What are the coefficients in 3x+4-5+6y?
Group of answer choices

x and y

-5 and 4

3 and 6

4 and 5

The conditions would be represented by the following set of inequalities:

An inequality can be defined as a mathematical relation for comparing two (2) or more integers or variables in an equation based on any of the following:

In this scenario, the ratio of fruit to nuts in the crunchy trail mix is equal to 1:3. Therefore, 1/4 of each bag contain fruits while 3/4 contain nuts.

Mathematically, these conditions would be represented by the following set of inequalities:

1/2 × (c + 5f) ≤ 30  ⇒ c + 5f ≤ 60.

1/2 × (3c + 3f) ≤ 50  ⇒ 3c + 3f ≤ 100.

c ≥ 0. f ≥ 0.

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Answer :

a) It is given that

Everyday a machine makes 500000 staples and puts them into the boxes.

The machine need 170 staples to fill a box

One box contans = 170 staples.

Total number of staples = 500000

Number of box required to fill 500000 staples = Total number of staples/No. of staples 1 box contains.

\( \: :\implies \) 500000 /170

\( :\implies \: \) 2941 (approx)

Therefore, 2941 boxes are required to fill with 500000 staples.

b) It is given that,

Each staple is made of 0.21 g of metal .

Total weight of metal = 1 kg = 1000 g

1 staple = 0.21 g

Number of staples = weight of metal/ Weight of 1 staple.

\( \: :\implies \) 1000/0.21

\( \: :\implies \) 4761 (approximately)

Therefore, 4761 staples can be made from 1 kg of the metal.

The coefficient of the second term, 6x⁴, is 6.

The terms of the polynomial are:

-4y⁵, 6x⁴, 9w³, -4w, -1

The coefficient of the second term, which is 6x⁴, we look at the number in front of the variable term.

The coefficient is 6.

Therefore, the list of terms is:

-4y⁵, 6x⁴, 9w³, -4w, -1

Each term represents a separate component of the polynomial, where the variable is raised to a certain power and multiplied by its coefficient.

The coefficients indicate the scalar value by which each term is multiplied.

The polynomial's terms are -4y5, 6x4, 9w3, -4w, and -1.

Looking at the number in front of the variable term, we can determine the second term's coefficient, which is 6x4.

There is a 6 coefficient.

As a result, the terms are as follows: -4y5, 6x4, 9w3, -4w, and -1.

Each term represents a different part of the polynomial, where the variable is multiplied by its coefficient and raised to a given power.

The scalar value by which each phrase is multiplied is shown by the coefficients.

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Answer:

40 ft

Step-by-step explanation:

(i do not have a step by step explanation but it's correct.)

Answer:

p = 6

Step-by-step explanation:

5 + 2/3 (2p - 6) = 9

5 + 4/3p - 4 = 9

1 + 4/3p = 9

4/3p = 8

p = 6

Answer:

p= 6

Step-by-step explanation:

Solve for p:

(2 (2 p - 6))/3 + 5 = 9

Put each term in (2 (2 p - 6))/3 + 5 over the common denominator 3: (2 (2 p - 6))/3 + 5 = 15/3 + (2 (2 p - 6))/3:

(15/3 + (2 (2 p - 6))/3) = 9

15/3 + (2 (2 p - 6))/3 = (2 (2 p - 6) + 15)/3:

((2 (2 p - 6) + 15)/3) = 9

2 (2 p - 6) = 4 p - 12:

((4 p - 12) + 15)/3 = 9

Grouping like terms, 4 p - 12 + 15 = 4 p + (15 - 12):

(4 p + (15 - 12))/3 = 9

15 - 12 = 3:

(4 p + 3)/3 = 9

Multiply both sides of (4 p + 3)/3 = 9 by 3:

(3 (4 p + 3))/3 = 3×9

(3 (4 p + 3))/3 = 3/3×(4 p + 3) = 4 p + 3:

(4 p + 3) = 3×9

3×9 = 27:

4 p + 3 = 27

Subtract 3 from both sides:

4 p + (3 - 3) = 27 - 3

3 - 3 = 0:

4 p = 27 - 3

27 - 3 = 24:

4 p = 24

Divide both sides of 4 p = 24 by 4:

(4 p)/4 = 24/4

4/4 = 1:

p = 24/4

The gcd of 24 and 4 is 4, so 24/4 = (4×6)/(4×1) = 4/4×6 = 6:

Answer: p = 6

Answer:

Part A)

2048π/3 cubic units.

Part B)

8192π/15 units.

Step-by-step explanation:

We are given that R is the finite region bounded by the graphs of functions:

\(f(x)=4\sqrt{x}\text{ and } g(x)=x\)

Part A)

We want to find the volume of the solid of revolution obtained when rotating R about the x-axis.

We can use the washer method, given by:

\(\displaystyle \pi\int_a^b[R(x)]^2-[r(x)]^2\, dx\)

Where R is the outer radius and r is the inner radius.

Find the points of intersection of the two graphs:

\(\displaystyle \begin{aligned} 4\sqrt{x} & = x \\ 16x&= x^2 \\ x^2-16x&= 0 \\ x(x-16) & = 0 \\ x&=0 \text{ and } x=16\end{aligned}\)

Hence, our limits of integration is from x = 0 to x = 16.

Since 4√x ≥ x for all values of x between [0, 16], the outer radius R is f(x) and the inner radius r is g(x). Substitute:

\(\displaystyle V=\pi\int_0^{16}(4\sqrt{x})^2-(x)^2\, dx\)

Evaluate:

\(\displaystyle \begin{aligned} \displaystyle V&=\pi\int_0^{16}(4\sqrt{x})^2-(x)^2\, dx \\\\ &=\pi\int_0^{16} 16x-x^2\, dx \\\\ &=\pi\left(8x^2-\frac{1}{3}x^3\Big|_{0}^{16}\right)\\\\ &=\frac{2048\pi}{3}\text{ units}^3 \end{aligned}\)

The volume is 2048π/3 cubic units.

Part B)

We want to find the volume of the solid of revolution obtained when rotating R about the y-axis.

First, rewrite each function in terms of y:

\(\displaystyle f(y) = \frac{y^2}{16}\text{ and } g(y) = y\)

Solving for the intersection yields y = 0 and y = 16. So, our limits of integration are from y = 0 to y = 16.

The washer method for revolving about the y-axis is given by:

\(\displaystyle V=\pi\int_{a}^{b}[R(y)]^2-[r(y)]^2\, dy\)

Since g(y) ≥ f(y) for all y in the interval [0, 16], our outer radius R is g(y) and our inner radius r is f(y). Substitute and evaluate:

\(\displaystyle \begin{aligned} \displaystyle V&=\pi\int_{a}^{b}[R(y)]^2-[r(y)]^2\, dy \\\\ &=\pi\int_{0}^{16} (y)^2- \left(\frac{y^2}{16}\right)^2\, dy\\\\ &=\pi\int_0^{16} y^2 - \frac{y^4}{256} \, dy \\\\ &=\pi\left(\frac{1}{3}y^3-\frac{1}{1280}y^5\Bigg|_{0}^{16}\right)\\\\ &=\frac{8192\pi}{15}\text{ units}^3\end{aligned}\)

The volume is 8192π/15 cubic units.

Step-by-step explanation:

yes there is a distance formula

\(distance = \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} } \)

let me do 15th question, in this i take distance between Point W(-4,2)and X(-2,4)

WX=√[(-4 - -2)² +(2-4)²]

WX= √[(-2)²+(-2)²]

WX= √4+4

WX=√8

Similarly find XY ,YZ ,ZW you will get

XY= √8

YZ=√8

ZW=√8

ALL SIDES ARE EQUAL THAT MEANS ITS SQUARE

ALL SQUARES ARE RECTANGLE BECAUSE ITS HAVE PARALLEL SIDES AND ANGLES ARE 90°

ALL SQUARES ARE RHOMBUS BECAUSE ALL SIDES ARE EQUAL

ALL SQUARES ARE PARALLELOGRAM BECAUSE ALL SIDES ARE PARALLEL

so in this question it will be parallelogram, square, rectangle , RHOMBUS

Hope u do the same thing in 17 , 18 and 19

Answer: R(7, 9), S(6, 7), T(2, 3), U(8, 5), V(5, 5)

Answer:

Sam and Tom

Step-by-step explanation:

5 × 2= 10

6 × 2= 12

5/6= 10/12

The highest height for the daily rainfall were for 5 and 6 inches

Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.

From the given dot plot, we see the number of times for each height of rainfall.

Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.

Thus, we conclude those were the highest heights for the daily rainfall.

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The full question with the answer options is as follows:

Each figure below represents a fraction. Which figure is NOT equivalent to the others?

the answer options are as follows:

a.  \(\frac{2}{3}\)

b.  \(\frac{4}{6}\)

c.  \(\frac{3}{4}\)

d. \(\frac{8}{12}\)

Answer:

The correct answer is c:

Step-by-step explanation:

To know when two or more fractions are equivalent, we must multiply the numerator of one fraction by the denominator of the other fraction, the result must be the same value.

\(\frac{2}{3} x \frac{4}{6}\) =   (2x6) =12   ;  (3x4)=12

\(\frac{2}{3} x \frac{8}{12}\) = (2x12)=24 ;    (3x8) =24

\(\frac{4}{6} x \frac{8}{12}\) = (4x12)=48;     (6x8)=48

\(\huge\boxed{\boxed{\bold{10\ \bftext{minutes}}}}\)

\(\hrulefill\)

First, let's change both of these times into just minutes. (We know that one hour is sixty minutes.)

\(\text{First time: } 1*60+25=60+25=85\)

\(\text{Second time: } 1*60+\frac{1}{4}*60=60+15=75\)

Now, just subtract:

\(85-75=\large\boxed{10}\)

Answer:

2\(\pi\) \(units^{2}\)

Step-by-step explanation:

BC is equal to 4 because 5*4=20.

The radius is 2. The equation for the area of a circle is \(\pi r^2\).

Therefore, if we plug in 2 we will get \(4\pi\).

But then we divide by 2 to get 2\(\pi\) \(units^{2}\) as our answer.

Hope this helped! :)

Answer:

p=14 ft

Step-by-step explanation:

The figure that meets these conditions is the square

The perimeter:

4(3.5) = 14 ft.

Hope this helps

The simplified sum of the second and forth integers are; -1 + 5 = 4

An integer is defined as a whole number that can be positive, negative, or zero. Examples of integers are: -7, 2, 9, 18, 125, and 9803

Now, we are given the consecutive integer sequence as;

x, 1, 3, 5

Now, since the integers are consecutive, then the common difference is the same. Thus;

1 - x = 3 - 1

1 - x = 2

x = 1 - 2

x = -1

Sum of first and fourth term = -1 + 5 = 4

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Answer:

29.8%

Step-by-step explanation:

\(\frac{3+19+46+23+52+6+11+47+51+32+1+15+82}{13} \approx 29.8\%\)

Answer:

x = 2

Step-by-step explanation:

8 = 6x + -2x

8 = 4x

8 = 4x

4 4

2 = x

Answer

6 is the correct answer.

Step-by-step explanation:

You need to know sin(60) = root(3)/2 = a/(4root(3)), then you can solve for 'a', get a = 6.

Answer:

Step-by-step explanation:

B is the midpoint of AC. It means:

And we have a common side BD:

a) As per above we only have two sides congruent and this information is not sufficient to state the triangles ABD and CBD are congruent.

b) In addition to the two sides we also have:

With this additional information we have three sides congruent, so the triangles are congruent by SSS postulate.

The required probability is 3 √7 / 32.

Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.

Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7

The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is:  P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.

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Answer:

306.25-156.25/70-50 =150/20=7.5 ft/mph

Step-by-step explanation:

For every 1 mph over 50 mph a car is traveling, its braking distance increases by 7.5 ft

The required braking distance between the one that can travel at 50 mph and one traveling at 70 mph is 7.5 ft/mph.

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,
Distance traveled when applying brake when speed is 70 mph is 306.25,
Distance traveled when applying brake when speed is 50 mph is 156.25 ft

The rate of change of braking is given as,

= 306.25-156.25/70-50
= 150/20
=7.5 ft/mph

Thus, the required braking distance between the one that can travel at 50 mph and one traveling at 70 mph is 7.5 ft/mph.

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The 5 is in the hundreds place so the value of the 5 is 500.

Subtracting 1 from 5 the number becomes 4 ( 5-1 = 4) which would mean the new value would be 400

The answer is b. 400

1.

The location of w and t on the number line arenot exact so you will need to approximate .

In the first point w, it is between -4 and - 3 but closer than -4 compared to -3.Additionally, the point w is located at a position greater than -3.5 .It will be okay to approximate point w at -3.6.

w= -3.6

In the second point t, it is located between 0 and 1 but closer to 0 than 1. Additionally, t is less than 0.5 because it is located at a position less than 0.5, hence it is approximately at : t = 0.4

w= -3.6 and t = 0.4 -------approximated actual values

The two real numbers for w and t will be :

w= - 4 and t = 0 ---------approximated real numbers.

NB;

w= -3.7 and t= 0.3 is also a correct approximate because the difference of +/- 0.1 can be allowed for this case.

Answer:

Hello, the answer is 141.82

hope this helps

Step-by-step explanation: