Given the expression x- + 8x + 5, find the equivalent
expression in vertex form.
(x+4)² – 11
(x+8)2 + 21
(x+4) +9
(x+8) ² – 59

For f to be continuous at some point x = c, you require that

• f(c) exists and is finite, and

• the limits of f as x approaches c from either side match, and their value must be f(c)

For f to be differentiable at x = c, you require that

• f is continuous at c (i.e. the above conditions are all met), and

• the derivative f ' is continuous at c

Without having the graph of f ', you can assess whether the last condition is met by some function by mentally tracing a tangent line to the graph as you get closer to c. If the slope of the tangent doesn't change, then the function is differentiable. This is usually accompanied by jumps or sharp corners in the graph.

Some examples:

• every polynomial is both continuous and differentiable

• the absolute value function |x| is continuous but not differentiable at x = 0

• 1/x is neither continuous nor differentiable at x = 0

(a) Neither continuous nor differentiable

Why? f has a vertical asymptote at x = -2 and f (-2) does not exist. f is not continuous, and therefore not differentiable.

(b) Neither continuous nor differentiable

Why? From the left, f is approaching 2.5, while from the right, it's approaching 5.

(c) Neither continuous nor differentiable

Why? The limits from either side of x = 2 match and are equal to 0.5, but f (2) itself does not exist (which is indicated by the point being a hollow circle).

If the circle was instead filled in, so that f (2) = 0.5, then f would be continuous there, but still not differentiable. Notice the sharp corner. Or, using the tangent-line analysis, the slope of the tangent to the left of x = 2 is negative, but to the right it would be positive.

(d) Both continuous and differentiable

Why? f doesn't have any special features at x = 3 that would suggest it's not continuous nor differentiable.

(e) Neither continuous nor differentiable

Why? Similar reasoning as in (a). There's another vertical asymptote, but the graph shows f (4) = 1. However, the limits from either side of x = 4 are positive infinity, not 1.

Answer:

obtuse

Step-by-step explanation:

Let 5 = a, 7 = b, 10 = c

if a^2 + b^2 = c^2, then the triangle is a right triangle by the converse of the Pythagorean Theorem

If a^2 + b^2 > c^2, then the triangle is an acute triangle by Theorem 8-4

if a^2 + b^2 < c^2, then the triangle is an obtuse triangle by Theorem 8-3

a^2 = 25

b^2 = 49

c^2 = 100

25 + 49 < 100, therefore the triangle is an obtuse

Answer:

60 candies

Step-by-step explanation:

Answer:

B. A regular polygon is a shape with sides that are all equal to each other.

We see that for shape B, the sides are not equal to each other, as some sides are longer than others.

Hope this helps!

Answer:

6 more girls than boys

Step-by-step explanation:

5 out of 12 are boys  (multiply both sides of equation by 3 because 3x12 = 36)

7 out of 12 are girls   (multiply both sides of equation by 3 because 3x12 = 36)

so: 15 out of 36 are boys

so: 21 out of 36 are girls

21-15 = 6 more girls than boys

Answer: There are 6 more girls than boys

Step-by-step explanation:

To find how many more girls there are we need to find what one block equals to.

We use this equation to find it.

36 = ( 5 + 7 )x

36 = 12x

3 = x

or

x = 3 (same thing)

So each block represents 3 girls/boys

The girls have 2 more meaning there are 6 more girls than boys.

Answer:

1 8/21

Step-by-step explanation:

5/7 = 15/21

2/3 = 14/21

15/21+14/21=29/21

Answer:

x = 19/22

Step-by-step explanation:

8x-12+36x = 26

44x - 12 = 26

44x = 38 (add 12 on both sides)

x = 19/22 (divide bot sides by 44 and simplify)

Answer:

m<5=101.9    m<8=101.9

Step-by-step explanation:

alternate interior and vertical angles

Answer:

(a) m∠5=<4[alternate angle]=101.9°,

(b) m∠8=<5[vertically opposite angle]=101.9°,

Answer:

[tex]y = 4x[/tex]

Step-by-step explanation:

Given

[tex]x = 44[/tex]

[tex]y = 176[/tex]

Required

Determine the relationship between x and y

First, we calculate the unit rate, using:

[tex]y = kx[/tex]

Where k is the unit rate.

Substitute 176 for y and 44 for y

[tex]176 = k * 44[/tex]

Divide both sides by 44

[tex]\frac{176}{44} = \frac{44*k}{44}[/tex]

[tex]\frac{176}{44} = k[/tex]

[tex]4 = k[/tex]

[tex]k = 4[/tex]

Substitute 4 for k in [tex]y = kx[/tex]

[tex]y = 4x[/tex]

Hence, the relationship between x and y is: [tex]y = 4x[/tex]

Answer:

15 is answers

x=5

Step-by-step explanation:

4x-5

4×5-5

20-5

15

Answer:

Beck actually caught 45 fish

Step-by-step explanation:

System of Equations

We call the following variables:

x = number of fish Ally caught

y = number of fish Beck caught

They caught a total of 75 fish, thus:

x + y = 75      [1]

If Ally had caught twice as much fish as she actually did, and Beck had caught three times as many fish as he actually did, then Ally would have caught 75 fewer fish than Beck, thus:

3y = 2x + 75      [2]

From [1]:

x = 75 - y      [3]

Substituting in [2]:

3y = 2(75 - y) + 75

Operating:

3y = 150 - 2y + 75

Simplifying:

5y = 225

Dividing by 5:

y = 45

Beck actually caught 45 fish

Answer:

Beck caught 45 fish

Step-by-step explanation:

a = number of fish Ally caught

b = number of fish Beck caught

They caught a total of 75 fish, so we have:

b + a = 75  

From the facts in our question we know Ally would have caught 75 fewer fish than Beck.

3b = 2a + 75  

a = 75 - b

3b = 2(75 - b) + 75

3b = 150 - 2b + 75

5b = 225

5b ÷ 5 = 225 ÷ 5

b = 45

Beck caught 45 fish.

Answer:

48 units

Step-by-step explanation:

36 is 75% of what number

36 = .75n

n = 36/.75

n = 48

Answer:

3(5−13)

Step-by-step explanation:

..............

Answer:

-3(5x-13)

Step-by-step explanation:

The greatest common factor is 3 and you want the # with the variable to be positive, usually, so just factor -3 out and that's what you get.

Answer:

The answer is 30%

Step-by-step explanation:

((5-3.5)/5) × 100%

Answer:

30%

Step-by-step explanation:

the other guy is right

Answer: y+1 = -2(x-2) is the correct answer

Step-by-step explanation: I just took the exam :)

9514 1404 393

Answer:

Step-by-step explanation:

Angles are related in this geometry by being either congruent or supplementary. Corresponding and vertical angles are congruent; any linear pair of angles is supplementary.

The given angle 5 is on the southwest corner of the intersection of the parallel line with the transversal. All southwest and northeast angles are congruent to that. That is, angles 4, 5, 6, 7, 8, 9 will all have the same measure. The remaining angles will have the supplementary measure.

Angles 4, 5, 6, 7, 8, 9 are 82°

Angles 1, 2, 3, 10, 11, 12 are 98°

_____

As you know, supplementary angles total 180°, so each is found by subtracting the other from 180°: 180° -82° = 98°.

Answer:

= 50

Step-by-step explanation:

Answer:

blue 7.3

Step-by-step explanation:

Answer:

7.3

Step-by-step explanation:

There are 7 groups with 10 parts in each, 7 complete rows are filled in. 3 are left in the last row. This means that there are 7 wholes with 3 left over. 7.3

Answer:

A. 3.4.5

Step-by-step explanation:

I looked it up and it forms a right angle.

Answer:

620 milliliters

Step-by-step explanation:

1 milliliter= 0.001 liters

0.62L= move the decimal point 3 places to the left

0.62

06.2

062.

0620.

620 milliliters

Answer:

17

Step-by-step explanation:

ABC, which is 9z - 1, and CBD, which is 6z + 58, make up ABD, which is a total of 87 degrees.

in order to find the measurement of ABC, you first need to solve for z.

since ABC and CBD make up ABD, add those measurements and set them equal to 87, which is the measure of ABD.

9z - 1 + 6z + 58 = 87

combine like terms starting with the z terms. (it doesn't matter which like terms you combine first)

9z - 1 + 6z + 58 = 87 ⇒ 15z - 1 + 58 = 87

combine the next set of like terms.

15z - 1 + 58 = 87 ⇒ 15z + 57 = 87

subtract 57 from both sides of the equation. it'll cancel itself out on the left, leaving you with 15z = 30 after subtracting 57 from 87.

divide both sides of the equation by 15.

15z/15 = 30/15 ⇒ z = 2

now, plug in 2 for z in each of your equations for the measurements of ABC and CBD.

ABC = 9z - 1 ⇒ 9(2) - 1 ⇒ 18 - 1 ⇒ 17

CBD = 6z + 58 ⇒ 6(2) + 58 ⇒ 12 + 58 ⇒ 70

now, your measurements are

ABD: 87

ABC: 17

CBD: 70

check your work by adding the measurements of ABC and CBD and setting them equal to ABD, or 87.

17 + 70 = 87

87 = 87

since both sides of the equation are equal to 87, you know that your measurements are correct.

therefore, the measure of ABC is 17 degrees.

Answer:

x=5

Step-by-step explanation:

subtract 4x from both sides

7x-4x=4x-4x+15

3x=15

divide by 3 on both sides

3x/3=15/3

x=5

Answer:

77 = m∠D  =  m∠E

Step-by-step explanation:

In a triangle the sum of the measures of the angles = 180.  So m∠D  + m∠E + m∠F = 180

Let  m∠D = m∠E = x

Then x + x + 26 = 180

2x + 26 = 180

2x = 154

x = 77 = m∠D  =  m∠E

Answer:

x<-10

Step-by-step explanation:

You can write this inequality:

5-x>15

Solving it:

5-x>15

-x>10

x<-10

Answer:

x= -15/2 or -7.5

x= -1/2 or -0.5

Step-by-step explanation:

please make me brainliest

Answer:

Not C

Step-by-step explanation:

wrong

Answer:

4x² + 16x + 15 = 0

Step-by-step explanation:

We'll begin by determining the solutions to the graph.

The solutions to the graph is obtained by taking the values where the graph cut through the x–axis. This is illustrated below:

The solutions to the graph are:

x = –1.5 or –2.5

Finally, we shall determine the equation for the graph as follow:

x = –1.5 or x = –2.5

x = –3/2 or x = –5/2

Cross multiply

2x = –3 or 2x = –5

Rearrange

2x + 3 = 0 or 2x + 5 = 0

Combine

(2x + 3)(2x + 5) = 0

Expand

2x(2x + 5) + 3(2x + 5) = 0

4x² + 10x + 6x + 15 = 0

4x² + 16x + 15 = 0

Thus, the equation for the graph is:

4x² + 16x + 15 = 0