Write an explicit formula for an, the nth term of the sequence
64, -16, 4,....

Answer:

(you got it right, not quite sure why it isn't there though!)

Step-by-step explanation:

remember PEMDAS

parentheses first

(8g+5) but we can't add them up since they not like terms

now we go from left to right (since we have Multiplication first and then Addition)

distribute the 4 to the (8g+5)

which makes it 32g +20

now we go back to the equation,

32g +20 + 6

are there any like terms we can combine?

yes, the 20 and the 6

20+6=26

leaving us with

Answer:

Hour elapsed 0 1 2 3 4

Grams 1986 1032.7 537 279.2 145.2

Explanation:

To find the amount left after 1 hour, 3 hours, and 4 hours, we need to find the common ratio.

Since we know the initial amount and the amount left after 2 hours, the ratio of these quantities is the square of the common ratio, so

r² = 537/1986

r² = 0.2704

r = √0.2704

r = 0.52

Then, the amount left after 1 hour is the initial amount multiplied by the common ratio, so

For 1 hour

Amount left = 1986(0.52) = 1032.7 grams

In the same way, the amount left after 3 and 4 hours is

For 3 hours

Amount left = 537(0.52) = 279.2 grams

For 4 hours

Amount left = 279.2(0.52) = 145.2 grams

Therefore, the complete table is

Hour elapsed 0 1 2 3 4

Grams 1986 1032.7 537 279.2 145.2

Answer:

The answer is option A.

The identified acute angles in the diagram are: D. Angle WZY and angle WXY.

An acute angle can be described as any angle that has a degree measure that is below 90 degrees, in order words, it is smaller than a right angle.

For example, an acute angle is attached below, which is 62°, and it is less than a right angle or 90 degrees. Angles 30°, 45°, 60°, 75°, etc are all regarded as acute angles because they are less than a right angle or 90 degrees.

In quadrilateral WXYZ, the acute angles that are less than a right angle, and are below 90 degrees are: D. Angle WZY and angle WXY.

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Answer: Length = 10√2

Step-by-step explanation: You have to use the pythagorean theorem

Answer:

Step-by-step explanation:

y = 1.416x − 0.76

For (7, 8):

residual value = Measured value - Predicted value

residual value = (actual y-coordinate of the point, y2) - (value of y from the equation, y1)

When x = 7:

value of y from the equation, y1 = 1.416*7 - 0.76

                                                  y1 = 9.912 - 0.76

actual y-coordinate of the point, y2 = 8

From:

residual value = (actual y-coordinate of the point, y2) - (value of y from the equation, y1)

residual value = y2 - y1

residual value = 8 - 9.152

Answer:

A: -1.152

Step-by-step explanation:

I did it and it was right!

Using proportions, it is found that:

42. x and y are not proportional.

43. The number 21 is 60% of 35.

44. The number 27 is 36% of the number 75.

Two variables, x and y, will represent a proportional relationship if the ratio between them is always the same.

From the table, the ratios are given as follows:

Different ratios, hence the variables x and y are not proportional.

To find the percentage of a number, the decimal equivalent of the percentage is multiplied by the number.

The decimal equivalent of a percentage of 60% is:

60/100 = 0.6.

Hence the percentage of 35 is calculated as follows:

0.6 x 35 = 21.

The percentage that the number 27 represents of the number 75 is given by the division of 27 by 75 multiplied by 100%, hence:

27/75 x 100% = 36%.

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First step is to write the equation in slope-intercept form

[tex]x - 5y = 5\\-5y = -x+5[/tex]      To make simplification easier, multiply negative to both sides

[tex]5y = x-5\\[/tex]  Now, you must divide 5 to both sides to isolate the variable

[tex]y = \frac{x}{5} - 1[/tex] To tell the slope more easily, turn [tex]\frac{x}{5}[/tex] into [tex]\frac{1}{5} x[/tex]

To rewrite the equation: [tex]y = \frac{1}{5} x - 1[/tex]

Now, you are able to see the slope(m) being [tex]\frac{1}{5}[/tex]

Next, you use the formula y=mx+b to solve for b (replace your newly found slope and points "x" and "y"

[tex]20 = (\frac{1}{5} *-15) + b\\20 = -3 + b\\b -3 = 20\\b = 23[/tex]

Final Answer:   [tex]y = \frac{1}{5} + 23[/tex]

Hope this helps :)

The simplified form of the expression [tex](3x^2+4x+2)-(7x^2+2x+5)[/tex] is [tex]-4x^2+2x-3[/tex].

In the given question,

The given expression is [tex](3x^2+4x+2)-(7x^2+2x+5)[/tex].

We have to solve the given expression.

To solve this question we use have to follow some rule.

Some Rules are

In this given question to solve the expression we firstly solve the bracket.

When we multiply the term under the bracket with minus sign then all sign under the bracket will also be changed

Now simplifying the expression.

[tex]=3x^2+4x+2-7x^2-2x-5[/tex]

Now we combine the similar term.

[tex]=(3x^2-7x^2)+(4x-2x)+(2-5)[/tex]

[tex]=-4x^2+2x-3[/tex]

Hence, the simplified form of the expression [tex](3x^2+4x+2)-(7x^2+2x+5)[/tex] is [tex]-4x^2+2x-3[/tex].

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The positive exponent for the given expression is [tex]\frac{1}{4^6}[/tex].

The given expression is [tex](4^{-2})^3[/tex].

A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ.

The given expression can be simplified as follows

[tex](4^{-2})^3[/tex] = [tex]4^{-2\times3}=4^{-6}[/tex]

So, the positive exponent = [tex]\frac{1}{4^6}[/tex]

Therefore, the positive exponent for the given expression is [tex]\frac{1}{4^6}[/tex].

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60 milligrams of medication A should be used this week

Given:

Last week, 130 milligrams of Medication A was mixed with 117 milligrams of Medication B

This week, 54 milligrams of medication B was used

To find:

the milligrams for medication A used this week

To determine the milligrams of medication A used, we will apply the ratio of medication A to B

Last week:

A : B = 130 : 117

This week:

A : B = A : 54

Hence, 60 milligrams of medication A should be used this week

[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] is the inverse function and it means the time in seconds it will take the ball to attain a certain height in feet.

Given:

[tex]f(x) = 1048 - 16x^{2}[/tex]

Since the function f(x) is the height (h), we can write the function as :

[tex]h = 1048 - 16x^{2}[/tex]

We will make x the subject:

[tex]16x^{2} = 1048 - h[/tex]

[tex]x^{2} = \frac{1048 - h}{16}[/tex]

[tex]x = \sqrt{\frac{1048 - h}{16} }[/tex]

[tex]x = \sqrt{65.5 - 0.0625h }[/tex]

Since:

[tex]x = f^{-1} (h) = \sqrt{65.5 - 0.0625h }[/tex]

Thus:

[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex]

Therefore, the inverse function is  [tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] and it is a function describing the amount of time (in seconds) it takes for the ball to reach a height of h feet.

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Answer:

c = 23

Step-by-step explanation:

To start, the interior of ∠L is needed to complete the equation. Since the total value of an interior and exterior angle is equal to 180°, we can confirm that 180° - 83° = 97°. Now, we can plug in the numbers.

(2c + 51)° = 97°

Next, you want to subtract 51 from both sides.

(2c + 51) - 51 = 97 - 51

2c = 46

Lastly, you isolate c by dividing 46 by 2.

c = 46 ÷ 2

c = 23

Answer:

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

i got it right on the exam!

Answer: 1 dollar per bottle

Step-by-step explanation:

       If they cost $20 and she bought 20 bottles, we can use division.

$20 / 20 bottles = 1 dollar per bottle

The location of the center of dilation in the figure and the image formed following the dilation is the point N

The scale factor of the dilation is 0.5

A dilation transformation resizes an object such that the lengths of the sides of the image (the object formed) following the dilation of the original image has sides that are a constant multiple of the side lengths of the original object.

The center of dilation is a reference and fixed point, such that the center of is in the same location relative to the preimage and the image.

The location or point shared by both the figure LMNO and the image of LMNO formed following the dilation, which is figure L'M'N'O' is the point N.

Therefore;

The scale factor of the dilation is found using the definition of a scale factor, which is the ratio of the scale of a new figure to the scale of an original figure, therefore:

[tex]The \ scale \ factor,\, s.f. = \mathrm{\dfrac{Length \ of \ the \ sides \ of \ L'M'N'O'}{Length \ of \ the \ sides \ of \ LMNO}}[/tex]

MN = 6 units

LO = 6 units

ML = ON = √(6² + 2²) = 2·√(10)

M'N' = L'O' = 3 units

M'L' = O'N' = √(3² + 1²) = √(10)

Which gives:

[tex]s.f. = \dfrac{M'L'}{ML} =\dfrac{\sqrt{10} }{2 \cdot \sqrt{10} } = \dfrac{1}{2}=0.5[/tex]

The scale factor of the dilation is, s.f. = 0.5

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Three decimal that sum of 114.056 is 52.2+34.15+28.5.

What is decimal?

decimal is a term that describes the base-10 number system, probably of the most commonly used the  number system. The decimal number system of  consists of ten single-digit numbers.

We will represent this as 1.5 pizzas in decimal form. In this case, the dot stands in for the decimal point, the number before the dot, in this case "1," represents one whole pizza, and the number after the decimal point, or the fractional part, represents the other half of the pizza. You may have seen decimal numbers similar to these while grocery shopping, on a scale, or even during a baseball game.

Sol- we have to add three decimal that have a sum of 114.056 no parts are given here.

Let's take

X+Y+Z = 114.056

We need to add any particular number here

Let's put 52+34+28

Still we need .056 extra

So we have to add points here

52.2+34.15+28.5

So these are 3 decimal point.

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Answer:

10 1/2 as an improper fraction is [tex]\frac{21}{2}[/tex]

the reciprocal of 10 1/2 is [tex]\frac{2}{21}[/tex]

so [tex]\frac{21}{2} * \frac{2}{21} = 1[/tex]

below is an image of the rest of the answers

Answer: It will take just 1 hour & 36 minutes with 4 large pumps & 4 small pumps

Step-by-step explanation:

Given that the numbered disks are placed in a box, you need to find the probability of selecting an odd number, given that a green disk is selected.

Therefore, you need to use the Conditional Probability Formula:

In this case, let be "A" the event of selecting an odd number, and "B" the event of selecting a green disk.

You can identify that:

- There are a total of 8 disks.

- There are 4 green disks that have odd numbers.

- There are a total of 7 green disks.

Therefore, you can determine that:

And:

Then, you can substitute values into the formula and evaluate:

Hence, the answer is:

Step 1

Given

Required: To arrange them from smallest to largest.

Note: 0.5 = 1/2

Step 2

Find the lowest common multiple of the numbers in the denominator : 3,8,2 and 5

Hence, the lowest common multiple will be

Step 3

Use the LCM to arrange the numbers as seen below

From the numbers gotten from using the LCM, we can now conclude

Step 4

Arrange them from smallest to largest

We can arrange them as follows

Answer:

59 degrees(triangle on the right)

Step-by-step explanation:

The total degrees of a triangle is 180 so add 76+45=121.

180-121=59

The probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is [tex]0.01667496[/tex].

What is probability?

Probability is defined as the possibility of an event to occur.

An automated weight monitor can detect underfilled cans of beverages with probability [tex]0.98[/tex]

Thus probability of success will be [tex]p=0.98[/tex]

So probability of failure [tex]q=1-p=1-0.98=0.02[/tex]

To find the first wrong detection happening on the tenth trial the first nine trials must be success followed by failure in the tenth trial.

Thus, required probability [tex]=p^9q^1=(0.98)^9(0.02)=0.01667496[/tex]

Hence the probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is [tex]0.01667496[/tex].

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The person must buy 10 gumballs so that she gets 4 gumballs that are the same color.

Given, gumball machine contains 9 red gumballs

7 white gumballs and

8 blue gumballs.

we are asked to determine the least number of gumball a person must buy to be sure that she gets 4 gumballs that are the same color.

If a person gets three gumballs of each of the three colors, that is, 9 gumballs, then the 10th gumball must be the fourth one for one of the colors. Therefore, the person must buy 10 gumballs.

Hence 10 gumballs should be purchased.

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The slope of the line is given as -2/3.

We are also given the point (1, 1) in which this line passes through.

Before we can plot the graph of the line, we need to know the equation of the line first.

The values given are more than enough to find the equation of the line.

The formula used to get the equation of the line is given below:

Now, with this formula, let us find the equation of the line.

Thus, the equation of the line is:

Now, using a graph calculator, let us plot this equation.

After doing this, the following is the result:

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given equation

STEP 2: Find the value of x

Cross multiply the equation

Divide both sides by 4

Hence, the value of x is -18

There is no slope, hence the equation of the line will be in the form y = b. Then the equation of the line that is perpendicular to the given line and passes through the point (1, 5) exists (A) y = 5.

The equation of a perpendicular line to a line in point-slope form is expressed as:

Determine the slope:

Since there is no slope, hence the equation of the line will be in the form y = b.

Therefore, there is no slope, hence the equation of the line will be in the form y = b. Then the equation of the line that is perpendicular to the given line and passes through the point (1, 5) exists (A) y = 5.

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Correct question:

2) Choose the correct answer.

A given line passes through points (2, 3) and (2, 3). Determine the equation of thethe line that is perpendicular to the given line and passes through the point (1,5).

(A) y = 5

(B) x = -1

(C) x=5

(D) y= -1/2x + 13/3

(E) y = -1

Answer:

realto, hindi ako sure eh

Step-by-step explanation:

tama yan