20 POINTS!!

What is the GCF of 24 a^3b and 36 ab^2?

a. 2 ab
b. 4 a^3b
c. 12 ab
d. 72 a^3b^2

Answer:

Step-by-step explanation: 2× (9×4-35) +27

Using BODMAS

= 2× (36-35)+27

=2×(1) + 27

=2 + 27

=29

Answer:

Given:

Area of the rectangle  = 30 square inches.

length of the sides are whole numbers.

Solution:

The base of the rectangle  is  x and the height is y

We know that Area of the rectangle  = [tex]length \times breadth[/tex]

That is

30 = [tex]x \times y[/tex]

The possible values of length and breadth

length x : 1    2      3      5    6    10   15    30

breath  y: 30   15    10   6     5    3      2      1

Now

30 =  xy

[tex]y = \frac{30}{x}[/tex]

when y increases x decreases and vice versa

Answer:

Cross multiply

Step-by-step explanation:

[tex]\frac{2x+1}{3}\geq 5\\\\ 2x+1\geq 15\\2x\geq 15-1\\2x\geq 14\\\frac{2x}{2}\geq \frac{14}{2}\\ x\geq \frac{(2)(7)}{2}\\ x\geq 7[/tex]

Simplified expression is 6y² - 24y - 51. Value for y=-2 is 21 and value for y=3 is  -69.

Step-by-step explanation:

⇒ 6y² - 21y - 3y + 12 - 63

⇒ 6y² - 24y - 51

⇒ 6y² - 24y - 51 = 6(-2)² - 24(-2) - 51 = 24 + 48 - 51 = 21

⇒ ⇒ 6y² - 24y - 51 = 6(3)² - 24(3) - 51 = 54 - 72 - 51 = -69

Answer:

A, C, and E are correct

Step-by-step explanation:

B can't be right because 2 is an exponent, not a coefficient

D can't be right because 6 doesn't go into 7

Hope this helped!

Answer:

Part 1) [tex]f(x)=(x-2)^{2}-16[/tex]

Part 2) The function's correct axis of symmetry is x=2

Option f(x) = (x - 2)² - 16, x = 2

Step-by-step explanation:

we have

[tex]f(x)=x^{2} -4x-12[/tex]

This is a vertical parabola open upward

The vertex is the minimum

Part 1) Convert to vertex form

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]f(x)=(x^{2} -4x+2^2)-12-2^2[/tex]

[tex]f(x)=(x^{2} -4x+4)-16[/tex]

Rewrite as perfect squares

[tex]f(x)=(x-2)^{2}-16[/tex] ----> function in vertex form

Te vertex is the point (2,-16)

Part 2) Find the axis of symmetry

we know that

The equation of the axis of symmetry of a vertical parabola  is equal to the x-coordinate of the vertex

The vertex is the point (2,-16)

therefore

The function's correct axis of symmetry is x=2

Final answer:

The function f(x) = x² - 4x - 12 rewritten in vertex form is f(x) = (x - 2)² - 16, and the axis of symmetry for this function is x = 2.

Explanation:

To rewrite the function f(x) = x² - 4x - 12 in vertex form, we need to complete the square. This involves the following steps:

The axis of symmetry for a parabola in the form (x - h)² is always x = h, which in this case is x = 2.

Therefore, the correct answer is f(x) = (x - 2)² - 16, x = 2.

There are 120 combination in 12345.

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given that;

To find number of combination in 12345.

Since, There 5 digits in the given number.

Hence, Possible combinations are,

⇒ 5!

⇒ 5 × 4 × 3 × 2 × 1

⇒ 120

Thus, There are 120 possible combination in 12345.

Learn more about the combination visit:

brainly.com/question/28065038

#SPJ3

Complete question is,

How many combinations with 12345 without repeating the numbers?

Answer:

ight man that answer is 43 your welocome smart aint i

Step-by-step explanation:

Answer:

answers: 8

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

given total number of students = 49

fraction of students that gave speeches = 5/7

number of students that gave speeches

= (5/7) x 49

= (5 x 49) / 7

= 245/7

= 35

Answer:35 students have their speeches

Step-by-step explanation:

1/7 of 49 is 7, so if it is 5/7 of the students multiply 5x7

To sum the numbers in scientific notation, you add the coefficients and keep the exponent. The correct sum of 2.5 \(\times\) 10^10 and 7.8 \(\times\) 10^10, expressed in proper scientific notation, is 1.03 \(\times\) 10^11.

To find the sum of 2.5 \(\times\) 10^10 and 7.8 \(\times\) 10^10, you add the two numbers while keeping the same exponent since they are like terms in scientific notation. You calculate 2.5 + 7.8 which equals 10.3. Therefore, the sum in scientific notation is 10.3 \(\times\) 10^10.

However, in proper scientific notation, this number should have only one non-zero digit to the left of the decimal point. So, we adjust this sum by writing it as 1.03 \(\times\) 10^11 by moving the decimal one place to the left and increasing the exponent by 1. Thus, the correct answer is 1.03 \(\times\) 10^11, which correlates with option C.

https://brainly.com/question/31621311

#SPJ2

Answer:10, hope it helps!! :)

Step-by-step explanation:

22 + 62 ÷ 22=

4 + 36 ÷ 4=10

The area of Nevada, based on map measurements converted to actual miles using the map's scale, is calculated to be approximately 156,800 square miles.

The question relates to finding the area of the state of Nevada using its scaled measurements from a map. Given that the scale on the map is 1/2" to 20 miles, and the physical distances measured on the map are 8" wide and 12.25" long, we need to convert these measurements into actual miles before calculating the area. To do this conversion, we set up a proportion based on the scale given:

By cross-multiplying, we find that x, the actual length in miles, is approximately 490 miles. Having converted both the width (8" which is equivalent to 320 miles) and the length, we can now calculate the area of the trapezoid that represents Nevada. Assuming the shape is close to rectangular for simplicity, the area would be width × length, or:

Area = 320 miles × 490 miles = 156,800 square miles.

Step-by-step explanation:

-5 5/6 ÷(-2 1/6)

Turn them into improper fractions

-35/6 and -13/6

Change the division sign to multiply

-35/6 × -13/6

Making -13/6 into -6/13

Solve

-35/6 × -6/13 = 210/78

Simplify

Answer:

35/13

Edit: if you want it to be a mixed number, it will be 2 9/13

Answer:

-5 5/6 ÷(-2 1/6)

Turn them into improper fractions

-35/6 and -13/6

Change the division sign to multiply

-35/6 × -13/6

Making -13/6 into -6/13

Solve

-35/6 × -6/13 = 210/78

Simplify explanation:

Answer:

1/10

Step-by-step explanation:

1/6 / 1 2/3

Convert 1 2/3 to 5/3.

1/6 / 5/3

1/6 x 3/5

3/30 or 1/10

The result of the division of 1/6 by 1 2/3 can be found by first converting 1 2/3 to an improper fraction, then taking the reciprocal of this fraction and multiplying it by 1/6. This gives the result as 1/10.

To solve this fraction division problem, we first need to convert the mixed number 1 2/3 to an improper fraction. A mixed number like 1 2/3 means one plus 2/3, and it can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator. For 1 2/3, this means: (1*3 + 2)/3 = 5/3.

Now, we have the problem 1/6 / 5/3. In fraction division, we can replace the division with multiplication by the reciprocal of the second fraction. The reciprocal of a fraction is created by switching the numerator and the denominator. So, the reciprocal of 5/3 is 3/5.

Our equation 1/6 / 5/3 then becomes 1/6 * 3/5 = 3/30 = 1/10 when simplified. Hence, the result of 1/6 divided by 1 2/3 in its simplest form is 1/10.

https://brainly.com/question/1622425

#SPJ3

The value of x = 7

What are linear equalities in one variable?

The linear equation in one variable is an equation that is expressed within the form of ax+b = zero, where a and b are integers, and x is a variable and has only one answer.

Conclusion: For example, 2x+3=8 is a linear equation having a single variable in it. therefore, this equation has only one solution, which is x = 5/2.

3 (x+6)= 39

3x + 18 = 39

3x = 39 - 18

3x = 21

x = 21/3

x = 7

The above question is an example of linear equalities in one variable.

learn  more about linear equalities in one variable here https://brainly.com/question/6196569

#SPJ2

Answer:54

Step-by-step explanation:

(12 x 4) = 48

(12 x .5) = 6

48 + 6 = 54

Answer:

Therefore other two sides of the triangle are 4 and 5.

Step-by-step explanation:

Given one leg of a right triangle has a length of 3

Let other sides of the triangle be x and x+1 [ since they are consecutive]

According to the problem,

3²+x²=(x+1)²

⇔9 + x²=x²+2x+1

⇔2x+1=9

⇔2x=9-1

⇔2x=8

⇔x=4

Therefore other two sides of the triangle are 4 and 5.

To find the lengths of the other two sides of the right triangle with one leg of length 3, we can use the Pythagorean theorem. The lengths of the other two sides are 4 and 5.

To find the lengths of the other two sides of the right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Since one leg has a length of 3, let's call the lengths of the other two sides x and x+1. We can set up the equation:

3^2 + x^2 = (x+1)^2

Simplifying the equation:

9 + x^2 = x^2 + 2x + 1

Subtracting x^2 from both sides:

9 = 2x + 1

Subtracting 1 from both sides:

8 = 2x

Dividing both sides by 2:

4 = x

So, the lengths of the other two sides are 4 and 5.

https://brainly.com/question/19649203

#SPJ3

Answer:

Step-by-step explanation:

The the 3 consecutive numbers be

X, X + 1, X + 2

: X + X + 2 = 60

2X = 60 - 2

2X = 58

X = 58/2

X = 29

THE NUMBERS ARE 29, 30 AND 31

Answer:

c

Step-by-step explanation:

Answer:

[tex]x=14[/tex]

Step-by-step explanation:

Considering the small triangle in which the one side and two angles are given:

Finding the third angle of the small triangle

Sum of angles of the triangle is [tex]180[/tex]°

as two angles are given i.e 90° and 45°, so third angle is 180°-(90°+45°)

Third angle in the small triangle is 45°.

As the opposite angles are 45° joining together to form 90° angle, therefore the small triangle is an isosceles triangle in which the opposite sides are equal.

Therefore the two sides are 7 and 7 of small triangle, so By Pythagoras theorem the third side is

[tex]H=\sqrt{P^2+B^2}\\ \\=\sqrt{7^2+7^2}\\\\=\sqrt{98} \\H=7\sqrt{2}[/tex]

Similarly the bigger triangle is also an isosceles triangle whose base is determined i.e  [tex]7\sqrt{2}[/tex] = perpendicular length of bigger triangle.

Applying the Pythagoras theorem in bigger triangle:

           [tex]x=\sqrt{(7\sqrt{2})^2+(7\sqrt{2})^2 }\\x=\sqrt{98+98}\\\\ x=\sqrt{196} \\\\x=14[/tex]

Answer:

See the attached image for the answers and the working out.

Step-by-step explanation:

The nth term of the sequences 2, 5, 10, 17... and 2, 8, 18, 32... are n² + 1 and 2n² respectively.

Sequences are a group of numbers written in a specific order such that the nth term of the sequence can be determined using some logic or formula.

It is given that the nth term of the sequence 1, 4, 9, 16... is n squared.

2, 5, 10, 17...

1² + 1, 2² + 1, 3² + 1, 4² + 1...

This is of the form n² + 1. The nth term can be found using the formula n² + 1.

2, 8, 18, 32...

2×1², 2×2², 2×3², 2×4²...

This is of the form 2n². The nth term can be found using the formula 2n².

Therefore, we have found that the nth term of the sequences 2, 5, 10, 17... and 2, 8, 18, 32... are n² + 1 and 2n² respectively.

Learn more about sequences here: https://brainly.com/question/7882626

#SPJ2

Answer: 20 tests

Step-by-step explanation: She does every test in 2 1/2 mins. So she can do 20 in 50 mins.

Answer:

w=9 feet

l=11 feet

Step-by-step explanation:

Let the length of the rectangle be l and width be w

Condition 1:

l=2+w --------(I)

Condition 2:

2l+2w=40--------(2)

Putting eq (1) in (2)

2(2+w)+2w=40

4+2w+2w=40

4+4w=40

4w=40-4

4w=36

Dividing both sides by 4

w=9

Now

Putting w=9 in eq (1)

l=2+9

l=11

Answer:

1/3 (39.09)=17 thats all thanks

Answer:x^2 +15x +36

Step-by-step explanation:

Answer: 1/3

Step-by-step explanation:

Using zero as a counterexample, it disproves the conjecture '-x is negative', because when x=0, -x (which becomes -0) equals 0, not negative.

A counterexample is an example that disproves a statement or proposition. In this case, we are given the conjecture '-x is negative'. If x is an integer, it can be positive, negative, or zero. To counter this statement, we can use zero as a counterexample. When x=0, -x (which becomes -0) is not negative but equals to 0. This proves that the original conjecture is not always correct, as it can have exceptions.

https://brainly.com/question/33840085

#SPJ2

Answer:

  x = 17

Step-by-step explanation:

Vertical angles are congruent, so ...

  5x° = 85°

  x = 85°/5° . . . . . . divide by the coefficient of x

  x = 17

{y|y is a real number}

The range of the translated function is {[tex]y|y[/tex] is a natural number}.

Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5), and irrational numbers such as √3, π(22/7), etc., are all real numbers.

The numbers which are not real and are Imaginary are known as not real or non-real numbers. Non-real numbers cannot be represented on the number line. Some of the types or examples of the non-real numbers are √−2,6√−54.

The real number, in mathematics, is a quantity that can be expressed as an infinite decimal expansion. Real numbers are used in measurements of continuously varying quantities such as size and time, in contrast to the natural numbers 1, 2, 3, …, arising from counting.

Learn more about real numbers here: https://brainly.com/question/1770447

#SPJ2

Answer:

b

Step-by-step explanation: