Determine whether each of the following problems
will have a rational or an irrational answer. Your
answer should be either the word "rational or
"irrational."
18 + 1

Given:

Two chords intersect each other inside the circle.

To find:

The value of x.

Solution:

According to intersecting chords theorem, if two chords intersect each other inside the circle, then the product of two segments of one chord is equal to  the product of two segments of second chord.

In the given circle,

[tex]AE\times CE=BE\times DE[/tex]

[tex](3x-11)\times (5x-4)=(x+2)\times (-x+17)[/tex]

[tex]15x^2-12x-55x+44=-x^2+17x-2x+34[/tex]

[tex]15x^2-67x+44+x^2-15x-34=0[/tex]

[tex]16x^2-82x+10=0[/tex]

Divide both sides by 2.

[tex]8x^2-41x+5=0[/tex]

Splitting the middle term, we get

[tex]8x^2-40x-x+5=0[/tex]

[tex]8x(x-5)-1(x-5)=0[/tex]

[tex](8x-1)(x-5)=0[/tex]

Using zero product property, we get

[tex](8x-1)=0[/tex] or [tex](x-5)=0[/tex]

[tex]x=\dfrac{1}{8}[/tex] or [tex]x=5[/tex]

For [tex]x=\dfrac{1}{8}[/tex], the side AE is negative. So, [tex]x=\dfrac{1}{8}[/tex] is not possible.

Therefore, the required solution is [tex]x=5[/tex].

Answer:

I think it's C. cause I multipled 16 by 7

Answer:

I think the answer is 5 hope it helps

Answer:

36 Km

Step-by-step explanation:

Por favor, encontrar el archivo adjunto

Answer:

It looks like 35 miles per hour

Step-by-step explanation:

if you look at the vertical line between 0 and 2 (which is the one hour mark) on the horizontal axis of the graph you can see the line of the graph crossed under the 40 mi. Therefore the train traveled about 35 miles in one hour (or 35 mph) because there are no other answers under 40.

Answer:

a) 140000

b) 1000000

c) 9000000

Step-by-step explanation:

a) 687x164

700 * 200 =140000

b) 476x2354

500*2000=1000000

c) 8612x1497

9000*1000=9000000

Answer:

8 books were in each box

Step-by-step explanation:

According to the Question,

Assume X is the Number of Books In Each Box.

Algebraic Expression,

4X + 3 = 35

4X = 35 - 3

4X = 32  ⇔  X=8 books in Each Box.

[tex]\longrightarrow{\blue{ C. \: 2 {x}^{2} + 4x - 30 = 0 }}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] \frac{6}{x} = \frac{2x + 4}{5} [/tex]

[tex] \: 6 \times 5 = x \: (2x + 4)[/tex]

➺ [tex] \: 30 = 2 {x}^{2} + 4x[/tex]

➺ [tex] \: 2 {x}^{2} + 4x - 30 = 0[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

2x+15y=2960

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

98deg

Step-by-step explanation:

Angles in a triangular add to 180.

180-(53+45) is the top angle.

Angles on a line add a up to 180

180 - triangles top angle = x

The standard deviation of the distribution of sample proportions is rounded to the nearest hundredth.60 Are taken but the single is 1.

The population proportion is .6. If samples of size 60 are taken, determine the standard deviation of the distribution of sample proportions rounded to the nearest hundredth.

The Sampling Distribution of the Sample Proportion

and standard deviation σˆP=√pq/n.

This is given by the formula Z=(X-m)/s where Z is the z-score, X is the value you are using, m is the population means and s is the standard deviation of the population. Consult a unit normal table to find the proportion of the area under the normal curve falling to the side of your value.13

Learn more about standard deviation at

https://brainly.com/question/475676

#SPJ2

Answer:

[tex]1. \: \: a = 4[/tex]

[tex]2. \: \: y = 16[/tex]

Step-by-step explanation:

[tex]1. \: \: a + 5 = 9[/tex]

[tex]a = 9 - 5[/tex]

[tex]a = 4[/tex]

[tex]2. \: \: y−4=12[/tex]

[tex]y=12+4[/tex]

[tex]y = 16[/tex]

Answer:

ok for this problem lets subtract 25 for 100 to get 75 so know we know we have to multiple 20 by 0.75 to get 15 dollars for the reduced price

Answer:

One was to write this ratio is lets say you where ordering 100 Happy Platters this mean you would get 200 corn and 300 flour.

another way is lets say you got a Happy Platter and split it in half with some one else you would get 1 corn and 1.5 flour

Answer:

14a^2

Step-by-step explanation:

3a^2+4a^2+7a^2

Combine like terms

Factor out a^2

a^2(3+4+7)

a^2(14)

14a^2

Answer:

14 a²

Step-by-step explanation:

3a² + 4a² + 7a²

collect like terms

(3 + 4 + 7)a² .. ( factor out :- a²)

calculate the sum

14 a²

Answer:

Se garantiza que [tex]\cos 2\alpha \cdot (\tan 2\alpha - \tan \alpha) = \tan \alpha[/tex].

Step-by-step explanation:

A continuación, vamos a emplear las siguientes identidades trigonométricas:

[tex]\cos 2\alpha = \cos^{2} \alpha - \sin^{2}\alpha[/tex] (1)

[tex]\tan 2\alpha = \frac{2\cdot \tan \alpha}{1-\tan^{2}\alpha}[/tex] (2)

Ahora aplicamos estas identidades a la identidad descrita en el enunciado:

[tex]\cos 2\alpha \cdot (\tan 2\alpha - \tan \alpha) = \tan \alpha[/tex]

[tex](\cos^{2}\alpha - \sin^{2}\alpha)\cdot \left(\frac{2\cdot \tan \alpha}{1-\tan^{2}\alpha} - \tan \alpha \right) = \tan \alpha[/tex]

[tex](\cos^{2}\alpha -\sin^{2}\alpha) \cdot \left[\frac{2- (1-\tan^{2}\alpha)}{1-\tan^{2}\alpha} \right]\cdot \tan\alpha = \tan \alpha[/tex]

[tex](\cos^{2}\alpha - \sin^{2}\alpha) \cdot \left[\frac{1+\tan^{2}\alpha}{1-\tan^{2}\alpha} \right] = 1[/tex]

[tex](\cos^{2}\alpha -\sin^{2}\alpha)\cdot (1 + \tan^{2}\alpha) = 1 - \tan^{2}\alpha[/tex]

[tex]\cos^{2}\alpha \cdot (1-\tan^{2}\alpha)\cdot (1 + \tan^{2}\alpha) = (1-\tan^{2}\alpha)[/tex]

[tex]\cos^{2}\alpha \cdot (1+\tan^{2}\alpha) = 1[/tex]

[tex]\cos^{2}\alpha\cdot \sec^{2}\alpha = 1[/tex]

[tex]1 = 1[/tex]

Por tanto, se garantiza que [tex]\cos 2\alpha \cdot (\tan 2\alpha - \tan \alpha) = \tan \alpha[/tex].

Answer:

Step-by-step explanation:

a) -14 , -9 , -4 , 1 ................

Common difference = d = 2nd term - 1st term

           = -9-[-14]

           = -9 + 14

          d = 5

The next term can be got by adding 5 to the previous term

5th term = 1 + 5 = 6

6th term = 6 + 5 = 11

7th term = 11 + 5 = 16

Next 3 terms are : 6 , 11 , 16

[tex]b) \frac{5}{6},\frac{2}{3},\frac{1}{2},\frac{1}{3},.....\\\\d = \frac{2}{3}-\frac{5}{6}\\\\=\frac{2*2}{3*2}-\frac{5}{6}\\\\=\frac{4}{6}-\frac{5}{6}\\\\=\frac{-1}{6}\\\\a_{5} = \frac{1}{3}+\frac{-1}{6}=\frac{1*2}{3*2}+\frac{-1}{6}=\frac{2}{6}+\frac{-1}{6}=\frac{1}{6}\\\\a_{6}=\frac{1}{6}+\frac{-1}{6}=0\\\\a_{7}=0+\frac{-1}{6}=\frac{-1}{6}\\\\\\Next 3 terms : \frac{1}{6},0,\frac{-1}{6}[/tex]

Answer:

6

Step-by-step explanation:

So here are the numbers that are factors of 34 and multiples of 7

1,2,14,17,56,91

So count the numbers, 6. And that's ur answer, believe me

Answer:

x=0

Step-by-step explanation:

4 ( 2.5) ^x = 4

Divide each side by 4

4/4 ( 2.5) ^x = 4/4

( 2.5) ^x = 1

Take the log of each side

log  ( 2.5) ^x =  log (1)

x log ( 2.5) = log 1

x log (2.5) = 0

Divide each side by log (2.5)

x = 0

Answer:

45°

Step-by-step explanation:

Reference angle is defined as The smallest angle that the standard position of a given angle will make with the x-axis.

Now, the given angle 225 lies in third quadrant. So, for us to find the reference angle, we will have to subtract 180 from it to get;

225 - 180 = 45°

Answer:

B=112

Step-by-step explanation:

Angle B is on the same line as angle A(68). They would need to combine for a total of 180 degrees. So 68-180=112

Answer:

b = 112°

Step-by-step explanation:

The two angles from a straight line. so, they add to 180° .

b + 68° = 180°

subtract 68° from each side

b + 68° - 68° = 180° - 68°

b = 112°

Answer:

50/7 or 7 1/7

Step-by-step explanation:

Answer:

24 servngs

Step-by-step explanation:

3 cups makes 9 servings.

The rate of servings to cups is 9 servings to 3 cups which is a unit rate of 3 servings per cup.

1 quart = 4 cups

2 quarts = 2 * 4 quarts = 8 cups

3 serviongs/cup * 8 cups = 24 servings

Answer: 24 servings

Answer:

ok so first we add 10 plus 7 together since if you don't show up you fail

which is 17

so out of 100 students 17 failed both

now we subtract 71 from 80 to get 9

so we add that together with 17 so

17+9=26 so 26 students failed both

Hope This Helps!!!

Answer:

5. 2 hours 45 minutes 6. 7:23 7. 10:05 8. 1 hour 34 minutes

Step-by-step explanation:

I mean u gotta be lying about staying up all night to do these 4 problems but heres the answers

Answer:

5. 2 hours 45 mins

6. 7:23 start

7. 10:05

8. 1 hour 34 mins

Answer:

f(x) = 4*e^(0.05*x)

Step-by-step explanation:

We want to find the equation for the graph.

The first thing we can see, is that, as the value of x increases, also does the value of y.

So f(x) increases as x increases.

Then we can discard the options with negative exponents, as those decrease when x increases.

Then the remaining options are:

f(x) = 4*e^(0.05*x)

f(x) = 4*e^(0.5*x)

In the graph, we can see that:

f(5) ≈ 5

So let's check that with the two remaining options:

For the first one we have:

f(5) = 4*e^(0.05*5) = 5.13

While for the second option we have:

f(5) = 4*e^(0.5*5) = 48.73

Then the correct option is the first one:

f(x) = 4*e^(0.05*x)