Find the GCF if the following terms . (30x^5 ,60x^3)

4.6

1) Since 3/4x = 3.45, then we can solve it for x

3/4x = 3.45 Multiply both sides by 4 to eliminate the fraction

3x =13.80 Divide both sides by 3

x= 4.6

2) So x is equal to 4.6, and that is the answer

The image of the rectangle ABCD translated 6 units to the right and 3 units up is shown below .

In the question ,

a rectangle is given

the vertex of the rectangle ABCD is given as

A(-10,-6) , B(-10,-2) , C(-6,-2) , D(-6,-6) .

On applying the translation 6 units to right and 3 units up ,

the rule is (x,y)→(x+6,y+3)

by applying the rule for the translation

we get image as

A'(-4,-3) ,B'(-4,+1) , C'(0,1) , D'(0,-3)

The image is plotted below .

Therefore , The image of the rectangle ABCD translated 6 units to the right and 3 units up is shown below .

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Answer: it would be D because m∠NSO+m∠OSL+m∠LSM+m∠MSN=360°  

and m∠LSM+m∠SML+m∠MLS≠360° doesnt equal 360 degrees so that one is wrong ∠LSM≅∠NSM is a false statement same with m∠LSO+m∠MSO=180° its false so it would be (D)

hope i helped

Step-by-step explanation:

The percentage error of Shaun's estimate is 44%

Here, we want to get the percentage error

We can get this by using the formula below;

We have the error as the difference between the estimated value and the actual value

The difference is;

The percentage error is;

This is approximately 44%

If  the weights (in pounds) of the gaskets in a batch are 0.58, 0.63, 0.65, 0.53, and 0.61. The gaskets  that should be thrown out is 0.53  and the inequality is: 0.54 ≤ w ≤ 0.66.

Using this formula to determine the mean

Mean = ∑x/n

Mean = 0.58 + 0.63 + 0.65 + 0.53 + 0.61 /5

Mean = 3/6

Mean = 0.6

Since the mean is 0.6 the gasket that are less than 0.53 and more than 0.66 (0.6±0.06) should be thrown out which in turn means that 0.53 should be thrown out.

Inequality :

0.54 ≤ w ≤ 0.66

Therefore 0.53 should be thrown out.

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Answer

The temperature at an altitude of 8,000 feet is 44° F

SOLUTION

Problem Statement

The question tells us that air temperature drops by 4 degrees Fahrenheit for every 1,000 feet above sea level. We are asked to calculate the temperature at 8,000 feet, close to the summit of Guadalupe Peak.

Solution

To solve this question, we simply compute the temperature changes for each 1,000 increase in height and then generalize. With the generalization, we can find the temperature at any height.

The temperature at 0 feet is 76°F (At sea level)

The temperature at 1,000 feet is 76°F - 4°F = 72° F

The temperature at 2,000 feet (2 x 1,000 feet) is 76°F - 4°F - 4°F (76°F - 2 x 4°F)

The temperature at 3,000 feet (3 x 1,000 feet) is 76°F - 4° F - 4° F - 4° F (76° F - 3 x 4° F)

And so on.

We can see a pattern developing and with this pattern, we can make a generalization about the temperature decrease for every increase in altitude.

Thus, we can solve the question by substituting n = 8 for an altitude of 8,000 feet. This is done below:

8 x 1000 feet = 8,000 feet is:

Final Answer

The temperature at an altitude of 8,000 feet is 44° F

The equation of the line passing through the points: (3,-10.5) and (1,-7.5) is [tex]3x+2y+12=0.[/tex]      

Every point on a line fulfills the equation of that line, which means that every point on the line represents every other point on the line.

The equation of a line passing through two-points [tex](x_{1} ,y_{1} )[/tex] and [tex](y_{1} ,y_{2} )[/tex] is given by the formula,

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

So, the equation of the line passing through the points (3,-10.5) and (1,-7.5) will be-

⇒[tex]y-(-10.5)=\frac{-7.5-(-10.5)}{1-3} *(x-3)[/tex]

⇒[tex]y+10.5=\frac{-7.5+10.5}{-2} *(x-3)[/tex]

⇒[tex]y+10.5=\frac{3}{-2} *(x-3)[/tex]

⇒[tex]y+10.5=\frac{-3x}{2} +\frac{9}{2}[/tex]

⇒[tex](y+10.5)*2=-3x+9[/tex]

⇒[tex]2y+21=-3x+9[/tex]

⇒[tex]2y+3x+21-9=0[/tex]

⇒[tex]3x+2y+12=0[/tex]

Hence, the equation of the line passing through the points (3,-10.5) and (1,-7.5) is  [tex]3x+2y+12 =0[/tex].

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Given:

The objective is to find hte value of x.

The value of x can be calculated by basic proportionality theorem.

Thus, the required equation is obtained.

The value of x is,

Hence, the value of x is 10.5

we have the following:

Therefore, the answer is 121.7 yards

It will cost $348.7 to buy fencing to go around the rectangular garden.

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Answer:

126.5 cm²

Step-by-step explanation:

Hello!

This shape can be split into a rectangle and a triangle.

The rectangle's dimensions are 8 and 11, and the base and height of the triangle are 11 and 7 respectively.

The combined area is 88 + 38.5 which is 126.5 cm².

Answer:

C

Step-by-step explanation:

[tex]\frac{74000}{8000}=9.25 \times 10^1[/tex]

There are 7 % of Americans over age 100 who were there in 2000 and the number of Americans growing by 54% over age 100 changed in 2000.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable

The number of Americans over age 100 can be approximated by

[tex]P(t) = 0.07e^{0.54t}[/tex]

where is P(t) measured in millions and t is measured in decades.

Also, t = 0 corresponds to 2000.

⇒ [tex]P(t) = 0.07e^{0.54t}[/tex]

Substitute the t = 0 in the above function, and we get

⇒ [tex]P(t) = 0.07e^{0.54\times0}[/tex]

⇒ P(t) = 0.07 e°

⇒ P(t) = 0.07

Convert decimals into fractions, and we get

⇒ P(t) = 7 / 100

This represents 7 out of 100 which is 7 % of Americans over age 100 who were there in 2000.

Thus, the number of Americans growing by 54% over age 100 changed in 2000.

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Description of the function over each part of its domain is:

So, we examine the displayed graph.

The y values are constant from x = 0 to x = 12,000.

So slope = 0.

Then,

Slope = 0 and the domain is constant at (0,12000).

Domain (12000, 38000) is declining with a negative slope.

Therefore, description of the function over each part of its domain is:

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The correlation coefficient of the data provided is -0.52.

Correlation is a measure that is used in statistics to determine the linear relationship that exists between two variables. Correlation can be positive, negative or zero.

Positive correlation is when two variables move in the same direction. Negative correlation is when two variables move in opposite directions. Zero correlation is when there is no relationship between the variables.

Correlation can be determined using a financial calculator. When the financial calculator is used, the correlation coefficient is -0.52

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Answer:

Explanation:

To complete the missing values, we have to evaluate the function at the x-values given.

For example, to find the number below x = -1, we will put in x = -1 into y = (1/6)^x.

Putting in x = - 1 in y = (1/6)^x gives

which simplifies to give

Similarly, for the missing value below x = -2, we put in x = - 2 into y = (1/6)^x to get

which simplifies to give

Similarly, for the missing value below x = 2, we put in x = 2 in y = (1/6)^x to get

which simplifies to give

Hence, the missing value to be put in is 36.

To summerise, the missing values are

x | -2

The function that represents the cost function is c(x) = 75 + 0.25x

To find the cost function c(x), we have to write a linear equation or linear function to represent this.

The cost function can be expressed as a function of the number of copies made which can be represented as

[tex]c(x) = 75 + 0.25x[/tex]

The cost of printing x number of pages is c(x) = 75 + 0.25x

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The time it would take Mowgli from the home to the beach and from the beach to the home on foot is 48 minutes.

Based on the assumption that the average speed that Mowgli travels from the home to the beach and from the beach to the home is constant, the time it takes from the home to the beach and from the beach to the home should be equal.

Time from the home to the beach = 32 /2 = 16 minutes

The time it took Mowgli to walk from the home to the beach = 40 - 16 = 24 minutes

Time it would take Mowgli to travel from the home to the beach and from the beach to the home = 24 x 2 =48 minutes

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Answer:

Explanation:

To complete the table, we need to replace each value of x and calculate the value of y.

So, if x = - 16, y is equal to:

If x = -8, y is equal to:

If x = 0, y is equal to:

If x = 8, y is equal to:

If x = 16, y is equal to:

So, the complete table is:

x y

-16 -8

-8 -5

0 -2

8 1

16 4

Finally, we can graph the table, so:

A nail's length in x weeks of m=0.7 slope with a growth rate of mm per week b starting length follows.

The slope-intercept form of a straight-line equation is indicated by y = mx + b. X and y denote the line's distance from the x- and y-axes, respectively. When x = 0, the value of b equals y, and m indicates how steep the line is.

Given, r(0) = 12

According to the question, fingernail increases by 0.7 millimeters every week. So, m = 0.7 which is the slope of the equation of a straight line.

r(0) = 12 is the b of the y = mx + b.

Now, the final equation is:

r(x) = 0.7x + 12

As a result, the slope of r(x) length of a nail in x number of weeks of m=0.7, with growth rate in mm per week b starting length.

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Point C is between points A and B, this point divides the line AB into two segments:

One segment goes from point A to point C and can be named line segment AC

The second segment goes from point C to point B and can be named line segment CB

The correct option is the third one AC,CB

Step-by-step explanation:

answer is 8

detail is in the picture

The probability that a randomly selected person in the country enjoys cooking or shopping or both will be;

⇒ P (C ∪ S) = 0.76

What is mean by Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

48% of people in a certain country like to cook.

And, 54% of people in the country like to shop, while 26% enjoy both activities.

Now,

Probability to like the cook P (C) = 48%

Probability to like the shop P (S) = 54%

Probability to like the both activity P (C∩S) = 26%

So, Probability to like the both activity P (C ∪ S) is calculated as;

P (C ∪ S) = P (C) + P (S) - P (C ∩ S)

P (C ∪ S) = 48% + 54% - 26%

P (C ∪ S) = 102% - 26%

P (C ∪ S) = 76%

P (C ∪ S) = 0.76

Thus, The probability that a randomly selected person in the country enjoys cooking or shopping or both will be;

⇒ P (C ∪ S) = 0.76

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The type of reasoning used to find the next amount of train cars is an arithmetic sequence, it can be assumed that the next amount of train cars that in the sequence is 6.

The difference between successive words in an arithmetic series is known as the common difference y. The existence of the nth term of an arithmetic sequence is given by the following rule:

x1 = x1 + (n-1)y;

Where x1 is the first term.

In the context of this problem, from the image, the number of train cars can be modeled by the following sequence exists (0, 2, 4, ...).

Which exists an arithmetic sequence with:

Therefore the next term of the sequence is given by:

4 + 2 = 6.

This is because 4 is the last term and 2 is the common ratio.

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Answer:

1.50t + 3 < 9

Step-by-step explanation:

each taki is $1.50

each Gatorade is $3 and he only bought one so its $3.

total cost of taking and Gatorade is less than $9

Answer:

1.50t + 3 < 9

Step-by-step explanation

each taki is $1.50

each Gatorade is $3 and he only bought one so its $3.

the total cost of taking and Gatorade is less than $9

Answer: 8 inches

Step-by-step explanation:

1) Set up the equation

If you know both sides of the triangle are 6 inches you can set a Pythagorean equation. C is the hypotenuse

[tex]6^2+6^2=c^2\\36+36=c^2\\72=c^2\\\sqrt{72} = \sqrt{c^2} \\8.485 = c[/tex]

2) Rounding

After you found 8.485, the tenth place is less the 5, so it will round down to 8 inches.

The answer is 8 inches

EXPLANATION

Given the sequence:

C. 3, 12, 27, 48, 75

First, we need to calculate the difference between terms:

12-3 = 9 27-12 = 15 48-27 = 21 75 - 28 = 27

Arithmetic relationship: 9, 15 , 21, 27

To obtain the sequence we use the following formula:

Now, we need to calculate the appropriate difference between terms:

15-9 = 6 21-25 = 6 27 - 21 = 6

So the constant difference is 6 and the nth term will be:

nth = 6n + 3

*a1=3

So, the relationship will be:

n Value Relationship

1 12 3 + (6*1 +3)

2 27 12 + (6*2 + 3)

3 48 27 + (6*3 + 3)

4 75 48 + (6*4 + 3)

5 108 75 + (6*5 + 3)

n n-1 + (6n+3) n-1 + (6n+3)

Explicit function: y = (n-1) + (6n+3)

Answer:

Choice E and F

Step-by-step explanation:

acute = less than 90

Answer:

Explanation: We have to find the mean of the total scores shown, the formula for the mean is as follows:

Using the formula (1) the mean of the score is calculated as follows:

Therefore the answer is Option(D).