Learning Unit 5 Discussion Question -- Introduction to Algebra
33 unread replies. 33 replies. To prepare for this class discussion, you can either look at prices of a grocery product online or in a grocery store. Pick a product that comes in at least two different sizes and compare the unit prices of that product at the same store or online. Pick a product and compare the unit price of that product at two different stores/online shops (the sizes can be the same or different). Give your answer in cents per unit size and round your answer to the nearest hundredth. Which is the better deal

Answer:

on dividing both side of the second eqn by 6 you get

y+1/2x=2

so they are parallel to each other

[

keep in mind that:

any two equations are parallel if they have same coefficient for x and y but different constant values.

]

Answer:

slope(m1)= -coeff.of x/coeff.of y

:.m1= -1/2

slope(m2)= -coeff.of x/coeff.of y

:.m2= -1/2

so it is parallel to each other......

Answer:

y = 1x-5

Step-by-step explanation:

See attached worksheet.

We'll look for a line with the form y=mx+b, where m is the slope and y is the y-intercept.

Pick any two points on the line, but pick ones that are clearly on known lines so that the points are more accurate.  Pick one at the x=o point, if it can be read clearly.  The vaue of y at x=0 is the y-intercept.

Follow the steps in the attachement to find the equation of the line, which is

  y=1x-5

The measure of angle abc is 64 degrees.

An angle bisector is simply a line or ray that divides an angle into two equal parts.

Given that;

Line bm bisects angle abc.

First, we determine the measure of angle abm.

Since line bm bisects angle abc, it divides the angle into two equal parts.

Hence;

Angle mbc = angle abm

Angle abc = angle mbc + abm

Plug in the value

Angle abc = 32 degrees + 32 degrees

Angle abc = 64 degrees.

Therefore, 64 degrees is the measure of ∠b.

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The area of the composite figure is 96. 522 cm²

First, we need to know that the formula for the area of a triangle is expressed as;

Area = 1/2 × base × height

Now, substitute the values, we have;

Area = 1/2 × 6 × 8

Multiply the values

Area = 1/ 2 × 48

Divide the values

Area = 25 cm²

The area of the sector is represented as;

Area = θ/360 πr²

substitute the values

Area = 82/360 × 3.14 × 10²

Area = 71. 522 cm²

The total area of the figure = 25 + 71. 522 = 96. 522 cm²

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By trignometric property, The 630 .18 feet tall is the gateway arch .

What is the definition of trigonometry?

Trigonometry is a discipline of mathematics that examines certain functions of angles and how to use them in computations. A common angle in trigonometry has six different functions. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc).

As given

The angle of elevation from a park bench 778 feet from the base of the Gateway Arch in St. Louis, Missouri is 39 degrees.

Now by using the trignometric property

        tanθ = perpendicular/base

        As diagram is given below .

              θ = 39

             tan39° = AB/CB

        CB = 778 feet

         tan39° = 0.81 (approx)

       0.81 = AB/778

AB = 0.81 × 778

AB = 630 .18 feet

Therefore, the 630 .18 feet tall is the gateway arch .

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The length of the intercepted arc is (35 - 14√2 ) units.

what is length?

Length is a physical quantity that describes the distance between two points. It is typically measured in units such as meters, centimeters, inches, or feet. In mathematics, length can refer to the size of a geometric object,

In the given question,

We know that the length of an arc of a circle is given by the formula L = r*theta, where r is the radius of the circle and theta is the angle in radians subtended by the arc at the center of the circle.

Here, the radius of the circle is 7 units and the angle subtended by the arc is 5π/4 radians. Therefore, the length of the intercepted arc is:

L = 7*(5π/4) = (35π/4) units.

To express the answer in simplest form, we need to rationalize the denominator. Multiplying both the numerator and denominator by 2√2, we get:

L = (35π/4)(2√2/2√2)

= (35*π*√2)/(8) units.

Finally, simplifying this expression, we get:

L = (35 - 14√2) units.

Therefore, the length of the intercepted arc is (35 - 14√2) units

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Answer:

The > (Greater Than) symbol

Step-by-step explanation:

The absolute value symbol makes the value inside positive by calculating the inside's distance from 0. -6 is 6 units away from zero.

|-6| = 6, and 6 is greater than 2

There are 24 possible 3 digit numbers that can be formed using numerals 3,2,7 and 9 without repetition.

Since repetition is not allowed, the first digit can only be 3, 2, 7 or 9. Each of the four digits can be chosen in 4 ways.

For the second digit, the choices are now reduced to 3, 2 or 7 (since 9 has already been used). There can be 3 ways to pick the second digit.

For the third digit, the choices are now reduced to 2 or 7 (since 3 and 9 have already been used). There can be 2 ways to pick the third digit.

Therefore, there are 4 x 3 x 2 = 24 possible 3 digit numbers that can be formed using numerals 3,2,7 and 9 without repetition.

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Answer:

B. -3/2

Step-by-step explanation:

Plot the Graph, then look for the rise over run. This equation has a rise of -6, and a run of 4. so [tex]\frac{-6}{4}[/tex], or -[tex]\frac{3}{2}[/tex]

The inequality -1/2 ≤ ab ≤ 1/2 implies [tex](ab)^2[/tex] ≤ 1/4, and squaring bοth sides οf the inequality gives us  [tex](ab)^2[/tex] ≤ 1/4 as required.

Tο prοve that -1/2 ≤ ab ≤ 1/2 fοr  [tex]a^2+b^2 = 1[/tex]and a, b ∈ ℝ, we can start by nοting that:

-1 ≤ a ≤ 1 (because [tex]a^2 \le a^2 + b^2 = 1[/tex], sο -1 ≤ a ≤ 1)

-1 ≤ b ≤ 1 (because [tex]b^2 \le a^2 + b^2 = 1[/tex], sο -1 ≤ b ≤ 1)

Multiplying these inequalities, we get:

-1 ≤ ab ≤ 1

Nοw, we need tο shοw that ab cannοt equal ±1. If ab = 1, then we have:

[tex]a^2 + b^2 = 1[/tex]

[tex]a^2 + 2ab + b^2 = 1 + 2ab[/tex]

[tex](a + b)^2 = 1 + 2ab[/tex]

Since a and b are bοth between -1 and 1, a + b is between -2 and 2, sο [tex](a + b)^2[/tex] is between 0 and 4. Therefοre, we have:

1 + 2ab ≤ 4

Simplifying, we get:

ab ≤ 3/2

This cοntradicts the fact that ab = 1, sο ab cannοt equal 1. Similarly, if ab = -1, we get:

[tex](a + b)^2 = 1 - 2ab[/tex]

Since [tex](a + b)^2[/tex] is nοnnegative, we have:

1 - 2ab ≥ 0

Simplifying, we get:

ab ≤ 1/2

This cοntradicts the fact that ab = -1, sο ab cannοt equal -1. Therefοre, we have -1 < ab < 1, which implies -1/2 ≤ ab ≤ 1/2.

Taking the square οf bοth sides οf -1/2 ≤ ab ≤ 1/2, we get:

[tex]1/4 \le a^2b^2 \le 1/4[/tex]

Adding [tex]a^2 + b^2 = 1[/tex]tο bοth sides, we get:

[tex]5/4 \le 1 + a^2b^2 \le 5/4[/tex]

Dividing by 2, we get:

[tex]5/8 \le (1 + a^2b^2)/2 \le 5/8[/tex]

Since [tex](1 + a^2b^2)/2[/tex] is the average οf [tex]a^2[/tex] and [tex]b^2[/tex], we have:

[tex]5/8 \le (a^2 + b^2)/2 \le 5/8[/tex]

Simplifying, we get:

5/8 ≤ 1/2 ≤ 5/8

Therefοre, the inequality -1/2 ≤ ab ≤ 1/2 implies [tex](ab)^2 \le 1/4[/tex], and squaring bοth sides οf the inequality gives us  [tex](ab)^2 \le 1/4[/tex] as required.

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Answer:

20√2

Step-by-step explanation:

20√2 = 28.284...

Check the picture below.

The common difference of the arithmetic sequence in which a1=3 and a4=15 is d = 4

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is  [tex]T_n = a + (n-1)d[/tex]

(for all positive integer values of n)

And thus, the common difference is  [tex]T_{n+1} - T_n[/tex]

for all positive integer values of n

Given that a1=3 and a4=15

nth term of G.P is ;

Calculation:

[tex]T_n = a + (n-1)d[/tex]

a1 = 3

a2 = 3+ d

a3 = 3+ d

a4=15

3 + 3d = 15

d =4

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If 1% of the phones were broken, then the number of good phones is 99% of 4,028:

99/100 x 4,028 = 3,987.72 (rounded to 3,988)

Out of the 3,988 good phones, 50% were sold to another city:

50/100 x 3,988 = 1,994

So, the remaining number of good phones that were sold locally is:

3,988 - 1,994 = 1,994

To find the percentage of phones sold locally, we need to divide the number of phones sold locally by the total number of phones:

1,994 / 4,028 = 0.494

Then, we can convert this decimal to a percentage and round to the nearest one percent:

0.494 x 100 ≈ 49%

Therefore, approximately 49% of the phones were sold locally.

The exponential function that gives the amount of medication y  in the body after x hours is:

           [tex]y = 400(\frac{2}{3} )^x[/tex]

What is an exponential function?

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth. When the input variable x appears as an exponent in the formula f(x) = aˣ, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x. A constant serves as the exponent in an exponential function, but not the other way around (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

The complete question is given below.

The initial value of the medication = 400 mg

This is the value of a.

a = 400

b is the growth or decay factor in the exponential function formula.

In this question, it is the decay factor.

b = 1-r

where r is the decay rate = 1/3

b = 1-1/3 = 2/3

The exponential function is given by the formula:

y = abˣ

[tex]y = 400(\frac{2}{3} )^x[/tex]

Therefore the exponential function that gives the amount of medication y  in the body after x hours is:

           [tex]y = 400(\frac{2}{3} )^x[/tex]

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f(x) = (8/9)(x-3)² - 4 which has a vertex at (3,-4) and passes through the point (0,4).

What is a quadratic equation?

A quadratic equation is a second-degree polynomial equation of the form:

ax² + bx + c = 0

where a, b, and c are constants, and x is the variable. Quadratic equations can have one, two, or zero real solutions, depending on the values of the constants a, b, and c. The solutions can be found using the quadratic formula:

x = (-b ± [tex]\sqrt{b^2 - 4ac}[/tex]) / 2a or by factoring the quadratic expression into two linear factors.

A quadratic function can be expressed in the form:

[tex]$$f(x) = a(x-h)^2 + k$$[/tex]

where (h,k) is the vertex of the parabola.

From the problem, we have the vertex (h,k) = (3,-4). Substituting these values into the equation gives:

[tex]$$f(x) = a(x-3)^2 - 4$$[/tex]

To find the value of a, we use the fact that the function passes through the point (0,4). Substituting x=0 and y=4 into the equation gives:

[tex]$$4 = a(0-3)^2 - 4$$[/tex]

Simplifying and solving for a, we get:

a=8/9

Therefore, the quadratic function is:

f(x) = (8/9)(x-3)² - 4

which has a vertex at (3,-4) and passes through the point (0,4).

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So the scale factor of triangle ABC to triangle DEF is 2/5.

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that their corresponding angles are equal, and their corresponding sides are proportional.

Here,

To verify if the two triangles are similar, we need to check if their corresponding angles are congruent and if their corresponding sides are proportional.

Checking corresponding angles:

∠A corresponds to ∠D

∠B corresponds to ∠E

∠C corresponds to ∠F

Checking corresponding sides:

AB/DE = 10/25 = 2/5

BC/EF = 16/40 = 2/5

CA/FD = 20/50 = 2/5

Since the corresponding angles are congruent and the corresponding sides are proportional, we can conclude that triangle ABC is similar to triangle DEF. To find the scale factor of triangle ABC to triangle DEF, we can take any corresponding side and divide it by the corresponding side of the other triangle. For example:

AB/DE = 2/5

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After caculating, a) Matrix is given below, b) C₁ = 65460/193,C₂ = 48480/193, C₃ = 64460/193, c)The mass input to reactor 3 is reduced by 40g/day and d) Change of concentration is Δ C₃ = 2950/193

To solve the system of equations, we can use Gaussian elimination or any other suitable method. Here, we will use Gaussian elimination:

Given:

15C₁-2C₂-C₃=4000

-3C₁+18C₂-6C₃=1500

-4C₁-C₂+12C₃=2400

Therefore:

[tex]A=\left[\begin{array}{ccc}15&-3&-1\\-3&18&-6\\-4&-1&12\end{array}\right][/tex][tex]B=\left[\begin{array}{ccc}4000\\1500\\2400\end{array}\right][/tex]

a) The inverse matrix of A would be

[tex]A^-^1\left[\begin{array}{ccc}14/193&37/2895&12/965\\4/193&176/2895&31/965\\5/193&9/965&87/965\end{array}\right][/tex]

b) For solution of [C] = [A^-1][B]

[tex]C=\left[\begin{array}{ccc}C1\\C2\\C3\end{array}\right] =\left[\begin{array}{ccc}14/193&37/2895&12/965\\4/193&176/2895&31/965\\5/193&9/965&87/965\end{array}\right] \\[/tex]

C₁ = 65460/193

C₂ = 48480/193

C₃ = 64460/193

c) For increasing the concentration [C₁] by 10

C₁ = 65460/193 +10

=67390/193

Now again,

[tex]\left[\begin{array}{ccc}15&-3&-1\\-3&18&-6\\-4&-1&12\end{array}\right] \left[\begin{array}{ccc}67390/193\\48480/193\\64460/193\end{array}\right] =\left[\begin{array}{ccc}4150\\1470\\2360\end{array}\right][/tex]

So from the calculation= 2360 -2400= -40

Therefore the mass input to reactor 3 is reduced by 40g/day

d) Now again reducing mass input

[tex]B=\left[\begin{array}{ccc}4000-500\\1500-250\\2400\end{array}\right] = \left[\begin{array}{ccc}3500\\1250\\2400\end{array}\right] \\\\C=\left[\begin{array}{ccc}C1\\C2\\C3\end{array}\right] = \left[\begin{array}{ccc}173530/579\\130640/579\\61510/193\end{array}\right][/tex]

Δ C₃=C₃-C₃’

=64460-61510/193

= 2950/193

Δ C₃ = 2950/193

Therefore that is the change of concentration.

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The estimated probability of the spinner landing on blue is 0. This means the spinner will not land on blue.

Probability is the measure of how likely an event is to occur out of the number of possible outcomes. It is expressed in terms of a number between 0 and 1, where 0 means that the event is impossible and 1 means the event is certain. Probability is used to calculate the likelihood of an event or outcome in a variety of situations, from predicting the weather to playing the lottery.

The estimated probability of the spinner landing on blue can be calculated by using the ratio of the frequency of red to the frequency of green.

As the ratio is 4 : 7, the frequency of red is 4/11 of the total frequency of 100 spins. The frequency of green is 7/11 of the total frequency of 100. Therefore, the frequency of blue is 100-(4/11+7/11) which is 1 – (11/11) = 0.

Therefore, the estimated probability of the spinner landing on blue is 0. This means the spinner will not land on blue.

To calculate the estimated probability, first we need to calculate the total frequency of all the sections. This is done by adding all the frequencies of the sections together. In this case, the total frequency is 100. Then using the ratio of the frequency of red to the frequency of green, calculate the frequency of red and the frequency of green. Subtract the total frequency and the total frequency of red and green from the total frequency, to get the frequency of blue. Finally, divide the frequency of blue by the total frequency and convert it into a decimal. This will give us the estimated probability of the spinner landing on blue.

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The probability of getting a score less than 4.3 for standard postage is 0.77

In this scenario, f(x) = (3/125) x^2 is a probability density function for the weight of a letter, x, for standard postage where x ∈ (0,5). Thus, the integral of the probability density function between two bounds would give the probability of the event occurring. The probability of getting a score less than 4.3 can be calculated as follows:Pr(X < 4.3) = ∫_0^4.3(3/125) x^2 dx= [(3/125) * (1/3) * 4.3^3] - [(3/125) * (1/3) * 0^3]= 0.77

Thus, the probability of getting a score less than 4.3 for standard postage is 0.77.

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Answer:

$17,520

Step-by-step explanation:

The total can be found using multiplication.

48 x 365

Use long multiplication to solve this.

After solving, you should get $17,520.

Answer:

-16t^2 + 120t + 50

Step-by-step explanation:

Using the given values, we can write the model for this situation as:

h(t) = -16t^2 + 120t + 50

To determine how long it takes the thrown object to reach maximum height, we need to find the time at which the object reaches its maximum height. The maximum height occurs at the vertex of the parabolic path, which is given by:

t = -b / 2a

where a = -16, b = 120.

Substituting these values, we get:

t = -120 / 2(-16) = 3.75 seconds

Therefore, it takes 3.75 seconds for the thrown object to reach maximum height.

Answer:

1/12

Step-by-step explanation:

Lets look at all of the answers:

1/2

1/6

1/9

1/12

1/12 is closest to 0 because a higher denominator means a lower number that is closer to 0.

May I please have brainliest? I put a lot of thought and effort into my answers so I would really appreciate it. Thanks!

Answer:

The value of x is -2.

Step-by-step explanation:

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

Multiplying

x(x+3) +2(x+3) - [x(x-3) +2(x-3) =0

x² +3x +2x +6 -[x²-3x +2x -6] =0

Opening the bracket

x²+3x +2x +6 -x²+3x-2x+6=0

Adding the like terms

6x+12=0. [x²-x²=0]

6x = -12

x = -12 ÷6

x = -2

If a rectangle is 10cm long and its perimeter is 26 cm, then the breadth of the rectangle is 3 cm

Let's assume the breadth of the rectangle to be 'b' cm.

We know that the perimeter of a rectangle is the sum of the lengths of all four sides.

Therefore, the perimeter of the given rectangle = 2(length + breadth)

Given, the length of the rectangle = 10 cm and the perimeter = 26 cm.

So, 2(10 + b) = 26

Simplifying this equation, we get:

20 + 2b = 26

Move 20 to right hand side of the equation

2b = 26 - 20

2b = 6

b = 6/2

b = 3 cm

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Answer:87.84$

Step-by-step explanation:

72------100%

x----------122%

x=122*72/100=87.84$

Overall, there are infinitely many possible combinations of angle measures that satisfy the equation x + (75.3 - x) = 75.3.

It is true that 75.3 = 75.3 when the equation x + (75.3 - x) = 75.3 is reduced to its simplest form. This means that any value of x that falls within the range of possible angle measurements, which is 0 to 75.3 degrees, will satisfy the equation.

As a result, the number of possible combinations of angle measurements that fulfil the equation is unlimited. The particular values of each angle can vary, but each combination will consist of two angles whose measures total up to 75.3 degrees.

For instance, if the sum of the two angles is 75.3 degrees, one conceivable angle combination is 30 degrees and 45.3 degrees. The combination of 60 degrees and 15.3 degrees is another conceivable one.

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Answer:

it could be either A or D

SLAP ME IF I AM WRONG!

Step-by-step explanation:

Including the monthly premium the total money spent using plan 1 spend for insurance with 2 office visits in a month is $230.

In a nutshell, insurance is a contract, symbolised by a policy, in which a policyholder receives financial security or compensation from an insurance firm against losses. In order to make payments to the insured more manageable, the firm combines the risks of its clients.

Insurance policies are intended to protect against the possibility of monetary losses, large and little, that may be brought on by harm to the insured or their property or by liability for harm or injury given to a third party.

From the given table we see that the value of the monthly premium for individuals is $170.

Now, the value of office visit is: $30.

There are 2 office visits thus, 2(30) = 60.

The total money spent is:

170 + 60 = 230

Hence, including the monthly premium the total money spent using plan 1 spend for insurance with 2 office visits in a month is $230.

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