Find the area of the figure

(A) f(x+h)

(B) f(x + h) - f(x)

(C)

The 30-60-90 ratio is a special right triangle that always has angles with measures: 30º, 60º, and 90º. Its side lengths have also the same relationship one with another.

For any 30-60-90 the ratio is as follows:

The side opposite to the 30º angle has length: z

The side opposite to the 60º angle has a length z√3

The side opposite to the 90º angle has a length: 2z

Following these ratios, you can determine the side lengths of the triangle.

The measure opposite to the 60º angle is z√3 = 9√3 → From this we can determine the value of z, which is z=9

Once we know the value of z, we can calculate the values of the sides opposite to the other angles.

The side opposite to the 30º angle is y= z= 9

The side opposite to the 90º angle is x= 2z= 2*9 = 18

Answer:

The 14-inch pizza cut into 8 slices.

Explanation:

The deep-dish pizza forms a cylindrical shape.

To make comparisons, we find the volume of each slice of pizza in each case.

Case 1

A 14-inch pizza that is 3 inches deep.

Radius = 14/2 = 7 inches

Height = 3 inches

Since it is cut into 8 slices:

Case 2

A 16-inch pizza that is 2 inches deep.

Radius = 16/2 = 8 inches

Height = 2 inches

Since it is cut into 7 slices:

Conclusion

The volume of a slice of pizza in the first case (the 14 -inch pizza cut into 8 slices) is larger, therefore it should be chosen to get the most food.

The slope of a line from given points (19,-16), (-7, -15) is - 1/26

Slope :

In Mathematics, Slope of a line defined as the direction of the line and the change in y-coordinate with respect to x - coordinate. Slope of a line is denoted by 'm'

The formula for slope of a line which passes through the points (x₁, y₁) and (x₂, y₂) is given by Slope (m) =  (y₂– y₁)/(x₂ – x₁)

Here, we have pair of points (19,-16), (-7, -15)

Take (x₁, y₁) = (19,-16) and (x₂, y₂) = (-7, -15)

Slope (m) = [-15 -(-16) ] / [ -7 -19 ]

= [ - 15+16] / [ -26 ]  

= [ 1 ] / [ -26 ]  

= - 1/26

Therefore,

The slope of line from given points (19,-16), (-7, -15) is - 1/26

Learn more about Slope at

https://brainly.com/question/28882561

Given the function :

we need to find the value of 3f(5) x f(2)

so, to find the value of f(5), substitute with x = 5 at the given function

And to find the value of f(2) , substitute with x = 2 at the given function

so,

The expression (28 + 70) as a multiple of a sum of whole numbers with no common factor is given as

7x(4+10). This is further explained below.

Generally, An express is a finite combination of symbols that have been formed according to principles that rely on the context in which it is used. In mathematics, an expression is also known as a mathematical expression.

In conclusion, When expressed as a multiple of a total of whole numbers that do not have a common component, the equation (28 + 70) is written as 7 times (4 + 10).

Read more about expression

https://brainly.com/question/14083225

#SPJ1

The contra positive of the conditional statement is given as follows:

If an item is not made from copper, then it is not a pendant.

A conditional statement is modeled as follows:

p -> q.

In which:

Hence the statement is read as:

If p then q.

The contra positive of the statement is given by:

~q -> ~p.

Hence it is read as:

If not q, then not p.

In the context of this statement, the hypotheses and the conclusion are given, respectively, by:

Hence the contra positive of the statement is:

If an item is not made from copper, then it is not a pendant.

The statement is missing and is given as follows:

"If an item is a pendant, then the item is made from copper".

More can be learned about the contra positive of a conditional statement at https://brainly.com/question/11073037

#SPJ1

SOLUTION:

Case: Secant secant theorem

Secant-Secant Power Theorem: If two secants are drawn from an external point to a circle, then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant

Method:

Final answer:

x = 11

For a quadratic [tex]ax^2+bx+c[/tex], the sign of its determinant, given by

[tex]\Delta = b^2 - 4ac[/tex]

"determines" the nature of its roots. In particular, if [tex]\Delta<0[/tex], then the quadratic has two distinct non-real roots.

Now, we have

[tex]3z^2 - 9z = n-3 \implies 3z^2 - 9z - (n-3) = 0[/tex]

with determinant

[tex]\Delta = (-9)^2 - 4\cdot3(n-3) = 117 - 12n[/tex]

Solve for [tex]n[/tex] such that [tex]\Delta<0[/tex].

[tex]\Delta = 117 - 12n < 0 \implies 12n > 117 \implies n > \dfrac{117}{12} \\\\ ~~~~ \implies \boxed{n > \dfrac{39}4}[/tex].

Hello!

For a line with slope '0':

⇒ the equation is 'y = y-coordinate of point that the line passes through'

Since the line passes through (-1, -4) and has the slope of '0'

⇒ y = -4

Hope that helps!

Given:

Total Number of teaspoons of peppercorns = 27

Amount of teaspoons you need for one serving of brief brisket = 0.25

Let's find the amount of servings can be made.

To find the amount of servings that can be made, apply the formula:

Thus, we have:

Therefore, 108 servings can be made.

ANSWER:

108

Using the uniform distribution, it is found that:

a) The probability that the friend is between 10 and 20 minutes late is of 1/3.

b) There is a 30% probability that the friend will arrive within 9 minutes.

The uniform has two bounds, a and b, and each outcome of the distribution is equally as likely.

From the image given at the end of the answer, the bounds are given as follow:

a = 0, b = 30.

The probability of finding a value between c and d in the distribution is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

Hence, the probability that the friend is between 10 and 20 minutes late is given as follows:

P(10 <= X <= 20) = (20 - 10)/(30 - 0) = 1/3.

The 30th percentile of the distribution, which is what item b is asking, is given as follows:

0.3 x (30 - 0) = 0.3 x 30 = 9 minutes.

The complete problem is given by the image at the end of the answer.

More can be learned about the uniform distribution at https://brainly.com/question/28852504

#SPJ1

Answer: 19 cm

Step-by-step explanation:

Substituting into the formula for the area of a trapezoid,

[tex]\frac{1}{2}(x-4)(x+4+x+9)=99\\\\\frac{1}{2}(x-4)(2x+13)=99\\\\(x-4)(2x+13)=198\\\\2x^2 +5x-250=0\\\\(2x+25)(x-10)=0\\\\x=-12.5, 10[/tex]

However, as x must be positive (since length must be positive), x=10. This means the length of the longer base is 19 cm.

THe diagonal, BD divides the rectangle into two right angle triangles.

BD represents the hypotenuse

BC represents the opposite side

DC represents the adjacent side

We would determine BD by applying the pythagorean theorem which is expressed as

The length of the diagonal, BD is 13.9m to the nearest tenth

Answer:

[tex]4xy^3[/tex]

Step-by-step explanation:

3xy^3 + x^2y^5/xy^2

The two lines are neither parallel nor perpendicular.

What is condition for perpendicular, parallel?

if two given lines are parallel, perpendicular, or neither, we need to compare their slopes. For this, we need to make sure that their equations are in the form y = mx + b. This represents the equation of a straight line in the slope-intercept form, where m is the slope and b is the y-intercept.

If the given lines have the same slope, they’re parallel to one another. On the other hand, if they have slopes that are opposite reciprocals, i.e., the slopes have opposite signs and are flipped fractions of one another, they are perpendicular to each other. Else, they are neither.

The given lines are

- 3x + 6y = 12 or, y = (1/2)x + 2 ... (1)

y = - 3x + 10 ... (2)

The gradient of the lines (1) and (2) are 1/2 and (- 3) respectively.

Since the gradients are not equal, the lines are not parallel and also since (1/2) × (- 3) ≠ - 1, the lines are not perpendicular to each other.

Hence we can conclude that the given two lines are neither parallel nor perpendicular.

To know more about condition for parallel and perpendicular, visit:

https://brainly.com/question/17957900

#SPJ13

Answer:

  C.  100

Step-by-step explanation:

If 60 songs are played in 3 hours, 80 songs in 4 hours, and 120 songs in 6 hours, you want to know the number played in 5 hours.

Considering the rate of change of songs per hour, we find ...

  hours 3-4: 80-60 = 20 songs, over the 1-hour period

  hours 4-6: 120 -80 = 40 songs, over the 2-hour period

It appears that the number of songs being played is steady at 20 songs per hour. Then 5×20 = 100 songs were played in 5 hours.

Answer:

Step-by-step explanation:

Answer:

[tex]{ \tt{(5)(3) - (2 - 7) \div 4}}[/tex]

- We are going to simplify the expression using BODMAS

- From our expression, relating it to BODMAS, Brackets come first, so let's first operate the brackets

[tex] = { \tt{(5 \times 3) - ( \frac{2 - 7}{4}) }} \\ \\ = { \tt{15 - ( - \frac{5}{4} )}} \\ \\ = { \tt{15 + 5 \div 4}}[/tex]

- Then in our last expression, Division comes next

[tex] = { \tt{15 + \frac{5}{4} }} \\ [/tex]

- Then addition comes last

[tex] = { \tt{ \frac{65}{4} }} \\ [/tex]

- Simplifying our answer into mixed fraction and decimal format;

[tex] = { \tt{16 \frac{1}{4} \: \: or \: \: 16.25}}[/tex]

[tex]{ \boxed{ \delta}}{ \underline{ \mathfrak{ \: \: beicker}}}[/tex]

Step 1:

Let the number of hours = m

Flat fee = $25

Fees charge per hour = $30

Step 2:

Money Ronnie made from his first customer = $175

Write an equation.

30m + 25 = 175

Step 3:

Solve the equation.

Final answer

5 hours

each box costs $3 : The cost of one box = $3

12 boxes of cookies : The total number of boxes = $12

For the total cost of 12 boxes : Multiply the cost of one box by the number of boxes

The total cost of 12 boxes = 12 x $3

The cost of 12 boxes = $36

The cost of 12 boxes of cookies ia $36

Answer : $36

In order to find the margin of error, we need to know that the width of the confidence interval is equal to 2 times the margin of error.

The width of this confidence interval is given by:

If the width is 2 times the margin of error, we have:

The margin of error is equal to 3, therefore the correct option is D.

The percent of people that were completely satisfied (%PS) can be calculated with the formula:

Where PS is the number of persons that were completely satisfied and TP is the total number of persons, in this case, the total number of persons is the sum of each number of persons from each category:

And as we can see from the figure, the number of completely satisfied people is 1100, then the percent of people that were completely satisfied is:

The percent of people that were completely satisfied is 55%

You just have to divide 1100 by the total people which is 2000, and then just multiply by 100, and that's it

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Here the domain of the relation is {3,x,9,5}.

The given relation is a function only if x not takes any of the value 3, 9 or 5.

So, option B is correct.

Given

Answer

The graph is given by y = -3/2|x|

The graph of |y| = x/2

The graph of y = |x|

The graph of -1/2 |y| = x

Answer:

Step-by-step explanation:

6a) f(1)=-3

b) x=-5 x=-1 x=1

:]

Setting h=0 and solving for t we get:

Since t<0 does not have real meaning, we get that:

Answer: 6.5 seconds.

Answer:or a polynomial of the form

a

x

2

+

b

x

+

c

, rewrite the middle term as a sum of two terms whose product is

a

⋅

c

=

7

⋅

−

12

=

−

84

and whose sum is

b

=

25

.

7

x

2

−

3

x

+

28

x

−

12

Factor out the greatest common factor from each group.

Tap for more steps...

x

(

7

x

−

3

)

+

4

(

7

x

−

3

)

Factor the polynomial by factoring out the greatest common factor,

7

x

−

3

.

(

7

x

−

3

)

(

x

+

4

)

Step-by-step explanation:

Answer

The function that describes the height of the rocket in terms of the is