A rectangular patio has an area of 91 fl. The length is 6 feet
longer than the width. Find the dimensions of the patio area
Solve by completing the square, Find the width and the length interms of w. Write an equation for the total area Find b/2 Find the dimensions.

Answer:

12

Step-by-step explanation:

3•4=12

Answer:

.6*.3=.18

Step-by-step explanation:

when two events must both happen, multiply their probabilities. (and=*, or=+)

Answer:

[tex]\frac{13-7\sqrt{3}}{2}[/tex]

Step-by-step explanation:

We need to rationalize the denominator of [tex]= \frac{5-\sqrt{3}}{4+2\sqrt{3}}[/tex]. For rationalizing we multiply the equation by [tex]\frac{4-2\sqrt{3}}{4-2\sqrt{3}}[/tex]

So, solving

[tex]= \frac{5-\sqrt{3}}{4+2\sqrt{3}}*\frac{4-2\sqrt{3}}{4-2\sqrt{3}} \\=\frac{(5-\sqrt{3})(4-2\sqrt{3})}{4+2\sqrt{3}*4-2\sqrt{3}}\\=\frac{(5-\sqrt{3})(4-2\sqrt{3})}{(4)^2-(2\sqrt{3})^2}\\= \frac{5(4-2\sqrt{3})-\sqrt{3}(4-2\sqrt{3})}{16-(4*3)}\\=\frac{20-10\sqrt{3}-4\sqrt{3}+2*3}{16-12}\\=\frac{20+6-14\sqrt{3}}{4}\\=\frac{26-14\sqrt{3}}{4}\\= \frac{2(13-7\sqrt{3})}{4}\\=\frac{13-7\sqrt{3}}{2}[/tex]

Answer:

0.25

Step-by-step explanation:

Answer:

x ≈ 8.66

Step-by-step explanation:

Using the sine ratio in the right triangle

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex]

Multiply both sides by 10

10 × sin60° = x, thus

x ≈ 8.66 ( to 2 dec. places )

Answer:

 π units^2.

Step-by-step explanation:

The area = π r^2   where  r = the radius and the radius = 1/2 * the diameter.

So the radius of this circle = 1/2 * 2 = 1.

The required area =  π * 1^2

= π units^2.

ANSWER

Exact form: π units square.

Or 3.14 square units.

EXPLANATION

The area of a circle is calculated using the formula:

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

From the diagram, the diameter of the circle is d=2 units.

The radius is half of the diameter which is 1 unit.

We substitute r =1 into the formula to obtain;

[tex]Area = \pi \times {1}^{2} [/tex]

[tex]Area = \pi \: [/tex]

In decimal form, the area is

[tex]Area =3.14 \: square \: units[/tex]

Word form: 4 to 15

Fraction form: 4/15

Ratio form: 4:15

The ratio has been written in three different forms as 4:15, 0.266:1 or 1:3.75.

When a number is divisible by another number then it can be written in the form of p:q, if two ratios are equal then they are said to be in proportion.

The number of walks in the baseball game is 4

The number of hits in the baseball game is 15

The ratio of walks to hits is 4 :15

The ratio of walks to hits is 0.2666 : 1

The ratio of walks to hits is 1 : 3.75

Therefore, the ratio has been written in three different forms as 4:15, 0.266:1 or 1:3.75.

To know more about Ratio

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Answer:

x = -94/17, y = -6, z = -48/17

Step-by-step explanation:

If solving this system of equations is what you want, here's the answer.

Answer:

(x + 2)² + (y - 2)² = 64

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 2, 2), thus

(x + 2)² + (y - 2)² = r²

Given C = 2πr = 16π ( divide both sides by 2π )

r = [tex]\frac{16\pi }{2\pi }[/tex] = 8

Hence

(x + 2)² + (y - 2)² = 64 ← equation of circle

To find the equation of the circle with center at (-2,2) and a circumference of 16π, first calculate the radius r=8 from the circumference, then use the formula (x+2² + (y-2)² = 64.

The question asks for the equation of a circle with a given center and circumference. The center of the circle is located at (-2,2), and the circumference is 16π. First, we calculate the radius of the circle using the formula for circumference, C = 2πr, where C is the circumference and r is the radius. Since C = 16π, we can solve for r to find that the radius r = 8 units.

Next, we use the standard equation of a circle, which is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is its radius. Therefore, substituting h = -2, k = 2, and r = 8 into the equation, we get (x + 2)² + (y - 2)² = 64, which is the equation that represents the circle with the given center and circumference.

Step-by-step explanation:

Let's say R is the initial radius of the sphere, and r is the radius at time t.

The volume of the sphere at time t is:

V = 4/3 π r³

Taking derivative with respect to radius:

dV/dr = 4π r²

This is a maximum when r is a maximum, which is when r = R.

(dV/dr)max = 4π R²

This is 4 times the sphere's initial great circle area, but not the great circle circumference.  The problem statement contains an error.

Answer:

Final answer is -63.

Step-by-step explanation:

Given expression is [tex]-|-9| \times |7|[/tex].

Now question says to simplify that expression [tex]-|-9| \times |7|[/tex]

| | indicates absolute function which results only in positive output so |-9| gives 9 only

and |7| gives 7.

then we can rewrite the expression as :

[tex]-|-9| \times |7|[/tex]

[tex]=-(9) \times (7)[/tex]

[tex]=-9 \times 7[/tex]

[tex]=-63[/tex]

Hence final answer is -63.

Check the picture below.

Answer: Option C

The equation is:

[tex](x+8)^2 +(y+3)^2=9[/tex]

Step-by-step explanation:

First we must calculate the midpoint between the two given points.

Then the midpoint will be the radius of the circumference

The midpoint between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is:

[tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

In this case the points are:

(-5 -3) and (-11 -3)

The the center is:

[tex](\frac{-5-11}{2}, \frac{-3-3}{2})[/tex]

[tex](-8,\ -3)[/tex]

Then the equation is:

[tex](x+8)^2 +(y+3)^2=r^2[/tex]

To find r we substitute one of the points in the equation and solve for r

[tex](-5+8)^2 +(-3+3)^2=r^2[/tex]

[tex](3)^2 +0=r^2[/tex]

[tex]r^2 =3^2[/tex]

[tex]r =3[/tex]

Finally the equation is:

[tex](x+8)^2 +(y+3)^2=9[/tex]

Answer:

Option C

Step-by-step explanation:

The standard form of equation of circle is:

(x-h)^2+ (y-k)^2=r^2

As we only know two points on the circle which are the ends of diameter.

As we know

Radius=Diameter/2

We have to find the length of diameter using the distance formula first to calculate radius. So,

Diameter= √((-11-(+5))^2+(-3-(-3)^2 )

= √((-11+5)^2+(-3+3)^2 )

=√((-6)^2+(0)^2 )

= √36

=6

Now,  

Radius=6/2

=3

As the diameter passes through centre, so the mid-point of diameter will be centre of the circle:

Mid-point=((x_1+x_2)/2,(y_1+y_2)/2)

=((-5-11)/2,(-3-3)/2)

=((-16)/2,(-6)/2)

=(-8,-3)

Putting the values of radius and centre in standard form

(x-h)^2+ (y-k)^2=r^2

(x-(-8))^2+ (y-(-3))^2=3^2

(x+8)^2+ (y+3)^2=9

So the correct answer is option C ..

Answer:

12 mm : 5 meters

Step-by-step explanation:

We need to write the ratio of drawing: real life

48 mm: 20 meters

We can divide each term by 4

48mm/4 : 20 meters/4

12 mm : 5 meters

Answer:

The data set "types of fruit at the grocery store" is qualitative.

The correct answer is B.

The correct option is a. quantitative, discrete.

The data set "types of fruit at the grocery store" is quantitative because it involves counting the number of different types of fruit, which is a numerical value. Furthermore, it is discrete because the count of fruit types will result in whole numbers, with no fractional or continuous values between them. For example, one cannot have 3.5 types of fruit; it must be a whole number such as 3 or 4. Therefore, the data is not qualitative as it is not about the characteristics or attributes of the fruit but rather the count of different categories of fruit. It is also not continuous as the number of fruit types cannot vary smoothly and must be counted in whole units.

For this case we have that by definition of trigonometric relations of rectangular triangles, that the sine of an angle is given by the opposite leg to the angle on the hypotenuse of the triangle. So:

[tex]Sin (45) = \frac {leg} {h}[/tex]

Where h is the hypotenuse.

[tex]\frac {\sqrt {2}} {2} = \frac {leg} {h}[/tex]

We cleared h:

[tex]h = \frac {2leg} {\sqrt {2}}[/tex]

We rationalize:

[tex]h = \frac {2leg} {\sqrt {2}} * \frac {\sqrt {2}} {\sqrt {2}}\\h = \frac {2 \sqrt {2} * leg} {2}\\h = \sqrt {2} * leg[/tex]

ANswer:

Option A

The square root of 189

the square root of 189

Answer:

[tex]\boxed{x^{2} + 2x - 8}[/tex]

Step-by-step explanation:

6. Practice

The dimensions of the current park are x long and x wide.

The new park will be 4 longer and 2 thinner.

Its new dimensions will be x + 4 long and x – 2 wide.

Its new area will be

A = width × length = (x – 2)(x + 4)

Find the product

[tex]\begin{array}{lll}\textbf{Steps} & \textbf{Problem: }(x - 2)(x + 4) & \\\textbf{1. List variables} & a = x - 2 & \\ & b = x & \\ & c = 4 &\\\textbf{2. Distribute (x - 2)} & (x -2)(x + 4)\\ & = (x - 2)(x) + (x - 2)(4)\\\textbf{3. Distribute x and 4} & x^{2} -2x + 4x - 8\\\textbf{4. Combine like terms}& x^{2} + 2x - 8\\\end{array}\\\text{The area of the updated skatepark will be }\boxed{\mathbf{ x^{2} + 2x - 8}}[/tex]

The expression 36a^2 - 49b^2 can be factored into the product of two binomials by applying the difference of squares formula. The factored form of the expression is (6a - 7b)(6a + 7b).

The expression 36a^2 - 49b^2 is a difference of squares. A difference of squares is a special type of binomial that can be factored into the product of two binomials.

In general, if you have an expression of the form x^2 - y^2, this is equal to (x - y)(x + y).

In the case of the expression 36a^2 - 49b^2, 36a^2 is the square of 6a, and 49b^2 is the square of 7b. Therefore, the expression 36a^2 - 49b^2 can be factored into (6a - 7b)(6a + 7b).

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Final answer:

The expression 36a² - 49b² is factored as (6a + 7b)(6a - 7b) using the difference of squares identity a² - b² = (a + b)(a - b).

Explanation:

The expression 36a² - 49b² is a difference of squares which can be factored using the identity a² - b² = (a + b)(a - b). In this case, the expression can be written as (6a)² - (7b)². This resembles the identity where a is 6a and b is 7b. Applying the identity, we get:

(6a + 7b)(6a - 7b)

This is the factored form of the given expression. To understand why this works, we recognize that squaring a number and then subtracting the square of another number creates two terms, one positive and one negative, whose products with themselves give us the original expression. The factored form thus represents two binomials that reflect the sum and the difference of the square roots of the original terms, respectively.

Answer:

25%

Step-by-step explanation:

The chance of flipping heads or tails is 50%.

We have to flip heads or tails 3 times.

To make this easier, I will convert 50% to 1/2 for the time being.

Since the chance of getting heads or tails is 1/2 and there are 3 flips, multiply 1/2 to the power of 3, which is 1/8

1/8 is the probability of getting this outcome.

Answer:

Part 1) 0.08

Part 2) $75.6

Part 3) y=230+0.08x

Part 4) The minimum amount to sell is $3,500

Step-by-step explanation:

Part 1) Give the decimal form of 8%

we know that

To convert percentage number to decimal number, divide by 100

8%=8/100=0.08 ----> decimal form

Part 2) If you make $945 in sales, how much will you make from your 8% commission?

Multiply the percentage of commission in decimal number by the total amount in sales

so

0.08*($945)=$75.6

Part 3) Create an expression representing how much you will make in one week if you sell  

x amount of sales.

Let

x-----> amount of sales in a week

y ----> total earned in a week

we know that

The linear equation that represent this situation is

y=230+0.08x  

Part 4) Create an inequality using the expression in problem 3 to find how much you need  to sell at a MINIMUM to make your goal

we know that

The inequality that represent the situation is

[tex]230+0.08x \geq 510[/tex]

Solve for x

Remember that x is the amount of sales in a week

[tex]0.08x \geq 510-230[/tex]

[tex]0.08x \geq 280[/tex]

[tex]x \geq 280/0.08[/tex]

[tex]x \geq 3,500[/tex]

The minimum amount to sell is $3,500

Answer: -3

Step-by-step explanation:8-5=3 take the negative so it’s -3

[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ \cline{1-1} r=0.8\\ a_1=10\\ n=5 \end{cases} \\\\\\ a_5=10(0.8)^{5-1}\implies a_5=10(0.8)^4\implies a_5=4.096[/tex]

Answer:

i dont real know

Step-by-step explanation:

Answer:

A model can show people how you did it so you don't have to explain it. It also helps people who learn visually

Step-by-step explanation:

Answer:

The advantages of using a model are familiar objects to represent unfamiliar things, can help you visualize, or picture in your mind, something that is difficult to see or understand, can help scientists communicate their ideas, etc while the disadvantages of using a model is the cost of running several different simulations may be high,time,people's reactions,etc.

Step-by-step explanation:

Answer: 72

Step-by-step explanation:

722 —> 720

9 —> 10

72 divided by 1 is 72

x: females

x+14: males

so 34=x+x+14

To find the number of males and females in the biology class, we can create a system of equations based on the given information and then solve for the variables. After solving the equation, we find that there are 10 females and 24 males in the biology class.

To find the number of males and females in the biology class, we can create a system of equations based on the given information:

Let's assume the number of females in the class is 'x'.

The number of males in the class is then 'x + 14'.

Since the total number of students in the class is 34, we can write the equation:

x + (x + 14) = 34

Simplifying the equation, we have 2x + 14 = 34.

Subtracting 14 from both sides, we get 2x = 20.

Dividing both sides by 2, we find x = 10.

Therefore, there are 10 females and 24 males in the biology class.

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Answer - 3.2 hours

because 4.48 miles divided by 1.4 mph equals 3.2

Answer:

3.2 hrs

Step-by-step explanation:

Recall that distance = rate times time, so:

4.48 mi = (1.4 mph)(time), and:

                                          4.48 mi

the elapsed time was ------------------- = 3.2 hours

                                       1.4 mph

Answer:

0.42

Step-by-step explanation:

There are total 7 end points, 3 of them lead to winning $10 and the other ones lead to nothing

so, [tex]\frac{3}{7}[/tex] = 0.42

Answer:

Option B. [tex]212.1\ cm^{2}[/tex]

Step-by-step explanation:

step 1

Find the central angle of the shaded sector

Remember that the diameter divide the circle into two equal parts ( 180 degrees each part)

so

Let

x -----> the measure of the central angle of the shaded sector

∠x+72°=180°

∠x=180°-72°=108°

step 2

Find the area of the circle

The area of the circle is

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

we have

[tex]r=15\ cm[/tex]

assume

[tex]\pi=3.1416[/tex]

substitute

[tex]A=(3.1416)(15)^{2}[/tex]

[tex]A=706.86\ cm^{2}[/tex]

step 3

Find the area of the shaded sector

Remember that the area of the complete circle subtends a central angle of 360 degrees

so

by proportion find the area of a sector by a central angle of 108 degrees

[tex]\frac{706.86}{360}=\frac{x}{108}\\ \\x=706.86*108/360\\ \\x=212.1\ cm^{2}[/tex]

Answer:

This is your answer.

Step-by-step explanation:

Hope is helps!!

Answer: (x+1) (x+2) (x+5)

Step-by-step explanation: