Find the slope of the line y= -3x+7

Answer:

Graph 2 which has both solid and dashed line

Step-by-step explanation:

Given the linear inequalities :

y>2/3x+3 - - - (1)

y ≤ -1/3x+2 - - - (2)

One quick observation that can be made from the two graphs is the type of line used to plot the two linear inequalities;

Inequalities that uses either the < or > sign are plotted using a dashed line while inequalities with makes use of ≤ or ≥ are plotted using the solid line. Therefore we can conclude that the graph which uses both the solid line and the dashed line to represent the linear inequality conditions is the correct choice.

Answer:

The vector equation

[tex]r = (2 + 3t)i+ (2.4 + 2t)j+ (3.5 - t)k[/tex]

The parametric equation

[tex]x = 2 + 3t\\y = 2.4 + 2t\\z = 3.5-t[/tex]

Step-by-step explanation:

Given

[tex]Point = (2,2.4,3.5)[/tex]

[tex]Vector = 3i + 2j - k[/tex]

Required

The vector equation

First, we calculate the position vector of the point.

This is represented as:

[tex]r_0 = 2i + 2.4j + 3.5k[/tex]

The vector equation is then calculated as:

[tex]r = r_o + t * Vector[/tex]

[tex]r = 2i + 2.4j + 3.5k + t * (3i + 2j - k)[/tex]

Open bracket

[tex]r = 2i + 2.4j + 3.5k + 3ti + 2tj - tk[/tex]

Collect like terms

[tex]r = 2i + 3ti+ 2.4j + 2tj+ 3.5k - tk[/tex]

Factorize

[tex]r = (2 + 3t)i+ (2.4 + 2t)j+ (3.5 - t)k[/tex]

The parametric equation is represented as:

[tex]x = x_0 + at\\y = y_0 + bt\\z = z_0 + ct[/tex]

Where

[tex]r = (x_0 + at)i +(y_0 + bt)j+(z_0 + ct)k[/tex]

By comparison:

[tex]x = 2 + 3t\\y = 2.4 + 2t\\z = 3.5-t[/tex]

Answer:

4.32 = k

Step-by-step explanation:

8/k = 5/2.7

We can solve using cross products

8* 2.7 = 5k

21.6 = 5k

Divide each side by 5

21.6/5 = k

4.32 = k

Answer: 5k = 21.6 and k = 4.32

there you go have a good day bye

Step-by-step explanation:

Answer:

5.5inches

Step-by-step explanation:

1331/8=166.375

then length of a side is = cubic root of 166.375

=³√166.375

5.5

Answer: i need the formula and i got you.

Step-by-step explanation:

Answer:

hey what's

Step-by-step explanation:

a question wow okay the answer is

Answer:

ΔEFG ~ ΔRPQ - Angle Angle Angle Theorem

ΔEFG ~ ΔRFQ - Side Side Side Proportional Theorem

Step-by-step explanation:

First set : using triangle sum theory to find missing angle. Letters should match congruent angles when creating statement.

Second set :

[tex]\frac{EG}{RQ}[/tex] = [tex]\frac{10}{12}[/tex] =  [tex]\frac{5}{6}[/tex]

[tex]\frac{EF}{RF}[/tex] =  [tex]\frac{15}{18}[/tex] =  [tex]\frac{5}{6}[/tex]

[tex]\frac{FG}{FQ}[/tex] =  [tex]\frac{20}{24}[/tex] =  [tex]\frac{5}{6}[/tex]

Answer:

Number of pineapples= 10

number of pears = 19

number of kiwis = 10 -2 = 8

Step-by-step explanation:

Cost of a pear = $ 0.50

Cost of a pineapple = $ 1.5

cost of a kiwi = $ 0.3

Let the pineapples = p

Number of pears = 9 + p

Number of kiwis = p - 2

The cost is

0.15 p + 0.5 (9 + p) + 0.3 (p - 2) = 13.50

0.15 p + 4.5 + 0.5p + 0.3 p - 0.6 = 13.50

0.95 p = 9.6

p = 10

Answer: There is 3 pineapples, 12 pears and 10 kiwis

Hope this help :)

Answer:

60 ft

Step-by-step explanation:

The answer has to be in feet units

Now that we know the height is 5 cm equivalent to 150 feet, what is the width of the building in feet units

5 cm = 150 ft

Rule: multiply cm by 30 to get the ft

2 cm = ?

2 cm × 30 = 60 ft

2 cm = 60 ft

Answer:

veoba

Step-by-step explanation:

Answer:

100-70=30 so

55*0.3=16.5

Hope This Helps!!!

Answer:

Answer :

70% less than 55 is

16.5

Answer:

Hello dude

[tex] - 1 \frac{21}{24} + 1 \frac{22}{24} = + \frac{1}{24} [/tex]

so it's positive

HAVE A NİCE DAY

Step-by-step explanation:

GREETİNGS FROM TURKEY ツ

Answer:

(0, -1)

Step-by-step explanation:

It's helpful if we think of slope in the context of rise over run.

Since the point (1, 1) lies on the line, because of the slope 2, if we subtract x by 1 to get to x = 0, then we'll be subtracting y by 2.

By that logic, the answer must be (0, -1).

Answer:

The first term is 6; the common difference in 0.8.

Step-by-step explanation:

The nth term is:

[tex] a_n = a_1 + (n - 1)d [/tex]

The sum of the first n terms is:

[tex] S_n = \dfrac{n(a_1 + a_n)}{2} [/tex]

[tex] a_{n} = a_1 + (n - 1)d [/tex]

[tex] a_{11} = a_1 + (11-1)d [/tex]

[tex] a_1 + 10d = 14 [/tex]        Equation 1

[tex] S_n = \dfrac{n(a_1 + a_n)}{2} [/tex]

[tex] S_{26} = \dfrac{26(a_1 + a_{26})}{2} [/tex]

[tex] \dfrac{26(a_1 + a_1 + 25d}{2} = 416 [/tex]

[tex] \dfrac{52a_1 + 650d)}{2} = 416 [/tex]

[tex] 26a_1 + 325d = 416 [/tex]        Equation 2

Equation 1 and Equation 2 form a system of equations in 2 unknowns.

To eliminate a_1, subtract 26 times Eq. 1 from Eq. 2.

[tex] 65d = 52 [/tex]

[tex] d = \dfrac{52}{65} [/tex]

[tex] d = \dfrac{4}{5} = 0.8 [/tex]

[tex] a_1 + 10d = 14 [/tex]

[tex] a_1 + 10 \times 0.8 = 14 [/tex]

[tex] a_1 + 8 = 14 [/tex]

[tex] a_1 = 6 [/tex]

Answer:

The first term is 6; the common difference in 0.8.

Answer:

D. None of the above

Step-by-step explanation:

Both triangles have the same shape but different size. Their area cannot be the same. Also, the ratio of their corresponding side lengths are the same.

Thus:

8/4 = 10/5 = 6/3 = 2

This implies that both triangles are similar.

Therefore, both triangles cannot have the same area, they are not of the same size and cannot be congruent to each other.

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Equivalent question: Find the slope of line going through points (1,-5) and (10,13).

Line points up vertically and subtract. Then put 2nd difference on top of first difference.

(1,-5)

(10,13)

---------'subtracting

-9, -18

So the slope of the line gong through point's (1,-5) and (10,13) is -18/-9=2.

The common difference of an arithmetic sequence whose first term is -5 and whose tenth term is 13 is 2.

Answer:

sorry i cannot help you

Answer:

Step 1

Because the number in front of the bracket is 1 and it is also affected by the negative sign(-),5 is supposed to be negative not positive because (negative by positive is negative)

And since the first step has an error in it,the remaining steps would also be wrong.

Answer:

mehoimehoihoi

Step-by-step explanation:

Answer:

1.a+4=11

a=7

2.6=g+8

g=2

3.

?

4.k+8=3

k=-5

5.j+0=9

j=9

6.12+y=15

y=3

7.h-4=0

h=4

8.m-7=1

m=8

9.w+5=4

w=-2

10.b-28=33

b=61

11.45+f=48

f=3

12.n+7.1=8.6

n=1.5

Hope This Helps!!!

Find the values of the sine, cosine, and tangent for ∠A

a. sin A = [tex]\frac{\sqrt{13} }{2}[/tex],  cos A = [tex]\frac{\sqrt{13} }{3}[/tex],  tan A = [tex]\frac{2 }{3}[/tex]

b. sin A = [tex]3\frac{\sqrt{13} }{13}[/tex],  cos A = [tex]2\frac{\sqrt{13} }{13}[/tex],  tan A = [tex]\frac{3}{2}[/tex]

c. sin A = [tex]\frac{\sqrt{13} }{3}[/tex],  cos A = [tex]\frac{\sqrt{13} }{2}[/tex],  tan A = [tex]\frac{3}{2}[/tex]

d. sin A = [tex]2\frac{\sqrt{13} }{13}[/tex],  cos A = [tex]3\frac{\sqrt{13} }{13}[/tex],  tan A = [tex]\frac{2 }{3}[/tex]

d. sin A = [tex]2\frac{\sqrt{13} }{13}[/tex],  cos A = [tex]3\frac{\sqrt{13} }{13}[/tex],  tan A = [tex]\frac{2 }{3}[/tex]

The triangle for the question has been attached to this response.

As shown in the triangle;

AC = 36ft

BC = 24ft

ACB = 90°

To calculate the values of the sine, cosine, and tangent of ∠A;

i. First calculate the value of the missing side AB.

Using Pythagoras' theorem;

⇒ (AB)² = (AC)² + (BC)²

Substitute the values of AC and BC

⇒ (AB)² = (36)² + (24)²

Solve for AB

⇒ (AB)² = 1296 + 576

⇒ (AB)² = 1872

⇒ AB = [tex]\sqrt{1872}[/tex]

⇒ AB = [tex]12\sqrt{13}[/tex] ft

From the values of the sides, it can be noted that the side AB is the hypotenuse of the triangle since that is the longest side with a value of [tex]12\sqrt{13}[/tex] ft (43.27ft).

ii. Calculate the sine of ∠A (i.e sin A)

The sine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the hypotenuse side of the triangle. i.e

sin Ф = [tex]\frac{opposite}{hypotenuse}[/tex]             -------------(i)

In this case,

Ф = A

opposite = 24ft (This is the opposite side to angle A)

hypotenuse = [tex]12\sqrt{13}[/tex] ft (This is the longest side of the triangle)

Substitute these values into equation (i) as follows;

sin A = [tex]\frac{24}{12\sqrt{13} }[/tex]

sin A = [tex]\frac{2}{\sqrt{13}}[/tex]

Rationalize the result by multiplying both the numerator and denominator by [tex]\sqrt{13}[/tex]

sin A = [tex]\frac{2}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }[/tex]

sin A = [tex]\frac{2\sqrt{13} }{13}[/tex]

iii. Calculate the cosine of ∠A (i.e cos A)

The cosine of an angle (Ф) in a triangle is given by the ratio of the adjacent side to that angle to the hypotenuse side of the triangle. i.e

cos Ф = [tex]\frac{adjacent}{hypotenuse}[/tex]             -------------(ii)

In this case,

Ф = A

adjacent = 36ft (This is the adjecent side to angle A)

hypotenuse = [tex]12\sqrt{13}[/tex] ft (This is the longest side of the triangle)

Substitute these values into equation (ii) as follows;

cos A = [tex]\frac{36}{12\sqrt{13} }[/tex]

cos A = [tex]\frac{3}{\sqrt{13}}[/tex]

Rationalize the result by multiplying both the numerator and denominator by [tex]\sqrt{13}[/tex]

cos A = [tex]\frac{3}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }[/tex]

cos A = [tex]\frac{3\sqrt{13} }{13}[/tex]

iii. Calculate the tangent of ∠A (i.e tan A)

The cosine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the adjacent side of the triangle. i.e

tan Ф = [tex]\frac{opposite}{adjacent}[/tex]             -------------(iii)

In this case,

Ф = A

opposite = 24 ft (This is the opposite side to angle A)

adjacent = 36 ft (This is the adjacent side to angle A)

Substitute these values into equation (iii) as follows;

tan A = [tex]\frac{24}{36}[/tex]

tan A = [tex]\frac{2}{3}[/tex]

Answer:

Step-by-step explanation:

multiplication of two rational numbers produce a rational number.

9514 1404 393

Answer:

  (a)  21

Step-by-step explanation:

The product of the lengths to the near and far circle intercepts are the same for the two lines. For the tangent, the near and far intercepts are the same point, so we have ...

  (36)(36) = (27)(27+x)

  48 = 27+x . . . . . . . . . . divide by 27

  x = 21 . . . . . . . . subtract 27

Answer:

[tex]\displaystyle y - \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{2} \bigg( x - \frac{\pi}{4} \bigg)[/tex]

General Formulas and Concepts:

Algebra I

Coordinates (x, y)

Functions

Function Notation

Point-Slope Form: y - y₁ = m(x - x₁)

Pre-Calculus

Calculus

Derivatives

Derivative Notation

Trig Derivative:                                                                                                          [tex]\displaystyle \frac{d}{dx}[sin(u)] = u'cos(u)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = sin(x)[/tex]

[tex]\displaystyle x = \frac{\pi}{4}[/tex]

Step 2: Differentiate

Step 3: Find Tangent Slope

Step 4: Find Tangent Equation

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

9x² - 4/3x + ¼

Step-by-step explanation:

(3x - ½)²

(3x - ½)(3x -½)

9x² - ⅔x - ⅔x + ¼

9x² - 4/3x + ¼

Answer:

The probability that Swallows will win the trophy is 0.8064

The probability that Rucks will win the trophy is 0.1936

Step-by-step explanation:

For each game, there are only two possible outcomes. Either the Swallows win, or they do not. The probability of them winning a game is independent of any other game, which means that the binomial probability distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Probability the Swallows wins is 0.56

This means that [tex]p = 0.56[/tex]

2 games:

This means that [tex]n = 2[/tex]

The probability that Swallows will win the trophy is

Probability they win at least one game, so:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{2,0}.(0.56)^{0}.(0.44)^{2} = 0.1936[/tex]

Then

[tex]P(X \geq 1) = 1 - 0.1936 = 0.8064[/tex]

0.8064 = 80.64% probability the Swallows win the trophy and 0.1936 probability that the Rucks win the trophy.

round 5.7255 to thousands place

place after thousands place (5) rounds up the 5 before it

therefore 5.726 ur ans

MARK above ANS as branliest

Answer:

option d is correct answer

Answer:

Step-by-step explanation:

D looks good

Step-by-step explanation:

[tex]3x + 7 = 12- 2x \\ 3x + 2x = 12 - 7 \\ 5x = 5 \\ x = \frac{5}{5} \\ x =1[/tex]