Mr. Carpenter built a wooden gate as shown: which is the closest to the length in feet of the diagonal board that Mr. Carpenter used to brace the wooden gate?

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

To solve this, we would first need to see how many times 7 can fit into 24.

7 + 7 + 7 = 21.

We can see that is fits 3 times into 24, but what about the remaining 3? We can take that 3 and make it into a fraction of 7, making it [tex]\frac{3}{7}[/tex].

Now, putting the 3 and the 3/7 together, we get  [tex]3\frac{3}{7}[/tex].

Answer:

the answer is in the picture

Answer:

System: A system of two equations that can be written in the form of y = mx + b where m is the slope and b is the y-intercept.

Graph: The graph of these two equations would be two straight lines in a coordinate plane.

Solution: The solution of the system would be the point where the two lines intersect on the coordinate plane, which represents the values of x and y that satisfy both equations.

Slope and y-intercept of 4x = y - 6:

Slope: 4 (m)

y-intercept: -6 (b)

Slope and y-intercept of 4y = 3x -5:

Slope: 3/4 (m)

y-intercept: -5/4 (b)

Note that the slope is the coefficient of x in the equation, and the y-intercept is the constant term in the equation. The solution can be found by equating the two equations and solving for x and y.

Answer: 45 degrees

Step-by-step explanation:

1 clockwise rotation = 360 degrees

1/8 a clockwise rotation = 360/8 = 45 degrees

Answer:

1. x = 10.46

2. y = 5.2

Step-by-step explanation:

1.

[tex]cos17^{0} =\frac{10}{x}[/tex]

[tex]x=\frac{10}{cos17^{0} }[/tex]

[tex]x=10.46[/tex]

2.

Angle F = 180 - 42 - 48 = 90° (is a right triangle)

[tex]sin48^{0} =\frac{y}{7}[/tex]

[tex]y=7sin48^{0}[/tex]

[tex]y=5.2[/tex]

Hope this helps

P(A or B) =

Formula: P(AUB)=P(A)+P(B)-P(A n B)

We roll six-sided die.

Then sample space ={1,2,3,4,5,6}

And

Event A: Roll an odd number.

Odd numbers are {1,3,5}

Event B: Roll a number less than 5

Number less than 5 are {1,2,3,4}

So, Probability P(A)=

Probability P(B)=

Now, the odd number which is less than 5 are {1,3}

So, P(A n B)=

Since P(AUB)=P(A)+P(B)-P(A n B)

Therefore, P(A or B) = 1/6

95% of the scores fall within (mean - 2 * standard deviation) and (mean + 2 * standard deviation)

The empirical rule (68-95-99.7% Rule) states that for a normal distribution, 68% of the values are within one standard deviation from the mean, 95% of the values are within two standard deviation from the mean and 99.7% of the values are within three standard deviation from the mean

95% of the values are within two standard deviation from the mean = mean ± 2 * standard deviation = (mean - 2 * standard deviation, mean + 2 * standard deviation)

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Answer:

A is what I think is a independent variable

Step-by-step explanation:

Well a independent variable is something that stands alone and does not change by the other variables you are trying to measure. So for example b would not be since it relies on the number of cookies sold to figure out the total of money made.

The value of q in the arithmetic sequence is 1/2

An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k. This is in contrast to a geometric sequence where each term increases by dividing/multiplying some constant k. Example: a1 = 25. a(n) = a(n-1) + 5.

The common difference of arithmetic sequence is found by subtract subtracting the first from the second term. This means

d = 2q+2 - q = q+2

the sum of term is a(n) = a +( n-1)d

for third term it will be a(3) = q+ (3-1) q+2

a(3) = q +2(q+2)

the third term = 5q+ 3

5q+3 = q+ 2q+4 = 3q+4

5q+3 = 3q+4

collect like terms

5q-3q = 4-3

2q = 1

q = 1/2

therefore the value of q = 1/2

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Answer:

0.36km/

Step-by-step explanation:

speed= distance/time

14.4km/40min

= 0.36km/min

The values of G(x), At x = 0, 2, 4 are G(0) = 0, G(2) = 12 and G(4) = 12.

A function that is piecewise defined by numerous subfunctions, each of which has a separate domain interval for which it is applicable.

Piecewise definition is more of an expression of the function than it is a property of the function.

Given, A piecewise function G(x) defined by,

- 3x, x < 2 and 12, x ≥ 2.

Therefore, The value of G(x), At x = 0 is,

G(0) = - 3(0).

G(0) = 0.

At x = 2 the function G(x) is,

G(2) = 12.

At x = 4, the function G(x) is,

G(4) = 12.

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Answer:

5, -2

Step-by-step explanation:

the triangle are congruent by AAA

What is congruent by AAA?

It can also be stated as the AAA (angle-angle-angle) similarity theorem, which states that two triangles have identical corresponding angles if and only if their corresponding sides are proportionate.given, ABC and XYZ, are congruent according to the AAA rule by looking at the image provided below. According to the AAA congruence rule, two triangles are said to be congruent if two of their respective sides and angles are equal to those of two other triangles and their respective sides and angles, respectively.

In the given two triangles,

The ratio of the sides are similar

And hence the angles are similar.

Hence the triangle are congruent by AAA

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The approximation of 341.12 to 1 decimal place is 341.1.

To approximate 341.12 to 1 decimal place, you can follow these steps:

For example, if you want to approximate the number 341.12 to 1 decimal place, follow these steps:

341.12 * 10 = 3411.2

Round 3411.2 to the nearest whole number, which is 3411.

3411 / 10 = 341.1

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Answer:

341.1

Step-by-step explanation:

When you round to the first decimal place, or to the nearest tenth, the number in the hundredth point place will determine whether you round up or down. If the hundredths digit is a number between 5 and 9, round up to the nearest whole number. If it's a number between 0 and 4, you would "round down" by keeping the tenths place the same.

341.12

The number in the hundredths place is 2, which means that we would round down the first decimal place by keeping it the same:

341.1

Answer:

a=3c/2+5b/2

Step-by-step explanation:

First open parenthesis

5a-5b=3a+3c

Than subtract A's and add b and c's

2a=3c+5b

Divide by two

a=3c/2+5b/2

Both relation (year, percent of men) and (year, percent of women) are functions.

What is a function?

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.

Now,

In given data

For every input (i.e. year) there is a unique output (i.e. percent of men/ percent of women)

Hence, Given relation (year, percent of men) and (year, percent of women) are functions.

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Jeremy needs an amount of $7.75 cash to buy 3 comic books.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The function f(x) = 5.25x − 8 represents the amount of cash required to purchase x comic books after using his gift card.

To determine the amount of cash Jeremy needs to buy 3 comic books, we can substitute 3 for x in the function f(x) = 5.25x − 8.

So, f(3) = 5.25(3) − 8 = 15.75 − 8 = 7.75

Therefore, he needs $7.75 cash to buy 3 comic books.

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The question seems to be incomplete the correct question would be:

Jeremy has an $8 gift card to use to buy comic books. Each comic book costs $5.25. The function f(x) = 5.25x − 8 represents the amount of cash required to purchase x comic books after using his gift card. How much cash does Jeremy need to buy 3 comic books?

Bryn is wrong as he says that the journey will definitely take less than an hour and a quarter

time = 1.17 hours = 1 hour 42 minutes

What is speed?

The definition of speed is. a measurement of how quickly an object's location changes in any direction. Speed is defined as the ratio of distance to the amount of time it took to cover that distance.

Average speed= distance / time

time= distance /Average speed = 80/68  hours

time = 1.17 hours = 1 hour 42 minutes

So, Bryn is wrong as he says that the journey will definitely take less than an hour and a quarter.

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The expression to show the total number of songs on Iris's playlist after {w} weeks is → y = 120 + 4w.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that Iris has 120 songs on her playlist. Each week, she downloads 4 new songs.

We can write the expression to show the total number of songs on Iris's playlist after {w} weeks as -

y = 120 + 4w

Therefore, the expression to show the total number of songs on Iris's playlist after {w} weeks is → y = 120 + 4w.

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The two transformation that would map triangle ABC onto triangle A'B'C' include the following:

In Geometry, dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have TO apply a dilation to the coordinates of the preimage by using a scale factor of 1/2 centered at the origin as follows:

Ordered pair A (-2, 2) → Ordered pair A' (-2 × 1/2, 2 × 1/2) = Ordered pair A' (-1, 1).

Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).

Ordered pair C (-4, 4) → Ordered pair C' (-4 × 1/2, 4 × 1/2) = Ordered pair C' (-2, 2).

Furthermore, by applying a reflection over the y-axis to the coordinates of triangle A'B'C', the image coordinates include the following:

(x, y)                               →              (-x, y)

Ordered pair A' (-1, 1)    →    Ordered pair A'  (-(-1), 1) = (1, 1).

Ordered pair B' (-2, 1)    →    Ordered pair B' (-(-2), 1) = (2, 1).

Ordered pair C' (-2, 2)    →    Ordered pair C' (-(-2), 2) = (2, 2).

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The equation relating temperature and time is given by 3y = -10x + 130

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the temperature be represented as y

Let the time be represented as x

Now , let the first point be P = P ( 1 , 40 )

Let the second point be represented as Q = Q ( 7 , 20 )

The slope of the line between the points m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 40 - 20 ) / ( 1 - 7 )

On simplifying the equation , we get

Slope m = -20/6

Slope m = -10/3

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 40 = ( -10/3 ) ( x - 1 )

On simplifying the equation , we get

y - 40 = ( -10/3 )x + 10/3

Adding 40 on both sides of the equation , we get

y = ( -10/3 )x + 130/3

Multiply by 3 on both sides of the equation , we get

3y = -10x + 130

when x = 1 am

3y = -10 + 130

3y = 120

y = 40 degrees

when x = 7am

3y = -70 + 130

3y = 60

y = 20 degrees

Hence , equation representing temperature and time is 3y = -10x + 130

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Answer:

Each of them will get 42/3 = $14.00

Cami saves half of her money which is 14/2 = $7.00

Cami has 14 - 7 = $7.00 to spend.

Adding, Substracting, multiplication and division. If we add the same number to both sides of an equation, both sides will remain equal. That would make this equation algebra.

Given data :

10(y-13) = 10(y+13)

y = 10*-13 = y = 10 * 13

-130 = 130

both sides will remain equal

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Step-by-step explanation:

Move the decimal point one place to the right

Answer:

Step-by-step explanation:

1.

[tex]\displaystyle\\\frac{1}{5}x+15=-5 \\\\\frac{1}{5}x+15-15=-5-15\\\\\frac{1}{5}x=-20[/tex]

Multiply both parts of the equation by 5:

[tex]x=-100[/tex]

2.

[tex]4-3x=5\\\\4-3x-4=5-4\\\\-3x=1[/tex]

Divide both parts of the equation by (-3):

[tex]\displaystyle\\x=-\frac{1}{3}[/tex]

3.

[tex](3x)^0+(8x+70)^0=180^0\\\\(3x)^0+(8x)^0+70^0=180^0\\\\(11x)^0+70^0-70^0=180^0-70^0\\\\(11x)^0=110^0[/tex]

Divide both parts of the equation by 11:

[tex]x=10[/tex]

[tex]m\angle TRS=(8(10)+70)^0\\\\m\angle TRS=(80+70)^0\\\\m\angle TRS=150^0[/tex]

4.

[tex]\$ 25(5)+\$250=\\\\\$125+\$250=\\\\\$375[/tex]

5.

[tex]\displaystyle\\\frac{x}{15}=\frac{30}{18}[/tex]

Multiply both parts of the equation by 15:

[tex]\displaystyle\\x=\frac{30(15)}{18} \\\\x=\frac{450}{18}\\\\x=25[/tex]

The inverse function would be x = (y + 3) / -3 and the domain of the inverse function would be (-infinity, -1/3].

What is the inverse function?

An inverse function is a function that "undoes" another function. The inverse function, denoted as f^-1, reverses the direction of the original function, so that if the original function maps x to y, the inverse function maps y to x.

To find the inverse function of a given function, you can switch the x and y variables and solve for y. The inverse function will also have a different domain and range than the original function.

For example, for the function y = 1 - 3x, where x belongs to the interval [-2, 2],

First, we need to switch the x and y variables to get x = 1 - 3y.

Now we need to solve for y,

y = (x + 3) / -3

So the inverse function of y = 1 - 3x, where x belongs to the interval [-2, 2], is

x = (y + 3) / -3

The domain of the original function is [-2, 2] and the range is (-infinity, -1/3], whereas the domain of the inverse function is (-infinity, -1/3] and the range is [-2, 2].

Hence, The inverse function would be x = (y + 3) / -3 and the domain of the inverse function would be (-infinity, -1/3].

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The meaning of the y-intercept in this situation is that: A) When the cab travels 0 miles, the total fee will be $14.00.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line and passes through the points (2, 17) and (5, 21.5) by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 17 = (21.5 - 17)/(5 - 2)(x - 2)

y - 17 = 4.5/3(x - 2)

y - 17 = 1.5(x - 2)

y = 1.5x - 3 + 17

y = 1.5x + 14

Therefore, the y-intercept is equal to 14.

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