ΔDEF is formed by lines tangent to the circle, where = 13.7, = 9, and = 14. Determine the perimeter of ΔDEF.
Question 1 options:

1)

68.4

2)

73.4

3)

73.7

4)

73.1

Answer:

13ft 10.2in

Step-by-step explanation:

First let's convert 3ft to in.

3 * 12 = 36 in

Now let's find the angle

We use tangent because we know the opposite and adjacent distances.

tan x = 36/13

tan x = 2.7692

On your calculator, input the value of your tangent. Then press "inv." This should give you the angle associated with that value. The angle associated with tan 2.7692 is 70.14 degrees.

Now that we know the angle we can find the height.

We use tangent again.

tan 70.14 = x / 5     We don't know the opposite but we know the adjacent length is 5ft.

2.77 * 5 = x

13.85 ft = x

To get it in ft and inches multiply .85 by 12

.85 * 12 = 10.2

13ft 10.2in

Answer:

0.3581<x<0.4429

Step-by-step explanation:

Using the formula for calculating the confidence interval of the population proportion p expressed as:

Confidence interval = p ± Z * √p(1-p)/n

p is the population proportion = x/n

p = 200/500

p = 0.4

Z is the z-score at 95% CI = 1.96

n is the sample size = 500

Substituting the given parameters into the formula we will have;

Confidence interval = 0.4 ± 1.96 * √p(1-p)/n

Confidence interval = 0.4 ± 1.96 * √0.4(0.6)/500

Confidence interval = 0.4 ± 1.96 * √0.24/500

Confidence interval = 0.4 ± 1.96 * √0.00048

Confidence interval = 0.4 ± 1.96 * 0.0219

Confidence interval = 0.4±0.04294

Confidence interval = (0.3571, 0.4429)

Hence the confidence interval of the population mean is 0.3581<x<0.4429

(4). If we break down this piecewise function, we have 3 main expressions to deal with, 'h(x) = 5 if {x ≥ 4}' (represented by the green graph) 'h(x) = x if {0 ≤ x ≤ 4}' (represented by the blue graph) and 'h(x) = 1 / 2x + 2 if {x < 0}' (represented by the red graph).

Take a look at the attachment below for your graph of these 3 functions / expressions.

(5). For this part we want to determine the average rate of change of the function f(x) = 4x² - 5x - 8 over the interval [- 2,3]. Remember that to calculate average rate of change between the 2 points we use the following formula...

f(b) - f(a) / b - a,

f(3) = 4(3)² - 5(3) - 8 = 4(9) - 15 - 8 = 36 - 15 - 8 = 13,

f(- 2) = 4(- 2)² - 5(- 2) - 8 = 4(4) + 10 - 8 = 16 + 10 - 8 = 18

13 - 18 / 3 - (- 2) = - 5 / 5 = - 1

Therefore the average rate of change of the function f(x) = 4x² - 5x - 8 over the interval [- 2,3] will be - 1.

Answer:

0.89736

Step-by-step explanation:

We solve this question using z score formula

Z score = x - μ/σ

x = raw score

μ = population mean

σ = population standard deviation

Hence,

x = 258, μ = 220, σ = 30

Z = 258 - 220/30

=1.26667

Probability value from Z-Table:

P(x<258) = 0.89736

Therefore, the probability that his weights is less than 258 kg is 0.89736

Answer:

Both angles are right angles.

Step-by-step explanation:

Supplementary angles sum to 180°. Since we know that both angles are congruent, let's call them x and x. We can write the following equation:

x + x = 180

2x = 180

x = 90°

Therefore, we can conclude that both angles are right angles.

Answer:

Angles that are both congruent and supplementary each have a measurement that is equal to 90°.

Step-by-step explanation:

Answer:

-7x+24

Step-by-step explanation:

(2*2-3x+7) - (-3*2+4x-7)

11-3x+13-4x

-7x+24

Answer:

-7x +24

Step-by-step explanation:

2*2-3x+7) - (-3*2+4x-7)

11-3x+13-4x

-7x+24

Answer:

Option A.

Step-by-step explanation:

Note: Let as consider, we have to find the total amount after 9 years.

It is given that,

Principal amount = $1000

Rate of compound (yearly) interest = 15% = 0.15

Time = 9 year

The formula for total amount is

[tex]M=P(1+i)^n[/tex]

where, P is principal, i is rate of interest and n is number of years.

Substituting P=1000, i=0.15 and n=9, we get

[tex]M=1000(1+0.15)^9[/tex]

[tex]M=1000(1.15)^9[/tex]

[tex]M=1000(3.5178763)[/tex]

[tex]M=3517.8763[/tex]

[tex]M\approx 3517.88[/tex]

So, the total amount after 9 years is $3517.88.

Therefore, the correct option is A.

Answer:

7.36

Step-by-step explanation:

7.3564 would round to 7.36

Answer:

7.36

Step-by-step explanation:

To round off a decimal to the hundredths or a number to the right you do this, if the number to the right of the hundredths is 4 or less you remove all the other digits including the hundredths, if the number is 5 or more you add one to the digit in the hundredths.

Answer:

4.472135955

Step-by-step explanation:

The row of table reveals the x-intercept could be second ( -4, 0).

The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function.

The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 because at that value of x, the function f(x) lies on x-axis where y is 0.

Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.

We have to find Which row of table reveals the x-intercept.

Thus, We can conclude that the second row shows the unit rate.

Hence, the row of table reveals the x-intercept could be second ( -4, 0).

Learn more about x-intercept here:

https://brainly.com/question/14764115

#SPJ5

Answer:

The answer is D

Step-by-step explanation:

One this to remember when doing it is that all negatively skewed graphs or plots will always have the outlier that is on the left of the rest

Answer:

A double integral can be written as:

[tex]\int\limits {f(x, y)} \, dx dy[/tex]

Now, to do this integral, we first can fix one of the variables, like in this case, we can fix x.

Now, with x fixed, this will be a function of only one variable, y, then we can do the integration over y.

Once the function is integrated over y, we can now do the integration over x.

Then the correct option will be:

" Varying the order variable y"

We keep x fixed, and integrate over the other variable.

Answer:

[tex]y=-4x+13[/tex]

Step-by-step explanation:

We are given the two points (3, 1) and (2, 5) and we want to find the equation of the line containing the given points.

First, find the slope of the line:

[tex]\displaystyle \begin{aligned} m &= \frac{\Delta y}{\Delta x} \\ \\ &= \frac{(5)-(1)}{(2)-(3)} \\ \\ &= \frac{4}{-1} \\ \\ &= -4 \end{aligned}[/tex]

Hence, the slope of the line is -4.

Since we know the slope and a point, we can consider using the point-slope form, given by:

[tex]y-y_1=m(x-x_1)[/tex]

Let's use (3, 1) as the chosen point, and we will substitute -4 for the slope m. This yields:

[tex]\displaystyle y-(1)=-4(x-(3))[/tex]

To convert into slope-intercept form, solve for y:

[tex]\displaystyle \begin{aligned} y - 1 &= -4 (x - 3) \\ y - 1 &= -4x + 12 \\ y &= -4x + 13 \end{aligned}[/tex]

In conclusion, the equation of the line is:

[tex]y=-4x+13[/tex]

Answer:

Step-by-step explanation:

Y=-4x+13

Answer: 115

Step-by-step explanation: Supplementary angles add to 180, so 180-65 = 115

Answer:

115 degrees

Step-by-step explanation:

A supplementary angle is an angle that add up to 180 degrees

Because of the this we can create an equation that solves for x

65 + x = 180

x = Missing angle measure

All you have to do to solve for x is to subtract 65 from both sides, making x 115

Answer:

34

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

(b - 2a)² + bc

Step 2: Define variables

a = 6

b = 5

c = 3

Step 3: Plug in

(5 - 2(6))² + 5(-3)

Step 4: Multiply

(5 - 12)² - 15

Step 5: Parenthesis

(-7)² - 15

Step 6: Exponents

49 - 15

Step 7: Subtract

34

Answer:

He invested 3,000 at 7% and 4,000 at 9%.

Step-by-step explanation:

From the information given, you can write the following equations:

x+y=7,000 (1)

0.07x+0.09y=570 (2)

You can solve for x in (1)

x=7,000-y (3)

Now, you can replace (3) in (1) and solve for "y":

0.07(7,000-y)+0.09y=570

490-0.07y+0.09y=570

0.02y=80

y=80/0.02

y=4,000

Finally, you can replace the value of "y" in (3):

x=7,000-4,000

x=3,000

According to this, the answer is that he invested 3,000 at 7% and 4,000 at 9%.

The question is incomplete. Here is the complete question.

(a) How many three-digit numbers can be formed from the digits 0,1,2,3,4,5 and 6, if each digit can be used only once?

(b) How many of these are odd numbers?

(c) How many are greater than 330?

Answer: (a) 180

              (b) 75

               (c) 105

Step-by-step explanation:

(a) In the group, there are 7 digits. A three-digit number can not start with zero, otherwise, it will be a 2-digit number. So:

For the hundreds position, there are 6 choices.

For the tens position, since the digit can be used only once, there are 6 choices.

For the unit position, there are 5 choices.

The total three-digit number formed is: 6*6*5 = 180

(b) To form an odd number, the unit position must be an odd digit, then:

unit position has 3 choices;

hundreds position has 5 choices;

tens position has 5 remaining choices.

The total three-digit odd number is: 3*5*5 = 75

(c) The number formed must be greater than 330, so:

If the number start with a 3, to be greater, there are 3 other choices (4, 5 and 6), so Tens position has 3 choices and Unit position has 5 choices.

Total number is: 3*5 = 15

Another possibility is the number starts with a digit bigger than 3 and so,  there are 3 choices.

Tens position has 6 choices;

Unit position has 5 choices;

Total possibilities are: 3*6*5 = 90

The total number of ways a three-digit number is greater than 330 is:

90 + 15 = 105

Answer:

Step-by-step explanation:

You are given a graph and wish to determine whether or not it represents a function.  Draw a vertical line through this graph and count the number of times the vertical line intersects the graph.  

If exactly once, the graph passes the vertical line test and we say the graph represents a function.

If more than once, the graph fails the test and does not represent a function.

This is because a function assigns one and only one y value to any input value x in the domain.

Answer:

Step-by-step explanation:

vertical line test: a test that uses any kind of straight stuff (i.e line, pen, etc.) to go over the graph and check whether or not there are two points on one vertical line.

In a function, one domain (x value) can only have one range (y value).

NOTE: one range can have multiple domains

This means through vertical line test, if there are two points on one vertical line, it will not be a function.

Answer:

x^2-6x+9  

Step-by-step explanation:

for f=x^2 subsititude x with g(x) = x-3 in which will give you (x-3)^2 using the perfect square formula ((a-b)^2=a^2-2ab+b^2)  in which a=x, b=3. you shall then get x^2 -2x · 3 + 3^2 to get x^2-6x+9  

Answer:

  6

Step-by-step explanation:

Since you're familiar with your multiplication tables, you know that ...

  42 = 6 × 7

There are 6 tiles in each of the 7 rows.

Answer:

The value of n in this equation is -3/4

Step-by-step explanation:

5 - (n - 4) = 3 (n + 2)

Distribute the negative to (n - 4) and distribute 3 to (n + 2).

5 - n + 4 = 3n + 6

Add 4 to -5.

9 - n = 3n + 6

Subtract 9 from 6.

-n = 3n - 3

Subtract 3n from n.

4n = -3

Divide 4 by -3.

n = -3/4

Answer:

-2y + 2

Step-by-step explanation:

Let's first remove the parentheses.  (x - y + 1) becomes x - y + 1 and -(x + y - 1) becomes -x -y + 1.   Combine like terms:

x - y + 1 - x - y + 1 = -2y + 2

Answer:

-2y + 2

Step-by-step explanation:

(x - y + 1) - (x + y - 1)

remove ( )

= x - y + 1 - x - y + 1

simplify

= -2y + 2

Answer:

241.3 feet

Step-by-step explanation:

From the above question, we solve for this using the law of cosines

Law of cosines

a² = b² + c² -2bc Cos A

a =  √b² + c² -2bc Cos A

a = The distance between the bases in Little League =  60 feet

b = ???

c = The distance from home plate to the fence in dead center at the Oak Lawn Little League field =  280 feet

A = It makes an angle of 45°

This is because the distance 60 feet and 280 feet are perpendicular to each other and they meet at a point that divides a right angle 90° into equal parts.

a = √280² + 60² - 2 × 280 × 60  × Cos 45

a = 241.33216 feet

Approximately = 241.3 feet

How far is it from the fence in dead center to third base? 241.3 feet

Answer:

4

Step-by-step explanation:

y = mx+b where m is slope so the slope is 4

Answer:

slope is 4

Step-by-step explanation:

The equation y=mx+b is the linear equation and m represents slope. In this case m is 4

Answer:

2x-3= x+1

or, 2x- x = 1+3

or, x = 4

so, x = 4

NOW,

6= 2y/3

or, 6×3 =2y

or, 18/2 = y

so, y = 9

X = 4 and Y = 9

ANS

Answer:

2

Step-by-step explanation:

-r^2+5ry+4y^2

= -(-2)^2+5(-2)(3)+4(3)^2

= -(4)+5(-6)+4(9)

= -4-30+36

= 36-30-4

= 36-34

= 2

Answer:

Step-by-step explanation:

The quantity of food required for the two cats for one day is ...

  (3/4 can) + (1/2 can) = (3/4 +2/4) can = 5/4 can

Then the cost per day for cat food is ...

  $5/(3 cans) × (5/4 can/day) = $25/12 /day

We note that the cost for some number of days will be the product of this factor and the number of days, rounded up to the next higher $5.

1. The cost for 60 days is ...

  (60 days)($25/12 /day) = $25 × 60/12 = $125

A 60-day supply of cat food costs $125.

__

2. A 29-day supply costs ...

  (29 day) × $25/12 /day = $60 5/12, rounds up to $65 for 29 days

A 30-day supply costs ...

  (30 day) × ($25/12 /day) = $62.50, rounds up to $65 for 30 days

A 31-day supply costs ...

  (31 days) × ($25/12 /day) = $64 7/12, rounds up to $65 for 31 days.

These costs are all the same.

_____

3 cans last, on average, 2 2/5 days. That means some purchases of 3 cans will last for 2 days, and some will last for 3 days. It so happens that the purchase made to cover day 29 will also cover day 30 and day 31.

Answer:

12 feet

Step-by-step explanation:

For an inclined roof, the rise is the vertical distance from the roof rafter to the vertical top plate while the run is the distance from the edge of the wall to half of the center of the ridge.

The slope is the ratio of the rise to run. Given a rise to run ratio of 3 to 4. The house is 32 feet wide.

The run of the roof =  half of the width of the roof = 1/2 × 32 feet = 16 feet

Let the rise of the roof (height of the attic) be x, hence:

rise to run ratio = height of attic/ run of roof

3/4 = x/16

x = 3/4 × 16

x = 12 feet

The height of the attic is 12 feet