What is the measure of arc ab
34
70
110
104

Answers:

i) It can graze an area of approximately 961.625 square meters

ii) The ungrazed area is roughly 802.375 square meters

note: I used pi = 3.14 which is approximate; if you want more accuracy, use more decimal digits in pi

===============================================

Explanation:

Check out the attached image below for a visual diagram.

The area of a circle is the formula

A = pi*r^2

Use r = 35 as the radius and pi = 3.14 as the approximation for pi, to get,

A = pi*r^2

A = 3.14*35^2

A = 3846.5

Then divide this by 4 to get the area of a quarter circle

A/4 = 3846.5/4 = 961.625

This is the approximate area the horse can graze

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

Subtract this from 42^2 = 42*42 = 1764 because this is the area of the entire square. Doing this will get you the ungrazed area

Ungrazed area = (entire plot) - (grazed area)

Ungrazed area = (entire area of square) - (area of quarter circle)

Ungrazed area = 1764 - 961.625

Ungrazed area = 802.375

Answer:

A. 33/56

Step-by-step explanation:

Make them have the same denominator of 56

so you get for the first one 49/56

the second one will be 16/56

subtract both and you get your answer of 33/56

Answer: A. 33/56

Step-by-step explanation:

To get the number of pages left, all we need to do is to subtract 2/7 from 7/8

number of pages left = 7/8 - 2/7

=49 - 16 / 56

= 33/56

Answer:

The answer is A.

Step-by-step explanation:

To solve this problem, use the inverse operation of multiplication, which is division. 72 ÷ 8 = 9. Since the problem stated "which inequality gives the minimum number of packages he will need to buy?" 9 is the minimum number. Therefore, A is the answer.

Show Work:

8p ≥ 72

÷8    ÷8

 p ≥ 9

Answer:

A     p≥9

Step-by-step explanation:

Answer:

[tex]a_{52}[/tex] = - 394

Step-by-step explanation:

these are the terms of an arithmetic sequence with nth term

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d

where d is the common difference and [tex]a_{1}[/tex] the first term

d = - 18 - (- 10) = - 10 - (- 2) = - 2 - 6 = - 8 and [tex]a_{1}[/tex] = 14, hence

[tex]a_{52}[/tex] = 14 + (51 × - 8) = 14 - 408 = - 394

Answer:

The 14th term is -58

Step-by-step explanation:

The formula for an arithmetic sequence is

an = a1+d(n-1)

where a1 is the first term

d is the common difference and

n is the term number

a1 = 7

d = 2-7 = -5

Check -3-2 = -5   so d = -5

an = 7 -5(n-1)

We want the 14th term

a14 = 7 -5(14-1)

a14 = 7 -5(13)

a14 = 7 -65

a14 = -58

Answer:

1/12

Step-by-step explanation:

6 x 2 = 12

6 = the original amount of slices

2 = it was cut in half so multiply by 2

each slice now represents 1/12

Answer:

Each slice represents 1/12th of the total pizza.

Step-by-step explanation:

1 = 1/6 = 1/12

Answer:

D 1/40

Step-by-step explanation:

Of the dogs at the show, 1/12 were hounds

Of the hounds, 3/10 were English foxhounds

To determine how many at the show were English foxhounds, we multiply 1/12 by 3/10

1/12* 3/10 = 3/120 = 1/40

Answer:

your number is n= -3

Step-by-step explanation:

Answer:

n=-3

Step-by-step explanation:

4n-2n=-6

2n=-6

2 x n / 2 = 6 / 2 then simplify to get the answer! Hope this is Helpful! ;3

Answer:

             = 1092 people/ sq mile  

Step-by-step explanation:

Population density is the number of people per unit of area.

We know the population is 1627260

The are is 1490 mi ^2

Population density = 1627260/1490

                                 =1092.120805  people / sq mile

Round to the nearest whole number

                                  = 1092 people/ sq mile  

Answer:

30 girls

Step-by-step explanation:

10 x 2= 20

15x2=30

For every 10 boys there are 15 girls. since 20 is just 10 multiplied by 2 you can multiply 15 by 2

Answer:

7.81

Step-by-step explanation:

Given points (-2,-2)  and (3, 4)

To find distance between points we apply distance formula

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

(x1,y1) is (-2,-2)  and (x2,y2) is (3,4)

Plug in the values in the formula

[tex]D = \sqrt{(3-(-2))^2+(4-(-2))^2}[/tex]

[tex]D = \sqrt{(5)^2+(6)^2}[/tex]

[tex]D = \sqrt{25+36}[/tex]

[tex]D = \sqrt{61}[/tex]

D= 7.810249676

Round to nearest hundredth

So distance = 7.81

Answer:

red  2/3

blue 1/2

The lines do not have the same slope so they are  not parallel

Step-by-step explanation:

We can find the slope of the red line by using the formula

m = (y2-y1)/(x2-x1)

We have the points (0,2) and (3,4)

m= (4-2)/ (3-0)

  = 2/3

We can find the slope of the blue line by using the formula

m = (y2-y1)/(x2-x1)

We have the points (0,-2) and (4,0)

m= (0--2)/ (4-0)

  = (0+2)/(4-0)

  = 2/4

 =1/2

The lines  do not have the same slope so they are  not parallel

Answer: popcorn = $5.75 per bag

Step-by-step explanation:  

Set up the equation for each person.

Let x represent the cost of one drink and y represent the cost of one bag of popcorn.

           drinks    popcorn       Cost                     EQUATION

Naomi:      9            8            $111.25                9x + 8y = 111.25

Sofia:         3            2           $33.25                 3x + 2y = 33.25

Next, solve the system:

9x + 8y = 111.25   →    1(9x + 8y = 111.25)   →    9x + 8y = 111.25

3x + 2y = 33.25   →  -3(3x + 2y = 33.25)   → -9x  - 6y = -99.75

                                                                                2y =  11.50

                                                                                  y =  5.75

Answer:

System of equations :

$111.25=$9x+$8y

$33.25=$3x+$2y

The cost of 1 drink = $x = $7.25

The cost of 1 popcorn bag = $y = $5.75

Step-by-step explanation:

Given :  

Naomi spends a total of $111.25 on 9 drinks and 8 bags of popcorn.

Sofia spends a total of $33.25 on 3 drinks and 2 bags of popcorn.

To Find : A system of equations that can be used to find the price of one drink and the price of one bag of popcorn.

Solution :

Let cost of 1 drink = $x

⇒ cost of 9 drinks = $9x

⇒ cost of 3 drinks = $3x

Let cost of 1 popcorn bag = $y

⇒Cost of 8 popcorn bags = $8y

⇒Cost of 2 popcorn bags = $2y

Since Naomi spends a total of $111.25 on 9 drinks and 8 bags of popcorn.

So, equation will be : $111.25=$9x+$8y  --(A)

Since, Sofia spends a total of $33.25 on 3 drinks and 2 bags of popcorn.

So, equation will be :  $33.25=$3x+$2y--(B)

SOLVING A and B by using substitution method

finding value of x from equation B :

[tex]x=\frac{33.25-2y}{3}[/tex]

Putting this value in Equation (A)

⇒[tex]111.25=9(\frac{33.25-2y}{3})+8y[/tex]

⇒[tex]111.25=99.75-6y+8y[/tex]

⇒[tex]111.25=99.75+2y[/tex]

⇒[tex]y = 5.75[/tex]

Thus, cost of 1 popcorn bag =y = $5.75

Now put this value of y in equation A to get value of x

⇒$111.25=$9x+$8(5.75)

⇒$111.25-$46 = 9x

⇒$65.25 = 9x

⇒65.25/9 = x

⇒$7.25 = x

Thus, The cost of 1 drink = $x = $7.25

[tex](10^4)^2[/tex]

When you multiply an exponent directly into another exponent, you multiply the exponents.

For example:

[tex](x^{2})^3=x^{2(3)}=x^6[/tex]

[tex](x^5)^3=x^{5(3)}=x^{15}[/tex]

So:

[tex](10^4)^2=10^{4(2)}=10^8=100,000,000[/tex]

Answer:

it is 200000

Step-by-step explanation: ok you want me to show you! huh! :)

so you do 10 times the 4 which is 100000

next you times it by 2 which is equal to 200000

so your answer is 200000

Answer:

C

5(10)+10=60

-2(-5)+7=17

Step-by-step explanation:

Answer:

35[tex]\pi[/tex]

Answer:

C = 35 * pi

Step-by-step explanation:

The circumference is pi * d

The new diameter is 5 cm longer than the given one.

d = 30 + 5

d = 35

C = 35 * pi

Answer:

14.99

Step-by-step explanation:

20.02=50-2t

20.02-50= -2t

-29.98= -2t

Since we know that there are exactly 180 degrees in any triangle, and if each angle is equal to 45 degrees, we must add 45 to 45 and then subtract the result from 180 to find the 3rd angle. Since 45+45=90,we subtract 180-90 and get 90 degrees or a right angle.

The measure of the third angle is 90° a right angle isosceles triangle.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sum of all the interior angles in a triangle is 180°.'

Given, a triangle with a measure of its two angles is 45° and 45°.

∴ The measure of the third angle is 180° - (45 + 45)°.

= 180° - 90°.

= 90°.

It is an isosceles right-angle triangle.

learn more about triangles here :

https://brainly.com/question/16886469

#SPJ2

To find the better buy, calculate the unit price of each item by dividing the cost by the weight, and compare them. The first item at $1.50 for 5 oz has a lower unit price ($0.30 per oz) than the second item at $1.20 for 3 oz ($0.40 per oz), so it is the better buy.

To determine which is the better buy between two products, you need to calculate the unit price for each and then compare them.

The unit price is the cost per unit of weight or volume.

Final answer:

To find the better buy between $1.50 for 5 oz and $1.20 for 3 oz, calculate the cost per ounce for each and compare. The first option is cheaper at $0.30 per ounce compared to the second option at $0.40 per ounce.

Explanation:

To determine which is the better buy between $1.50 for 5 oz and $1.20 for 3 oz, we need to calculate the cost per ounce for each option.

Step-by-step Comparison

Therefore, the better buy is the first option, $1.50 for 5 oz, since it has a lower cost per ounce.

Answer:

Step-by-step explanation:

Sandy only because the 2 prisms overlap

[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&7020\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill \end{cases}[/tex]

[tex]\bf 7020\geqslant 4500(1+0.03t)\implies \cfrac{7020}{4500}\geqslant 1+0.03t\implies \cfrac{39}{25}\geqslant 1+0.03t \\\\\\ \cfrac{39}{25}-1\geqslant 0.03t\implies \cfrac{14}{25}\geqslant 0.03t\implies \cfrac{~~\frac{14}{25}~~}{0.03}\geqslant t\implies \cfrac{56}{3}\geqslant t \\\\\\ 18\frac{2}{3}\geqslant t\impliedby \textit{18 years and 8 months}~\hfill \boxed{0 \leqslant t \leqslant 18\frac{2}{3}} \\\\\\ ~\hspace{34em}[/tex]

check the picture below.

bearing in mind that "t" cannot be less than 0.

Answer:

x=1

Step-by-step explanation:

Question says to use a graphing calculator or online application to find the solution to [tex]3-x = x^3 + x[/tex] to the nearest tenth.

So we will create two equations y = 3-x and [tex]y = x^3 + x[/tex] using each sides of the given equation.

Now we graph both equation using some online calculator or graphing calculator. I'm going to use Desmos calculator.

Intersection point of both graphs will give the solution.

From graph we see that intersection point is at (1,2).

We are looking for value of x only.

Hence final answer is x=1

Answer:5

Step-by-step explanation:

The question is about finding the length of a rectangle. By creating and solving a quadratic equation with provided information, the width and length of the rectangle are 4 cm and 6 cm respectively.

The problem involves finding the length of a rectangle. To solve this, we need to consider the fact that we know information about the dimensions and area of the rectangle. The area of a rectangle is obtained by performing the multiplication of the length and the width. In this specific problem, it's stated that the length is 2 cm more than the width, and we also know that the area of the rectangle is 24 cm2.

Let's represent the width by x. Therefore, the length would be x+2. Since the area is the length multiplied by the width, we create the equation x*(x+2) = 24, which simplifies to x2+2x=24. Subtracting 24 from both sides, we get x2+2x-24 = 0.

This a quadratic equation and we'll solve for x using the quadratic formula, which results in x = 4 or x = -6. Since the width cannot be negative, x = 4 cm. After this, substitute the width (x) into the length equation. The length (x + 2) is 4 cm + 2 cm = 6 cm.

https://brainly.com/question/32403169

#SPJ2

The length of the rectangle is [tex]\( 2\sqrt{7} \)[/tex]cm.

To solve this problem, let's denote the width of the rectangle as [tex]\( w \)[/tex] cm. According to the information given, the length of the rectangle is then [tex]\( w + 2 \)[/tex] cm. The area of a rectangle is given by the product of its length and width, so we can set up the following equation:

[tex]\[ w \times (w + 2) = 24 \][/tex]

Expanding the equation, we get:

[tex]\[ w^2 + 2w = 24 \][/tex]

To solve for [tex]\( w \)[/tex], we need to rearrange the equation into standard quadratic form:

[tex]\[ w^2 + 2w - 24 = 0 \][/tex]

Now, we can factor this quadratic equation:

[tex]\[ (w + 6)(w - 4) = 0 \][/tex]

Setting each factor equal to zero gives us two possible solutions for [tex]\( w \)[/tex]:

[tex]\[ w + 6 = 0 \quad \text{or} \quad w - 4 = 0 \] \[ w = -6 \quad \text{or} \quad w = 4 \][/tex]

Since the width of a rectangle cannot be negative, we discard[tex]\( w = -6 \)[/tex] and accept [tex]\( w = 4 \)[/tex] cm as the width of the rectangle.

Now that we have the width, we can find the length by adding 2 cm to the width:

[tex]\[ \text{Length} = w + 2 = 4 + 2 = 6 \text{ cm} \][/tex]

However, we need to check if this length satisfies the area condition:

[tex]\[ \text{Area} = w \times \text{Length} = 4 \text{ cm} \times 6 \text{ cm} = 24 \text{ cm}^2 \][/tex]

This confirms that the length is indeed 6 cm when the width is 4 cm. Therefore, the length of the rectangle is [tex]\( 2\sqrt{7} \)[/tex] cm, since [tex]\( 6 = 2\sqrt{7} \)[/tex] when rounded to the nearest whole number.

Answer: 35.6 (choice A)

To get this answer, add up the values: 39+42+27+45+25 = 178

Next, divide that result by 5 because there are 5 scores added up in the previous step. Doing this division gets us to: 178/5 = 35.6

Answer:

19(42 + 58)

Step-by-step explanation:

Assuming x = multiply, you are trying to solve the distributive property. Divide common factors from both terms (in this case 19).

~

Answer:

19(42 + 58)

Step-by-step explanation:

19 * 42 + 19 * 58 =

= 19 * (42 + 58)     <-------  this is the expression

= 19 * 100

= 1900

Put the vales of x and y to the expression:

[tex]x=-1;\ y=3\\\\\dfrac{5x^{-6}y^{-2}}{y}=\dfrac{5(-1)^{-6}(3)^{-2}}{3}=\dfrac{5(-1)^6\left(\dfrac{1}{3}\right)^2}{3}=\dfrac{5(1)\left(\dfrac{1}{9}\right)}{3}=\dfrac{\dfrac{5}{9}}{3}\\\\=\dfrac{5}{9}\cdot\dfrac{1}{3}=\boxed{\dfrac{5}{27}}[/tex]