Which of the following is the correct expansion of (x + 3)(x + 4)?

Answer: \(5\sqrt 5\)

Step-by-step explanation:

Sol \(\sqrt 125\) = \(\sqrt{25.5}\)

= \(\sqrt{25}\)  x  \(\sqrt{5}\)

\(5 \sqrt{5}\)

Answer:

942.48 meters

Step-by-step explanation:

The circumference of a circle can be calculated using the formula:

Circumference = π * Diameter

where π (pi) is a mathematical constant approximately equal to 3.14159.

Given a diameter of 300 meters, we can calculate the circumference as follows:

Circumference = 3.14159 * 300

Circumference ≈ 942.48 meters

Therefore, the circumference of a circular amphitheater with a diameter of 300 meters is approximately 942.48 meters.

1. x = 13, y = 11.5

2. x = 39, y = 123

Step-By-Step Explanation: For the first diagram, you can see that 10x - 42 = 6x + 10 by way of vertical angles. Vertical angles are two opposite angles created by the same two lines, meaning that they will ALWAYS be congruent. Solving for x, you get that 4x = 52, or that x = 13. There is another thing. Both of the diagrams have a total angle measurement of 360, since they both go all the way around. Knowing that, 6x + 10 + 8y must be equal to half of that, or 180. Solving for 88 + 8y = 180 (since you know the value of x), you know that 8y = 92, or x = 11.5.

For number two, the concept is very similar, but this time there's more angles. You can immediately see that there are 3 pairs of vertical angles. The value of the angle squishes between the x - 10 and the 3x + 6 is x - 11; again, vertical angles. The angle squished between 3x + 6 and x - 11 is x - 10 (vertical angles!). Last, you know that 3 x + 6 = y, since they are vertical angles. Combining 2(x-11) and 2(x-10) and 2(3x+6) [remember, y = 3x + 6!!], you get that 10 x = 390, and x = 39. Plug that in for the value of y, which is 3x + 6, giving you 123 degrees.

Answer:

1.6538461538461538461538461538462

Step-by-step explanation:

I don't get is it dividing?

Answer:

\((-\infty,2)\)

Step-by-step explanation:

Since \(-3x+6\nless 0\), then \(x\ngtr 2\), therefore, the domain of the function is \((-\infty,2)\).

The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.

Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:

y - 3 = 1(x - (-1))

Simplifying:

y - 3 = x + 1

Now, we can rewrite the equation in the standard form:

y = x + 4

Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

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Answer: he took 60 grapes to school

Step-by-step explanation:

you just have to think about this. if you have given a friend 15 grapes and you are left with 45. So, for you to have 45 left you must have left home with 60 grapes.

Mathematically, lets represent how many he brought to school with x

15+45=x

X= 60

Answer:

2

Step-by-step explanation:

2*3+3*4 x 1/3 power 2

6+12 x 1/9

18 x 1/9

2 x 1 (because 9 and 18 are cutted by each other)

2

2

To evaluate the expression (2b+3a)×(c^2) when a=4, b=3, and c=1/3, we substitute the given values into the expression and perform the indicated arithmetic operations:

(2b + 3a) × (c^2)

= (2(3) + 3(4)) × ((1/3)^2) (substitute a=4, b=3, c=1/3)

= (6 + 12) × (1/9) (evaluate 2(3) + 3(4) and (1/3)^2)

= 18/9

= 2

Therefore, when a=4, b=3, and c=1/3, the expression (2b+3a)×(c^2) equals 2.

Based on the number of seats on the balcony, the number of seats in the theatre are 600 seats.

The balcony is said to have 120 seats and these are 1/5 of the total seats in the theatre.

The total number of seats in the theatre are:

= Number of seats on balcony / Proportion of seats this represents

Solving gives:

= 120 ÷ 1/5

= 120 ÷ 0.2

= 600 seats

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That is

Great Question!

The problem we have at hand is known to be a function, which maps elements from one set of objects, ( the domain ) onto another, the range. If we were to consider an ordered pair, say ( x, y ), then the function would map x onto y. The inverse function is simply the reverse. Take the ordered pair (-4,0). Function g would map - 4 onto 0, such that \(g( - 4 ) = 0\). Therefore, the inverse function would map 0 onto - 4, resulting in \(g^{-1}( 0 ) = - 4\). And there you have it! Our first part is answered!

____

This second bit here is interesting. Let \(y = h( x )\) -

\(y = 4x + 3\) - Switch x and y,

\(x = 4y + 3\) - And now solve this equation for y,

\(x - 4y = 3,\\- 4y = - x + 3,\\y = 1 / 4x - 3 / 4\)

As you can see, we have taken the inverse of h( x ). As y = h( x ), we can thus conclude the following -

\(h^{-1}(x) = 1 / 4x - 3 / 4\)

____

The composition (h^-1 o h)(-5) is, in other words, h^-1(h(-5)). We can therefore calculate h(-5) and then take it's inverse -

\(h(-5) = 4(-5) + 3,\\h(-5) = - 20 + 3,\\h(-5) = - 17\)

Now we can take it's inverse -

\(h^{-1}(-17) = 1 / 4( - 17 ) - 3 / 4,\\- 17 / 4 - 3 / 4,\\= - 5!\)

Our solution for this last bit is - 5. And, if you don't feel like reading through this entire explanation just take a look at the " summed up " answer below,

\(g^{-1}( 0 ) = - 4,\\\\h^{-1}( x ) = 1 / 4x - 3 / 4,\\\\( h * h^{-1} )( - 5 ) = - 5\)  I do hope that helps you!

Answer:

Or 50

Step-by-step explanation:

Answer:

12.57m

Step-by-step explanation:

c=22/7*2*2=12.57m

Answer:

0.5: 0.2: 0.4:

Fair Coin Blue Block Blue Marble

Soccer Ball Red Block

Dice Yellow Marble

Tennis Ball

Step-by-step explanation:

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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The equation of the line in point-slope form is y + 1 = 2(x + 8).

What is equation of line?

An equation with terms that have variables x and y independently and a degree of one is referred to be a line equation in a two-dimensional coordinate system. A linear equation is any equation with degree 1. The relationship between the x and y coordinates of any point on a straight line is known as the equation of a straight line.

The point-slope form of the equation of a line with slope m and passing through the point (x1, y1) is given by:

y - y1 = m(x - x1)

Using the given information, we have:

m = 2

x1 = -8

y1 = -1

Substituting these values into the point-slope form, we get:

y - (-1) = 2(x - (-8))

Simplifying, we get:

y + 1 = 2(x + 8)

This is the equation of the line in point-slope form.

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Answer:

Step-by-step explanation:

what is 12/21 + 18/21 + 14/21

(12 + 18 + 14)/21 =

44/21

The distance that Mr. Stein drove can be represented by the expression: \(140 - x\)

A mathematical phrase made up of one or more variables, constants, and arithmetic operations like addition, subtraction, multiplication, and division is known as an algebraic expression. Exponentiation and other mathematical operators could also be present.

Let's assume that Mr. Smith drove "x" miles before Mr. Stein took over the driving.

Then, the total distance they traveled is 140 miles.

So, the distance that Mr. Stein drove can be represented by the expression:

140 - x

Therefore, This is because if Mr. Smith drove "x" miles, then the remaining distance that needed to be covered by Mr. Stein would be the difference between the total distance of 140 miles and the distance already driven by Mr. Smith.

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Answer:

1/4 of them were rotten

rotten ones = 1/4 × 12 = 3

ones that weren't rotten = 12 - 3 = 9

The statement that is not true is (a) A = 74 degrees

From the question, we have the following parameters that can be used in our computation:

The dilation of ABC by a scale factor of 2

This means that

Scale factor = 2

The general rule of dilation is that

using the above as a guide, we have the following:

AC = 2 * 5 = 10

C = 53 degrees

BC = 2 * 3 = 6

A = 37 degrees

Hence, the statement that is not true is (a) A = 74 degrees

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Answer:

Slope of line g = \(1\frac{1}{3}\)

Step-by-step explanation:

* Mathematics rule: If two lines are perpendicular to each other, then the product of their slopes is equal to -1 .

∴ \(-\frac{3}{4}\) × slope of line g = -1

Slope of line g = -1 ÷ \(-\frac{3}{4}\) = 4/3 = \(1\frac{1}{3}\)

Answer:

x= −1/2, x=52/5

Step-by-step explanation:

2(x+7)=13

(2)(x)+(2)(7)=13(Distribute)

2x+14−14=13−14

2x=−1

2x/2=−1/2

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

5(x−7)=17

(5)(x)+(5)(−7)=17(Distribute)

5x+−35=17

5x−35=17

5x−35+35=17+35

5x=52

5x/5=52/5

Answer:

y = 5

Step-by-step explanation:

\(14y-7y=35\\7y=35\\y=5\)

14 minus 7 is 7

7Y is equal to 35

divide both sides by 7 is equal to 5

Answer: 13x+284/4

Step-by-step explanation:

Combine multiplied terms into a single fraction:

52x−7+34x+1452−7+34+14

Combine multiplied terms into a single fraction:

5x2−7+34x+1452−7+34+14

Add the numbers:

5x2−7+3x4+1452−7+34+14 And that’s your answer

Answer:

0.5

Step-by-step explanation:

Circumference of a circle = 2πr.

Given, circumference = 3.14 meters.

Therefore,

2πr = Circumference of a circle

or, 2πr = 3.14.

or, 2 × 3.14r = 3.14,[Putting the value of pi (π) = 3.14].

or, 6.28r = 3.14.

or, r = 3.14/6.28.

or, r = 0.5.

Minimum = 49

Median = 52

1st quartile = (49+51+51+52 ) /4

. Lower part = 203/4 = 50.75

3rd quartile = (52+53+55+67)/4

Upper part= 217/4 = 54.25

Now find maximum

Maximum M = 67

Answer:

As there are six seats in a row and the first person in the row is a woman and the people alternate woman, men, the possibility is

W

M

W

M

W

M

in that order.

Now as we four women, three seats for women can be filled in

X

4

P

3

=

24

ways

and similarly as we four men, three seats for men can be filled in

X

4

P

3

=

24

ways

Hence, total

24

×

24

=

576

permutations.

Step-by-step explanation: