Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

Kindly help!​

Answer:

25

Step-by-step explanation:

2x+2+5x+3=180

7x=175

x=24

The equation which he have solved is [tex]10/x^{2} -1=15/3x-3[/tex] as in this 1 is the extraneous solution.

Given four equations in which first equation is [tex]10/x^{2} -1=15/3x-3[/tex],second is (x+2)/(x+3)=6x/8, third is (4x-4)/(x+6)=x-1/10, fourth is 4/x-1=x+2/10.

We have to find such a equation which have a valid solution and one extraneous solution.

We have to solve these equation:

[tex]10/x^{2} -1=15/3x-3[/tex]

The above exprssion is not defined for x=1 so 1 is an extraneous solution. Simplifying the above equation by doing cross multiplication.

10(3x-3)=15([tex]x^{2} -1[/tex])

30(x-1)=15(x-1)(x+1)   [We know that [tex]A^{2} -B^{2} =(A+B)(A-B)[/tex]

2=x+1

x=1

In the given equation 1 makes the denominator zero and 1 is the solution of the equation derived from cross multiplication.

Hence the correct equation which Sean solves is option A which is [tex]10/x^{2} -1=15/3x-3[/tex].

Learn more about equation at https://brainly.com/question/2972832

#SPJ4

The given question is incomplete as it should include the given figure.

Answer:see photo #15

Step-by-step explanation:

Options 1, 3 and 5. The true statements based on the fact that c and d are parallel are:

The sum of the angles m<4 + m<3 = 180

m<4 + 82 = 180

m<4 = 180 - 82= 98

From the question we have the first as alternate interior angles. The second is corresponding angles and the last option is vertical angles.

Read more on angles here:

https://brainly.com/question/26033691

#SPJ1

The equation that is true and one that matches the set of ordered pairs of functions is option C. f (0) = 6

Note that a function can be made to be a given set of ordered pairs such as the ordered pairs (2,4), (3,5), (4,6)  can have  input functions of ​​(as domain) 2,3,4 and output functions of ​​(as range) of 4,5,6.

So when you see the ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2, –1)} one can see that the option that matches to the set of ordered pairs of functions above is f (0) = 6 value x = 0, f (x) = y = 6, ordered pairs (0.6)

See full question below

The function f (x) is given by the set of ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2, –1)}:Which equation is true?

f(-10)=1

f(2)=-10

f(0)=6

f(1)=-10

The answer choices are :

f (-10) = 1 values ​​x = -10, f (x) = y = 1, ordered pairs (-10,1)

f (2) = - 10 values ​​x = 2, f (x) = y = -10, ordered pairs (2, -10)

f (0) = 6 value x = 0, f (x) = y = 6, ordered pairs (0.6)

f (1) = - 10 values ​​x = 1, f (x) = y = -10, ordered pairs (1, -10)

Learn more about ordered pairs from

https://brainly.com/question/6200217

3SPJ1

Reason:

These angles are both in the same corresponding direction. Both are in the same western corner, or point to the west. If the lines were parallel, then the corresponding angles would be congruent.

The simplest form of the given algebraic expression √(250c³/9d⁶) is; 5c * (√10c)]/3d³

We are given the algebra problems as;

√(250c³/9d⁶)

Now 250c³ can be broken down into 250 = 25c² × 10c

Thus, we now have;

√(250c³/9d⁶) = [√(25c²) * (√10c)]/√9d⁶

When we breakdown the above expression, we have;

5c * (√10c)]/3d³

Read more about Algebra Problems at; https://brainly.com/question/723406

#SPJ1

Answer:

the answer is a

Step-by-step explanation:

i got it right

The pair of equations that has (0, 8) as its solution is: A. equation A and equation C.

The solution to a system of linear equations that are graphed is the pair of x and y coordinates of the points where two lines intersect.

In the graph given, the lines representing equations A and C intersect at point (0, 8). Therefore, the pair of equation that has a solution of (0, 8) is: A. equation A and equation C.

Learn more about solution of a system of equations on:

https://brainly.com/question/847634

#SPJ1

The difference is 2003.

The formula for the sum of the first n even numbers is SE = n^{2} + n, (E standing for even).

The sum of the first n odd numbers is SO = n^{2}, (O standing for odd).

Knowing this, plug 2003 for n,

SE - SO= (2003^{2} + 2003) - (2003^{2}) = 2003

The difference is 2003.

A number that can be divided into two halves, i.e. into two equal parts is called an even number. Even numbers are exactly divisible by 2 which means the remainder will be 0.

Learn more about Even numbers here: https://brainly.com/question/251701

#SPJ4

Answer:

the graph is symmetric about the line y=-1

Step-by-step explanation:

A function is symmetric about y=a when the following is true for all points: f(a-x) = f(a+x). By just looking at the graph, it appears to be symmetric about y=-1, and it can be further proven, by finding the difference of two points, that have the same y-value. So for example if you look at (0, 1) and (-2, 1). The difference between 0 and -1 is 1, and the difference between -2 and -1, is also 1. And this appears to be true for all the other values as well. So the graph is symmetric about the line y=-1

Answer:

The graph is symmetric about the line x=-1

Step-by-step explanation:

Since

[tex]17^a = 16 = 4^2 \implies 17^{a/2} = 4[/tex]

it follows that

[tex]17^b = 4 \implies 17^{a/2} = 17^b \implies \dfrac a2 = b \implies a = 2b[/tex]

Then

[tex]2^{a - b} = 2^{2b - b} = 2^b[/tex]

so that

[tex]\dfrac1{2^{a-b}} = 2^{-b}[/tex]

We also have

[tex]17^b = 4 \implies b = \log_{17}(4)[/tex]

so we can go on to say

[tex]\dfrac1{2^{a-b}} = \boxed{2^{-\log_{17}(4)}}[/tex]

Answer: 48 and 12.

Step-by-step explanation:

Let the smaller number is x. Hence, the larger number is 4*x.

The difference between 2 number is 36.

So,

4*x-x=36

3*x=36\ |:3

x=12.

4*x=12*4

4*x=48.

Good luck an' have a nice day!

As per my explanation to (b) above, the largest number of primes that could factor such a number is 4.

Note that  2,3,5 and 7   are the smallest primes, then use the reasoning from

(b) above. we are looking for four exponents, that, when 1 is added to each and all are multiplied together, would equal 20.

But no such integers  k, l, m, and n  exist such that (k + 1)(l + 1)(m + 1) (n + 1)  = 20 where k, l,m, and n ≥ 1 so this number, whatever it is, can't have 4 prime factors

Let's drop 7 out of the mix and suppose it has just 3 prime factors 2, 3, and 5 again we are looking for three exponents,  that, when 1 is added to each and all are multiplied together, would equal 20.  Put another way, we are looking for k, l and m ≥ 1   such that (k + 1)(l + 1)(m + 1) = 20

Note that the  only possibility here  is when we have 2 *2 *5  = 20 and the smallest possible product would be 2^(4 )* 3^(1) * 5^(1) =  2^4 * 3 * 5 = 240

Now......the only remaining possibility is  that this number is composed of the two smallest primes, 2 and 3,  and we are looking for  some k  and l ≥ 1 such that (k + 1)(l + 1) = 20 clearly, the only possibilities  are when k = 4 and l = 5, or vice-versa

So this number would factor as either 2^3 * 3^4   = 648  or 2^4 * 3^3 = 432 and both are > 240.

Learn more about positive integers at

https://brainly.com/question/1367050

#SPJ4

The line having the equation, y = -2x + 5, has a slope = -2, and y-intercept = (0, 5). Thus, option A is the best choice.

The slope of a line is the tangent of the angle that the line makes with the positive side of the x-axis.

The y-intercept of a line is the point at which the line intersects the y-axis.

The standard form of a line is y = mx + b, where m represents the slope of the line, and b represents its y-intercept.

In the question, we are asked to identify the slope and the y-intercept of the line whose equation is y = -2x + 5.

Comparing the given equation of the line, y = -2x + 5, with the standard equation of a line, y = mx + b, we can say that,

m = -2, and b = 5.

Representing b as an ordered pair, we get (0, 5), as b represents the y-intercept which is a point on the y-axis, where the x-coordinate is always equal to zero.

Thus, we get the slope = -2, and the y-intercept = (0, 5).

The option representing the answer is option A.

Learn more about the slope and the y-intercept of a line at

https://brainly.com/question/1479018

#SPJ4

Answer:

12.198

hope it helps

12.198

To round over 7 into 8, the ten-thousandth place needs to be 5 or over, and as we can see the ten-thousandth place is 5.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation/Question:}[/tex]

[tex]\mathbf{7n - (4n - 3)}[/tex]

[tex]\huge\textbf{Convert equation/question to:}[/tex]

[tex]\mathbf{= 7n - 1(4n - 3)}[/tex]

[tex]\huge\textbf{Solving the equation/question:}[/tex]

[tex]\mathbf{= 7n - 1(4n) - 1(-3)}[/tex]

[tex]\mathbf{= 7n - 4n + 3}[/tex]

[tex]\huge\textbf{Combine the like terms:}[/tex]

[tex]\mathbf{= (7n - 4n) + 3}[/tex]

[tex]\mathbf{= 7n - 4n + 3}[/tex]

[tex]\mathbf{= 3n + 3}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{3n + 3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

Brand A

Step-by-step explanation:

If you divide both brands to find how much one can costs, brand B costs more per can.

79 ÷ 3 = 26.34

87 ÷ 4 = 21.75

That being said, if brand B were to sell 4 cans instead of 3 it would be more than brand A's 4 cans. Brand A is cheaper than brand B would be.

Since the y-intercept b = 2, hence the equation of the line will be y = -x +2

The formula for calculating the slope of a line is expressed as:

Slope = y2-y1/x2-x1

Given the coordinate points  (0, 2) and (2, 0)

Slope = 0-2/2-0
Slope = -1

Since the y-intercept b = 2, hence the equation of the line will be y = -x +2

Learn. more on equation of a line here: https://brainly.com/question/18831322

#SPJ1

Answer:

c

Step-by-step explanation:

The sample size suggested by this statement is 664 option second is correct.

It is defined as an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]

Where   Z is the z-score at the confidence interval

            s is the standard deviation

            n is the number of samples.

At 99% confidence Z = 2.576

By using the MOE formula:

0.05 = 2.376×√(0.5(0.5)/n)

After calculating

n = 663.57 ≈ 664

Thus, the sample size suggested by this statement is 664 option second is correct.

Learn more about the Margin of error here:

brainly.com/question/13990500

#SPJ1

The probability that the colour changes, while she is watching, is 1/7

Concept: Event probability = number of favorite results /Total number of results

It is given that the traffic light runs repeatedly in the following time cycle: green for 30 seconds, then yellow at 3  seconds, and then red for 30 seconds.

This means that the traffic light passes through 63 seconds to complete one-time cycle.

It is also given that Leah chooses a random 3 second time interval to watch the light.

We should find the probability that the color changes while Leah is looking.

The green light will change after 30 seconds and after three seconds it will change to yellow light, that is at 33 second it is yellow and after another 30 seconds it will change to red light.

Now let time t=0

The light changes at three different times: t=30,t = 33 and t = 63

This means that the light will change if Leah watches at intervals [27,30]

, [30,33] or [60,63]

Since each interval is 3 seconds and there are 3 intervals, Leah will have a chance of 9 seconds.

That makes a total of 9 seconds out of 63

⇒Probability that Leah watches the color change=Number of seconds she watches/Total seconds

=9/63=17

∴ The probability that Leah observes the color change is 1/7

For more information about probability, visit https://brainly.com/question/24756209

#SPJ4

Answer:

The expression is 42-17-19 OR 42-(17+19).

Step-by-step explanation:

First, we can indicate that we can use subtraction because is giving them away for his birthday.

"He gave one each to the 17 students in his class and to the 19 students in the other third-grade class".

That represents taking away 17 and 19 means that it is subtracting them.

Hope this helps. (:

The required function (f/g)(x) is 3√4x/2x+3 where x ≠ -3/2

Given the functions;

f(x) = ∛4x

g(x) = 2x + 3

We want to find the resulting function (f/g)(x);

(f/g)(x) = f(x)/g(x)

Thus, (f/g)(x) = ∛4x/(2x + 3)

Restriction to the function occurs at the point where the denominator is equal to zero.

Thus;

2x + 3 = 0

2x = -3

x = -3/2

Thus, the required function (f/g)(x) is 3√4x/2x+3 where x ≠ -3/2

Read more about Restriction Function at; https://brainly.com/question/23718282

#SPJ1

Answer:

-1 <= x <= 1

Step-by-step explanation:

√((1-2x+x^2)+2-2x^2)

= √((1-x)^2 + 2*(1-x)(1+x) )

điều kiện là 1 - x > =0 và 1+x >=0

giải 2 bất phương trình trên ta thu đc kết ququả

Inequalities help us to compare two unequal expressions. The algebraic expression for fifteen more than n is at least 48 is n+15 ≥ 48; n≥33. Thus, the correct option is C.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The given statement "fifteen more than n is at least 48" can be written in the form of an algebraic expression as,

n+15 ≥ 48

Solving the inequality,

n ≥ 48 - 15

n  ≥ 33

Hence, the algebraic expression for fifteen more than n is at least 48 is n+15 ≥ 48; n≥33. Thus, the correct option is C.

Learn more about Inequality:

https://brainly.com/question/19491153

#SPJ1

Answer:

Step-by-step explanation:

exterior angle of a polygon = 360° ÷ number of sides

71% is the required probability here.

What is a probability simple definition?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

                                        The probability serves as a gauge for the possibility that an event will occur. and a The probability equation is stated by the following notation: P(E) = Number of Favorable Outcomes/Number of Total Outcomes.

The number of customers out of 5 who agree to take the survey here could be modelled as a binomial distribution given as

 x ` Bin (n = 5 , p = 0.22 )

Thus the probability here is computed as

P(X≥ 1) = 1 - P(X = 0) = 1 - (1 - 0.22)⁵

           = 0.71 %

Therefore 71% is the required probability here.

Learn more about probability

brainly.com/question/30034780

#SPJ1

(4x + 5)(3x + 10) or 12x² + 55x +50

Forming the Expression for the Area of Rectangle

The formula for the area of a rectangle is given as,

Area, A = length × breadth

Here, the dimensions of the rectangle are given as,

length = (4x + 5)

breadth = (3x + 10)

∴ The equation for the area of the rectangle is,

A = (4x + 5)(3x + 10)

A = 12x² + 55x +50

Hence, 12x² + 55x +50 is the required expression.

Degree and Classification of the Expression

The highest power of a variable that is present in an expression is known as its degree.

Since the degree of the expression formed in part a is 2, it is classified to be a quadratic expression.

Closure Property For Polynomials

When the output is the same kind of object as the inputs, an expression is said to be closed. The expression obtained for the area of the rectangle is a combination of constants and variables closed under multiplication and addition.

Hence the expression formed in part a indicates at the closure property for polynomials.

Learn more about an expression here:

https://brainly.com/question/14083225

#SPJ4

The coordinates of the endpoints of line segments T'V' are; T'(-1, 2) and V'(0, 1).

It follows from the task content that the transformation involved in the formation of the image from the pre-image is dilation by a scale factor of 1/4.

On this note, given that the coordinates of T and V from the task content are; (-4, 8) and (0,4), it follows that the coordinates of the endpoints as required are; T'(-1, 2) and V'(0, 1).

Read more on dilations;

https://brainly.com/question/3457976

#SPJ1

Answer:

2511

Step-by-step explanation:

These problems are solved using the trigonometric function. Trigonometric functions provides the ratio of different sides of a right-angle triangle.

The trigonometric function refer to function that are periodic in nature and which lend insight to the relationship between angles and the sides of a triangle that is right angled.

The solutions to x in the respective problems is given as follows:

1st.) x = 5 /Sin(30°)

x = 10

!) sin(45°) = 4/x

x = 4/sin(45°)

x = 4√2

I) Cos(45°) = √3 / x

x = √3 / Cos(45°)

x = √6

E) Tan(60°)

= (3√3) / x

x = (3√3) / 3

W) It is to be noted that for right-triangle that is isosceles in nature, the angle made by the legs and the hypotenuse is always 45°.

x = 45°

N) x² + x² = (7√2)²

x = 7

V) Tan(60°) = 7 / x

x = 7√3/3

K) x² + x² = (9)²

x = 9/√2

Y) Sin(60°) = 7√3/x

x = 14

M) Sin(30°) = x/11

x = 11/2

T) Sin(45°) = x/√10

x = √5

A) x + 2x + 90° = 180°

x = 30°

O) Sin(45°) = √2 / x

x = 2

R) Tan(30°) = x / 4

x = 4/√3

= 4√3 / 3

S) Sin(60°) = x / (10/3)

x = (5√3) / 3

Learn more about Trigonometric functions at:
https://brainly.com/question/1143565
#SPJ1