Find the GCF of 21, 63 and 105.​

Answer:

No, Monica did not correctly factor out the GCF

Step-by-step explanation:

The given expression is [tex]12x^3+6y^2+18xy+24x[/tex]

The prime factorization of each term are:

[tex]12x^3y=2^2\times3\times x^3\times y[/tex]

[tex]6y^2=2\times3\times y^2[/tex]

[tex]18xy=2\times3^2\times x\times y[/tex]

[tex]24x=2^3\times3\times x[/tex]

The greatest common factor is the product of the least powers of the common factors.

[tex]GCF=2\times3=6[/tex]

The greatest common factor is 6.

If we factor the GCF, we obtain:

[tex]6(2x^3+6y^2+3xy+4)[/tex]

Therefore Monica did not correctly factor out the GCF

The solution of the given inequality is (- √5) ≤ x ≤ (+√5).

"An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. "

The given inequality is:

x² - 5 ≤ 0

⇒ x² ≤ 5

⇒ x ≤ (± √5)

Therefore, the solution is (- √5) ≤ x ≤ (+√5).

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Problem #1= 7 5/12- 6 1/12= 1 4/12 which is simplified to 1 1/3

The answer to the first problem is 1 1/3 feet.

Problem #2= 28(3/4)= 84/4= 21

The answer to the second problem is 21 points.

Hope this helps!

Answer:

x intercepts: (-1, 0) and (5, 0)

vertex: (2, 9)

axis of symmetry: x = 2

Step-by-step explanation:

The x intercepts are where y = 0.

0 = -(x + 1)(x − 5)

x = -1, x = 5

So the x intercepts are (-1, 0) and (5, 0).

The x coordinate of the vertex is halfway between the x intercepts.

x = (-1 + 5) / 2

x = 2

So the vertex is at (2, 9).

The axis of symmetry passes through the vertex.

x = 2

For this case we have that the area of the figure is given by the area of a rectangle plus the area of a square. By definition, the area of a rectangle is given by:

[tex]A = a * b[/tex]

According to the figure we have:

[tex]a = 9 \sqrt {2}\\b = 8 \sqrt {2} -2 \sqrt {2} = 6 \sqrt {2}[/tex]

So, the area of the rectangle is:

[tex]A = 9 \sqrt {2} * 6 \sqrt {2} = 54 (\sqrt {2}) ^ 2 = 54 * 2 = 108[/tex]

On the other hand, the area of a square is given by:

[tex]A = l ^ 2[/tex]

Where:

l: it is the side of the square

According to the figure we have:

[tex]l = 2 \sqrt {2}[/tex]

So:

[tex]A = (2 \sqrt {2}) ^ 2 = 4 * 2 = 8[/tex]

Finally, the area of the figure is:

[tex]A_ {t} = 108 + 8 = 116[/tex]

Answer:

116

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})~\hspace{10em} slope = m\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-2)=-2(x-3) \\\\\\ y+2=-2x+6\implies y=-2x+4[/tex]

Step-by-step explanation:

the correct answer is c

Answer:

512 is a perfect cube.

Step-by-step explanation:

because 8*8*8=512

Answer:360

Step-by-step explanation:

1 ton = 2000 pounds

8000/2000 =4

4x90= 360.00

Answer is 360.00 for shipping

[tex]\huge{\boxed{\$360}}[/tex]

Each pound contains [tex]2000[/tex] pounds, so divide [tex]8000 \div 2000[/tex] to find the number of tons. [tex]8000 \div 2000=4[/tex]

Now, just multiply [tex]\$90*4=\boxed{\$360}[/tex]

Answer:

The factors are (3x+1)(2x+1)

Step-by-step explanation:

The expression is:

6x^2 + 5x + 1

We have to break the middle term to find its factors. For this first we have to multiply the coefficient of 1st terms with the constant term:

6*1 = 6

Now we have to find any two numbers whose product is 6 and whose sum is the middle term:

3*2=6

3+2=5

Now break the middle term by these two numbers.

6x^2 + 5x + 1

6x^2+3x+2x+1

Group the first two terms and last two terms:

(6x^2+3x)+(2x+1)

Now take out common factor from each term:

3x(2x+1)+1(2x+1)

(3x+1)(2x+1)

Therefore the factors are (3x+1)(2x+1)....

Answer:

(2x + 1)(3x + 1)

Step-by-step explanation:

Given

6x² + 5x + 1

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 6 × 1 = 6 and sum = + 5

The factors are + 3 and + 2

Use these factors to split the x0 term

6x² + 3x + 2x + 1 ( factor the first/second and third/fourth terms )

= 3x(2x + 1) + 1 (2x + 1) ← factor out (2x + 1) from each term

= (2x + 1)(3x + 1) ← in factored form

Answer:

Step-by-step explanation:

31 is prime. It can't be factored. The way I'm reading the directions, you should enter 31.

Answer:

31

Step-by-step explanation:

The prime factorization of 31 is 1 x 31 = 31.

You have to multiply the number by 1 to find its prime factorization.

However, it is usually written as just 31.

Answer:

C. 5√3

Step-by-step explanation:

To figure this out, we need to apply the Pythagorean Theorem, a² + b² = c², where c is the "HYPOTENUSE". In this case, c is already found for us [10], so the operation we use whenever the hypotenuse is defined is deduction, or subtraction. Apply the Pythagorean Theorem: a² + 25 = 100; 75 = a². Now, to find a, we need to find two numbers that multiply to 75, where one of them is a PERFECT SQUARE, and in this case, they are 3 and 25. Since the square root of 25 is 5 [in this case, NO NON-NEGATIVE root], that gets moved to the outside of the radical, and 3 [NON-PERFECT SQUARE] stays wrapped under the radical, ending up with 5√3. You understand?

I am joyous to assist you anytime.

Answer:

It's A, -16.

Step-by-step explanation:

solve by moving all terms with d to the left hand side

subtract 8d from both sides

d + 1 = - 15

- 15 - 1 = -16

-16 = d

The answer is a -16.

When you only have an equation in one variable to solve you will transpose the variable together and get the outcome on the other side.

When you transpose a variable or a constant on the other side, their function gets changed, so you can add, subtract, multiply or divide on both the sides the effect would not change, but you have to keep in mind about the equality holding true.

9d+1=8d-15

As you have to group the variable then subtract 8d on both sides

d+1=-15

After that, you transpose +1 from LHS to RHS

d = -16

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Answer:

Option B [tex]g\left(x\right)=\left|x-4\right|+6[/tex]

Step-by-step explanation:

we have

[tex]f\left(x\right)=\left|x\right|[/tex]

The vertex is the point (0,0)

If to the parent function apply

Shift 4 units to the right and Shift 6 units up

The rule of the translation is

(x,y) ------> (x+4,y+6)

so

The vertex of the new function is (4,6)

therefore

the equation of the new function is

[tex]g\left(x\right)=\left|x-4\right|+6[/tex]

Answer:

just entered the answer and it was |x-4|+6

hope that helps!

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

[tex]sinx+cosx=\frac{cosx}{1-tanx}+\frac{sinx}{1-cotx}\\[/tex] proved.

Step-by-step explanation:

[tex]sinx+cosx=\frac{cosx}{1-tanx}+\frac{sinx}{1-cotx}\\[/tex]

Taking R.H.S

[tex]\frac{cosx}{1-tanx}+\frac{sinx}{1-cotx}\\[/tex]

Multiply and divide first term by cos x and second term by sinx

[tex]=\frac{cosx*cosx}{cosx(1-tanx)}+\frac{sinx*sinx}{sinx(1-cotx)}[/tex]

we know tanx = sinx/cosx and cotx = cosx/sinx

[tex]=\frac{cos^2x}{cosx(1-\frac{sinx}{cosx} )}+\frac{sin^2x}{sinx(1-\frac{cosx}{sinx})}\\=\frac{cos^2x}{cosx-sinx}+\frac{sin^2x}{sinx-cosx}[/tex]

Taking minus(-) sign common from second term

[tex]=\frac{cos^2x}{cosx-sinx}-\frac{sin^2x}{cosx-sinx}[/tex]

taking LCM of cosx-sinx and cosx-sinx is cosx-sinx

[tex]=\frac{cos^2x-sin^2x}{cosx-sinx}[/tex]

We know a^2-b^2 = (a+b)(a-b), Applying this formula:

[tex]=\frac{(cosx+sinx)(cosx-sinx)}{cosx-sinx}\\=cosx+sinx\\=L.H.S[/tex]

Hence proved

Answer:

Step-by-step explanation:

x = 1, y = 12

x = 2, y = 9

x = 3, y = 6

x = 4, y = 3

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{9-12}{2-1}=\dfrac{-3}{1}=-3[/tex]

Answer:

y = - x - 5

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 )

here slope m = - 1 and y- intercept c = - 5, hence

y = - x - 5 ← equation of line

Jean's car :

(12 1/2) / (5/12) =

(25/2) / (5/12) =

25/2 * 12/5 =

150/5 = 

30 miles per gallon

Miranda's car :

(20 5/7) / (5/7) =

(145/7) / (5/7) =

145/7 * 7/5 =

145/5 =

29 miles per gallon

most fuel efficient is Jean's car....it gets 30 miles per gallon

Answer:

most fuel efficient is Jean's car gets 30 miles per gallon

Step-by-step explanation:

Answer:

15-8  

HOPE THIS HELP

Step-by-step explanation:

Answer:

15 - 8i

Step-by-step explanation:

5√9-√(-64) = ?  Rewrite -√(-64) as -8i.

Then we have 5(3) - 8i, or 15 - 8i.

Answer:(6,12)

Step-by-step explanation:

Answer:

They used 3.14 for pi:

[tex]V=\frac{4}{3} \pi r^3[/tex]

[tex]V=\frac{4}{3} (3.14)(5)^3[/tex]

Step-by-step explanation:

[tex]V=\frac{4}{3}\pi r^3[/tex] is the volume of a sphere with radius r.

I think that is the diameter given in the picture.

The radius is half the diameter.

So the radius is 5 since the diameter is 10.

Plug in this gives you:

[tex]V=\frac{4}{3} \pi (5)^3[/tex]

Answer:

THE ANSWER IS B

HOPE THIS HELPS

Step-by-step explanation:

I DID IT ON EDG

[tex]\bf \textit{recalling that }~\hfill i^4=1~\hfill i^3=-i~\hfill i^2=-1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 5i^4+2i^3+8i^2+\sqrt{-4}\implies 5(1)+2(-i)+8(-1)+\sqrt{-1\cdot 4} \\\\\\ 5-2i-8+\sqrt{-1}\cdot \sqrt{2^2}\implies -2i-3+i\cdot 2\implies ~~\begin{matrix} -2i \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-3~~\begin{matrix} +2i \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill -3+0i~\hfill[/tex]

Answer:

96π units²

Step-by-step explanation:

area of shaded sector (A) = area of circle × fraction of circle

A = πr² × [tex]\frac{\frac{3\pi }{4} }{2\pi }[/tex]

   = 16² × [tex]\frac{3\pi }{8}[/tex]

   = 256 × [tex]\frac{3\pi }{8}[/tex]

   = 32 × 3π

   = 96π units²

Answer:

Area of sector : 96 π unit².

Step-by-step explanation:

Given : The measure of central angle XYZ is 3pi/4 radians.

To find : What is the area of the shaded sector?

Solution: We have given central angle XYZ is 3pi/4 radians.

Area of sector : [tex]\frac{1}{2}[/tex] (radius)²* central angle.

Plug the values central angle  = [tex]\frac{3\pi }{4}[/tex] , radius = 16 units.

Then ,

Area of sector : [tex]\frac{1}{2}[/tex] (16)²* [tex]\frac{3\pi }{4}[/tex].

Area of sector : [tex]\frac{1}{2}[/tex] * 256 * [tex]\frac{3\pi }{4}[/tex].

Area of sector :  128 * [tex]\frac{3\pi }{4}[/tex].

Area of sector : 32 * 3 π

Area of sector : 96 π unit².

Therefore, Area of sector : 96 π unit².

Answer:

The area of ABCD is 24 units²

Step-by-step explanation:

* Lets explain how to solve the problem

- All the point in a vertical line have the same x-coordinates

- The length of the vertical line is y2 - y1

- All the point in a horizontal line have the same y-coordinates

- The length of the horizontal line is x2 - x1

- The horizontal and the vertical lines are perpendicular to each other

- The trapezoid has two parallel bases not equal in length and the other

 two sides are nonparallel sides

- The area of the trapezoid = 1/2 (sum of the two // bases) × height

* Lets solve the problem

∵ ABCD is a quadrilateral

∵ A = (-2 , 3) , B = (4 , 3) , C = (4 , -2) , D = (-2 , 0)

∵ Side AD has same x-coordinates in A and D (-2)

∴ AD is vertical side

∴ AD = 3 - 0 = 3

∵ Side BC has same x-coordinates in B and C (4)

∴ BC is vertical side

∴ BC = 3 - (-2) = 3 + 2 = 5

∵ AD and BC are vertical lines

∴ AD // BC

∵ Side AB has same y-coordinates in A and B (3)

∴ AB is horizontal side

∴ AB = 4 - (-2) = 4 + 2 = 6

∵ The horizontal and the vertical lines are perpendicular to each other

∴ AB is perpendicular on AD and BC

∵ The side CD is not vertical or horizontal

∴ ABCD has only two parallel sides AD and BC

∵ AD ≠ BC

∴ ABCD is a trapezoid

∵ The two parallel bases are AD and BC

∵ Its height is AB

∵ AD = 3 , BC = 5 , AB = 6

∴ Its area = 1/2 (3 + 5) × 6 = 1/2 (8) × 6 = 4 × 6 = 24 units²

* The area of ABCD is 24 units²

Answer:

24 square units

i did the test

Step-by-step explanation:

Answer:

0 real solutions

Step-by-step explanation:

I guess you are looking for the number of real solutions? Correct me if I'm wrong.

There is something called the discriminant that can help us determine this without actually solving f(x)=0 for x.

The discriminant is the thing inside the square root in the quadratic formula.

It is the thing that reads b^2-4ac.

If b^2-4ac:

A) is negative, then you have 0 real solutions (you could say 2 complex solutions)

B) is positive, then you have 2 real solutions

C) is 0, then you have 1 real solution

So comparing 3x^2+5x+10 to ax^2+bx+c, you should see that a=3, b=5, and c=10.

b^2-4ac

=5^2-4(3)(10)

=25-120

=-95

That is a negative result so you have no real solutions.

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

[tex]\huge\text{Decimals, fractions, \& negatives are below 0!}[/tex]

[tex]2\dfrac{21}{30}\ = 2\times30+21 \ = 2\times 30 = 60+21= 81\rightarrow \dfrac{81}{30}[/tex]

[tex]2\dfrac{1}{2}\ = 2\times2+1=2\times2=4+1=5\rightarrow\dfrac{5}{2}[/tex]

[tex]-\dfrac{32}{40}=-\dfrac{32}{40}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer:}-\dfrac{32}{40}, \ 2\dfrac{1}{2}, \ 2\dfrac{21}{30}}}\huge\checkmark[/tex]

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

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Step-by-step explanation:

For this case we must convert 21 hours to seconds!

We have that by definition, 1 hour equals 3600 seconds. Then, making a rule of three we have:

1h ------------> 3600s

21h ----------> x

Where "x" represents the number of seconds equivalent to 21 hours.

[tex]x = \frac {21 * 3600} {1} = 75600[/tex]

Thus, 21 hours represent 75600 seconds.

Answer:

75600 seconds.

Step-by-step explanation:

With each draw, the probability of selecting a green marble is 2/3 and the probability of selecting a yellow marble is 1/3.

To pick two of the the same color, they can either pick green twice or yellow twice.  

P = (2/3)(2/3) + (1/3)(1/3)

P = 5/9

To pick two different colors, they can either pick green first then yellow, or yellow first then green.

P = (2/3)(1/3) + (1/3)(2/3)

P = 4/9

Expected value for Derek is:

D = (5/9)(-1) + (4/9)(1)

D = -1/9

The expected value for Mia is:

M = (5/9)(1) + (4/9)(-1)

M = 1/9

Check the picture below.

The distance across the lake is 210 meters, and this is found using the concept of similar triangles and proportionality.

The correct answer is option B.

To find the distance across the lake, we can use the concept of similar triangles. Given that the triangles are similar, we can set up a proportion to find the missing side length.

Let's label the sides of the larger triangle as A, B, and C and the sides of the smaller triangle as X, Y, and Z. The given values are:

A = 70 m (the length of the larger triangle)

X = 20 m (the length of the smaller triangle)

Y = 60 m (the width of the smaller triangle)

We want to find side C, which represents the distance across the lake.

We can set up a proportion between the corresponding sides of the two similar triangles:

A / X = B / Y = C / Z

Plugging in the given values:

70 m / 20 m = C / 60 m

Now, solve for C by cross-multiplying:

70 m * 60 m = 20 m * C

4200 m² = 20 m * C

To isolate C, divide both sides by 20 m:

C = 4200 m² / 20 m

C = 210 m

So, the distance across the lake (side C) is 210 meters. This is the solution based on the concept of similar triangles and the given side lengths.

Therefore, from the given options the correct one is B.

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