answer the question below

The expression [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]

What is algebraic expression ?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

According to question

⇒     [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex]

⇒   taking LCM of 4, 5 = 20

now [tex]\[\frac{4(4+6a)-5(1+3a)}{20}[/tex]

⇒ (16 +24a - 5 - 15a)/20

⇒ ((24a - 15a) - (16-5))/20

⇒ (9a - 11)/20

hence, the expression  [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]

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The dimensions that could be the measurements of a similar triangle are; base = 7.8 cm and height = 18 cm

Two triangles are said to be similar provided that they have the same ratio of corresponding sides and an equal pair of corresponding angles.

Now, we are given the side lengths of the triangle as a base length of 3.9 cm and a height of 9 cm.

Thus, this means that a similar triangle will have same ratio of side lengths. Thus;

If new height is h and new base is b, then we have;

9/h = 3.9/b

Thus,

h/b = 9/3.9

If we multiply the right side top and bottom by 2, then we have;

h/b = 18/7.8

18 and 7.8 cm could be similar dimensions.

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Answer:

4

6

y=4x+6

Step-by-step explanation:

check the attached file

he group g and the positive integer n = 3 satisfy the conditions given in the problem.

Let g be the 6th group isomorphic to the rotationally symmetric group of regular hexagons. Let n = 3.

Since |g| = 6, it is clear that n |g|. Split. However, the action of g on any set cannot have orbitals of magnitude 3. To see this, note that the order of each element of g is either 1, 2, or 3. If an element of g has degree 1, then its orbit under the action of g is the element itself with magnitude 1.

If the elements of g have degree 2, then the orbitals under the action of g have magnitude 2. If the elements of g have degree 3, then the orbitals under the action of g have magnitude 3. However, g only has order elements. Since it is of order 3 (that is, a rotation of 120 degrees), the effect of g cannot have an orbit of magnitude 3.

Hence, the group g and the positive integer n = 3 satisfy the conditions given in the problem.

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The scale factors of the given figures and their similarity statements are:

1. ΔHJG ~ ΔCAB; 1/3

2. ΔNPM ~ ΔABC; 2

3. KJML ~ CDAB; 2

Using proportions, the values of x are:

4. x = 10

5. x = 6

6. x = 30

The scale factor = the ratio of the corresponding sides of the similar figures = New figure/original figure.

1. The similarity statements of the given figures is, ΔHJG ~ ΔCAB

Scale factor = 4/12 = 1/3

2. ΔNPM ~ ΔABC

Scale factor = 14/7 = 2

3. KJML ~ CDAB

Scale factor = 12/6 = 2

4. 40/x = 20/5

Cross multiply:

20x = 200

Divide both sides by 20

x = 10

5. 18/x = 21/7

21x = 126

x = 6

6. 6/x = 3/15

3x = 90

Divide both sides by 3

x = 30

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Answer:

Equation 1 - x + 4y = 12

Equation 2 -  2x + 4x = 16

Cost of 1 Cheeseburger - $4

Cost of 1 Taco - $2

Step-by-step explanation:

Cheeseburger(x) and Taco(y)

x + 4y = 12 and 2x + 4y = 16

x = - 4y + 12

2(- 4y + 12) + 4y = 16

- 8y + 24 + 4y = 16

- 4y = - 8

y = 2

x + 4(2) = 12

x + 8 = 12

x = 4

Step-by-step explanation:

3x - 3y=3 which means 3x=3+4y

3x/3=3/3+4y/3 devide both sides by 3 to find c

x=1+4/3y we solve x instead of y

3(1+4/3y)-4y=3 replace x instead of y

Any value of y makes the equation True.

Answer:

-2

Step-by-step explanation:

The composition of A and B represents by the set A o B = {(2,2),(4,0)}

What is a set of ordered pair?

An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.

Given sets are

A = {(1,2), (-3,0), (4,7)}

B = {(2,1), (0,3), (4,-3)}

The inputs of B are 2, 0, and 4.

The outputs of B are 1, 3, and -3.

The inputs of A are 1, -3, and 4.

The outputs of A are 2, 0, and 7.

The composition can be written as A o B = A(B(x)

A(B(2)) = A(1) = 2

A(B(0)) = A(3) = not valid [Since 3 is not an input of A].

A(B(4)) = A(-3) = 0

The composition is {(2,2), (4,0)}.

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Step-by-step explanation:

Hope u get it x=3×3

x=9

It didn't include in the photo

The length of segment AY is 16.7 ft if the length of segment BC is 16.7 ft

From the question, we have the following parameters that can be used in our computation:

BC = 16.7 ft

The measures of the angles are not given

However, the marks on the side lengths imply that:

Using the above as a guide, we have the following:

AY = BC

This is because these segments are parallel segments

Recall that parallel segments are equal segments

Substitute the known values in the above equation, so, we have the following representation

AY = 16.7

Hence, the length of AY is 16.7 ft

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The angle of rotation is 90 degrees.

What is a square?

In a square, all the sides are equal in length and all the angles are right angles (90 degrees). The center of a square is the point that is equidistant from all four vertices, and it is also the point of intersection of the diagonals of the square.

The angle of rotation about the center that maps AB to BC is 90 degrees.

If we rotate the square about its center, the sides of the square will rotate to new positions. For example, if we rotate the square 90 degrees counterclockwise (as specified in the question), side AB will rotate to the position of side BC.

The angle of rotation that maps AB to BC is the angle through which the square was rotated.

Hence, the angle of rotation is 90 degrees.

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Answer:

slope of the line =

y2 - y1 / x2 - x1

take the appropriate point namely:

(-1,-3) as (x1,y1)

(1,3) as (x2,y2)

(you can change the position whether {-1,-3) as {x2,y2} or {1,3} as {x1,y1})

3 - (-3) / 1 - (-1)

3 + 3 / 1 + 1

6 / 2

= 3

Answer:

Choice D : x > - 1

Step-by-step explanation:

Left hand side (LHS) of the inequality can be siimplified

[tex]2\left(x-3\right)-5x = 2x - 6 - 5x = -3x -6\\\\[/tex]

Inequality becomes

[tex]-3x-6 < x-2[/tex]

Move x to the left side and -6 to the right side:

[tex]-3x - x < -2 + 6\\\\-4x < 4\\\\[/tex]

Multiply both sides by -1(the inequality sign changes to >)

[tex]4x > -4\\\\[/tex]

Divide both sides by 4:
[tex]x > -1[/tex]

The number line corresponding to this is the fourth choice

Division problem with quotient of 3 and a remainder of 28 are-

The given data is-

To estimate:

division problem?

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The gallons after 8 hours will be 3400 gallons.

Expression refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

Numbers, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations.

In this case, the reactor coolant tank is being filled with coolant at the rate of 400 gallons per hour with t>0 measure in hours.

Therefore, the gallons after 8 hours will be:

= 200 + 400(8)

= 200 + 3200

= 3400 gallons.

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The graph representation of the given distribution is attached below.

The term graph in math refers the visual representation of the collection of data that has the x and y coordinate values.

Here we have given that Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams and we need to find the graphical representation of the distribution.

Here by using the values in the foregoing ANOVA table are quickly produced by the calculator, including the test statistic and the p-value of the test calculator shows :

=> F=0.66853555

=> p = 0.530548

And the FACTOR df =2 and SS=23.212

=> MS = 11.606

Here  the ERROR df = 12

=> SS=208.324

=>  MS = 17.36

Here by using the f distribution for the test of three different means.

Then the value of the test statistic (F-value) is 0.668 and the p -value for the test is 0.5301

When we plot the graph for the distribution then we get he graph like the following.

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[tex]340.11[/tex] or [tex]\frac{32651}{96}[/tex].

[tex]\frac{(\frac{309*317}{9-4+7})}{8x3}[/tex]

[tex]\frac{(\frac{309*317}{9-4+7})}{24}[/tex]

[tex]\frac{(\frac{309*317}{12})}{24}[/tex]

[tex]\frac{(\frac{97953}{12})}{24}[/tex]

[tex]\frac{(8162.75)}{24}[/tex]

[tex]340.11[/tex] or [tex]\frac{32651}{96}[/tex].

Value is a discontinuity is undefined when [tex]x=-5[/tex] or [tex]x=3[/tex] The answer is then the third choice. [tex]\frac{x^2+7 x+1}{x^2+2 x-15}=\frac{x^2+7 x+1}{(x+5)(x-3)}[/tex]

What is discontinuity?

A discontinuous function is a graph function that is not linked to any other functions. If the left-hand limit of f(x) and the right-hand limit of f(x) both exist but are not equal, then the function f(x) is said to have a discontinuity of the first sort at x = a.

A zone within the earth where a sudden change in physical properties, such as the velocity of earthquake waves, occurs. Such a zone marks the boundary between the different layers of the earth, as between the core and mantleSee also Mohorovičić discontinuity.

In mathematics, functions, and applications, continuous functions are crucial. Not all functions, nevertheless, are continuous. A function is said to have a discontinuity at that point in its domain if it is not continuous elsewhere in its domain.

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The complete answer for the verbal expression into an algebraic inequality is  [tex]\frac{n}{-3} +5 \geq 12[/tex] .

What are inequality?

In arithmetic, the relationship between 2 values that are not equal is outlined by inequalities. difference means that not equal. Generally, if 2 values don't seem to be equal, we tend to use “not equal (≠)”.

Main body:

First, let's call "a number": n

"The quotient" means we are dividing.

Therefore, "the quotient of a number and -3" can be written as:

n÷ -3

now we need to add 5 to the expression ,

[tex]\frac{n}{-3} +5[/tex]

The quotient of a number and -3 plus 5 is at least 12.

so the expression found out till is equal to at least 12 which means sign used is " ≥"

Hence , the complete answer is  [tex]\frac{n}{-3} +5 \geq 12[/tex] .

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The reasonable amount Ester will spend on vegetables is $27

The amount is the value in $ which Ester will spend on vegetable and fruits in the grocery market. To determine the amount we have to determine the average of the current  expenditure for the current period

The given parameters are

The range of values to spend

$40 to $50

Percentage of amount to spend = 20%

Number of weeks = 3

Average amount to be spend = (40+50)/2 = 90/2 = $45

(20/100)*45/1 = 9

In the next 3 weeks

In the nest 3 weeks Ester spends ($3*9)= $27

In conclusion, Ester spends $27 in the next three weeks

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To answer this question we need to make use of Linear Programming

The solution is:

x = 170 units

y = 345 units

z(max) = 2235 rupees

To solve a linear programming problem, we need to formulate the model  

The Objective Function

Let´s call x the number of product 1 manufactured

and y the number of product 2 manufactured

Then the Objective Function is:

z = 3× x + 5×y    to be maximize

The set of constraints are:

                             D1           D2

                           ( min. )     ( min. )

Product  1 (x)          1               3

Product 2 (y)          2              2            

Availability            860        1200

First constraint:

Time available in D1:  860 minutes

1×x  +  2×y  ≤ 860

Second constraint:

Time available in D2: 1200 minutes

3×x  +  2×y  ≤ 1200

General constraint:   x ≥ 0  ;  y ≥ 0   integers ( we will assume only complete products at the end of the period no fractions )

Then the model is:

z = 3× x + 5×y    to be maximize

Subject to:  

1×x  +  2×y  ≤ 860

3×x  +  2×y  ≤ 1200

x ≥0   y ≥ 0   integers

With the help of Avtomat we get the solution:

x = 170 units

y = 345 units

z(max) = 2235 rupees

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The measure of the angle S is 112° in the following parallelogram.

What is parallelogram?

A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of a polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. In a parallelogram, the opposing sides are of equal length, and the opposite angles are of equal size. A parallelogram has adjacent angles that add up to 180 degrees.

Given, ∠T= 11x + 2

∠V = 10x + 8

From the above definition, opposite angles are equal

So, ∠T = ∠V

or, 11x + 2 = 10x + 8

or, 11x - 10x = 8 - 2

or, x = 6

∠V= 10x + 8 = 10*6 + 8 = 68 degree

From the above definition, adjacent angles add up to 180 degrees

∠V + ∠S = 180°

or, 68° + ∠S =180°

or, ∠S = 180° - 68° = 112°

Hence, the measure of the angle S is 112°.

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The equation of line passes through the points (1, -4) and (4, 5) will be;

⇒ y = 3x - 7

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (1, -4) and (4, 5).

Now,

Since, The equation of line passes through the points (1, -4) and (4, 5)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (5 - (-4)) / (4 - 1)

m = 9 / 3

m = 3

Thus, The equation of line with slope 3 is,

⇒ y - (-4)= 3 (x - 1)

⇒ y + 4 = 3x - 3

⇒ y = 3x - 3 - 4

⇒ y = 3x - 7

Therefore, The equation of line passes through the points (1, -4) and (4, 5) is given as;

⇒ y = 3x - 7

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Evaluating the expression a² + b ÷ 3 for each set of given values we have

The expressions are evaluated using substitution as done below

for a = 4, b=3

substituting the the values of a and b

= a² + b ÷ 3  

= 4² + 3 ÷ 3

= 16 + 1

= 17

For a=2, b=21

substituting the the values of a and b

= a² + b ÷ 3

= 2² + 21 ÷ 3

= 4 + 7

= 11

For a = 3, b = 6

substituting the the values of a and b

=  a² + b ÷ 3

=  3² + 6 ÷ 3

= 9 + 2

= 11

substituting the values yielded the results as 17, 11 and 11

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The graph (created with MS Excel) of the height the box is lifted to the number of times Brennan turns the crank to lift the box which is the graph of the proportional relationship, y = x, is attached.

A proportional relationship is one in which one variable (the output variable) is a constant multiple of the another variable known as an input variable.

The number of times Brennan turns the crank = x

The height to which the box is lifted = y

The points on the graph are; (15, 15), and (45, 45)

The ratio of the y-values to the x-values is 15/15 = 45/45 = 1, which indicates that the relationship is a proportional relationship

A point on the graph of a proportional relationship is the point (0, 0), therefore, the points on the graph are; (0, 0), (15, 15), and (45, 45)

Please find attached the graph of the proportional relationship between the number of times Brennan turns the crank to the height to which the box is lifted created with MS Excel

The relationship between the variables x and y is; y = x

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A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.

In the given question, a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa.

We have to calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints.

Sample size: n = 13

Sample mean: x’ = 8.52 mps

Sample standard deviation: s = 0.78 mps

95% lower confidence bound for the true average proportional limit stress of all such joints

Level of Significance (α) = 1-95% = 5% = 0.05

α/2 = 0.025

So the value of t(α/2) = 1.8

The confidence interval = x’± t(α/2)*s/√n

Now putting the value:

The confidence interval = 8.41± (1.8)*(0.78)/√12

The confidence interval = 8.41± (1.8)*(0.226)

The confidence interval = 8.41± 0.4068

The confidence interval = (8.41- 0.4068, 8.41+ 0.4068)

The confidence interval = (8.01, 8.82)

A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.

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The right question is:

A sample of 12 joint specimens of a particular type gave a sample mean proportional limit stress of 8.41 mpa and a sample standard deviation of 0.78 mpa.

Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.)

(a)     [tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]

(b)       [tex]n = {\frac{p_{n-1} -p_{n} }{0.4p_{0}} }[/tex]

Given,

         Initial salmon population [tex]p_{0}=5000[/tex]

         Extraction rate = 40% per year

(a) Formula for recursion,

         For the first year,

                [tex]p_{1} =p_{0} -0.4p_{0}+n[/tex]

         For the second year,

                [tex]p_{2} =p_{1} -0.4p_{0} +n[/tex]

         For the n'th year,

               [tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]

(b) The value of n,

        From the above equation,

                [tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]

                  [tex]n = {\frac{p_{n-1} -p_{n} }{0.4p_{0}} }[/tex]

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Each year, 40% of the salmon population is extracted from a farming pond.

a. The recursion to describe Pn is Pn = 0.6 Pn-1 + N.

b. The value of N is 3000.

According to the recursion equation, the quantity of fish at the start of the nth year. Pn, is equal to 0.6 times the quantity at the start of the year before, Pn-1, plus the constant quantity of wild salmon that is restocked every year, N.

b. We can set the recursion equation equal to the initial population of 5000 fish in order to get the value of N that ensures the quantity of fish stays constant at the start of each year. Now we have the equation.

0.6Pn-1 + N = 5000. Solving for N gives us N = 3000.

Therefore, a. Pn = 0.6 Pn-1 + N. b.  3000.

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a) The maximum height of the rock is of: 5.50 metres.

b) The time that the rock was in the air is of: 2.12 seconds.

c) The distance which the rock landed is of: 12.72 meters.

The height of the projectile is modeled using a quadratic function, as follows:

y = -4.905t² + v(0)sin(60)ºt + h(0).

The parameters are given as follows:

Considering the values of these parameters, the function is given as follows:

y = -4.905t² + 10.39t.

The coefficients are given as follows:

a = -4.905, b = 10.39, c = 0.

The maximum height is obtained as the y-coordinate of the vertex, as follows:

Hmax = -(10.39² - 4(4.905)(0))/(4(-4.905)) = 5.50.

The rock hits the ground when:

y = 0.

Hence:

-4.905t² + 10.39t = 0

t(-4.905t + 10.39) = 0.

4.905t = 10.39

t = 10.39/4.905

t = 2.12 seconds.

The horizontal distance is given as follows:

x = v(0)cos(60º)t

Hence:

x = 12 x 0.5 x 2.12 = 12.72 meters.

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The correct statement about histograms is given as follows:

d. All of these choices are true.

An histogram is a graph that shows the number of times each element of x was observed.

Each element is said in case that the histogram can represent element by element, but in the case of distribution with a wider range of possible output values, the histogram is divided into classes, and then the histogram shows the number of observations that were observed for each class, which cover the complete range of observations, meaning that the histogram is a summary of interval data.

The above paragraph, in case the histogram covers a wide range of data, means that all the statements in this problem are correct, and thus option d is correct.

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