find the slope of the line passing through the points (-2,5) and (3/2,2)

Answers

Answer 1

Answer:

slope = - [tex]\frac{6}{7}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = ([tex]\frac{3}{2}[/tex], 2)

m = [tex]\frac{2-5}{\frac{3}{2}-(-2) }[/tex]

   = [tex]\frac{-3}{\frac{3}{2}+2 }[/tex]

   = [tex]\frac{-3}{\frac{7}{2} }[/tex]

  = - 3  × [tex]\frac{2}{7}[/tex]

  = - [tex]\frac{6}{7}[/tex]


Related Questions

a^2/9=b^2/16 and a^2+b^2=100

Answers

Answer:

a=6 and b=8

Step-by-step explanation:

a^2=(9/16)b^2. Substitute this in the second equation, you get b^2+b^2*(9/16)=100, b^2=100*16/25=8 and a=6

HELP: Find the length of an arc of a circle with a 10-cm radius associated with a central angle of 126 degrees. Give your answer in exact and approximate form to the nearest hundredth. (Show and explain your work)

THANK YOU!!

Answers

[tex]\it L_{arc}=\dfrac{2\pi R\cdot angle}{360^o}=\dfrac{2\pi\cdot10\cdot126^o}{360^o}=\dfrac{2520^o}{360^o}\cdot \pi=7\pi\approx7\cdot3,14 \Rightarrow\\ \\ \\ \Rightarrow\ L_{arc}\approx21,98\ cm\approx22\ cm[/tex]

Please help me anyone

Answers

Answer:

Quelles caractéristiques ces mots ont-ils en commun ? Cliquez sur tout ce qui s'applique.

[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]

Step-by-step explanation:

Can someone help me please!

Answers

Answer:

[tex] \sqrt{ - 147} = \sqrt{147} \times \sqrt{ - 1} = 7i \sqrt{3} [/tex]

I hope I helped you ^_^

The answer ; √ –108 = √108 × √–1 = 6i √3

helppppppppppppppppppp helppppppppppppp

Answers

•5×7^2

HOPE ITS HELPFUL ^_^

RHONA

Is 64 a rational number or irrational?

Answers

Answer:

Step-by-step explanation:

the answer is irrational hope this helps

Answer:

Rational.

Step-by-step explanation:

64 is a rational number because it's a whole number. Irrational numbers are real numbers including: [tex]\pi, \sqrt{2}[/tex], and etc. Basically, rational numbers are anything that can be expressed as the quotient of two integers: 64/1

Felicia wants to build a kite with the shape shown. If AC is 60 cm, how many centimeters are in the length of BD?

Answers

Answer:

Step-by-step explanation:

By applying tangent rule in the given right triangle AOB,

tan(30°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{BO}{OA}[/tex]

[tex]OA=BO(\sqrt{3})[/tex]

By applying tangent rule in the given right triangle BOC,

tan(60°) = [tex]\frac{OC}{BO}[/tex]

OC = BO(√3)

OA + OC = AC

[tex]BO(\sqrt{3})+BO(\sqrt{3}) =60[/tex]

2√3(BO) = 60

BO = 10√3

OC = BO(√3)

OC = (10√3)(√3)

OC = 30

By applying tangent rule in right triangle DOC,

tan(60°) = [tex]\frac{OD}{OC}[/tex]

OD = OC(√3)

OD = 30√3

Since, BD = BO + OD

BD = 10√3 + 30√3

BD = 40√3

      ≈ 69.3

I need help for this question!!​

Answers

Part (i)

We start with five dots to make the pattern in figure 1.

In figure 2, we add on 1 dot to each arm of the X shape. So that means we've added 4 dots total going from 5 to 5+4 = 9 dots.

In figure 3, there are 9+4 = 13 dots

So the pattern is simply "add 4" to get the next term. Again, this is because we add one dot per arm.

The first three terms of this arithmetic sequence are: 5, 9, 13

Your teacher wants to know what the general nth term is

We start with a = 5 and the common difference is d = 4

T(n) = nth term

T(n) = a + d(n-1)

T(n) = 5 + 4(n-1)

T(n) = 5 + 4n - 4

T(n) = 4n + 1

Let's try it out. Say we want to plug in n = 2

T(n) = 4n + 1

T(2) = 4(2) + 1

T(2) = 8 + 1

T(2) = 9

This works because the second figure indeed has 9 dots. I'll let you confirm the other figures.

Answer:  4n + 1

============================================================

Part (ii)

Your teacher wants to know how many dots occur when n = 50

T(n) = 4n + 1

T(50) = 4(50)+1

T(50) = 200 + 1

T(50) = 201

Verifying this through drawing dots is going to be a very tedious task, and I don't recommend it unless you really want to. Hopefully the verification process of T(2) = 9, and similar (for small values of n) is enough to convince you that this equation works as intended.

Answer: 201

I NEED HELP JANSJEHEHSHSBSBSBSH

Answers

Answer:

The answer is a translation

Step-by-step explanation:

In Math, translation is the displacement of a shape or object from one place to another.

Since the picture shows that the shape moved from one place to the next while remaining the same size, it is translation.

For all of the Following use the function LaTeX: P\left(x\right)\:=\:\left(x+3\right)^2+2 . My original vertex is

Answers

Answer:

A) Q(x) = (x + 3)² + 5, and the vertex is (-3, 5)

B) R(x) = (x - 3)² + 2, and the vertex is (3, 2)

C) S(x) = (x - 1)² - 5, and the vertex is (1, -5)

Step-by-step explanation:

The given function is P(x) = (x + 3)² + 2

The given function is a parabolic function in vertex form, f(x) = a·(x - h)² + k, and vertex, (h, k)

By comparison, the vertex of the function P(x) = (x + 3)² + 2 is (-3, 2)

A) A function f(x) translated α units UP gives

f(x) (translated α units UP) → f(x) + α

A translation of the function 3 units UP is given by adding 3 to the given function as follows;

Q(x) = P(x) + 3

∴ Q(x) = (x + 3)² + 2 + 3 = (x + 3)² + 5

Q(x) = (x + 3)² + 5, and the vertex by comparison to f(x) = a·(x - h)² + k, and vertex, (h, k) is (-3, 5)

B) A function f(x) translated b units RIGHT gives;

f(x) translated b units right → f(x - b)

∴ P(x) = (x + 3)² + 2 translated 6 units RIGHT gives;

P(x) = (x + 3)² + 2 (translated 6 units RIGHT) → R(x) = (x + 3 - 6)² + 2 = (x - 3)² + 2

R(x) = (x - 3)² + 2, and the vertex by comparison is (3, 2)

C) A function translated α units DOWN and b units RIGHT is given as follows;

[tex]f(x) \ translated \ by\ \dbinom{b}{a} \rightarrow f(x - b) - a[/tex]

Therefore, the given function, P(x) = (x + 3)² + 2, translated 7 units DOWN and 4 units RIGHT gives;

[tex]P(x) = (x + 3)^2 + 5 \ translated \ by\ \dbinom{4}{-7} \rightarrow P(x - 4) - 7 = S(x)[/tex]

S(x) = P(x - 4) - 7 = (x + 3 - 4)² + 2 - 7 = (x - 1)² - 5

[tex]P(x) = (x + 3)^2 + 5 \ translated \ by\ \dbinom{4}{-7} \rightarrow (x - 1)^2 - 5= S(x)[/tex]

S(x) = (x - 1)² - 5, and the vertex by comparison is (1, -5)

All points of the step function f(x) are graphed.

On a coordinate plane, a step graph has horizontal segments that are each 2 units long. The left end of each segment is an open circle. The right end of each segment is a closed circle. The left-most segment goes from (negative 4, 1) to (negative 2, 1). Each segment is 1 unit higher and 2 units farther to the right than the previous segment. The right-most segment goes from (2, 4) to (4, 4).
What is the domain of f(x)?

{x| –4 < x ≤ 4}
{x| –3 < x ≤ 4}
{x| 1 < x ≤ 4}
{x| 2 < x ≤ 4}

Answers

Answer:

A. {x| –4 < x ≤ 4}

Step-by-step explanation:

Answer:

{x| –4 < x ≤ 4}

Step-by-step explanation:

Edge Quiz 2023

What is the factored form of 3x+24y?

3(x+8y)
3xy(x+8y)
3(3x+24y)
3xy(3x+24y)
HELP!!

Answers

Answer:

A is the answer to your question

Step-by-step explanation:

To do this, just distribute the 3 to each of the coefficient and see if it would result in the same coefficients in the original expression.

Answer:

3(x + 8y)

Step-by-step explanation:

Multiply 3 by the numbers in parentheses and you will get 3x + 24y

hey help me please lol

Answers

Answer:

r = 5

Step-by-step explanation:

Side 1: 7

Side 2: 2 + r

To determine r, we subtract 2 from both sides to get the following:

Side 1: 5

Side 2: r

5 and r are the same, so 5 must equal 5.

Therefore, r = 5.

How do I solve part A

Answers

You have to put them into order, then multiple the two sides kf the triangle then put them together

Answer:

you have to put them in order

2^3*2^4=2^x

Solve for X PLZ HELP

Answers

Answer:

7

Step-by-step explanation:

if the bases of the exponents are the same then we can add the powers. so 2^3 * 2^4 = 2^7 = 128.

Answer:

7

Step-by-step explanation:

2^3⋅2^4= 2^7

2^7=2^x

since it had the same base you wouldn't need to worry about it you can just focus on the exponent.

7=x

swap it over

x=7

Need help asap algebra 2 math

Answers

life hack: if you own a TI-84 graphing calculator you can just input that into the calculator on the graphing part and then you see which equation’s graph matches the graph you were given in the problem.
Answer: Choice C

f(x) = 5x^2 + 25x + 30

============================================================

Explanation:

The roots, aka x intercepts, of this curve are x = -3 and x =  -2. This is where the graph crosses the x axis.

Since x = -3 is a root, this makes x+3 a factor of the quadratic. Similarly, x = -2 leads to x+2 as another factor. I'm using the zero product property.

So far we have found that the polynomial is (x+3)(x+2). This isn't the full factorization because if we plugged x = -1 into that expression, then we would get

y = (x+3)(x+2)

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

y = (2)(1)

y = 2

But we want y = 10 instead. So we must multiply that factorization by 5 to jump from 2 to 10 (i.e. 5*2 = 10)

Therefore, the full factorization of this parabola is y = 5(x+3)(x+2)

Now let's expand everything out and simplify

y = 5(x+3)(x+2)

y = 5(x^2+2x+3x+6)

y = 5(x^2+5x+6)

y = 5x^2+5*5x+5*6

y = 5x^2 + 25x + 30

Choice C is the final answer

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

To check this, we can plug in x = -3 and we should get 0

y = 5x^2 + 25x + 30

y = 5(-3)^2 + 25(-3) + 30

y = 5(9) + 25(-3) + 30

y = 45 - 75 + 30

y = -30 + 30

y = 0

This proves that x = -3 is a root of y = 5x^2 + 25x + 30

I'll let you check x = -2. You should also get y = 0 when plugging this x value in.

Plugging x = -1 should lead to y = 10 as the last bit of confirmation. I'll let you check this one as well.

The local pizza restaurant offers free delivery if you live within a 6-mile radius of the restaurant. The restaurant is located at the origin. Ada’s house is 4 miles west and 5 miles north of the restaurant at point (–4, 5). Does Ada’s house lie on or within the circle representing the area that gets free delivery?

No, the distance from the restaurant to Ada’s house is miles, which is greater than the 6-mile maximum radius.
Yes, the distance from the restaurant to Ada’s house is exactly 6 miles.
No, the distance from the restaurant to Ada’s house is 7 miles, which is greater than the 6-mile maximum radius.
Yes, the distance from the restaurant to Ada’s house is miles, which is less than the needed 6-mile radius.

Answers

Answer:

No adda doesnt get free delivery

Step-by-step explanation:

Answer: A) No, the distance from the restaurant to Ada’s house is Square Root of 41 miles, which is greater than the 6-mile maximum radius.

Step-by-step explanation:

work out the values of a and b in the identity 5(7x + 8) + 3(2x + b) = ax+ 13

will give brainiest!!!

Answers

Answer:

a=41  b=-9

Step-by-step explanation:

By expanding the brackets on the left hand side of the equation you get,35x + 40 + 6x + 3b and by simplifying you get 41x + 40 + 3b.by comparing the x and constant terms on either side you find that a = 41, and3b + 40 = 13, rearranging b = -9.

Answer from Gauth math

Answer:

Hello,

Step-by-step explanation:

We are going to use identification of terms.

[tex]5(7x+8)+3(2x+b)=ax+13\\\\35x+40+6x+3b=ax+13\\\\41x+40+3b=ax+13\\\\\\\Longrightarrow \left\{\begin{array}{ccc}a&=&41\\3b+40&=&13\\\end{array}\right.\\\\\\\Longrightarrow \left\{\begin{array}{ccc}a&=&41\\b&=&-9\\\end{array}\right.\\\\[/tex]

Produced by myself

A. A polynomial of the 5th degree with a leading coefficient of 3 and a constant of 2.

Answers

3x^5 + 2
The ^ sign means the number after it is an exponent.

if p(x) = x²+4x-3,then evaluate p(2)-p(-1)+p(1÷2)

Answers

Answer:

2

Step-by-step explanation:

Which of the following expressions are equivalent to -44+ 40?
Choose all answers that apply:
-4(11 - 10)
B
2(-22 +20)
None of the above

Answers

Answer:

answer for your question is B 2(-22+20)

Pre calc homework online

Answers

Answer:

Step-by-step explanation:

t = [tex]cos^{-1} (\frac{3}{5})[/tex]

t ≈ 53°

cos t = cos (- t) = [tex]\frac{3}{5}[/tex]  

sec ( [tex]\pi[/tex] + t ) = -  [tex]\frac{5}{3}[/tex]

Find the sum of all natural numbers between 25 and 210 which are either divisible by 3 or divisible by 4? Please let me know ​I will mark you Brainliest

Answers

Let S be the sum of the integers 25-210:

S = 25 + 26 + 27 + … + 208 + 209 + 210

Let S₃, S₄, and S₁₂ denote the sums of the integers in S that are multiples of 3, 4, or 12, respectively. We'll also count how many terms each sum involves; it'll be useful later.

S₃ = 27 + 30 + 33 + … + 204 + 207 + 210 … … … (62 terms)

S₃ = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

S₄ = 28 + 32 + 36 + … + 200 + 204 + 208 … … … (46 terms)

S₄ = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

S₁₂ = 36 + 48 + 60 + … + 180 + 192 + 204 … … … (15 terms)

S₁₂ = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

Let's look at S₃ :

S₃ = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

By reversing the order of the sum, we get

S₃* = 3 (70 + 69 + 68 + … + 11 + 10 + 9)

Of course S₃ = S₃*, I'm just calling it something else temporarily. Notice that every term in the same position of either sum adds up the same number.

9 + 70 = 79

10 + 69 = 79

11 + 68 = 79

and so on. Then

S₃ + S₃* = 3 (79 + 79 + 79 + … + 79 + 79 + 79)

or

2S₃ = 3 × 62 × 79   ==>   S₃ = 7,347

We can compute the other two sums in the same way.

S₄ = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

S₄* = 4 (52 + 51 + 50 + … + 9 + 8 + 7)

==>   2S₄ = 4 × 46 × 59  ==>   S₄ = 5,428

S₁₂ = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

S₁₂* = 12 (17 + 16 +15 + … + 5 + 4 + 3)

==>   2S₁₂ = 12 × 15 × 20   ==>   S₁₂ = 1,800

Then the sum you want is

S₃ + S₄ - S₁₂ = 10,975

We subtract S₁₂ because each of its terms is counted twice (once in S₃ and again in S₄).

someone measured the living room of their house and it is 12ft by 16 feet. what will the dimensions of the doll house living room be if every foot of the actual house is equal to 1/2 inch in the doll house?

Answers

Answer:

6ft by 8ft

Step-by-step explanation:

12 / 2 is 6 and 16 / 2 is 8

What are 3 expressions equivalent to 4x-2

Answers

Answer:

1 2x-4,x-42,2-4x I hope it will help you please follow me

Ken makes $400 a week before a 5% raise, and then another 6% raise. What is his weekly pay now? Can someone please help me with this

Answers

Answer:

$445.20

Step-by-step explanation:

First, find his pay after the 5% raise:

400(1.05)

= 420

Find his pay after the 6% raise:

420(1.06)

= 445.2

So, his weekly pay is now $445.20

I need help solving

Answers

The answer to ur question is 20. You just need to set it up into proportions

13. please help with this

Answers

Answer:

Looking at the question and goin step by step

we get to know that equation formed wud be ->

product of nine and a number - 9*x = 9x

added to 6 => 9x+6

gives us 24

so

9x + 6 = 24

now 9x = 18 and x = 18/9 = 2

and now keeping x value = 9 *(2)+6 we get 18+6 = 24

so lhs = rhs = 24

9x+6=24 option a

-8x - (3x + 6 ) = 4 - x

Answers

Answer:

-1

Step-by-step explanation:

Remember PEMDAS! Start with distributing the parentheses -(3x+6) so you get -8x-3x-6=4-x and simplify. Then you get -11x-6=4-x and combine like terms which equals -10=10x. Simplify and you get -1.

The solution to the equation -8x - (3x + 6) = 4 - x is x = -1.

What is the solution to the equation?

Given the equation in the question:

-8x - (3x + 6 ) = 4 - x

To solve the equation -8x - (3x + 6) = 4 - x, simplify the equation by isolating all terms with variable x:

-8x - (3x + 6 ) = 4 - x

Distribute the negative sign inside the parentheses:

-8x - 3x - 6 = 4 - x

Combine like terms on both sides of the equation:

-11x - 6 = 4 - x

Add 6 to both sides:

-11x - 6 + 6 = 4 + 6 - x

-11x = 4 + 6 - x

-11x = 10 - x

Next, add x to both sides:

-11x + x = 10 - x + x

-10x = 10

Divide both sides of the equation by -10:

x = -10/10

x = -1

Therefore, the value of x is -1.

Learn more about equations here: brainly.com/question/14686792

#SPJ6

1. David and Darlene Jasper have one child, Sam, who is 6 years old (birthdate July 1, 2013). The Jaspers reside at 4639 Honeysuckle Lane, Los Angeles, CA 90248. David's Social Security number is 577-11-3311, Darlene's is 477-98-4731, and Sam's is 589- 22-1142. David's birthdate is May 29, 1986 and Darlene's birthday is January 31, 1988. David and Darlene's earnings and withholdings for 2019 are: David: Earnings from Apple Company (office man

Answers

Answer:

hi

Step-by-step explanation:

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