There are two boys and a girl on a trivia team. Two questions remain. One team member is randomly picked to answer the first question and a different member is picked to answer the second question.

The measure of the arc of the sinkhole that falls within the restaurants property is -21°

Let x be the angle at the dollar store at the intersection

Now the angle of the grocery store at the intersection, y is 2/3 that of the dollar store. So, y = 2x/3

Since both x and y are supplementary,

x + y = 180°

x + 2x/3 = 180°

5x/3 = 180°

x = 180° × 3/5

x = 36° × 3

x = 108°

The gas station has the same angle at the intersection but has 88° more of the sinkhole edge to stabilize. So, the angle the gas station store subtends at the sinkhole is z = x + 88°

Also, since the grocery stores property has 2/3 of the angle in the intersection at the dollar store has, but has 5° more of the sinkhole edge to stabilize. The angle the grocery store subtends at the sinkhole is k = y + 5° = 2x/3 + 5°

Let k' be the angle subtended by the restuarant at the sinkhole.

Since the sinkhole is a circle, we have that

x + z + k + k' = 360°

x + x + 88° + 2x/3 + 5° + k' = 360°

8x/3 + 93° + k' = 360°

8x/3 + k' = 360° - 93°

8x/3 + k' = 267°

So, making k' subject of the formula, we have

k' = 267° - 8x/3

Substituting the values of the variables into the equation, we have

k' = 267° -  8 × 108°/3

k' = 267° - 288°

k' = -21°

So, the measure of the arc of the sinkhole that falls within the restaurants property is -21°

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Answer:42 is the third quartile

Step-by-step explanation:

Answer:

(- 3, 1 )

Step-by-step explanation:

2x - 2y = - 8 → (1)

x + 2y = - 1 → (2)

adding the 2 equations term by term will eliminate y

3x + 0 = - 9

3x = - 9 ( divide both sides by 3 )

x = - 3

substitute x = - 3 into either of the 2 equations and solve for y

substituting into (2)

- 3 + 2y = - 1 ( add 3 to both sides )

2y = 2 ( divide both sides by 2 )

y = 1

solution is (- 3, 1 )

Answer:

(–3, 1)

Step-by-step explanation:

Step 1: Solve for x

2x – 2y = –8 -----------(1)

x + 2y = –1. -------------(2)

⇒2x + x| -2y + 2y |= -8 -1

⇒3x = -9

⇒3x/3 = -9/3

⇒x = -3

Step 2; Solve for y

x + 2y = –1

(-3) + 2y = -1

-3 + 2y + 3 = -1 + 3

2y = 2

2y/2 = 2/2

y = 1

So, ( x,y) ⇒(-3,1)

Step-by-step explanation:

line equation

y = ax + b

a is the slope, b is the y-intercept.

a slope perpendicular to another slope flips x and y upside down and flips the sign.

so, the slope perpendicular to 2/7 is -7/2.

so, our desires line function looks like

y = -7/2 × x + b

to get b we use the given point (and it's x and y coordinates = values).

-8 = -7/2 × 8 + b = -7×4 + b = -28 + b

b = 20

so, the full line equation is

y = -7/2 × x + 20

Δ = (-5)² - 4*1*6 = 25 - 24 = 1 = 1²

x' = (5 + 1) / (2*1) = 6/2 = 3

x" = (5-1) / (2*1) = 4/2 = 2

2 solutions : 2 and 3

x² - 5x + 6 = (x - 2) (x - 3)

Answer:

  (d)  k = 8

Step-by-step explanation:

The value k in the equation ...

  g(x) = f(x) +k

represents a vertical translation by k units.

__

The vertex coordinates for f(x) and g(x) are ...

  f(x): vertex = (-3, -3)

  g(x): vertex = (-3, 5)

This means ...

  f(-3) = -3

  g(-3) = 5 = f(-3) +k = -3 +8   ⇒   k = 8

_____

Additional comment

Translations of various kinds are often most easily seen by comparing points where the graph has a distinctive feature. On this graph, that is the vertex.

Answer:

her balance aka ADB would be 372.08

Answer:

147

Step-by-step explanation:

4/7 people in chairs

7/8 of chairs, rest are standing

8 empty chairs

empty chairs = 1/8

full chairs = 8 x 8

7/8 = 64.

4/7 = 64

1/7 = 64 / 4

1/7 = 21

7/7 = 21 x 7

7/7 = 147

There are 147 people in the room.

There are 147 people in the room.

The given is,

Four-sevenths of the people in a room are seated in seven-eighths of the chairs.

The rest of the people are standing.

there are 8 empty chairs, how many people are in the room in a room are seated in seven-eighths of the chairs.

The rest of the people are standing.

We have to determine there are 8 empty chairs, how many people are in the room.

Four-sevenths of the people.

4/7 people in chairs.

7/8 of the chairs, rest are standing

The 8 empty chairs,

The empty chairs = 1/8

The full chairs = 8 x 8

7/8 = 64.

4/7 = 64

1/7 = 64 / 4

1/7 = 21

7/7 = 21 x 7

7/7 = 147

There are 147 people in the room.

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[tex]y = - x {}^{2} + 6x - 15[/tex]

[tex]y {}^{ \gamma } = - 2x + 6[/tex]

[tex]y {}^{ \gamma } = 0[/tex]

[tex] - 2x + 6 = 0[/tex]

[tex] - 2x = - 6[/tex]

[tex]2x = 6[/tex]

[tex]x = 3[/tex]

[tex]y = - (3) {}^{2} + 6(3) - 15[/tex]

[tex]y = - 9 + 18 - 15[/tex]

[tex]y = - 9 + 3[/tex]

[tex]y = - 6[/tex]

[tex]==============================[/tex]

In order to find the vertex of a parabola, we use the following formula:

[tex]\mathfrak{\displaystyle\frac{-b}{2a} }[/tex]

Please remember that a parabola looks like this:

[tex]\tt{y=ax^2+bx+c}[/tex]

Now you know what a and b stand for.

In this case, a = -1, and b is 6:

[tex]\mathfrak{\displaystyle\frac{-6}{2(-1)} }[/tex]

Simplify:

[tex]\mathfrak{\displaystyle\frac{-6}{-2}}[/tex]

[tex]\mathfrak{3}\\=======================================[/tex]

[tex]\mathcal{DiAmOnD}\\\tt{A~Creative~Helper}}}}[/tex]

1,200 divide by 600 = 2 students

2 students multiply by 50% is 100 students.

So, approximately 100 students ride their bicycles home.

(If not correctly, I am truly sorry)

Answer:

D. 48 feet

Step-by-step explanation:

Ladder (50 ft) = hypotenuse

Floor distance (14 ft) = b

Wall (unknown) = a

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

[tex]a^2+14^2=50^2[/tex]

[tex]a^2+196=2500[/tex]

[tex]a^2=2500-196[/tex]

[tex]a=\sqrt{2304}[/tex]

[tex]a=48[/tex]

Hope this helps!

Answer:

48 feet

Step-by-step explanation:

Here,

c = 50 ft

b = 14 ft

To find : the height of the wall that the ladder reaches ( a ) = ?

Formula : -

a² + b² = c²

a² = c² - b²

= 50² - 14²

= ( 50 x 50 ) - ( 14 x 14 )

= 2500 - 196

= 2304

= 48 x 48

a² = 48²

a = 48 feet

Answer:

Here,

n(A)={0,1,3,5,6}

n(B)={1,2,3,7}

n(AUB)=?

we know that,

AUB={0,1,2,3,5,6,7}

Step-by-step explanation:

is it okay ?

hopefully it works <3 ❣️

11.9 - last one

Step-by-step explanation:

Adjacent + hypotenuse = Cos / Cah

Cos32 = x/14

x14

11.87... = x

So, 11.9 to nearest tenth

Hope this helps!

k must be greater than or equal to 22.75 to have two different zeros.

Second order polynomials are algebraic expressions that observe the following form:

[tex]p(x) = a\cdot x^2 + b\cdot x + c[/tex]   (1)

Where:

For polynomials of the form p(x) = 0, we can infer the nature of their roots by applying the following discriminant:

d = b² - 4 · a · c   (2)

According to (2), there are three cases:

Now we have the following discriminant case:

-(3 + 2 · k)² - 4 · (1) · (4) ≠ 0

-(9 + 6 · k + 4 · k²) - 16 ≠ 0

-9 - 6 · k - 4 · k² - 16 ≠ 0

4 · k²+ 6 · k +25 ≠ 0

This characteristic polynomial has two conjugated complex roots, then we conclude that all values of k must positive or negative, but never zero. By graphng tools we find that k must be greater than or equal to 22.75 to have two different zeros.

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Answer:

isn't the answer 12/20

add the number of pets to make 20

then there are 12 cats

as a fraction

12/20

Answer:

  k = 3

Step-by-step explanation:

The value of k is the amount by which the function f(x) is translated upward to give the function g(x). We can compare y-intercepts to see that the y-intercept of g(x) is 5 -2 = 3 units more than the y-intercept of f(x). This means ...

  g(x) = f(x) +3

Comparing to ...

  g(x) = f(x) +k

we see that k = 3.

Answer:

Step-by-step explanation:

. Volume: A measure of _space  occupied by a _three dimensional _ figure.

1. Base: The surface on which an object stands on.

1. Height: The _vertical distance from top to bottom, creates a _90° degree angle with the base.

1. Inverse Operation: The opposite of a math operation; the opposite of addition is subtraction and the opposite of multiplication is division.

1. Diameter: A straight line going from one side of a point on a circle to the other through the _center.

1. Radius: The distance from the center to the point of a circle;or half of the diameter.

Volume of a Cylinder

A cylinder is a three dimensional object with a circular base and top.

To find the volume of a cylinder we use the following formula:πr²h

Answer:

Probably 81.

Maybe 18.

See explanation below.

Step-by-step explanation:

(6 + 3)² = 9² = 9 × 9 = 81

(6 + 3) × 2 = 9 × 2 = 18

I think you mean the first expression in which 2 is an exponent, but since it's not clear, I solved it both ways.

16.5/3 = 5.5

Step-by-step explanation:

becuase he needs to walk 16.5 miles. and he can walk 3 miles per x(hour)

you need to devide distance by speed to get time.

Answer:

Step-by-step explanation:

Divide the circle into 10 parts and color 2 parts black and 8 parts red.

The population of the island with growth rate of 4.5% per year and the current population is 1500 is 1953 after 6 years.

Let y represent the population after x years.

Given that the growth rate is 4.5% per year and the current population is 1500.

Hence a = 1500, b = 100% + 4.5% = 104.5% = 1.045

y = 1500(1.045)ˣ

After 6 years:

y = 1500(1.045)⁶ = 1953

The population of the island with growth rate of 4.5% per year and the current population is 1500 is 1953 after 6 years.

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Answer:

  3

Step-by-step explanation:

The "initial value" of a function is the value when the independent variable is zero.

  f(0) = 3(5/4)^0 = 3×1 = 3

The initial value of the function is 3.

Answer:

11x-3

11

Step-by-step explanation:

and that's the answer

Explanation:

A direct proportion is of the form y = kx

To find k, pick any row to divide the y over x value

No matter which row you go for, the constant of proportionality is 2. Meaning that we double the x value to get to y.

Therefore, we go from y = kx to y = 2x

Answer:

[tex]\frac{dx^{2} (x+1)S^{2} }{2(x^{2} +6x+3)^{2} }+ C[/tex]

Step-by-step explanation: