The doctor tells Evelyn that she needs to exercise enough to burn at least 700 calories each day. She prefers practicing yoga or jogging. While practicing yoga she burns 5 calories per minute, and while jogging she burns 8 calories per minute. Let x be the number of minutes she spend practicing yoga and let y be the number of minutes she spends jogging. Write an inequality that models this situation.

Answer:

same slope, different intercepts (parallel lines essentially)

Step-by-step explanation:

The number sentence that applies the commutative property to the example is 4 × 3 = 12

Commutative property can be additive or multiplicative. It is a way of changing the position of a function or value in an expression without affecting the result

Examples are

A +B = B +A

AB = BA

Although the value were interchanged, the result were not affected. Hence the number sentence that applies the commutative property to the example is 4 × 3 = 12 since changing 3 and 4 does not affect the result

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The surface area of trapezoidal prism is: D. 385.6 yd².

Surface area = (b1 + b2)h + PH.

The parameters are:

b1 = 10 yd

b2 = 6 yd

h = 4.6 yd

Perimeter of base (P) = 6 + 10 + 5 + 5 = 26 yd

H = 12 yd

Plug in the values

Surface area = (10 + 6)4.6 + (26)(12)

Surface area = 385.6 yd²

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The combinations of ordered triplets that are possible is equal to: A. 18.

Since the common difference (d) between the consecutive terms in an arithmetic progression (AP) is constant, we have:

d = y - x = z - y

Rearranging the terms, we have:

x = y - d

z = y + d

From the given equation:

x + y + z = 30

y - d + y + y + d = 30

3y = 30

y = 30/3

y = 10.

So the arithmetic progression (AP) is given by:

(10 - d), 10, (10 + d)....

Since the common difference (d) is a natural number which would be from 1 to 9, the combinations of ordered triplets that are possible is as follows:

Number of possibilities = 9 × 2

Number of possibilities = 18.

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Complete Question:

If x, y, z are three natural numbers in A.P. such that x + y + z = 30 then the possible number of ordered triplet (x, y, z) is?

A. 18

B. 19

C. 20

D. 21

The monthly interest payment is 162

Interest, in its most simple form, is calculated as a percent of the principal.

First,

monthly interest rate,

= 0.24/12

= 0.02.

Now,

Average monthly interest,

=0.02×$675

= $13.50.

Thus, the annual interest payments,

= 12×$13.50

= $162

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Answer: I prefer to find the area of the base first and then multiply by the height

Answer:

The perimeter of the garden is [tex]12a[/tex].

Step-by-step explanation:

[tex]3a+14+4(a-6)+10+5a=12a[/tex]

Answer:

Step-by-step explanation:

The vertex and direction of opening can be read from the vertex-form equation of a quadratic.

Consider the "parent" quadratic function ...

  y = x²

For this function, the value of y cannot be negative. Larger positive values of x will give larger positive values of y. And, negative values of x that have greater magnitude (are farther from the y-axis) will also give larger positive values of y.

This means that the farther away from the y-axis an x-value is, the farther away from the x-axis is the corresponding y-value. The graph of this is said to "open upward." This will be the case for any positive coefficient of x². (Red graph in the first attachment.)

If the coefficient of x² is negative, then larger-magnitude x-values result in more negative y-values. This makes the graph "open downward." (Blue graph in the first attachment.)

The vertex form of a quadratic equation is ...

  y = a(x -h)² +k . . . . . . vertex (h, k); vertical scale factor 'a'

The value of 'a' is the coefficient of the x² term when this is simplified to standard form: y = ax² +bx +c. That is, the sign of 'a' tells you whether the graph opens upward (a > 0) or downward (a < 0).

The other constants in the vertex form equation tell you how the function has been translated. The value of k is a vertical translation quantity. Since it is added to each function value, it tells the number of units the function is translated upward.

The value h is a horizontal translation quantity. It seems slightly counter-intuitive that the function graph is translated to the right h units when h is subtracted from the x-value. That is the case.

As you may have noticed from the graphs in the first attachment, the vertex (turning point) of the parent function graph is at (x, y) = (0, 0). The vertex of the function ...

  y = a(x -h)² +k

is located at (x, y) = (h, k).

You want the opening direction of y = -2(x +3)² -1. You need look no further than the leading minus sign. It tells you the graph opens downward. (Red graph in the second attachment.)

Of course, the -1 at the end of the equation is the vertical translation of the vertex. That vertex is (-3, -1), as shown by the graph.

You want the vertex of y = -1/2(x +5)² +7. Writing this so the binomial term has a minus sign, we have ...

  y = -1/2(x -(-5))² +7

Comparing this to the vertex form ...

  y = a(x -h)² +k

we identify the parameters to be ...

  a = -1/2 . . . . opens downward

  h = -5

  k = 7 . . . . the vertex is (h, k) = (-5, 7)

The graph is the blue graph in the second attachment. It opens downward and has its vertex at (-5, 7).

__

Additional comment

A lot of math is about matching patterns. Here, you're asked to match the given equations to the "vertex form" pattern, and identify corresponding parts of the pattern: the leading coefficient (a), the horizontal translation (h), and the vertical translation (k). Once you know what the parts of the pattern mean, you can answer the questions easily.

Answer:

[tex]f=-18a^2+3[/tex]

Step-by-step explanation:

Given equation:

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

[tex]\textsf{Apply exponent rule} \quad (ab)^n=a^n b^n:[/tex]

[tex]\implies f=3-2(3^2a^2)[/tex]

Rewrite 3² as 9:

[tex]\implies f=3-2(9a^2)[/tex]

Remove the parentheses:

[tex]\implies f=3-2 \cdot 9a^2[/tex]

Multiply the numbers 2 · 9 = 18 :

[tex]\implies f=3-18a^2[/tex]

Rearrange to make the variable the first term:

[tex]\implies f=-18a^2+3[/tex]

Answer:

Option D

Step-by-step explanation:

This function has vertex at origin

Let's verify

Put (0,0)

Hence verified

Answer:

[tex]f(x)=-x^2[/tex]

Step-by-step explanation:

Vertex form of a quadratic function:

  [tex]y=a(x-h)^2+k[/tex]  

where:

If the vertex is at the origin:

Substituting the vertex into the equation:

[tex]\implies y=a(x-0)^2+0[/tex]

[tex]\implies y= ax^2[/tex]

Comparing with the available answer options:

[tex]f(x)=-x^2[/tex]  has its vertex at the origin.

Additional Information:

[tex]\textsf{The vertex of }\:f(x)=(x+4)^2 \: \textsf{ is }\:(-4,0)[/tex]

[tex]\textsf{The vertex of }\:f(x)=x(x-4) \: \textsf{ is }\:(2,-4)[/tex]

[tex]\textsf{The vertex of }\:f(x)=(x-4)(x+4) \: \textsf{ is }\:(0,-16)[/tex]

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Answer:

a = sqrt(c^2 - b^2)

see image.

Step-by-step explanation:

If you square both sides of the equation, you get the Pythagorean Theorem back again.

c = sqrt(a^2 + b^2)

c^2 = a^2 + b^2

Solve for a means to get a all by itself on one side of the equation. Subtract b^2 and then take the square root. See image.

[tex]y = 2x {}^{2} + e {}^{ - x {}^{4} } [/tex]

[tex] \frac{dy}{dx} = 4x +( e {}^{ - x {}^{4} } )( - 4x {}^{3} )[/tex]

[tex] \frac{dy}{dx} = 4x - 4x {}^{3} e { }^{ - x {}^{4} } [/tex]

[tex] \frac{dy}{dx} = 4x(1 - x {}^{2} e {}^{ - x {}^{4} } )[/tex]

[tex] \frac{dy}{dx} = 0 \\ 4x = 0 \: \: \: \: \: 1 - x {}^{2} e {}^{ - x {}^{4} } = 0[/tex]

[tex]4x = 0 \\ x = 0 \: \: \: \: \: \: y(0) = 0 + e {}^{0} = 1[/tex]

Answer:

  18x

Step-by-step explanation:

The HCF is the highest factor common to both expressions. We can find it by factoring both expressions and identifying common factors.

  36(x³+x²y-12xy²) = 18x·2·(x +4y)(x -3y)

  54(x³y+4x³y²-21xy) = 18x·3y·(x +7)(x -3)

The highest common factor is 18x.

In a playing card there are 52 cards. (i) '2' of spades: Number of favourable outcomes i.e. '2' of spades is 1 out of 52 cards.

The area of the square of the leg 6 is 36 square units.

The area of the square of the leg 8 is 64 square units.

The area of the square of the hypotenuse square is 100 square units.

The length of the hypotenuse is 10 units.

Formula Used

Area of square, A = [tex](a)^{2}[/tex]

Here, [tex]a[/tex] is the length of the side of the square.

Pythagoras Theorem is given as,

[tex]h^{2} =p^{2} +b^{2}[/tex]

Here, [tex]h, p, b[/tex] are the hypotenuse, perpendicular, and the base of a right angle triangle respectively.

Area of the Square of the Leg 6

Length of the edge of the square = 6 units

Area of square = 6*6

= 36 square units

Area of the Square of the Leg 8

Length of the edge of the square = 8 units

Area of square = 8*8

= 64 square units

Area of the Hypotenuse Square and the Length of the Hypotenuse

Applying Pythagoras theorem,

[tex]h^{2} = (8)^{2} +(6)^{2}[/tex]

[tex]h^{2} = 64+36[/tex]

[tex]h = \sqrt{100}[/tex]

[tex]h = 10 units[/tex]

Therefore, the area of the hypotenuse square is 100 square units and the length of the hypotenuse comes out to be10 units.

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Answer: in the picture

Step-by-step explanation:

Solution: Check the picture I uploaded.

The angle-bisector construction can be used to bisect any angle and this is proven by:

The angle-bisector construction means that a line is made that can divide an angle into two congruent angles.

This is shown by the fact that all the radii of a circle are congruent and that the corresponding parts of congruent triangles are also congruent (CPCTC) when an angle bisector is made on a circle or triangle respectively.

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the sequence is:

Translation, then reflection.

The correct option is the second one.

We start with figure 1.

In the image, we can see that the image is shifted 4 units up and 4 units left to make figure 2.

Then you can see that the image is reflected across a horizontal line to make figure 3, you can see that because now the "L" is facing upwards.

Then the sequence is:

Translation, then reflection.

The correct option is the second one.

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Answer:

you can use the spreadsheet

Answer:

  -4sin(2x)

Step-by-step explanation:

Angle sum identities can be used to simplify this expression.

The cosine function is even, so cos(-x) = cos(x). The cosine of the sum is ...

  cos(90°+x) = cos(90°)cos(x) -sin(90°)sin(x) = -sin(x)

Then the numerator simplifies to ...

  4cos(-x)cos(90°+x) = -4cos(x)sin(x) = -2sin(2x)

Matching the denominator expression to the sine of a sum relation, we see

  sin(30° -x)cos(x) +sin(x)cos(30° -x) = sin((30°-x) +x) = sin(30°) = 1/2

The simplified expression is the ratio of the simplified numerator to the simplified denominator:

  = -sin(2x)/(1/2)

  = -4sin(2x)

f(x) = x^4 - 5x^3 + x^2 + 21x - 18

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

Explanation:

The root x = -2 means x+2 is a factor. This is because we add 2 to both sides of x = -2 to get x+2 = 0.

Similarly, x = 3 leads to x-3 being another factor. It's a double root so we really have two copies of (x-3)

The last root is x = 1 which gives the factor x-1.

The four factors are: (x+2)(x-3)(x-3)(x-1)

Let's use the FOIL rule to expand out the first two factors

(x+2)(x-3) = x^2-3x+2x-6 = x^2-x-6

Do the same for the last two factors

(x-3)(x-1) = x^2-1x-3x+3 = x^2-4x+3

--------------------

So far we have:

(x+2)(x-3) = x^2-x-6

(x-3)(x-1) = x^2-4x+3

which leads to  

(x+2)(x-3)(x-3)(x-1) = (x^2-x-6)(x^2-4x+3)

From here I'll use the box method to multiply these trinomials. Check out the diagram below. Each inner cell is the result of multiplying the headers. Example: x^2 times x^2 = x^4 in the upper left corner.

I've color-coded the inner cells to show the like terms. Add up those like terms:

Therefore we end up with

(x^2-x-6)(x^2-4x+3) = x^4 - 5x^3 + x^2 + 21x - 18 which is choice B

--------------------

To verify this answer, plug in x = 0 and you should get y = -18 to show that we have the correct y intercept. If we tried this with choice A, then we'd get y = 18 which helps eliminate choice A.

Furthermore, plug in x = -2 into choice B and you should get y = 0 as an output. The same applies to x = 3 and x = 1. This confirms that they are roots or x intercepts of the polynomial.

Another way to verify the answer is to use something like WolframAlpha to type in (x+2)(x-3)(x-3)(x-1). Under the "expanded form" subsection, it says x^4 - 5x^3 + x^2 + 21x - 18

Given that, one digit of a two digit number is three times the other digit.

Let assume that digit at ones place be x.

digit at ones place be x.So, digit at tens place be 3x.

digit at ones place be x.So, digit at tens place be 3x.So, two digit original number = 10 × 3x + 1 × x = 30x + x = 31x

Now, number formed on interchanging its digits, i.e.

Reverse number = 10 × x + 1 × 3x = 10x + 3x = 13x

According to statement, if we interchange the digits of this two digit number and add the resulting number to the original number, we get 88.

[tex]\begin{gathered}\sf \: 31x + 13x = 88 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: 44x = 88 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: x = \dfrac{88}{44} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf\implies \: x = 2 \\ \\ \end{gathered}[/tex]

So, two digit number is 31 × 2 = 62

Hence,

[tex]\begin{gathered}\sf\implies \: \boxed{ \bf{ \:Original \: number \: = \: 62 \: \: }} \\ \\ \end{gathered}[/tex]

[tex]\rule{190pt}{2pt}[/tex]

Answer:

26 or 62

Step-by-step explanation:

If one of the two digits of a two-digit number is three times the other digit, then the options for the two-digit number are:

If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88.

From inspection of the listed pairs of numbers, the only pair that sums to 88 is 26 and 62:

⇒ 26 + 62 = 88

Therefore, the original number is either 26 or 62.

The function for the given situation is f(x)=35.0-0.7x.

Given that, Mark bought 10 pound of two types of candies, caramel candies for $2.80 per pound and chocolate candies for $3.50 a pound.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Now, the function for the given situation is as follows:

If x is the weight of the less expensive candy, the 10-x is the weight of the high expensive candy.

So, f(x)=2.80x+3.50(10-x)

⇒ f(x)=2.80x+35.0-3.50x

⇒ f(x)=35.0-0.7x

Therefore, the function for the given situation is f(x)=35.0-0.7x.

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Answer:

p=10

Step-by-step explanation:

-7+p=3

+7-7+p=3+7

p=10

Answer:

Hello! The answer to this question is 10.

Step-by-step explanation:

You have to get p by itself so we will add 7 to both sides:

-7 + p = 3

+7        +7

-------------

p = 10

When doing so, we get p = 10.

You can check your work:

-7 + 10 ⇒ 10 - 7 = 3

Therefore, p = 10 is the correct answer.

Answer:

Anne has n

Fiona has 3n

3n=6

so n=2

so Anne have 2

The price of the washer and the dryer set is $720.

The commission earned by Alice is $36.

Percentage can be described as a fraction an amount expressed as a number out of hundred. Percentage is a measure of frequency.

Price after the mark up = ( + percentage mark up) x cost price

(1  + 0.20) x $600  = $720

Commission earned by Alice = 5% x 720 = $36

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Answer:

step-by-step explanation:

A 7/1 ARM is a mortgage that has a fixed interest rate in the beginning, then switches to an adjustable or variable one. The 7 in 7/1 indicates the initial fixed period of seven years. After that, the interest rate adjusts once yearly based on the index stated in the loan agreement, plus a margin set by the lender.

Answer: 1/12

Step-by-step explanation:

The total area of the rectangle needs to be 1.

Since 20-8=12, the height needs to be 1/12.

1. The Year-0 net cash flow is -$1,061,500.

2. The net operating cash flows in Years 1, 2, and 3 are as follows:

Year 1: $288,750 ($386,000 x 1 - 0.25)

Year 2: $288,750 ($386,000 x 1 - 0.25)

Year 3: $288,750 ($386,000 x 1 - 0.25)

3. The additional Year-3 cash flow (i.e, the after-tax salvage and the return of working capital) is $468,750 {($599,000 x 1 - 0.25) + $19,500}.

4. The NPV of the project is ($13,139).

5. The machine should not be purchased because it does not yield a positive NPV.

The net present value (NPV) shows the difference between the present value of cash inflows and the present value of cash outflows over a period of time.

It is determined by calculating the present values of cash flows using their present value factors as below:

Initial cash outlay = $1,061,500 ($1,020,000 + $22,000 + $19,500)

Salvage value = $599,000

Increase in net working capital = $19,500

Annual savings before tax = $386,000

Tax rate = 25%

Annuial savings after tax = $288,750 ($386,000 x 1 - 0.25)

Year      Cashflows        PV Factor     Present Value

0          -$1,061,500               1             -$1,061,500

1              $288,750          0.901           $260,164

2             $288,750          0.812          $234,465

3             $288,750          0.731            $211,076

3             $468,750          0.731          $342,656

Net present value                                -$13,139

Thus, the project should not be undertaken by The Campbell Company due to the negative NPV that it yields.

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