The graph of y = f(X) is shown.
b) Find the roots of f(X) = 0
c) Find f(0)

The answer after simplification is 48[tex]\sqrt{2}[/tex]

We are required to simplify two values in square root form

Given values are :

4[tex]\sqrt{32}[/tex]+4[tex]\sqrt{128}[/tex]

4([tex]\sqrt{32}[/tex]+[tex]\sqrt{128)}[/tex]

Now we know that

32= [tex]2^{5}[/tex]

128=[tex]2^{7}[/tex]

Putting these values inside the square root,

we know that square root is to the power 1/2

our equation becomes

4([tex]\sqrt{2^{5} } +\sqrt{2^7[/tex])

removing the square root,
4([tex]2^{5/2}+2^{7/2}[/tex])

Now we know that 4 is 2 to the power 2 , and taking 2^5/2 as common, we get:

[tex]2^{2}*2^{5/2}(1+2^{2/2})[/tex]

16[tex]\sqrt{2}[/tex](3)

=48[tex]\sqrt{2}[/tex]

The answer after simplification is 48[tex]\sqrt{2}[/tex]

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Answer: x  ≤ 4.5

Step-by-step explanation:

Since the inequality goes left and has a closed circle it would be x  ≤ 4.5

Answer:

[tex] \rightarrow \sf \: −31[/tex]

Step-by-step explanation:

[tex] \rightarrow \sf \frac{1}{4} (4)-5(6)-2[/tex]

[tex] \rightarrow \sf \: \frac{1}{4} \times \frac{4}{1} - 30 - 2[/tex]

[tex] \rightarrow \sf \: 1 - 30 - 2[/tex]

[tex] \rightarrow \sf \: - 31[/tex]

Answer:

It's 54 Degrees

Step-by-step explanation:

Answer:20

Step-by-step explanation:

m = [tex]\frac{4}{25}[/tex]  0r m = [tex]-\frac{16}{15}[/tex]

|2m+3/5|=|1-3m/6|

Split into two equations

⇒[tex]2m + \frac{3}{5} = 1 - \frac{3m}{6}[/tex] or

⇒[tex]2m + \frac{3}{5} =-( 1 - \frac{3m}{6})[/tex]

[tex]2m + \frac{3}{5} = 1 - \frac{3m}{6}[/tex]

multiply both side of the equation by the common denominator

⇒2m × 30 + [tex]\frac{3 * 30}{5}[/tex] = 30 - [tex]\frac{3 m * 30}{6}[/tex]

⇒2m×30 + 18 = 30 -15m

⇒60 m + 18  = 30  -15m

⇒60m  + 15m = 30 - 18

⇒75m = 12

⇒m = [tex]\frac{12}{75}[/tex]

⇒m = [tex]\frac{4}{25}[/tex]

[tex]2m + \frac{3}{5} =-( 1 - \frac{3m}{6})[/tex]

reduce the fraction

⇒[tex]2m + \frac{3}{5} =-( 1 - \frac{m}{2})[/tex]  

remove brackets

⇒[tex]2m + \frac{3}{5} = - 1 + \frac{m}{2}[/tex]

multiply both side of the equation by the common denominator

⇒2m × 10 +  [tex]\frac{3 * 10}{5}[/tex] = -10 + [tex]\frac{ m * 10}{2}[/tex]

⇒2m × 10 + 6 = -10 + 5m

⇒20 m + 6 = - 10 + 5m

⇒20m - 5m = - 10 -6

⇒15m = -16

⇒m = [tex]-\frac{16}{15}[/tex]

we get,

m = [tex]\frac{4}{25}[/tex]  0r m = [tex]-\frac{16}{15}[/tex]

Equations with fractions involve solving equations where the unknown variable is part of the numerator and/or the denominator of the fraction.  

To solve equations with fractions we need to work out what the value of the unknown variable. We solve equations by using the “balancing method” by applying the inverse operation to both sides of the equation.

The inverse operation of addition is subtraction.

The inverse operation of subtraction is addition.

The inverse operation of multiplication is division.

The inverse operation of division is multiplication.

How to solve equations with fractions

In order to solve equations with fraction:

Identify the operations that are being applied to the unknown variable.

Apply the inverse operations, one at a time, to both sides of the equation.

Write the final answer, checking that it is correct.

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Graham drove 32.58 miles in one hour and it took 1.84 minutes to drive a mile

Miles Graham drove in 13 hours = 423 miles

Unitary method: A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. It is a technique that we employ for the majority of math calculations.

Part a:

Miles driven in one hour = Total miles driven/Total no. of hours taken

= 423/13 = 32.58 miles

Part b:

Hours took to drive a mile = Total no. of hours taken/ Total miles driven

= 13/423  = 0.030 hours or 1.84 minutes

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The percentage of the questions which of are intermediate​ level are 31 %.

It is given in the question that practice questions for a textbook are marked with difficulty levels of​ easy, intermediate, and difficult.  It is also given that 42 of the 136 practice questions are rated as​ intermediate.

We have to find the percentage of the questions which of are intermediate​ level .

We know that,

Percentage of intermediate questions = (Number of intermediate questions/Total number of questions)*100

Hence, from the data given in the question, we can write,

Percentage of intermediate questions = (42/136)*100 = 30.88 % ≈ 31 %

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Answer: 26

Step-by-step explanation:

(-4)(-2)-6(2-5)=

-(-8)-6*2-6*(-5)=

-(-8)-12-(-30)=

8-12+30=

30+8-12=

38-12=26

After solving the equation, x = 3/2 is the value of x in 2x = 3.

⇒ 2x = 3

⇒ x = 3/2

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Answer:

28 points

Step-by-step explanation:

The given expression would be simplified by solving for the negative exponent.

In this expression, the base term is 3x^2/3 and the exponent is -1.

A positive exponent tells us how many times a number is multiplied by itself while the negative exponent tells us how many times the base number has to be divided. It can also be described as the number of times the reciprocal of the base number is multiplied by itself.

The negative exponent rule states that: a^-x=1/a^x

Hence, applying the rule:

(3x^²/₃)^-1=1/(3x^²/₃)^1

Multiplying the power and simplifying,

1/(3x^²/₃)^1=1/3^1x^²/₃*1=1/3x^²/₃

The simplest form of the expression (3x^²/₃)^-1 is 1/3x^²/₃.

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Based on the sequence, the number that is closest to 300 is 310

The sequence of numbers is given as

30, 70, 110, 150

The increment in the sequence is given as

40

This means that we keep increasing the numbers by 40

So, the other numbers in the sequence are

30, 70, 110, 150, 190, 230, 270, 310, 350, 390.....

The number 300 is between 270 and 310

However, 310 is closer to 300 than 270

Hence, the number that is closest to 300 is 310

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Complete question

The numbers in this sequence increases by 40 each time. this sequence is continues with the same rule which number will be closest to 300

30, 70, 110, 150

Answer: 118728

Step-by-step explanation:

You can just simply find this answer using a calculator.

Days it took the grass to grow 1 centimeter and  centimeters the grass grew in 1 day

0.625 days to grow 1 cm.

16/10 = 1.6 cm in 1 day.

According to the law of proportion, any two ratios or fractions must be equal.

In only a week and a half, the grass in Jamie's backyard grew by 16 cm. it is expanding at an unchanging pace.

We need to determine how many days have passed since the grass has grown one centimeter.

Let's say that x represents the number of days that the grass grew one centimeter.

Given the following definition of proportion:

16/10=1/x

16x = 10

x = 0.625 days

As a result, one centimeter of grass growth occurred after 0.625 days had passed.

b)

Change x into 1. Because x is the number of days.

16/10=1/1

16/10

1.6

'In conclusion, in 1 day, 1.6 cm will grow.

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Answer:

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

The domain is all real numbers where x does not equal -2 and the range is all real numbers where f(x) does not equal -8

The domain of the function is the set of input values of the graph while the range of a function is the set of output values of the graph.

The given parameter is:

f(x) = (x^2 - 4x - 12)/(x + 2)

Based on the definition above, the range of a function is the set of y values of the graph while the domain is the set of x values of the graph

Set the denominator not equal to 0

So, we have

x + 2 ≠ 0

Evaluate

x ≠ -2

This means that the domain is all real numbers where x does not equal -2

For the range, we use a graphing calculator

From the graphing calculator, we have

f(x) ≠ -8

This means that the range is all real numbers where f(x) does not equal -8

Hence, the domain is all real numbers where x does not equal -2 and the range is all real numbers where f(x) does not equal -8

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Complete question

What are the domain and range of the function f(x) = (x^2 - 4x - 12)/(x + 2)

[tex]\displaystyle\\Answer:\ I=\sqrt{\frac{M}{7} }[/tex]

Step-by-step explanation:

Answer/Step-by-step explanation:

f(6) = 3x² - 5

f(6) = 3(6)² - 5

f(6) = 3(36) - 5

f(6) = 108 - 5

f(6) = 103

(x, y) = (6, 103)

I hope this helps!

Answer:

→ 2 + (3 × x) = 30

Answer: y=2x-2

Step-by-step explanation:

X intercept is 1

Hence,

(1,0)

Thus,

(1,0)     (-1.-4)

                      Equation of a straight line:

                             [tex]\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]                

x₁=1       x₂=-1        y₁=0        y₂=-4

[tex]\displaystyle\\\frac{x-1}{-1-1} =\frac{y-0}{-4-0} \\\\\frac{x-1}{-2} =\frac{y}{-4} \\\\[/tex]

Multiply both parts of the equation by -4:  

(2)(x-1)=y

2x-2=y

Answer:

[tex]y=2x-2[/tex]

Step-by-step explanation:

The x-intercept is when the line crosses the x-axis, so when y = 0.

Therefore, the two points on the line are:

To find the equation of the line when given two points from the line, first find the slope:

[tex]\textsf{slope}\:(m)=\dfrac{\textsf{change in $y$}}{\textsf{change in $x$}}=\dfrac{-4-0}{-1-1}=2[/tex]

Now substitute the found slope and one of the points (1, 0) into the point-slope form of a linear equation:  

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-0=2(x-1)[/tex]

[tex]\implies y=2x-2[/tex]

Therefore, the equation of the line is:

[tex]y=2x-2[/tex]

 713   

1,000

Hope this helps!

The correct congruent statement are as follows:

The triangle ABC and PQR are congruent triangle.

Therefore,

ΔABC ≅ ΔPQR

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

Therefore,

∠A ≅ ∠P

∠B ≅ ∠Q

∠C ≅ ∠R

Hence,

AB ≅ PQ

AC ≅ PR

BC ≅ QR

Therefore, the correct congruent statement are as follows:

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If Colton is 1.55 meters tall. At 1 p.m., he measures the length of a tree's shadow to be 44.35 meters. the height of the tree to the nearest hundredth of a meter. is 12.85 meters.

First step is to find the distance that he is horizontally from the top of the shadow

Distance = 44.35 meters - 39 meters

Distance = 5.35 meters

Second step is to make use of equal proportion and find the height

5.35/ 1.55 = 44.35/x

5.35x = 1.55 × 44.35

x=  1.55 × 44.35 /5.35

x= 12.849

x= 12.85 meters (Approximately)

Therefore If Colton is 1.55 meters tall. At 1 p.m., he measures the length of a tree's shadow to be 44.35 meters. the height of the tree to the nearest hundredth of a meter. is 12.85 meters.

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Answer: 78

Step-by-step explanation: multiply 44 by 2 because there are two sides on the rectangle and then you add 5 and 5 because yet again there are two sides so when you get your answer subtract 10 from the 88 and then you get 78 there is your explanation and equation

Rectangle with perimeter 44 ft has its length and breadth 13 ft and 9 ft respectively.

Dimension of rectangle : 13 × 9

Given, that perimeter of rectangle is 44 ft .

Now, perimeter of rectangle is given by:

P = 2(l + b)

l = Length of rectangle .

b = Breadth of rectangle.

Let the breadth of rectangle be 'x' m.

Then length will be (2x -5) ft.

Substitute the values in the perimeter formula,

[tex]44 = 2(x + 2x -5)\\22 = 3x -5\\x = 9[/tex]

Thus the breadth of rectangle is 9 ft .

Length of rectangle is 5 ft less than twice its breadth.

Length = 2(9) - 5

Length = 13 .

Therefore the dimensions of rectangle is 13 × 9.

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It should be noted that the value of (2 × 10^5)(3 × 10^-4) in scientific notation will be 6 × 10 or 0.6 × 10².

It should be noted that scientific notation is used to illustrate numbers that are either too large or when the numbers are too small.

In this case, it should be noted that (2 × 10^5)(3 × 10^-4)

Therefore, the appropriate value will be:

= (2 × 10^5)(3 × 10^-4)

= 6 × 10

Therefore, it should be noted that the value of (2 × 10^5)(3 × 10^-4) in scientific notation will be 6 × 10 or 0.6 × 10².

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Answer:

1. 60 seconds.

2. 9 minutes.

3. 3 minutes, 180 seconds.

4. 300 seconds, 5/60 horas.

The amount after 10 years is $11,842.43

In continuous compounding the number of times by which compounding occurs tends to infinity.

In order to calculate the amount use the following formula

A= Pe^rt

where P represents the initial amount, e is the mathematical constant having value 2.7182, r is the rate of interest and t is the time period

Here the principal amount is $6000, r is 6.8 and time period t is 10 years

A = $6000 x 2.718⁽¹⁰ ˣ ⁶·⁸ %⁾

A = 6000 x 2.718⁽¹⁰ ˣ ⁶·⁸÷¹⁰⁰⁾  

A = 6000 x 2.718 x 0.68

A = $ 11,842.43

Therefore the total amount calculated after 10 years is $ 11,842.43

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Answer: The decimal equivalent to 2/9 = 0.22

Step-by-step explanation:

Define Decimal equivalent :

The decimals with the same number of decimal places are called like decimals. Equivalent decimals are decimal numbers that have the same value. For example, 3.42, 6.05 are like decimals as they have two decimal places. For example, 0.3 and 0.30 are equivalent decimals as they present the same value.

How do you find the equivalent decimal?

To find the decimal equivalent of a fraction, divide the numerator by the denominator. Because the number in the numerator is smaller than the number in the denominator, you have to place the decimal point after it and add zeros. Then complete long division.

Given data,

Find the decimal equivalent to 2/9.

To get a fraction into a decimal you have to divide the fraction. I was taught since the 2 is the numerator, it gets divided out of and the 9 is what you're dividing the 2.

so, we can write,

                        x = 2/9

where,          numerator = 2

                     denominator = 9

Then, x = 2/9 = 0.22

Therefor, the decimal equivalent to 2/9 = 0.22

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Answer:

-21/8

Step-by-step explanation:

3 (3/8) * -7/3

= 9/8 * -7/3

= 3/8 * -7

= -21/8