Find the missing exterior angles in triangle

Using an exponential function, it is found that the value of the function when x = 4 is of f(4) = 15.95.

It is modeled by:

[tex]y = ab^x[/tex]

In which:

In this problem, we have that f(-1)=5, hence:

[tex]5 = ab^{-1}[/tex]

[tex]\frac{a}{b} = 5[/tex]

a = 5b

We also have that f(7)=32, hence:

[tex]32 = ab^7[/tex]

Since a = 5b:

[tex]5b^8 = 32[/tex]

[tex]b = \sqrt[8]{\frac{32}{5}}[/tex]

b = 1.2612.

a = 5b = 5 x 1.2612 = 6.306.

Hence the function is given by:

[tex]y = 6.306(1.2612)^x[/tex]

Then, when x = 4, we have that:

[tex]y = 6.306(1.2612)^4 = 15.95[/tex]

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

The proportion that satisfies the geometric mean (altitude) theorem for the triangle is 2/h = h/3

According to the theorem, the ratio similar sides of a right triangle are equal. From the given diagram, we are to determine the proportion satisfies the geometric mean (altitude) theorem for the triangle.

Taking the ratio of the base to the height, we will have:
MK/KL = KL/KN

Substitute the measure of the sides

2/h = h/3

Hence the proportion that satisfies the geometric mean (altitude) theorem for the triangle is 2/h = h/3

Learn more on mean altitude theorem here; https://brainly.com/question/10216660

Answer:

its D, 2/h = h/3

Step-by-step explanation:

Answer:

x + y = 9

Step-by-step explanation:

Line is passing through the points (9, 0) and (0, 9)

-> y - intercept (b) = 9

& slope (m) = (9 - 0)/(0 - 9) = 9/(-9) = -1

Equation of line in slope-intercept form is given as:

y = mx + b

Plugging in the values of m and b in the above equation, we find:

y = (-1)x + 9

-> y = -x + 9

-> x + y = 9

This is the required equation of the line

[Note: there are several other points through which line is passing and those points can also be selected for finding the required equation]

The approximate angle that the wire meet the ground is 56.4 degrees

The given set up result in a right triangle. A right triangle has one of its angles as 90degrees.

From the given diagram, we are to caculate the measure of beta. Using the SOH CAH TOA identity

sinβ = opposite/hypotenuse

sinβ = 10/12

sinβ = 0.8333

β = arcsin(0.8333)

β = 56.4 degrees

Hence the approximate angle that the wire meet the ground is 56.4 degrees

learn more on SOH CAH TOA here: https://brainly.com/question/22307176

Answer:

B

Step-by-step explanation:

angles on the circumference of a circle subtended on the same arc are congruent , then

x = 52°

Answer:

D. 20°

Step-by-step explanation:

just do an elimination, since 52° is big then X it obviously can't be 96°. And that leaves us with 32° and 20°. As you can see 32° is bigger than X then it's 20° ♡

11% of $150 =

10% = $15

1% = $1.50

$15+$1.50= $16.50

$150-$16.50= $133.50

Clementine has $133.50 left

Answer: Taxes: 11 & 16.50 Earnings after: 133.50

Step-by-step explanation: ok

Answer:

? = 85°

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × 3 = 540°

sum of the angles around a point = 360° , so

interior angle on right = 360° - 250° = 110°

sum the interior angles and equate to 540°

110° + 115° + 120° + 110° + ? = 540° , that is

455° + ? = 540° ( subtract 455° from both sides )

? = 85°

Diameter=6units

Area:-

Answer:

Height of the rectangular prism is 10.1 millimeters

Step-by-step explanation:

Rectangular Prism Formula = Length * Width * Height
1,919mm^3 = 10 mm * 19mm * height

height = 10.1 millimeters

The cost of 1 purse will be £14.

And, The cost of 1 watch will be £13.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The cost of 1 purse and 1 watch is £27.

The cost of 2 purses and 1 watch is £41.

Now,

Let the cost of 1 purse = x

And, The cost of watch = y

So, We can formulate;

⇒ x + y = £27    ......(i)

And, The cost of 2 purses and 1 watch is £41.

So, We can formulate;

⇒ 2x + y = £41          ..........(ii)

Subtract (i) from (ii), we get;

⇒ 2x + y - x - y = 41 - 27

⇒ x = £14

And, From equation (i), we get;

⇒ x + y = £27

⇒ £14 + y = £27

⇒ y = £27 - £14

⇒ y = £13

Thus, The cost of 1 purse will be £14.

And, The cost of 1 watch will be £13.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

Answer:

90 is the answer

Step-by-step explanation:

360° / 4= 90°

Answer:

Reasons will be definitions, postulates, properties and previously proven theorems. “Given” is only used as a reason if the information in the statement column was given in the problem. Use symbols and abbreviations for words within proofs.

Step-by-step explanation:

Reasons will be definitions, postulates, properties and previously proven theorems. “Given” is only used as a reason if the information in the statement column was given in the problem. Use symbols and abbreviations for words within proofs.

Answer:

X = 1

Step-by-step explanation:

1) Move the 3x to the left hand side and change its sign:

4x-19+3x=-12

2) Move 19 to the right hand side and change its sign:

4x+3x=-12+19

3) collect the like terms:

4x+3x= 7x

-12+19= 7

4) Divide both sides by 7

X = 1

Answer:

4x − 19 = −3x − 12

Let's first get rid of any constants, either from the left or right side.

I'll start with the left, by using the inverse operations.

The inverse operation of subtraction (since 19 is negative) is addition.

So, we add 19 to both sides.

Remember that whenever we use inverse operations we need to do the same for the other side, consequently both sides.

+19             +19

Now, we'll end up with:

4x = -3x + 7

Let's get rid of other terms(grouping them), such as -3x.

We do this by adding 3x to both sides because the inverse operation of subtraction (since 3 is negative) is addition.

Add 3x to both sides,

+3x     +3x

7x = 7

Get rid of the co-efficient of x, which is 7.

We do this by dividing by 7 from both sides since the inverse operation of multiplication (because 7 is being multiplied by x) is division.

Divide by 7 from both sides:

÷7 ÷7

x = 1, the value of x is 1.

Answer:

267.95 cm³ (nearest hundredth)

Step-by-step explanation:

Formulae

[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3\quad\textsf{(where r is the radius)}[/tex]

[tex]\textsf{Diameter of a circle}=\sf 2r\quad\textsf{(where r is the radius)}[/tex]

Given:

⇒ radius = 8 ÷ 2 = 4cm

[tex]\begin{aligned}\implies \textsf{Volume} &=\sf \dfrac43 \cdot 3.14 \cdot 4^3\\ & = \sf 267.95\:cm^3\:(nearest\:hundredth)\end{aligned}[/tex]

Answer:

267.95 cm³

Step-by-step explanation:

Volume of a sphere

Here, diameter = 8 cm.

But, diameter = 2 x radius

Therefore, radius = 4 cm.

Solving

Answer: B. The volume of the cylinder is smaller than the volume of the prism.

Step-by-step explanation

Did the test!

The volume of the cylinder is smaller than the volume of the prism.

We have given that,

a. The volume of the cylinder is greater than the volume of the prism

b. The volume of the cylinder is smaller than the volume of the prism.

C. The volume of the cylinder is the same as the volume of the prism

d.You cannot compare the volumes of different shapes

We have to determine the,

the volume of a cylinder with a radius of 3 units and a height of 12 units compared to the volume of a rectangular prism with dimensions 16 units x 16 units x 9 units.

[tex]v=\pi r^2h[/tex]

The volume of the cylinder is smaller than the volume of the prism.

To learn more about the volume of the cylinder visit:

https://brainly.com/question/14944363

#SPJ5

Answer:

1.2

Step-by-step explanation:

9.2 + 8d = 73.2

d = 8

then first term is   9.2 - d = 1.2

The first term of an arithmetic sequence is 1.2 with a common difference of 8.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have:

Tenth term of an arithmetic sequence = 73.2  or

a+(10-1)d = 73.2 ....(1)

Second term of an arithmetic sequence = 9.2 or

a+(2-1)d = 9.2 .....(2)

Where a is the first term and d is a common difference.

Solving equations (1) and (2)

From the equation (2) put the value of d in the equation (1), we get:

a+9(9.2-a) = 73.2

a+82.8 - 9a = 73.2

-8a = -9.6

a = 1.2

Thus, the first term of an arithmetic sequence is 1.2 with a common difference 8.

Learn more about the sequence here:

brainly.com/question/21961097

Amy's average speed during her whole journey from London to Newcastle (300 miles) was 51.422 miles per hour.

This is calculated by taking the total distance and dividing it into the total time.

First part of ther journey: 165 miles at 60mph, which is equal to 2.75 hours

Second part of her journey: 135 miles in 3.083 hours (3 hours and 5 minutes)

Average speed: 300 miles / 5.834 = 51.422 miles per hour

Learn more about average speed in: https://brainly.com/question/12322912

The correct answer to the simplified form of the mixed fraction equation is determined as [tex]\frac{67x}{10} + 9[/tex].

The given fraction is written as follows;

[tex]3 (\frac{7}{5} x + 4)-2(\frac{3}{2} -\frac{5}{4} x)[/tex]

[tex]=3 (\frac{7}{5} x + 4)-2(\frac{3}{2} -\frac{5}{4} x)\\\\= \frac{21}{5} x + 12 - 3 + \frac{5x}{2} \\\\= \frac{21}{5} x +9 + \frac{5x}{2}\\\\= \frac{42x + 90+ 25x}{10} \\\\= \frac{67x}{10} + 9[/tex]

Thus, the correct answer to the simplified form of the mixed fraction equation is determined as [tex]\frac{67x}{10} + 9[/tex].

Learn more about mixed fractions here: https://brainly.com/question/1746829

Answer:

third one is the correct answer

Answer:

5 cm height

Step-by-step explanation:

V = L * W * H

V / (L* W) = H      =  5cm height

Answer:

$3h

Step-by-step explanation:

w=$44+$12h

w=$35+$15h

$44+$12h=$35+$15h

         -12              -12

$44=$35+$3h

-35    -35

$9=3h

/3   /3

$3=h

Answer:

Step-by-step explanation:

The average rate of change of a function on an interval is the ratio of the change in function value to the length of the interval.

__

The average rate of change of f(x) on the interval [5, 10] is ...

  (f(10) -f(5))/(10 -5) = (-0.1(10²) -(-0.1(5²)))/(10 -5) = (-0.1(10 -5)(10 +5))/(10 -5)

  = -0.1(10 +5) = -1.5 . . . . average rate of change of f(x)

The average rate of change of g(x) is calculated the same way, and the simplification of the calculation is the same. The average rate of change of g(x) is ...

  -0.4(10 +5) = -6 . . . . average rate of change of g(x)

The ratio of the average rates of change is ...

  g'(x)/f'(x) = -6/-1.5 = 4

The rate of change of g(x) is 4 times that of f(x).

_____

Additional comment

In the above, we made use of the factoring of the difference of squares in order to simplify the expression: a² -b² = (a +b)(a -b). This let us cancel the denominator factor to show us an interesting fact about the rate of change of a quadratic function.

If we generalize the result we found above, we see that the average rate of change of h(x) = kx² on the interval [a, b] is ....

  h'(x) = k(b +a) . . . . . squared term coefficient times the sum of the ends of the interval

You will notice that (b+a)/2 is the midpoint of the interval, so the average rate of change can also be expressed as ...

  h'(x) = 2k × (midpoint of interval [a, b])

The linear function that can be used to find the amount in dollars Luis can spend on entertainment is given by:

f(x) = (x - 35)/6.

A linear function is modeled by:

y = mx + b

In which:

In this problem:

Hence, the function is given by:

f(x) = (x - 35)/6.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1