What is the common factor of the numerator and denominator in the expression [tex]\frac{(2x+3)(x-4)}{(x-4)(x+4)}[/tex]

Enter your answer as a binomial, like this: x + 7

Answer:

The residual value is -0.75

Step-by-step explanation:

we know that  

The residual value is the observed value minus the predicted value.

RESIDUAL VALUE=[OBSERVED VALUE-PREDICTED VALUE]

where

Predicted value.--> the predicted value given the current regression equation

Observed value. --> The observed value for the dependent variable.

in this problem

we have the point (1,4)

so

The observed value is 4

Find the predicted value  for x=1

[tex]y =1.5(1)+3.25=4.75[/tex]

predicted value is 4.75

so

RESIDUAL VALUE=(4-4.75)=-0.75

Answer:

-0.75

Step-by-step explanation:

Answer:

Answer:2.4

Step-by-step explanation:

The correct answer will be 2.4

Hope this helped

By writing the quotient in lowest terms, 3 and 1/8 divided by 1 and 2/3 equals 5 and 5/24.

To divide 3 and 1/8 by 1 and 2/3, we can follow these steps:

Step 1: Convert the mixed numbers to improper fractions.

3 and 1/8 = (3 * 8 + 1) / 8 = 25 / 8

1 and 2/3 = (1 * 3 + 2) / 3 = 5 / 3

Step 2: Invert the divisor (the second fraction) and multiply.

25/8 ÷ 3/5 = 25/8 * 5/3

Step 3: Simplify the fractions if possible.

The numerator of 25/8 and the denominator of 5/3 have a common factor of 5.

25/8 * 5/3 = (5 * 25) / (8 * 3) = 125/24

Step 4: Express the improper fraction as a mixed number (if necessary).

125/24 can be expressed as 5 and 5/24.

Therefore, 3 and 1/8 divided by 1 and 2/3 equals 5 and 5/24.

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The solution to [tex]\(3\dfrac{1}{8} \div 1\dfrac23\) is \(\frac{15}{8}\),[/tex] expressed as a fraction in its simplest form after converting the mixed numbers to improper fractions and performing division.

Let's solve [tex]\(3\dfrac{1}{8} \div 1\dfrac23\)[/tex]

convert the mixed numbers into improper fractions:

[tex]\(3\dfrac{1}{8} = \frac{3 \times 8 + 1}{8} = \frac{24 + 1}{8} = \frac{25}{8}\)[/tex]

[tex]\(1\dfrac23 = \frac{1 \times 3 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3}\)[/tex]

Now, we have:

[tex]\(\frac{25}{8} \div \frac{5}{3}\)[/tex]

To divide by a fraction, we multiply by its reciprocal:

[tex]\(\frac{25}{8} \times \frac{3}{5}\)[/tex]

Multiply the numerators and denominators:

Numerator:[tex]\(25 \times 3 = 75\)[/tex]

Denominator: [tex]\(8 \times 5 = 40\)[/tex]

Therefore, [tex]\(3\dfrac{1}{8} \div 1\dfrac23 = \frac{75}{40}\)[/tex]

Reduce the fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor, which is 5:

[tex]\(\frac{75}{40} = \frac{75 \div 5}{40 \div 5} = \frac{15}{8}\)[/tex]

Hence,[tex]\(3\dfrac{1}{8} \div 1\dfrac23 = \frac{15}{8}\).[/tex]

Answer:

6.95 feet

Step-by-step explanation:

The shape of the cot is rectangular. A diagonal of the rectangle divides the rectangle into two Congruent Right Angled triangles. The length and width of the rectangle become the legs of the right triangle and the diagonal is the hypotenuse of the right triangle.

In order to find the length of the hypotenuse which is the diagonal in this case we can use the Pythagoras Theorem. According to the theorem, square of hypotenuse is equal to the sum of square of its legs. So for the given case, the formula will be:

[tex]\textrm{(Diagonal)}^{2}=\textrm{(Length)}^{2}+\textrm{(Width)}^{2}\\\\ \textrm{(Diagonal)}^{2}=6^{2}+3.5^{2}\\\\ \textrm{(Diagonal)}^{2}=48.25\\\\ \textrm{(Diagonal)}=\sqrt{48.25}=6.95[/tex]

Thus, rounded of to nearest hundredth foot, the diagonal distance from corner to corner is 6.95 feet

Answer:

x=0.27

Step-by-step explanation:

We are given the equation;

[tex]1.2*10^{4x}-4.2=9.9[/tex]

The first step is to add 4.2 on both sides of the equation;

[tex]1.2*10^{4x}=14.1[/tex]

The next step will be to divide both sides of the equation by 1.2;

[tex]10^{4x}=11.75[/tex]

Next we take natural logs on both sides of the equation;

[tex](4x)ln10=ln11.75[/tex]

Finally, we divide both sides by 4*ln10 and simplify to determine x;

[tex]x=\frac{ln11.75}{4ln10}=0.27[/tex]

Final answer:

After solving the given system of equations, the value of y is determined to be 6.4, but this answer does not match any of the provided choices. There appears to be an error in the options given or the original equations.

Explanation:

To find the value of y in the solution to the system of equations, we first need to solve the system. We have two equations:

x + y = 1

2x – 3y = –30

From the first equation, we can express x in terms of y:

x = 1 - y

Next, we substitute this expression for x into the second equation:

2(1 - y) - 3y = -30

Expanding this equation:

2 - 2y - 3y = -30

Combining like terms:

-5y = -32

Divide both sides by -5 to find the value of y:

y = 32 / 5

Now, we can see that none of the options provided in the question (-8, -3, 3, 8) match the correct value we found, which is 6.4. It seems there might be an error in the options provided. However, if the question intended for y to be an integer, then we should re-examine the arithmetic or consider that there might be a typo in the original equations or options given.

Answer:

the answer is 5

Step-by-step explanation:

25/5=5 & 5*5=25

Answer:

The Answer Is 5 because every square number has to equal the number by multiplying by 2 to get your Answer 5 x 5 = 25 which 5 is multiplied 2 times 5 and 5 which gives you your answer 25.

Step-by-step explanation:

Plz Mark Brainliest

Answer:

  968π ≈ 3041 . . . cubic units

Step-by-step explanation:

The usual formula for the volume of a cylinder is ...

  V = πr²h

For your given dimensions, the volume is found by putting the values into the formula and doing the arithmetic.

  V = π(11²)(8) = 968π . . . . cubic units

 V ≈ 3041 cubic units

Answer:

continuously

Step-by-step explanation:

The more compounding you have, the greater the yield.  Obviously of the three, compounding continuously is the largest.  In math, we used the mathematical constant "e" to compute continuous compounding.

Answer:

197 million square miles

Step-by-step explanation:

Remark

What the equator is telling you is that the circumference around the earth is approximately 24902 miles. So before you can find the surface area, you need to find the radius of that circumference.

Equations

C = 2*pi*r

Area = 4pi*r^2

Solution

Radius

C = 24902

pi = 3.14

r = ?

24902 = 2 * pi * r

r = 24902 / (2 * pi)

r = 3965.29

==========

Surface Area

Area = 4 * pi * r^2

Area = 4 * 3.14 * 3965.29^2

Area = 4 * 3.14 * 15,723,498

Area = 197 000 000 square miles

Final answer:

The approximate surface area of the Earth, an oblate spheroid, is calculated using the mean radius derived from the average of the equatorial and polar radii, resulting in an estimated surface area of around 197 million square miles.

Explanation:

Calculating Earth's Surface Area

To approximate the surface area of the Earth, we will use the formula for the surface area of a sphere, which is 4πr². Since the Earth is not a perfect sphere but rather an oblate spheroid, we will use the mean radius. The equatorial radius is approximately 3963.296 miles, and the polar radius is 3949.790 miles. Thus, the mean radius would be the average of these two measurements.

First, we calculate the mean radius:

(3963.296 + 3949.790) / 2 = 3956.543 miles

Now, plug the mean radius into the formula for the surface area of a sphere:

Surface Area = 4π(3956.543)² ≈ 197,000,000 square miles

This calculation provides an approximation of the Earth's surface area, taking into account its oblate spheroid shape.

Answer:

 the answer is B (5 square root 2, 315°), (-5 square root 2, 135°)

Step-by-step explanation:

1) Let A be the point (x, y) = (5, - 5)  

=> x = 5 and y = - 5  

r = √(x² + y²) = √(25 + 25) = √50 = ± 5√2  

tan Θ = - 5/5 = - 1  

=> Θ = (i) 315º or - 45º ; (ii) 135º or - 225  

Hence, the Polar Coordinates of A are (i) (5√2, 315º) (ii) (- 5√2, 135º)

Two pairs of polar coordinates for the point is option b,

Here we assume that A be the point (x, y) = (5, - 5)  

So,

x = 5 and y = - 5  

Now

[tex]r = \sqrt(x^2 + y^2) = \sqrt(25 + 25) = \sqrt50 = \pm 5\sqrt2[/tex]

tan Θ = - 5/5 = - 1  

Now

(i) 315º or - 45º ; (ii) 135º or - 225  

So, the polar coordinates should be (5 square root 2, 315°), (-5 square root 2, 135°)

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Answer: option c.

Step-by-step explanation:

To solve the exercise you must apply the formula given in the problem, which is the following:

[tex]y=33,430e^{0.0397t}[/tex]

The problem asks for the projected population of Bakersfield in 2010.

Therefore, keeping on mind that  t is th number of years since 1950, you have that:

[tex]t=2010-1950\\t=60[/tex]

Substitute the value of t into the formula.

Therefore, you obtain:

 [tex]y=33,430e^{0.0397(60)}=361,931[/tex]

Answer:

Vertices at (-7, 5) and (-1, 5).

Foci at (-9, 5) and (1,5).

Step-by-step explanation:

(x + 4)²/9 - (y - 5)²/16 = 1

The standard form for the equation of a hyperbola with centre (h, k) is

(x - h²)/a² - (y - k)²/b² = 1

Your hyperbola opens left/right, because it is of the form x - y.

Comparing terms, we find that

h = -4, k = 5, a = 3, y = 4

In the general equation, the coordinates of the vertices are at (h ± a, k).

Thus, the vertices of your parabola are at (-7, 5) and (-1, 5).

The foci are at a distance c from the centre, with coordinates (h ± c, k), where c² = a² + b².

c² = 9 + 16 = 25, so c = 5.

The coordinates of the foci are (-9, 5) and (1, 5).

The Figure below shows the graph of the hyperbola with its vertices and foci.

I think a but I’m not quite sure

Answer:

It would be A. 40 square units (:

Step-by-step explanation:

Answer:

4.780 °

144''

Step-by-step explanation:

Given that,

door's level is 12 feet off the ground

the ramp can not have an incline surpassing a ratio of 1:12

An incline surpassing a ratio of 1:12 , means that every 1" of vertical rise requires at least 12" of ramp length

So,

1' rise = 12' length

12' = 12'x12

   = 144''

now we know the length and height of ramp so we can use trigonometry identities to find the angle

sinФ = height / length

sinФ = 12 / 144

sinФ =  sin^-1(12/144)

Ф       =  4.780 °

➷ Pythagoras' theorem is only suitable for right triangles, which this isn't.

The Sine rule would not be applicable as there isn't any side and paired angle given

The best option for this would be the Law of Cosines as it is suitable for when you are given two sides and an angle between the.

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:  Third option is correct.

Step-by-step explanation:

Since we have given that

ABC is triangle with its dimensions:

AB = 11

AC = 13

∠A = 108°

BC = a

We need to find the length of 'a'.

So, we can use "Law of cosines" as we have given two sides and one angle.

So, it becomes,

[tex]\cos A=\dfrac{b^2+c^2-a^2}{2bc}\\\\\cos 108^\circ=\dfrac{11^2+13^2-a^2}{2\times 13\times 11}\\\\-0.3=\dfrac{121+169-a^2}{286}\\\\-0.3\times 286=290-a^2\\\\-85.8=290-a^2\\\\-85.8-290=-a^2\\\\375.8=a^2\\\\a=\sqrt{375.8}\\\\a=19.38[/tex]

Hence, Third option is correct.

Answer:

[tex]A1=28.3\ m^{2}[/tex],[tex]A2=78.5\ m^{2}[/tex],[tex]A3=132.7\ m^{2}[/tex]

Step-by-step explanation:

we know that

The area of a circle is equal to

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

Part 1) Find the area of the circle with diameter 6 m

we have

[tex]r=6/2=3\ m[/tex] -----> the radius is half the diameter

substitute the values

[tex]A1=(3.14)(3)^{2}=28.3\ m^{2}[/tex]

Part 2) Find the area of the circle with diameter 10 m

we have

[tex]r=10/2=5\ m[/tex] -----> the radius is half the diameter

substitute the values

[tex]A2=(3.14)(5)^{2}=78.5\ m^{2}[/tex]

Part 3) Find the area of the circle with diameter 13 m

we have

[tex]r=13/2=6.5\ m[/tex] -----> the radius is half the diameter

substitute the values

[tex]A3=(3.14)(6.5)^{2}=132.7\ m^{2}[/tex]

The areas of the circles with diameters 6m, 10m, and 13m are approximately A₁=28.3 m², A₂ =78.5 m², and A₃=132.7 m², respectively.

To determine the area of each circle, we use the formula for the area of a circle: A = πr², where A is the area and r is the radius of the circle. First, we need to find the radii of the circles, which are half of their diameters.

Therefore, the areas of the circles are approximately 28.3 m², 78.5 m², and 132.7 m² respectively.

The question is about the mathematical modeling of a vineyard's grape production. As the number of vines increases, the individual yield of each vine decreases by 1%. An equation, such as P = 5000 - 50(n-500), is a possible mathematical model to represent this situation.

This question appears to require a detailed understanding of mathematical modeling and percentage decrease concept. The problem presented describes the decrease in grape production per vine as the number of vines planted per acre increases. It's an example of an inverse relationship, when one variable increases the other variable decreases.

The initial production quantity is 10 lb of grapes per vine when there are 500 vines per acre. However, for every additional vine planted, there is a subsequent 1% drop per vine. This means that if 501 vines are planted, each vine then produces only 99% of 10 lbs, or 9.9 lbs, and so on.

To model this mathematically, an equation could possibly be P = 5000 - 50(n-500), where P is the production of grapes in pounds, and n is the number of vines. This formula might help to calculate the maximum yield that could be obtained according to the number of vines.

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Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

• 1 + cot² x = csc²x and csc x = [tex]\frac{1}{sinx}[/tex]

• sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x

Consider the left side

sin²Θ( 1 + cot²Θ )

= sin²Θ × csc²Θ

= sin²Θ × 1 / sin²Θ = 1 = right side ⇔ verified

-----------------------------------------------------------------

Consider the left side

cos²Θ - sin²Θ

= cos²Θ - (1 - cos²Θ)

= cos²Θ - 1 + cos²Θ

= 2cos²Θ - 1 = right side ⇒ verified

Answer:

C

Step-by-step explanation:

f(x)=x-16 is just a straight line with a slope of one at a y intercept of -16. Therefore, x can hit all numbers in the x axis making the domain x is in the element of all real numbers.

Answer:

all real numbers

Step-by-step explanation:

literally the domain can be anything but the range is limited because of the vertical line check

Answer:

option B

x = 1 + 3√6  or x = 1 - 3√6

Step-by-step explanation:

Given in the question an equation,

3(x-1)² - 162 = 0

rearrange the x terms to the left and constant to the right

3(x-1)² = 162

(x-1)² = 162/3

(x-1)² = 54

Take square root on both sides

√(x-1)² = √54

x - 1 = ±3√6

x = ±3√6 + 1

So we have two values for x

x = 3√6 + 1    OR  x = -3√6 + 1

Answer:

b.x = 1+3√6, 1-3√6

Step-by-step explanation:

We have given a quadratic equation.

3(x-1)²-162  = 0

We have to find the solution of given equation by taking the square root of both sides.

Simplifying above equation, we have

3(x-1)² = 162

Dividing above equation by 3, we have

(x-1)² =  54

Taking square root to both sides of equation, we have

x-1 = ±√54

x = ±√54+1

x = ±√(9×6)+1

x = ±3√6+1

x = 1+3√6, 1-3√6  which is the solution of given equation.

Answer:

11.3cm = RC

Step-by-step explanation:

We can find the radius by using Pythagorean theorem and finding RC

a^2 + b^2 = c^2

RQ^2 + QC^2 = RC^2

We are given QC = 8

QC is the perpendicular bisector of PR so QR is 1/2 PR

QR = 1/2 (16) = 8

RQ^2 + QC^2 = RC^2

8^2 + 8^2 = RC^2

64+64 = RC^2

128 = RC^2

Take the square root of each side

sqrt(128) = sqrt(RC^2)

11.3137 = RC

Rounding to the nearest tenth

11.3cm = RC

1) look for parallel lines for example the bottom one is 6 and 3, from here you will know the size is 2x. So what you do is 10 = 2(2x -5)

10 = 4x-10

20 = 4x

x = 5

2) (i cant see, the image is not clear :()

[tex]\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 9^{\frac{2}{3}}\implies (3^2)^{\frac{2}{3}}\implies 3^{2\cdot \frac{2}{3}}\implies 3^{\frac{4}{3}}\implies \sqrt[3]{3^4}\implies \sqrt[3]{3^3\cdot 3^1}\implies 3\sqrt[3]{\stackrel{\textit{this one}}{3}}[/tex]

Answer:

\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 9^{\frac{2}{3}}\implies (3^2)^{\frac{2}{3}}\implies 3^{2\cdot \frac{2}{3}}\implies 3^{\frac{4}{3}}\implies \sqrt[3]{3^4}\implies \sqrt[3]{3^3\cdot 3^1}\implies 3\sqrt[3]{\stackrel{\textit{this one}}{3}}

Step-by-step explanation:

Answer:

 x² - 3x - 10 = 0

Step-by-step explanation:

Given there are 2 solutions then the equation is a quadratic.

Since the solutions are x = - 2 and x = 5 then

the factors are (x + 2) and (x - 5) and

f(x) = (x + 2)(x - 5) ← expand factors

     = x² - 3x - 10, hence the equation is

x² - 3x - 10 = 0

The equation that yields the solutions x = -2 and x = 5 is: x^2 + 0.00088x - 0.000484 = 0. We can solve this equation using the quadratic formula.

The equation that yields the solutions x = -2 and x = 5 is:

x^2 + 0.00088x - 0.000484 = 0

To solve this equation, we can use the quadratic formula:

x = (-b +/- sqrt(b^2 - 4ac))/(2a)

Plugging in the values from the equation, we get:

x = (-0.00088 +/- sqrt((0.00088)^2 - 4(1)(-0.000484)))/(2(1))

Simplifying further, we have:

x = (-0.00088 +/- sqrt(0.0000007744 + 0.001936))/0.002

Continuing to simplify, we get:

x = (-0.00088 +/- sqrt(0.0027104))/0.002

Finally, we have the two possible solutions:

x = (-0.00088 + sqrt(0.0027104))/0.002 and x = (-0.00088 - sqrt(0.0027104))/0.002

Answer:

Step-by-step explanation:

Volume = length * width * height.

Volume = 20 * 10 * 5

The tub can hold 1000 cubic feet of water.

The amount of water tub hold is 28316.8 liters.

Space is used by every three-dimensional object. The volume of this space is used as a measurement. The volume of an object in three-dimensional space is the amount of space it occupies within its boundaries. The capacity of the object is another name for it.

An object's volume can help us figure out how much water is needed to fill it, like how much water is needed to fill a bottle, aquarium, or water tank.

Given shape of bath tub is rectangular prism

which is  20 feet long, 10 feet wide, and 5 feet deep

length = 20 feet

width = 10 feet

height = 5 feet

to find the capacity of tub we need to calculate volume of tub

volume for rectangular prism = l x b x h

V = 20 x 10 x 5 = 1000 cubic feet

and 1 cubic feet = 28.3168 liter

1000 cubic feet = 28316.8 liter

Hence, the capacity of tub is 28316.8 liters.

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Answer:

The answer is (b)

Step-by-step explanation:

* Lets check how to find the inverse of the matrix,

 its dimensions is 2 × 2

* To know if the inverse of the matrix exist find the determinant

- If its not equal 0, then it exist

* How to find the determinant

- It is the difference between the multiplication of

 the diagonals of the matrix

Ex: If the matrix is [tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right][/tex]

     its determinant = ad - bc

- After that lets swap the positions of a and d, put negatives

 in front of b and c, and divide everything by the determinant

- The inverse will be [tex]\left[\begin{array}{ccc}\frac{d}{ad-bc} &\frac{-b}{ad-bc}\\\frac{-c}{ad-bc} &\frac{a}{ad-bc}\end{array}\right][/tex]

* Lets do that with our problem

∵ The determinant = (9 × 9) - (-2 × -10) = 81 - 20 = 61

- The determinant ≠ 0, then the inverse is exist

∴ The inverse is [tex]\frac{1}{61}\left[\begin{array}{ccc}9&2\\10&9\end{array}\right][/tex]=

   [tex]\left[\begin{array}{ccc}\frac{9}{61}&\frac{2}{61}\\\frac{10}{61} &\frac{9}{61}\end{array}\right][/tex]

* The answer is (b)

Answer:

d. $43.00

Step-by-step explanation:

Karli's total cost is ...

total cost = material cost + labor cost

= ($8.00/10 gal)·(5 gal) + ($13.00/h)·(3 h)

= $4.00 + $39.00

= $43.00

Answer:

Step-by-step explanation:

56 ft is the answer