use wxy to find the measure of

Answer:

The solutions for x are [tex]x = 4[/tex] and [tex]x = -1.5[/tex].

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

2x² - 5x - 12 = 0

This means that [tex]a = 2, b = -5, c = -12[/tex]

Solution:

[tex]\Delta = (-5)^2 - 4(2)(-12) = 121[/tex]

[tex]x_{1} = \frac{-(-5) + \sqrt{121}}{2*2} = 4[/tex]

[tex]x_{2} = \frac{-(-5) - \sqrt{121}}{2*2} = -1.5[/tex]

The solutions for x are [tex]x = 4[/tex] and [tex]x = -1.5[/tex].

Answer:

a and b are positive

Step-by-step explanation:

We are given that

[tex]a-3>b-3[/tex]

[tex]b>4[/tex]

We have to find that a and b are positive or negative.

We have

[tex]b>4[/tex]

It means b is positive and greater than 4.

[tex]a-3>b-3[/tex]

Adding 3 on both sides

[tex]a-3+3>b-3+3[/tex]

[tex]a>b>4[/tex]

[tex]\implies a>4[/tex]

Hence, a is positive and greater than 4.

Therefore, a and b are positive

Answer:  x = 14

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

Explanation:

For any triangle, the three inside or interior angles always add to 180

M+N+P = 180

32+64+6x = 180

6x+96 = 180

6x = 180-96

6x = 84

x = 84/6

x = 14

Answer:

4s-9t-7

Step-by-step explanation:

multiply the negative one with all terms inside the bracket, since they are all unlike terms the answer remains the same

Answer:

2 1/6

Step-by-step explanation:

6.5x=2x+1.6=1/3

1/3*6.5=2 1/6

Answer:

-( cube root of 2x)-6(cube root of x)

Answer:

D.

Step-by-step explanation:

cos is positive and sin is negative

=>

it must be in quadrant IV.

you remember, 1 = sin² + cos²

1 = sin² + (3/5)² = sin² + 9/25

25/25 = sin² + 9/25

16/25 = sin²

sin = 4/5 or -4/5

and as sin of this angle is < 0, our solution is -4/5

Answer:

y = 2x + 12

Step-by-step explanation:

the formula for a line is typically

y = ax + b

a is the slope of the line (expressed as y/x ratio describing how many units y changes, when x changes a certain amount of units).

b is the offset of the line in y direction (for x=0).

we have the points (3, -4) and (-7, 1).

to get the slope of the line let's wander from left to right (x direction).

to go from -7 to 3 x changes by 10 units.

at the same time y changes from 1 to -4, so it decreases by 5 units.

so, the slope is -5/10 = -1/2

and the line equation looks like

y = -1/2 x + b

to get b we simply use a point like (3, -4)

-4 = -1/2 × 3 + b

-4 = -3/2 + b

-5/2 = b

so, the full line equation is

y = -1/2 x - 5/2

now, for a perpendicular line the slope exchanges x and y and flips the sign.

in our case this means +2/1 or simply 2.

so, the line equation for the perpendicular line looks like

y = 2x + b

and to get b we use the point we know (-2, 8)

8 = 2×-2 + b

8 = -4 +b

12 = b

so, the full equation for the line is

y = 2x + 12

Answer:

2x-y+12= 0 or y = 2x+12 is the answer

Step-by-step explanation:

slope of the line joining (3,-4) and (-7,1) is 1-(-4)/-7-3

= -5/10

= - 1/2

slope of the line containing (-2,8) and that is perpendicular to the line containing (3,-4) and (-7,1) = 2

Equation of the line line containing (-2,8) and that is perpendicular to the line containing (3,-4) and (-7,1) is y-8 = 2(x-(-2))

y-8 = 2(x+2)

y- 8 = 2x+4

y=2x+12 (slope- intercept form) or 2x-y+12= 0 (point slope form)

Step-by-step explanation:

circumference =pi × diameter

=(22/7)×2.2

=6.914ft

Answer:

6.91 feet

Step-by-step explanation:

Answer:

hmmmmm please send the pic again

Answer:

[tex]-29.5-\frac{38}{15}x[/tex]

Step-by-step explanation:

First, we must expand out the -5.

-5 times 2/3x is equal to -10/3x, and -5 times 6 is equal to -30. 1/2 minus 30 is equal to -29.5, and 4/5x minus 10/3x is equal to -38/15x.

Answer:

Step-by-step explanation:

The idea here is to create lines according to the constraints we were given, graph the lines (which are actually inequalities), and then shade in the region that satisfies the inequality. Let's start at the beginning of the problem and we'll get our lines (inequalities) written.

The total number of boxes that can be produced according to the constraints is 800, so the inequality for that is

x + y ≤ 800 and solving for y:

y ≤ 800 - x

Another constraint on the white chocolate is that it has to be less than or equal to 200 boxes, so:

y ≤ 200

The max number of white chocolate boxes is half the number of milk chocolate, so:

y ≤ (1/2)x

The min number of milk chocolate boxes produced is:

x ≥ 0 and

The min number of white chocolate boxes produced is:

y ≥ 0 (This means that it is a possibility of making 0 milk chocolate boxes and all white chocolate boxes OR there is a possibility of making 0 white chocolate boxes and all milk chocolate boxes)

The production equation (which is used later) is:

2.25x + 2.50y (you make a profit of $2.25 on every milk chocolate box you sell and profit of $2.50 on every white chocolate box you sell).

The bold equations are the ones that need to be graphed (see graph below). Where those 3 lines intersect are the vertices of feasible region:

(0, 0), (400, 200), (600, 200), (800, 0).

Then take each x and y value from a coordinate and plug it into the profit equation (we don't need to use (0, 0)) starting with x = 400 and y = 200:

2.25(400) + 2.5(200) = $1400

Now using x = 600 and y = 200:

2.25(600) + 2.5(200) = $1850

Now using x = 800 and y = 0:

2.25(800) + 2.5(0) = $1800

So our max profit as seen by the evaluations is $1850, and that occurs when we sell 600 boxes of milk chocolate and 200 boxes of white chocolate.

Answer:

A

Step-by-step explanation:

Slope = term that multiply x

y intercept = the number without a variable

Answer:

Step-by-step explanation:

Answer:

spped of the plane in calm air=121 km/h

speed of the wind= 4km/h

Step-by-step explanation:

Let say V the speed of the plane in calm air

and v the speed of the wind

Flying with a tailwind, a flight crew flew 500 km in 4 hours ==> 500= (V+v)*4

Flying against the tailwind, the crew flew 468 km in 4 hours ==> 468 = (V-v)*4

We divide the 2 equations by 4 and then add the 2 results equations:

(500+468)/4=2V ==> V=121 (km/h)

We replace that value in the first equation:

V+v=500/4=125

v=125-121=4 (km/h)

Answer:

116 people are expected to have heard the rumor after 6 days total have passed since it was initially spread.

Step-by-step explanation:

Logistic function:

The logistic function is given by:

[tex]P(t) = \frac{K}{1 + Ae^{-kt}}[/tex]

In which:

[tex]A = \frac{K - P(0)}{P(0)}[/tex]

Considering that K is the carrying capacity, k is the growth/decay rate and P(0) is the initial population.

Suppose a rumor is going around a group of 210 people.

This means that [tex]K = 210[/tex]

Initially, only 34 members of the group have heard the rumor:

This means that [tex]P(0) = 34[/tex] and:

[tex]A = \frac{210 - 34}{34} = 5.1765[/tex]

So

[tex]P(t) = \frac{210}{1 + 5.1765e^{-kt}}[/tex]

3 days later 69 people have heard it.

This means that [tex]P(3) = 69[/tex], and we use this to find k.

[tex]69 = \frac{210}{1 + 5.1765e^{-3k}}[/tex]

[tex]69 + 357.1785 e^{-3k} = 210[/tex]

[tex]357.1785 e^{-3k} = 141[/tex]

[tex]e^{-3k} = \frac{141}{357.1785}[/tex]

[tex]\ln{e^{-3k}} = \ln{\frac{141}{357.1785}}[/tex]

[tex]-3k = \ln{\frac{141}{357.1785}}[/tex]

[tex]k = -\frac{\ln{\frac{141}{357.1785}}}{3}[/tex]

[tex]k = 0.3098[/tex]

So

[tex]P(t) = \frac{210}{1 + 5.1765e^{-0.3098t}}[/tex]

How many people are expected to have heard the rumor after 6 days total have passed since it was initially spread?

This is P(6), so:

[tex]P(6) = \frac{210}{1 + 5.1765e^{-0.3098*6}} = 116[/tex]

116 people are expected to have heard the rumor after 6 days total have passed since it was initially spread.

Answer:

see explanation

Step-by-step explanation:

1

2(3x + 1) = 4(x + 2) ← distribute parenthesis on both sides

6x + 2 = 4x + 8 ( subtract 4x from both sides )

2x + 2 = 8 ( subtract 2 from both sides )

2x = 6 ( divide both sides by 2 )

x = 3

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

2

6x = 4(x - 3) ← distribute parenthesis

6x = 4x - 12 ( subtract 4x from both sides )

2x = - 12 ( divide both sides by 2 )

x = - 6

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

3

2(4x + 7) = 4x + 30 ← distribute parenthesis on left side

8x + 14 = 4x + 30 (subtract 4x from both sides )

4x + 14 = 30 ( subtract 14 from both sides )

4x = 16 ( divide both sides by 4 )

x = 4

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

4

50 = - (y + 22) ← distribute parenthesis by - 1

50 = - y - 22 ( add 22 to both sides )

72 = - y ( multiply both sides by - 1 )

- 72 = y , that is

y = - 72

Answer:

[tex]x=-\frac{15}{382}[/tex]

Step-by-step explanation:

32 × 12x + 1 = 2x - 14

384x + 1 = 2x - 14

384x + 1 - 1 = 2x - 14 - 1

384x = 2x - 15

384x - 2x = 2x - 2x - 15

382x = - 15

382x ÷ 382 = - 15 ÷ 382

[tex]x=-\frac{15}{382}[/tex]

Answer:

Mean = 83.15

Median = 90

Mode = 88

Range = 110

Outlier = 5

Step-by-step explanation:

Mean - (88+92+76+42+88+90+100+110+115+5+88+92+95)/2 = 83.15

Median - 5, 42, 76, 88, 88, 88, 90, 92, 92, 95, 100, 110, 115 = 90

Mode - 88, 92, 76, 42, 88, 90, 100, 110, 115, 5, 88, 92, 95 = 88

Range - 115 - 5 = 110.

Outlier - 88, 92, 76, 42, 88, 90, 100, 110, 115, 5, 88, 92, 95 = 5

hope it helps :)

please mark brainliest!!! (took a lot effort!)

Answer:

Step-by-step explanation:

Arrange the data from the lowest to the highest value ( after you rearrange them count to see if you still have the same amount of values -13 numbers)

5, 42, 76, 88, 88, 88, 90, 92, 92, 95, 100, 110, 115

Mean: sum up all the values /number of values

mean = (5+42+76+88+88+88+90+92+92+95+100+110+115)/13 ≅83.15

Median: is the number in the middle (or if you have an even amount of numbers you do the average of the 2 middle numbers)

median = 90

Mode: is the number that appears the most (a data set can have more than one mode if different numbers appear with the same frequency )

mode= 88

Range: is the difference between the biggest and smallest value

range = 115-5 = 110

Outlier: is a value that is significantly different than the rest of the values

outlier = 5

Answer:  

Step-by-step explanation:

[tex]\displaystyle\ \!\!6(x-2)>15 \\\\6x-12>15 \\\\6x>27\\\\ \boldsymbol{x>4,5 \ \ or \ \ x\in(4,5\ ; \infty)}[/tex]

Answer:

look this up ok

Step-by-step explanation:

Graph axis of symmetry vertex and max and min, domain and range

Answer:

Part A:

x + y = 50

y = x + 20

Part B:

Ted spends 35 minutes practicing the breaststroke every day.

Part C: It is not possible, as 45 + 65 isn't 50.

Step-by-step explanation:

9514 1404 393

Answer:

  B.  4

Step-by-step explanation:

The product of segment lengths to the near and far circle intercepts is the same for both secants.

  5(5 +(x-1)) = 4(4 +(x+2))

  5(x +4) = 4(x +6) . . . . . simplify inside parentheses

  5x +20 = 4x +24 . . . eliminate parentheses

  x = 4 . . . . . . . . . . . . subtract 20+4x

Answer:

The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]

Step-by-step explanation:

Radius of the can:

The radius of the can is given by:

[tex]r^2 = \frac{V}{h\pi}[/tex]

In which V is the volume and h is the height.

In this question:

[tex]V = 1280\pi, h = 16[/tex]

Thus

[tex]r^2 = \frac{V}{h\pi}[/tex]

[tex]r^2 = \frac{1280\pi}{16\pi}[/tex]

[tex]r^2 = 80[/tex]

[tex]r = \sqrt{80}[/tex]

[tex]r = \sqrt{5*16}[/tex]

[tex]r = \sqrt{5}\sqrt{16}[/tex]

[tex]r = 4\sqrt{5}[/tex]

The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]

Answer:

D: one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf

Step-by-step explanation:

A pair of 2 dependent events are simply those in which the choice of the second item depends on taking the first item such that the probability changes.

Because when the first item is taken without replacement, the sample size would have reduced and as such picking the exact same item will reduce the probability.

Now, what this means in relation to the question is that for 2 of the events to be independent, they must be on the same shelf and of same type of book such that the second book can't be selected until the first one has been selected.

The only option that fits this definition is option D where both books are on the same shelf and they are same type of books.

Answer:

one of the nonfiction books on the bottom shelf, and a second nonfiction book from the bottom shelf

Step-by-step explanation:

Total People=5+7+4=16

We know

[tex]\boxed{\sf P(W)=\dfrac{No.\:of\:women}{Total\:People}}[/tex]

[tex] \\ \sf \longmapsto \: p(w) = \frac{7}{16} [/tex]

Answer:

(i) The probability of at least 2 successes is 0.2093.

(ii) The probability of at least one but no more than 3 successes is 0.9548.

Step-by-step explanation:

Now the total number of cases = {1, 2, 3, 4, 5, 6} = 6.

Favourable cases = {1, 6} = 2.

[tex]p = \frac{2} {3} = \frac{1} {3} \\\\q = 1- p\\\\q = \frac{2}{3} \\\\n=5[/tex]

i) at least 2 successes,

[tex]P(X\geq 2) = (^{n}C_{x} )\times p^{x} \times (1-p)^{n-x}\\\\P(X\geq 2) = 0.2093[/tex]

ii) at least one but no more than 3 successes,

[tex]P(X\leq 3) = (^{n}C_{x} )\times p^{x} \times (1-p)^{n-x}\\\\P(X\leq 3)= 0.9548[/tex]

Answer:

18.65

Step-by-step explanation:

1/4+2/5+18=18.65

18.65

hope it helps you good luck