Set up a proportion to solve for x in the following similar triangles.

Answer:

[tex]2y^2-7y+6=0[/tex]

Step-by-step explanation:

We are given that [tex]\alpha[/tex] and [tex]\beta[/tex] are the zeroes of the polynomial [tex]6y^2-7y+2[/tex]

[tex]y^2-\frac{7}{6}y+\frac{1}{3}[/tex]

We have to find a quadratic polynomial whose zeroes are [tex]1/\alpha[/tex] and [tex]1/\beta[/tex].

General quadratic equation

[tex]x^2-(sum\;of\;zeroes)x+ product\;of\;zeroes[/tex]

We get

[tex]\alpha+\beta=\frac{7}{6}[/tex]

[tex]\alpha \beta=\frac{1}{3}[/tex]

[tex]\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha \beta}[/tex]

[tex]\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7/6}{1/3}[/tex]

[tex]\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7}{6}\times 3=7/2[/tex]

[tex]\frac{1}{\alpha}\times \frac{1}{\beta}=\frac{1}{\alpha \beta}[/tex]

[tex]\frac{1}{\alpha}\times \frac{1}{\beta}=\frac{1}{1/3}=3[/tex]

Substitute the values

[tex]y^2-(7/2)y+3=0[/tex]

[tex]2y^2-7y+6=0[/tex]

Hence, the quadratic polynomial whose zeroes are [tex]1/\alpha[/tex] and [tex]1/\beta[/tex] is given by

[tex]2y^2-7y+6=0[/tex]

Answer:

The expected value is an expression of the weighted average and can be taken as the (arithmetic) mean

As the number of trials is increased in a binomial experiment, the expected values obtained, in each of the set of trials continuously tend to the theoretical expected value

Step-by-step explanation:

Answer:

La ecuación genérica para un círculo centrado en el punto (a, b), de radio R, es:

(x - a)^2 + (x - b)^2 = R^2

Entonces si miramos a nuestra ecuación:

(x + 2)^2 + (y - 3)^2 = 121

Tendremos el centro en:

(-2, 3)

el radio está dado por:

R^2 = 121

R = √121 = 11

La gráfica de esta circunferencia se puede ver en la imagen de abajo.

Answer:

34 should be added to it to make it 20

hmm...let me think a little bit

Step-by-step explanation:

hmmm ..... i dont know so sorry

i am very very sory

Answer:

hope it helps.

Answer:

the answer is 3x2-10x+6=0

Answer:

5

Step-by-step explanation:

2x - y when x = 0 and y = -5

2(0) - (-5) =

= 0 + 5

= 5

Answer:

5

Step-by-step explanation:

2x-y

2(0)-(-5)

0-(-5)

0+5

5

Answer:

C

Step-by-step explanation:

Since it's the product, the two numbers must be multiplied together. -3 * x will equal 21, so -3x=21. By dividing both sides by -3, we see that x=-7

Answer:

x = 42.5

Step-by-step explanation:

A triangle inscribed inside of a circle using the diameter of the circle as it's hypotenuse is a right triangle ( a 90 degree triangle ) where the angle opposite of the hypotenuse is the 90 degree angle ( angle C )

Hence angle C = 90

If angle C = 2x + 5

Then 2x + 5 = 90

Notice that we just created an equation that we can use to solve for x

We now solve for x algebraically

2x + 5 = 90

Step 1 subtract 5 from both sides

2x + 5 - 5 = 90 - 5

Outcome: 2x = 85

Step 2 divide both sides by 2

2x/2 = 85/2

Outcome: x = 42.5

Answer:

The correct answer is -2 , -4

Step-by-step explanation:

if x = -2 and y = -4

-5x-3y=22

so :

-5(-2)-3(-4)=22

10+12=22

22=22

end.

Answer:

1. a. (ii) 1/27

Step-by-step explanation:

1st one is already given, I will give you the answer to the second one,

³√27/9²

= 3/81

= 1/27

Answered by GAUTHMATH

Answer:

17/42 or in decimal 0.405

Step-by-step explanation:

Add: 1 4/7+2/3- 1 5/6= 47/21- 1 5/6

Subtract: 47 - 1 5/6 = 17/42

Simplify: 17/42

Answer:

Step-by-step explanation:

eq. of line with slope m and intercept 3 is

y=mx+3

∵ it passes through (10,53)

53=10m+3

10m=53-3=50

m=50/10=5

y=5x+3

so standard form of eq. is

5x-y+3=0

or

5x-y=-3

Answer:

74820

Step-by-step explanation:

9.5% of 3000 is 285

there are 12 months in a year

so 12 times 21 equals 252

so 285 times 252 add 3000 equals 74820

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

Explanation:

Choice B has the GCF x we can factor out like so

10x^4-5x^3+70x^2+3x = x(10x^3-5x^2+70x+3)

Showing that choice B is not prime. If a polynomial can be factored, then we consider it not prime. It's analogous to saying a number like 15 isn't prime because 15 = 3*5, ie 15 can be factored into something that doesn't involve 1 as a factor.

In contrast, we consider 7 prime because even though 7 = 1*7, there aren't any other ways to write this integer as a factorization if we don't involve 1.

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

Choice C is a similar story. This time we can factor out 3

3x^2 + 18y = 3(x^2 + 6y)

So we can rule this out as well.

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

Choice D is a bit tricky, but we can use the difference of cubes factoring rule

a^3 - b^3 = (a-b)(a^2+ab+b^2)

where in this case a = x and b = 3y^2

Note how b^3 = (3y^2)^3 = 3^3*(y^2)^3 = 27y^(2*3) = 27y^6

All of this means choice D can be factored and it's not prime either.

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

We've ruled out choices B through D. The answer must be choice A.

If you let w = x^2, then w^2 = x^4

The polynomial w^2+20w-100 is prime because setting it equal to zero and solving for w leads to irrational solutions. I'm assuming your teacher wants you to factor over the rational numbers.

Because w^2+20w-100 can't be factored over the rational numbers, neither can x^4+20x^2-100. This confirms that choice A is prime.

Answer:

[tex]Sets = 27[/tex]

Step-by-step explanation:

Given

[tex]Coin = 1[/tex]

[tex]Toss = 5[/tex]

Required

Number of outcomes with at most 3 heads

First, we list out the sample space of a toss of coin 5 times

[tex](HHHHH)[/tex], [tex](HHHHT)[/tex], [tex](HHHTT)[/tex], [tex](HHTTT)[/tex], [tex](HTTTT)[/tex], [tex](TTTTT)[/tex], [tex](TTTTH)[/tex], [tex](TTTHH)[/tex], [tex](TTHHH)[/tex], [tex](THHHH)[/tex], [tex](HTHTH)[/tex], [tex](THTHT)[/tex], [tex](HHTHH)[/tex], [tex](TTHTT)[/tex], [tex](HTTHT)[/tex], [tex](THHTH)[/tex], [tex](THHHT)[/tex], [tex](HTTTH)[/tex], [tex](THHTT)[/tex], [tex](HTTHH)[/tex], [tex](HHTTH)[/tex], [tex](TTHHT)[/tex], [tex](TTHTH)[/tex], [tex](HHTHT)[/tex], [tex](HTHTT)[/tex], [tex](THTHH)[/tex], [tex](THTTH)[/tex], [tex](HTHHT)[/tex], [tex](HTHTT)[/tex], [tex](THTHH)[/tex], [tex](HHHTH)[/tex], [tex](TTTHT)[/tex]

Next, we list out all outcomes with at most 3 heads

, , [tex](HHHTT)[/tex], [tex](HHTTT)[/tex], [tex](HTTTT)[/tex], [tex](TTTTT)[/tex], [tex](TTTTH)[/tex], [tex](TTTHH)[/tex], [tex](TTHHH)[/tex], , [tex](HTHTH)[/tex], [tex](THTHT)[/tex], , [tex](TTHTT)[/tex], [tex](HTTHT)[/tex], [tex](THHTH)[/tex], [tex](THHHT)[/tex], [tex](HTTTH)[/tex], [tex](THHTT)[/tex], [tex](HTTHH)[/tex], [tex](HHTTH)[/tex], [tex](TTHHT)[/tex], [tex](TTHTH)[/tex], [tex](HHTHT)[/tex], [tex](HTHTT)[/tex], [tex](THTHH)[/tex], [tex](THTTH)[/tex], [tex](HTHHT)[/tex], [tex](HTHTT)[/tex], [tex](THTHH)[/tex], [tex](TTTHT)[/tex]

So, the number of set is:

[tex]Sets = 27[/tex]

Answer:

200

Step-by-step explanation:

Given: they can type 120 words in 3 minutes

Find number of words they can type in 1 minute: Words typed in 1 minute = 120/3=40

Solution: Words typed in 5 minutes = 40 * 5 = 200

Answer:

200 words

Step-by-step explanation:

First we need to find the words per minuite the student can type

we can do this by taking the number of words typed in 3 mins and dividing it by 3

120/3 = 40

Now we know she types 40 words per min

multiply 40 by 5 to get the no. of words typed in 5 mins

40*5=200

200 is the words she types in 5 mins

pls give brainliest

Answer:

i dont see a diagram ?

Step-by-step explanation:

Answer:

AC is greater than BC because segment AC is the hypotenuse of right triangle ABC, and the hypotenuse is the longest side of a right triangle.

Answer:

400 in.²

Step-by-step explanation:

Surface area of the triangular prism = bh + L(s1 + s2 + s3)

Where,

b = 8 in.

h = 15 in.

s1 = 17 in.

s2 = 15 in.

s3 = 8 in.

L = 7 in.

Plug in the values

S.A = 8*15 + 7(17 + 15 + 8)

S.A = 120 + 7(40)

S.A = 120 + 280

S.A = 400 in.²

Hello,

The conic is a parabola ,

vertex (-1,3)

focus : (-1,-2)

directrix: y=8

equation: y= - 1/20x²-1/10*x+59/20

solution in picture

The vertex is v(-1,3) , focus is f(-1,8) and the equation of directrix is          y = -2.

A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line. The equidistant from a fixed point called the focus (F), and the fixed-line is called the directrix (x + a = 0).

For the given situation,

The standard form of equation of parabola is given by, [tex]y=\frac{1}{4p}(x-h)^{2}+k[/tex]

The vertex is given by [tex]v(h,k)[/tex]

The focus is given by [tex]f(h,k-p)[/tex]

The equation of directrix is given by [tex]y=k+p[/tex]

The given equation is [tex](x+1)^{2} =-20(y-3)[/tex]

On rearranging the given equation in standard form,

⇒ [tex](x+1)^{2} =-20y+60[/tex]

⇒ [tex](x+1)^{2} -60=-20y[/tex]

Divide by 20 on both sides,

⇒ [tex]\frac{(x+1)^{2}}{20} +4 = y[/tex]

⇒ [tex]y=\frac{-1}{(4)(5)} (x+1)^{2} +3[/tex]

On comparing the above equation with the standard form,we get

[tex]p=-5, h=-1, k=3[/tex]

⇒ [tex]k-p=3-(-5)\ =8[/tex]

Hence we can conclude that the vertex is v(-1,3), focus is f(-1,8) and equation of directrix is y=-2.

Learn more about a parabola here

https://brainly.com/question/7492359

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Answer:

y = 2[tex](x - 3)^{2}[/tex] - 1

Step-by-step explanation:

y = 2[tex]x^{2}[/tex] - 12x + 16  

y = 2([tex]x^{2}[/tex] - 6x + 8)        ( Factor out 2 )

y + 9= 2([tex]x^{2}[/tex] - 6x + 9) + 8 ( Complete the square [tex](\frac{-b}{2} )^{2}[/tex] ) Add 9 both sides  

y + 9 = 2 [tex](x - 3)^{2}[/tex] + 8      (Subtract 9 each side)  

y = 2 [tex](x - 3) ^{2}[/tex] - 1         ( simplify )

Answer:

His average speed is

12 km/hr

.

Step-by-step explanation:

Remember the triangle of Speed, Distance and Time. If you remember it, you'll ace these kinda questions.

I had trouble with these formulas but the triangle helped me a LOT! Anyways, let's get back to the question. The formula for average speed is pretty much the same as the formula for just speed. The average speed formula is

Average speed

=

Total Distance

Total Time

So......

48 km

4 hr

=

12 km/hr

My source

I hope this explanation helps you!

Answer:

A) 60%

Step-by-step explanation:

24/40

= 0.6

0.6*100

= 60%

I really hope this is right and it helps.

Step-by-step explanation:

The two equation will intersect each other at the point which will be the solution of the given two equations , and the given equations are ,

[tex]\implies 2x -y +6=0\\\\\implies 2x + 3y -6=0[/tex]

On subtracting the given equations we have,

[tex]\implies -y - 3y +6 -(-6) = 0 \\\\\implies -4y = -12 \\\\\implies y = -12/-4\\\\\implies y = 3 [/tex]

Put this value in any equation , we have ,

[tex]\implies 2x -3 +6 =0\\\\\implies 2x = -3 \\\\\implies x =\dfrac{-3}{2} \\\\\implies x =-1.5 [/tex]

Hence the lines will Intersect at ,

[tex]\implies\underline{\underline{ Point=(-1.5, 3)}}[/tex]

for the first one x = 1/2 y-3" and y = 2 x + 6 and for the other one is x =  − 3 /2  y+ 3  and y= − 2 /3  x + 2

how i did this Step 1: Add -3y to both sides.

Step 2: Add 6 to both sides.

Step 3: Divide both sides by 2.

Answer:

think it is D

Step-by-step explanation:

look at the X axis and the number at the Y axis

The equation best models the relationship between x and y is y=-5x+125.

We have given that,

John reads an equal number of pages of a book every week. The graph below shows the number of pages of the book left to read, y, after x weeks.

We have to determine the equation best models the relationship between x and y.

The three main ways to represent a relationship in math are using a table, a graph, or an equation.

The X-axis and the number at the Y-axis.

Therefore, The equation best models the relationship between x and y is y=-5x+125.

To learn more about the graph visits:

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Answer:

option C

Step-by-step explanation:

2, 4, 6

i don't know whether it is correct or not...

Answer:

Step-by-step explanation:

See the picture

It should be self-explanatory

The top part of the angle a is:

The bottom part of the angle a is:

The measure of angle a is:

Firstly, draw a line parallel to UT

Something like in the picture

Now,

a = BNU

Also,

BNU + BNM = 165°