1. A small garden has a perimeter of 24 1/4 ft. If the lengths is 8 ft, what is the area of the garden.

2. Lynn is putting tiles on her bathroom floor. Each tile measures 1 square foot each. The floor measures 4 1/2 ft by 3 3/4 ft. How many tiles will she need to cover the floor?

3. A dog pen is 3 1/3 yards wide by 5 2/3 yards long. What is the area of the dog pen?

ATTACHED IS THE SOLUTION!!

Answer:

The evaluated function for the indicated values is given below.

The value of f(-3) is 20 .

The value of f(2) is 10 .

The value of f(-a) is [tex]$2|-3 a-1|$[/tex].

The value of -f(a) is [tex]$-2|3 a-1|$[/tex].

The value of f(a+h) is [tex]$2|3 a+3 h-1|$[/tex].

Step-by-step explanation:

A function [tex]$f(x)=2|3 x-1|$[/tex] is given.

It is required to evaluate the function at [tex]$f(-3) ; f(2) ; f(-a) ;-f(a) ; f(a+h)$[/tex].

To evaluate the function, substitute the indicated values in the given function to determine the output values and simplify the expression.

Step 1 of 5

The given function is [tex]$f(x)=2|3 x-1|$[/tex].

To evaluate the function at f(-3), substitute -3 in the given function [tex]f(x)=2|3 x-1|$\\ $f(-3)=2|3(-3)-1|$\\ $f(-3)=2|-9-1|$\\ $f(-3)=2|-10|$\\ $f(-3)=2(10)$\\ $f(-3)=20$[/tex]

Step 2 of 5

To evaluate the function at $f(2)$, substitute 2 in the given function.

[tex]f(x)=2|3 x-1|$\\ $f(2)=2|3(2)-1|$\\ $f(2)=2|6-1|$\\ $f(2)=2(5)$\\ $f(2)=10$[/tex]

Step 3 of 5

To evaluate the function at f(-a), substitute -a in the given function.

[tex]$$\begin{aligned}&f(x)=2|3 x-1| \\&f(-a)=2|3(-a)-1| \\&f(-a)=2|-3 a-1|\end{aligned}$$[/tex]

Step 4 of 5

To evaluate the function at -f(a), substitute a in the given function.

[tex]f(x)=2|3 x-1|$\\ $-f(a)=-2|3(a)-1|$\\ $-f(a)=-2|3 a-1|$[/tex]

Step 5 of 5

To evaluate the function at f(a+h), substitute a+h in the given function. [tex]$f(x)=2|3 x-1|$[/tex]

[tex]$$\begin{aligned}&f(a+h)=2|3(a+h)-1| \\&f(a+h)=2|3 a+3 h-1|\end{aligned}$$[/tex]

The product of the polynomials, (x + 2)(x - 2) = x² - 4.

Given the following expression, (x + 2)(x - 2), to find the product, apply the distributive property as shown below:

(x + 2)(x - 2)

x(x - 2) + 2(x - 2)

x² - 2x + 2x - 4

Combine like terms together

x² - 4

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Answer:

D. 16, 9, 8

Step-by-step explanation:

sum of any two sides of triangles must be greater than the third side

only the fourth option follows this rule

The complete table is

x -12 -6 3 15

y -6 5 15 15

The domain is given as:

Domain = {-12, -6, 3, 15}.

The incomplete table is given as

x

y -6 5 15 15

Enter the domain in the x values

x -12 -6 3 15

y -6 5 15 15

Hence, the complete table is

x -12 -6 3 15

y -6 5 15 15

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The spherical ball for the machine with a radius of 2 centimeters, has a mass of 278.1 grams and will have a density of 8.29 grams per cm³, which is identical to the density of Terbium's 8.23 grams per cm³.

Thus, we can say that Terbium is the material used to make the spherical ball.

The density of an object is given as the ratio of its mass and its volume.

Density = Mass/Volume.

In the question, we are informed that a spherical ball for a machine was made with a radius of 2 centimeters.

Thus, the volume of the spherical ball, using the formula for the volume of a sphere, V = (4/3)πr³, where r is its radius, can be calculated as:

V = (4/3)π(2)³ cm³ = 32π/3 cm³ = 33.51032 cm³.

The mass of the ball is given to be 278.1 grams.

Thus, its density = 278.1/33.51032 grams per cm³ = 8.2989355 grams per cm³.

We know that the density of Terbium is 8.23 grams per cm³.

Thus, the spherical ball for the machine with a radius of 2 centimeters, has a mass of 278.1 grams, will have a density of 8.29 grams per cm³, which is identical to the density of Terbium's 8.23 grams per cm³.

Thus, we can say that Terbium is the material used to make the spherical ball.

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Answer: copper

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Mean: 9+6+18+2+13+3+5= 56/7 = 8

Median: 2,3,5,6,9,13,18 the middle number is 6

mode:none

Answer:

ASA Postulate

Step-by-step explanation:

The two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. (Angle, Common Side, Angle)

Answer:

Hence the expression [tex]$$(p+12)(p-5)=p^2+8p-60$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\frac{\begin{matrix}{} & {} & p & + & 12 \\ \times & {} & p & - & 5 \\ \end{matrix}}[/tex]

____________

[tex]{\frac{\begin{matrix}{} & - & 5p & - & 60 \\ {{p}^2} & + & 12p & {} & {} \\ \end{matrix}}{\begin{matrix}{{p}^2} & + & 8p & - & 60 \\ \end{matrix}}}$$[/tex]

The following equation simplified by factoring or distributing:

1.) 2(x + 3)

= 2x + 6

2.) 2(x + 3 + y)

= 2x + 6 + 2y

3.) −5 (2x − 3)

= -10x + 15

4.) –5(–8w + p)

= 40w - 5p

5.) 20 + 32w

= 4(5 + 8w)

6.) 84 + 36z

= 12(7 + 3z)

7.) (2x - 6)(5x + 7)

= 10x² + 14x - 30x - 42

= 10x² - 16x - 42

8.) (y - 10)(4y + 2)

= 4y² + 2y - 40y - 20

= 4y² - 38y - 20

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Answer:

B

Step-by-step explanation:

Answer:

In polynomial function f(x) = 5x² + 2x³ + 4 the leading coefficient is 5.

The leading coefficient of a polynomial is the coefficient of the leading term 5x².

Step-by-step explanation:

Answer:

1)D 2) Can't see the function

The angle ∠14 and angle ∠16 are the supplementary angles. Then the measure of angle ∠16 will be 188° – 5x.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

The line l and the line m are parallel to each other.

The angle ∠7 = 4x – 3 and angle ∠14 = 5x – 8.

Then the measure of angle ∠16 will be

The angle ∠14 and angle ∠16 are the supplementary angles. Then we have

    ∠14 + ∠16 = 180°

5x – 8 + ∠16 = 180°

              ∠16 = 180° – 5x + 8

              ∠16 = 188° – 5x

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Answer:

1. Function

2. Not a function

3. Function

4. Not a function

Step-by-step explanation:

A function just means that for each input it outputs only 1 output. This output isn't necessarily unique. So for example if you're just given: f(2) = 3 and f(1) = 3, this is a function since each input only outputs 1 value, even though the output isn't unique, but if you're given: f(3) = 2, f(2) = 1, f(3) = 3. that's not a function since f(3) outputs both 2 and 3.

Anyways now that you hopefully understand this, let's look at each image.

Relation 1: (Function)

   So for each input (the domain) it's only pointing to one output (range), even if multiple input (the domain) are pointing to the same output (the range), it's still a function.

Relation 2: (Not a function)

   This is not a function, since if you look at the input 7 (the range), you'll see it outputs two things (range). It outputs -6 and -7. So this is not a function

Relation 3: (Function)

   This is a function since each x-value (input) has only one y-value (output). So it's a function

Relation 4: (Not a functio)

   This is not a function, since there are multiply coordinates with the same x-coordinate (input) and different y-coordinates (output). The x-coordinate 2 has the output b, y, and m, and since no value is given for these variables, it can be assumed they're different values, thus it's not a function.

Answer:

The exterior angle is 77

Step-by-step explanation:

The measure of the exterior angle of a triangle is equal to the sum of the two opposite interior angles.

2x+11 = x +44

First we need to find x

Subtract x from each side

2x+11-x = x+44

x +11 = 44

Subtract 11 from each side

x+11-11 = 44-11

x =33

Now we can find the exterior angle

2x+11 = 2(33)+11 = 66+11 = 77

The exterior angle is 77

Answer:

The temperature decreased by 9 degrees.

Step-by-step explanation:

Since the temperature in the morning was 2*C & at night, the temperature was -7*C, the temperature had to decrease using this equation =>  ||-7 + 2|| = x, with -2 being the temperature loss added as well. All we have to do is 7+2 = x & 9 = x, with x being the temperature drop.

Answer:

9 degrees Celcius

Step-by-step explanation:

The difference between 2 and -7 is 9.

Based on the lateral area of the cylinder, the volume of the cylinder can be calculated to be 139.5 cm³.

When given the lateral surface area of a cylinder, you can find the volume as:

= Area of lateral surface x (radius / 2)

Solving gives:

= 55.8 x (5 / 2)

= 55.8 x 2.5

= 139.5 cm³.

Missing part of the question:

Radius of the cylinder is 5cm.

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Using translation concepts, the function is given by:

C. [tex]y = \sqrt{x - 1} + 4[/tex].

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The graphed function is the square root function shifted one unit to the right(x -> x - 1), and four units up(y -> y + 4), hence the function is:

C. [tex]y = \sqrt{x - 1} + 4[/tex].

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Reflecting over y=x maps (x,y) onto (y,x).

So, the answer is A. (-8, 3).

Answer:

Step-by-step explanation:

Using the given exponential function, it is found that the colony would have 852 bacteria after 10 days.

The exponential function for the colonies' size is given as follows:

[tex]F = I(1 + r)^t[/tex]

In which:

The parameters are given as follows:

I = 55, r = 0.73, t = 5, as 10/2 = 5.

Hence the amount will be given by:

[tex]F = 55(1 + 0.73)^5 = 852[/tex]

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Answer:

I think it is 72

Step-by-step explanation:

but the question doesn't make sense because it should tell the number of spoons per 1 cup of sugar, perhaps it was a copy-paste mistake?

The algebraic expression of the given sentence is: 7(x - 1).

Let the unknown number be represented as x.

The word "difference" means subtraction which is "-". Multiplied means times.

We would have the following:

"Difference of x and 1" is: x - 1

x - 1 multiplied by 7 would be: 7(x - 1)

Therefore, the algebraic expression is: 7(x - 1).

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In a 30°-60°-90° triangle,  the length of the longer leg is √3 times the length of the shorter leg and  length of the hypotenuse is twice the length of the shorter leg.

ACF is a 30º-60º-90º triangle because of the following reasons;

Based on a theorem, in a 30°-60°-90° triangle, it is said that the length of the longer leg is √3 times the length of the shorter leg and  length of the hypotenuse is twice the length of the shorter leg,

1 → short leg = 1

2 → hypotenuse = 2

√3 → long leg = √3

Using the Pythagorean theorem., we have that

a² + b² = c²

1² + b² = 2²

b² = 2² - 1²

b² = 4 - 1

b² = 3

√b² = √3

b = √3

Thus, in a 30°-60°-90° triangle,  the length of the longer leg is √3 times the length of the shorter leg and  length of the hypotenuse is twice the length of the shorter leg.

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Place name of eights are ten thousands place & tens place & 80000, 80 are the values respectively.

The expanded form of a number is splitting of numbers based on place value. The place are ones, tens, hundreds, thousands, ten thousand etc

that is, the number represented by the sum of each digit multiplied by its place value is called the expanded form of a number.

Example : Expanded form of 4567 is 4000+500+60+7. where 4 is in thousands place, 5 is in hundreds place, 6 is in tens place and 7 is in ones place.

Given that, The speed of light is 186,282 miles per second.

The number is 186282.

Expanding the number, we get,

186282 = 100000+80000+6000+200+80+2

Here in the number 186282, eight present in the ten thousands place and in the tens place.

Since one eight is in ten thousands place, so the value is 80000

And the another eight is in the tens place, so the value is 80.

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Answer:

2x^2 + 5x - 3

Step-by-step explanation:

Area = length (a) * width (b)

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

2x^2 + 6x - x - 3 (combine like terms)

2x^2 + 5x - 3

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Answers:

Lower bound = 41.3

Upper bound = 41.5

===========================================================

Explanation:

49.15 is the smallest f can be while 49.24 is the largest it can be. Well technically we could have something like 49.2499 or 49.24999 and so on. We slowly approach 49.25 but never actually get there

So the variable f is between 49.15 and 49.25 inclusive of the first value but excluding the second value. We can write it as [tex]49.15 \le f < 49.25[/tex]

For similar reasoning, [tex]7.75 \le g < 7.85[/tex]

-----------------

If we wanted to subtract those variables and get the smallest result possible, then we need to pick values that are closest together. It might help to set up a number line.

This means we'd go for f = 49.15 and g = 7.85

The lower bound for f-g is f-g = 49.15-7.85 = 41.3

In contrast, the upper bound is when the two variables are spaced as far apart as possible. The upper bound is f-g = 49.25 - 7.75 = 41.5

Answer:

See below

Step-by-step explanation:

49.2     could  be       49.15 <= f < 49.25

7.8        could be       7.75 <= f < 7.85

Lower bound of   f- g    would then be    49.15  - 7.85 > 41.3

upper bound     49.25 - 7.75 < 41.5

 41.3  < f-g < 41.5

Answer:

Step-by-step explanation:

There are 26 letters, so there are 26

3

 possible 3-letter sequences.

the number of these which are palindromes can be computed as follows:

26 choices for the first letter

26 choices for the second letter

1 choice for the third letter ( it has to agree with the first)

number of ways  =26

2

Probability of a letter palindrome =26

2

/26

3

=1/26

there are 10 digits, so there are 10

3

 sequences of digits.

Reasoning as above, the number of digit-palindromes is (10)(10)(1)=10

2

so the probability of a digit-palindrome is 10

2

/10

3

=1/10

The events

D - digit palindrome

L - letter palindrome

are independent but not mutually exclusive.

So, P(LorD)=P(L)+P(D)−P(LandD)

P(LorD)=P(L)+P(D)−P(L)P(D)

=1/26+1/10−(1/26)(1/10)

=10/260+26/260−1/260

=35/360=7/52

Answer:

Step-by-step explanation:

Total Students = 20 + 18 = 38 students

For boys percentage = 20/38 * 100

Boys percentage = 52.6%

For girls percentage = 18/38 * 100

Girls percentage = 47.3%

Answer:

(i) 52.631578947368 %

(ii) 47.368421052632 %

Step-by-step explanation:

there are :

20 boys  

18 girls

Total number of students 38

========================

(i) the percentage of boys in the class

[tex]=\frac{20}{38} \times100 = 52.631578947368 \ \%[/tex]

(ii) the percentage of girls in the class

[tex]=\frac{18}{38} \times100 = 47.368421052632 \ \%[/tex]

The approximate solution of the system of equations is x = 0.75

The functions are given as:

f(x) = x^4 + 9x^2 - 3

g(x) = (1/2)^x - 2

Calculate the values of the function from -1 to 1

x             f(x)      g(x)

-1            7          8

-0.75    2.38   6.72

-0.5   -0.69     5.66

-0.25  -2.43   4.76

0          -3       4

0.25    2.43   3.36

0.5      -0.69   2.83

0.75    2.38   2.38

1          7        2

From the above table, we have:

f(0.75) = g(0.75) = 2.38

Hence, the approximate solution of the system of equations is x = 0.75

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