If a nonlinear system of equations contains one linear function that touches the quadratic function at its minimum, then the system has which of the following?
A. No solution
B. Infinitely many solutions
C. One solution
D. Two solutions

Using the combination formula, the number of ways to order the pizzas in each case is given as follows:

a) 638 ways if Grogg must order at least five toppings.

b) 937,024 ways if each pizza must have at least three toppings.

c) 1024 ways if Lizzie's pizza must have at least four toppings and Grogg's must have at least one topping.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials.

[tex]C(n,x) = \frac{n!}{x!(n-x)!}[/tex]

For this problem, the order of the toppings is not important, which is why the combination formula is used.

Hence the numbers of pizzas from 0 to 10 toppings are given as follows:

In item a, Greg must order at least five, hence the number of ways is:

252 + 210 + 120 + 45 + 10 + 1 = 638 ways.

In item b, each must have at least three toppings, hence the number of ways for each is:

120 + 210 + 252 + 210 + 120 + 45 + 10 + 1 = 968 ways.

968 ways for each, two people, hence, by the Fundamental Counting Theorem, the number of ways is:

968² = 937,024 ways.

In item c, the number of ways is the sum of all the possible toppings, except zero, from the conditions given, hence:

1 + 10 + 45 + 120 + 210 + 252 + 210 + 120 + 45 + 10 + 1 = 1024 ways.

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1) Finding the zeros of this function f(x) =x² +3x -18

f(x) = x²+3x-18 Factoring this equation, and rewriting it

Which two numbers whose sum is equal to 3 and their product is equal to 18?

6 -3 = 3 and 6 *-3 = -18

So we can rewrite as (x +6) (x-3)

(x+6)(x-3)=0 Applying the Zero product rule, to find the roots

x+6=0,

x=-6

x-3=0,

x=3

S={3,-6}

2) Setting a table, plugging in the values of x into the factored form: (x-6)(x-3)

x | y |

1 | -14 (1 +6)(1-3) =-14

2 | -8 (2 +6)(2-3) =-8

3 | 0

4 | 10

-5 | -8

-6 | 0

3) Plotting the function:

A path bounds a circular lawn at a park. if the inner edge of the path is 132 ft. around, Approximate the amount of area of the lawn inside a circular path​ ?

CIRCULAR LAWN

Inner edge Perimeter = 132 feet

2 x pi x r = 132

2 x 22/ 7 x r = 132

r = 132 / ( 2 x 22/ 7 )

r = 132 x 7 / 44

r = 924 / 24

r

8) I

8.2)

hus , the answer is x=121

Answer:

Answer C
This statement is  not true

Step-by-step explanation:

Logarithms result in real values only for positive values of the argument i.e. log(x) results in a real value only for x > 0 So A is correct

Range is set of all real numbers -∞ < x < ∞ So B is correct

D is also correct. At x = 0, log is not defined

Only C is incorrect. If 0 < a < 1 the graph actually shows a downward trend ie logarithmic decline instead of growth

Based on the compound interest rate on the bank account and the number of months that Cameron invested the amount for, the money in his account will be £4,777.81

The amount that will be in the account after 2 years and 7 months can be found by the formula:

= Amount invested x ( 1 + periodic rate) ^ number of periods

The number of months (periods) is:

= 2 years + 7 months

= 31 months

The periodic rate is:

= 5% / 12 months a year

= 5/12%

The amount that Cameron will have in his bank account after 2 years and 7 months will be:

= 4,200 x (1 + 5/12%)³¹

= £4,777.81

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1. a)

Given:

Both numbers are positive.

Aim:

We need to find which one of the two numbers is greater than the other.

Explanation:

On a number line, numbers always increase so numbers to the right are greater than numbers to the left.

Mark the given points on the number line and find which number is right of another. numbers to the right are greater than numbers to the left.

For example.

The positive numbers are 17 and 20.

20 to the right are greater than 17 to the left

20 is greater than 17.

1. b)

Given:

Both numbers are negative.

Aim:

We need to find which one of the two numbers is greater than the other.

Explanation:

On a number line, numbers always increase so numbers to the right are greater than numbers to the left.

If both numbers are negative, the number closer to zero is the bigger number.

For example.

The negative numbers are -10 and -5.

-5 is closer to zero.

-5 is greater than -10.

1, c).

Given:

one number is positive and one number is negative

Aim:

We need to find which one of the two numbers is greater than the other.

Explanation:

On a number line, numbers always increase so numbers to the right are greater than numbers to the left.

The positive numbers are always to the right are greater than the negative numbers to the left.

Positive numbers are greater than negative numbers.

For example.

The positive number is 5 and the negative number is -8.

5 is greater than -8.

Answer: You can tell if a table shows a proportional relationship by calculating the ratio of each pair of values. If those ratios are, all the same, the table shows a proportional relationship.

SOLUTION

We want to find out at which points the lines

intersect.

To do this, we have to solve the equations simultaneously and look for the values of x and y.

This becomes

Dividing both sides by 1.5, we get x, this becomes

To get y, we substitute the x for 8 into equation 1 or 2. Let us use equation 1, we have

The numerical values (numbers) which makes the table show a proportional relationship between x and y are as follows:

x                     y___

2                    0.6

5                    1.5

8                    2.4

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Mathematically, a direct proportion can be represented by the following equation:

y = kx

Where:

Next, we would determine the numerical value of the constant of proportionality (k) as follows:

y = kx

k = y/x

k = 0.6/2

k = 0.3

When y = 1.5, the value of x is given by:

x = y/k

x = 1.5/0.3

x = 5.

When y = 2.4, the value of x is given by:

x = y/k

x = 2.4/0.3

x = 8.

In conclusion, the values of x are 5 and 8 while the value of y is 2.4.

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     A vector space, also known as a linear space, is a set whose elements, frequently termed vectors, can be added to and multiplied ("scaled") by figures known as scalars. Real numbers make up scalars most of the time, but they can also be complex numbers or, more broadly, components of any field.

        Every vector space has a scalar field F at its foundation (to be specified shortly).

Real and complex numbers are two examples of scalar fields.

Real numbers R:

C: Complex numbers.

We only utilize these fields in this context.

Definition : A group of objects in a vector space V have a (vector)

scalar multiplication defined as closed under both addition and multiplication

also satisfying the following axioms:

I For any x V and, F, ( + )x = x + x

(ii) α(βx)=(αβ)x

(iii) For all x, y V, x + y = y + x

(iv) For any x, y, and z > V, x + (y + z)=(x + y) + z.

(v) α(x + y) = αx + αy

(vi) O V z 0 + x = x, where 0 is commonly referred to as the origin

    Since V cannot be left using vector addition or scalar multiplication, the "closed" criterion described above states that for any, F and x, y V x + y V. Additionally, the "+" is in the field when we write for, F and x V ( + )x, but it is in the vector space when we write for x + y for x, y V. This symbol has a variety of uses.

(1) R2 is equal to the two-dimensional space (a1, a2) | a1, a2 R.

(2) In an n-dimensional space, Rn = (a1, a2,..., an) | a1, a2,..., an.

An "n-tuple" is (a1, a2,...,an).

(3) C, the field of complex numbers, to C2 and Cn, respectively, to R2 and Rn.

Pn = l n j = 0 ajxj | a0,

The polynomial space of all polynomials of degree n is denoted as Pn = l n j=0 ajxj | a0, a1,...,an R M. Be aware that this covers polynomials of all degrees, not only those with n degrees exactly.

(5) fp = (ai,...) | ai p, |ai| R. Vectors in the form of infinite-tuples of numbers make up this space. To properly designate the field, we would write fp(R) or fp(C).

Trigonometric polynomials TN = F N n=1 a sin nx | a1,...,an R k are included in the list.

Typical vecs in Rn e1 = (1, 0,... , 0)

e2 = (0, 1, 0,... , 0) (0, 1, 0,... , 0)

e3 = (0, 0, 1, 0,... , 0) (0, 0, 1, 0,... , 0)

.\s.\s.\sen = (0, 0,... , 0, 1) (0, 0,... , 0, 1)

The unit vectors that point in the n orthogonal directions are those.

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a) 620° is an angle coterminal to 360°. The reference angle associated with 260° is 260°.

b) The measure of 260° in radian system equals to 13π / 9 radians.

Two angles are coterminal when they share the same initial and terminal sides. Two consecutive coterminal angles have a difference of 360° (2π radians). Then, we can find any angle of a family of coterminal angles by using this formula:

θ' = θ + i · 360°

Where:

a) If we know that θ = 260° and i = 1, then the measure of an example of coterminal angle is:

θ' = 260° + 1 · 360°

θ' = 620°

620° is an angle coterminal to 360°.

The reference angle is the angle whose measure is equal to or greater than 0° and equal to or less than 360°. Thus, the reference angle associated with 260° is 260°.

b) According to radian system, 2π radians are equal to 360°. Thus, the measure of 260° is found by the following simple rule of three:

x = 260° × 2π / 360°

x = 13π / 9 rad

The measure of 260° in radian system equals to 13π / 9 radians.

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The required probability would be 0.146 that it takes 3 shots for the marksman to hit the long-range target.

The probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

A marksman has a probability of 0.322 for hitting a certain long-range target which is given in the question.

It takes the marksman 3 shots to hit the long-range target = P(E)

Required probability = P(E)

Here no long-range hits in the 1st two shots = (E₁)

And a long-range hit on the 3rd shot = (E₂)

P(E) = P( (E₁) and (E₂))

P(E) = (1 - 0.288) (1-0.288)(0.288)

P(E) = 0.146

Therefore, the required probability would be 0.146 that it takes 3 shots for the marksman to hit the long-range target.

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Answer:

7⁷¹

Step-by-step explanation:

Let's do it this way

7⁴^³ × 7⁷

Let's firstly apply indices since the base is the same

7⁴^³+ (⁷)

(4³ = 4×4×4 can be rewrite)

7⁴×⁴×⁴ + ⁷

7⁶⁴+⁷

= 7⁷¹

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Answer:

Raise 7 to the power of 4

Step-by-step explanation:

2401

The system of inequatilies that is represented in the graph is:

y ≥ –x² – x + 1

y > 2x² + 3

We can confirm this statement since the first equation implies that the system doesn't include any point bellow the parabola y = -x² - x + 1, and the second equation implies that the system must include only points above the parabola y = 2x² + 3

Using the number line to find the coordinate of P that represents the weighted average of the set of points we see that the value of 6 represents the weighted average of the coordinates.

The ordinary arithmetic mean is comparable to a weighted arithmetic mean. The primary difference between the two is that the weighted arithmetic mean takes into account the fact that not all of the data points contribute the same amount to the overall average; rather, some data points contribute more than others.

Generally, the equation for Average weight is mathematically given as

[tex]Av=\frac{ (3 * 2 + 8 * 3)}{(2 + 3)}[/tex]

Consider the quotient in question.

Average weight = 6

As a direct result of this, the value 6 was determined to be the weighted average of the coordinates.

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The radius of the volleyball to the nearest tenth of an inch is 8.3

The formula is

= √ 3v/4π

volume(v) = 288

π = 3.142

= √ 3×288/4×3.142

= √ 864/12.6

Next step is to get the square root of 68.6

= √ 68.6

= 8.29

Hence the radius of the volley ball is 8.3 inches

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The horizontal and vertical axes are the two axes of the coordinate plane.

The origin is the location where these two axes come together. What is the y-coordinate of C' if ABC is mirrored across the z-axis to produce AA'B'C'?

Answer :

(-3,2)

Detailed explanation:

The right response is C (-3,2). The bold line moving up and down in the middle of the page is the y axis. If you could take up the triangle and turn it on its side, you could. In Point C's landing zone (-3,2).

Point C is situated two spaces to the right of the y-axis, as you can also see. The x axis is still three spaces below it.

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Answer:

6 4/6

Explanation:

To sum 2 3/6 and 4 1/6, we first need to convert the mixed numbers to fractions as follows

Now, we can add the numbers as

Finally, when we divide 40 by 6, we get 6 as a quotient and 4 as a remainder, so 40/6 is equivalent to

Therefore, the answer is 6 4/6

The standard deviation for the number of people with the genetic mutation in such groups is 3.1305.

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

Let X be the number of people with genetic mutation is a group of 500,

The formula of standard deviation is given as

[tex]SD=\sqrt{n*p(1-p)} \\SD=\sqrt{500*0.02*0.98} \\SD=3.1305[/tex]

The standard deviation of the given sample is 3.1305

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Answer:   The answer is 18 Girls and 13 Boys. (18 + 13 = 31)

The ratio for girls to boys would 18:13

Step-by-step explanation:  Confirmed correct.

Answer:

43 for the first one

Step-by-step explanation:

108+29=

43

By using the equations of sides and angles and congruence properties, the values of x and y are equal to 34 and 8, respectively. (Correct choice: A)

Herein we find two triangles that are congruent when the share the same sides and angles in magnitudes and distribution. As triangle CDE and triangle LMN are congruent, then we have following relationships:

DE = LN                                          (1)

CE = MN                                         (2)

m ∠ D = m ∠ L                                (3)

m ∠ C = m ∠ M                               (4)

By (1):

2 · y + 1 = 17

2 · y = 16

y = 8

By (2):

MN = 4 · 8 - 3

MN = 29

By (3):

x + 17 = 51

x = 34

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Given:

You have $1000 to invest a year and have an account earning 4% compound continuously.

Required:

How much money will you have at the end of the year.

Explanation:

We know the formula for continuously compound interest is

Here,

We have initial amount $1000, annual interest rate 4% and length of time 1 year

.

Now,

Answer:

So, $1040.81 money will have at the end of the year.

[tex]5x + 5x = - 2 + 9 \\ 10x = 7 \\ \frac{10x}{10} = \frac{7}{10} \\ x = \frac{7}{10} [/tex]

ATTACHED IS THE SOLUTION

⇒The trick here is to find the value of m first using the equation given.

[tex]\frac{m-1}{m} =3\\m-1=m(3)\\m-1=3m\\m-3m=1\\-2m=1\\\frac{-2m}{-2}=\frac{1}{-2} \\m=-\frac{1}{2}[/tex]

⇒Note I used cross multiplication to solve for  m

Now to find what [tex]\frac{m^{3} -1}{m^{3} }[/tex] substitute the value of m in the expression and simplify.

[tex]=\frac{(-\frac{1}{2}) ^{3} -1}{(-\frac{1}{2} )^{3} } \\\\=\frac{-\frac{1}{8}-1 }{-\frac{1}{8} } \\=\frac{-\frac{9}{8} }{-\frac{1}{8} } \\=9[/tex]

⇒The value is 9

Goodluck!!

Answer:

Step-by-step explanation:

We are asked to graph an inequality . y≥2x - 3

The boundary line of our given inequality will be a solid line as we have greater than or equal to ≥ sign.

The boundary line of our given inequality would be .y=2x - 3

Now, we will test point (0,0) to shade in the correct region as:

0≥2(0)-3

0≥0-3

0≥-3

It should look something like this: