What is the equation of the line?

Step-by-step explanation:

The given expression is :

[tex]\dfrac{2-\sqrt5}{2+3\sqrt5}=\sqrt5 x+y[/tex] ....(1)

Taking LHS of the above expression

[tex]\dfrac{2-\sqrt5}{2+3\sqrt5}[/tex]

Rationalizing both denominator and numerator.

[tex]\dfrac{2-\sqrt5}{2+3\sqrt5}\times \dfrac{2-3\sqrt5}{2-3\sqrt5}=\dfrac{4-6\sqrt5-2\sqrt5+15}{2^2-(3\sqrt5)^2}\\\\=\dfrac{19-8\sqrt5}{4-45}\\\\=\dfrac{19-8\sqrt5}{-41}\\\\=\dfrac{\sqrt5 \times 8}{41}+(\dfrac{-19}{41})[/tex]

Equation (1) becomes,

[tex]\dfrac{\sqrt5 \times 8}{41}+(\dfrac{-19}{41})=\sqrt 5\ x+y[/tex]

Equating both sides,

[tex]x=\dfrac{8}{41}[/tex] and [tex]y=\dfrac{-19}{41}[/tex]

Hence, this is the required solution.

Answer:

ED= 38º EA= 144º BDC= 308º

Step-by-step explanation:

Answer:

Step-by-step explanation:

On Tuesday, Hayley only has 15 cups of flour and 9 eggs, but she has more than enough butter and

sugar Which system of linear inequalities can Hayley use to model this situation where b represents the

number of loaves of banana bread and represents the number of loaves of zucchini bread?

Answer:

x = 2

Step-by-step explanation:

3(x - 1) = 23 - 5(x + 2) ← distribute parenthesis on both sides

3x - 3 = 23 - 5x - 10

3x - 3 = 13 - 5x ( add 5x to both sides )

8x - 3 = 13 ( add 3 to both sides )

8x = 16 ( divide both sides by 8 )

x = 2

Answer:

x=2

Step-by-step explanation:

Answer:

x + 7 ft and  x + 15 ft as the dimensions of the outside border of the walkway.

Step-by-step explanation:

[tex]x^{2} +12x + 20 = (x + 2)(x + 10)[/tex]

The dimensions of the fountain is x + 2 and x + 10

Adding the 5-ft walkway, we get x + 7 ft and  x + 15 ft as the dimensions of the outside border of the walkway.

30 hours of vdvdkdjdbdvdkdjevjexhsjshdhevdkddjdjddhdhdbd jdmdjdhdbdjdissksjdjddhdkfjhfdjhddkhddhhdbd bb gun

Step-by-step explanation:

e kuan na dayun

Answer:

49°

Step-by-step explanation:

106 + 135 + 70 + x = 360

311 + x = 360

x = 49°

here's the answer :

=》

In similar figures, the ratio of the lengths of their corresponding sides are equal and corresponding angles are congruent.

hence, A. equal and congruent is correct.

Answer:

equal and congruent

Step-by-step explanation:

equal and congruent

Answer:

116200

Step-by-step explanation:

10x10x10x8.3x14=116200

Sorry if wrong :(

Answer:

Its C

Step-by-step explanation:

Answer:

[tex]\left[\begin{array}{ccc}11&15&-17\\-1&-4&-4\\17&15&-22\end{array}\right][/tex]

Option D will be your answer

[tex]-----------[/tex]

hope it helps...

have a great day!!

Answer:

20 cubic inches

Step-by-step explanation:

Answer:

7/8 pounds

Step-by-step explanation:

pounds collected in a day = number of pounds collected in 8 days / number of days

7/8

Answer:

370+150+150+100+30=800

Step-by-step explanation:

Answer:

2(4a - 4b) + 4(3a + 2b) = 20a

Step-by-step explanation:

2(4a - 4b) + 4(3a + 2b)

8a - 8b + 12a + 8b

8a + 12b - 8b + 8b

20a+ 0 = 20a

Thus, 2(4a - 4b) + 4(3a + 2b) = 20a

-TheUnknownScientist

Answer:

(3)

(4)

Step-by-step explanation:

but I could be wrong

Answer:

The school was open for 240 days

Step-by-step explanation:

216 / x = 90%/100%

216*100= 21,600

21,600/90 = 240

Answer:

this question is a bit confusing.

Step-by-step explanation:

here's what I think is the answer

9x-6=6x+9

3x=15

x=5

Answer:

The answer is B

Step-by-step explanation: yo mum u dont need one

Answer:

Your answer is b

Step-by-step explanation:

Step-by-step explanation: None

Answer:

c. 2000 meters per hour

Answer:

24 slices of pizza were available to be eaten

Step-by-step explanation:

Here, we want to get the number of slices of pizza available to be eaten

From the question;

a slice is 1/6 of a pizza

So the number of slices in a full pizza would be 1 divided by 1/6 = 1* 6/1 = 6 slices

In each of the pizzas, there were 6 slices;

So the number of slices in 4 pizzas would be 6 * 4 = 24 slices

So, 24 slices of pizza were available to be eaten by the girls

Answer:

[tex]\displaystyle \angle A=30^\circ[/tex]

Step-by-step explanation:

We are given that in Circle O, Arc BAC measures 300°.

Recall that arc lengths will always total 360°. Therefore:

[tex]\stackrel{\frown}{BAC}+\stackrel{\frown}{CB}=360^\circ[/tex]

By substitution:

[tex]300+\stackrel{\frown}{CB}=360[/tex]

Thus:

[tex]\stackrel{\frown}{CB}=60^\circ[/tex]

∠A intercepts Arc CB. Since it is an inscribed angle, it will be half of its intercepted arc. In other words:

[tex]\angle A=\displaystyle \frac{1}{2}\stackrel{\frown}{CB}[/tex]

Therefore:

[tex]\displaystyle \angle A=\frac{1}{2}(60)=30^\circ[/tex]

Answer:

C. his conclusion represent correlation and causation

Answer:

Follows are the responses to this question:

Step-by-step explanation:

[tex]H_O: \mu=220\\\\H_a:\mu \neq 220\\\\[/tex]

0.05 degree of significance for two tail tests and n-1= 9 df, critica t= 2.262

When the absolute value of the test statistic |t| >2.262, the decision rule rejects[tex]H_0[/tex].

[tex]\mu=220\\\bar{x}=228.200\\n=10.00\\smaple \ std \ deviation = 18.200\\std\ error \ ' sx= \frac{s}{\sqrt{n}} =5.7553\\test stat t=\frac{(x-\mu) \times \sqrt{n}}{sx}=1.4248\\p value=0.1880\\[/tex]

In point c:

It does not reject[tex]H_0[/tex], because it has the sample that not contradicts the manufacturer's claim

In point d:

For point 1:  

The value of p is 0.1880 , that is higher than the 0.05

For point 2:

Yes

Answer:

m<PRQ=15°

Step-by-step explanation:

so we're given that PQ and RQ are sides of a regular 12-sided polygon (dodecagon)

a regular polygon is a polygon that has all angles be the same measure AND have all sides be the same length

because of that, PQ=RQ, and ΔPQR is isoceles

now we need to find what the question is asking for: m<PRQ

because of base-angles theorem, m<PRQ=m<RPQ

we need to find m<PQR

a dodecagon is 1800° in measure

and we need 1/12th of that measure, since <PQR is 1 out of the 12 interior angles on the dodecagon (a dodecagon has 12 vertecies, so 12 angles). Also because the polygon is regular, every interior angle has the same measure.

so find the measure of <PQR

<PQR= 1/12*1800=150°

now to find the measure of <PRQ:

there are 180° in a triangle

so subtract 150° from 180°

180°-150°=30°

30° is the sum of the base angles (<PRQ is one of the base angles in a triangle)

the base angles are the same measure, so that means the measure of <PRQ is 1/2 the measure of the sum of the base angles

therefore m<PRQ=15°

hope this helps!

Answer:

$13.31

Step-by-step explanation:

blehn  b;eoj

Answer:

$13.31

Step-by-step explanation:

First, take the original price and apply the discount of 20% by converting the percentage into a decimal (0.2)

16 x 0.2

= 3.2

Next, take away that amount from the original price

16 - 3.2

= 12.8

Now calculate the tax with the new price by converting the percentage into a decimal (0.04)

12.8 x 0.04

= 0.512

Finally, add the tax to the new amount

12.8 + 0.512

= 13.312

Round if necessary.

Answer:

150

Step-by-step explanation:

15 fail

90 percent pass

15=10 percent

135=90 percent

150

Step-by-step explanation:

90%passed

100%-90%=10% failed

10%=15 students

100%=x students

10x=1500

x=1500/10

x=150 number of students appeared in the exam.

Answer:

everything is in the picture

Answer:

42

Step-by-step explanation:

Area of parallelogram us 1/2 × bh

1/2 ×14×6

=42

Answer:

16

Step-by-step explanation:

From the question given above, the following data were obtained:

Sum of N term (Sₙ) = 292

2nd term (T₂) = 8.5

5th term (T₅) = 13

Number of terms (N) =?

Next, we shall determine the first term (a) and the common difference (d) of the series. This can be obtained as follow:

T₂ = a + d

8.5 = a + d ........ 1

T₅ = a + 4d

13 = a + 4d ........ 2

Subtract equation 1 from equation 2 i.e

(2) – (1)

.. 13 = a + 4d

– 8.5 = a + d

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

4.5 = 3d

Divide both side by 3

d = 4.5 / 3

d = 1.5

Substitute the value of d into any of the equation to obtain the value of a. Here, we shall use equation 1.

8.5 = a + d

d = 1.5

8.5 = a + 1.5

Collect like terms

8.5 – 1.5 = a

a = 7

Finally, we shall determine the number of terms as follow:

Sum of N term (Sₙ) = 292

Common difference (d) = 1.5

First term (a) = 7

Number of terms (N) =?

Sₙ = n/2[2a + (n – 1)d]

292 × 2 = n[(2 × 7) + (n – 1)1.5]

584 = n[14 + 1.5n – 1.5]

584 = n[12.5 + 1.5n]

584 = 12.5n + 1.5n²

Rearrange

1.5n² + 12.5n – 584 = 0

Using formula method, the value of n can be obtained as follow:

a = 1.5

b = 12.5

c = –584

n = –b ± √(b² – 4ac) / 2a

n = –12.5 ± √(12.5² – 4 × 1.5 × –584) / 2 × 1.5

n = –12.5 ± √(156.25 + 3504) / 3

n = –12.5 ± √(3660.25) / 3

n = –12.5 ± 60.5 / 3

n = –12.5 + 60.5 / 3 or –12.5 – 60.5 / 3

n = 4 /3 or –73 / 3

n = 16 or –73 / 3

Since the number of terms can not be negative, therefore, the number of term is 16