Maya is solving the equation 2(1+7x)=72. She lists an explanation for each step as shown. Which is the missing explanation for Maya's first step after writing the given equation?

Answer:

The area of a rectangle is given by the formula:

area = length * breadth

In this case, the length of the rectangle is (x+2) cm and the breadth is (x) cm, so the area is:

area = (x+2) cm * (x) cm

= x^2 + 2x cm^2

We know that the area of the rectangle is 15 cm^2, so we can set up the following equation:

x^2 + 2x cm^2 = 15 cm^2

We can solve for x by using the quadratic formula:

x = (-2 +/- sqrt(4 - 41(-15))) / (2*1)

= (-2 +/- sqrt(64)) / 2

= (-2 +/- 8) / 2

= (-4, 2)

We have two solutions for x, so we need to consider both of them to find the dimensions of the rectangle.

If x=-4, then the length of the rectangle is (x+2) cm = (-4+2) cm = (-2) cm and the breadth is (x) cm = (-4) cm. Since the length and breadth of a rectangle must both be positive, this solution is not valid.

If x=2, then the length of the rectangle is (x+2) cm = (2+2) cm = 4 cm and the breadth is (x) cm = 2 cm. These dimensions give us a valid rectangle with an area of 15 cm^2.

The perimeter of the rectangle is the sum of all four sides, so the perimeter is 2 cm + 2 cm + 4 cm + 4 cm = 12 cm.

Therefore, the value of x that gives us a rectangle with an area of 15 cm^2 and a perimeter of 12 cm is x=2.

On solving the provided question, we can say that - As a result, Orthocenter triangle is the answer to the given triangle issue (0, - 5 ).

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

determine LN's slope.

[tex]m = (y2 - y1)/ (x2- x1) = 1-5/8-0 = 2[/tex]

formula for altitude

[tex]y - 1 = 2(x - 3) (x - 3)\\y - 1 = 2x - 6\\[/tex]

y = 2x - 5

Altitude of N and LM

[tex]m = (y2 - y1)/ (x2- x1) = 1-5/3-0 ⇒ -3/4\\y - 1 = (x - 8) (x - 8)\\y - 1 = x - 6\\[/tex]

y = x - 5

[tex]8x - 20 = 3x - 20\\5x - 20 = - 20 \\5x = 0 = > x = 0\\[/tex]

y =0 - 5 = - 5

It is the orthocenter (0, - 5 )

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer:

51

Step-by-step explanation:

Hope this helps

180-90-39

Answer:

1500006875

Step-by-step explanation:

Multiply 2 numbers at a time

The coordinates of the inflection points are (3, 0) and it concave upwards

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

g(t) = t^2 - 27/t

Express properly

So, we have

g(t) = t² - 27/t

Calculate the second derivative

So, we have

g''(t) = 2 - 54/t³

Set the differentiated equation to 0

2 - 54/t³ = 0

So, we have

2t³ = 54

Divide by 2

t³ = 27

Take the cube roots

t = 3

Substitute t = 3 in g(t) = t² - 27/t

g(3) = 3² - 27/3

g(3) = 0

This means that the inflection point occurs at t = 3 and the coordinates of the inflection point are (3, 0)

Recall that

g''(t) = 2 - 54/t³

Next, we check if the second derivative exist at t = 0,

g''(0) = 2 - 54/0³

g(0) = undefined

The undefined value implies that the graph has a vertical inflection point at t = 0

And as such, the graph of the function is concave upward

Read more about inflection points at

https://brainly.com/question/29249123

#SPJ1

Answer:

5x+9

Step-by-step explanation:

Answer:

I got 14

Step-by-step explanation:

Answer:

[tex]\implies \sec 3 30^o = \dfrac{2}{\sqrt3}=\dfrac{2\sqrt{3}}{3}[/tex]

Step-by-step explanation:

Given :-

And we need to find out its value . Firstly we know that 330° lies in 4th quadrant . And In fourth quadrant , cosine and secant are positive . Therefore , the result will be positive. Now we know that ,

[tex]\implies \sec (360^o-\theta)= \sec\theta [/tex]

Using this ,

[tex]\implies \sec (330^o) \\\\\rm\implies sec(360^o-30^o) \\\\\rm\implies \sec 30^o [/tex]

And the value of sec 30° is ,

[tex]\implies \sec 30^o = \dfrac{2}{\sqrt3}[/tex]

And by question we need to write it with a rational denominator .So on rationalising the denominator , we have ,

[tex]\implies \sec 30^o = \dfrac{2}{\sqrt3}=\boxed{\red{\dfrac{2\sqrt3}{3}}}[/tex]

Hence the required answer is 2√3/3.

Answer:

Step-by-step explanation:

To figure out how long it would take Fine Floors to install carpeting in a room that measures 11 feet 9 inches by 13 feet 4 inches, we first need to determine how many square yards of carpeting are needed for the room. We can start by converting the dimensions of the room from feet and inches to yards, since that's the unit of measurement we're working with.

To convert feet to yards, we divide by 3. For example, 11 feet is equal to 11/3 = 3.67 yards. To convert inches to yards, we divide by 36 (since there are 36 inches in a yard). For example, 9 inches is equal to 9/36 = 0.25 yards.

So the length of the room in yards is 3.67 + 0.25 = 3.92 yards, and the width of the room in yards is 13/3 + 4/36 = 4.33 + 0.11 = 4.44 yards.

To determine the total area of the room in square yards, we multiply the length and width: 3.92 * 4.44 = 17.38 square yards.

Now that we know how many square yards of carpeting are needed for the room, we can use that information to calculate how long it would take Fine Floors to install the carpeting. Since we know that Fine Floors can install 15 square yards of carpeting in 4 hours 30 minutes, we can use that as the ratio for our calculation.

To calculate how long it will take to install 17.38 square yards of carpeting, we use the proportion:

(15 sq. yards) / (4 hours 30 minutes) = (17.38 sq. yards) / (x hours)

Cross multiplying and solving for x, we find: x = (4 hours 30 minutes) * (17.38 sq. yards) / (15 sq. yards)

So it would take Fine Floors approximately 5 hours and 11 minutes to install carpeting in a room that measures 11 feet 9 inches by 13 feet 4 inches.

Answer:

Ratios and fractions are connected. A ratio of 3 to 14 is the same thing as 3/14. Multiply 686 by 3/14. You will get 147. That is your amount of zinc. If we simplify 147/686, or 147:686, we get 3:14 confirming our answer.

Answer:

-----------------------------------

Let the amount of zinc be x. Then we have equal ratios:

Solve it for x:

Answer:

15*n=p

Step-by-step explanation:

904.32 is the volume.

Volume of sphere

= (4/3)πr³

= (4/3) × 3.14 × (6cm)³

= (4/3) × 3.14 × 6cm × 6cm × 6cm

= 4 × 3.14 × 2cm × 6cm × 6cm

= 904.32 cm³

Answer:

IT IS EASY FORMULAE OF SPHERE IS 4/3πr³ so,

Step-by-step explanation:

                                                    put the value,

                                              =   4/3 * 3.14 *  6³

                                              =  1.333 * 3.14 * 216

                                              =  4.18562 * 216

                                               =  904.09 cm³ ans

Answer:

The expression "d-7 / 2" can be written in words as

Step-by-step explanation:

The expression "d-7 / 2" can be written in words as "the quotient of d minus 7, divided by 2".

This is the operation of subtracting 7 from d and then dividing the result by 2.

Answer:

$25.50

Step-by-step explanation:

85 X 0.3 (30%)=25.5

$25.50

The two congruent segments in the figure are LJ and LI.

What is congruency?

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.

An included angle is found between two sides that are under consideration.

Thus, two triangles having two pairs of corresponding sides and one pair of corresponding angles that are congruent to each other is not enough justification for proving that the two triangles are congruent based on the SAS Congruence Theorem.

In the figure, the two segments marked are LI and LJ these two segments are congruent to each other.

Congruency means the shape and the size of the segments will be equal to each other.

Hence, the two congruent segments in the figure are LJ and LI.

To learn more about congruency visit,

brainly.com/question/2938476

#SPJ1

Answer:

hope this helped

Step-by-step explanation:

Answer:

I think this is right

Step-by-step explanation:

Answer:

-28(x + 2) = (y - 1)²

Step-by-step explanation:

..............

The equation (y + 1)² = -12(x - 2) represents the given parabola.

What is a parabola?

A parabola is a U-shaped plane curve. It is assumed to be mirror symmetrical. A parabola is produced by the intersection of a right circular cone and a plane parallel to the cone.

The vertex is at (-2, 1) and the directrix is x = 5.

Therefore, the vertex of the given parabola is at 2nd quadrant.

Again, the directrix is also parallel to the y-axis.

As a result, the parabola will open towards the left.

The general form of a parabola is (y - k)² = 4a(x - h)

Here, h and k are x and y coordinates respectively of the vertex.

Now, the coordinates of the focus are (h + a , k) and the directrix is at x = h − a.

Therefore, h - a = 5 (as, x =5)

⇒ 2 - a = 5

⇒ a = -3

Therefore, the equation of the parabola is (y − k)² = 4a(x − h)

⇒ [y - (-1)]² = 4(- 3)(x - 2)

⇒ (y + 1)² = -12(x - 2)

The equation of the parabola that has a vertex (2 , -1) and a directrix

of x = 5 is (y + 1)² = -12(x - 2)

Learn more about parabola here: https://brainly.com/question/4074088

#Tag#SPJ2

if functions  f(x) = 2x²-4x-6 and g(x)= 2x+7 then f(g(x)) is 8(x+2)(x+4)

A relation is a function if it has only One y-value for each x-value.

Given functions are f(x)= 2x²-4x-6

g(x)=2x+7

We need to find expression of f(g(x))

f(g(x))=f(2x+7)

Now replace x with 2x+7 in f(x)

f(2x+7)=2(2x+7)²-4(2x+7)-6

=2(4x²+49+28x)-8x-28-6

Apply distributive property

=8x²+98+56x-8x-28-6

Add the like terms

=8x²+48x+64

f(g(x))=8(x+2)(x+4)

Hence, if functions f(x) = 2x²-4x-6 and g(x)= 2x+7 then f(g(x)) is 8(x+2)(x+4)

To learn more on Functions click:

https://brainly.com/question/21145944

#SPJ1

Answer:

7.1 [tex]in^{2}[/tex]

Step-by-step explanation:

The surface of an ice-hockey puck is shaped as a circle. This means that the surface area of this circle is calculated by the following formula

A= [tex]\pi r^{2}[/tex]

If the measurement of one side to the other is 3 inches, this would be the diameter. The radius is half of the diameter, so in this scenario, it would be 1.5 inches. We can now plug this value into the formula and solve for the surface area.

A = [tex]\pi r^{2}[/tex]

A = [tex]\pi 1.5^{2}[/tex]

A = [tex]\pi * 2.25[/tex]

A = 7.068 or 7.1 [tex]in^{2}[/tex] (rounded to the nearest tenth)

Answer:

proportion

Step-by-step explanation:

Answer:

B) 1

Step-by-step explanation:

65 (1) +1 = 66

80 (1) = 80

66 + 80 = 146

Answer:

A subset is when all of the elements in the subset are in the actual set. A proper subset is a subset which the actual set has at least on more element than the proper subset.

Step-by-step explanation:

For example, Set A, {1,2,3} is a subset of B {1,2,3}. But Set C, {1,2} is a proper subset of B. Set {5,8} is a subset of {2,5,8}.

Answer:

y = 3

Step-by-step explanation:

2y + 4 = 10

2y = 6

y = 3

Answer:

Step-by-step explanation:

Well it would be funchen because as you see it just makes sence

Answer:

not a function

Step-by-step explanation:

In a function, an input gives only one output. As you can see from the graph, the input which is 4 produces 3 different outputs which are 2, 3 and 4, thus it cannot be a function.

Answer:

5/2

Step-by-step explanation:

cscθ = 1/sinθ = 1/(2/5) = 1 x (5/2) = 5/2

We know,

[tex] \boxed{sin( \theta) = \frac{1}{csc( \theta)} }[/tex]

So,

=》

[tex] \dfrac{2}{5} = \dfrac{1}{ \csc( \theta) } [/tex]

=》

[tex] \csc( \theta) = \dfrac{5}{2} [/tex]

Answer:

The number of shuttles completed successfully is recorded as the score of that runner. The score is recorded in Level. Shuttles format (e.g. 9.5). The maximum laps on the PACER test is 247, which former Central Middle School student Dennis Mejia achieved, the only person to ever reach such a level.

Step-by-step explanation:

The statement five less than four times a number is greater than or equal

to 3 indeed has a solution results to 2.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A statement five less than four times a number is greater than or equal to 3.

Let, The unknown number be 'n'.

Therefore, The numerical form of the statement is,

4n - 5 ≥ 3.

4n ≥ 8.

n ≥ 2.

So, Yes 2 is a solution.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ1

The length of PZ is 7 units.

According to the centroid theorem, the triangle's centroid is located 2/3 of the way between the vertex and the side midpoints.

Given:

As, Centroid is the point where all median of a Triangle intersect.

Here, we have centroid 'P'.

Now, using the property of Centroid that the Centroid of the triangle is at 2/3 of the distance from the vertex to the mid-point of the sides.

So, SP = 1/3 SZ => SZ = 3SP

and, PZ = 2/3 SZ => SZ = 3/2 PZ

Then, 3SP = 3/2 PZ

3(3.5) = 3/2 PZ

10.5 x 2 = 3 PZ

21 = 3PZ

PZ = 7 units

Learn more about centroid here:

https://brainly.com/question/10708357

#SPJ1

Answer:

Step-by-step explanation:

SOLVE..

3/12=?/4

or,(3×4)/12=?(cross muntiply )

or,1=?

therefore 1 is yhe reguired ans..