The measure of the exterior angle of the triangle is

Answer:

96 apple pies, 64 cherry pies, and 48 blueberry pies.

Step-by-step explanation:

6 + 4 + 3 = 13, and 208 / 13 = 16. Now multiply each number in the ratio by 16, so 6 x 16 = 96, 4 x 16 = 64, and 3 x 16 = 48. You can check your answer by adding all 3 numbers and making sure it adds up to 208. Hope that helps

Answer:

138 feets

Step-by-step explanation:

Given that :

Angle of depression (α) = 16°

Elevation = height = 450 feets

Appling trigonometry :

From the picture attached :

Height / elevation = 450 feets (Adjacent)

Distance = d (opposite)

Tan α = opposite / Adjacent

Tan 17 = d / 450

450 tan17 = d

450 * 0.3057306 = d

d = 137.57880

Hence, distance between a point on the ground directly below the helicopter and the landing pad 138 feets

The distance between a point on the ground directly below the helicopter and the landing pad is 129.03 feet.

Given that,

The helicopter is flying at an elevation of 450 feet.

It is within sight of the landing pad and the pilot finds that the angle of depression to the landing pad is 16∘.

We have to determine,

The distance between a point on the ground directly below the helicopter and the landing pad.

According to the question,

The angle of depression =  16°,

Elevation = height = 450 feet

And d is the distance,

The angle of depression is an important component used in trigonometric operations.

The angle of depression is formed when the observer stands on a ground higher than the object which he is trying to observe.

Therefore, The angle of depression is,

[tex]Tan16 = \dfrac{d}{450}\\\\0.28 = \dfrac{d}{450}\\\\d = 450 \times 0.28\\\\d = 129.03 \ feet[/tex]

Hence, The distance between a point on the ground directly below the helicopter and the landing pad is 129.03 feet.

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Answer:

24 or 25, because of the max height it can reach on the graph, its reaching the maximum height it can go

-

Answer:

Not a function

Step-by-step explanation:

If you use the line/ pencil test ***I think that's what it's called...

you put a pencil flat on the graph and if it touches more than one point, it is not a function. This only works with some graphs.But it works with this one.  

Answer:

/

Step-by-step explanation:

Answer:

Step-by-step explanation:

The nth term of an exponential sequence is expressed as ar^n-1

The nth term of a linear sequence is expressed as Tn = a + (n-1)d

a is the first term

r is the common ratio

d is the common difference

n is the number of terms

Let the three consecutive terms  of an exponential sequence be a/r, a and ar

second term of a linear sequence = a +d

third term of a linear sequence = a + 2d

sixth term of a linear sequence = a + 5d

Now if the three consecutive terms  of an exponential sequence are  the second third and sixth terms  of a linear sequence, this is expressed as;

a/r = a + d ..... 1

a = a + 2d ..... 2

ar = a+ 5d .... 3

From 2: a = a + 2d

a-a= 2d

0 = 2d

d = 0/2

d = 0

Substitute d = 0 into equation 1:

From 1: a/r = a + d

a/r = a+0

a/r = a

Cross multiply

a = ar

a/a = r

1 = r

Rearrange

r = 1

Hence the common ratio of the exponential sequence is 1

Answer:

There would be 1080 bacteria in the culture.

Step-by-step explanation:

Initial number of bacteria = 40

Given that

culture of bacteria triples by the end of each hour

Number of bacteria after 1 hour = 40*3 (multiplying initial number of bacteria by 3)

Number of bacteria after 1 hour = 120

number of bacteria after 2 hours = 3*Number of bacteria after 1 hour = 3*120

number of bacteria after 2 hours =360

number of bacteria after 3 hours = 3*Number of bacteria after 2 hour = 3*360 = 1080

Thus,

there would be 1080 bacteria in the culture.

Answer:

1080 bacteria

Step-by-step explanation:

Answer:

4 is D = 23

Step-by-step explanation:

the coefficient is the number before the letter

Answer:

The system of inequalities shown in the graph is x ≤ 4 and y > 1 ⇒ C

Step-by-step explanation:

In the given figure, there are 2 lines, let us find the equations of them, then write the inequalities which represent the shaded areas

∵ The purple line is a vertical line

∵ It is cross the x-axis at the point (4, 0)

→ By using the first rule above

∴ The equation of the purple line is x = 4

∵ The purple line is solid and the shaded area left the line

∴ The sign inequality is ≤

∴ The inequality of the purple area is x ≤ 4

∵ The blue line is a horizontal line

∵ It is cross the y-axis at the point (0, 1)

→ By using the second rule above

∴ The equation of the blue line is y = 1

∵ The blue line is dashed and the shaded area above the line

∴ The sign inequality is >

∴ The inequality of the blue area is y > 1

∴ The system of inequalities shown in the graph is x ≤ 4 and y > 1

Answer:

C

Step-by-step explanation:

The absolute value function always gives a positive result, that is

| - a | = | a | = a

Given

| - 12 | - | - 3 |

= 12 - 3

= 9 → C

Answer:

800 miles

Step-by-step explanation

Step one

A truck can be rented from

Company A for ​$130 a day plus ​$0.20 per mile

Let the number of miles be x

And the total charges be y

y=130+0.2x—-------1

Company B charges ​$50 a day plus ​$0.30 per mile

y=50+0.3x--------2

Equate 1 and 2

130+0.2x=50+0.3x

130-50=0.3x-02x

80=0.1x

x=80/0.1

x=800 Miles

Answer:

Here is the summary:

Step-by-step explanation:

Given the equation

The points which satisfy the equation y=13x+5

y = 13x+5

Checking the point (0, 5)

5 = 13(0)+5

5 = 0 + 5

5 = 5

TRUE

Checking the point (-2, -21)

-21 = 13(-2)+5

-21 = -26 + 5

-21 = -21

TRUE

The points which satisfy the equation y=-3x

y = -3x

Checking the point (0, 0)

0 = -3(0)

0 = 0

TRUE

Checking the point (-5, -15)

y = -3x

-15 = -3(-5)

-15 = -15

TRUE

Checking the point (-3, 9)

y = -3x

9 = -3(-3)

9 = 9

TRUE

The points which satisfy the equation y=x-10

y = x-10

Checking (8, -2)

-2 = 8 - 10

-2 = -2

TRUE

Therefore, from the above calculations we conclude the summary:

Here is the summary:

Answer:

Step-by-step explanation:

The required graph of the given function d(x)=−1/2x−3 has been shown.

Given that, to plot the graph of the linear function,  d(x)=−1/2x−3.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
The graph of the liner function d(x)=−1/2x−3 can be plot by putting the values of the x in the equation which gives the value of y by calculating such an ordered pair we can plot the curve of the liner equation on the graph. i.e.
At x = 0
d(0) = -1/2 * (0) - 3
d(0) = -3
So, the ordered pair will be (0, -3).
Now, put x = 2
d(2) = -1/2 * 2 - 3
d(2) = -1 - 3
d(2) = - 4
So the ordered pair will be (2, -4)
joining these two points will show the graph of the given equation d(x)=−1/2x−3.

Thus, the required graph of the given function d(x)=−1/2x−3 has been shown.

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Answer:

60%

Step-by-step explanation:

she probably eats almost 60% of the cocoa contained in the chocolate. which is high and would increase the caffeine levels in her body

Answer:

24

Step-by-step explanation:

first you multiply 200 by 12, Then you divide that by 100. your final product is 24, hope that helps

Answer:

C. 6%

Step-by-step explanation:

First we need to divide the amount of people who got the allergic reaction by how many people were there.

So: 12 ÷ 200 = 0.06

Now, we need to multiply 0.06 by a whole percent, the whole percent is 100.

So: 0.06 × 100 = 6

6% of the people had a mild allergic reaction.

Answer:

z<-4

Step-by-step explanation:

-2z-5>3

Add 5 to both sides.

-2z>8

Divide both sides by -2.

Z<-4

The sign must change because you are dividing by a negative.

Answer:

2 2/19

Step-by-step explanation:

5 cases in 2 3/8 hours

The unit rate of cases per hour is calculated by dividing the number of cases by the number of hours.

5/(2 3/8) = 5/(19/8) = 5 * 8/19 = 40/19 = 2 2/19

Answer:

2 2/19 cases per hour

Step-by-step explanation:

5 ÷ 2 3/8

~Turn the fraction on the left into an improper one

5 ÷ 19/8

~Copy Dot Flip

5/1 * 8/19

~Multiply

40/19 or 2 2/19

Best of Luck!

Answer:

x=2

Step-by-step explanation:

Answer:

TUNNEL:

f(x) = -2/4.9  [tex]x^{2}[/tex]  + 9.8

TRUCK:

Width (m) < 9.8

Height (m) <  -2/4.9 ( [tex]Width^{2}[/tex] /4 - [tex]4.9^{2}[/tex] )

Step-by-step explanation:

Please see attachment

If the maximum height of the tunnel is the same as its maximum width, 9.8 meters, The quadratic model to represent the tunnel will be f(x)= (-2/4.9)x²+9.8.

Any function of the form[tex]\rm f(x) =ax^2+bx+c[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.

It is given that, If the maximum height of the tunnel is the same as its maximum width, 9.8 meters.

We have to determine a quadratic model to represent the tunnel.

The quadratic function is formed as,

f(x) =K(x-x₁)(x-x₂)

x₁=width/2

x₁=9.8/2 = 4.9

x₂= -x₁ = -4.9

Substitute the obtained value as,

f(x) = K(x-4.9)(x-(-4.9))

f(x) =K(x²-4.9²)

f(0)=9.8

The value of K is obtained as a result,

K=-2×4.9/(4.9)²

K= -2/4.9

Substitute the value of K as,

f(x) = -2/4.9(x²-4.9²)

f(x) = (-2/4.9)x²+2×4.9

f(x)= (-2/4.9)x²+9.8

Thus, if the maximum height of the tunnel is the same as its maximum width, 9.8 meters, The quadratic model to represent the tunnel will be f(x)= (-2/4.9)x²+9.8.

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Answer:

10

Step-by-step explanation:

refer attachment for detailed answer

Answer:

x=0.16

Step-by-step explanation:

Answer:

third option

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

[tex]\frac{1}{4}[/tex] [tex](2)^{k-1}[/tex] ← is in this form

with a₁ = [tex]\frac{1}{4}[/tex] and r = 2

Answer:

Step-by-step explanation:

if our motorcycle use 70 miles per gallon

and 1mile=1.6 km

the motorcycle travels 70*1.6=112 km per gallon

for 60 km it needs

60/112=0.54 gallons

Answer:

the square root of 5.494 is 2.34

Step-by-step explanation:

The computation of the square root of 5.494 is as follows"

According to the question it is mentioned that

The number is 5.494

Now the square root of the above number is

[tex]\sqrt{5.494}[/tex]

= 2.34

Hence, the square root of 5.494 is 2.34

Therefore the same is to be considered

Answer:

Number = 92

Step-by-step explanation:

Let the unit digit is x and that of tens digit is y.

ATQ,

x+y = 11 ....(1)

The unit's digit is 7 less than the ten's digit

x = y-7 ...(2)

Put the value of x from equation (2) in (1)

y-7+y = 11

2x-7 = 11

2x = 11+7

2x = 18

x = 9

Put the value of x in equation (1)

9+y = 11

y = 2

Hence, the number is 92.

Answer:

13

Step-by-step explanation:

Ok so we will eliminate some numbers first. The width is 12, but the total on the perimeter is 24. 50-24 = 26

26 is not the length, so divide that by 2, and get 13

Proof:

x=2

13x=26

12x=24

24+26 = 50

Answer:

54 - 3d

Step-by-step explanation:

In order to find the cost of 3 DVDs we would simply need to multiply the expression given by 3. In order to do so we must use the distributive property and distribute the 3 to both the initial price of the dvd and the discount price, like so...

3(18 - d)  ... in order to distribute we multiply 3 by 18 and then by d seperately

(3 * 18) - (3 * d)

54 - 3d

That would leave us the expression 54 - 3d

Answer:

6/7

Step-by-step explanation:

greatest common factor: 4

24/4=6

28/4=7