Please help me out with this

Answer:

1. The correct answer option is B.

2. The correct answer option is C.

4. The correct answer option is D.

Step-by-step explanation:

1. [tex]\frac{3}{x^2+14x+48}[/tex] ÷ [tex]\frac{3}{10x+60}[/tex]

Changing division to multiplication by taking the reciprocal of the latter fraction:

[tex]\frac{3}{x^2+14x+48} \times \frac{10x+60}{3}[/tex]

[tex]\frac{3}{(x+6)(x+8)} \times \frac{10(x+6)}{3}[/tex]

Cancelling the like terms to get:

[tex]\frac{10}{(x+8)}[/tex]

The correct answer option is B. [tex]\frac{10}{(x+8)}[/tex]

2. [tex]\frac{4x^2+36}{4x} \times \frac{1}{5x}[/tex]

Factorizing the terms and then cancelling the like terms to get:

[tex]\frac{4(x^2+9)}{4x} \times \frac{1}{5x}[/tex]

[tex]\frac{x^2+9}{5x^2}[/tex]

The correct answer option is C. [tex]\frac{x^2+9}{5x^2}[/tex].

4. [tex]\frac{\frac{4t^2-16}{8} }{\frac{t-2}{6} }[/tex]

Changing division to multiplication by taking the reciprocal of the latter fraction:

[tex]\frac{4t^2-16}{8} \times \frac{6}{t-2}[/tex]

[tex]\frac{4(t-2)(t+2)}{8} \times \frac{6}{t-2}[/tex]

Cancelling the like terms to get:

[tex]3(t+2)[/tex]

The correct answer option is D. [tex]3(t+2)[/tex].

Answer:

[tex](x-y)^4=x^4-x^3y+6x^2y^2-4xy^3+y^4[/tex].

Step-by-step explanation:

We want to find the polynomial that will result from expanding:

[tex](x-y)^4[/tex].

Recall that we can use the Pascal's triangle to obtain the coefficient as:

1     4    6   4   1

Also note how the negative sign is going to alternate.

The power of x will decrease from left to right while the power of y increases from left to right

The expansion then becomes:

[tex](x-y)^4=x^4-x^3y+6x^2y^2-4xy^3+y^4[/tex].

Answer:

The Answer is A!!!!

Step-by-step explanation:

Answer: It's easy and simple!

Step-by-step explanation: Split it into rectangles and multiply the height and length. Than add it together and Then you have your answer.

Answer:

It depends on the figure.

Step-by-step explanation:

The compound figures we're generally concerned with are combinations of rectangles, triangles, circles or parts of circles, with or without cutouts of those shapes. The area is the sum of the areas of the component shapes, less the areas of any cutouts.

__

Consider the attached examples:

7) This is half a circle together with two triangles. Or, the two triangles can be considered to be a rectangle with a triangular cutout.

The area is the sum of the areas of the semicircle and the rectangle, less the area of the triangular cutout.

__

8) This can be considered as a square with a square cutout. The area is the difference between the area of the larger square and the area of the smaller one. Alternatively, one can find the area by finding the length of the centerline of the shaded area and multiplying that by the width of the shaded area.

__

9) The area of this figure can be considered to be the total of the area of the bottom rectangle and the top triangle. Alternatively, one can cut the figure into two trapezoids (with a vertical line) and sum their areas.

Answer:

8.75 cubic feet

Step-by-step explanation:

Your new dresser will be [tex]\frac{2}{5}^{ths}[/tex] larger than your old dresser.

This means that your new dresser wil be

[tex]1+\dfrac{2}{5}=\dfrac{5+2}{5}=\dfrac{7}{5}[/tex]

of your old dresser.

Your old dresser can hold 6.25 cubic feet, so your new dresser can hold

[tex]\dfrac{7}{5}\cdot 6.25=7\cdot 1.25=8.75\ ft^3[/tex]

Final answer:

To find the volume of the new dresser, find 2/5ths of the old dresser's volume (6.25 cubic feet) and add it to the original volume, resulting in a new dresser's volume of 8.75 cubic feet.

Explanation:

To calculate the volume of the new dresser, which will be 2/5ths larger than the old dresser, we will first determine what 2/5ths of the old dresser's volume is, and then add that to the original volume. The old dresser has a volume of 6.25 cubic feet.

Calculate 2/5ths of 6.25 cubic feet: (2/5) × 6.25 = 2.5 cubic feet

Add the additional volume to the original volume to get the new dresser's volume: 6.25 + 2.5 = 8.75 cubic feet

So, the new dresser will hold 8.75 cubic feet of items.

Answer:

7, 5

Step-by-step explanation:

_________________________________________________

Answer:

7 and 5

Step-by-step explanation:

So we can start with 1 and 4. We can see they added 3 to 1. Ok, that's the first part.

Then, they took 4 and subtracted 2. We can see they subtracted 2. Ok, that's the second part.

We can see they keep doing this:

Add 3, subtract 2. Add 3, subtract 2. and so on, until we get to 4. They just subtracted 2, so we can add 3. So, our first unknown number would be 7. We can then subtract 2, making the second unknown number 5.

Hope I helped, soz if I'm wrong ouo.

~Potato.

Copyright Potato 2019.

Answer:

B. A hamburger sells for $5 but costs $0.15 to make, giving a net income of $3.35.

Step-by-step explanation:

It's the right answer, for many wrong reasons:

- The units aren't the same... since the 5 is expressed in dollars and the the costs would be expressed in cents.

- There could only have one production cost per burger... so it's not a second variable.  

- Of course, the calculation in the statement is also wrong ($5.00 - $0.15 doesn't equal $3.35)

So, for all these three reasons, that statement cannot be expressed in the given equation.

For this case we have by definition, that a hemisphere represents half of a sphere.

Its volume is given by:

[tex]V = \frac {2} {3} \pi * r ^ 3[/tex]

Where "r" represents the radius.

Substituting the data and clearing the radio we have:

[tex]\frac {2} {3} \pi * r ^ 3 = 18 \pi\\\frac {2} {3} * r ^ 3 = 18\\r ^ 3 = 18 * \frac {3} {2}\\r ^ 3 = 27\\r = \sqrt [3] {27}\\r = 3[/tex]

Thus, the radius of the hemisphere is 3 inches.

Answer:

[tex]3 \ in[/tex]

Answer: these nats

Step-by-step explanation:verry carefully

The area of the triangle will be 14 square units. Then the correct option is C.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The triangle ABC with vertices A(2, 3), B(1, -3), and C(-3, 1).

Then the area of the triangle is given as,

A = 1/2 | {[2 x (-3) + 1 x 1 + (-3) x 3] - [3 x 1 + (-3) x (-3) + 2 x 1]} |

A = 1/2 | {[-6 + 1 - 9] - [3 + 9 + 2]} |

A = 1/2 | {-14 - 14} |

A = 1/2 x 28

A = 14 square units  

The area of the triangle will be 14 square units. Then the correct option is C.

More about the triangle link is given below.

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Answer:

see explanation

Step-by-step explanation:

Corresponding angles are associated with parallel lines

L and M would have to be parallel but not so cannot name a corresponding angle.

If they were parallel then ∠7 would correspond to ∠3

Answer:

A) x-3 and D) x+9

Step-by-step explanation:

x^2 + 6x - 27

You need to find two numbers that multiply to -27 and add up to 6

Those two numbers are -3 and 9, because 9 * -3 = -27 and 9+ -3 = 6

So you add those to x and those are your two factored binomials

(x-3) and (x+9)

Answer:

[tex]\texttt{The summation form} = \sum\limits_{n=1}^{15} 3^{(n-1)}=7,174,453[/tex]

Step-by-step explanation:

We can find the total number of shaded triangles in the first 15 figures by first finding the pattern between the first, second, and the third triangles.

We can see that the number of shaded triangles of T₂ is 3 times more compared to T₁. Also, the number of shaded triangles of T₃ is 3 times more compared to T₂. Then we can conclude that the numbers of shaded triangles form a geometric sequence with:

For the summation form, we can find each term using the geometric sequence formula:

[tex]\boxed{U_n=U_1\cdot r^{(n-1)}}[/tex]

[tex]U_n=1\cdot 3^{(n-1)}[/tex]

[tex]U_n=3^{(n-1)}[/tex]

Then, the summation form for the 1st 15 term =

[tex]\displaystyle\sum\limits_{n=1}^{15} 3^{(n-1)}[/tex]

We can also find the summation by using the geometric series formula:

[tex]\boxed{S_n=\frac{U_1(r^n-1)}{r-1} ,\ \texttt{for r > 1}}[/tex]

Then, for S₁₅:

[tex]\begin{aligned}S_{15}&=\frac{U_1(r^{15}-1)}{r-1}\\\\&=\frac{1(3^{15}-1)}{3-1} \\\\&=\bf 7,174,453\end{aligned}[/tex]

Answer:

its the second one

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

the answer is B, is this a lesson or a quiz?

Answer:

(a + b, c )

Step-by-step explanation:

Using the midpoint formula

given 2 points (x₁, y₁ ) and (x₂, y₂ ) then midpoint is

[ [tex]\frac{x_{1}+x_{2}  }{2}[/tex], [tex]\frac{y_{1}+y_{2}  }{2}[/tex] ]

let (x₁, y₁ ) = P(0, 0) and (x₂, y₂ ) = R(2a+2b, 2c), then

midpoint = [ [tex]\frac{0+2a+2b}{2}[/tex], [tex]\frac{2c}{2}[/tex] ]

               = [tex]\frac{2(a+b)}{2}[/tex], c ] = (a + b, c )

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\cos(x+y)[/tex]

Let [tex]v=x+y[/tex], so that [tex]\dfrac{\mathrm dv}{\mathrm dx}-1=\dfrac{\mathrm dy}{\mathrm dx}[/tex]:

[tex]\dfrac{\mathrm dv}{\mathrm dx}=\cos v+1[/tex]

Now the ODE is separable, and we have

[tex]\dfrac{\mathrm dv}{1+\cos v}=\mathrm dx[/tex]

Integrating both sides gives

[tex]\displaystyle\int\frac{\mathrm dv}{1+\cos v}=\int\mathrm dx[/tex]

For the integral on the left, rewrite the integrand as

[tex]\dfrac1{1+\cos v}\cdot\dfrac{1-\cos v}{1-\cos v}=\dfrac{1-\cos v}{1-\cos^2v}=\csc^2v-\csc v\cot v[/tex]

Then

[tex]\displaystyle\int\frac{\mathrm dv}{1+\cos v}=-\cot v+\csc v+C[/tex]

and so

[tex]\csc v-\cot v=x+C[/tex]

[tex]\csc(x+y)-\cot(x+y)=x+C[/tex]

Given that [tex]y(0)=\dfrac\pi2[/tex], we find

[tex]\csc\left(0+\dfrac\pi2\right)-\cot\left(0+\dfrac\pi2\right)=0+C\implies C=1[/tex]

so that the particular solution to this IVP is

[tex]\csc(x+y)-\cot(x+y)=x+1[/tex]

Answer: OPTION B

Step-by-step explanation:

You need to remember that, to subtract radicals, the indices and the radicands must be the same.

Given the expression [tex]3\sqrt{2}-\sqrt{2}[/tex], you can identify that both have index 2 and the radicands are 2 (The numbers that are inside of radicals), therefore, you can conclude that the subtraction can be made.

Then, you must subtract the terms in front of the radicals. Therefore, you get:

[tex]3\sqrt{2}-\sqrt{2}=2\sqrt{2}[/tex]

You can observe that this matches with the option B.

Answer:

The correct answer is option B.  2√ 2

Step-by-step explanation:

It is given that, 3√ 2 – √ 2

To find the correct option

3√ 2 – √ 2  can be written as,

3√ 2 – √ 2  = √ 2 (3 - 1)   taking √ 2  as common

 = √ 2  * 2

 = 2√ 2

Therefore the correct answer is 2√ 2 .

The correct option is option b.  2√ 2

Answer:

10.4 cm

Step-by-step explanation:

The volume (V) of a pyramid is calculated using

V = [tex]\frac{1}{3}[/tex] area of base × height (h)

area of square base = 6² = 36, thus

[tex]\frac{1}{3}[/tex] × 36h = 120

12h = 120 ( divide both sides by 12 )

h = 10 cm

To find the slant height (s) consider the right triangle from the vertex to the midpoint of the base and from the midpoint of base to the side.

That is a right triangle with hypotenuse s and legs 10(h) and 3 (midpoint of the base )

Using Pythagoras' identity then

s² = 10² + 3² = 100 + 9 = 109

Take the square root of both sides

s = [tex]\sqrt{109}[/tex] ≈ 10.4 cm

Answer:

C. 6 kg

Step-by-step explanation:

Let m represent the mass of plates on one side of the barbell. Then the total weight of the barbell is ...

2m +24 = 60 . . . . . kilograms

m +12 = 30 . . . . . . . divide by 2

m = 18 . . . . . . . . . . . subtract 12

The mass of plates on one side of the barbell must total 18 kg. If they all have the same mass, then that must be a divisor of 18. In whole numbers, that would include plates of mass 1, 2, 3, 6, 9, 18 kg.

The only one of these on your list of answer choices is ...

6 kg

7,4 is the answer to the question

Answer:

[tex]x=7/4[/tex]

Step-by-step explanation:

the equation is:

[tex]xy=k[/tex]

To find the value of [tex]x[/tex], we need to substitute the values that we know for [tex]y[/tex] and [tex]k[/tex]:

[tex]y=4[/tex]

and

[tex]k=7[/tex]

so, we substitute this values into the equation

[tex]xy=k[/tex]

[tex]x(4)=7[/tex]

and we clear for [tex]x[/tex], for this we move the 4 to the right dividing:

[tex]x=7/4[/tex]

Answer:

The second photo.

Step-by-step explanation:

If you use a graphing calculator, you can easily find the answer.

Answer:

  see below

Step-by-step explanation:

Comparing the given equation to the standard-form equation of a circle ...

  (x -h)^2 +(y -k)^2 = r^2 . . . . . circle centered at (h, k) with radius r

we find that ...

  h = 2, k = -5, r = 2

So, the circle you're looking for is centered at (2, -5) and has a radius of 2.

Answer:

d. :)

Step-by-step explanation:

Answer:

D. The average rate of change is greater for interval D than for interval C because the line is increasing more quickly at interval D than at interval C.

Step-by-step explanation:

The difference between C and D interval is the lowest.

This means that line is increasing more quickly at interval D as compared to others.

Therefore, option D is the right answer.

Answer:

1

Step-by-step explanation:

The production cost of company 1 never gets below 340 (at x=20), found e.g., by equating the derived function to 0.

You can figure out that g(x) = 0.05x^2 -7x + 300, but you already know that company 1 has higher cost based on the example values for g(x).

Answer:

Hi!

The answer is:

Based on the given information, the minimum production cost for company __1__ is greater.

Step-by-step explanation:

You have to find the minimum value of a f(x), so you need to differentiate it, set it to zero and solve for x. Then differentiate the function again and calculate the value of the second derivative at the maximum or minimum points to find out whether it is a maximum or a minimum.

[tex]f(x) = 0.15x^2 - 6x + 400[/tex]

[tex]\frac{df}{dx}=2 * 0.15x - 6 = 0.30x - 6 [/tex] First derivative.

[tex][tex]\frac{d^2f}{dx^2} = 2 [/tex][/tex] Second derivative. Confirm it's a minimum point.

Minimum occurs at:

0.30x − 6 = 0

0.30x = 6

x = 6/0.30

x = 20

Replace x on equation f(x):

f(20) = 0.15 * 20² - 6 * 20 + 400 = 340.

For g(x), the value of minimum cost is:

g(70) = 55.

Answer:

c

Step-by-step explanation:

Here's how this works:

Get everything together into one fraction by finding the LCD and doing the math.  The LCD is sin(x) cos(x).  Multiplying that in to each term looks like this:

[tex][sin(x)cos(x)]\frac{sin(x)}{cos(x)}+[sin(x)cos(x)]\frac{cos(x)}{sin(x)} =?[/tex]

In the first term, the cos(x)'s cancel out, and in the second term the sin(x)'s cancel out, leaving:

[tex]\frac{sin^2(x)}{sin(x)cos(x)}+\frac{cos^2(x)}{sin(x)cos(x)}=?[/tex]

Put everything over the common denominator now:

[tex]\frac{sin^2(x)+cos^2(x)}{sin(x)cos(x)}=?[/tex]

Since [tex]sin^2(x)+cos^2(x)=1[/tex], we will make that substitution:

[tex]\frac{1}{sin(x)cos(x)}[/tex]

We could separate that fraction into 2:

[tex]\frac{1}{sin(x)}[/tex]×[tex]\frac{1}{cos(x)}[/tex]

[tex]\frac{1}{sin(x)}=csc(x)[/tex]  and  [tex]\frac{1}{cos(x)}=sec(x)[/tex]

Therefore, the simplification is

sec(x)csc(x)

Answer: rotation

Step-by-step explanation:

Rotation is required to map DEF onto D'EF'

Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.

Rotation exists as the operation or act of turning or circling something.

Rotation exists in the circular movement of an object around an axis of rotation. A three-dimensional object may include an infinite numeral of rotation axes.

To know more about rotation refer to :

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Answer:

100 in²

Step-by-step explanation:

Since the figures are similar

the linear ratio of sides = a : b , then

ratio of areas = a² : b²

ratio of sides = 15 : 21 = 5 : 7

ratio of areas = 5² : 7² = 25 : 49

let the area of the smaller figure be x then by proportion

[tex]\frac{25}{x}[/tex] = [tex]\frac{49}{196}[/tex] ( cross- multiply )

49x = 4900 ( divide both sides by 49 )

x = 100

Area of smaller figure is 100 in²

Answer:

True

Step-by-step explanation:

we know that

sin(90°)=1

sin(270°)=-1

sin(-90°)=-sin(90°)=-1

sin(-90°)=sin(270°)

therefore

For sin(x)=-1

the values of x are x=-90° and x=270° ------> is true

To express the given information in a linear equation, the setup time and hourly rate per square foot should be considered in the equation y = 4 + (1/1000)x.

To express the information in a linear equation:

The answer is:

The correct option is:

C) [tex](9^{3})^{3}=9^{9}[/tex]

To solve the problem, we need to remember the power of a power property, it's defined by the following way:

[tex](a^{m})^{n}=a^{m*n}[/tex]

When we have a power of a power, we need to keep the base and then, the new exponent will be the product between the two original exponents.

So, we are given the expression:

[tex](9^{3})^{3}[/tex]

Then, calculating we have:

[tex](9^{3})^{3}=9^{3*3}=9^{9}[/tex]

Hence, we have that the correct option is:

C) [tex](9^{3})^{3}=9^{9}[/tex]

Have a nice day!

Answer:

The correct answer is option C)  9^9

Step-by-step explanation:

Points to remember

Identities

(xᵃ)ᵇ = xᵃᵇ

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

It is given that (9^3)^3

To find the correct option

(9^3)^3 can be written as, (9³)³

By using above identities,

(9³)³ = 9³ ˣ³

 = 9⁹

Therefore the correct answer is option C).  9^9

Answer:

Option B is correct.

Step-by-step explanation:

300 cm^3 of snow melts into 33 cm^3 water. We need to find how much water is produced if 600 cm^3 of snow is melt.

Solving using unitary method:

300 cm^3 of snow melts into water = 33 cm^3

1 cm^3 of snow melts into water = 33/300

600 cm^3 of snow melts into water = 33/300 *600

                                                           = 66 cm^3

So, Option B is correct.

Answer:

b) true

c) false

d) true

e) true

Step-by-step explanation:

b) Any line that contains an interior point of a circle is a secant of the circle. The center is an interior point, so a line that contains the circle center is a secant.

__

c) Chords of different lengths intercept arcs of different measures

__

d) Any line perpendicular to a radius at the point where the radius meets the circle is a tangent to the circle. The endpoint of a diameter is the endpoint of a radius, so a line perpendicular there will be a tangent.

__

e) The measure of an inscribed angle is half the measure of the intercepted arc, so all inscribed angles that intercept equal arcs are equal.

The statement 'If a line contains the center of a circle, it is a secant of the circle.' is true. The statement 'If 2 chords intersect a circle, they intercept equal arcs.' is false. Statements 'If a line is perpendicular to a diameter at one of its endpoints, then it is tangent to the circle.' and 'Inscribed angle that intercept equal arcs are equal.' are both true.

b) True. If a line contains the center of a circle, it does pass through the circle at two points, therefore it's a secant of the circle.

c) False. Two chords intersecting inside a circle do not always intercept equal arcs. The length of the arcs they intercept depends on their distance from the center of the circle, not on the mere fact that they intersect.

d) True. If a line is perpendicular to a diameter at one of its endpoints, it does indeed result in a tangent to the circle. This is because the line touches the circle at exactly one point (the endpoint), fulfilling the definition of a tangent line.

e) True. Inscribed angles that intercept (cut off) equal arcs are indeed equal. This is a basic theorem in circle geometry.

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Answer:

The correct option is D

Step-by-step explanation:

The correct option is D.

They both have the same height, assuming that each coin has same volume, then how can coins in 1 stack have different volume than coins in another stack no matter how you stack them.

Like two cylinders with same base area and height have same volume. Like wise rectangle and parallelogram with same base and same perpendicular height having same area....

D) they have the same volume