the area of the rectangular park is 4 1/2 square miles. if the length is 1/2 mile, how wide is the park?

Answer:

80%

Step-by-step explanation:

(54-30)/30 *100 = 80%

Answer:

[tex]9y^2-4x^2-36y+16x-16=0[/tex]

Step-by-step explanation:

The given hyperbola has equation:

[tex]\frac{(y-2)^2}{4}-\frac{(x-2)^2}{9}=1[/tex]

We multiply through by 36 to get:

[tex]9(y-2)^2-4(x-2)^2=36[/tex]

We expand to get:

[tex]9(y^2-4y+4)-4(x^2-4x+4)=36[/tex]

[tex]9y^2-36y+36-4x^2+16x-16=36[/tex]

[tex]9y^2-36y-4x^2+16x-16=0[/tex]

The equation of the hyperbola in general form is:

[tex]9y^2-4x^2-36y+16x-16=0[/tex]

Let's call trade balance b, exports e and imports i.

We now construct formula.

[tex]b=\Delta{ei}=e-i[/tex]

Put in the data from last year.

[tex]b=968-1658=\boxed{-690}[/tex]

U.S trade balance for that year is -690 billion dollars.

Answer:

D. 12

Step-by-step explanation:

Answer:

D 12

Step-by-step explanation:

8h > 64

Divide each side by 8

8h/8 > 64/8

h > 8

H must be greater than 8

The only value in your list greater than 8 is 12

[2 1 | 1 0 ] • x = [5 | 10]

We multiply by the inverse of

[2 1 | 1 0 ]

det( [2 1 | 1 0] ) = -1

=> [2 1 | 1 0 ]^(-1) = (-1)•[0 -1 | -1 2 ] =

= [0 1 | 1 -2]

=> [2 1 | 1 0 ] • x = [5 | 10]

=> x = [2 1 | 1 0 ]^(-1) • [5 | 10]

=> x = [0 1 | 1 -2] • [5 | 10]

=> x = [0+10 | 5-20]

=> x = [10 | -15]

Answer:

No solution

Step-by-step explanation:

Rearrange into quadratic form: 3x² + 0x - 3 = 0

Quadratic formula: when ax² + bx + c = 0: x = (-b ± √(b² - 4ac))/2a

Plug in: x = 0 ± √(0 - 4*3*3))/2a

From this, we can conclude that this equation has no solution, as 0 - 4*3*3 will definitely be negative, and a negative number can not be square rooted.

Answer:

maybe you add then all up

Answer: W = 700 divided by a+18

Step-by-step explanation:

a) We can plug in $358 into A(w), since A(w) represents the amount of money Dale needs. So,

358 = 700 - 18w

Subtract: -342 = -18w

Divide: w = 19 weeks

b) We can plug in 6 into w, since w represents the number of weeks Dale saves money. So,

A(w) = 700 - 18(6)

Multiply: A(w) = 700 - 108

Subtract: A(w) = $592

Answer:

D.

Step-by-step explanation:

For this case we have:

Let k> 0:

To graph [tex]y = f (x) + k,[/tex] the graph k units is moved up.

To graph [tex]y = f (x) -k[/tex], the graph moves k units down.

Let h> 0:

To graph[tex]y = f (x-h)[/tex], the graph moves h units to the right.

To graph [tex]y = f (x + h),[/tex] the graph moves h units to the left.

So, we have:

[tex]y = f (x) = - \sqrt [3] {x}[/tex]

Shifted 7 units up and 4 to the right means:

[tex]k = 1\\h = 4[/tex]

[tex]y = f (x) = - \sqrt [3] {x-4} +7[/tex]

Answer:

Option B

Answer:

[tex]y=\tan \frac{1}{2} \pi[/tex]

Step-by-step explanation:

The given graph has a period of [tex]2\pi[/tex], because the graph repeats after every [tex]2\pi[/tex] units.

The formula for finding the period of a tangent function is

[tex]T=\frac{\pi}{b}[/tex]

We substitute the period to get;

[tex]2\pi=\frac{\pi}{b}[/tex]

This implies that;

[tex]b=\frac{\pi}{2\pi}[/tex]

Therefore[tex]b=\frac{1}{2}[/tex]

Hence the function represented by the graph is

[tex]y=\tan \frac{1}{2} \pi[/tex]

Answer:

2

Step-by-step explanation:

Given Data:

total distance= 850 miles

gas tank holds gas= 15 gallons

mileage = 72/3.2 miles/gallon

if

72 miles uses= 3.2 gallon

then

850 miles uses= x gallons

by cross-multiplication we get

72x=3.2(850)

x=37.778

i.e. 850 miles will use 37.7778 gallon of gas

Asgas tank holds 15 gallons

number of times gas tank is used up= 37.3/15

                                                            = 2.518

rounding off

number of times gas tank is used up=3

As they filled the gas tank at the start of the road trip, hence 3-1=2

ADDITIONAL STOPS FOR GAS WILL THEY NEED TO MAKE TO GET TO THEIR DESTINATION =2 !

Answer:

20 cents.

Step-by-step explanation:

You can drop 2 zeros from both the price and the amount of pencils. If 1000 pencils costs 20.00 dollars then 10 pencils cost .20 dollars or 20 cents.

Answer:

The correct answer is last option

x¹⁶y²²

Step-by-step explanation:

Points to remember

Identities

Xᵃ * Xᵇ = X⁽ᵃ ⁺ ᵇ⁾

Xᵃ/Xᵇ = X⁽ᵃ ⁻ ᵇ⁾

(Xᵃ)ᵇ = Xᵃᵇ

To find the correct answer

It is given an expression {X⁶Y⁸}³/X²Y²

By using identities we can write,

{X⁶Y⁸}³/X²Y² = X⁶ˣ³ Y⁸ˣ³/X²Y²

 = X¹⁸Y²⁴/X²Y²

 = X⁽¹⁸ ⁻ ²⁾ * Y⁽²⁴ ⁻ ²⁾

 = X¹⁶Y²²

Therefore the correct answer is last optionX¹⁶Y²²

ANSWER

40°

EXPLANATION

The opposite sides of a rhombus are parallel.

This implies that, the diagonal is a transversal.

This means that,

m<1 and m<2 are alternate interior angles.

Since alternate interior angles congruent,

m<1 =m<2=40°

The correct choice is C.

He can fit 4 boxes along the wall

Answer:

[tex]\large\boxed{\left[\begin{array}{ccc}43&6\\-70&-33\end{array}\right] }[/tex]

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}8&3\\-7&2\end{array}\right] \cdot\left[\begin{array}{ccc}8&3\\-7&-6\end{array}\right] \\\\=\left[\begin{array}{ccc}(8)(8)+(3)(-7)&(8)(3)+(3)(-6)\\(-7)(8)+(2)(-7)&(-7)(3)+(2)(-6)\end{array}\right] \\\\=\left[\begin{array}{ccc}43&6\\-70&-33\end{array}\right][/tex]

Answer:

D

Step-by-step explanation:

43, 6

-70, -33

Answer:

If you're asking for the formula to find the area of a triangle, its:

1/2bh

b = base

h = height

Answer:

D

Step-by-step explanation:

Answer: D

Step-by-step explanation:

Answer:

D. 40%

Step-by-step explanation:

You can fill in the table completely

[tex]\begin{array}{cccc}&\text{Hamburgers}&\text{Pizza}&\text{Total}\\\text{Adults}&0.24&0.36&0.6\\\text{Children}&0.11&0.29&0.4\\\text{Total}&0.35&0.65&1\end{array}[/tex]

From this table you can state that the probability that a randomly selected person is a child is 0.4 that is 40%.

The percentage of the people surveyed are children is:

                               40%

We are given a table as follows:

                            HAMBURGERS               PIZZA             TOTAL

ADULTS                   0.24                              0.36                0.6

CHILDREN                0.11                               0.29                 0.4

TOTAL                      0.35                              0.65                   1

Now we are asked to find the percent of students that were surveyed.

From the table we may see that the probability of children who were surveyed are:

     0.11+0.29=0.40

( since, the second column gives the total of the probability of children)

Hence, in percentage form it is given by:

0.40×100=40%

          Hence, the answer is:

               40%

Answer:

900 cuboc unit

Step-by-step explanation:

Volume of pryamid= 1/3× area× height

= 1÷3×15^15×8

= 900cubic unit

For this case we have by definition, that the area of a square base pyramid is given by:

[tex]V = \frac {L ^ 2 * h} {3}[/tex]

Where:

L: It's the side of the square base

h: It's the height of the pyramid

We have that[tex]L = 15 \ units[/tex], then [tex]L ^ 2 = 15 ^ 2 = 225 \ units ^ 2[/tex]

Substituting:

[tex]V = \frac {225 * 8} {3}\\V = 600 \ units ^ 3[/tex]

Finally, the volume of the pyramid is [tex]600 \ units ^ 3[/tex]

Answer:

[tex]600 \ units ^ 3[/tex]

Since supplementary angles add up to 180°, you would subtracted the measurement that you have from 180°.

Ex.

180-x= y

X being the measurement that you have, and y being the missing measurement.

Answer:

9 ft

Step-by-step explanation:

The ladder is 15 foot

The height the ladder reaches from the bottom of the wall is 12 ft

The distance (x) from the bottom of the wall to the foot of the ladder is:

Applying the Pythagorean theorem;

x = [tex]\sqrt{15^2 - 12^2}[/tex] = 9 ft

A 15 foot ladder needs to be placed at a distance of 9 foot from the base of the house so that it exactly reaches the top of a 12 foot wall.

In this case;

Therefore;

We are going to find the distance of the ladder from the base of the house on the ground which is the other leg.

Using Pythagoras theorem;

[tex]a^{2} + b^{2} = c^{2}[/tex]

Taking the horizontal distance of the ladder from the wall as b

Then;

[tex]b^{2} = c^{2} -a^{2}[/tex]

therefore,

[tex]b^{2} = 15^{2} -12^{2}[/tex]

[tex]b^{2} = 225 -144[/tex]

[tex]b^{2} = 81[/tex]

[tex]b = \sqrt{81} \\b= 9 ft[/tex]

Hence; the ladder needs to be placed at a distance of 9 foot from the base of the house.

Keywords: Right triangle, Pythagoras rule

Level; High school

Subject: Mathematics

Topic: Pythagoras theorem

Answer:

(3a-1)(3a+1)

Step-by-step explanation:

We can quickly see with this problem that it is the difference of two squares as 9a^2 is (3a)^2 and 1 is 1^2 and therefore can factorise quickly using this rule.

x^2-y^2 = (x-y)(x+y) where x = 3a and y = 1

ANSWER

[tex]{(3 {a})^{2} } - {1}^{2} = (3a + 1)(3a - 1)[/tex]

EXPLANATION

We want to simplify completely:

[tex]9 {a}^{2} - 1[/tex]

We express the two terms as difference of two squares;

[tex] {(3 {a})^{2} } - {1}^{2} [/tex]

Recall and apply the following identity;

[tex]{x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]

We apply this identity to obtain:

[tex]{(3 {a})^{2} } - {1}^{2} = (3a + 1)(3a - 1)[/tex]

Answer:

$47, 17.5%

Step-by-step explanation:

When she buys the $20 book, she can get 40% off either the $15, $12, or $10 book.  She'll save the most by getting 40% off the $15 book.

Then, when she buys the $12 book, she'll get %40 off the $10 book.

The total she pays is:

20 + (0.60)(15) + 12 + (0.60)(10)

20 + 9 + 12 + 6

47

Without the discounts, the cost of the books would have been:

20 + 15 + 12 + 10

57

So she saves $10.  10 out of 57 is approximately 17.5%.

Answer:

see explanation

Step-by-step explanation:

The length of the arc is calculated as

arc = circumference of circle × fraction of circle

      = 2πr × [tex]\frac{90}{360}[/tex] ← r = 1

      = 2π × [tex]\frac{1}{4}[/tex] = [tex]\frac{\pi }{2}[/tex] ≈ [tex]\frac{3.14}{2}[/tex] = 1.57

The mean, or average, of the data set is 3 defective toys per sample group. Therefore set 0.3 and 0.5 are the most accurate representations.

Option C) 0.3

Answer:

(x - 3)(4x² + 6x + 9)

Step-by-step explanation:

This is a difference of cubes which factors in general as

a³ - b³ = (a - b)(a² + ab + b²)

8x³ = (2x)³ ⇒ a = 2x

27 = 3³ ⇒ b = 3

Hence

8x³ - 27

= (2x)³ - 3³

= (2x - 3)( (2x)² + (2x × 3) + 3²)

= (2x - 3)(4x² + 6x + 9)

Answer: A

48+ 36 = 84  

84/4 = 21 groups  

there are 21 groups of 4 balloons  

if segments OX = OC and perpendicular to those chords, then AB = YZ, the chords are also equal.

5 unit to left, 3 units down is the correct answer.