Tyrone makes a scale drawing of his backyard. The scale from the backyard to the
drawing is 2 ft to 1 in. The width of the patio on the drawing is 8 in. What is the
width of Tyrone's actual patio? Show your work.

We need to know about logarithm to solve this problem. The value of the given logarithm is 1.

Logarithm is an exponent that the base is raised to inorder to get a certain number. There are few rules of logarithm, log a +log b can be written as log ab, log a -log b can be written as log a/b, when the number whose logarithm is calculated has been raised to a power then the power can be multiplied to the log itself. When logarithm is written as log with no mentioned base then the base is 10. The log of a number same as the base is always 1 and the log of 1 is always zero because a nonzero number raised to zero is always 1. We will be using these rules to find the value of the given logarithm.

[tex]log_{9}9[/tex]=1 since [tex]9^{1} =9[/tex]

Therefore we found the value of the given logarithm to be 1.

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The equation is in slope intercept form.

The standard form is 1 / 2 x + y = 3

Linear equation can be represented in different form. It can be written in slope intercept form and standard form.

The slope intercept form is as follows:

y = mx + b

where

Therefore, the linear equation y = - 1 / 2 x  - 3 is represented in slope intercept form.

A linear equation in standard form is express as follows:

Ax + By = C

where

A, B and C are constant.

Hence, the equation y = - 1 / 2 x  - 3 in standard form is as follows:

1 / 2 x + y = 3

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The  standard form of (4 × 10⁴) + (6 × 10²) is 40,600.

Standard form is a way of writing down very large or very small numbers easily.

For finding standard form of the given equation we will solve the equation then whatever answer we will, it will be  the standard form.

Let's begin by solving the roots 10 first :

 (4 × 10⁴) + (6 × 10²) = (4 × 10 × 10 × 10 × 10) + (6 × 10 × 10)

                                  = (4 × 10000) + (6 × 100)

                                  =  40000 + 600

                                  = 40,600

Hence the standard form of the given equation is 40,600.

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Answer:

∠ 10 = 86°

Step-by-step explanation:

∠ 7 and ∠ 10 are same- side interior angles and sum to 180° , that is

∠ 7 + ∠ 10 = 180°

94° + ∠ 10 = 180° ( subtract 94° from both sides )

∠ 10 = 86°

Answer:

There will be 15 2/3 cups in the mixture.

Step-by-step explanation:

3 3/5 + 2 2/3 = 3 9/15 + 2 10/15 = 5 19/15

= 6 4/15

6 4/15 × 2 1/2 = 94/15 × 5/2 = 47/3 = 15 2/3

So there will be 15 2/3 cups in the mixture.

The mean of of −26,39,−10,−16,12,31 is 5 which is determined by summing up the numbers and dividing by 6

What is the mean?

The mean is the sum of the integers divided by the number of integers therein, in other words, the mean is determined sum , having computed the sum we divide by 6 since there are six numbers in the distribution

sum=-26+39-10-16+12+31

sum=30

mean=sum/n

n=6(there are six numbers)

mean=30/6

mean=5

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The zeros of p(x)=x2-1 is:

1,-1

When Andrew goes bowling, his scores are normally distributed with a mean of 115 and a standard deviation of 11 . Then the probability of his score being between 86 and 115 is 0.2047

Mean = μ = 115

SD = σ = 11

Let x1 be the first data point and x2 the second data point

We have to find the z-scores for both data points

x1 = 86

x2 = 106

So,

Z1 = ( x1- mean)/ SD

   = 86- 115 / 11

   = -29/11

   = -2.6363

Z2 =  ( x2-mean)/SD

    = 106 -115 /11

     = -0.8181

And We have to find area to the left of both points then their difference to find the probability.

So, Area to the left of z1 = 0.00427

Area to the left of z2 = 0.20897

Probability to score between 135 and 167 = z2-z1 =  0.20897-0.004270

                                                                                 = 0.2047

Hence,

The probability of his score being between 86 and 115is 0.2047

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This transformation would be shifted vertically.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given Data

First, we decide which library function most closely resembles the function we are given. Our function has an x² because

We'll make use of the library there.

the formula f (x) = x²

Knowing the library function we'll use presently, we need a set of

The formula h(x) = x²

(4.1)

(9,6)

(16,13)

We know the graph of h (x) will be the same as that of f (x), but pushed upward 2 units since 2 + 2 is of the form y = f (x) + c.

As a result, by taking our points from the graph of f (x) = x 2 and subtracting 3 to each of the y-values, we may generate points on the graph of h (x).

points from the f (x) = x² graph working with.

f(x)                g(x)

(4,1)                (4,2)

(9,6)                  (9,7)

(16,13)             (16,14)

Thus we have obtained the graph of f(x)=x²-3; g(x) = f(x) + 1

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For the given statement conclusion it was drawn using the law of syllogism.

Option A is our correct answer

The Law of Syllogism states that,

If the following two statements are true:

- If p, then q.

- If q, then r.

Then the third statement is true:

- If p, then r.

We have,

p - If you do the unit review, q - you will do well on the test.

q - If you do well on the test, r - then you will do well in the course.

Therefore, p - if you do the unit review, r - then you will do well in the course.

This is in the form of:

- If p, then q.

- If q, then r.

Then the third statement is true:

- If p, then r.

Thus this conclusion was drawn using the law of syllogism.

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According to the solving equation  the ball will be in the air for:

5.3 seconds

A linear equation is an algebraic equation of the form y=mx+b, including only a constant and a first-order (linear) component, where m is the slope and b is the y-intercept. The preceding is sometimes referred to as a "linear equation with two variables," where y and x are the variables.

y = ax2 + bx + c

When:

x = 0 , y = 6

y = a(0)2 + b(0) + c = 6

c = 6

When x = 2, y = 22

a(2)2 + b(2) + 6 = 22

4a + 2b = 16

On dividing the entire equation by 2,

2a + b = 8 → (1)

When x = 4, y = 22

a(4)2 + b(4) + 6 = 22

16a + 4b + 6 = 22

16a + 4b = 16

On dividing the entire equation by 4,

4a + b = 4 → (2)

Subtracting (1) from (2)

2a = -4

a = -2

b = 4 - 4(-2) = 4 + 8

b = 12

y = -2x2 + 12x + 6

y = -2x + 12x + 6

Solve the equation.

On solving using quadratic formula,

x = (-12 ± √(144 - 4*-2*6) ) / -4

x = (-12 ± 13.8564) / -4

x ≈ -0.46 and x ≈ 6.46

The ball is above seconds

-2x2 + 12x + 6 = 10

2x2 - 12x + 4 = 0

On solving the above equation using quadratic formula,

x ≈ 0.354 and x ≈ 5.646

So, the ball is above 10 feet for about,

5.646 - 0.354 = 5.3 seconds

5.3 seconds

According to the solving the ball will be in the air for:

5.3 seconds

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A composite function exists as a function that depends on another function. A composite function exists formed when one function exists substituted into another function.

The value of g(3x) = 9x.

In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.

Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.

Let the two functions be f(x) = 3x and g(x) = x²

f(g(x)) = f(x²)

f(x²)  =  3x²

simplifying the above equation, we get

g(f(x)) = g(3x)

g(3x) = (3x)²

g(3x) = 9x

Therefore, the value of g(3x) = 9x.

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Answer: 60

Step-by-step explanation:

Step 1: In order to find the answer to this question we need to figure out what the total number of combinations we could make.

Step 2: To figure out the total number of combinations multiply each number. 4x5x3= 60.

Step 3 (explanation): The answer is 60, because we are finding out the total combinations for both the sweaters and pants and the shoes.

The value of x in the equation 7 x² + 196 = 0 will be ± 2 i√7.

We are given the equation as:

7 x² + 196 = 0

We need to solve the equation to find the value of x.

Subtracting 196 from both the sides, we get that:

7 x² + 196 - 196 = 0 - 196

7 x² = - 196

Now divide both the sides by 7, we get that:

7 x² / 7 = - 196 / 7

x² = - 28

Square root both the sides, we get that:

x = √ - 28

Using the properties of complex numbers, we get that:

x = ± 2 i√7

Therefore, we get that, the value of x in the equation 7 x² + 196 = 0 will be ± 2 i√7.

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Answer:

9x + 2

Step-by-step explanation:

(2x + 3) + (7x - 1)

2x + 3 + 7x - 1

9x + 2

I hope this helps!

Shine have 4 Quarters, 8 Dimes, and 16 Nickels coins.

From the given question we get the relationship between Quarters(Q), Dimes(D) and Nickle(N) in the form of ratio i.e.,

Ratio of Dime and Quarters = 2: 1 , and

Ratio of Nickle and Dime = 2:1

Therefore ratio between them,

Q : D : N = 1 : 2 : 4

Let's take Quarters to be x.

So we get the ratio as x:2x :4x

Thus, given that the total value is $2.60.

Therefore

0.25x + 0.2 (2x) + 0.05(4x) = 2.60

0.65x = 2.60

x = 4

Therefore with the ratio we get

Quarters = 4, Dimes = 8, Nickels = 16

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Answer:

529

Step-by-step explanation:

Answer: 1185

Step-by-step explanation: add 328 and 857

The possible two-course meals that could be ordered assuming diners must order one meal from each category are;

It follows from the task content that the categories are as indicated below;

Starters Mains

Garlic Bread

Prawns Soup

Chicken Risotto

The condition that diners must order one meal from each category simply leaves the diners with;

Consequently, the expected number of possible two-course meal combination is; 3 × 3 = 9.

Ultimately, the possible two-course meals that could be ordered assuming diners must order one meal from each category are as listed above.

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Answer:

51

Step-by-step explanation:

Answer: The Answer is A.

Step-by-step explanation:

The lower and upper bounds for the following to the given degrees of accuracy are: a- 64 mins (63.5 ≤ 64 < 64.5) c- 30m/s (27.5 ≤ 30 < 32.5) b- 20g (15 ≤ 20 < 25) d-7500mm (7450 ≤ 7500 < 7550)

The upper and lower bounds can be found by dividing the degrees of accuracy by 2 and then subtracting and adding with the value to give the lower and upper bounds respectively.

For a- 64 mins (nearest 1 min)

As the degree of accuracy is to the nearest 1 min;

1 min ÷ 2 = 0.5 min

Upper bound = 64 + 0.5 = 64.5 min

Lower bound = 64 - 0.5 = 63.5 min

For c- 30m/s (nearest 5m/s)

5m/s ÷ 2 = 2.5 m/s

Upper bound = 30 + 2.5 = 32.5 m/s

Lower bound = 30 - 2.5 = 27.5 m/s

For b- 20g (nearest 10g)

10g ÷ 2 = 5

Upper bound = 20 + 5 = 25g

Lower bound = 20 - 5 = 20g

For d- 7500(nearest 100mm)

100mm ÷ 2 = 50mm

Upper bound = 7500 + 50 = 7550mm

Lower bound = 7500 - 50 = 7450mm

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Since both terms are perfect squares, factor using the difference of squares formula, ( [tex]a^{2}-b^{2} =(a+b)(a-b)[/tex] )

Answer: yes, because you can't score negative numbers in a game and the absolute value is really just making all numbers positive unless there is a negative variable outside of the absolute value symbols

Step-by-step explanation: brainliest?

Answer:

B/a

Step-by-step explanation:

Because 1/a is still the same as a to power negative one and so 1/b. 1/a divided by 1/b is b/a

The simplified form of trigonometric expression, cosec θ / sin θ + cos θ cot θ is 1.

Given,

The trigonometric expression = cosec θ / sin θ + cos θ cot θ

We have  to simplify this expression.

For that we can use trigonometric identities.

cosec θ = 1 / sin θ

cot θ = cos θ / sin θ

We can substitute the above given identities in the expression.

Then we get,

cosec θ / sin θ + cos θ cot θ = (1 / sin θ) / (sin θ + cos θ x (cos θ/sin θ))

= (1 / sin θ) / ((sin²θ + cos²θ) / sin θ)

Cancel sin θ from both numerator and denominator.

= 1 / sin² θ + cos² θ

We know that sin² θ + cos² θ = 1

So, we get,

1 / sin² θ + cos² θ = 1 / 1 = 1

Therefore, the simplified form of  cosec θ / sin θ + cos θ cot θ is 1.

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Answer:

X = -1

Step-by-step explanation:

1. expand the right side of the equation

8x + 6

7x + 5 = 8x + 6 should look like this

2. minus 7x on both sides

5 = 1x + 6 should look like this

3. minus 6 on both sides

-1 = 1x should look like this

4. divide by 1 from the x on both sides

-1 = x this is the only answer for this equation

The inequality that models the situation is $50 + n*$25 ≤ $175 with that, we can see that the student can take, at most, 5 classes.

Here we know that Mr. Bass chares his students $25 per lesson, plus a fixed fee of $50.

Then if you attend to n of his classes, the total amount that you need to pay is:

$50 + n*$25

If you want to pay no more than $175, then we can write the inequality:

$50 + n*$25 ≤ $175

Now we want to solve that inequality for n.

$50 + n*$25 ≤ $175

n*$25 ≤ $175 - $50

n*$25 ≤ $125

n ≤ $125/$25 = 5

So the student can take, at most, 5 classes.

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