Find the slope of
(14, 8) and (7, -6)

Answer:

-7x^2 + 15x +7

Step-by-step explanation:

-7x^2 + 5x + 10 - (-10x + 3)

-7x^2 + 5x + 10 + 10x -3.......when u distribute it multiple by -1

-7x^2 + 15x +7 ...... simplify by collecting like term.

Answer:

8

Step-by-step explanation:

Answer:

Hi, there your answer is 4

Step-by-step explanation:

If the first term is \(a\), then the second term is \(ar\), the third is \(ar^2\), the fourth is \(ar^3\), and the fifth is \(ar^4\).

We're given

\(\begin{cases}ar=6\\ar^4=48\end{cases}\implies\dfrac{ar^4}{ar}=r^3=8\implies r=2\implies a=3\)

So the first five terms in the GP are

3, 6, 12, 24, 48

Adding up the first four gives a sum of 45.

If you were asked to find the sum of many, many more terms, having a formula for the n-th partial sum would convenient. Let \(S_n\) denote the sum of the first n terms in the GP:

\(S_n=3+3\cdot2+3\cdot2^2+\cdots+3\cdot2^{n-2}+3\cdot2^{n-1}\)

Multiply both sides by 2:

\(2S_n=3\cdot2+3\cdot2^2+3\cdot2^3+\cdots+3\cdot2^{n-1}+3\cdot2^n\)

Subtract this from \(S_n\), which eliminates all the middle terms:

\(S_n-2S_n=3-3\cdot2^n\implies -S_n=3(1-2^n)\implies S_n=3(2^n-1)\)

Then the sum of the first four terms is again \(S_4=3(2^4-1)=45\).

The graph of the first five terms can be seen in the image at the end.

We know that we have an arithmetic sequence:

3, -10, -23, -36

The common difference is what we get when we subtract two consecutive terms, we will get:

d = -36 - (-23) = -3

Then the recursive relation is:

a(n) = a(n - 1) - 13

At the moment we know:

a(1) = 3

a(2) = -10

a(3) = -23

a(4) = -36

Then fifth term will be:

a(5) = a(4) - 13 = -36 - 13 = -49

Now to graph it, we use the "n-th" value as the input, then we need to graph the five points (1, 3), (2, -10), (3, -23), (4, -36), (5, -49).

The graph can be seen in the image below:

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Use the property of determinant det(AB) = det(A)det(B) and the fact that A and A' have the same transpose to show that det(AAT) = (det(A))^2, and then use the fact that AAT is similar to A'A to conclude that they have the same characteristic polynomial. Option C is the correct answer.

Start with det(AAT). Use the formula det(AB) = (det A)(det B) to write det(AAT) = (det A)(det A). Then use the formula AAT = EI.

We can show that A and A' have the same characteristic polynomial by showing that they have the same eigenvalues.

Let λ be an eigenvalue of A with corresponding eigenvector x. Then we have:

Ax = λx

Multiplying both sides by A' on the left, we get:

A'Ax = A'λx

Using the fact that A'A = AA' = I, we can simplify this expression to:

x = λA'x

This shows that λ is also an eigenvalue of A' with corresponding eigenvector A'x. Therefore, A and A' have the same set of eigenvalues, which means that they have the same characteristic polynomial.

To prove this using determinants, we start with det(AAT). Using the property det(AB) = (det A)(det B), we can write:

det(AAT) = det(A)det(AT)

Since det(AT) = det(A) (which can be shown using the fact that det(AT) = det(A) and the property det(AB) = det(A)det(B)), we can simplify this expression to:

det(AAT) = (det A)^2

Using the fact that AAT = EI, we can write:

det(AAT) = det(EI)

Since det(EI) = 1, we have:

(det A)^2 = 1

Taking the square root of both sides, we get:

det A = ±1

This means that A and A' have the same set of eigenvalues, which implies that they have the same characteristic polynomial.

So, the correct option is C.

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Answer:

None of the answers provided are equivalent

Step-by-step explanation:

To solve it would be best to simplify each of the expressions you have listed by combining like terms all the x^2 terms have been bolded, the x terms italicized, and the constant terms are underlined

(4x + 1.2) + (2x ^ 2 - 6x + 5) = 2x ^ 2 - 6x + 6.2

(x ^ 2 - 5x + 13) + (x ^ 2 + 3x - 6) = 2x^2 -2x +7

(4x ^ 2 - 6x + 11) + (2x ^ 2 - 4x + 4) = 6x^2 -10x +15

(5x ^ 2 - 8x + 120) + (- 3x ^ 2 + 10x - 13) = 2x^2 + 2x + 107

Solution:

Note that:

Simplify the equation to find x.

The value of x is 6.

Our approximation for sqrt(49.2) is approximately 7.01428571.

To use linear approximation to approximate √(49.2), we first need to find the equation of the tangent line to f(x) = √(x) at x = 49.

1. Find the derivative of f(x): f'(x) = d(√(x))/dx = 1/(2*√(x))
2. Evaluate f'(x) at x = 49: f'(49) = 1/(2*√(49)) = 1/14
So, the slope (m) of the tangent line is 1/14.

3. Evaluate f(x) at x = 49: f(49) = √(49) = 7
4. Use the point-slope form of a linear equation to find b: y - 7 = (1/14)(x - 49)
5. Solve for b: b = 7 - (1/14)(49) = 0

Now, we have the equation of the tangent line: y = (1/14)x

Finally, use the tangent line equation to approximate sqrt(49.2):
y ≈ (1/14)(49.2) = 3.51428571

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When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .

According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.

The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.

Therefore,

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

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Answer:

r = -15

Step-by-step explanation:

2r + 8 - r = -7

~Combine like terms

r + 8 = -7

~Subtract 8 to both sides

r = -15

Best of Luck!

Answer:

hii

Step-by-step explanation:

Group Like Terms

2r-r+8=-7

Add smiliar elements

r+8=-7

Subtract 8 form both sides

r+8-8=-7-8

SImplify

r=-15

Answer:

70° and 110° .

Step-by-step explanation:

Answer:

B) b2

Explanation:

b · b = b²

b + b = 2b

2 × b = 2b

2 × b × b = 2b × b = 2b²

Answer:

A) 2b ( b×b = twice b )

hope this help

Answer:

231

Step-by-step explanation:

\(3+jk+k^{3} \\\\j=2\\\\k=6\\\\3+jk+k^3\\\\=3+(2)(6)+(6)^3\\\\=3+12+216\\\\=231\)

The value of expression for the given j and k value is 231.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is 3+jk+k³. When j=2 and k=6.

Substitute j=2 and k=6 in the expression 3+jk+k³, we get

3+2×6+6³

= 15+216

= 231

Therefore, the value of expression for the given j and k value is 231.

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Answer:

the answer is b

Step-by-step explanation:

ive did it before

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

A number's  root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as  or as 3 x 3.

Here,

If an equation have 2 roots , it means it is a quadratic function

If D=0, a quadratic function has two roots that are equal.

D (discriminant) = 0

=>b24ac=0 is required for a polynomial function to have equal roots.

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

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Answer:It will take 5 sec for a parachute to open.I did it on a piece of paper for u to show u more information

Step-by-step explanation:

Solving quadratic equation 16 t² -60t -100=0 formed by Projectile Motion Formula and given conditions it is found that it takes t = 5 seconds to fall from 1000 feet to 900 feet before the parachute opens.

Quadratic equation is an equation which contains one unknown variable and the highest power of this unknown variable is 2. Let x be the unknown variable then the standard quadratic equation in x is given by

ax²+bx+c =0, where a, b, c are constants and a≠0

We can solve this equation by factorizing ax²+bx+c and  putting those factors equal to zero to solve for x.

Projectile Motion Formula h = -16 t² + v t + s,

where t = time in seconds

h = height of the projectile

v = initial velocity

s= starting height of fall

Given s = 1000 feet, v= 60 feet per second, h = 900 ft

And t we have to find.

Projectile motion equation becomes:

900 = -16 t² + 60 t + 1000

⇒16 t² -60t + 900-1000=0

⇒16 t² -60t -100=0, which is a quadratic equation in variable t

Factorizing this quadratic equation

⇒ 16t² - 80t + 20t -100 =0

⇒16t(t -5) + 20( t - 5 ) =0

⇒ (16t +20) ( t-5)=0

Putting these factors equal to zero

16t +20 =0 ⇒ t = -20/16, which is neglected as time cannot be negative.

t-5 = 0⇒ t =5

Therefore it takes 5 seconds to fall from 1000 feet to 900 feet before the parachute opens.

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Answer:

<ABC= 86 degrees

Step-by-step explanation:

Answer:

(x+4)(3x-2)(x+1)

Step-by-step explanation:

Answer:

x=−414

Step-by-step explanation:

Let's solve your equation step-by-step.

x

−18

=23

Step 1: Multiply both sides by -18.

x

−18

=23

(

x

−18

)*(−18)=(23)*(−18)

x=−414

Answer:

\( {y}^{2} - 14y + 45 \\ \\ {y}^{2} - 9 y + 5y - 45 \\ \\ y(y - 9) - 5(y - 9) \\ \\ (y - 5)(y - 9)\)

Here's the solution :

\( {y}^{2} - 4y+ 45\)

\( {y}^{2} - 9y - 5y + 45\)

\(y(y - 9) - 5(y - 9)\)

\((y - 5)(y - 9)\)

therefore, the roots are 5 and 9

An analogous equation can be created by factoring a quadratic equation. 5x^2 = (x-2) * (x+2) + 488 can give integers 9, 11,13.

In algebra, quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as

\({ax^{2}+bx+c=0}\)

where a 0 and x denotes an unknown and a, b, and c denote known numbers, Since there is no ax2 term, the equation is linear (and not quadratic) if a = 0 (and b 0). The coefficients of the equation, denoted by the numbers a, b, and c, are the quadratic coefficient, linear coefficient, and constant or free term, respectively.

The roots or zeros of the expression on the left-hand side of the equation are the values of x that fulfill the equation. There can only be two solutions to a quadratic problem. One claims that a problem is a double root if there is just one solution. There are either two real solutions, one real double root, two complex solutions that are complex conjugates of one another, or two real solutions if all the coefficients are real values. If complex roots are included, a quadratic equation will always have two roots; a double root counts as two. An analogous equation can be created by factoring a quadratic equation.

According to the formula, if 5x2 = x2 - 4 + 488, then 5x2 = x2 + 484.

For 4x2 = 484, subtract x2 from each side, resulting in x2 = 121.

For x = 11, square root each side.

TEST: 5*121 = 9*13 + 488, so 605 is equal to 117 plus 488.

The middle odd number, x, is equal to 11.

The figures are 9, 11, and 13.

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Answer:

The answer is A

Answer:

C

Step-by-step explanation:

Answer:

4 + x

Step-by-step explanation:

10 boxes will be required by the printing company

Company can fit 7000 calendars in 1 box

7000 calendars = 1 box

1 calendar = 1/7000

70000 calendar = 1/7000 * 70000

= 10 boxes

10 boxes will be required by the printing company

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Answer:

Hey bud the answer is: Reflect over the y-axis, reflect over the x‒axis, rotate 180°

Got the same question on the test. Sorry about the inconvienience of the other person.

Step-by-step explanation:

Reflect over the y-axis, reflect over the x-axis, and rotate 180° will be the same. Then the correct option is B.

It is the image of the point which is located in the opposite direction of a given point.

The trapezoidal ABCD is shown.

The trapezoidal ABCD rotated 180 degrees about the origin then it is reflected about the x-axis and y-axis. Then the image will remain the same.

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Answer:

4x - 43

Step-by-step explanation:

7x - 28 - 3x - 15

7x - 3x - 28 - 15

4x - 43

The simplified expression is 4x - 43.

The correct option is A.

A term is a single mathematical phrase. It might consist of only one variable—a letter—one number—positive or negative—or several variables multiplied but never added or subtracted. A number is placed in front of some nouns that have variables. Coefficients are numbers that come before phrases.

As per the information provided, it is given that,

7(x - 4) - 3(x + 5)

Expanding the brackets and simplifying, we get:

7(x - 4) - 3(x + 5)  = 7x - 28 - 3x - 15

7(x - 4) - 3(x + 5)  = 4x - 43

Therefore, the expression is 4x - 43.

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Answer:

The function is a direct variation function with a constant of variation of 1.5.

Step-by-step explanation:

I just took the test :/

Answer:

The function is a direct variation function with a constant of variation of 1.5.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

You can use the Pythagorean theorem to find the length of the unknown side.

For that, let the unknown side be x.

Let us solve now.

2² + x² = ( 2√5)²

4 + x²  = 2√5 × 2√5

4 + x² = 2 × 2 × √5 × √5

4 + x² = 4 × 5

4 + x² = 20

x² = 20 - 4

x² = 16

x = √16

x = 4

Hope this helps you :-)

Let me know if you have any other questions :-)