find the slope of the line (-3,-2) (1,6)

Answer:

Answer:

Solution given:

f(x)=5x-3

let

y=f(x)

y=5x-3

interchanging role of x and y

x=5y-3

x+3=5y

y=[tex]\frac{x+3}{5}[/tex]

$o,

f-¹(x)=[tex]\frac{x+3}{5}[/tex]

we conclude that

f-¹(x)≠g(x)

Each pair of function are not inverses.

g(x)=x/5+3

let g(x)=y

y=x/5+3

interchanging role of x and y

x=y/5+3

x-3=y/5

doing crisscrossed multiplication

5(x-3)=y

y=5x-15

g-¹(x)=5x-15

So

g-¹(x)≠f-¹(x)

Each pair of function are not inverses.

Answer:

51°

Step-by-step explanation:

Reference angle (θ) = ?

Opposite side length = 31

Hypotenuse length = 40

Apply SOH, which is;

Sin θ = Opp/Hyp

Plug in the values

Sin θ = 31/40

θ = sin^{-1}(31/40)

θ = 51° (neatest whole degree)

Answer:

Step-by-step explanation:

a)

*Prob-less 89.44%

b)

*Prob-Between 86.40%

Z1=-1.88 Z2=1.25

c)

*Prob-less 10.56%

Answer:

77 cm²

Step-by-step explanation:

The figure can be decomposed into two rectangles.

✔️Area of rectangle 1:

Area of rectangle 1 = length * width

length = 3.5 cm

width = 8 cm

Area of rectangle 1 = 3.5*8 = 28 cm²

✔️Area of rectangle 2:

Area of rectangle 2 = length * width

length = 14 cm

width = 3.5 cm

Area of rectangle 2 = 14*3.5= 49 cm²

✔️Area of the figure = 28 + 49 = 77 cm²

Answer:

24

Step-by-step explanation:

hypontuse equal ONE of the side lengths times square root of 2 (a.k.a X)

so if you multiplies 12 square root 2 by square root 2, you get 12(2)

√2 times √2 equals 2

12 times 2 equals 24, which is your answer

Answer:

60

Step-by-step explanation:

Information needed: a whole circle is 360 degrees.

Explanation: you need a protractor to see how many degree's it is

Answer:

x = 14.4

Step-by-step explanation:

x is sin(angle 24/30)×24

how do we get the angle at 24/30 ?

by using the extended Pythagoras for baselines opposite other than 90 degrees.

c² = a² + b² - 2ab×cos(angle opposite of c)

in our example the angle 24/30 is opposite of the side 18.

so,

18² = 24² + 30² - 2×24×30×cos(angle 24/30)

324 = 576 + 900 - 1440×cos(angle 24/30)

324 = 1476 - 1440×cos(angle 24/30)

1440×cos(angle 24/30) = 1152

cos(angle 24/30) = 1152/1440 = 576/720 = 288/360 = 144/180 = 72/90 = 36/45 = 12/15 = 4/5

angle 24/30 = 36.9 degrees

x = sin(36.9) × 24 = 14.4

Answer:

FnH = {Meagan}

Step-by-step explanation:

Given the following sets and events:

S = {Albert, Betty, Abel, Jack, Patty, Meagan}

F = {Betty, Patty, Meagan},

H = {Abel, Meagan}

P = {Betty, Abel}.

In order to get FnH

The intersection of F and H is the element that is common to both sets. Hence for the set given, we can see that Meagan is common to both sets, therefore:

FnH = {Meagan}

Answer:

Following are the solution to the given points:

Step-by-step explanation:

Normal Distribution:

[tex]\mu=50\\\\\sigma= 6\\\\Z=\frac{X-\mu}{\sigma} \sim N(O,l)[/tex]

For point a:

[tex]P(X< 56)=\frac{(56-50)}{6}= \frac{6}{6}=1\\\\[/tex]

[tex]=P(Z<1)\ From\ \sigma \ Table=0.8413\\\\P(X>= 56)=(1-P(X< 56))=1-0.8413=0.1587\\\\[/tex]

For point b:

[tex]P(X< 49)=\frac{(49-50)}{6}=-\frac{1}{6} =-0.1667\\\\=P(Z<-0.1667)\ From\ \sigma \ Table\\\\=0.4338[/tex]

For point c:

To Find [tex]P(a\leq Z\leq b)= F(b) - F(a)\\\\[/tex]

[tex]P(X< 45)=\frac{(45-50)}{6}=\frac{-5}{6} =-0.8333\\\\P (Z<-0.8333) \ From \ \sigma \ Table\\\\=0.20233\\\\P(X< 55)=\frac{(55-50)}{6} =\frac{5}{6}=0.8333\\\\P ( Z< 0.8333) \ From \ \sigma\ Table\\\\=0.79767\\\\P(45 < X < 55) =0.79767-0.20233 =0.5953[/tex]

Answer:

The percent error in his calculation is 5.26%.

Step-by-step explanation:

Percent error:

Number of misses multiplied by 100 and divided by the correct value.

In this question:

Total of 72 + 4 = 76 people. 4 were missed, so:

[tex]E = \frac{4(100)}{76} = \frac{400}{76} = 5.26[/tex]

The percent error in his calculation is 5.26%.

Answer: 5.55 which is 5.6.

Step-by-step explanation:

You take the number of misses (4) and multiply it by 100= 400

then you divide that by the total people (72)

400/72= 5.55 or 5.6

the answer is on the photo

Answer:

A committee of one boy and one girl can be chosen in 252 different ways.

Step-by-step explanation:

Given that a class contains 18 girls and 14 boys, and for all parts of this question, each boy and girl are distinguishable from one another, to determine in how many ways can a committee of one boy and one girl be chosen, the following calculation has to be done:

18 x 14 = X

252 = X

Therefore, a committee of one boy and one girl can be chosen in 252 different ways.

Answer:

combination  91 ways

Step-by-step explanation:

This is a combination since order doesn't matter

Permutation are when order matter

14 choose 2 order doesnt matter

14*13

--------

2*1

91 different ways

Answer:

concave up:(-3, ∞)

concave down: (-∞, -3)

inflection point: (-3, 0)

Step-by-step explanation:

Concave up is when the slope increases, and concave down is when the slope decreases. Here, we can see that, as we move left to right, when x is less than -3, the slope starts out really high (y is increasing rapidly) but is decreasing. Then, as x reaches -3, the slope starts to rise, and the change in y gets higher and higher.

Given this information, we can say that the function is concave down from (-∞, -3) as it is going down from all values until x=-3 and is concave up from (-3, ∞) as it is going up from all values past x= -3 , with an inflection point of (-3, 0) as that is when the change in slope goes from down to up.

Answer:

277 cm

Step-by-step explanation:

[tex]A=l*w\\3,878=l*14\\l=\frac{3,878}{14} \\l=277[/tex]

Answer:

A

Step-by-step explanation:

A is the only graph with slope (1/4)

9514 1404 393

Answer:

Step-by-step explanation:

"Periods" will be filled with the number of years (1) times the number of periods per year (quarterly = 4). periods = 4

"Rate" is likely filled with the rate of interest divided by the number of periods per year. rate = 4%/4 = 1%

Then the total amount is found by ...

  total amount = principal × (1 + rate)^(periods)

  = 575 × (1.01^4) = 598.35

The total interest is the difference between this amount and the principal.

  total interest = total amount - principal

  = 598.35 -575 = 23.35

_____

We believe we have made reasonable assumptions regarding the intent of the columns in the table. Your best bet is to compare this problem to the worked examples in your curriculum materials.

9514 1404 393

Answer:

  0.65 ≤ x ≤ 2.35

Step-by-step explanation:

The ± symbol is pronounced "plus or minus." Then 1.5 ± 0.85 means ...

  1.5 + 0.85 = 2.35   or   1.5 - 0.85 = 0.65

These are said to be the end points of a closed* interval, so the interval is ...

  0.65 ≤ x ≤ 2.35

This is graphed as solid dots at 0.65 and 2.35 and the number line shaded between those dots.

_____

* "closed" means the endpoints are included in the interval. An interval is "open" if the endpoint is not included. The inequality for that is written using the < symbol instead of the ≤ symbol.

Answer:

Move triangle ABC over 2 and up 1

Step-by-step explanation:

A transformation in geometry is to essentially move a shape. To move ABC onto A1B1C1 you would move triangle ABC over 2 and up 1.

Answer:

A and B        because if you count they both have 16 and C has 25

Answer:

do your own work its not hard

Step-by-step explanation:

Step-by-step explanation:

the might help you for your answer

Answer:

5.89 mi/h

Step-by-step explanation:

This problem can be solved by using different methods. I will use vectors since it's the simplest way in which we can solve it. This can be solved by using related rates of change though.

First, we start by drawing a diagram with the velocity vectors.

A= velocity of the first person

B= velocity of the second person

C= velocity in which they are moving away from each other.

Since there is no acceleration in the problem, we can suppose we are talking about constant speeds, so the velocity at which they are moving away from each other will always remain constant. (It doesn't matter what time it is, the velocity will always be the same)

Having said this we can solve this problem by using the components, by using law of cosines or graphically. I will use law of cosines. The idea is to find the length of side c.

Law of cosines:

[tex]C^{2}=A^{2}+B^{2}-2ABcos \gamma[/tex]

so we can solve the formula for C so we get:

[tex]C=\sqrt{A^{2}+B^{2}-2ABcos \gamma}[/tex]

and now we can substitute the values we know:

[tex]C=\sqrt{(4)^{2}+(8)^{2}-2(4)(8)cos 45^{o}}[/tex]

[tex]C=\sqrt{16+64-32\sqrt{2}}[/tex]

[tex]C=\sqrt{80-32\sqrt{2}} mph[/tex]

if we want an exact answer, then that will be the exact answer, which approximates to:

C=5.89 mph

Answer:  [tex]-\infty < y < \infty[/tex] which is choice A

This is the set of all real numbers.

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

Explanation:

If you were to graph this function, then it spans infinitely upward and infinitely downward as well. That means that we can land on any y value we want, and that's why the range is the set of all real numbers.

Another approach we could take is to swap x and y to get [tex]x = \sqrt[3]{y+8}[/tex] which solves to [tex]y = x^3-8[/tex] . This is the inverse of the original function your teacher gave you. Recall that the domain and range swap roles when going from the original function to the inverse. What this means is that because the domain of

Domain of inverse = set of all reals

Range of original = set of all reals

Answer:

y = -0,1x + 1

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

Let x and y represent the cost of a hot dog and a hamburger, respectively. The the two purchases can be described by ...

  3x +2y -9.75 = 0

  2x +3y -10.25 = 0

We can list the coefficients of these general-form equations in 2 rows, listing the first one again at the end:

  3, 2, -9.75, 3

  2, 3, -10.25, 2

Now, we can form differences of cross-products in adjacent pairs of columns:

  d1 = (3)(3) -(2)(2) = 9 -4 = 5

  d2 = (2)(-10.25) -(3)(-9.75) = -20.50 +29.25 = 8.75

  d3 = (-9.75)(2) -(-10.25)(3) = -19.50 +30.75 = 11.25

Then the solutions are found from ...

  1/d1 = x/d2 = y/d3

  x = d2/d1 = 8.75/5 = 1.75

  y = d3/d1 = 11.25/5 = 2.25

The cost of one hot dog is $1.75; the cost of one hamburger is $2.25.

_____

Additional comment

This is my simplification of the "cross-multiplication method" of solving a pair of linear equations. That method can be found described on web sites and in videos. This version, and the versions described elsewhere, are variations on Cramer's Rule and on the Vedic Maths method of solving equations. Each of those do similar differences of cross products, perhaps in less-easily-remembered fashion.

For a given pair of columns with coefficients ...

  a b

  c d

The cross-product we form is ad -cb.

Answer:

C    

If x = o then f(0) = 4(2) * 0 = 0

If f(x) = 4(2) 0 - 13

then f(x) = -13 at x = 0

Answer:

it will indeed be c

Step-by-step explanation:

deesnuts