Solve for x and y:3x + 7y= 2212x + 28y = 88Select one:a. There is no solution.b.x = 5, y = 1c. The solution is (0,0).d. There are an infinite number of solutions.

Answer:

6x² + 19x + 15

Step-by-step explanation:

2x(3x+5)+3(3x+5)

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

= 6x² + 9x + 10x + 15

= 6x² + 19x + 15

So, the answer is 6x² + 19x + 15

We can start by simplifying the left side of the equation using the distributive property:

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

= 6x^2 + 10x + 9x + 15

= 6x^2 + 19x + 15

Now we can compare this expression with the right side of the equation, which is a polynomial in x with unknown coefficients a, b, and c:

ax^2 + bx + c

Since the two sides are equal, their corresponding coefficients must be equal as well. This gives us a system of three equations in three unknowns:

a = 6 (the coefficient of x^2)

b = 19 (the coefficient of x)

c = 15 (the constant term)

Therefore, the solution to the equation 2x(3x+5)+3(3x+5)=ax^2+bx+c is:

2x(3x+5)+3(3x+5) = 6x^2 + 19x + 15

The total number of sides of a regular polygon with each exterior angle of measure 30 degrees is equal to 12.

Let us consider 'n' be the number of sides of the regular polygon.

Let 'y' be the measure of each of the exterior angle of regular polygon.

y = 30 degrees

Measure of each of the exterior angle of regular polygon 'y'

= ( 360° ) / n

⇒ n = ( 360° / y )

Substitute the value we get,

⇒ n = ( 360° / 30° )

⇒ n = 12

Therefore, the number of sides of a regular polygon with each of the exterior angle 30 degrees is equal to 12.

Learn more about regular polygon here

brainly.com/question/12092158

#SPJ4

The above question is incomplete, the complete question is:

How many sides does a regular polygon have when each exterior angle measures 30 degrees?

Based on the context, the range of this function is given by: C. [−7, 7]

A range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values, which are shown on the y-axis of a graph.

The vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of function f(x) shown, we can infer and logically deduce the following:

Range = [−7, 7]

Read more on range here: brainly.com/question/17295757

#SPJ1

Answer:

Number of $ 8 priced tickets = 210

Number of $10 priced tickets = 140

Number of $ 12 priced tickets = 70

Step-by-step explanation:

Framing and solving equations with three variables:

Let the number of $ 8 priced tickets = x

Let the number of $10 priced tickets = y

Let the number of $ 12 priced tickets = z

  Total number of tickets = 420

                 x +  y + z = 420           --------------(i)

         Total income = $ 3920

        8x + 10y + 12z = 3920      ----------------(ii)

Combined number of $8 and $10 priced tickets= 5 * the number of $12 priced tickets

                      x + y  = 5z

                x + y - 5z = 0         -------------------(iii)

(i)        x + y + z = 420

(iii)      x + y - 5z = 0

       -     -     +      +   {Subtract (iii) from (i)}

                    6z = 420

                      z = 420÷ 6

                     \(\sf \boxed{\bf z = 70}\)

(ii)            8x + 10y + 12z = 3920

(iii)*8       8x + 8y - 40z   = 0  

             -       -     +            -           {Now subtract}

                     2y  + 52z = 3920   -----------------(iv)

Substitute z = 70 in the above equation and we will get the value of 'y',

                 2y + 52*70 = 3920

                2y + 3640   = 3920

                               2y = 3920 - 3640

                               2y = 280

                                 y = 280 ÷ 2

                                 \(\sf \boxed{\bf y = 140}\)

substitute z = 70 & y = 140 in equation (i) and we can get the value of 'x',

         x +  140 + 70 = 420

                  x + 210 = 420

                          x  = 420 - 210

                          \(\sf \boxed{x = 210}\)

Number of $ 8 priced tickets = 210

Number of $10 priced tickets = 140

Number of $ 12 priced tickets = 70

Answer:

hope you understand the answer please mark brainlist

Answer:

Step-by-step explanation:

y = (2x^2-2x+3x-3)(x-4)

y = (2x^2+x-3)(x-4)

y = 2x^3+x^2-3x-8x^2-4x+12

y = 2x^3-7x^2-7x+ 12

a : 2x^3

b : 2

c : 3

d

lim x-> +oo x^3(2-7/x-7/x^2 + 12/x^3)

lim x-> +oo  +oo(2-7/oo - 7/oo + 12/oo)

lim x->+oo   +oo(2-0-0+0)

lim x->+oo    +oo

lim x-> -oo x^3(2-7/x-7/x^2 + 12/x^3)

lim x-> -oo  -oo(2-7/-oo - 7/-oo + 12/-oo)

lim x-> -oo   -oo(2-0-0+0)

lim x-> -oo    -oo

e

y = 2x^3-7x^2-7x+ 12

y’ = [2(x+h)^3 - 7(x+h)^2 - 7(x+h) + 12 - 2x^3 +7x^2 + 7x - 12]/h

y’ = [2(x^3+h^3+3x^2h+3h^2x) -7(x^2+h^2+2xh)-7x-7h-2x^3+7x^2+7x]/h

y’ = [2x^3+2h^3+6x^2h+6h^2x-7x^2-7h^2-14xh-7h-2x^3+7x^2]/h

y’ = [2h^3+6x^2h+6h^2x-7h^2-14xh-7h]/h

y’ = h (2h^2 + 6x^2 + 6hx - 7h - 14x - 7)/h

y’ = 2h^2 + 6x^2 + 6hx - 7h - 14x - 7

lim h->0  (6x^2 - 14x - 7)

y’ = 6x^2 - 14x - 7

y’’ = [6(x+h)^2 - 14(x+h) - 7 - 6x^2 + 14x + 7]/h

y’’ = [6(x^2+h^2+2xh) -14x-14h -6x^2+14x]/h

y’’ = [6x^2+6h^2+12xh-14h-6x^2]/h

y” = h(6h+12x-14)/h

y” = 6h + 12x - 14

lim h->0 (12x-14)

y” = 12x -14

12x - 14 = 0

6x - 7 = 0

x = 7/6

(2 *7/6+3)(7/6-1)(7/6-4)

(7/3 + 3) ( 1/6) (-17/6)

(16/3)(-17/36)

4/3 * -17/9

-68/27

turning point (7/6 ; -68/27)

f

(2x + 3)(x - 1)(x - 4) = 0

x = -3/2

x = 1

x = 4

A( -3/2,0)

B (1,0)

C (4,0)

g

y= 12

D (0, 12)

Answer:

a.  2x³

b.  2

c.  3

d.  As x → -∞, f(x) → -∞.   As x → ∞, f(x) → ∞.

e.  (-0.4, 13.6) and (2.8, -18.6).

f.  (-1.5, 0),  (1, 0),  (4, 0)

g.  (0, 12)

h.  See attachment.

Step-by-step explanation:

Given polynomial:

\(y=(2x+3)(x-1)(x-4)\)

Leading term and Leading coefficient

The given polynomial is in factored form.

To find the leading term and the leading coefficient, simply multiply the variable terms of the factors:

\(\implies 2x \cdot x \cdot x = 2x^3\)

Therefore:

Degree of the polynomial

The degree of the polynomial is the exponent of the leading term.

Therefore, the degree of the given polynomial is 3.

End behaviour

As the degree of the polynomial is odd and the leading coefficient is positive, the end behaviour of the function is:

Turning points

The x-values of the turning points are when the derivative of the function equals zero.

Expand the polynomial:

\(\implies y=(2x+3)(x-1)(x-4)\)

\(\implies y=(2x+3)(x^2-5x+4)\)

\(\implies y=2x^3-10x^2+8x+3x^2-15x+12\)

\(\implies y=2x^3-7x^2-7x+12\)

Differentiate:

\(\implies \dfrac{\text{d}y}{\text{d}x}=6x^2-14x-7\)

Set it to zero and solve for x:

\(\implies 6x^2-14x-7=0\)

Solve using the quadratic formula:

\(\implies x=\dfrac{-(-14) \pm \sqrt{(-14)^2-4(6)(-7)}}{2(6)}\)

\(\implies x=\dfrac{14 \pm \sqrt{364}}{12}\)

\(\implies x=\dfrac{14 \pm 2\sqrt{91}}{12}\)

\(\implies x=\dfrac{7\pm \sqrt{91}}{6}\)

\(\implies x \approx-0.4, \;2.8\; \; \sf (1\;d.p.)\)

Substitute the found values of x into the original polynomial to find the y-values of the turning points:

\(x=\dfrac{7- \sqrt{91}}{6}\implies y=13.6\; \; \sf (1\;d.p.)\)

\(x=\dfrac{7+ \sqrt{91}}{6}\implies y=-18.6\; \; \sf (1\;d.p.)\)

Therefore, the turning points of the polynomial (to the nearest tenth) are:

x-intercepts

The x-intercepts are when the function equals zero.

As the function is already in factored form, simply equal each of the factors to zero and solve for x:

\(\implies (2x+3)=0 \implies x=-1.5\)

\(\implies (x-1)=0 \implies x=1\)

\(\implies (x-4)=0 \implies x=4\)

Therefore, the x-intercepts are:

y-intercept

The y-intercept when x = 0:

\(\implies y=(2(0)+3)(0-1)(0-4)\)

\(\implies y=3 \cdot -1 \cdot -4\)

\(\implies y=12\)

Therefore, the y-intercept is:

Sketch the graph

To sketch the graph:

The true statement about RR and AR measure is that all of the given options (A, B, C, and D) are accurate. Therefore, the correct answer is E, "NONE of the above."

A. Relative Risk (RR) is indeed a useful measure in etiologic studies of disease. It quantifies the association between a specific exposure and the risk of developing a particular disease or condition. By comparing the risk of disease between exposed and unexposed individuals, researchers can assess the strength of the relationship.

B. Attribute Risk (AR) is a measure of the proportion of disease risk that can be attributed to a specific exposure. It indicates the excess risk of disease associated with the exposure. AR is valuable in understanding the impact of a particular factor on the occurrence of a disease and can aid in making informed decisions regarding prevention and control strategies.

C. Attributable Risk (AR) has significant applications in clinical practice and public health. It helps identify modifiable risk factors and guides interventions to reduce the burden of disease. AR estimates can be used to allocate resources effectively, implement targeted prevention programs, and develop public health policies.

D. Relative Risk (RR) does indicate the strength of association between disease and exposure. It compares the risk of disease in exposed individuals to the risk in unexposed individuals. The magnitude of RR reflects the degree of association, with higher values indicating a stronger relationship between the exposure and the disease outcome.

Since all of the statements provided in the options (A, B, C, and D) are true, the correct answer is E, "NONE of the above."

Learn more about Measure:

brainly.com/question/28913275

#SPJ11

An obtuse triangle and right angle triangle can always be used as counter examples to the given statement.

What is acute angle?

An angle which is measuring less than 90 degrees is called an acute angle. This angle is smaller than the right angle

What is obtuse angle?

An obtuse angle is a type of angle that is always larger than 90° but less than 180°. In other words, it lies between 90° and 180°.

What is right angle?

A right angle is an angle of exactly 90 degrees or \pi /2 radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles..

Hence, an obtuse triangle and right angle triangle can always be used as counterexamples to the given statement " All angles in a triangle are acute".

To learn more about triangles, visit:

brainly.com/question/2773823

#SPJ4

Based on the ratings system and the summarize() and mean() functions, the code chunk to add is summarize(mean(Rating)) and the mean rating is 3.185933.

To find the mean rating, the complete code should be trimmed_flavors_df %>% summarize(mean(Rating)).

This code would allow you to see the mean rating of your data by combining the summarize() and mean() functions such that you can display summary statistics.

Because of the "mean()" function, the statistic that will be displayed is the mean rating which in this case would be 3.185933.

Find out more on code chunks at https://brainly.com/question/28209816

#SPJ1

The probability of guessing the correct answer for each question is 1/4, while the probability of guessing incorrectly is 3/4.

To calculate the probability of answering at most one correct answer, we need to consider two cases: answering zero correct answers and answering one correct answer.

For the case of answering zero correct answers, the probability can be calculated as (3/4)^5, as there are five independent attempts to answer incorrectly.

For the case of answering one correct answer, we have to consider the probability of guessing the correct answer on one question and incorrectly guessing the rest. Since there are five questions, the probability for this case is 5 * (1/4) * (3/4)^4.

To obtain the probability of answering at most one correct answer, we sum up the probabilities of the two cases:

Probability = (3/4)^5 + 5 * (1/4) * (3/4)^4.

Therefore, by calculating this expression, you can determine the probability of answering at most one correct answer among five questions when guessing randomly.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

Answer: \(270\ in.^3\)

Step-by-step explanation:

Given

Volume of a gas varies inversely with pressure i.e.

\(V\propto \dfrac{1}{P}\\\\PV=\text{constant}\)

Initially, \(V_1=450\ in.^3,P_1=3\ psi\)

Then, pressure increases to \(P_2=5\ psi\)

\(\therefore P_1V_1=P_2V_2\\\Rightarrow 3\times 450=5\times V_2\\\Rightarrow V_2=3\times 90\\\Rightarrow V_2=270\ in.^3\)

Thus, volume decreases to \(270\ in.^3\).

Answer:

a + b = 5.30

a + b = 7

No

Step-by-step explanation:

Expressing the information as system of linear equation :

Let apples = a, oranges = b

If $5.30 is charged for one apple and one orange, then we have ;

a + b = 5.30 - - - (1)

If $14 is charged for 2 apples and 2 oranges, then we have ;

2a + 2b = 14 - - - - (2)

a + b = 7

Since both equations gives varying combined cost for equal amount of the fruit, then a unique cost cannot be obtained for each fruit from the systems of equation using simultaneous equation process.

From (1)

a = 5.30 - b

Put a = 5.30 - b in (2)

2(5.30 - b) + 2b = 14

10.6 - 2b + 2b = 14

10.6 = 14 - - - - - (variables cancels out).

Answer:No the System has no solution

Step-by-step explanation:

Answer:

B. Make a table of equal ratios to find how long it takes each printer to print 120 photos and find the difference would be an appropriate process to determine how much longer it will take Khalil's printer to print 120 photos than Alex's.

Step-by-step explanation:

To use this process, we can set up a table showing the ratio of photos printed to time taken for each printer. Then we can use these ratios to find how long it would take each printer to print 120 photos, and find the difference between the two times to determine how much longer it would take Khalil's printer.

Area of the given shape = Area( Triangle + Square + Rectangle)

Area of Triangle = 1/2 x base x height

= 1/2 x (7-2) x (9-5)

= 1/2 x 5 x 4

= 10

Area of square = side × side

= (7-2) x ( 9-4)

= 5 x 5

= 25

Area of rectangle= base x height

= 2 x 5

= 10

Therefore , the area of given shape = 10+25+10 = 45

there are 6 different ways can Audrey put all 3 flowers into 2 vases so that each vase has at least one flower.

A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

Given, Audrey has 3 different flowers and 2 different vases.

First, we can choose which two flowers will go into the first vase. We can do this by selecting 2 out of the 3 flowers, which can be done in C(3,2) = 3 ways:

{flower 1, flower 2}, {flower 3}

{flower 1, flower 3}, {flower 2}

{flower 2, flower 3}, {flower 1}

Once we have chosen the flowers for the first vase, the remaining flower must go into the second vase. So there is only one way to assign the remaining flower to the second vase.

Therefore, there are 3 ways to choose the flowers for the first vase, and 1 way to assign the remaining flower to the second vase, giving us a total of 3 x 2 = 6 different ways to put all 3 flowers into 2 vases so that each vase has at least one flower.

Learn more about Permutation and combination here:

https://brainly.com/question/15268220

#SPJ1

The logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

The exponential function in this problem is defined as follows:

8e^x-5 = 0.

The equation can be sorted isolating the exponential as follows:

8e^x = 5.

e^x = 5/8.

The natural logarithm(symbolized by the ln) is the opposite of the exponential function, hence the logarithmic form of the equation is presented as follows:

ln(e^x) = ln(5/8).

As stated above, the natural logarithm and the exponential functions are inverse functions, meaning that:

ln(e^x) = x.

Thus the logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

More can be learned about exponential functions and logarithms at https://brainly.com/question/25537936

#SPJ1

Answer:

Its either A or D

Step-by-step explanation:

8% simple interest of 800 once is 64 dollars. I am not sure if it is 8% every year. If it is every year then the interest is 320 dollars. Good Luck.

Brainliest Please

Happy holidays

Answer:

you didnt put a question

Step-by-step explanation:

It is requred to test the exactness of the given ODE and then find its general solution. Then, if the given ODE is not exact, an integrating factor must be used to make it exact.

This given ODE is:(2xy - 2y²e^(3x))dx + (x² - 2ye^(2x))dy = 0.To verify the exactness of the given ODE, we determine whether or not ∂Q/∂x = ∂P/∂y, where P and Q are the coefficients of dx and dy respectively, as follows: P = 2xy - 2y²e^(3x) and Q = x² - 2ye^(2x).Then, we have ∂P/∂y = 2x - 4ye^(3x) and ∂Q/∂x = 2x - 4ye^(2x).Thus, since ∂Q/∂x = ∂P/∂y, the given ODE is exact.To solve the given ODE, we have to find a function F(x,y) that satisfies the equation Mdx + Ndy = 0, where M and N are the coefficients of dx and dy respectively. This is accomplished by integrating both P and Q with respect to their respective variables. We have:∫Pdx = ∫(2xy - 2y²e^(3x))dx = x²y - y²e^(3x) + g(y), where g(y) is a function of y. We differentiate both sides of this equation with respect to y, set it equal to Q, and then solve for g(y). We have:(d/dy)(x²y - y²e^(3x) + g(y)) = x² - 2ye^(2x)Thus, g'(y) = 0 and g(y) = C, where C is a constant.Substituting the value of g(y) in the equation above, we get:x²y - y²e^(3x) + C = 0, as the general solution.The given ODE is exact, so we can solve it by finding a function that satisfies the equation Mdx + Ndy = 0. After integrating both P and Q with respect to their respective variables, we find that the general solution of the given ODE is x²y - y²e^(3x) + C = 0.

To know more about integrating factor visit:

brainly.com/question/32554742

#SPJ11

Answer:

B. \(a^3b\)

Step-by-step explanation:

Exponent Rule: \((b^m)^n = b^{mn}\)

Exponent Rule: \(\frac{b^m}{b^n} =b^{m-n}\)

Step 1: Write expression

\(\frac{(ab^2)^3}{b^5}\)

Step 2: Exponent Exponents

\(\frac{a^3b^6}{b^5}\)

Step 3: Simplify

\(a^3b\)

Answer:

b = 107

c = 73

Step-by-step explanation:

107° and angle b are opposite side. Therefore, both angles must have same value.

Therefore, b = 107

107° and angle c are supplementary. That means both angles add up to 180°.

107°+c=180°

c = 180°-107°

c = 73°

Therefore, c = 73

The experimental and theoretical probability for each result are:

                                    Theoretical  Experimental

P(5)                                      1/6              7/40

P( 1 or 6)                               1/3              7/20

P(no more than 4)                2/3             21/40

P(greater than 2)                  2/3                7/10

Probability determines the chances that an event would happen. Experimental probability is the probability of an event happening based on the result of an experiment that has been carried out multiples time.

Theoretical probabilities:

P(5) = number of sides with 5 / total number of sides = 1/6

P( 1 or 6)  = number of sides with 1 / total number of sides + number of sides with 6 / total number of sides  = 1/6 + 1/6 = 1/3                  

P(no more than 4)   = number of sides that is no more than 4 / total number of sides  = 4/6 = 2/3

P(greater than 2) = number of sides greater tha 2 / total number of sides   = 4/6 = 2/3      

Experimental probabilities:

P(5) =  number of times there was a result of 5 / total number of times the die was rolled = 7/40

P( 1 or 6) = (number of times there was a result of 1 / total number of times the die was rolled) + (number of times there was a result of 6 / total number of times the die was rolled )

2/40 + 12/40 = 14/40 = 7/20    

P(no more than 4) = sum of results no more than 4 / total number of times the die was rolled = ( 2 + 10 + 5 + 4) = 21/40

P(greater than 2) = sum of results greater than 2 / total number of times the die was rolled = (7 + 12 +5 + 4) / 40 = 28/40 = 14/20

To learn more about experimental probability, please check: https://brainly.com/question/23722574

#SPJ1

Answer:

Step-by-step explanation:

it is 2x

Answer:

\(\frac{35\pi }{3} cm\)

Step-by-step explanation:

Arc formula when given in degrees:

Arc= degrees x \(\pi\)/180 x radius

Let's plug in the numbers. Note that it is in terms of pi so we have to make the final answer with pi in it. (simplify!)

Let's also note that this is stating the major arc, which means we need the arc distance for the 'pacman' shape, not the actual mouth.

Since a circle is 360 degrees and the minor arc is 60 degrees, the degree of the major arc should be 300. Radius is the same.

Arc= 300 x \(\pi\)/180 x 7

Let's simplify.

Arc=5\(\pi\)/3 x 7

Arc=35\(\pi\)/3 cm

Wxndy~~

Answer:

Can you insert pictures of the graph? I might be able to help you then.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Exact Form: x(39)/(2)

Mixed form:x=19(1)/(2)

Answer:

39/2

Step-by-step explanation:

2x/3-9=4

2x/3=13

2x=39

x=39/2

Answer:

20 units²

Step-by-step explanation:

I have included the answer as well as an explanation and formula above. Note that the formula is only for area of trapeziums/trapezoids

Answer:

DE = 6 cm

Step-by-step explanation:

The concept behind this question is the Chord-Chord Power Theorem. This product states that "if two chords intersect in a circle, then the products of the lengths of the chords segments are equal". In this case:

CE × DE = AE × BE

4 × DE = 8 × 3

4 × DE = 24
DE = 6 cm

Hope this helps!