, the length of EF is √(2.25+2.25) = √(9) = 3.

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Answer:

Step-by-step explanation:

Hope this helps u !!

Answer:

( 1 , 2 )

Step-by-step explanation:

x + 4y = 9

x = 9 - 4y .... ( 1)

2x - 4y = -6 ...( 2)

substitute the 9 - 4y as x in the second equation

2( 9 - 4y ) - 4y = -6

distribute 2

18 - 8y - 4y = -6

combine like terms

18 - 12y = -6

Subtract 18 from both sides

18 - 18 - 12y = -6 - 18

- 12y = - 24

divide both sides by -12

-12y / -12 = -24/-12

y = 2

Now , substitute the 2 as y in the second equation

2x - 4y = -6

2x - 4 ( 2 ) = -6

2x - 8 = -6

add 8 to both sides

2x - 8 + 8 = -6 + 8

2x = 2

divide both sides by 2

2x / 2 = 2/2

x = 1.

Recovered memory in CSA refers to the new development of abusive memories. Repressed memory is when the patient believes the CSA occurred, even though they have no specific memory of the event.

Recovered memory:

The term "recovered memory" implies that at some point the memory must become inaccessible to conscious awareness (as opposed to "continuous memory"). Although the term is not ideal, it is clear that people often fail to report important events, such as known hospitalizations (Loftus, 1993). In 1995, the debate over reclaiming memory was near its most violent climax. Hundreds of people have recovered memories of child sexual abuse (CSA), and sometimes in therapy it is thought that repressed or dissociative memories need to be recovered for a person to 'heal'.

Repressed Memory:

Repressed memory is a purported psychiatric phenomenon involving the inability to recall autobiographical information, usually traumatic or stressful. The concept has its origins in psychoanalytic theory, where repression is understood as a defense mechanism that keeps painful experiences and unacceptable impulses out of awareness. Repressed memory is a controversial concept, especially in a legal context, where it is used to unjustly and inaccurately accuse individuals, causing significant harm. Meanwhile, a working group from the American Psychological Association has stated that while "most people who were sexually abused in childhood remember some or all of what happened to them, it is possible to remember long-forgotten abuses.

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It take the auxiliary equipment to fill the order working alone x is 70/3

Formulate based on the conditions stated:

10 * x/(10+x) = 7

In a defined fraction, the denominator cannot be zero.

10+x is not equal 0

Equation from inequality:

10+x=0

Unknown terms should be moved to the left side of the equation:

x = -10

Equation to inequality conversion

x is not equal to 10

As the domain, append the inequality:x is not equal to 10

Divide the common denominator by both sides of the equation:

10x(10+x)/10+x = 7(10+x)

Cut the fractions in half:

10x = 7(10+x)

Use the law of multiplicative distribution

10x = 70 +7x

Unknown terms should be moved to the left side of the equation:

10x-7x=70

combining similar terms 3x =70

Subtract the coefficient of the variable from both sides of the equation:

x = 70/3

the intersection, then: 70/3

get the outcome:x = 70/3

It take the auxiliary equipment to fill the order working alone x is 70/3

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The coordinates of the missing vertex of the rectangle is (2,1).

To determine the missing vertex of a rectangle, we can use the fact that opposite sides of a rectangle are parallel and equal in length.

Given three vertices of a rectangle: (2,5), (7,5), and (7,1), we can observe that the missing vertex should form a right angle with the vertex (7,1) and lie on the same horizontal line as the vertex (2,5).

Since the y-coordinate of the missing vertex should be the same as the y-coordinate of the vertex (2,5), we can determine that the missing vertex has the coordinates (2,1).

Therefore, the missing vertex of the rectangle is located at (2,1).

Correct Question:

Three vertices of a rectangle are shown on the grid.

What are the coordinates of the missing vertex?

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The coordinates of the missing vertex are determined by finding the midpoint of the given vertices and adding the vector from the midpoint to the third vertex. By following this process, we can find the missing vertex of a rectangle on a grid.

To find the missing vertex of a rectangle on a grid, we need to use the properties of rectangles. Let's say the given vertices are A(x1, y1), B(x2, y2), and C(x3, y3). We can determine the coordinates of the missing vertex D by following these steps:

By following these steps, we can determine the coordinates of the missing vertex D.

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  The algebraic expression or sigma (summation) notation is given by:

∑ = 10(100 + 10)/2

And its value is ∑ = 550

 The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.

  The equation for this type of problem is:

∑ = n(a1 + an)/2

  Our values are:

100+90+80+ . . . . . . +10

∑ = 10(100 + 10)/2

∑ = 10(110)/2 = 5(110)

∑ = 550

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A quadratic inequality represented by the graph is y≥x²+2x+2.

The vertex from the given graph is (-1, 1) and the coordinate point is (1, 5).

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line.

The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h, k) denotes the vertex.

Substitute (x, y)=(1, 5) and (h, k)=(-1, 1) in y = a(x-h)² + k, we get

5=a(1+1)²+1

⇒ 4=4a

⇒ a=1

Substitute a=1 and (h, k)=(-1, 1) in y = a(x-h)² + k, we get

y=1(x+1)²+1

⇒ y=1(x²+2x+1)+1

⇒ y=x²+2x+2

⇒ y≥x²+2x+2

Therefore, a quadratic inequality represented by the graph is y≥x²+2x+2.

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Answer:

x-7>0

Straight answer: x-7

Step-by-step explanation:

Assuming that the timber is X cm long and 7cm was cut off, there remaining amount is x - 7cm. In order for 7cm to be cut off, the timber must have been > 7cm long => x > 7 => x - 7 > 0

Answer: 4x

2x + 2x=4x

The probability of drawing a winning pair which is a pair with the same color OR same letter 0.9388.

The problem we are dealing with is related to probability which is referred to as Probability is essentially how likely something is to happen. At whatever point we're uncertain approximately the result of an occasion, we will conversation around the probabilities of certain outcomes—how likely they are.

Since we are provided with four red cards and four green cards so, the total possible combination of the  8 cards will be

C(8,2) = 28

out of which  2*C(4,2)=12 are the  pairs of the same color

therefore the probability of picking a pair with the same color OR same letter is

1 - (12*4)/28^2 = 0.9388

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Step-by-step explanation:

there are a few things from school everybody has to burn into their brains for life. one of them : Pythagoras for right-angled triangles :

c² = a² + b²

c is the Hypotenuse (the triangle side opposite of the 90° angle), a and b are the triangle legs.

now, it depends on what you teacher agreed with you regarding naming the sides of such a triangle.

sometimes "base" is the Hypotenuse (baseline), sometimes it is one of the legs, and then the height is the second leg (as the legs are standing at a 90° or right angle at each other).

we have to assume the second one, as for the first one we have not enough information to solve the question (because with just a given Hypotenuse and the height to the Hypotenuse we can draw infinitely many different triangles with different perimeters).

so, we have

Hypotenuse² = 24² + 7² = 576 + 49 = 625

Hypotenuse = sqrt(625) = 25 m

the perimeter of the triangle is then

25 + 24 + 7 = 56 m

The extended ring R[a], obtained by adjoining an element a to a ring R, is indeed a ring isomorphic to R. This is demonstrated by showing that R[a] satisfies the properties of a ring and by constructing an isomorphism between R[a] and R.

To prove that adjoining an element a to a ring R gives a ring isomorphic to R, we need to show that the extended ring R[a] satisfies the definition of a ring and that there exists an isomorphism between R[a] and R.

First, let's define the extended ring R[a]. The elements of R[a] are represented as polynomials in a with coefficients from R. An element in R[a] can be written as:

R[a] = {r₀ + r₁a + r₂a² + ... + rₙaⁿ | r₀, r₁, r₂, ..., rₙ ∈ R}

where n is a non-negative integer and r₀, r₁, r₂, ..., rₙ are coefficients from R.

Now, let's prove the two main properties of a ring for R[a]:

Closure under addition and multiplication:

For any two elements (polynomials) p = r₀ + r₁a + r₂a² + ... + rₙaⁿ and q = s₀ + s₁a + s₂a² + ... + sₘaᵐ in R[a], the sum p + q and product p * q are also elements of R[a]. This can be proven by applying the distributive property and associativity of addition and multiplication.

Existence of additive and multiplicative identities:

The additive identity in R[a] is the polynomial 0, and the multiplicative identity is the polynomial 1. These identities satisfy the properties of an additive and multiplicative identity, respectively, when added or multiplied with any element in R[a].

Next, we need to show that there exists an isomorphism between R[a] and R, which means there is a bijective map that preserves the ring structure.

Consider the function φ: R[a] → R defined as φ(r₀ + r₁a + r₂a² + ... + rₙaⁿ) = r₀. This function maps each polynomial in R[a] to its constant term.

We can prove that φ is an isomorphism by verifying the following:

a) φ preserves addition: φ(p + q) = φ(p) + φ(q) for any p, q in R[a].

b) φ preserves multiplication: φ(p * q) = φ(p) * φ(q) for any p, q in R[a].

c) φ is bijective: φ is both injective and surjective.

The proofs for these properties involve applying the distributive property and associativity of addition and multiplication, and considering the coefficients of the polynomials.

Hence, we have shown that adjoining an element a to a ring R gives a ring isomorphic to R, denoted as R[a] ∼ R.

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\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ h=9 \end{cases}\implies V=\pi (6)^2(9)\implies V=324\pi~in^3\)

Answer:

The missing value for the cats is 15

Step-by-step explanation:

10+5=15

Answer:

Missing value for dogs is 2. The missing value for cats is 80

Step-by-step explanation:

In the chart it goes from 10 cats to 5 cats. To turn 10 into 5 you have to divide 10 by 2. So to find how many dogs would go with 5 cats, you have to divide the amount of dogs by 2 as well. 4 divided by 2 is 2. So the missing value for dogs is 2.

Now, in the dog row, it goes from 2 to 32. We have to find 2 times _____ is 32.

2 times 16 is 32 so we multiply the 5 dogs by 16 as well. 5 times 16 is 80. So the missing value for cats is 80.

I hope that made sense.

The lengths of the two boards (234 inches and 246 inches) and adding them together, we find that the combined length of the boards is 480 inches.

To find the total length of the two boards, you need to add their individual lengths together.

Step 1: Identify the length of each board. The first board is 234 inches long, and the second board is 246 inches long.

Step 2: Add the lengths of the boards together.

234 (length of first board) + 246 (length of second board) = 480

So, the total length of the two boards on the shelf is 480 inches. This means that if you were to place the two boards end-to-end, they would cover a distance of 480 inches.

In summary, by identifying the lengths of the two boards (234 inches and 246 inches) and adding them together, we find that the combined length of the boards is 480 inches. This calculation helps us understand the total amount of space the boards would occupy if placed side by side.

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Answer:

B and C

Step-by-step explanation:

A is incorrect, as a translation simply moves an object. It cannot flip an object, as would be needed here, since ∠1 and ∠2 open in opposite directions.

B is correct, as ∠2 results when ∠1 is reflected over a vertical line.

C is correct, as ∠2 results when ∠1 is rotated 180º about the vertex.

D is incorrect, as vertical angles are congruent.

Answer:  10

Step-by-step explanation:

20% is 10% of 50 % because you /   100 in half and 20 in half and it's the same thing the answer is 10, my guy.

Answer:

$2,526.86

Step-by-step explanation:

1. 3,000-4.2%= 2,874

2. 2,874-4.2%= 2,753.29

3. 2,753.29-4.2%= 2,637.65

4. 2,637.65-4.2%= 2,526.86

Therefore, liquid water is considered to be unstable on Mars due to the cold temperatures, low atmospheric pressure, and the UV radiation. All of these environmental factors make it difficult for liquid water to persist.

Liquid water is unstable on Mars due to its cold, dry environment. Because the atmospheric pressure is too low to hold liquid water, the water on Mars quickly evaporates, sublimates, and/or is broken down by the ultraviolet radiation in the atmosphere.
The average temperature of the surface of Mars is −63 °C, which is well below the freezing point of water. Because of this, liquid water cannot exist on the surface of Mars. When temperatures are slightly higher, water can exist as a liquid, but it cannot stay in this state for very long.
The atmosphere on Mars also does not contain enough pressure to sustain liquid water. Even when water vapor is present, it will quickly evaporate in the low-pressure environment. Additionally, the UV radiation in the Martian atmosphere will break down water molecules quickly.

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a) The mean of 12 college students is 118.5; b) the median of 12 college students is 117.

In mathematics, particularly statistics, there are various types of means. Each mean is used to summarize a certain subset of data, frequently in order to better comprehend the overall worth of a data set.

The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution. It is sometimes referred to as "the middle" value in a data set.

Given that,

The dot plot represents the distribution of wages earned during a one-week period by 12 college students

a) Mean = \(\frac{sum of observations}{total number of observations}\)

Mean = \(\frac{112+113+116+116+116+118+118+119+119+124+124+124}{12}\)

Mean = \(\frac{1419}{12}\)

Mean = 118.5

b) median = middle value

The data is

112, 113, 116, 118, 119, 124

The middle value of the data is

116+118 = 234

Median = \(\frac{234}{2}\)

Median = 117

c) Yes, a box plot of the same data have allowed to find the mean and median.

Therefore, the mean of 12 college students is 118.5; the median of 12 college students is 117.

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The smallest positive solutions for the given modular equations are:

a) x = 10 b) x = 6 c) x = 11

a) For the equation 11 + x ≡ 7 (mod 14), we need to find the smallest positive value of x that satisfies this congruence. We can subtract 11 from both sides of the equation, yielding x ≡ -4 (mod 14). To find the smallest positive value, we add 14 to -4 until we get a positive result. In this case, adding 14 to -4 gives us x ≡ 10 (mod 14), which is the smallest positive solution.

b) In the equation 5x + 1 ≡ 3 (mod 7), we subtract 1 from both sides to obtain 5x ≡ 2 (mod 7). To find the smallest positive value of x, we multiply both sides by the modular inverse of 5 modulo 7. In this case, the modular inverse of 5 is 3, so multiplying both sides by 3 gives us x ≡ 6 (mod 7) as the smallest positive solution.

c) For the equation \(7^x\) ≡ 4 (mod 13), we need to determine the smallest positive value of x. To solve this, we can systematically calculate the powers of 7 modulo 13 until we find one that is congruent to 4. After checking the values, we find that \(7^{11}\) ≡ 4 (mod 13), making x = 11 the smallest positive solution to the equation.

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Answer:

the ratio would be 6:2 or 6/2. Yes, the ratio of sugar to flour change when I compare the single batch to the double batch.

Step-by-step explanation: