What is the solution to the system of equations?

Answer:

x= 4

[tex]perpendicular (p) = \sqrt{x} + 1[/tex]

[tex]base(b) = 2 \sqrt{x} [/tex]

[tex]hypotenuse(h) = 2 \sqrt{x} + 1[/tex]

According to the Pythagoras Theoram,

p²+b²= h²

[tex] {( \sqrt{x } + 1) }^{2} + {(2 \sqrt{x} )}^{2} = {(2 \sqrt{x} + 1)}^{2} [/tex]

Answer:

4

Step-by-step explanation:

2√x, √x + 1, 2√x + 1 sides of triangle

√x= y

2y, y+1, 2y+1

(2y)²+(y+1)²= (2y+1)²

4y²+y²+2y+1= 4y²+4y+1

y²-2y=0

y=0 (discarded as side can't be zero) or y= 2

so √x=2 ⇒ x= 4

Answer:

the independent variable is 32 (price of the car in dollars) as it stands alone without a variable and 1.95 is the dependent (cost per mile)

Answer: The answer is B I believe

Step-by-step explanation:

Answer:

y-intercept : (0,5), D

axis of symmetry : x = 3, E

Answer:

4 sets

Step-by-step explanation:

1 gallon contains 8 pints. It takes 2 pints per table, so we should divide 8 by 2.

By doing this, we get 4, therefore he can stain 4 sets of tables with a gallon of stain.

Answer:

The answer is; the snail moved 1 inch every 20 minutes.

Step-by-step explanation:

120 divided by 6 is 20

Answer:

A) 1 Over 20 of an inch per minute

Step-by-step explanation:

I took this test and got 100

Answer:

4

Step-by-step explanation:

Multiples of 7 and 3 are 21, 42, 63, 84

Hope this helps.

Answer:

21, 42, 63, 84

Step-by-step explanation:

Cards with both star and circle are multiples of both 3 and 7, ie 3*7= 21

21, 21*2= 42, 21*3= 63, 21*4= 84

So 21, 42, 63 and 84 are the required numbers

Answer:

U = x^2

hope this helped!

Answer:

x^2

Step-by-step explanation:

The person above me is spitting mad facts and da TRUTH and also UNUS ANNUS

Answer:

5.75 feet is the same as 5 ft 9 inches (because 12 in = 1 ft and 0.75 * 12 = 9 so its 9 in). 7 ft 10 in - 5 ft 9 in = 2 ft 1 in.

Answer:16

Step-by-step explanation:

32/16=2

8*2=16

Hope that helps :D

Answer:

16

Step-by-step explanation:

Direct variation

y = kx

16 = k*8

Divide each side by 8

16/8 = 8k/8

2 = k

The equation is y =2x

y =2x

Let y =32

32 = 2x

Divide by 2

32/2 = x

16 =x

Answer:

V = 200 pi units ^3

Step-by-step explanation:

The volume of a cone is given by

V = 1/3 pi r^2 h

V = 1/3 pi ( 10 ^2) (6)

V = 1/3 pi (100) *6

V = 200 pi

Answer:

Option (3)

Step-by-step explanation:

Explicit formula of the sequence is,

[tex]a_n=3^n+4[/tex]

From this explicit formula,

First term of the sequence will be,

[tex]a_1=(3^1)+4[/tex]

[tex]a_1=7[/tex]

Second term of the sequence,

[tex]a_2=(3^2)+4[/tex]

[tex]a_2[/tex] = 13

3rd term of the sequence,

[tex]a_{3}=(3^3)+4[/tex]

   = 31

Sequence formed,

7, 13, 31 ..........

From the given options,

Recursive formula,

[tex]a_n=3a_{n-1}-8[/tex]

[tex]a_2=3(a_1)-8[/tex]

[tex]a_2=3(7)-8[/tex]

[tex]a_2=21-8[/tex] = 13

[tex]a_3=3a_2-8[/tex]

[tex]a_3=3a_2-8[/tex]

[tex]a_3=3(13)-8[/tex]

    = 39 - 8

    = 31

Sequence formed from this recursive formula will be,

7, 13, 31........

Therefore, Option (3) will be the answer.

Answer:

C

Step-by-step explanation:

i took the test

Answer:

Step-by-step explanation:

Assume that the two prisms have bases of equal area.

Then the volume of the rectangular prism is V = (base area)(height).

The volume of the triangular prism is V = (1/3)(base area)(height)

We could compare the two volumes by creating the ratio inequality

  (1/3) (base area)(t-height)

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

      (base area)(r-height)

The triangular prism will have the greater volume for (1/3)((t-height) > r-height.

Answer:

The price at the end of the week is $33.

Step-by-step explanation:

We are given that on Monday the price of a company’s stock is $30 per share. On Tuesday, the stock price drops $3, on Wednesday it rises $7, on Thursday it rises $3, and on Friday it drops $4.

The price of a company’s stock on Monday = $30 per share

So, the mathematical statement that represents the situation is given by;

Price of company’s stock on Monday = $30

On Tuesday, the stock price drops $3, so the price of company’s stock on Tuesday = Price of company’s stock on Monday - Drop in price on Tuesday

              = $30 - $3 = $27

On Wednesday, the stock price rises $7, so the price of company’s stock on Wednesday = Price of company’s stock on Tuesday + Rise in price on Wednesday

              = $27 + $7 = $34

On Thursday, the stock price rises $3, so the price of company’s stock on Thursday = Price of company’s stock on Wednesday + Rise in price on Thursday

              = $34 + $3 = $37

On Friday, the stock price drops $4, so the price of company’s stock on Friday = Price of company’s stock on Thursday - Drop in price on Friday

              = $37 - $4 = $33

Hence, the price at the end of the week is $33.

Answer:

3(3+4n)

Step-by-step explanation:

Answer:

173.6

Step-by-step explanation:

0.7(248)

173.6

Answer:

£ 173.6

Step-by-step explanation:

£248 *0.30= 74.4

£248 -74.4 =173.6

Answer:

Step-by-step explanation:

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Where

r represents the radius of the cylinder

h represents the height of the cylinder

π is a constant

The formula for determining the volume of a cone is expressed as

Volume = 1/3πr²h

Where

r represents the radius of the cone

h represents the height of the cone

This means that the volume of the cone is 1/3 × volume of cylinder. Since the volume of the given cylinder is 230 cubic units, then

Volume of cone = 1/3 × 230 = 76.7 cubic units

Answer:

[tex]\frac{x+6}{x}[/tex]

Step-by-step explanation:

=> [tex]\frac{x^2+4x-12}{x^2-2x}[/tex]

=> [tex]\frac{x^2+6x-2x-12}{x(x-2)}[/tex]

=> [tex]\frac{x(x+6)-2(x+6)}{x(x-2)}[/tex]

=> [tex]\frac{(x-2)(x+6)}{x(x-2)}[/tex]

Cancelling (x-2)

=> [tex]\frac{x+6}{x}[/tex]

Answer:

Step-by-step explanation:

85% of 2500 m

= 85/100 × 2500 = 2125 m

hope this helps

plz mark it as brainliest!!!!!!

Answer:

2125

Step-by-step explanation:

85% times 2500

I belive,

The experimental probability could be more, the same or less than the theoretical probability of rolling a 1 (which is 1/6).  

The larger your sample (i. e., as you go beyond 60 tosses), the closer the two different probabilities are likely to be.  (Think:  Law of Large Numbers).

Answer:

Step-by-step explanation:

Jsiehsjsndj im here to get you a brainliest

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Just stick it into a calculator lol

The answer is step 2. hope it helps.

Answer:

step 2

Step-by-step explanation:

Answer:

3018

Step-by-step explanation:

an = a1 + (n-1)d

a1 is the first term in the sequence = 24

n is the term number which is 500

d is the common difference

Take the second term and subtract the first term to find the common difference

d = 30-24 = 6

a500 = 24 + (500-1) *6

          =24+ 499*6

          =24 + 2994

          =3018

Answer:

3018 is the correct answer.

Answer:

3375/13

Step-by-step explanation:

it's found though this equation  [tex]\frac{84375/25}{325/25}[/tex]

Answer:

[tex]3375/13[/tex]

Step-by-step explanation:

[tex]84,375/325[/tex]

Divide the numerator and denominator by 25.

[tex]3375/13[/tex]

[tex]=259.615385[/tex]

Answer:

C

Step-by-step explanation:

The diagonals of a rhombus are perpendicular bisectors of each other.

Thus the angle at the intersection of the diagonals is 90°

The sum of the 3 angles in a triangle = 180°

Sum the angles in the lower triangle and equate to 180, that is

90 + x + x + 40 = 180

2x + 130 = 180 ( subtract 130 from both sides )

2x = 50 ( divide both sides by 2 )

x = 25 → C

The value of x is 25.

What are some of the properties of a rhombus?

Given

ABCD is a rhombus,

∠CAD = x°,

∠BDA = (x + 40)°.

Find the equation in x

Let the point where the diagonals intersect be E.

Then, using the property of the rhombus ∠AED = 90°.

We know, in a triangle that the sum of all the three interior angles equals 180°. So, we get,

     ∠AED + ∠BDA + ∠CAD = 180°

⇒                 ∠BDA + ∠CAD = 180° - ∠AED

                                                = 180° - 90° = 90°      (∠AED = 90°)

Put the given values of these angles,

          (x + 40)° + x° = 90°.

This is the equation to be solved to obtain x.  

Solve for x  

           (x + 40)° + x° = 90°

⇒   (2x)° = 90° - 40° = 50°

⇒         x° = (50 / 2)°

⇒         x = 25.

The required value of x is 25.

Learn more about the properties of a rhombus here

https://brainly.com/question/12189679

#SPJ2

Answer:

The correct option is;

(B) 30

Step-by-step explanation:

The equations are;

x² - 2·m·x - 5·n = 0.............(1)

Solution = p, q

x² - 2·p·x - 5·q = 0..............(2)

Solution = m, n

For equation (1), we have;

x² - 2·m·x - 5·n = 0 = (x - p)·(x - q)

x² - 2·m·x - 5·n = x² -x·p - x·q + q·p = x² -x·(p + q) + q·p

2·m = p + q..............(3)

5·n = -q·p..............(4)

Given the similarity between equation (1) and (2), we have;

2·p = m + n..............(5)

5·q = -m·n..............(6)

Therefore;

m = (p + q)/2

n = -q·p/5

Substituting the value of m and n in equation (5) and (6), we have;

2·p = (p + q)/2  - q·p/5.............(7)

5·q = (p + q)/2·q·p/5.............(8)

Making q the subject of equation (7) gives;

[tex]q = \dfrac{-7.5 \cdot p}{p -2.5}[/tex]

Substituting the value of q above in equation (8) gives;

[tex]-\dfrac{75\cdot p}{2\cdot p-5}=-\dfrac{3\cdot p^{4}-30\cdot p^{3}}{4\cdot p^{2}-20\cdot p+25}[/tex]

By cross multiplying and collecting like terms we have;

6·p⁵ -75·p⁴-150·p³+1500·p²-1875·p = 0

Which gives

(p+0)(p-1.91)(p-2.5)(p+5)(p-13.1)

p = 1.91 or 2.5 or -5 or 13.1

q = 24.27 or undef or -5 or -9.27

m = 13.09 or undef or -5 or 1.95

n = -9.27 or undef or -5 or -24.29

Therefore, p + q + m + n = 1.91 + 24.27 + 13.09 + (-9.27) = 30

The correct option is (B) 30

Answer:

x = -2

y = 4

Step-by-step explanation:

6x-5y=-32

-7x+8y=46

Solve for x in the first equation.

6x = -32 + 5y

x = (-32 + 5y) /6

x = 5/6y - 16/3

Put x as 5/6y - 16/3 in the second equation and solve for y.

-7(5/6y - 16/3) +8y = 46

-35/6y+112/3 +8y = 46

13/6y + 112/3 = 46

13/6y = 46 - 112/3

13/6y = 26/3

y = 26/3 × 6/13

y = 4

Put y as 4 in the first equation and solve for x.

6x-5(4)=-32

6x-20 = -32

6x = -32+20

6x = -12

x = -12/6

x = -2

Answer:

The first term as 2.

Pattern: Multiply the previous term and 2 to get the next term.

Step-by-step explanation:

The pattern is every term is 2× the previous term.

The sequence of the differences, 2, 4, 8, 16, 32, … is geometric. The pattern is every term is 2 times the previous term.

The geometric series is a series in which the ratio of two consecutive numbers is constant.

The sequence of the differences, 2, 4, 8, 16, 32, … is geometric.

So, The ratio of two consecutive numbers is constant.

r = 4/2 = 2

r = 8/4 = 2

Thus, The pattern is every term is 2 times the previous term.

Learn more about geometric series;

https://brainly.com/question/13041183

#SPJ2

Answer:

1. y = -2n + 9

2. y = (1/2)x + 1/2

Step-by-step explanation:

1.

The equation of a line is denoted by y = mx + b, where m is the slope and b is the y-intercept.

Slope is calculated by taking two coordinates and dividing the difference of the y-coordinates by the difference of the x-coordinates. The y-intercept is where the line intersects the y-axis.

Let's choose any two points on the line: (4, 1) and (3, 3). Then:

slope = m = (3 - 1) / (3 - 4) = 2 / (-1) = -2

Now, we can also see that at the point (0, 9), the line intersects the y-axis, so that means b = 9.

The equation is thus y = -2n + 9.

2.

Let's again choose any two points to find the slope: (1, 1) and (3, 2). Then:

slope = m = (2 - 1) / (3 - 1) = 1/2

We can see that the line crosses the y-axis at the point (0, 1/2), so that means b = 1/2.

The equation is thus y = (1/2)x + 1/2.

~ an aesthetics lover

Answer:

1. y = -2x + 9

2. y = (1/2)x + 1/2

Step-by-step explanation:

There was a mistake on the last one so I would like to correct it it is

y= -2x+9

The other one said -2n its -2x

19

Step-by-step explanation:

The first term of the arithmetic sequence is  4x+3.

An ordered group of numbers with a shared difference between each successive term is known as an arithmetic sequence.

The formula to find the nth term of an arithmetic sequence is,

aₙ= a+(n-1)d

Where a is the 1st term and d is the common difference.

Let the first term of sequence is a and the common difference is d.

Given that,

The 5th term of the arithmetic sequence = 16x+11,

⇒ a+4d= 16x+11      (1)

And the 9th term of the arithmetic sequence = 28x+19,

⇒ a+8d= 28x+19    (2)

To find the first term of the sequence, multiply equation (1) with 2 and subtract equation (2) from it.

(2a+8d)-(a+8d) = (32x+22) - (28x+19)

a = 4x+3

The first term of the arithmetic sequence is  4x+3.

To know more about Arithmetic sequence on :

https://brainly.com/question/1452631

#SPJ2

Answer:

<x = 36°

Step-by-step explanation:

In a regular decagon, Every interior angles is equal to 144.

So,

<x + 144 = 180 [Angles on a straight line]

<x = 180-144

<x = 36°