For csc 330:
a) state value of the ratio exactly
b) find one equivalent expression
c) draw a diagram to illustarte.

Answer:

ΔABC ≅ ΔEDF

Step-by-step explanation:

Triangle ABC is congruent to triangle EDF because they're the same size.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex] \sf\triangle ABC \cong \triangle DEF[/tex]

For checking congruency, we need to follow a proper order when choosing the triangle. because each triangle name is unique in itself.

So, According to Triangle ABC, we need to find the triangle with first two letters That resembles AB, that is :

and next should be :

[tex] \qquad \large \sf {Conclusion} : [/tex]

so, now we got the sense for naming, therefore the answer will be :

[tex] \sf\triangle ABC \cong \triangle DEF[/tex]

Answer:

  x = 3

  y = 8

Step-by-step explanation:

A matrix product exists if and only if the number of columns in the left matrix is equal to the number of rows in the right matrix.

For AB to exist, we must have ...

  columns of A = rows of B

  x +5 = y

For BA to exist, we must have ...

  columns of B = rows of A

  11 -y = x

Using the second equation to substitute for x in the first equation, we have ...

  (11 -y) +5 = y

  16 = 2y

  8 = y

Then the value of x is ...

  11 -8 = x = 3

The values of x and y are ...

__

Additional comment

The dimensions are A = 3×8; B = 8×3.

The system of equations that could be used to determine the number of small cars rented and the number of large cars rented is;

x + y = 10

x + y = 105x + 7y = 66

Let

Number of small cars rented = x

Number of large cars rented = y

x + y = 10

x + y = 105x + 7y = 66

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Answer:

-3

Step-by-step explanation:

[tex]f\left( x\right) =\sqrt{3x} \ \ \text{and} \ \ g\left( x\right) =x+3[/tex]

it’s clear that :

f is defined if and only if  x ≥ 0

Therefore ,

fºg is defined if and only if x + 3 ≥ 0

x + 3 ≥ 0

⇔ x ≥ -3

Then ,the smallest number that is in the domain of fºg is -3

Answer:

Step-by-step explanation:

eq. of line is 2x-3y=-3

its slope=(-co-efficient of x/co-efficient of y)=-2/-3=2/3

slope of line perpendicular to given line=-3/2

eq. of line through (-3,0) is

y-0=-3/2 (x+3)

2y=-3x-9

3x+2y=-9

or

any eq. perpendicular to given line is

3x+2y=c where c is a constant.

it passes through (-3,0)

3(-3)+2(0)=c

c=-9

reqd. eq. is

3x+2y=-9

The depreciation expense per unit of production for the Textile Company is D. $0.20.

The unit-of-production depreciation method uses the useful life of an asset based on the units of production and the depreciable amount to estimate the depreciation expense per unit.

For each period, the depreciation expense per unit is multiplied by the units of production to determine the period's total depreciation expense.

Cost of equipment = $40,000

Residual value = $6,000

Depreciable amount = $34,000 ($40,000 - $6,000)

Estimated useful life = 170,000 units

Depreciation expense per unit of production = $0.20 ($34,000/170,000)

Thus, the depreciation expense per unit of production for A Textile Company is D. $0.20.

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Answer:

  (a)  100 meters

Step-by-step explanation:

You want the width at the base of a cooling tower whose walls are modeled by the equation (x/20)² -((y-110)/48)² = 1.

The width at the base will be the difference in the values of x when y=0.

  (x/20)² -((0 -110)/48)² = 1

  (x/20)² = 1 +3025/576

  x = ±20/24√3601 ≈ ±50.01

The width will be 50.01 -(-50.01) ≈ 100 meters.

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The tires can be arranged in 24 ways. Computed using permutation.

The permutation is a way of selecting a smaller set from a larger set when the order of selection is not of concern.

For selecting r number of items, from n number of items, with the order of selection not being a concern, we can calculate the number of ways using permutation:

nPr = n!/(n - r)!.

In the question, we are asked the number of ways in which the four tires can be arranged on a car.

As we need to select 4 tires, from 4 tires, with any order, we will use permutation.

Thus, the number of ways can be calculated as 4P4, which can be calculated using the formula, nPr = n!/(n - r)!.

Thus, 4P4 = 4!/(4 - 4)! = 4!/0! = 24/1 = 24.

Thus, the tires can be arranged in 24 ways. Computed using permutation.

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Answer:

[tex]4a^{4} -11a^{3} + 6a^{2}[/tex]

Answer: False

Step-by-step explanation:

If the function has a negative slope, then it will decrease.

The probability of selecting two prime numbers is 1/6.

Probability determines the odds that a random event would happen. The odds that the random event would happen lie between 0 and 1.

The probability of selecting two prime numbers  = (number of prime numbers between 1 and 9 / total numbers between 1 and 9) x [(number of prime numbers between 1 and 9 / total numbers between 1 and 9) - 1]

Prime numbers between 1 and 9 = 2, 3, 5, 7

4/9 x 3/8 = 1/6

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The equation whose solution is the given quantity is 90,000,000 = 2,000,000w + 15,000w where w = $44.67

B = xz + yw

Where,

B = xz + yw

90,000,000 = (20 × 100,000w) + (15,000 × w)

90,000,000 = 2,000,000w + 15,000w

90,000,000 = 2,015,000w

w = 90,000,000 / 2,015,000

= 44.6650124069478

Approximately,

w = $44.67

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Answer:

2 hours

Step-by-step explanation:

If Thomas can paint 1/3 = 2/6 of the room in a hour and Brian can paint 1/6 of the room in an hour. Which means in an hour they can collectively paint 3/6 = 1/2 of the room. Now you need to find how long it would take then to paint 2/2 of the room. Knowing that 1/2+1/2 = 2/2, it would take them 2 hours to paint the room together

Using equivalent angles, the solutions to the equation are given as follows:

[tex]\theta = 255^\circ, \theta = 285^\circ[/tex]

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

In this problem, the equation is:

[tex]\sin{\theta} = -0.966[/tex]

Applying the inverse relation:

[tex]\theta = \arcsin{-0.966} = 255^\circ[/tex]

Which is on the third quadrant. The equivalent angle on the fourth quadrant is given as follows:

[tex]270^\circ + (270^\circ - 255^\circ) = 285^\circ[/tex]

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The equation between the number of days remaining and number of hours is given as y= -5x+50.

Let y be the number of days remaining and x be the no.of hours.

From the graph the slope of the line is given by m.

m=(y2 - y1)/(x2 - x1)

m=(30 - 40)/(4 - 2)

m= -10/2 = -5.

The above slope is in between points 2 and 4. As the line has a constant rate of growth the slope is the same between any points of the line.

Therefore the equation between the no.of days remaining and no.of hours is given by

y=mx +c.

y=-5x+c

Now to find the value of c. This can be determined by substituting the x and y values at a particular instant. For x=0,y=50. Therefore by these values, we get,

50= -5(0)+c

c=50.

Therefore the relation between the number of days remaining and number of hours is given as y= -5x+50.

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The plotting of the inequalities was done using geogebra online graphing calculator. The graph is attached.

Inequalities are the mathematical expressions in which both sides are not equal. It should be noted that in inequality, unlike in equations, we compare two values.

The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign. Inequality is an expression used to show the nonequal comparison of numbers and variables.

Given the system of inequalities:

3y > 2x + 12

3y - 2x > 12   (1)

2x + y < -5    (2)

Plotting the inequalities using GeoGebra online graphing calculator. The graph is attached

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When both expressions have the same value,  then they are equal to each other.

The equivalent is the expressions that are in different forms but are equal to the same value.

Consider the expressions 5 + 8k and 8k + 5.

Using k = 3

5 + 8k = 8k + 5

5 + 8(3) = 8(3) + 5

5 + 24 = 24 + 5

29 = 29

Using k = 5

5 + 8k = 8k + 5

5 + 8(5)= 8(5) + 5

5 + 40 = 40 + 5

45 = 45

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Complete question:

Consider the expressions 5 + 8k and 8k + 5. Determine why the expressions are equivalent.

Using k = 3 5 + 8k 8k + 5 5 + 8(3) 8(3) + 5 5 + 24 = 29 24 + 5 = 29

Using k = 5 5 + 8k 8k + 5 5 + 8(5) 8(5) + 5 5 + 40 = 45 40 + 5 = 45

Complete the statements.

If both expressions have the same value after substituting and simplifying two different values for the variable, then they are.

The value of both expressions when k = 3 is and when k = 5 is 45, so the expressions are.

The function that's illustrated in the graph is function D.

First, you look at the left side of the graph. You can tell by the shape that it is an x³ function.

Also, the filled-in circle means inclusive. so we know that when x is less than or equal to a number.

The answer that illustrates the information explained is D.

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Answer:

B.

Step-by-step explanation:

An open circle means to exclude the point.

A closed circle means to include the point.

In this graph we see a part of a parabola with an open circle above. The parabola starts at x = 1, but does not include x = 1, and the x values of the parabola increase.

A parabola has an x squared in the equation.

The solution has to have an equation with an x² as its greatest exponent, and also must include x > 1.

The lower part of the graph is a third degree polynomial, so it must have an x cube term, x³. Also, the greatest x value for the x³ function is x = 1, but x = 1 is included. Then all x values tot he left of x = 1 are also included, so for the cubic polynomial, the domain (x values) must be x ≤ 1.

The answer is B.

The probability of pulling a blue or yellow card, written as a reduced fraction is 7/50

From the question, we have the following probabilities:

P(Pink) = 1/5

P(Blue) = 1/25

P(Yellow) = 1/10

P(Black) = 1/15

The probability of pulling a blue or yellow card, written as a reduced fraction is the calculated as:

P(Blue or yellow card) = P(Blue card) + P(Yellow card)

Substitute the known values in the above equation

P(Blue or yellow card) = 1/25 + 1/10

Express 1/25 as 2/50 and 1/10 as 5/10

P(Blue or yellow card) = 2/50 + 5/50

Take the LCM

P(Blue or yellow card) = (2+ 5)/50

Evaluate the sum

P(Blue or yellow card) = 7/50

Hence, the probability of pulling a blue or yellow card, written as a reduced fraction is 7/50

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The possible length of the third side will be values that are less than 41 and greater than 5

For three sides to be the sides of a triangle, the sum of any two sides of the triangle must be greater than the third.

Given the two sides of a triangle have lengths 18m and 23m, the sum of the sides is given as:

sum = 18 + 23

Sum = 41

Let the third side be x, such that;

x + 18 >23

23 + x > 18

x >  23 - 18

x > 5

Similarly

x > -5

Hence the possible length of the third side will be values that are less than 41 and greater than 5

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Based on the triangle proportionality theorem, the true proportion is h/j=k/i

In the diagram that we have here, we have TU to be parallel to QR.

We have following

ST is equal to h, TQ is equal to j, SU is equal to k and UR is equal to i.

This can then be used to form the equation

ST/TQ = SU/UR

When we h/j = k/i

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The expected value of betting 32 is -$0.053, making the 4th option the right choice.

In the question, we are asked for the expected value of betting on 32, given that if we bet $1 on the number 32 and win, the house pays $36, and there are 38 slots.

The probability distribution can be shown as:

 x       $35       -$1

p(x)    1/38      37/38

as, if we get 32, which has the probability of 1/38, the winning number, we gain $35, and for the rest, having a probability of 37/38, the losing number, we lose -$1.

Thus, the expected value can be calculated as E(x) = ∑x.p(x).

Thus, the expected value = $35(1/38) + (-$1)(37/38) = -$2/38 = -$0.05263 ≈ -40.053.

Hence, the expected value of betting 32 is -$0.053, making the 4th option the right choice.

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The expression which is equivalent to the given expression in the task content is; 1/x²⁴.

It follows from the task content that the given expression is; ((x)^-6/x²)³.

Hence, it follows from the laws of indices that the expression can be evaluated as follows;

= (x^-8)³

= x^-²⁴

= (1/x²⁴).

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The box plot that represents the data is a box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 27 on the number line. A line in the box is at 24. The whiskers end at 11 and 31.(second option)

A box plot is used to study the distribution and level of a set of scores. The whiskers represent the minimum and maximum values.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. 75% of the scores represents the upper quartile.

The data arranged in ascending order : 11, 13, 23, 24, 24, 27, 31

Median = 24

First quartile = 1/4 x (7 + 1) = 2nd term =13

Third quartile = 3/4 x (7 + 1) = 6th term = 27

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Step-by-step explanation:

<1 congruent to <5.

<5 congruent to <7.

<1 congruent to <7.

Answer:

don't know but i need thee points

Step-by-step explanation:

Answer: D

Step-by-step explanation:

There are vertical asymptotes at x=7 and x=-3, so the denominator should have factors of (x-7) and (x+3).

This eliminates everything except for D.

In order to define the quantity of which of the two website produces a larger amount of content per single writer, Charlotte thought of:

Charlotte wants to know which website has more content per writer which means that she wants to know which website is more productive with writing.

One way she can do this is to check the average number of posts per writer per website. This would show her which website has a writer that writes more content on average.

Charlotte could also use average number of words per writer. This shows just how much writing the writers in each websites are doing, in terms of words. The website with the higher average words per writer is therefore providing more content.

Options for this question include:

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Answer:

B

Step-by-step explanation:

5x+y=10

-5x -5x

y= -5x+10

Answer:

x = 73

x = -35

Step-by-step explanation:

Here are the 8 numbers:

34, 31, 15, x, 17, 4, 20, 25

Here are the 8 numbers in ascending order with x as the greatest number:

4, 15, 17, 20, 25, 31, 34, x

x - 4 = 69

x = 73

Here are the 8 numbers in ascending order with x as the smallest number:

x, 4, 15, 17, 20, 25, 31, 34

34 - x = 69

-x = 69 - 34

-x = -35

x = -35

Answer:

x = 73

x = -35