6! = 3! • 2! = =
Evaluate each expression

Answer:  x < -12

Step-by-step explanation:

[tex]-\dfrac{1}{2}x>6\\\\\\\text{Multiply both sides by -2}\\\\(-2)\dfrac{-1}{2}x>(-2)6\\\\\\\text{Simplify - remember to flip the inequality symbol}\\x<-12[/tex]

Graph: ←-----------o -12

Interval Notation: (-∞, -12)

Answer:

x<-3

Step-by-step explanation:

Answer:

B. .12 is the decimal

Step-by-step explanation:

What you do is you divide 25 by 3. That will already give you a decimal and when you divide it out your answer is .12.

3/25=.12.

Answer:

The correct answer is 0.12

Step-by-step explanation:

3 = numerator

25 = denominator

Divide the numerator by the denominator to convert a fraction to a decimal.

3 ÷ 25 = 0.12  

as a decimal is  

0.12

.

Answer: The answer is B. 0.12

Step-by-step explanation:

Answer:

Answer is yes

Step-by-step explanation:

Given in the picture are two circles which are congruent.

This suggests that the radii of the two circles are equal.

Also the central angle of the two circles are congruent (given)

Consider triangles ABC and XYZ,

AC =XY:  AB = YZ:

Angle A = Angle X

By SAS theorem, the two triangles are congruent.

Hence BC = YZ

So yes is answer.

     Step-by-step explanation

i had to turn  my laptop just to read that

                 My

Both rectangles have the same dimensions and shape. P'Q'R'S' is a translated image of PQRS, shifted 3 units right and 3 units up. They are congruent but not identical due to their position.

Step-by-step comparison of rectangles PQRS and P'Q'R'S':

1. Original coordinates:

Assume specific coordinates for the vertices of rectangle PQRS. For example, let P = (1, 2), Q = (5, 2), R = (5, 6), and S = (1, 6).

2. Translation:

A translation moves every point in the shape the same distance and in the same direction. Since Rashid translated rectangle 3 units up and 3 units to the right, add 3 to x-coordinate and 3 to y-coordinate of each point in PQRS to find corresponding points in P'Q'R'S'.

3. New coordinates:

P' = (1 + 3, 2 + 3) = (4, 5)

Q' = (5 + 3, 2 + 3) = (8, 5)

R' = (5 + 3, 6 + 3) = (8, 9)

S' = (1 + 3, 6 + 3) = (4, 9)

4. Comparison:

Shape:

Both rectangles PQRS and P'Q'R'S' are rectangles because a translation preserves the shape of the original figure.

Size:

They have the same dimensions (length and width) as the translation only shifts the position without altering the size.

Orientation:

They maintain the same orientation relative to the axes, meaning their sides remain parallel and perpendicular to the x and y axes.

Position:

The key difference lies in their position. P'Q'R'S' is located 3 units to the right and 3 units above PQRS.

5. Rectangles PQRS and P'Q'R'S' are congruent (same size and shape) but not identical (different positions).

P'Q'R'S' is a translated image of PQRS, moved 3 units to the right and 3 units up.

Answer:

Ben had biked 8 miles

Step-by-step explanation:

You would need to take 12 and divide it by three . That would make 4. After that you would take 4 and multiply it by 2 since he rode 2/3 miles of 12.  Then you would end up with 8.

Final answer:

Ben has biked 8 miles of the 12 miles he wants to, as he has completed 2/3 of his intended distance.

Explanation:

To calculate the number of miles Ben has biked, we simply need to multiply the total distance he wants to bike by the fraction of the trip he has completed. Ben wants to bike 12 miles, and he has biked 2/3 of that distance. Multiplying these together gives us 2/3 * 12 = 8 miles. Therefore, Ben has biked 8 miles so far.

Answer:

The correct answer option is x = -16 and x = 16.

Step-by-step explanation:

We are given the following equation and we are to find the solution for this equation:

[tex] | \frac { x } { 2 } | = 8 [/tex]

For the given equation, involving the modulus, we will have a positive as well as a negative value for it in order to find its solution set.

[tex] \frac { x } { 2 } = - 8 [/tex] and [tex] \frac { x } { 2 } = 8 [/tex]

[tex] x = 8 \times 2 [/tex] and [tex] x = - 8 \times 2 [/tex]

x = -16 and x = 16

Answer:

The correct answer is last option

x = -16 or x = 16

Step-by-step explanation:

it is given that,

|x/2| = 8

To find the solution set

From this we can understand that , the value of x/2 = - 8 or x/2 = 8

If x/2 = -8 then  x = -8 * 2 = = -16

If x/2 = 8 then x = 8 * 2 = 16

Therefore the solutions are

x = -16 or x = 16

Answer:

Step-by-step explanation:

The formula of an area of a trapezoid:

[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]

We have:

[tex]b_1=12,\ b_2=5,\ h=5[/tex]

Substitute:

[tex]A=\dfrac{12+5}{2}\cdot5=\dfrac{17}{2}\cdot5=8.5\cdot5=42.5[/tex]

Answer:

[tex]\large\boxed{y=\dfrac{1}{4}x^2,\ y=-\dfrac{1}{2}x^2,\ y=\dfrac{3}{2}x^2}[/tex]

Step-by-step explanation:

The equation of a parabola: y = ax²

The larger the value of |a|, the narrower the parabola.

We have the following coefficients a:

[tex]\left|\dfrac{1}{4}\right|=\dfrac{1}{4},\ \left|-\dfrac{1}{2}\right|=\dfrac{1}{2},\ \left|\dfrac{3}{2}\right|=\dfrac{3}{2},[/tex]

We arrange the coefficients from the smallest to the largest:

[tex]\dfrac{1}{4}\ <\ \dfrac{1}{2}\ <\ \dfrac{3}{2}[/tex]

Therefore you have the answer:

[tex]y=\dfrac{1}{4}x^2,\ y=-\dfrac{1}{2}x^2,\ y=\dfrac{3}{2}x^2[/tex]

Answer:

Step-by-step explanation:

Since the length of one of the longer sides, a, has been given to be 6.3, plug it into the equation.

2(6.3) + b = 15.7

12.6 + b = 15.7

b = 15.7 - 12.6

b = 3.1

Answer:

Equation that can be used to find length of the base is b + 12.6 = 15.7  and the length of the base we get from this equation is 3.1 cm

Step-by-step explanation:

Given:

Length of the equal side of the Isosceles Triangle = a

Length of the base of the triangle = b

Equal sides are longer than base of the triangle.

Perimeter of the triangle = 15.7 cm

Equation representing given information = 2a + b = 15.7

To find: Equation that represent or can be used to find length of the base if longer side = 6.3 cm

Given Equation is the Equation representing the perimeter of the isosceles triangle.

Longer side  = 6.3 cm = Length of the Equal Sides of the triangle.

So, a = 6.3 cm

Now,

2 × 6.3 + b = 15.7

b + 12.6 = 15.7

b = 15.7 - 12.6

b = 3.1 cm

Therefore, Equation that can be used to find length of the base is b + 12.6 = 15.7  and the length of the base we get from this equation is 3.1 cm

Answer:

200ml

Step-by-step explanation:

5+2+3=10

400/10=40

Since lemon's ratio is 5, you multiply 40 by 5 to get 200.

Answer:

[tex]y^{5}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]

Hence

[tex]y^{2}[/tex] × [tex]y^{3}[/tex] = [tex]y^{(2+3)}[/tex] = [tex]y^{5}[/tex]

Yes there is because the change of rate for both the x and y-values is 2. It has a consistant rate of change.

Answer:

y = 54.1

Step-by-step explanation:

The big triangle is divided in two: one on  the left and one on the right. Lets start working with the right one.

We know the right triangle is a right triangle with legs 24 and 36, so we can use Pitagoras to find the hypotenuse (h), in a way that:

24^2 + 36^2 = h^2

1872 = h^2

Applying sqr root in both sides:

h = 43.27

So, the hypotenuse measures 43.27 or 43.3.

Now lets do the same with the triangle of the right which legs are 36 and y, lets find it hypotenuse (g):

36^2 + y^2 = g^2

1296 + y^2 = g^2

Now we will pass to the large triangle, which is composed by the left and the right triangles and has legs of 43.3 and g, and the hypotenuse is 24+y. Lets apply Pitagoras:

43.3^2 + g^2 = (24+y)^2

1875 + 1296 + y^2 = 24^2 + 48y + y^2

3171 + y^2 = 576 + 48y + y^2

As we have y^2 in both sides we can eliminate them

3171 + = 576 + 48y

Now subtract 576 in both sides:

3171 -576 = 576 + 48y - 576

2595 = 48y

Divide both sides by 48:

2595/48 = 48y/48

54.1 = y

So, the large hypotenuse measures 54.1+24 = 78.1. Lets verify:

43.3 ^2 + 1296 + 54.2^2 = 6,108.53

And the sqrd root of 6,108.53 is approximately 78.1. Verified!!!!

So, we can confirm: y = 54.1

Answer: option D.

Step-by-step explanation:

To solve this exercise you must apply the proccedure shown below:

- Apply the Distributive property (Remember that when you multiply two powers with the same base, you must add the exponents).

[tex]b^m*b^n=b^{(m+n)}[/tex]

- Add the like terms.

Therefore, you obtain that the product is:

[tex](2x^2+5x-3)(3x+7)=6x^3+14x^2+15x^2+35x-9x-21\\=6x^3+29x^2+26x-21[/tex]

An expression is defined as a set of numbers, variables, and mathematical operations. The product of (2x²+5x-3) and (3x+7) is 6x³ + 29x² + 26x - 21.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The product of (2x²+5x-3) and (3x+7) can be done as,

(2x²+5x-3) × (3x+7)

= 3x(2x²+5x-3) + 7(2x²+5x-3)

= 6x³ + 15x² - 9x + 14x² + 35x - 21

= 6x³ + 29x² + 26x - 21

Hence, the product of (2x²+5x-3) and (3x+7) is 6x³ + 29x² + 26x - 21.

Learn more about Expression:

https://brainly.com/question/13947055

#SPJ2

Find two "dots" where the line crosses the X and Y axis at real numbers.

(0,3) and (6,-1)

Now find the slope which is the difference in Y over the difference in x.

Slope = (-1 - 3) / (6-0) = -4 / 6 = -2/3

The answer is D.

Answer:

Part 1)

(1,H),(2,H)(1,T),(2,T)

Part 2)

1320

Part 4)

1/4

Part 5)

1/15

Step-by-step explanation:

Part 1)

Possible outcomes of cube={1,2,3,4,5,6}

Possible outcomes of coin=(H,t}

Now,  Andrew rolls the number cube once and flips the coin once

then possible outcome that contains only the outcomes in which the number cube lands on a number less than 3 are:

(1,H),(2,H)(1,T),(2,T)

Part 2)

Given:

population=1500 dogs

spots containing dogs= 15 out of every 125 dogs in the population have spots

spots containing dogs:

                                =1500/125

                                     =12    

                                     =12*15

                                     =180    

dogs in the population that do NOT have spots on their back

=1500-180=1320

Part 4)

Given:

classical songs=2

rock songs=13

rap=5

total songs= 2+13+5

                 =20

probability that the first song that Joel hears is a rap song= 5/20

                                     =1/4

Part 5)

Given:

3 Characters= elf, hobbit, or human

4 tools= magic, sword, shield, slingshot, or umbrella

Probability of first event , P(C)= 1/3

Probability of second event, P(T)=1/5

As both events are mutually exclusive so

P(magic elf)= P(C)*P(T)

                 =1/3+1/5

                 =1/15 !

Answer:

Step-by-step explanation:

I think 9. 10/50

10. 6/50

11. 44/50

Answer:

D. $240,000

Step-by-step explanation:

find $40,000 on the chart - then find 45 years old / 60% - go down the chart and over to the right and you'll find 6.0

multiply 40,000 * 6.0 = 240,000

hope this helps!!

The answer is D. 240,000

Hope this helps : )

The formula for lateral surface of a cylinder is:

SA = 2 *PI * r *h

Replace the letters with the given values:

400 = 2 * PI * r *40

Multiply the right side:

400 = r * 251.2

Divide both sides by 251.2:

r = 400 / 251.2

r = 1.59

The radius is 1.59 inches.

Answer: 1.59

Step-by-step explanation:

Set it up.

Make the equations equal to 180° because they are on a straight line. And a straight line adds up to 180°

Habeas corpus is the right to have one’s detention reviewed by a judge

Answer:

a prisoner’s right to inquire why he or she is being detained

Step-by-step explanation:

➷ Find the total number of pens:

5 + 3 + 2 = 10

The probability of taking a red the first time is 5/10

The probability of taking a blue the first time is 3/10

The probability of taking a green the first time is 2/10

If you want to take the same colored pen again, there would be 1 less of the total pen (as it hasn't been replaced) and there would be one less of that color (as one has already been taken)

Therefore:

The probability of taking a red again is 4/9

The probability of taking a blue again is 2/9

The probability of taking a green again is 1/9

Multiply the values for the same color together:

5/10 x 4/9 = 20/90

3/10 x 2/9 = 6/90

2/10 x 1/9 = 2/90

Add these values together:

20/90 + 6/90 + 2/90 = 28/90

Your answer is 28/90

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:  F) (x, y) → (x - 6, y  + 2)

Step-by-step explanation:

6 units to the left means subtract 6 from the x-value --> x - 6

2 units up means add 2 to the y-value --> y + 2

Answer: B, C, and D are all correct.

Step-by-step explanation:

Answer: B and D

Step-by-step explanation:

It would go between 7.32 and 7.37

It’s (x-6)(x+4) so the first one and last one

For this case we must factor the following expression:

[tex]x ^ 2-2x-24[/tex]

We must find two numbers that when added together give "-2" and when multiplied by "-24"

These numbers are:

[tex]-6\ and\ +4\\-6 + 4 = -2\\-6 * + 4 = -24[/tex]

So:

[tex]x ^ 2-2x-24 = (x-6) (x + 4)[/tex]

Answer:

[tex](x-6) (x + 4)[/tex]

Option A and D

answer :

y=-1/4x+5

my work:

y=mx+b

2=-1/4(12)+b

2=-3+b

+3 +3

5=b

y=-1/4x+5

Answer:

y = - [tex]\frac{1}{4}[/tex] 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 m = - [tex]\frac{1}{4}[/tex], hence

y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

To find c substitute (12, 2) into the partial equation

2 = - 3 + c ⇒ c = 2 + 3 = 5

y = - [tex]\frac{1}{4}[/tex] x + 5 ← equation of line

Answer:

342

Step-by-step explanation:

Let's see the difference is each successive values:

232 - 217 = 15

252 - 232 = 20

277 - 252 = 25

307 - 277 = 30

As we can see, each month the increase is 5 more than previous months' increase. Clearly from the pattern we can surmise that the next month (August), it will increase by 35 from the value of July.

Number of visitors in August = Number of Visitors in  July + 35 = 307 + 35 = 342

Answer:

342

Step-by-step explanation:

answer = 42

if you look at the triangle you see a small square in the corner indicating that the triangle is a 90 degree angle, therefore all the sides add up to 90. With this knowledge just add the values of the two known sides, 18 and 30, which is 48 and then subtract 48 from 90 which gives you the value of x, 42

Answer:

Step-by-step explanation:

Angles on one side of a straight line always add to 180°.

Therefore we have the equation:

[tex]35+(3x-15)+x=180[/tex]

[tex]35+3x-15+x=180[/tex]             combine like terms

[tex](35-15)+(3x+x)=180[/tex]

[tex]20+4x=180[/tex]           subtract 20 from both sides

[tex]4x=160[/tex]          divide both sides by 4

[tex]x=40[/tex]

∠DBE = 3x - 15. Substitute:

[tex]\angle DBE=\bigg(3(40)-15\bigg)^o=\bigg(120-15\bigg)^o=105^o[/tex]