Use the GCF and the Distributive Property to find the sum of 38 + 57

Answer:

the answer is 30 yd

Step-by-step explanation:

[tex] - 4w - 2 = |6w + 20| [/tex]

[tex] - 4w - 2 = |6w + 20| \\ - 4w - 2 = 6w + 20 \\ - 2 - 20 = 6w + 4w \\ - 22 = 10w \\ \frac{ - 22}{10} = w \\ \frac{ - { \cancel{22}}^{ \: \: 11} }{ \cancel{10}^{ \: \: \: 5} } = w \\ \frac{ - 11}{5} = w[/tex]

[tex] - 4w - 2 = |6w + 20| \\ - 4w - 2 = | - (6w + 20)| \\ - 4w - 2 = - 6w - 20 \\ 6w - 4w = - 20 + 2 \\ 2w = - 18 \\ w = \frac{ - 18}{2} \\ w = \frac{ - \cancel{18}^{ \: \: 9} }{ \cancel2} \\ w = - 9[/tex]

Answer:

1, 3, 13, 39

Step-by-step explanation:

because it is

For the values like (0.-4) and (1,3.5),the function is h(x)=9x-4.

Given a table which contain values of the function h(x) and the respective values of x.

We are required to form the function.

Function is basically the relationship between two or more variables that are expressed in equal to form. The values that we enter in the function are known as part of domain and the values that we get from the function is known as part of range of the function.

We have to just take two points like (0.-4) and (1,3.5).

We have to just form the equation.

y-(-4)={5-(-4)}/{1-0}(x-0)

y+4=9x

y=9x-4

h(x)=9x-4

Hence for the values like (0.-4) and (1,3.5),the function is h(x)=9x-4.

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Question is incomplete as it should include the attached figure.

The surface area of the sphere is 1232² feet.

The formula for the surface area of the sphere: 4πr²

Now, substitute  the values in the formula as follows:

Therefore, 1232² feet is the surface area of the sphere.

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The required measure of 41°C in Fahrenheit is given as 105.8°F.

Temperature is defined as the degree of measure of heat in an object.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Conversion from Celsius to Fahrenheit is given as,

F = (41°C × 9/5) + 32

F = 105.8°F

Thus, the required measure of 41°C in Fahrenheit is given as 105.8°F.

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Answer:

*HOPE THIS HELPS*

Step-by-step explanation:

Full explanation given in the picture

Answer: 48hm

Step-by-step explanation:

48hm = 4800m

480m < 4800m

The figure with 2 lines and 2 rays is drawn and labeled and can be seen in the attached picture.

In the question, we are asked to draw and label a figure that has at least 2 lines and 2 rays.

First, we need to note three things:

Now, we are asked to make a figure with 2 lines (that is, two endless collections of points) and 2 rays (that is, a part of the line with a fixed start point, but no end point).

This can be shown in the attached figure.

In the figure, AB and CD are the two lines, and PQ and XY are the two rays.

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Answer:

(i) 50 ft/s

(ii) 1750 ft

Step-by-step explanation:

(i)

The vertical speed is:

4500 ft / 90 seconds = 50 ft/s

(ii)

50 ft/s × 35 s = 1750 ft

By using the given notation and format, we see that the sample space for the experiment is:

( {R, B}, {R, G}, {R, Y}, {B, R}, {B, G}, {B, Y}, {Y, R}, {Y, G}, {Y, G}, {G, R}, {G, B}, {G, Y})

The sample space is the set of the total possible events or outcomes in a given experiment.

Here we have 4 candies and you select two, such that the events have the format:

(C₁, C₂)

For example, if the first candy you draw is red and the second is blue, then the event will be:

(R, B)

Which is different to the event when you first draw blue and then red, which is:

(B, R).

So we just need to write all the possible events, it will give use the sample space:

( {R, B}, {R, G}, {R, Y}, {B, R}, {B, G}, {B, Y}, {Y, R}, {Y, G}, {Y, G}, {G, R}, {G, B}, {G, Y})

Where the notation used is the given one:

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The maximum and minimum set of dimension for the rectangular field are-

A rectangle is a four-sided configuration with 90-degree angles at all four corners. A rectangle's sides are same length than the one opposite it.

The perimeter of the rectangular field is given in the form of equation;

4x + 3y = 100

Where the total area is given as;

y(x+x) = 374

2xy = 374

Solving the equation;

(4 x+3 y)² = 16x² + 12×2 x y + 9 y² = 10000

2 x y = 374,12.

2 x y = 12 × 374

2 x y = 4488

16x² + 9 y² = 10000 - 4488

16x² + 9 y² = 5512

Now, solve for the other set of value;

(4 x-3 y)² =  16x² - 12×2 x y + 9 y²

Put the value of 16x² + 9 y² = 5512.

(4 x-3 y)² =  5512 - 12×2 x y

Put 2xy = 374

(4 x-3 y)² =  5512 - 4488

(4 x-3 y)² = 1024

Case1: 4 x-3 y = √{1024}

4 x-3 y = 32

And, 4 x + 3 y = 100

Solving both;

8x = 132

x = 16.5

and y = (100 - 32)/6

y = 11.33

Case 2: 4 x - 3 y = -32

4 x + 3 y = 100

Solving both by elimination method.

x = 8.5 and y = 22

Thus, the minimum and maximum dimension for the rectangular garden are-

Maximum (x, y) = (8.50, 22)

Minimum (x, y) = (16.50, 11.33)

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Answer:

<

Step-by-step explanation:

Answer:

54.7

Step-by-step explanation:

19% of 288

0.19 * 288 = 54.72

54.72 = 54.7

Answer:

Estimated 60 and rounded 55 and normal 54.72.

Step-by-step explanation:

To get the estimated answer, first convert the percentage to a decimal: 19% = 0.19. Second, you have to round the 2 numbers so they are easier to multiply: 0.19 = 0.20 and 288 = 300. Now that you have the 2 rounded numbers, you can multiply them to get the estimated answer: 0.20 x 300 = 60 so 60 is your estimated answer.

To get the rounded answer, you first have to multiply the 2 given numbers, the whole number and the percentage (as a decimal), together: 0.19 = 54.72. Now that you have the answer to the multiplication problem, you can round the answer to the nearest whole number: 54.72 = 55 so the rounded answer is 55.

To get the exact answer, all you have to do is multiply the percentage (as a decimal), by the whole number to get the answer: 0.19 x 288 is 54.72 so the exact answer is 54.72.

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Answer:

16,384

Step-by-step explanation:

4^4 = 4×4×4×4=256

8^2 = 8×8=64

256×64=16,384

Answer:

16384 or [tex]2^{14}[/tex]

Step-by-step explanation:

This is easiest done by creating identical bases (the number being raised by the exponent, 4 and 8 here).

How do we do that? Well let’s start with [tex]4^{4}[/tex].

For both 8 and 4 the bases can be rooted to 2

[tex]\sqrt[3]{8} = 2 \\ \sqrt{4} = 2[/tex]

Because the root of 4 is 2, that means [tex]2^{2} =4[/tex].
Therefore, we can substitute [tex]2^{2}[/tex] for 4 in [tex]4^{4}[/tex], which looks like this:

[tex]2^{2^{4} }[/tex]

And, we should know that an exponent raised to an exponent is the same as multiplying those exponents together. This means [tex]2^{2^{4}} =2^{8}[/tex].

We can repeat the process with [tex]8^{2}[/tex]

[tex]8 = 2^{3} \\8^{2} =2^{3^{2} } \\2^{3^{2} } =2^{6}\\8^{2}=2^{6}[/tex]

Now that we have [tex]2^{8}\ and\ 2^{6}[/tex] we can continue. Given that the bases are the same we can simply add the exponents together when we multiply.

[tex]2^{8}[/tex] x [tex]2^{6}[/tex] = [tex]2^{14}[/tex] (or 16384).

The value of the product of the two decimal numbers is 35.2772 which is closest to 36 of all the given numbers.

The outcome of multiplication or an expression that specifies factors to be multiplied is a product.

The two numbers are 11.72 and 3.01

To multiply this two decimal numbers we will use the fraction property.

11.72 can be written as  [tex]\frac{1172}{100}[/tex] and 3.01 can be written as  [tex]\frac{301}{100}[/tex]

So the product of 11.72 and 3.01 is written as

[tex]=\frac{1172}{100}\times\frac{301}{100}\\\\\\=\frac{352772}{10000}[/tex]

= 35.2772

This number in decimal can be estimated to 36 because it is closest to the given options.

Hence the product is approximately 36.

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The two fractions that will give a sum between 0.75 and 1 are 3/7 + 5/9 and the larger fraction is 5/9

We want to find two fractions using the digits 3, 5, 7 and 9 to find the one that gives a sum between 0.75 and 1.

Since it has to be a sum between 0.75 and 1, it means that the denominator must be greater than the numerator. Thus, let us try as follows;

3/5 + 7/9

Factorize out 45 to get;

¹/₄₅((3 * 9) + (7 *5))

= ¹/₄₅(27 + 35)

= ¹/₄₅(52)

This will not work because it will lead to a sum greater than 1

Let us try another one;

3/7 + 5/9

Factorize out 63 to get;

¹/₆₃((3 * 9) + (5 *7))

= ¹/₆₃(27 + 35)

= 52/63

= 0.8254

Thus, the two fractions that will give a sum between 0.75 and 1 are 3/7 + 5/9 and the larger fraction is 5/9

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Answer:

you need to show the options at the bottom

Step-by-step explanation:

Answer:

the answer is two because the absolute value delete the negative in result not in question

Answer:

(0, 3)

[tex]x=0\\y=3[/tex]

Step-by-step explanation:

You can rewrite the first equation as [tex]y=3-x[/tex]. Then, you can substitute into the second equation as follows:

[tex]x-3(3-x)=-9\\x-9+3x=-9\\4x=0\\x=0\\[/tex]

Now, we can substitute this value into the first equation.

[tex]x+y=3\\0+y=3\\y=3[/tex]

Writing this in the form of [tex](x, y)[/tex] will yield [tex](0, 3)[/tex].

Remember when setting this out, align your equal signs and give good mathematical reasoning as shown above.

Hope this helps you!

The value of x, at which the second function's output exceeds  the first function's output is

[tex]$x \in\left(-\infty, \frac{1-\sqrt{29}}{2}\right) \cup\left(\frac{1+\sqrt{29}}{2}, \infty\right)$[/tex]

This is further explained below.

Generally, The second function's output exceeds (get bigger than) the first function's output for

[tex]$x \in\left(-\infty, \frac{1-\sqrt{29}}{2}\right) \cup\left(\frac{1+\sqrt{20}}{2}, \infty\right)$[/tex]

Given the functions f(x)=x+7 and f(x)=x^2

To know when to exceed, need to equate both functions.

[tex]$$\begin{aligned}&\Rightarrow x^2=x+7 \\&\Rightarrow x^2-x-7=0 \\&\mathrm{x}=\frac{-b+\sqrt{D}}{2 a} \text { and } \frac{-b-\sqrt{D}}{2 a} \\&\Rightarrow \mathrm{x}=\frac{1-\sqrt{29}}{2}, \frac{1+\sqrt{29}}{2}\end{aligned}$$[/tex]

f(x)=x^2 drops from infinity to zero and grows from zero to infinity; it cuts the graph of x+7 twice, and for each of those instances, it results in the same shape.

[tex]x \in\left(-\infty, \frac{1-\sqrt{29}}{2}\right) \cup\left(\frac{1+\sqrt{29}}{2}, \infty\right) f(x)=x^2$[/tex]  is greater than f(x)=x+7

As a result, the output of the second function surpasses (acquires a greater size than) the output of the first function for

[tex]$x \in\left(-\infty, \frac{1-\sqrt{29}}{2}\right) \cup\left(\frac{1+\sqrt{29}}{2}, \infty\right)$[/tex]

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Number of people called at 6 o clock using a base and exponent is 6^2

Number of people called at 8 o clock using a base and exponent is 6^3

Given data

At 4 o clock, Devon called 6 friends

At 6 o clock, each of his friends called 6 other friends

At 8'o clock, each of those friends called 6 of their friends

Let the friends Devin called at 4 o clock be represented by x

such that 6 friends will be = x + x + x + x + x + x = 6x

At 6 o clock, each of his friends called 6 other friends this means that each x called 6 friends assuming y this time, such that: y represents the number of friends called at 6 o clock by each x

each x called 6y this will lead to a total of

6y + 6y + 6y + 6y + 6y + 6y = 36y

Therefore 36 friends were called at 6 o clock which is equal to 6 * 6 = 6^2

using base and exponent we have

base = 6 and exponents = 2

Each of the 36 friends called their 6 friends again hence the total calls made is 36 * 6 = 216

using base and exponent

36 * 6 = 216

6^2 * 6^1 = 216

6^(2 + 1 ) = 216

6^3 = 216

base = 6

exponents = 3

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Answer:

Dimensions: 24, 24, 104

Total: 152 cm²

Step-by-step explanation(Triangles):

Given the triangles are equal to each other, we only need to solve one to get the other.

[tex]A = \frac{h \times b}{2} \\A = \frac{8 \times 6}{2}\\A = 24[/tex]

Therefore, the triangles' area are 24 cm.

Step-by-step explanation(Trapezoid):

Because of the height being unknown, we can define that using the side triangles. These triangles have a height of 8, so that also means the trapezoid has a height of 8. Now we can solve.

[tex]A = \frac{a+b}{2}\times h\\A = \frac{10+16}{2}\times 8\\A = 104[/tex]

Step-by-step explanation(Addition):

Finally, we add the 3 values.

[tex]24 + 24 + 104 = 152\:cm^2[/tex]

Lastly,

Hope this helps!

The LCM of the given polynomials x² - 81 and x² - 2x - 63 is (x - 9)(x + 7)(x + 9), which on expansion looks like x³ + 7x² - 81x - 567.

In the question, we are given two polynomials x² - 81 and x² - 2x - 63.

We are asked to find the LCM of the given polynomials.

To find the LCM of two polynomials, we multiply all the factors of both polynomials uniquely.

So first, we factor both the given polynomials.

x² - 81

= x² - 9² [∵ 81 = 9²],

= (x + 9)(x - 9) [Using the formula a² - b² = (a + b)(a - b)].

x² - 2x - 63

= x² - 9x + 7x - 63 [Mid-term factorization],

= x(x - 9) + 7(x - 9) [Grouping],

= (x + 7)(x - 9) [Grouping].

After factorizing the polynomials, we can note that the unique factors of x² - 81 and x² - 2x - 63 are (x + 9), (x -9), and (x + 7).

Thus, the LCM can be shown as their products, which is:

LCM = (x - 9)(x + 7)(x + 9), which on expansion looks like x³ + 7x² - 81x - 567.

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The value of the height is 17

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

Given:

Volume, V = 1/3πr²h

Volume= 1138.8,

π=3.14

r= 8

h= 3V/πr²

h= 3* (1138.8)/3.14* 8*8

h=3416.4/200.96

h=17

Hence, the value of height is 17

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Answer:

144

Step-by-step explanation:

24x6

24 6 times

24 + 24 + 24 + 24 + 24 + 24 = 144

i hopw this helped

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Answer:

The conditional statement is false and with the scenario it would still be false

Step-by-step explanation:

In the scenario it implies that you aren't a student and are most likely a teacher or tutor of some sort so the statement "If you go to school, then you are a student is false" because not all students go to school and in your scenario not only students go to school.

From the given coordinates, we can say that the Midpoint of AC = a/2, b/2 and the Midpoint of BD = a/2, b/2

Since the midpoints of the diagonals have the same coordinates, then we can conclude that AC and BD bisect each other.

From the given image, we see that the coordinates of parallelogram ABCD are;

A (0, 0)

B (a, 0)

C (a , b)

D (0, b)

Thus;

1) The coordinates of the midpoint of AC are;

Midpoint of AC = (0 + a)/2, (0 + b)/2

Midpoint of AC = a/2, b/2

2) The coordinates of the midpoint of BD are;

Midpoint of BD = (a + 0)/2, (0 + b)/2

Midpoint of BD = a/2, b/2

Since the midpoints of the diagonals have the same coordinates, then we can conclude that AC and BD bisect each other.

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The value of the function g(-2) is -46

A function can be defined as an expression, law , rule of hypothesis that explains or compares the relationship between two variables - the dependent and the independent variable.

Given the function;

g(x) = -4x³ - x² + 2x - 2

To determine the function, g(-2)

We substitute the value of x as -2 into the function, we have;

g(-2) = -4(-2)³ - (-2)² + 2(-2) - 2

expand the bracket

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

expand further

g(-2) = -32 - 8 - 4 - 2

g(-2) = -46

Thus, the value of the function g(-2) is -46

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