Write and solve the system of equations
7. Bustin' BBQ Pit sells sausage and brisket by the pound. Rusty orders 2 pounds of sausage and
3 pounds of brisket for his family and pays $21. Marta
orders 10 pounds of sausage and 14
pounds of brisket and pays $100.50. Find the cost per pound of the sausage, s, and brisket,b

A fifth-degree polynomial with three terms in standard form would be written as a\(x^{2}\) + b\(x^{4}\)+ c\(x^{3}\). The closure property states that a set is closed under a certain operation if performing that operation on any two elements of the set produces a result that is also an element of the set.

Part A: A fifth-degree polynomial with three terms in standard form would be written as a\(x^{2}\) + b\(x^{4}\)+ c\(x^{3}\). The coefficient of the highest degree term (x^5) must be non-zero and all the terms must be written in descending order of the degree. This is the definition of standard form for polynomials.

Part B: The closure property states that a set is closed under a certain operation if performing that operation on any two elements of the set produces a result that is also an element of the set. In this case, the set is polynomials and the operation is subtraction. An example of this property can be seen by subtracting two polynomials, such as 4\(x^{2}\) + 3x - 5 and \(x^{2}\) + 2. The result of this subtraction would be 3\(x^{2}\) + 3x - 5, which is also a polynomial and therefore an element of the set, demonstrating the closure property.

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A fifth-degree polynomial with three terms in standard form would be written as a\(x^{2}\) + b\(y^{2}\)+ c. The closure property states that a set is closed under a certain operation if performing that operation on any two elements of the set produces a result that is also an element of the set.

Part A: A fifth-degree polynomial with three terms in standard form would be written as a\(x^{2}\) + b\(y^{2}\)+ c. The coefficient of the highest degree term (\(x^{5}\)) must be non-zero and all the terms must be written in descending order of the degree. This is the definition of standard form for polynomials.

Part B: The closure property states that a set is closed under a certain operation if performing that operation on any two elements of the set produces a result that is also an element of the set. In this case, the set is polynomials and the operation is subtraction. An example of this property can be seen by subtracting two polynomials, such as 4\(x^{2}\) + 3x - 5 and  + 2. The result of this subtraction would be 3\(x^{2}\) + 3x - 5, which is also a polynomial and therefore an element of the set, demonstrating the closure property.

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Answer:

7/8

Step-by-step explanation:

7/5•5/8= 7•5/5•8

= 35/40

=7/8

hope this helps chu

If a polynomial function has integer coefficients, the every rational zero of the function has the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The rational zero theorem says that if a polynomial has integer coefficients then any rational zeros must be of the form p/q where p is the factor of the constant term and q is the factor pf the leading coefficients.

The rational zero theorem is used to determine the rational roots of a polynomial function.

Rational Zero Theorem statement:-

The rational zero theorem states that each rational zero(s) of a polynomial wit integer coefficients

f(x) = anxⁿ + an-1xⁿ⁻¹ + ... + a₂x² + a₁x + a₀ is of the form p/q where,

p is a factor of the constant a₀,

q  is a factor of the leading coefficient an,

and p and q are relatively prime.

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Since the total of the inner angles of the rhombus is 360 degrees, the angle mV has a value of 90.

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that come together at a point in the middle known as the angle's vertex. An angle that is in the plane where the rays are placed can be created by two rays. An angle is also produced when two planes collide. They are known as dihedral angles. In planar geometry, an angle is the form produced by two rays or lines that share a termination. The English word "angle" comes from the Latin word "angulus," which means "horn." The vertex, also known as the sides of the angle, is where the two rays' common terminals meet.

given

m∠V + m∠W + m∠X + m∠Y = 360

10x -27 + 2x + 19 = 180

12x - 8 = 180

188 = 12x

x = 15.66

m∠V + m∠X = 180

2x = 180

x = 90

Since the total of the inner angles of the rhombus is 360 degrees, the angle mV has a value of 90.

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Answer:

\(\sf 1. \quad \dfrac{3}{8}\)

\(\sf 2. \quad \dfrac{7}{24}\)

Step-by-step explanation:

Spinner 1 is divided into 6 congruent sections.

There are 3 red sections, 2 blue sections and 1 yellow section.

Therefore, the probability of spinning each of the three colors is:

    \(\bullet \quad \sf P(R_1)=\dfrac{3}{6}=\dfrac{1}{2}\)

    \(\bullet \quad \sf P(B_1)=\dfrac{2}{6}=\dfrac{1}{3}\)

    \(\bullet \quad \sf P(Y_1)=\dfrac{1}{6}\)

Spinner 2 is divided into 3 sections of differing sizes.

The red section is half of the spinner. The blue and yellow sections are quarters of the spinner.

Therefore, the probability of spinning each of the three colors is:

    \(\bullet \quad \sf P(R_2)=\dfrac{1}{2}\)

    \(\bullet \quad \sf P(B_2)=\dfrac{1}{4}\)

    \(\bullet \quad \sf P(Y_2)=\dfrac{1}{4}\)

If each spinner is spun once, then:

The probability that both spinners both show red is:

\(\sf P(R_1)\;and\;P(R_2)=\dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{4}\)

The probability that both spinners both show blue is:

\(\sf P(B_1)\;and\;P(B_2)=\dfrac{1}{3} \times \dfrac{1}{4}=\dfrac{1}{12}\)

The probability that both spinners both show yellow is:

\(\sf P(Y_1)\;and\;P(Y_2)=\dfrac{1}{6} \times \dfrac{1}{4}=\dfrac{1}{24}\)

Therefore, the probability that both spinners show the same colour is:

\(\sf P(R_1\;\&\;R_2)\;or\;P(B_1\;\&\;B_2)\;or\;P(Y_1\;\&\;Y_2)=\dfrac{1}{4}+\dfrac{1}{12}+\dfrac{1}{24}=\dfrac{9}{24}=\dfrac{3}{8}\)

If each spinner is spun once, the probability of getting a red from spinner 1 and a blue from spinner 2 is:

\(\sf P(R_1)\;and\;P(B_2)=\dfrac{1}{2} \times \dfrac{1}{4}=\dfrac{1}{8}\)

The probability of getting a blue from spinner 1 and a red from spinner 2 is:

\(\sf P(B_1)\;and\;P(R_2)=\dfrac{1}{3} \times \dfrac{1}{2}=\dfrac{1}{6}\)

Therefore, the probability of getting a red-blue combination is:

\(\sf P(R_1\;\&\;B_2)\;or\;P(B_1\;\&\;R_2)=\dfrac{1}{8}+\dfrac{1}{6}=\dfrac{7}{24}\)

answer: A survey

explanation: The manager of the restaurant is conducting a survey to determine which sandwich is more preferred by customers. He is taking a random sample of customers that have tried both sandwiches and asking them which sandwich they like best. The survey method is a statistical way of collecting data and it is a non-experimental design, because the manager is not controlling the variables that may affect the outcome. The outcome of this survey is based on the customers' preference of the sandwiches, and it is a way to gather data on their opinion

On solving the provided question, we can say that from the graphs The curve preceding technolοgical advancement is called PPF0. PPF1 is the curve following technological advancement.

Mathematicians use graphs to logically convey facts or values using visual representations οr charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue tοgether the nodes, οften referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of expοnential growth. a logarithmic graph in the shape οf a triangle

The curve preceding technolοgical advancement is called PPF0. PPF1 is the curve following technοlogical advancement.

Priοr to technological advancement, the opportunity cost of treating HIV/AIDS rises as the wοrld deviates from its PPF. The pοtential cost of treating more HIV/AIDS cases falls as a result of technοlogical advancements since less other commοdities and services must be sacrificed in οrder to treat more HIV/AIDS patients. Alternatively, the world might treat mοre HIV/AIDS patients right now by forgoing the same number of other commοdities and services.

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Answer:

\(Q(-2,3) \longrightarrow Q'(-1/3, 1/2) \\ \\ R(-3,1) \longrightarrow R'(-1/2, 1/6) \\ \\ T(2,-1) \longrightarrow T'(1/3, -1/6) \\ \\ W(2,4) \longrightarrow W'(1/3, 2/3)\)

Step-by-step explanation:

For a dilation at the origin, multiply each of the coordinates by the scale factor.

\(Q(-2,3) \longrightarrow Q'(-1/3, 1/2) \\ \\ R(-3,1) \longrightarrow R'(-1/2, 1/6) \\ \\ T(2,-1) \longrightarrow T'(1/3, -1/6) \\ \\ W(2,4) \longrightarrow W'(1/3, 2/3)\)

Answer:

The big container holds 30 gallons and the small container holds 20 gallons

Step-by-step explanation:

Let

The big container = x

Small container = y

The big container can hold 10 gallons less than twice the small

x = 2y - 10

Total gasoline in both containers = 50 gallons

x + y = 50

Substitute x = 2y - 10 into the equation

2y - 10 + y = 50

3y = 50 + 10

3y = 60

Divide both sides by 3

y = 60 / 3

= 20

y = 20 gallons

Recall,

x + y = 50

x + 20 = 50

x = 50 - 20

= 30

x = 30 gallons

The big container holds 30 gallons and the small container holds 20 gallons

Answer:

The big container has 30 gallons and the small container has 20 gallons.

Step-by-step explanation:

So, the height of the pedestal is ((h1−h2)tanβ+h2tanα)/tanα−tanβ.

To find the height of the pedestal, we can use the concept of angles of elevation. The angle of elevation is the angle between the horizontal line of sight and the line of sight to an object above the horizontal.

From the given information, we know that the angles of elevation of the top and bottom of the statue from a point h2 metres above the ground level are α and β respectively.

We can use the tangent of the angle of elevation to find the height of the object. The tangent of the angle of elevation is equal to the height of the object divided by the distance from the base of the object to the point of observation.

Let's call the height of the pedestal as "h3"

So we can write the following equations:

h1/((h3+h1)-h2)= tan(α)

h1/((h3)-h2)= tan(β)

By solving the above equations we can get the value of h3 which is the height of the pedestal.

((h1−h2)tanβ+h2tanα)/tanα−tanβ

This is the final equation which gives the height of the pedestal.

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Answer:

The answer is B because it's correct you guessed it right

Step-by-step explanation:

Answer:

Unpredictable

Step-by-step explanation:

Cuz if u look at it it is also random and u cant predict a random thing, so its quite simply unpredictable

Answer:

yes

Step-by-step explanation:

they are congruent

Answer:

the answer is 100

Step-by-step explanation:

as it is told to round the factors to nearest whole no. 19.8 will be 20 and 5 will remain same... 20*5 is 100

Answer:

c) 44

Step-by-step explanation:

Answer:

the first 3 is 30 the second is 3/10

Step-by-step explanation:

                                               Question 1)

Given the function

f(x) = 2|x+10| - 6

You need to remember that:

f(x) = y

f(0) means we need to determine the value of y at x = 0.

so substitute x = 0 in the function

\(f\left(x\right)\:=\:2|x+10|\:-\:6\)

\(f\left(0\right)\:=\:2|0+10|\:-\:6\)

         \(=2\left|10\right|-6\)

Apply absolute value:    \(\left|a\right|=a,\:a\ge 0\)

         \(=2\cdot \:10\)

         \(=20\)

Thus,

\(f\left(0\right)\:=\:20\)

                                               Question 2)

Given the fuction

g(x) = x+1

substitute g(x) = 20 in the function

20 = x+1

x = 20-1

x = 19

Thus,

x = 0

                                                  Question 3)

Given the function

f(x)=2|x+10|-6

substitute x = 1 in the function

f(1)=2|1+10|-6

f(1)=2|1+10|-6

f(1) = 2|11| - 6

Apply absolute value:    \(\left|a\right|=a,\:a\ge 0\)

f(1) = 2(11) - 6

f(1) = 22 - 6

f(1) = 16

Given the function

g(x)=x+1

substitute x = 0 in the function

g(0) = 0+1

g(0) = 1

Thus,

g(0)+f(1) = 16+1

             = 17

The equivalent fraction for \(\frac{11}{12}\) and \(\frac{17}{18}\) is \(\frac{22}{24}\) and \(\frac{34}{36}\) respectively.

There are two or more fractions that are equivalent even if their numerators and denominators are different. For instance, 1/2 is the same as (or equal to) 25/50 or 500/1000. Every time, the fraction is written as "one half" in its simplest form.

The equivalent fraction for \(\frac{11}{12}\) is -

\(\frac{11}{12}\) × \(\frac{2}{2}\) =\(\frac{22}{24}\)

The equivalent fraction for 17/18 is -

\(\frac{17}{18}\) × \(\frac{2}{2}\) = \(\frac{34}{36}\)

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The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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we have shown that there exists a countable collection of numbers {fp(x) : x ∈ X} ⊆ [0,1] such that μ(E) = Σfp(x) for any E ⊆ X, which completes the proof as shown below

Let (X, P(X)) be a countable set with the sigma-algebra P(X), and let μ be any measure on (X, P(X)). We want to prove that there exists a countable collection of numbers {fp(x) : x ∈ X} ⊆ [0,1] such that μ(E) = Σfp(x) for any E ⊆ X.

To prove this, we first consider the case where μ(X) < ∞. In this case, we define fp(x) = μ({x})/μ(X) for each x ∈ X. Since X is countable, we can express it as the countable union of singletons X = ⋃{x_n : n ∈ ℕ}, and thus we have:

μ(E) = μ(⋃{x_n : n ∈ ℕ} ∩ E) = Σμ({x_n} ∩ E) = Σfp(x_n)μ(X) = Σfp(x_n)

for any E ⊆ X, where the third equality follows from countable additivity of μ.

For the case where μ(X) = ∞, we can partition X into countably many disjoint sets of finite measure by taking E_n = {x ∈ X : 1/n ≤ μ({x}) < 1/(n-1)}, and defining fp(x) = Σn fp(x)1{x ∈ E_n} for each x ∈ X. Then, by countable additivity of μ, we have:

μ(E) = Σμ(E ∩ E_n) = ΣΣfp(x)1{x ∈ E_n}μ(X) = Σfp(x)

for any E ⊆ X, where the second equality follows from countable additivity of μ.

Thus, we have shown that there exists a countable collection of numbers {fp(x) : x ∈ X} ⊆ [0,1] such that μ(E) = Σfp(x) for any E ⊆ X, which completes the proof.

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The length of the rectangular garden given the area and width is 8/7 miles

A rectangle is a form of quadrilateral having opposing sides parallel and four right angles. The area of a rectangle can be calculated by multiplying the length by width.

Area of a rectangular garden = length × width

16 = x × 14

16 = 14x

x = 16 / 14

x = 8/7 miles

Therefore, the length of the rectangular garden given the area and width is 8/7 miles.

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The number of pennies weighing as much s earth is  193 × 10²⁴

Index forms are described as described as those forms that are used to represent numbers that are too large or small in more proper ways.

Other names for index forms are scientific notation and standard forms.

Ratio is described as the comparison of numbers or variables on the basis of their size.

It shows how many times one number contains another.

From the information given, we have that;

The earth weighs = 5. 972 × 10 ²⁴ kilograms

The penny weighs = 3.1 × 10 ⁻³ kilograms

Divide the values

= 5. 972 × 10 ²⁴/3.1 × 10 ⁻³

= 1.93 × 10 ²⁶

= 193 × 10²⁴

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Answer:

The answer is A=2/9 yards²

Step-by-step explanation:

The formula for a rectangle  is A=B x H  

So the equation is A= 1/3 yards x 2/3 yards  

I suppose this is right.

Answer:

3/10

Step-by-step explanation:

4+6+10

=20

6/20

=3/10

Answer:

$880

Step-by-step explanation:

Use the equation:

\(P=(1-d)x\) with d being the discount in a decimal form, and P being the price that was bought at.

220=(1-0.75)x

simplify parenthesis terms

220=0.25x

divide both sides by 0.25

880=x

So, the original price was $880.

Hope this helps! :)

Answer:

90°

Step-by-step explanation:

they are forming a right angle (90°).

Answer:

805 x 4 = 3,220

3,220 / 4 = 805

Step-by-step explanation:

Its the same thing but backwards!

Stay Safe!

Answer:

The 95% confidence interval is  \( 9.15<  \mu < 11.45 \)

Step-by-step explanation:

From the question we are told that

     The sample size is  n =  26

      The mean is  \(\= x = 10.3\)

       The standard deviation is  \(s = 3\)

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the margin of error is mathematically represented as  

      \(E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }\)

=>   \(E =  1.96 *  \frac{3}{\sqrt{26} }\)

=>   \(E = 1.1532 \)

Generally 95% confidence interval is mathematically represented as  

      \(\= x -E <  \mu <  \=x  +E\)

=>   \(10.3  -1.1532 <  \mu < 10.3  +  1.1532 \)

=>    \( 9.15<  \mu < 11.45 \)