a = √7 + √c and b = √63 + √d where c and d are positive integers.
Given that c: d = 1: 9
find, in its simplest form, the ratio a: b

Answers

Answer 1

Answer:

[tex]\displaystyle a:b=\frac{1}{3}[/tex]

Step-by-step explanation:

Ratios

We are given the following relations:

[tex]a=\sqrt{7}+\sqrt{c}\qquad \qquad[1][/tex]

[tex]b=\sqrt{63}+\sqrt{d}\qquad \qquad[2][/tex]

[tex]\displaystyle \frac{c}{d}=\frac{1}{9} \qquad \qquad [3][/tex]

From [3]:

[tex]9c=d[/tex]

Replacing into [2]:

[tex]b=\sqrt{63}+\sqrt{9c}[/tex]

We can express 63=9*7:

[tex]b=\sqrt{9*7}+\sqrt{9c}[/tex]

Taking the square root of 9:

[tex]b=3\sqrt{7}+3\sqrt{c}[/tex]

Factoring:

[tex]b=3(\sqrt{7}+\sqrt{c})[/tex]

Find the ration a:b:

[tex]\displaystyle a:b=\frac{\sqrt{7}+\sqrt{c}}{3(\sqrt{7}+\sqrt{c})}[/tex]

Simplifying:

[tex]\boxed{a:b=\frac{1}{3}}[/tex]


Related Questions

What is the y-intercept of the function below? Y=4x+4 (15 Points!)

Answers

The answer is 4. Remember y=mx+b. B is always the y intercept

Answer:

y- intercept = 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x + 4 ← is in slope- intercept form

with y- intercept c = 4

$27,200 at 9% compounded annually for 2 years

Answers

Answer:

A = $32316.30

Step-by-step explanation:

Simple Interest Rate Formula: A = P(1 + r)ⁿ

Step 1: Define variables

Principal amount P = 27200

Rate r = 9% or 0.09

Number of years n = 2 years

Step 2: Substitute and Evaluate for A

A = 27200(1 + 0.09)²

A = 27200(1.09)²

A = 27200(1.1881)

A = 32316.30

-20=-4x-6x solve this ??

Answers

Answer:

2=x

Step-by-step explanation:

-20=-4x-6x  combine -4x+(-6x)

-20=-10x   divide by -10

2=x

Answer:

answer is 2

Step-by-step explanation:

-20=-4x-6x  combine like terms

-20=-10x   divide

2=x

Gemma, a scuba diver, begins a dive on the side of a boat 4 feet above sea level. She descends 28 feet. Which integer represents Gemma’s position with respect to sea level?
–32
–24
24
32

Answers

Answer:

The answer is -24

Step-by-step explanation:

Because she was 4 feet above to begin with so 4-28=-24

Her current position is -32 because she descended 28 more than her current position earlier

5. During the football game, Justin caught three passes. One was for a touchdown and went 52 yards. The other was for a first down and was for 17 yards. The other was on a screen pass that did not work so well and ended up a gain of -10 yards. What was the total yardage gained by Justin on the pass plays?​

Answers

Answer:  59

Step-by-step explanation:

 +52 + 17 - 10

=       69   - 10

= 59

                        [tex]\huge\boxed{Your\;answer\;is\;59!}[/tex]

First, let's add [tex]52[/tex] and [tex]17[/tex].

[tex]52+17=69[/tex].

Next, we subtract [tex]10[/tex].

[tex]69-10=59[/tex].

Therefore, our final answer is [tex]59[/tex].

3. Which expression is not equivalent to mn + 5?
A. nm + 5 B. 5n + m C. 5 + mn D. 5 + nm

Answers

Answer: it is B. 5n + m

Step-by-step explanation: it is because 5 is not being multiplied by anything so it is incorrect.

The answer is B

Give thanks to this if ur from the UK

Probaly you all are American

Solve for x. 7 + 11x + 60 = -13 + 3x

Answers

Answer:

x = -10

Step-by-step explanation:

Step 1: Write equation

7 + 11x + 60 = -13 + 3x

Step 2: Solve for x

Combine like terms: 11x + 67 = -13 + 3xSubtract 3x on both sides: 8x + 67 = -13Subtract 67 on both sides: 8x = -80Divide both sides by 8: x = -10

Step 3: Check

Plug in x to verify it's a solution.

7 + 11(-10) + 60 = -13 + 3(-10)

67 - 110 = -13 - 30

-43 = -43

help asap
[tex]i \: dont \: understant[/tex]
please help​

Answers

Answer:

The answer is 5.8 km

Step-by-step explanation:

Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side c

Using Pythagoras theorem we have

c² = b² + a²

where

c is the hypotenuse

So we have

[tex] {c}^{2} = {5}^{2} + {3}^{2} \\ c = \sqrt{ {5}^{2} + {3}^{2} } \\ c = \sqrt{ 25 + 9} \\ c = \sqrt{34} \: \: \: \: \: \: \: \: \\ = 5.83095189...[/tex]

We have the final answer as

5.8 km to the nearest tenth

Hope this helps you

How do you solve linear equations (short definition)

Answers

Answer:

by moving x's onto one side and the constants to the other

Step-by-step explanation:

hope that helps

Which statement is true about the end behavior of the graphed function?

As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero
As the x-values go to positive infinity, the function's values go to positive infinity.

Answers

Answer:

(SEE EXPLANATION FIRST)

Answer D is TRUE because on the graph if you were to keep going left even after the picture of the graph ends, the graph will still keep going up infinite

Step-by-step explanation:

If this is the graph you can read the answer

Answer:

A.

As the x-values go to positive infinity, the function's values go to negative infinity.

Step-by-step explanation:

Someone please help me!!

Answers

Answer:B and E

Step-by-step explanation:

Which of the following is an equation of the line through (2, 3) and (-1, -12)?

Answers

Answer:

y = 5x - 7

Step-by-step explanation:

First point coordinates

x₁

2

y₁

3

Second point coordinates

x₂

-1

y₂

-12

Result

Slope (m)

5

m = -15 / -3 = -5 / -1 = 5

Your function

The entered points belong to an increasing, linear function.

Equation: y = 5x - 7.

Hope i helped :)

Solve for x.
2(-x + 4) – 3x + 2 = -5

Answers

Answer:

x=3

Step-by-step explanation:

2(-x + 4) – 3x + 2 = -5

-2x+8-3x+2=-5

-5x+10=-5

-5x=-15

x=3

X=3
If you need to show work I have no problem with putting it in the comments :)

A mechanic used 49 quarts of oil to change the oil in 7 cars. At this rate, how much oil would he use to change ths oil in 17 cars

Answers

Answer:

139 quarts

Step-by-step explanation:

Answer:

The mechanic would use 139 quarts for the 17 cars.

If two quantitative variables are highly correlated, does that necessarily result in causation?

Answers

Answer:

not necessarily

Step-by-step explanation:

differentiation from first principles. please help! question is attached :)

Answers

Answer:

d

Step-by-step explanation:

SKSKSKSKKSKSKSKSKSKSKSKS​

Answers

Answer:

hydroflask :P

Hm. If p is true, then q is true, if p is false, than q is false.

So, the inverse must be true.

The converse doesn't have to be true at all, and same with the contrapositive if I'm correct.

Pretty sure it's just the inverse. :)

(please comment if I'm wrong! I'll be happy to learn!)

A car travels 32 km due north and then 46 km in a direction 40 degrees west of north. Find the magnitude of the cars resultant vector nearest tenth

Answers

Answer:

Step-by-step explanation:

In order to find the magnitude of the car's final displacement (resultant displacement vector), we need the x and y components of each part of the car's journey. We will call them vector A and vector B. The info for the vectors is as follows:

A: magnitude 32 at an angle of 90.0

B: magnitude 46 at an angle of 40.0

The x components are found in the formula

A(x) = magA*cos(angle)

For A(x):

A(x) : 32cos(90.0) = 0.0 and

For B(x) : 46cos(40.0) = 35.2

For A(y): 32sin(90.0) = 32 and

For B(y): 46sin(40.0) = 3.0 × 10¹

To get the x components of the final vector, add the x components of A and B together:

C(x) : 0.0

       35.2

       35.2

To get the y components of the final vector, add the y components of A and B together:

C(y) :  32

         30

         62

Now to get the magnitude, throw it into the magnitude formula, which is identical to Pythagorean's theorem:

C(mag) = [tex]\sqrt{(35.2^2)+(62^2)}=71.3 km[/tex]

PLS HELP !!!!!!
Tell me the integers pls ! ASAP !

Answers

Answer:

-3 is the integer

4 would be greater than -3

what is the value of x 5x + 8

Answers

Answer:

2.3 is your answer sry if wrong

Step-by-step explanation:

Answer:

x=-3

Step-by-step explanation:

solve for x
(x/r)+(x/w)+(x/t)= 1

Answers

x/r + x/w + x/t = 1

x (1/r + 1/w + 1/t) = 1

x = 1 / (1/r + 1/w + 1/t)

To make the solution a bit cleaner, multiply through the numerator and denominator by the LCM of each fraction's denominator, rwt :

x = 1 / (1/r + 1/w + 1/t) • rwt / rwt

x = rwt / (rwt/r + rwt/w + rwt/t)

x = rwt / (wt + rt + rw)

Multiply. (2/5)(−5/4)

Answers

Answer:

-1/2 this is the answer

1
Domino's can make 4 pizzas using 3 1/2 cups of sauce. How many cups of sauce are needed to make 1

pizza?

Answers

7/8 or .875, that’s what I got

7/8 cups of sauce are needed to make 1 pizza.

What is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Domino's can make 4 pizzas using 3 1/2 cups of sauce.

Now, for 1 pizza he needed

= (3 1/2) /4

= (7/2)/ 4

= 7/2 x 1/4

= 7/8 cups of sauce.

Hence, 7/8 cups of sauce needed.

Learn more about Unitary Method here:

https://brainly.com/question/22056199

#SPJ2

A steel ball whose mass is 2.0 kg is rolling at a rate of 2.8 m/s. What is its momentum?



1) 1.4 kgm/s


2) .71 kgm/s


3) 5.6 kgm/s


4) 4.8 kgm/s

Answers

Answer:

mxv

Step-by-step explanation:

2.0x2.8=5.6

momentums equation is mass times velocity so 2.0kg is the mass and you multiply it by the velocity which is 2.8m/s and that is how you get your answer. your answer is number 3

3 minutes into hours

Answers

Answer:

ok

Step-by-step explanation:

John throws a ball upward at a rate of 22 meters per second from an
initial height of 3 meters. The height of the ball above the ground can
be approximated by h (t) = -16t2 + 22.0 + 3, where t represents
the amount of time, in seconds, since the ball has been released.
How many seconds will it reach the ground?

Answers

Answer:

  1.5 seconds

Step-by-step explanation:

The height equation is supposed to be ...

  h(t) = -16t^2 +22t +3

We want to find the positive value of t where h(t) = 0.

  0 = -16t^2 +24t -2t +3 . . . . facilitate factoring

  0 = -8t(2t -3) -1(2t -3) . . . . . factor by pairs

  0 = -(8t +1)(2t -3) . . . . . . . .  complete the factoring

The solutions to this are ...

  t = -1/8, 3/2

The ball will reach the ground in 1.5 seconds.

Solve the inequality. (hint: isolate the absolute value).
8 + |4v - 7| >17

Answers

Answer:

v <−1/2 or v >4

If angles are congruent, solve by setting expressions equal to each other.

True
False

Answers

Answer: True, angles that are congruent are equaled to each other

Which input has more than 1 output?

Answers

Answer: 4

Step-by-step explanation:

There are more than one 4

The input is 4 hope that helps

Evaluate 1/6 + 2/3. Can you please explain how you got your answer?

A. 3/18
B. 5/6
C. 1/5
D. 1 1/6

Answers

Answer:

5/6

Step-by-step explanation:

1/6 + 2/3

Get a common denominator of 6

1/6 + 2/3 *2/2

1/6 + 4/6

Add the numerators

5/6

Answer:

B

Step-by-step explanation:

1. Get the common denominator

2 × 2 = 4

_______ = (4/6)

3 × 2 = 6

(4/6)+(1/6)= 5/6

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