Which of the following are exterior angles? Check all that apply.
6
52
3
O A. 21
O B. 25
O c. 24
O D. 23
E. 22
O F. 26

Answer:

D, since it horizontal ellipse, a is greater than b

An ellipse has two foci. The correct option is D.

Suppose that the major axis is of the length 2a units and that the minor axis is of 2b units, and let the ellipse is centred on (h,k) with a major ellipse parallel to the x-axis, then the equation of that ellipse would be:

[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]

Coordinates of its foci would be:    (h±c, k) where    c² = a² - b²

If its major axis is parallel to the y-axis, then,

coordinates of its foci would be:  (h, k±c) where   c² = a² - b² and its equation would be:

[tex]\dfrac{(x-h)^2}{b^2} + \dfrac{(y-k)^2}{a^2} =1[/tex]

Given the foci at (3, 2) and (-9, 2) that pass through the point (-3, 10), therefore, the equation of the ellipse will be,

[tex]\dfrac{\left(x+3\right)^{2}}{100}+\dfrac{\left(y-2\right)^{2}}{64}=1[/tex]

Hence, the correct option is D.

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Answer:

[tex] \boxed{\sf d = -1 \ \ \ or \ \ \ d = -7} [/tex]

Step-by-step explanation:

[tex] \sf Solve \: for \: d \: over \: the \: real \: numbers: \\ \sf \implies {(d + 4)}^{2} = 9 \\ \\ \sf Take \: the \: square \: root \: of \: both \: sides: \\ \sf \implies \sqrt{ {(d + 4)}^{2} } = \sqrt{9} \\ \\ \sf 9 = {3}^{2} : \\ \sf \implies \sqrt{ {(d + 4)}^{2} } = \sqrt{ {(3)}^{2} } \\ \\ \sf \implies d + 4 = \pm 3 \\ \\ \sf \implies d + 4 = 3 \: \: \: \: \: or \: \: \: \: \: d + 4 = - 3 \\ \\ \sf Subtract \: 4 \: from \: both \: sides: \\ \sf \implies d + (4 - 4)= 3 - 4 \: \: \: \: \: or \: \: \: \: \: d + (4 - 4) = - 3 - 4 \\ \\ \sf \implies d = - 1 \: \: \: \: \: or \: \: \: \: \: d = - 7[/tex]

Answers:

5. Quadrilateral

6. Rhombus

7. Rectangle

8. Parallelogram

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

Explanations:

5. We don't know much about this other than it has 4 sides, so we simply say it is a quadrilateral. Quad = 4, lateral = side

-----------

6. The four sides are the same length as shown by the similar tickmarks. Therefore we have a rhombus. A rhombus is any quadrilateral with four equal sides. A square is a special type of rhombus, though in this case it appears to be a non-square type of rhombus, as the angles are not 90 degrees.

-----------

7. A rectangle has 4 angles that are all 90 degrees. Visually the tiny little square angle marker tells the reader we have a 90 degree angle.

-----------

8. We have a parallelogram here because the opposite sides are the same length. In addition, the opposite angles are the same measure. Through using the SSS congruence rule, we can do a bit of work to show that the alternate interior angles are congruent, leading to the opposite sides being parallel. So in short, the given info here is enough to prove we have opposite sides being parallel which is what makes a parallelogram possible.

The total depth covered  by the diver is 27(1/24) yards.

Yard is a unit to measure length. 1 yard is equal to 36 inches.

1 yard= 3 feet or (0.9144 meter)

What is

Given that,

First time depth reached by diver = 17(2/3) yards

In the second time, the depth reached by the diver is 9(3/8) yards more than the first time,

To find total depth,

Add depth covered by first time and second time,

Total depth = 17(2/3)+9(3/8)

                   =53/3+75/8

                   = 27(1/24)

The total depth covered by the diver is 27(1/24) yards.

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Answer:

-36

Step-by-step explanation:

[tex]-\frac{t}{2} -8 = 10\\-\frac{t}{2} = 18\\\frac{t}{2} = -18\\t = -36[/tex]

Answer:

Hey there!

We have an=a1(r^n-1), which is the formula for a geometric sequence.

The common ratio is 3, and 2 is the 1st term.

Thus, we have a1=2(3)^(n-1)

Hope this helps :)

Answer:

Hey there!

We have an=a1(r^n-1), which is the formula

for a geometric sequence.

The common ratio is 3, and 2 is the 1st

term.

Thus, we have a1=2(3)^(n-1)

Answer:

  125 in²

Step-by-step explanation:

Each triangular face has a base of 5 in and a height of 10 in. The area of it is given by the formula ...

  A = (1/2)bh

  A = (1/2)(5 in)(10 in) = 25 in²

The square base has an area given by the formula ...

  A = s² . . . . . where s is the side length

  A = (5 in)² = 25 in²

The total area is the sum of the areas of the 4 faces and the base:

  total area = 4 × (area of 1 face) + (area of base)

  total area = 4 × (25 in²) + 25 in²

  total area = 125 in²

Answer: The Surface Area is 125 in^

Step-by-step explanation:

Surface area = 4 × (area of 1 face) + (area of base)

total area = 4 × (25 in²) + 25 in²

Surface area = 125 in²

Answer:

6cot 50

Step-by-step explanation:

Tan 50=6/x

x= 6/(tan 50)

x= 6cot 50°

Answer:

? = 6 cot 50

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 50 = 6 /?

? tan 50 = 6

? = 6 / tan 50

We know that 1 / tan 50 = cot 50

? = 6 cot 50

Answer:

40z + 5

Step-by-step explanation:

I'm assuming you need to factor 32z + 4 + 8z + 3 - 4 + 2

Hope this helped

Answer:

The factored expression for the given equation is 4(8z⁴ + 2z³ - z²)

Step-by-step explanation:

In the problem, we a re given an equation.

32z⁴ + 8z³ - 4z²

We can factor out this equation by finding the common factor between all of the coefficients which are 32, 8, and 4.

A common factor between them is 4 because each number can be easily divided by 4. Each number is also a multiple of 4. So, when we are factoring, we will divide each number by 4 because 4 will be on the outside of the parentheses in the final answer.

4(8z⁴ + 2z³ - z²)

So, this is your factored expression from the given equation.

Answer:

The first equation can be multiplied by 3 and the second equation by 2.

Step-by-step explanation:

Given

[tex]2x+3y=25[/tex]

[tex]-3x + y=22[/tex]

Required

How to eliminate x

To eliminate x using addition, we have to do the following;

1. Take the coefficient of x in equation 1; Coefficient = 2

2. Take the coefficient of x in equation 2; Coefficient = -3

3. Multiply equation 1 by 3

[tex]3(2x + 3y = 25)[/tex]

[tex]6x +9y = 75[/tex]

4. Multiply equation 2 by 2

[tex]2(-3x + y = 22)[/tex]

[tex]-6x + 2y = 44[/tex]

5. Add both resulting equations

[tex]6x +9y = 75[/tex]  +  [tex]-6x + 2y = 44[/tex]

[tex]6x - 6x + 9y + 2y = 75 + 44[/tex]

[tex]11y = 75 + 44[/tex]

Notice that x has been eliminated;

Answer:

[tex]Angle = 96[/tex]

Step-by-step explanation:

Given

The frequency table

Required:

Determine the sectorial angle of "3"

First we need to determine the total frequency;

[tex]Total = 3 + 4 + 6 +8 + 5 + 4[/tex]

[tex]Total = 30[/tex]

The sectorial angle is calculated as thus;

[tex]Angle = \frac{Frequency}{Total\ Frequency} * 360[/tex]

Where Frequency of "3" = 8

So;

[tex]Angle = \frac{8}{30} * 360[/tex]

[tex]Angle = \frac{8* 360}{30}[/tex]

[tex]Angle = \frac{2880}{30}[/tex]

[tex]Angle = 96[/tex]

Hence; the sectorial angle of "3" is 96

Answer:

31 Pikachu bags were sold.

19 peanut bags were sold.

Step-by-step explanation:

Let's set up an equation of the total revenue of the day, where x is the number of Pikachu's sold.

We know that the number of Peanuts sold is 50-x (as the total needs to be 50)

We know that the total revenue is:

Number of Pikachus * Cost per Pikachus + Number of Peanuts * Cost per Peanuts

Using our definitions above:

Total Revenue = x * $3.68 + (50-x) * $0.76

We know that the revenue needs to be $128.52.

$128.52 = x * $3.68 + (50-x) * $0.76

Let's remove the $ signs.

128.52 = x * 3.68 + (50-x) * 0.76

Multiplying both 50 and -x with 0.76, "expanding" the parenthesis.

128.52 = x*3.68 + 50*0.76 - x*0.76

128.52 = x*3.68 + 38 - 0.76*x

Subtracting 38 from both sides

90.52 = 3.68*x - 0.76*x

We can simplify the right side.

90.52 = 2.92*x

We can divide both sides by 2.92:

31 = x

And flip it:

x = 31

So 31 Pikachus were sold (remember we claled that x), and as we know, the number of peanut bags sold is

50-x = 50-31 = 19

31 Pikachu bags were sold.

19 peanut bags were sold.

[tex] \LARGE{ \boxed{ \rm{ \pink{Solution:}}}}[/tex]

Let the number of peanut bags be x

Then, Number of pikachu bags = 50 - x

Given,

Then,

⇛ Total cost he gets from peanut bag = $0.76 × x

⇛ Total cost he gets from pikachu bag = $3.68(50 - x)

According to question,

⇛ $0.76x+ $3.68(50 - x) = $128.52

Solving this equation,

⇛ 0.76x + 184 - 3.68x = 128.52 (Removed $ symbol)

⇛ 184 - 2.92x = 128.52

⇛ 184 - 128.52 = 2.92x

⇛ 55.48 = 2.92x

Flipping the equation,

⇛ 2.92x = 55.48

⇛ x = 55.48 / 2.92

⇛ x = 19

Then,

⇛ 50 - x = 50 - 19 = 31

[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: peanut \: bags = 19}}}}}[/tex]

[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: pikachu \: bags = 31}}}}}[/tex]

━━━━━━━━━━━━━━━━━━━━

[tex]7\cdot6\cdot5\cdot4=840[/tex]

Answer:

1.791875241e13

Step-by-step explanation:

5.67811 x 10⁵ = 567811

3.15576 x 10⁷ = 31557600

31557600 x 567811 = 1.791875241e13

Answer:

1.791875241e13

Answer:

16,20,8,36

Step-by-step explanation:

he plans to have 2 tables for every 8 guest, which means 1 table for each 4 guest!

now:

2(tables)×4(number of people at each table)=8(number of guests

4×4=16

5×4=20

32(number of guests)÷4(number of people at each table)=8(number of tables)

9×4= 36

Answer:

Since there are 8 guests every 2 table we need to find how many guests are in one table:

8 ÷ 2 = 4 guests

4 tables = 4 x 4 = 16 guests

5 tables = 5 x 4 = 20 guests

32 guests = 32 ÷ 4 = 8 tables

9 tables = 9 x 4 = 36 guests

Hope this helps :D

Answer:

  B.  181.5√3 cm^2

Step-by-step explanation:

The area of a regular hexagon with side length s is given by ...

  A = (3√3/2)s²

For side length s = 11 cm, the area is ...

  A = (3√3/2)(11 cm)² = 363√3/2 cm²

  A = 181.5√3 cm²

Answer:

A

Step-by-step explanation:

The first option is correct.

The 8 count pack of AA batteries has a lower unit price of $0.79 per battery.

The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.

According to the given question.

Cost of a package with 8 AA batteries = $6.32

⇒ Cost of 1 AA battery of this package = [tex]\frac{6.32}{8}[/tex] = $0.79

And, cost of another package with 20 AA batteries = $16.00

⇒ Cost of 1 AA battery of another package = [tex]\frac{16}{20}[/tex] = $0.8

Hence, the 8 count pack of AA batteries has a lower unit price of $0.79 per battery.

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Answer:

Area=576 cm²

Perimeter=123.4 cm

Step-by-step explanation:

We have to assume that ABCD would form a square and not a rectangle.  If so, the area is simple:  24x24=576 (Just picture the half circle sliding into the empty space - it’s the same area.)

For the perimeter, we find it for the half circle first. 1/2(2)[tex]\pi[/tex](12)=37.7

Then add the top and bottom (24 and 24) to the left and right (37.7 And 37.7)

24+24+37.7+37.7=123.4

Answer:

x = ± 6

Step-by-step explanation:

x^2 = 36

Take the square root of each side

sqrt(x^2) = sqrt(36)

x = ± 6

Answer:

[tex]\large \boxed{\boxed{x=\pm 6}}[/tex]

Step-by-step explanation:

[tex]x^2 =36[/tex]

Take the square root on both sides.

[tex]\sqrt{x^2} =\pm \sqrt{36}[/tex]

Simplify.

[tex]x=\pm 6[/tex]

Answer: the domain is negative infinity to positive infinity

Step-by-step explanation:

the graph covers all x values

Hi I'mjust tryna get points for my sister this is actually the first time i use this app but yea, sorry if you got disappointed.

Answer:

Step-by-step explanation:

Answer:

a. Side lengths of ΔBEX are;

BE = 15 ft.

EX = 12 ft.

BX = 9 ft.

b. Side lengths of XEFY are;

XY = 6 ft.

EX = 12 ft.

FY = 7.5 ft.

EF = 7.5 ft.

c. Side lengths of YFGZ are;

GZ = 6 ft.

FY = 7.5 ft.

YZ = 2 ft.

FG = 2.5 ft.

d. Side length of triangle ZGC

GZ = 6 ft.

GC = 10 ft.

ZC = 8 ft.

Step-by-step explanation:

The given parameters are;

XY : YZ : ZC  is 3 : 1 : 4

The length of BC = 25 in.

The length of EB = 15 in.

Therefore, EC = √(BC² - EB²) = √(25² - 15²) = √400 = 20 in.

Given that EX║ YF║GZ, we have;

EF : FG : GC is 3 : 1 : 4 (Parallel lines cut segments in equal proportions)

Therefore;

EF = 20 × 3/(3 + 1 + 4) = 7.5 ft.

FG = 20×1/8 = 2.5 ft.

GC = 20×4/8 = 10 ft.

EC/EX = BC/EB

20/EX = 25/15

EX = 15×20/25 = 12 ft.

XC = √(EC² - EX²) = √(20² - 12²) = 16

XY : YZ : ZC  is 3 : 1 : 4

Therefore;

XY = 16 × 3/8 = 6 ft.

YZ = 16 × 1/8 = 2 ft.

ZC = 16 × 4/8 = 8 ft.

GZ = √(GC² - ZC²) = √(10² - 8²) = 6

Area of triangle ΔZGC = 1/2×6×8 = 24 ft²

XB = BC - XC = 25 - 16 = 9 ft.

Area of ΔBEX = 1/2×9×12 = 54 ft²

a. Side lengths of ΔBEX are;

BE = 15 ft.

EX = 12 ft.

BX = 9 ft.

FY = √(FC² - YC²) = √((10 + 2.5)² - (8 + 2)²) = 7.5 ft.

Area of YFGZ = (GZ + FY)/2 × YZ = (6 + 7.5)/2 × 2 = 13.5 ft²

Area of YFGZ = 13.5 ft²

Area of XEFY = XY × (EX + FY)/2 = 6 × (12 + 7.5)/2 = 58.5 ft.²

b. Side lengths of XEFY are;

XY = 6 ft.

EX = 12 ft.

FY = 7.5 ft.

EF = 7.5 ft.

c. Side lengths of YFGZ are;

GZ = 6 ft.

FY = 7.5 ft.

YZ = 2 ft.

FG = 2.5 ft.

d. Side length of triangle ZGC

GZ = 6 ft.

GC = 10 ft.

ZC = 8 ft.

[tex] \huge{ \bold{ \bigstar \: pythagoras \bigstar}}[/tex]

Pythagoras :

[tex] {10}^{2} = {x}^{2} + {x}^{2} [/tex]

[tex]100 = 2{x}^{2}[/tex]

[tex]100 \div 2 = {x}^{2} [/tex]

[tex]50 = {x}^{2} [/tex]

[tex]x = \sqrt{50} [/tex]

[tex]x = \sqrt{25 \times 2} [/tex]

[tex] \red{x = 5 \sqrt{2} }[/tex]

Answer:

Step-by-step explanation:

Compare this to a similar figure with hypotenuse √2 and leg lengths all 1.

Write and solve an equation of ratios, as follows:

  x        10

------ = ------

  1        √2

              10√2

'then x = --------  =  5√2

                  2

Answer:

False

Step-by-step explanation:

So, in Mathematics we use more precise language: When the order doesn't matter, it is a Combination. When the order does matter it is a Permutation.

Answer:

4) 3(x+2)

5) Cannot be factored

6)3(4x+10y)

Step-by-step explanation:

4)3x+6

3(x+2)

Proof:

3(x+2)

3x+6

5)2x-15

Cannot be factored.

6)12x+30y

3(4x+10y)

Proof:

3(4x+10y)

12x+30y

Hope this helps ;) ❤❤❤

Answer:

a) x greater than or equal to 10

b) x = 9

Step-by-step explanation:

a)

[tex]x + 5 \geqslant 15 \\ x \geqslant 15 - 5 \\ x \geqslant 10[/tex]

b)

[tex]2x < 18 \\ x = \frac{18}{2} \\ x = 9[/tex]

Step-by-step explanation:

Since the original price is $47.96 and bill rate is 7%, $47.96 × 1.07 ≈ $51.32

Answer:

$51.32

The amount of sales tax for the bill if the rate is 7% will be $3.36.

The quantity of anything is stated as though it were a fraction of a hundred.

Vince and 11 of his friends went out for pizza on Saturday night to celebrate Vince’s birthday.

The cost of the pizza and soft drinks before sales tax and tip was $47.96.

Then the amount of sales tax for the bill if the rate is 7% will be

⇒ $47.96 x 0.07

⇒ $3.36

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