Write an equation of each line that passes through the following points in slope-intercept form:
P (4, 1) and Q (3, –5)

help me please

Answer:

see explanation

Step-by-step explanation:

The terms form a geometric sequence with n th term

[tex]a_{n}[/tex] = a [tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] = ......

r = [tex]\frac{-6}{3}[/tex] = [tex]\frac{12}{-6}[/tex] = - 2 and a = 3, hence

[tex]a_{n}[/tex] = 3 [tex](-2)^{n-1}[/tex] ← explicit formula

Answer:

The average rate of change ​is m = 3.4 models of paper shredders per year

Step-by-step explanation:

The rate of change m of a function is:

[tex]m = \frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

In this problem the function receives a variable x = year and returns a variable f(x) = models of paper shredders

We know that for [tex]x = 1998[/tex], [tex]f(x) = 2[/tex]

We also know that for [tex]x = 2008[/tex], [tex]f(x) = 36[/tex].

Then we can calculate the average rate of change using these values.

[tex]m = \frac{f(2008)-f(1998)}{2008-1998}[/tex]

[tex]m = \frac{36-2}{2008-1998}[/tex]

[tex]m = 3.4[/tex]

The average rate of change in the number of paper shredder models produced by the company from 1998 to 2008 is 3.4 models per year.

To calculate the average rate of change, we can use the formula (Change in Y) / (Change in X). In this case, 'Y' is the number of paper shredder models and 'X' is the time, in years. In 2008 the company manufactured 36 models which is an increase from the 2 models they made in 1998.

The change in 'Y' (ΔY) would therefore be (36 - 2) = 34. The change in 'X' (ΔX) would be (2008 - 1998) = 10 years. Therefore, the average rate of change would be ΔY / ΔX = 34 / 10 = 3.4.

This suggests that, on average, the company has been producing an additional 3.4 models of paper shredders each year over this 10 year period in response to rising concerns about identity theft.

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Answer:

Step-by-step explanation:

Hello

7>1+6X

6>6X

x<1

Best regards

The possibility of randomly choosing one of the tiles is 1/9

The stock is now worth $415.84 .

Answer: The difference for the annual 9% increase is 31.5 The answer is $413.

Step-by-step explanation:

Since Paul bought his stock two years ago, the total difference is $63. 350+63=$413.

Answer:
A)400^1/2

E)20

C)-20

F)-400^1/2

Final answer:

The square roots of 400 are represented by A) 400^1/2, C) -20, and E) 20. These correspond to the positive and negative values that, when squared, result in 400. Options B) 40, D) 10, and F) -400^1/2 do not square to 400 and are therefore incorrect.

Explanation:

To find the square roots of the number 400, we look for numbers that when multiplied by themselves will equal 400. The square root of a number can be both positive and negative since both will square to give the original number.

Option A (400^1/2) represents the principal square root of 400, which is found by raising 400 to the power of 0.5. This is equal to 20, so option A is correct.

Option B (40) is not a square root of 400 because 40 * 40 equals 1600, not 400.

Option C (-20) is the negative square root of 400 because (-20) * (-20) equals 400, so option C is correct.

Option D (10) is incorrect because 10 * 10 equals 100, not 400.

Option E (20) is the positive square root of 400, so this is correct.

Option F (-400^1/2) is the negative principal square root of -400. Since 400 is positive, this option is not applicable, so option F is incorrect.

Therefore, the correct square roots of 400 from the given options are A) 400^1/2, C) -20, and E) 20.

is -8 a choice because im pretty sure it’s -8

Answer:

The y-intercept would be -2

The solution to the given equation that results in positive integer values for x and y is x=3, y=1. Therefore, multiplying x and y together, xy = 3.

The given mathematical equation is (x·2)+x(2^2)+(y·2^3)+(y·2^4)=42. We can simplify this to 2x + 4x + 8y + 16y = 42, which simplifies further to 6x + 24y = 42. Dividing the whole equation by 6 to make the calculation simpler, we get x + 4y = 7. The solution to this equation that has positive integers for both x and y is x = 3, y = 1. Therefore, to find the value of xy, you simply multiply x and y together, and get xy = 3.

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The positive integer solutions for[tex]\(x\)[/tex] and [tex]\(y\)[/tex] in [tex]\(x + 4y = 7\)[/tex] are [tex]\(x = 3\)[/tex] and[tex]\(y = 1\)[/tex]. The value of [tex]\(xy\)[/tex]  is 3.

Let's simplify the given expression and solve for x and y.

[tex]\( (x \cdot 2) + x \cdot (2^2) + (y \cdot 2^3) + (y \cdot 2^4) = 42 \)[/tex]

Simplify each term:

[tex]\( 2x + 4x + 8y + 16y = 42 \)[/tex]

Combine like terms:

[tex]\( 6x + 24y = 42 \)[/tex]

Divide both sides by the greatest common factor, which is 6:

[tex]\( x + 4y = 7 \)[/tex]

Now, we need to find positive integer solutions for x and y that satisfy this equation.

One possible solution is x = 3 and y = 1, as:

[tex]\( 3 + 4 \cdot 1 = 7 \)[/tex]

Now, find the product [tex]\(xy\)[/tex] :

[tex]\( xy = 3 \cdot 1 = 3 \)[/tex]

So, the value of [tex]\(xy\)[/tex]  is 3.

Answer:

should be about 35 but i dunno for sure because i don’t know how tall maria is

Answer:

A picnic table is on sale for 40% off. The original price of the picnic table is

x =  $144.10

Step-by-step explanation:

If we have a 40% sale, that means

The price of the product will be its original price minus 0.4 multiplied by the original price

New price = (x) - 0.4*(x)

New price = 0.6*(x)

If the original price was $144.10

New price = 0.6*$144.10 = $86.46

Answer:

x=144.10

Step-by-step explanation:

Which scenario is modeled by the equation (x) (0.6) = 86 dollars and 46 cents?

Answer:

x=6

Step-by-step explanation:

first you subtract 9 from 27, getting 18.

then you divide 18 by 3, which gives you 6.

therefore, X=6

Answer:

6

Step-by-step explanation:

3x+9=27

         -9

3x=18

divide 18 by 3

x=6

Answer:

A. both a relation and a function

Step-by-step explanation:

The given set of ordered pairs is

{(1,2),(2,3),(3,1),(4,4),(5,2)}.

This ordered pairs represent a relation.

The x-coordinates represent the domain and the co-domain or range is the set of the y-coordinates.

The relation is many-to-one relation.

All many-to-one relations are functions.

The correct choice is A.

Answer:

what do you want me to do?

Step-by-step explanation:

M<1=25

M<2=55

M<3=65

M<4=25

M<5=35

M<6=65

M<7=55

M<8=35

Hey there!

2x + 10 = 20

x = 5 so 2 x 5 = 10 + 10 = 20

Therefore, x = 5

Hope this helps you!

God bless ❤️

Brainliest would be appreciated

xXxGolferGirlxXx

Answer:

A=78.23in²

Step-by-step explanation:

First we need to solve for the radius. The volume of a cylinder can be found using the formula:

[tex]V=\pi r^{2} h[/tex]

Now we have the variables:

V = 1177.5 in³

h = 15

r = ?

[tex]1177.5=\pi r^{2}15[/tex]

[tex]\dfrac{1177.5}{15}=\dfrac{\pi r^{2} }{15}[/tex]

[tex]78.5=\pi r^{2}[/tex]

[tex]\dfrac{78.5}{\pi }=\dfrac{\pi r^{2} }{\pi }[/tex]

[tex]r^{2}[/tex]≅24.99

[tex]\sqrt{r^{2} }[/tex]≅[tex]\sqrt{24.99}[/tex]

r≅4.99in

Now since we're looking for the area of the base, we can use the formula for the area of a circle which is:

[tex]A=\pi r^{2}[/tex]

[tex]A=\pi (4.99)^{2}[/tex]

A=78.23in²

Answer:

Rate = 10%

Step-by-step explanation:

We are given with the following details.

Interest earned = $ 116.25

Principal = $ 1550

Interest Rate = r (say)

Time = 9 months

         = [tex]\frac{9}{12} years[/tex]

We are asked to determine the rate of interest for which we can earn 116.25 interest. As we are not specifically given whether it is a compound or simple interest , we assume it to be simple interest and solve .

The formula for simple interest is given as

[tex]Interest = Principal \times Rate \times time [/tex]

[tex]116.25=1550 \times r \times \frac{9}{12}[/tex]

[tex] r= \frac{116.25 \times 12}{1550 \times 9}[/tex]

r=0.1

Hence the r = 0.1

Hence the rate of interest is 10%

Answer:

[tex]\large\boxed{(x^2+4x+8)(2x-1)=2x^3+7x^2+12x-8}[/tex]

Step-by-step explanation:

Use FOIL: (a + b)(c + d) = ac + ad + bc + bd

[tex](x^2+4x+8)(2x-1)\\\\=(x^2)(2x)+(x^2)(-1)+(4x)(2x)+(4x)(-1)+(8)(2x)+(8)(-1)\\\\=2x^3-x^2+8x^2-4x+16x-8\qquad\text{combine like terms}\\\\=2x^3+(-x^2+8x^2)+(-4x+16x)-8\\\\=2x^3+7x^2+12x-8[/tex]

Answer:

The correct answer

(x² + 4x + 8)(2x - 1) = 2x³ + 7x² + 12x - 8  

Step-by-step explanation:

It is given that, (x² + 4x + 8)(2x - 1)

Points to remember

xᵃ * xᵇ = xᵃ⁺ᵇ

To find the product

(x² + 4x + 8)(2x - 1) = [(x²*2x) + (4x *2x) (8*2x)] - [x² + 4x + 8]

 = 2x³ + 8x² + 16x - x² - 4x -8

 = 2x³ + 8x² - x² + 16x - 4x -8  

 = 2x³ + 7x² + 12x - 8  

Count the number of cubes in the first layer.

There is 16 cubes in the first layer.

Now divide the total number of cubes by the cubes per layer:

48 cubes / 16 cubes per layer = 3 layers.

Answer:

6 1/5

Step-by-step explanation:

Answer:

Mixed Number Form: 7 1/22

Decimal Form: 7.045 repeating

Exact Form: 155/22

Hope this Helps!

Answer:

[tex](x^{9}y^\frac{1}{3})[/tex]

or

[tex](x^{9}\sqrt[3]{y})[/tex]

Step-by-step explanation:

Given in the question an expression

[tex](x^{27}y )^\frac{1}{3}[/tex]

We will apply the power rule

The "power rule" tells us that to raise a power to a power, just multiply the exponents.

[tex](x^{27*\frac{1}{3} }y^\frac{1}{3})[/tex]

[tex](x^{9}y^\frac{1}{3})[/tex]

As we know that

[tex]x^{1/n} = \sqrt[n]{x}[/tex]

so we can write the above expression as

[tex](x^{9}\sqrt[3]{y})[/tex]

Answer:

3∛(xy)

Step-by-step explanation:

(x27y)^1/3

Simplified form will be 3/x³y³

Because;

27^(1/3) = 3

x^(1/3) = ∛x

y^(1/3) = ∛y

Which gives us 3∛(xy)

Answer: 117.226666667 cm^3

Step-by-step explanation:

So, we all know the formula for working out the volume of a cone is

V= 1/3πr^2h

V = 1÷3 x 3.14 × r^2 x h

The radius is half the diameter. Your diameter is 8 so the radius would be 4. And 7 is your height by the way.

So let's plot it all in!

V= 1÷3 x 3.14 × 4^2 x 7

V = 117.226666667cm^3

Round to the nearest 10 = 117.2cm^3

To the nearest 100 = 117.23cm^3

To the nearest whole number = 117cm^3

Answer:

Surface area = 87.92 Sq Inch and Total surface area =138.16 Sq Inches

Step-by-step explanation:

Here we are required to find the surface area of a cone, The formula of surface area of a cone is given as under

r=4

l = 7

[tex]S_{s}=\pi*r*l[/tex]

[tex]S_{s}=3.14*4*7[/tex]

[tex]S_{s}=87.92[/tex]

Also the total surface area is given as

[tex]T_{s}=\pi*r^{2} + \pi*r*l[/tex]

We are given

Now we put the values of r and  l in main formula

[tex]s=\pi*4^{2} + \pi*4*7\\s=3.14*16+3.14*28\\s=50.24+87.95\\s=138.16[/tex]

Hence the Surface area is 87.92 sq inches and Total surface area of the cone is 138.16

Answer:

The answer is 90 cm cube

Step-by-step explanation:

V=Bh

B=lw

B=7.5cm x 4cm

B= 30 cm

H= 3cm

30cm x 3cm = 90cm

V= 90cm cube

Hopes this helps!

To rewrite the expression ln(9) = y as an exponential function, we can use the inverse relationship between logarithmic and exponential functions.

To transform the logarithmic equation ln(9) = y into an exponential form, recall the fundamental logarithm property: ln(x) = y can be expressed as e^y = x when using base 'e'. Applying this principle to our equation, ln(9) = y becomes e^y = 9. This represents the exponential function equivalent of the original logarithmic equation, where y is the exponent that, when applied to the base 'e', yields the result of 9. This conversion helps us understand the relationship between logarithmic and exponential expressions.

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divide 33/11 and it would give you 3 because your finding the rate of 11 pounds of meat hope it helps

To calculate the rate per pound for $33.00 worth of meat at 11 pounds, divide the total cost by the total weight, giving a rate of $3.00 per pound.

The question is asking to calculate the rate per pound for $33.00 worth of meat when 11 pounds of meat are bought. To find the rate, we divide the total cost by the total weight in pounds. The rate is the cost of one pound of meat.

Here's the step-by-step calculation:

Therefore, the rate for $33.00 for 11 pounds of meat is $3.00 per pound.

Answer:

9,12,15 because Pythagorean theorem

Answer:0.00929368029

Step-by-step explanation:

Answer:

0.00557620817

Step-by-step explanation:

C is your way to go!!!!!!! ;D

Answer:

Option A.

Step-by-step explanation:

According to this survey results :

Students : 80 like viking and 20 like patriot.

Teachers : 5 like viking and 15 like patriot.

In Option B it is given that patriot is more popular in students while viking is more popular in teachers which is not correct.

In option c patriot is equally popular in students and teachers, which is also not correct. because patriot is popular in 20% of students but 80% in teachers, which is not correct.

In option d there is no difference between students and teachers, this statement is also not correct because there is lots of differences in their choices.

In Option A it is said that viking is more popular in students but patriot is more popular in teachers. this is correct.

Answer:

A) "Viking" is more popular with students, but "Patriot" is more popular with teachers ~apex

Step-by-step explanation:

Answer:

(-6,2)

Step-by-step explanation:

An ordered pair is a solution if when substituted it makes the equation true. If when you substitute, it does not make the equation true then it is not a solution.

-3x - 7y = 4

Substitute:

-3(-5) - 7(2) = 4

15 - 14 = 4

1 = 4 FALSE

-3(2) - 7(-5) = 4

-6 + 35 = 4

29 = 4 FALSE

-3(2) - 7(-6) = 4

-6 + 42 = 4

36 = 4 FALSE

-3(-6) - 7(2) = 4

18 - 14 = 4

4 = 4 TRUE