3
(a)
The highest common factor and lowest common multiple of two numbers are
2x 52 x 7 and 22 x 3x 57 respectively. If one of the numbers is 22 x 52 x7, find the
other number. Express your answer as a product of prime factors in index notation.
Find the smallest positive integer p such that 1125xp is both a perfect square
and perfect cube. Explain your answer.
(b)

Answer:

see the picture

Step-by-step explanation:

hope it helps you

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[tex]40\leq4v\\\\4v\geq40 \ \ /:4\\\\v\geq10\\\\\huge\boxed{v\in\langle10;+\infty)}[/tex]

Answer:

[tex]v\geq 10\\[/tex]

Step-by-step explanation:

Divide both sides by 4.

Flip

[tex](h \times \: g)(b) = (b - 1)^{2} (5b - 9) \\ = ( {b}^{2} - 2b + 1)(5b - 9) \\ = 5 {b}^{3} - 19 {b}^{2} + 23b - 9[/tex]

[tex](h \times \: g)( - 6) = 5( - 6) ^{3} - 19( { - 6}^{2}) + 23( - 6) - 9 \\ = 5( - 216) - 19(36) - 138 - 9 \\ = - 1080 - 684 - 138 - 9 \\ = - 1911[/tex]

I hope I helped you^_^

The value of function (h·g)(b) for x=-6 is -867.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are g(b)=5b-9 and h(b)=(b-1)².

Now, (h·g)(b)=h(b)×g(b)

= (b-1)²×5b-9

= (b²-2b+1)×(5b-9)

= b²(5b-9)-2b(5b-9)+1(5b-9)

= 5b³-9b²-10b²+18b+5b-9

= 5b³-10b²+23b-9

Now, (h·g)(-6)

= 5(-6)³-10(-6)²+23(-6)-9

= -1080+360-138-9

= -867

Therefore, the value of function (h·g)(b) for x=-6 is -867.

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Welcome to Brainly! I'm happy to help!

We see that there are 1,610 meters in a mile. However, we are looking for millimeters, not meters. But, knowing the meters will help us out.

A millimeter is a very small measurement. There are 1,000 millimeters in 1 meter. A meter is much larger. So, if we want to convert 1,610 meters to millimeters, there are going to be way more millimeters because they are so minute.

This means that we will have to multiply. We know that there are 1,000 millimeters in 1 meter, so if we multiply our meters by 1,000 (which is basically just adding 3 zeros), we will get the number of millimeters in one mile!

1,610×1,000=1,610,000 (one million six hundred and ten thousand!)

Don't forget that we are looking for 3 miles though, so we can take the number of millimeters in one mile and multiply by three.

1,610,000×3=4,830,000 (four million eight hundred and thirty thousand!)

So, Tobias ran 4,830,000 millimeters!

Have a wonderful day and keep on learning! :D

Answer:

Just divide 2/3 by 3 (or multiply by 1/3), 6 times to get the answer.

Answer:

It is a dependent event, because it depends of the number she'll get rolling the die

Answer:

-1

Step-by-step explanation:

Answer: -1, 13

Step-by-step explanation:

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Midpoint formula:  (x2 + x1)/2, (y2 + y1)/2

(-6 + 4) / 2, (14 + 12) / 2

(-2) / 2, 26 / 2

(-1, 13)

Answer:

(2, -9)

Step-by-step explanation:

f(x) = (x + 1)(x - 5)

[tex] =f(x) = {x}^{2} - 5x + x - 5[/tex]

[tex] = f(x) = {x}^{2} - 4x - 5[/tex]

[tex] = f(x) = {1x}^{2} - 4x - 5[/tex]

[tex] = f(x) = {1x}^{2} + ( - 4x) - 5[/tex]

= a = 1, b = -4

[tex] = x = \frac{ - 4}{2 \times 1} [/tex]

[tex] = x = - \frac{ - 4}{2} [/tex]

[tex] = x - ( - 2)[/tex]

[tex] = x = 2[/tex]

= f(x) = (x + 1) x (x - 5); x = 2

= f(2) = -9

= (2, -9)

Answer:

B)642

Step-by-step explanation:

Between 1 and 9 , it will use 9 letters

Between 10 and 99, there are 90 different numbers and every number have 2 digits so it will use 180 letters

Between 100 and 250 , there are 151 different numbers and every number have 3 digits so it will use 453 letters

Totally it used 9+180+453=642

Answer:

Step-by-step explanation:

The set of all real numbers except for 100 in set builder notation (assuming the variable is x) is:

The very first x represents the variable.

The second with the R represents the number. Here, we want all real numbers.

And the third is the constraint. We want all real numbers except for 100.

Answer:

{ x | x ∈ R, x ≠ 100 }

Step-by-step explanation:

Real numbers (R) include all rational and irrational numbers.

Hence, If we need to write it in set-builder notation, we will write as:

{ x | x ∈ R, x ≠ 100 }

In words : "x such that x belongs to R, x is not equal to 100"

This shows that x is any real number except for 100.

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Step-by-step explanation:

1.) two tails :

total no. of outcomes possible is TT,TH,HT,HH

no. of outcomes with TT is 1

p( tails on both) = 1/4

2.) tails at least one:

no. of outcomes with one tails atleast is 3 (TT,th,ht,)

p( atelast one tails) = 3/4

3.) tails on one

no. of outcomes with one tails at most is 2 (th,ht)

p( atmost one tails) is 2/4= 1/2

4. no tails

no. of outcomes with no tails is 1(HH)

p( no tails) = 1/4

hope it's understandable.

Answer:

1.) two tails :

total no. of outcomes possible is TT,TH,HT,HH

no. of outcomes with TT is 1

p(tails on both) = 1/4

2.) tails at least one:

no. of outcomes with one tails atleast

is 3 (TT,th,ht,)

p(atelast one tails) = 3/4

3.) tails on one

no. of outcomes with one tails at most is 2 (th,ht)

p(atmost one tails) is 2/4= 1/2

4. no tails

no. of outcomes with no tails is 1(HH)

p(no tails) = 1/4

Answer:

-7, -6, -5

Step-by-step explanation:

-7 < -6

-5 > -6

-7 < -6 < -5

Answer:

A. b2 – 4ac = 0

Step-by-step explanation:

Hey user☺☺

Option a is correct

Because the graph has only one solution.

As the graph touches the x-axis at one point that means that it will have only one solution for x. But we know that a quadratic equation has two solutions. So the graph will have two equal solution and therefore the discriminant will be 0.

Hope this will help☺☺

Answer:

[tex]A_{BCF}[/tex] = 351 cm²

Step-by-step explanation:

Answer:

[tex]⚪ \: \: 1.27 \: u[/tex]

Step-by-step explanation:

[tex] - 0.62u + u + 0.89u \\ = ( - 0.62 + 1 + 0.89)u \\ = 1.27u[/tex]

Answer:

[tex]1\frac{1}{4}[/tex] cups

Step-by-step explanation:

3/4=3/5

3/4*1/3=3/5*1/3

1/4 = 1/5

1/4*5=1/5*5

5/4=5/5

5/4= 1 and 1/4 cups

Hope this helped! Please mark brainliest :)

~~ SUMMER ~~

Answer:

14x + 4

Step-by-step explanation:

The perimeter of a rectangle is the sum of all its sides. The rectangle have two sides with length 5x + 2, so:

(5x + 2)×2 = 10x + 4

And it also have two sides with length 2x, so:

(2x)×2 = 4x

And now just add it:

10x + 4 + 4x = 14x + 4

Answer: Perimeter = 14x + 4

Concept:

Here, we need to know how to find the perimeter of a rectangle.

Perimeter (rectangle) = 2 (l + w)

l = length

w = width

If you are still confused, you may refer to the attachment below for a graphical explanation.

Solve:

Given information

l = 5x + 2

w = 2x

Given expression

Perimeter = 2 (l + w)

Substitute values into the expression

Perimeter = 2 (5x + 2 + 2x)

Combine like terms

Perimeter = 2 (7x + 2)

Expand parentheses and apply the distributive property

Perimeter = 2 · 7x + 2 · 2

Perimeter = 14x + 4

Hope this helps!! :)

Please let me know if you have any questions

Answer:

[tex]3^{4}[/tex]

Step-by-step explanation:

                 81

               27    3

            9  3    

        3  3

3*3*3*3 = [tex]3^{4}[/tex]

Answer:

I think it's D.................

Answer:

-350ft

Step-by-step explanation:

so basically 605 is negative and 255 is a negative then you add those two then it would be -860 then you subtract the positive 475 and that will equal -350

Bachelor's degree salary = $53000

Master's degree salary = $66000

Step-by-step explanation:

Given that :

Let Salary of bachelor's degree holder = x

Salary of Master's degree holder = 2x - 40000

Master's salary + bachelor's salary = $119,000

Hence,

Master's salary + bachelor's salary = 119,000

2x - 40000 + x = 119,000

3x = 119000 + 40000

3x = 159000

x = 159000 / 3

x = $53,000

Bachelor's degree salary = $53,000

Master's degree salary ; 2x - 40000 ; 2(53000) - 40000 = $106,000 - $40,000 = $66000

The average yearly salary of an individual with a bachelor's degree is $58,000, and the average yearly salary of an individual with a master's degree is $66,000.

Let, the average yearly salary of an individual with a bachelor's degree as "B" and the average yearly salary of an individual with a master's degree as "M".

According to the information given:

The average yearly salary of an individual with a master's degree is $50 thousand less than twice that of an individual with a bachelor's degree:

M = 2B - $50,000

The combined yearly salaries of two people with each of these educational attainments earn $124 thousand:

B + M = $124,000

Now we can solve this system of equations to find the values of B and M.

Substitute the value of M from the first equation into the second equation:

B + (2B - $50,000) = $124,000

3B - $50,000 = $124,000

Now, solve for B:

3B = $174,000

B = $174,000 / 3

B = $58,000

Substitute the value of B back into the first equation to find M:

M = 2B - $50,000

M = 2 * $58,000 - $50,000

M = $116,000 - $50,000

M = $66,000

So, the average yearly salary of an individual with a bachelor's degree is $58,000, and the average yearly salary of an individual with a master's degree is $66,000.

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Answer:

[tex]x-1[/tex]

Step-by-step explanation:

Hi there!

Let [tex]x[/tex] represent "the number".

The difference of a number and 1

⇒ [tex]x-1[/tex]

I hope this helps!

Answer:

No!

Step-by-step explanation:

An integer is a a whole negetive number. A few examples are 4, -4, or even 4/4.

Answer:

20

Step-by-step explanation:

pq + 4

Given:

p = 4

q = 4

We plug the numbers in:

pq + 4

4(4) + 4

16 + 4

20

The answer you are looking for is 20.

Since p=4 and q=4,

Therefore,

pq+4

Substitute each of the given values of the variables,

(4)(4)+4

16+4

20

Answer:

-15(4) or -4(15) or 15(-4)

Step-by-step explanation:

As long as you stick with the same variables, you can change their position in the equation or change both of their signs. This should give you the same answer.

Let's say your equation was -2(6). This means you must multiply -2 and 6. This should give you -12. You could also phrase it as 2(-6) or -6(2) or 6(-2). They all give you -12 as a result.

Answer:

(-1)(15+15+15+15)

(-15)+ (-15)+ (-15)+ (-15)

Step-by-step explanation:

Answer:

.67

Step-by-step explanation:

There are three friends and two pies. You are splitting the pies not the people so you divide 2 by 3 to get 0.66666667. Meaning each girl got .67 or around 6/10 of a pie.

Answer:

x=6

Step-by-step explanation:

when there is no 'y' in equation, the line is always

parallel to y-axis