The equation p=2.5m+35 is the cost of making bracelets where ''p'' is the price and ''m'' is the cost of materials.If a bracelet sells for $115,how much was the material?

ANSWER

[tex]x=\frac{1}{2}[/tex] and [tex]y=\frac{1}{4}[/tex]

EXPLANATION

Given;

[tex]4x-12y=1[/tex]

and

[tex]6x+4y=4[/tex]

The augmented matrix of the two linear equation is given by;

[tex]\left[\begin{array}{ccc}4&-12|&-1\\6\:&\:\:\:4|&4\end{array}\right][/tex]

We now perform row operations;

[tex]\frac{1}{4}\times R_1 \rightarrow R_1 [/tex].

This gives us

[tex]\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\6\:&\:\:\:4|&4\end{array}\right][/tex]

[tex]R_2-6R_1 \rightarrow R_2[/tex]

[tex]\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\0\:&\:\:\:22|&\frac{11}{2}\end{array}\right][/tex]

[tex]\frac{1}{22}R _2 \rightarrow R_2[/tex]

[tex]\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\0\:&\:\:\:1|&\frac{1}{4}\end{array}\right][/tex]

[tex]R_1+3R_2 \rightarrow R_1[/tex]

[tex]\left[\begin{array}{ccc}1&0|&\frac{1}{2}\\0\:&\:\:\:1|&\frac{1}{4}\end{array}\right][/tex]

Hence [tex]x=\frac{1}{2}[/tex] and [tex]y=\frac{1}{4}[/tex]

Answer-

A. Brandon’s sound intensity level is 1/4th as compared to Ahmad’s.

Solution-

Given that, loudness measured in dB is

[tex]L=10\log \frac{I}{I_0}[/tex]

Where,

I   = Sound intensity,

I₀ = 10⁻¹² and is the least intense sound a human ear can hear

Given in the question,

I₁ = Intensity at Brandon's = 10⁻¹⁰

I₂ = Intensity at Ahmad's  = 10⁻⁴

Then,

[tex]L_1=10\log \frac{I_1}{I_0}=10\log \frac{10^{-10}}{10^{-12}}=10\log \frac{1}{10^{-2}}=10\log 10^{2}=2\times10\log 10=20[/tex]

[tex]L_2=10\log \frac{I_2}{I_0}=10\log \frac{10^{-4}}{10^{-12}}=10\log \frac{1}{10^{-8}}=10\log 10^{8}=8\times10\log 10=80[/tex]

[tex]\therefore \frac{L_1}{L_2} =\frac{20}{80} =\frac{1}{4}[/tex]

Answer:

a

Step-by-step explanation:

to find the vertical asymptote, set the denominator equal to zero and solve for x.

to find the horizontal asymptote, only evaluate the terms in the numerator and denominator that have the biggest exponent. Use the following rules (m is the exponent of the numerator and n is the exponent of the denominator):

m > n, then y = ∞ so there is no asymptote

m = n, then simplify the coefficients to determine the asumptote

m < n, then y = [tex]\frac{1}{infinity}[/tex] so the asymptote is y = 0

[tex]\frac{x^{2} + 3x - 2}{x - 2}[/tex]

m = 2, n = 1 ⇒ m > n so y = ∞

Answer: there is no horizontal asymptote

Answer:

Consider polygon G as a triangle or any quadrilateral, pentagon, Hexagon, Heptagon, Decagon,....

Now Polygon H is scaled copy of Polygon G by a scale factor of 1/4, it means

If the length of sides of triangle are a,b,c then scaled copy of triangle by using

1/4 means the new sides of polygon which is triangle will be a/4,b/4,c/4.

For example consider a parallelogram having sides 12 cm and 8 cm respectively.The scaled copy of parallelogram by a scale factor of 1/4 will be  of length 1/4×12,1/4×8 which is parallelogram having sides 3 cm and 2 cm respectively.

The set of ordered pairs in the mapping can be described as both a relation and a function.

The set of ordered pairs in the mapping can be described as a relation. A relation is a set of ordered pairs where one element from the first set is related to an element in the second set. In this mapping, each input has a corresponding output.

To determine if the set of ordered pairs is a function, we need to check if each input has only one corresponding output. If this is true, then it is a function. In this case, if each input in the mapping has a unique output, then it is both a relation and a function (a) both a relation and a function).

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The midpoint between -4 and 8 is answer B) 2

Answer:

Total temperature change 104.25 f.

Step-by-step explanation:

Average temperature change is calculated by dividing total temperature change by the total hours it took for the change.

We have been given the average temperature change.

We have to multiply average temperature change by the total number of hours it took for the temperature to change we get the total temperature change.

⇒ Total temperature change =  Average temperature change * total hours

                                                = [tex]-4.17*25[/tex]

                                                 =104.25 f

The answer is B (-6,5) becuase C is located at (-3,4). -3 - 3 is -6... and 4 + 1 is 5

If standard form means a+bi, then the answer is 7-26i. this is because if you use the distributive property, you get 15-26i+8i^2. i^2 in this situation is equal to -1. Once you multiply that to 8, you add it to 15 to get7. In standard form, 8 would be the a and b would be the -26

Answer:

The correct answer is: 17 - i

Step-by-step explanation:

You must use the distributive property.

The correct answer is option D

Option D:  A parallelogram with 4 right angles and opposite sides are equal best defines a rectangle because a rectangle must possess four right angles and opposite sides must be equal.

Let's call the width of our rectangle [tex]w[/tex] and the length [tex]l[/tex]. We can say [tex]l = w + 4[/tex], since the length is equal to 4 cm greater than the width.

Also remember that the perimeter of a rectangle is the sum of two times the width and two times the length, or [tex]P = 2l + 2w[/tex]. To solve this problem, we can substitute in the information we know, as shown below:

[tex]150 = 2(w + 4) + 2w[/tex]

[tex]150 = 4w + 8[/tex]

[tex]142 = 4w[/tex]

[tex]w = \frac{71}{2}[/tex]

Now, we can substitute in the width we found into the formula for length, which is [tex]l = w + 4[/tex]:

[tex]l = \frac{71}{2} + 4[/tex]

[tex]l = \frac{79}{2}[/tex]

The width of our rectangle is [tex]\boxed{\frac{71}{2} \,\, \textrm{cm}}[/tex] cm and the length of our rectangle is [tex]\boxed{\frac{79}{2} \,\, \textrm{cm}}[/tex]

Hey there!!  

Direct variation :

y = kx

( k is the constant )

And given : y = 5a when x = a

y = 5a can be written as y = 5x

Now we know 5 is the constant.

When x = 3a + 2 what is the value of y?

y = kx

y = 5 ( 3a + 2 )

y = 15a + 10

Hope my answer helps!!

Answer: Mitosis.

Explanation:

There are two main methods for replication: mitosis and meiosis. Mitosis is, in simplest of words, when cells split apart.

Mitosis is the simple replication of the cell and its contents. It is a type of cell division where two new daughter cells are duplicated by the DNA (deoxyribonucleic acid). Each of the daughter cells formed have the same number and same kind of the chromosomes present in them as their parent nucleus.

Therefore, it can be said that the daughter cells are identical to their parents as they have the same genetic code.

Answer:

0.375 is answer

Step-by-step explanation:

Given that the  math teacher gave her students two tests. On the first test, 80% of the class passed the test.  But only 30% of the class passed both tests.

Let A - the students pass I test

B = students pass second test

Then P(A) = 80%=0.8 and P(AB) = 30% =0.30

Required probability =probability that a student passes the second test, given that they passed the first one

= P(B/A) = P(AB)/P(A)

= 0.30/0.80

=3/8

=0.375

Right answer is 0.375

The probability that a student passes the second test, given that they passed the first one, is 0.375.

The subject of this question is Mathematics, specifically focusing on the concept of conditional probability. The question asks about the probability that a student passes the second test, given that they passed the first one. Given that 80% of the class passed the first test and 30% passed both tests, we can use the formula for conditional probability P(B|A) = P(A and B) / P(A). Here, A represents passing the first test, and B represents passing the second test.

P(B|A) = P(A and B) / P(A) = 0.30 / 0.80 = 0.375.

Therefore, the probability that a student passes the second test, given that they passed the first one is 0.375.

1. D) decreases, inverse

The average speed for each lap is given by:

[tex]v=\frac{S}{t}[/tex]

where S is the length of the lap (400 m) while t is the time taken to complete the lap. Since the time t increases at each lap, we see from the formula that v, the speed, decreases at each lap. This is an example of inverse relationship: when one of the two quantities increases (the time), the other one decreases (the speed).

2. A) Velocity on the y-axis, time on the x-axis

Acceleration is defined as the change in velocity divided by the time taken:

[tex]a=\frac{\Delta v}{\Delta t}[/tex]

In a graph, the slope of a line is given by the increment in y divided by the increment in x:

[tex]s=\frac{\Delta y}{\Delta x}[/tex]

Therefore, if we put velocity on the y-axis and time on the x-axis, we immediately see that the acceleration corresponds to the slope of the curve.

3. D) velocity

In fact, velocity consists of 1) speed and 2) direction. The speed can be calculated as:

[tex]v=\frac{S}{t}[/tex]

where S is the distance covered and t the time taken. So, by knowing these two quantities, Tim can calculate the speed of the trip. Tim also knows the direction of motion, so he can determine the velocity of the trip.

4. B) equal, different

The difference between speed and velocity is simple: speed is a scalar, and it is just the magnitude of the velocity, so "how fast" is the object moving, while velocity takes also into account the direction of motion, so it is a vector.

Therefore: the two cars have same speed (25 m/s), but they have different velocities, since they are moving into different directions (car A is moving from NY to Miami, while car B is moving from NY to Chicago).

28. B) 11 m

The distance travelled by the bag in free fall is given by:

[tex]S=\frac{1}{2}at^2[/tex]

where [tex]a=9.8 m/s^2[/tex] is the acceleration of gravity and t=1.5 s is the time. Replacing these numbers into the formula, we find

[tex]S=\frac{1}{2}(9.8 m/s^2)(1.5 s)^2 =11 m[/tex]

29. B) 10 m/s south

The boat is moving 20 m/s south, relative to the ground. The passenger is moving 10 m/s north, relative to the boat. Considering south as positive direction, the passenger's velocity relative to the ground is

[tex]v' = v_b + v_p = 20 m/s + (-10 m/s) = 10 m/s[/tex]

and the positive sign means it is due south.

30. B) direction

In fact, velocity is a vector, so it consists of a magnitude (the speed) and a direction. The speed can be determined by the distance and the time, in fact speed is defined as

[tex]v=\frac{d}{t}[/tex]

where d=distance and t=time; however, in order to determine velocity, we also need to know the direction of motion.

33. B) a velocity.

In fact, velocity is a vector, and it consists of a magnitude (the speed) and a direction. In this case, 10 m/s is the speed, while north is the direction.

34. C) Does the measurement include direction?

As stated in the previous question, a vector includes both magnitude and direction, while a scalar includes only a magnitude. Therefore, by asking if the measurement includes a direction, we are able to determine if the quantity is a vector or not.

Answer is 6 kg:

Given that Adam was asked to post a parcel.  The weight of the parcel was 12 lbs and 8 oz.

To convert the weight in kgs:

Let us convert oz into pounds first to make it uniform.

We have 16 0z. = 1 lb

Hence 8 oz. = 8/16 = 0.5 lbs

Weight of the parcel = 12.5 lbs.

We have the converting factor as

2.2 pounds make 1 kg.

Hence 12.5 pounds = 12.5/2.2 = 5.6818

So weight of the parcel in kg= 6. (after rounding off)

Answer: P = -19, Q = 18

Step-by-step explanation:

Px + Q = -19x + 18

Px = -19x                Q = 18

÷x     ÷x      

P   = -19

Answer:

We have

(16/5)x(29/4) = (16x29)/(5x4) = 464/20 = 116/5 = 23 1/5;

The correct answer is d. 23 1/5;

Step-by-step explanation:

First of all, let me break down the formula: [tex] x^2-y^2,\ 2xy,\ x^2+y^2 [/tex] is always a Pythagorean triple because you have

[tex] (x^2-y^2)^2+(2xy)^2 = x^4-2x^2y^2+y^4+4x^2y^2 = x^4+2x^2y^2+y^4 = (x^2+y^2)^2 [/tex]

So, for any [tex] x,y>0 [/tex] you can choose (let's suppose [tex] x>y [/tex]), these three numbers will always fall in the form [tex] a^2+b^2=c^2 [/tex], which is also the rule that works for right triangles. So, every time you choose two numbers [tex] x,y>0 [/tex], the legs will be [tex] x^2-y^2[/tex] and [tex] 2xy[/tex], while the hypotenuse will be [tex]x^2+y^2 [/tex].

We have to find a right triangles with legs 16 and an odd number. Well, the legs in the triple we are given are [tex] x^2-y^2[/tex] and [tex] 2xy[/tex], so we want one of this to be 16, and the other to be odd. But [tex] 2xy[/tex] can't be odd, because it has a 2 factor in it. So, it must be 16: we have

[tex] 2xy=16 \iff xy=8 [/tex]

The only ways we can choose two numbers [tex] x>y>0 [/tex] such that their product is 8 are:

[tex] x=8,\ y=1,\quad x=4,\ y=2 [/tex]

In the first case, the legs are

[tex] x^2-y^2 = 64-1 = 63,\ 2xy = 16 [/tex]

In the second case, the legs are

[tex] x^2-y^2 = 16-4 = 12,\ 2xy = 16 [/tex]

In this case both legs are even, so the only good choice is [tex] x=8,\ y=1[/tex]

So, the triangle we're working with has legs

[tex] x^2-y^2 = 64-1 = 63,\ 2xy = 16 [/tex]

and hypotenuse

[tex] x^2+y^2 = 64+1 = 65 [/tex]

The Pythagorean triple with leg lengths of 16 and an odd number is found by using the formulas x² - y², 2xy, and x² + y², taking x as an even integer. This provides us the a triple (3, 4, 5) which, after scaling by a factor of 4, gives us a right triangle with sides 12, 16 and 20.

In order to find a Pythagorean triple whose leg lengths are 16 and an odd number, we'll use the Pythagorean triple formulas x² - y², 2xy, and x² + y², where x and y are integers. Considering one leg length is 16, which is even, the other leg should be an odd number. As for the expression 2xy to be even, either x or y should be an even integer of their own. Thus, let's take x to be an even integer, namely 4, which will, in turn, give us the values as 2² - 1² = 3 and 2² + 1² = 5. Hence, the Pythagorean triple is (3, 4, 5) which gives us the lengths in a 1:1 ratio. Therefore, to find a right triangle with legs 16 and odd number, we just multiply each length by 4 to get (12, 16, 20).

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Answer:

The factor form of given expression is (x-4)(x-2i)(x+2i).

Step-by-step explanation:

The given expression is

[tex]x^3-4x^2+4x-16[/tex]

It can be written as

[tex]f(x)=x^3-4x^2+4x-16[/tex]

According to the rational root theorem, all possible rational roots are in the form of

[tex]\frac{a_0}{a_n}[/tex]

Where, a₀ is constant term and [tex]a_n[/tex] is leading coefficient.

[tex]f(4)=4^3-4(4)^2+4(4)-16=0[/tex]

Since the value of f(x) is 0 at x=4, therefore 4 is a root of the function and (x-4) is a factor of given expression.

Use synthetic method to find the remaining factors.

[tex](x^3-4x^2+4x-16)=(x-4)(x^2+4)[/tex]

[tex](x^3-4x^2+4x-16)=(x-4)(x^2-(2i)^2)[/tex]

[tex](x^3-4x^2+4x-16)=(x-4)(x-2i)(x+2i)[/tex]

Therefore the factor form of given expression is (x-4)(x-2i)(x+2i).

Answer:

(x-4)  (x-2i) (x+2i)

Step-by-step explanation:

x^3−4x^2+4x−16

I will factor by grouping

x^3−4x^2+  4x−16

The first group is the first 2 terms.  I can factor out an x^2

x^2 (x-4) + 4x-16

The second group I can factor out a 4

x^2 (x-4) + 4(x-4)

Now I can factor out (x-4)

(x-4)  (x^2 +4)

We know that x^2 + 4 factors into +2i and -2i  because

(a^2 -b^2) = (a-b) (a+b)  but  we have (a^2 + b^2)  = (a-bi)  (a+bi)

(x-4) (x-2i) (x+2i)

Lets say Alexis received 85, 89, 92, and x points in her four tests.

Average of a data set or the mean of a data set, we need to add all the values together and divide by the number of values in the set.

So here 85, 89, 92, and x are the values of the data set and the number of values are 4 (since there are 4 tests).

[tex]Avg=\frac{sum}{n}[/tex]

where 'n' represents the number of values and sum represents the total sum of the values.

Here we need to know how much Alexis need to score in her next test so that she can have an average of 90.

So we know the value of average that is 90.

Now,

[tex]90 = \frac{85+89+92+x}{4}[/tex]

Solving for 'x' we get:

[tex]90=\frac{266+x}{4}[/tex]

[tex]266+x=90 \times 4[/tex]

[tex]266+x=360[/tex]

Therefore,

[tex]x=360-266=94[/tex]

So, Alexis need to score at least 94 on her next test in order to have an average of at least 90.

The answer is B because you are takin away $50 a week. $200 is what she wants to have at the end off the summer. So that automaticly means it is ≥ 200. She is TAKING AWAY $50 a week. Meaning - 50w ≥ 200. Finally she has $800 to begin with. So, 800 - 50w ≥ 200.

Sorry if l am not very well at explaining this kind of stuff. Let me know if you need anymore help!!

Answer:

The correct option is C.

Step-by-step explanation:

The height of the ball is defined by a parabolic function.

Let the equation of the parabola is

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

Where, (h,k) is the vertex and a is stretch factor.

The maximum height of the ball is 15 feet in 2.2 seconds. So, the vertex is (2.2, 15).

The equation of the parabola is

[tex]f(x)=a(x-2.2)^2+15[/tex]

The initial height of the ball is 0.

[tex]f(0)=a(0-2.2)^2+15[/tex]

[tex]0=a(-2.2)^2+15[/tex]

[tex]a=-\frac{15}{(2.2)^2}[/tex]

[tex]a=-3.1[/tex]

The equation of the parabola is

[tex]f(x)=-3.1(x-2.2)^2+15[/tex]

The function takes 2.2 seconds to reach at maximum height, so after that it will take 2.2 seconds to reach at growth again.

[tex]2.2+2.2=4.4[/tex]

The ball will reach the growth at x=4.4.

The height can not be negative, therefore the value of x lies between 0 to 4.4. The domain of the function is

[tex]0\leq x\leq 4.4[/tex]

Therefore option C is correct.