Which of the following could be the rectangle's length and width?
(Area = length x width)
Choose all answers that apply:

A) 1 cm and 15 cm
B) 2 cm and 7 cm
C) 3 cm and 5 cm
D) 4 cm and 4 cm

Answer:

Negative

Step-by-step explanation:

x + 5 = -8

Subtract 5 from both sides to get x by itself

x = -13

Answer:

X is negative

Step-by-step explanation:

32 ounces of pure silver were used to make the silver alloy.

Here, we are given that a silversmith combines pure silver that costs $34.48 per ounce with 51 oz of a silver alloy that cost $25.35 per ounce.

Let the amount of pure silver = x oz

Cost of pure silver = $34.48 per ounce

Thus, total cost of pure silver = $34.48x

Similarly, amount of silver alloy = 51 oz

Cost of silver alloy = $25.35 per ounce

Thus, total cost of silver alloy = 25.35 x 51 = $1292.85

Now, the total weight of the new silver allow formed = (x + 51) Oz

and the cost of this new allow = $28.87 per ounce

Thus, the total weight of the new alloy = $28.87 (x + 51)

Hence, we can form the following equation-

$34.48x + $1292.85 = $28.87 (x + 51)

34.48x + 1292.85 = 28.87x + 1472.37

34.48x - 28.87x = 1472.37- 1292.85

5.61x = 179.52

x = 179.52/ 5.61

x= 32

Hence, 32 ounces of pure silver were used to make the silver alloy.

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Answer:

pretty sure it’s addition property of equality since you’re adding 5 to 10

Answer:

The figure is reflected over y = -2

Step-by-step explanation:

If you draw a horizontal line through y = -2, so will see that every point is the same distance from y = -2 but in the opposite direction.  For example, Point w is 3 units above  y= -2 and w' is three units below y = -2. That is true for every point on original to the image.

Answer:

x<0: 0<x<1; x>1

Step-by-step explanation:

The denominator cannot be 0 (since division by 0 is undefined), meaning x cannot be 0 or 1.

So, the domain is x<0: 0<x<1; x>1.

The average number of viewers over the two weeks is 3.85 x 10 ^4

The given parameters are

Week 1 = 3.6 x 10 ^4 viewers

Week 2 = 4.1 x 10 ^4 viewers

The average is calculated as

Average = (Week 1 + Week 2)/2

This gives

Average = (3.6 x 10 ^4 + 4.1 x 10 ^4)/2

Evaluate the sum

Average = (7.7 x 10 ^4)/2

Evaluate the quotient

Average = 3.85 x 10 ^4

Hence, the average number of viewers over the two weeks is 3.85 x 10 ^4

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The volume of the solid thus formed is [tex]\frac{26}{27} \pi[/tex] .

Let us think of any region that is enclosed by a function g(x) and the x-axis between x=a and x=b. If this region is rotated about the x-axis, the solid of rotation that results can be thought of as consisting of thin cylindrical discs with a width of dx and a radius of g (x). Therefore, by integrating the volume of this disc, the whole volume of the solid will be revealed.

Volume=[tex]\int^{a}_{b}\pi [g(x)]^2dx[/tex]

The given function is g(x)=(1/3)x+2 ranging from x=1 to x=3

Therefore volume of the solid formed is:

[tex]\int^{3}_{1}\pi [\frac{1}{3}x]^2dx\\=\int^{3}_{1}\pi [\frac{1}{9}x^2]dx\\=\pi \int^{3}_{1} [\frac{1}{9}x^2]dx\\\\=\pi [\frac{1}{27}x^3 ]^3_1\\= \frac{26}{27} \pi[/tex]

The volume of the solid thus formed is [tex]\frac{26}{27} \pi[/tex] .

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Answer:

8 x b + 9 = 7

Step-by-step explanation:

sum is to add and 8 times means to multiply it by 8

Answer:

w≈8.33

Step-by-step explanation:

Greetings !

Firstly recall rectangle area formula

Thus,

[tex]area \: of \: rectangle \: = length \: \times \: width[/tex]

Given values:-

require value:-

solution/ work-out:-

[tex]width = \: \frac{area \: of \: rectangle}{length} [/tex]

[tex]w = \frac{125}{15} [/tex]

[tex]w = 8.333...[/tex]

Hope it helps !!!

Yes , the equation y =8ˣ  defines y as a function of x.

Yes, because to fulfill the condition of an equation to be a function, a particular value of x must produce only one value of y and y =8ˣ fulfills the condition. This can be also tested using horizontal line test, which only cuts the graph at one point only,

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Answer:

-6

Step-by-step explanation:

1 x -5 is still -5, and the do .2 x -5 = -1 -1+-5= -6

Answer:

-12

Step-by-step explanation:

Given the following question:

7 + (-12) + (-7)
Using PEMDAS:
(-12) + (-7) = -19
7 + -19 = -12
= -12

Hope this helps.

=========================================================

Explanation:

Let's simplify the 7+(-12) portion first

Draw a vertical number line. Plot a point at 7. Then move down 12 units to arrive at -5

Or you could start at -12 and move up 7 units to arrive at -5

This tells us that 7+(-12) = -5

So the overall 7+(-12)+(-7) turns into -5+(-7)

-----------

Draw another vertical number line, or use the one already drawn in the previous section.

Plot a point at -5. Then move down 7 units to arrive at -12

Or start at -7 and move down 5 units to arrive at -12

Therefore, -5 + (-7) = 7+(-12)+(-7) = -12 is the final answer

-----------

Shortcut:

The 7 and -7 in the original expression add to 0. They cancel each other out. So we're left with -12

The value of st is 30.4

As S is the point in RT, it implies that RS+st=Rt. Therefore according to the question,

3x+6x-5=58

⟹9x=58-5

or

9x=53

⟹x=5.9

RS = 3×5.9=17.7

st=(6×5.9)-5=35.4-5=30.4

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-12v+6y+18

you multiply everything by -3, so -3×4v=-12v
-3×(-2y)=6y, since negative × negative=positive
-3×(-6)=18

i hope this helps :)

Answer:

9 26/30 or 9 13/15

Step-by-step explanation:

20/30 6/30

Answer:

9 13/15

Step-by-step explanation:

Answer:

x cannot equal seven, there's a mark for it in RSM menu

Step-by-step explanation:

so the answer is y = -7

Explanation:

A = last year's value = 290,700

B = this year's value = 312,000

C = change in values

C = B - A

C = 312,000 - 290,700 = 21,300

The positive result shows the increase of 21,300 more motorcycles made this year, compared to last year. A negative C value would represent a percent decrease.

Divide this change over the original.

C/A = (21,300)/(290,700) = 0.07327141382869

which is approximate. Let's say we rounded to four decimal places to get 0.0733 which then converts to the percentage 7.33%

By decomposing the figure into simpler ones, we conclude that the area of the irregular figure is 108 square inches.

Here we have an irregular figure that can be decomposed into 3 simpler figures, these are:

Remember that the area of a rectangle is the product between the two dimensions, so the areas of these 3 rectangles are:

a = 6in*8in = 48in^2

a' = 10in*4in = 40in^2

a'' = 5in*4in = 20in^2

Adding these areas we get:

48in^2 + 40in^2 + 20in^2 = 108 in^2

The area of the irregular figure is 108 square inches.

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The two examples can be 1 1/2 & 1 3/4 and 2 2/3 & 1 2/3.

According to Arun,

Sum of two mixed numbers <  Sum of the whole number part +  1

Now, lets take the example as 1 1/2 and 1 3/4

Their sum will be:

1 1/2 + 1 3/4 = 3 / 2 + 7 / 4

= 13 / 4 = 3 1/4

The sum of whole parts = 1 + 1 = 2

Adding 1 to it = 2 + 1 = 3

We can clearly see that 3 1/4 > 3.

It contradicts Arun's statement.

Another example can be:

2 2/3 + 1 2/3 = 8 / 3 + 5 / 3

= 13 / 3 = 4 1/3

Sum of whole part + 1 = 2 + 1 + 1 = 4

4 1/3 > 4

It contradicts Arun's statement.

Therefore, the two examples can be 1 1/2 & 1 3/4 and 2 2/3 & 1 2/3.

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If a parallelogram has an area of 7 square units, and the height corresponding to a base is [tex](\frac{1}{4})[/tex] units, then the base is 28 units.

As per the question statement, a parallelogram has an area of 7 square units, and the height corresponding to a base is [tex](\frac{1}{4})[/tex] units.

We are required to find out the base of the parallelogram.

To solve this question, we need to know the formula to calculate the area of a parallelogram, which goes as

Area of Parallelogram = (Base * Height)

Putting our data obtain from the question statement, in the above-mentioned formula, we can calculate the value of the base of our concerned parallelogram, i.e.,

[tex]7=(base*\frac{1}{4})\\or, base=(7*4)\\or, base = 28[/tex]
Therefore, base of our concerned parallelogram is 28 units.

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Answer: The answer for #2 is JA and TR I took the test:)

Step-by-step explanation:

Q1 option D is the correct answer: The inverse of the statement, If you have read many books, then you have learned many words, is If you haven't read many books, then you haven't learned many words.

Q2 Edges parallel to QP are

The inverse of a statement refers to a statement  that has opposite to the original statement to which the inverse is required. For example:

the statement: John is coming  

inverse of the statement: John is not coming

The edge refers to a side of the prism while parallel refers to a property of line that implies that the edges are equally spaced apart and will never intersect.

The diagram for Q2 is attached

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Answer:

15.1

Step-by-step explanation:

Answer:

its 1/3

Step-by-step explanation:

see picture for referance

The value of the expression p² + 13 will be A. 29.

It should be noted that the expression given is that p² + 13 and we are told that p = -4.

Therefore, we have to put the value of p into the expression. This will be:

p² + 13

= (-4)² + 13

= 16 + 13.

= 29

The value is 29.

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(a) The formula for velocity functions is:

f(t)=0.4t+4

g(t)=0.9t

(b) The slope of the v-t graph gives us the acceleration which as found above is 0.4 ft/sec². The slope of the v-t graph gives us the acceleration which as found above is 0.9 ft/sec².

(c) Damon is accelerating with 0.9 ft/sec² in intervals [4,8].

(d) Both are walking at a velocity of 7.2 ft/sec at t=8 sec.

What is velocity?

(a) For Alicia,

m=(Δv/Δt)=(8-4)/(10-0)=4/10=0.4

f(t)=0.4t+4

for Damon,

m=(Δv/Δt)=(9-0)/(10-0)=9/10=0.9

g(t)=0.9t

The formula for velocity functions is:

f(t)=0.4t+4

g(t)=0.9t

(b) Value and meaning of the slope is

m for Alicia =0.4

Slope is determined (Δv/Δt)=(8-4)/(10-0)=4/10=0.4 ft/sec².

So, the slope of the v-t graph gives us the acceleration which as found above is 0.4 ft/sec².

m for Damon=0.9

Slope is determined (Δv/Δt)=(9-0)/(10-0)=9/10=0.9 ft/sec².

So, the slope of the v-t graph gives us the acceleration which as found above is 0.9 ft/sec².

(c) Value and meaning of the average rate of change on the interval:

the average rate of change of Δ on the interval [4,8] =

[tex]\frac{Velocity\ at\ 8\ sec - Velocity\ at\ 4\ sec}{Time\ interval\ (8-4)\ sec}[/tex]

=(7.2-3.6)/(8-4)=(3.6/4)=0.9 ft/sec²

So, Damon is accelerating with 0.9 ft/sec² in intervals [4,8].

(d) Let both are walking with the same velocity at t sec.

So, Let's equate their velocities

0.4t+4=0.9t

t=4/0.5 = 8 sec

The velocity of Alicia at 8 sec = 0.4(8)+4 = 7.2 ft/sec

The velocity of Damon at 8 sec = 0.9(8) = 7.2 ft/sec

So, both are walking at a velocity of 7.2 ft/sec at t=8 sec.

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Answer: It can.

Step-by-step explanation:

If an 8 oz. cup of juice cost $1.20 and a 12 oz. cup of juice cost $1.44, there is a $0.24 difference between the money and cups of juice in ounces. If there were to be a constant rate of change, a 16 oz. cup of juice MUST cost $1.68

No, the relationship between cost and ounces of juice cannot be described by a constant rate.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

Cost of 8 ounce juice= $1.20

Cost of 12 ounce juice= $1.44

Now,

If the relationship between cost and ounces of juice was described by a constant rate, then the cost per ounce would be the same for both the 8-ounce cup and the 12-ounce cup. However, we can see that the cost per ounce is different for each cup:

For the 8-ounce cup: cost per ounce = $1.20 / 8 ounces = $0.15 per ounce

For the 12-ounce cup: cost per ounce = $1.44 / 12 ounces = $0.12 per ounce

Therefore, by algebra the cost per ounce is different for each cup, the relationship between cost and ounces of juice cannot be described by a constant rate.

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Solve the homogeneous equation

[tex]y'' + 3y' + 2y = 0[/tex]

Its characteristic equation is

[tex]r^2 + 3r + 2 = (r + 1) (r + 2) = 0[/tex]

with roots at [tex]r=-1[/tex] and [tex]r=-2[/tex], hence the characteristic solution is

[tex]y_c = C_1 e^{-x} + C_2 e^{-2x}[/tex]

For the nonhomogeneous equation, I'll use variation of parameters. We're looking for a solution of the form

[tex]y = u_1 y_1 + u_2 y_2[/tex]

to the equation

[tex]y'' + a(x) y'' + b(x) y = f(x)[/tex]

such that

[tex]\displaystyle u_1 = - \int \frac{y_2f(x)}{W(y_1,y_2)} \, dx[/tex]

[tex]\displaystyle u_2 = \int \frac{y_1 f(x)}{W(y_1,y_2)} \, dx[/tex]

The Wronskian [tex]W(y_1,y_2)[/tex] of the two fundamental solutions [tex]y_1=e^{-x}[/tex] and [tex]y_2=e^{-2x}[/tex] is

[tex]W(y_1,y_2) = \begin{vmatrix} y_1 & y_2 \\ {y_1}' & {y_2}' \end{vmatrix} = -e^{-3x}[/tex]

Then we have

[tex]\displaystyle u_1 = - \int \frac{e^{-2x} \cdot 4e^x \cos(3x)}{-e^{-3x}} \, dx = 4 \int e^{2x} \cos(3x) \, dx[/tex]

[tex]\displaystyle u_2 = \int \frac{e^{-x} \cdot 4e^x \cos(3x)}{-e^{-3x}} \, dx = -4 \int e^{3x} \cos(3x) \, dx[/tex]

Recall Euler's identity,

[tex]e^{(a+bi)t} = e^{at} (\cos(bt) + i \sin(bt))[/tex]

Then we have the general antiderivative

[tex]\displaystyle \int e^{(a+bi)t} \, dt = \frac1{a+bi} e^{(a+bi)t} + C = \frac{a-bi}{a^2+b^2} e^{(a+bi)t} + C[/tex]

Taking the real parts of both sides, we have

[tex]\displaystyle \mathrm{Re}\left\{\int e^{(a+bi)t} \, dt \right\} = \mathrm{Re}\left\{\frac{a-bi}{a^2+b^2} e^{(a+bi)t} + C\right\} \\\\ \int\,\mathrm{Re}\left\{e^{(a+bi)t}\right\} \, dt = \frac{e^{at}}{a^2+b^2} \mathrm{Re}\left\{(a-bi)(\cos(bt) + i \sin(bt))\right\} + C \\\\ \int e^{at} \cos(bt) \, dt = \frac{e^{at}}{a^2+b^2} (a\cos(bt)+b\sin(bt)) + C[/tex]

so that

[tex]\displaystyle u_1 = 4 \int e^{2x} \cos(3x) \, dx = \frac{4e^{2x}}{13} (2\cos(3x) + 3 \sin(3x))[/tex]

and

[tex]\displaystyle u_2 = -4 \int e^{3x} \cos(3x) \, dx = -\frac{2e^{3x}}3 (\cos(3x) + \sin(3x))[/tex]

We've found

[tex]y = u_1 y_1 + u_2 y_2[/tex]

[tex]\displaystyle y = \frac{4e^x}{13} (2\cos(3x) + 3 \sin(3x)) - \frac{2e^x}3 (\cos(3x) + \sin(3x))[/tex]

[tex]\displaystyle y = \frac2{39} e^x (5\sin(3x) - \cos(3x))[/tex]

Then the general solution to the differential equation is

[tex]\boxed{y(x) = C_1 e^{-x} + C_2 e^{-2x} + \frac2{39} e^x (5\sin(3x) - \cos(3x))}[/tex]