Find the largest negative integer of p for the equation 4x^2 + 8 = px to have real roots?

The fundamental counting principle is used to count the total number of possible outcomes that are in a situation.

The fundamental counting principle states that if there are n ways of doing something, as well as m ways of doing another thing, then there are n×m ways to perform both of these actions.

The Fundamental Counting Principle helps when determining the sample space of probability as it figures out the total number of ways the combination of events can occur. Therefore, it is used as a guide when determining the sample space of a probability.

Lastly, the limitation is that the Fundamental Counting Principle is that it assumes that each basic event is equally probable, which does not necessarily have to be true.

Learn more about counting principle on:

https://brainly.com/question/24358027

Answer:

The fundamental counting principle is used to count the total number of possible outcomes that are in a situation

Step-by-step explanation:

Answer:

[tex](1,\, 10)[/tex].

Step-by-step explanation:

Differentiate each function to find an expression for its gradient (slope of the tangent line) with respect to [tex]x[/tex]. Make use of the power rule to find the following:

[tex]g^\prime(x) = 3\, x^2 - 2\, a\, x[/tex].

[tex]h^\prime(x) = 2\, (2\, x) + b = 4\, x + b[/tex].

The question states that the graphs of [tex]g(x)[/tex] and [tex]h(x)[/tex] touch at [tex]x = 1[/tex], such that [tex]g^\prime(1) = h^\prime(1)[/tex]. Therefore:

[tex]3 - 2\, a = 4 + b[/tex].

On the other hand, since the graph of [tex]g(x)[/tex] and [tex]h(x)[/tex] coincide at [tex]x = 1[/tex], [tex]g(1) = h(1)[/tex] (otherwise, the two graphs would not even touch at that point.) Therefore:

[tex]1 - a + 6 = 2 + b + 3[/tex].

Solve this system of two equations for [tex]a[/tex] and [tex]b[/tex]:

[tex]\begin{aligned}& a + b = 2 \\ & 2\, a + b = -1\end{aligned}[/tex].

Therefore, [tex]a = -3[/tex] whereas [tex]b = 5[/tex].

Substitute these two values back into the expression for [tex]g(x)[/tex] and [tex]h(x)[/tex]:

[tex]g(x) = x^3 + 3\, x^2 + 6[/tex].

[tex]h(x) = 2\, x^2 + 5\, x + 3[/tex].

Evaluate either expression at [tex]x = 1[/tex] to find the [tex]y[/tex]-coordinate of the intersection. For example, [tex]g(1) = 1 + 3 + 6 = 10[/tex]. Similarly, [tex]h(1) = 2 + 5 + 3 = 10[/tex].

Therefore, the intersection of these two graphs would be at [tex](1,\, 10)[/tex].

9514 1404 393

Answer:

  2

Step-by-step explanation:

Each orange vertex is twice as far from the origin as the corresponding black vertex. Each orange line segment is twice as long as the corresponding black line segment. The scale factor is 2.

Answer:

add

Step-by-step explanation:

The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents. In this example, you can see how it works. Adding the exponents is just a short cut! The "power rule" tells us that to raise a power to a power, just multiply the exponents.

Hope this is helpful

Answer:

Add

Step-by-step explanation:

Hope it helps you

Please mark as brainliest

Thank You

Answer:

please mark as brilliant

Answer:

V = 12,348·π

Step-by-step explanation:

The given parameters of the glass Vase are;

The shape of the glass vase = A sphere

The radius of the vase, r = 21 inches

The given formula for finding the volume of a sphere is [tex]V = \dfrac{4}{3} \cdot \pi \cdot r^3[/tex]

Therefore, when r = 21 inches, we get;

[tex]V = \dfrac{4}{3} \cdot \pi \cdot 21^3 = {12,348 \cdot \pi}[/tex]

Therefore, the expression for finding the equation of the spherical glass vase, V = 12,348·π

Answer:

4 and 5

Step-by-step explanation:

Let the numbers be x and y

If their sum is 9, hence;

x + y = 9 ....1

When reversed

10y+x = 2(10x+y)

10y+x = 20x + 2y

10y - 2y = 20x - x

8y = 19x

y = 10x/8 ...2

Substitute equation 2 into 1;

From 1;

x+y = 9

x +(10x/8) = 9

18x/8 = 9

18x = 72

x = 72/18

x = 4

Since x+y =9

y = 9-x

y =9-4

y = 5

Hence the numbers are 4 and 5

Answer:

A. x + 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \frac{x^2 - 25}{x - 5}[/tex]

Step 2: Simplify

Answer:

Vertex is (-a, -6), where a ≠ 0.

General Formulas and Concepts:

Algebra I

Algebra II

Vertex Form: y = a(bx - h)² + k

Step-by-step explanation:

Step 1: Define

y = -3(x + a)² - 6

↓ Identify variables

a = -3

b = 1

(h, k) = (-a, -6)

Answer:

B.) 75

Step-by-step explanation:

Answer: B 75

Step-by-step explanation:

Answer:

113.04 is the answer

Step-by-step explanation:

Use the formula for finding the area of a circle.

Area= pi times radius to the second power.

First you had to divide your diameter by 2 to get 6. Then 6 squared, to get 36. Then finally 36x3.14.

Answer:

In other words y = 2-x

Put in some values of x and see which graph matches the given ys.

The last graph

Answer:

b

Step-by-step explanation:

Step-by-step explanation:

three solutions of the equation:

y = -2x - 1

=>

1) (0, -1)

2) (1, -3)

3) ( -1, 1)

Answer:

d) x + 3

Step-by-step explanation:

= x² + 5x + 6

Factorise :-

= x² + 2x + 3x + 6

= x(x + 2) + 3(x + 2)

= (x + 2)(x + 3) [Taking common]

Here we are getting (x + 3) as a factor of x² + 5x + 6 which will be either length or the width

Answer: Choice C

Yes, holidays are a subset and proper subset of the calendar year.

=========================================================

Explanation:

The set of days in the calendar year spans from Jan 1st to Dec 31st.

The set of holidays is a small subset of the previous set mentioned. Any holiday is found on the calendar, but not every day on the calendar is a holiday.

------------

Here's another example of a subset

A = set of all animals

B = set of dogs

Set B is a subset of set A because any dog is an animal. In other words, any individual in set B is also in set A, but not the other way around.

------------

Going back to the calendar example, the set of holidays is a subset and it's also a proper subset of all the days in the year. We say that set B is a proper subset of set A if B has less items in it compared to A.

If we had these two sets

A = {1,2,3,4,5,6}

B = {1,2,3}

We can see that B is a proper subset of set A since everything in B is found in A, and B is smaller than A. The only time we have a subset and not a proper subset is when we talk about the set itself. Any set is a subset of itself (not a proper subset of itself).

The True statement is

Yes, holidays are a subset and proper subset of the calendar year.

Sets are represented as a collection of well-defined objects or elements that are consistent from one person to the next. A capital letter represents a set. The cardinal number of a set is the number of items in a finite set.

The order of a set determines the number of elements in the set. It refers to the size of a set. The order of the set is often referred to as the cardinality.

The set of days in the calendar year spans from Jan 1st to Dec 31st.

The set of holidays is a subset of the previously described set. Any holiday can be found on the calendar, however not every day is a holiday.

let Set B is a Proper subset of set A if it contains fewer elements than A.

So, A = {1,2,3,4,5,6}

B = {1,2,3}

We can see that B is a proper subset of set A since everything in B is found in A, and B is smaller than A.

So, holidays are a subset and proper subset of the calendar year.

Learn more about Set here:

https://brainly.com/question/8053622

#SPJ3

Answer:

See explanation

Step-by-step explanation:  

(Please Find Diagram in the attachment)⇒Answer Drawing is Given There

According to the question,

Answer:ln is called the natural log, or log to the base e. ln can also be written as

So, we can write the given expression as

The property of logs is:

This mean if the number a is raised to log whose base is the same as the number a itself, then the answer will be equal to the argument of the log which is x.

In the given case, the number e and the base of log are the same. So the answer of the expression will be the argument of log which is 6.

so, we can write

Thus, the correct answer is option D

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex] {10}^{ - 4} [/tex]

Answer:

B

Step-by-step explanation:

These are corresponding angles if i remember correctly.

Answer:

Supplementary

Step-by-step explanation:

The angles add up to 180 degrees

Answer:

Let's define:

S as the rate at which Sara can weed a garden.

We know that:

S*30min = 1 garden

And let's define H as the rate at which Hamdan can weed a garden, we know that when they work together, they can complete the job in 20 minutes, then

(S + H)*20min = 1 garden

a) Here we get:

H*n = 1 garden

where n is the number of hours that he would take (note that in two previous equations we have minutes, so we need to use a change of units)

b) The equation is

(S + H)*20min = 1 garden

c) ok, we know two things:

(S + H)*20min = 1 garden

S*30min = 1 garden

first, let's convert both times to hours:

60 min = 1 hour

then:

30 min = (30/60) hours = 0.5 hours

20 min = (20/60) hours = 0.33 hours

Then the equations become:

(S + H)*0.33 hours = 1 garden

S*0.5 hours = 1 garden

Le's solve the second equation for S:

S = (1 garden /0,5 hours) = 2 gardens/hour.

Now we can replace this in the other equation to get:

(2 garden/hour + H)*0.33 hours = 1 garden

2 garden/hour + H = (1 garden)/(0.33 hours) = 3 gardens/ hour

H = 3 gardens/hour - 2 gardens/hour = 1 gardens/hour

This means that the rate of Hamdan is 1 gardens/hour, so he can weed a garden in one hour.

Then:

(1 garden/hour)*n = 1 garden

n = ( 1 garden)/((1 garden/hour)) = 1 hour

Answer: Graph A

Step-by-step explanation:

Answer:

[tex]7[/tex]

Solution:

This is a linear function. This means means that r is our rate of change.

To find r recal following formula

[tex]r=\frac{\Delta y}{\Delta x} = \frac{y_2-y_1}{x_2-x_1}[/tex]

Since this is a linear function we can choose any two points. I will choose the first two for simplicity

[tex]\Displaystyle \therefore r = \frac{42-14}{6-2}=\frac{28}{4}=7[/tex]

Answer:

B.

3m - 11 = 2m + 9

Amount Maddie earns = m = $20

Step-by-step explanation:

Let

Amount Maddie earns = m

Amount Lauren earns = 3m - 11

Amount Shannon earns = 2m + 9

If Lauren and Shannon both earned the same amount of money, how much money, m, did Maddie earn?

Amount Lauren earns = Amount Shannon earns

3m - 11 = 2m + 9

Collect like terms

3m - 2m = 9 + 11

m = 20

Amount Maddie earns = m = $20

B.

3m - 11 = 2m + 9

Complete question:

4x³ - 4x + 3 is divided by (2x - 1). Find the quotient and the remainder

Answer:

The quotient =  2x² +  x  - ³/₂  and the remainder = ³/₂

Step-by-step explanation:

Given function;

4x³ - 4x + 3 divided by (2x-1)

Use long division method to obtain the remainder and the quotient.

                               2x² +  x  - ³/₂

                            -----------------------

                 2x - 1 √4x³ - 4x + 3

                           - (4x³ - 2x²)

                           ----------------------------

                                    2x²  - 4x + 3

                                 - ( 2x² - x)

                             -----------------------------

                                        -3x + 3

                                      -(-3x + ³/₂)

                               ----------------------------

                                            ³/₂

Therefore, the quotient =  2x² +  x  - ³/₂  and the remainder = ³/₂

Answer:

5.4 units

Step-by-step explanation:

Hi there!

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (1,5) and (3,0)

[tex]d=\sqrt{(3-1)^2+(0-5)^2}\\d=\sqrt{(2)^2+(-5)^2}\\d=\sqrt{4+25}\\d=\sqrt{29}\\d=5.4[/tex]

Therefore, the distance between the two points when rounded to the nearest tenth is 5.4 units.

I hope this helps!

Answer:

Step-by-step explanation:

Answer:

all positive real numbers, (0, ∞)

Step-by-step explanation:

The log function is not defined for 0 or for negative numbers.

The domain of the log function is all positive real numbers.

Answer: all positive real numbers

Answer:

The outcomes produced by A would be greater than B. A further explanation is provided below.

Step-by-step explanation:

Given:

In process A,

Produced units = [tex]32x^{1.5}[/tex]

In process B,

Produced units = [tex]4x^3[/tex]

If the outcomes are equivalent then,

⇒ [tex]32x^{1.5}=4x^3[/tex]

⇒     [tex]x^{1.5} = 8[/tex]

By taking log both  sides, we get

⇒    [tex]log \ 8= 1.5 \ log \ x[/tex]

⇒          [tex]x=3.99[/tex]

Given:

The rule of translation is:

[tex](x+3,y-2)[/tex]

The trapezoid ABCD on the graph.

To find:

The coordinates of the point C'.

Solution:

From the given graph, it is clear that the coordinates of point C are (-2,4).

The rule of translation is:

[tex](x,y)\to (x+3,y-2)[/tex]

Using this rule of translation, we get

[tex]C(-2,4)\to C'(-2+3,4-2)[/tex]

[tex]C(-2,4)\to C'(1,2)[/tex]

Therefore, the coordinates of the point C' are (1,2).