1. The snow pack on Mt. Hood in the Oregon Cascades was 150 inches on
January 15th. Based on data taken in previous years, the snow pack decreases
about 11 inches a week after January 15th. What would be the rate of change?

Answer:

  25 yards long, 5 yards wide

Step-by-step explanation:

The given parameters can be used with the area and perimeter formulas for a rectangle to form an equation that can be solved for the dimensions.

The length and width can be represented by x and y. The formulas for area and perimeter give two equations relating these two variables:

  A = LW   ⇒   125 = xy

  P = 2(L+W)   ⇒ 60 = 2(x +y)

Using the second equation to write an expression for y, we have ...

  y = 30 -x

Substituting into the first equation gives ...

  125 = x(30 -x)

This suggests we can find x by looking for factors of 125 that total 30.

  125 = 1(125) = 5(25)

Factor totals are 126 and 30. This means we have ...

  x = 5, y = 30-5 = 25

or

  x = 25, y = 30 -25 = 5

The rectangle dimensions are 5 yards by 25 yards.

__

Additional comment

The two equations can also be solved graphically, as in the attachment.

The rectangle will be 25 yards long, and 5 yards wide.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

The given parameters can be used with the area and perimeter formulas for a rectangle to form an equation that can be solved for the dimensions.

The length and width can be represented by x and y. The formulas for area and perimeter give two equations relating to these two variables:

 A = LW   ⇒   125 = xy

 P = 2(L+W)   ⇒ 60 = 2(x +y)

Using the second equation to write an expression for y, we have ...

y = 30 -x

Substituting into the first equation gives ...

125 = x(30 -x)

This suggests we can find x by looking for factors of 125 that total 30.

125 = 1(125) = 5(25)

Factor totals are 126 and 30. This means we have.

x = 5, y = 30-5 = 25

x = 25, y = 30 -25 = 5

Therefore, the rectangle will be 25 yards long, and 5 yards wide.

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Answer:

Step-by-step explanation:

Factorize each term and find their GCF:

Their GCF is:

Answer:

hope it helps.

Answer:

41

Step-by-step explanation:

The table which  represents a quadratic relationship is in option \(D\).

A quadratic relationship is a mathematical relation between two variables that follows the form of a quadratic equation.

Quadratic sequence \(=an^2 +bn+c\)

So, According to the definition mentioned above if table follows the  form of a quadratic equation then it is in quadratic relationship.

So,

To find out quadratic relationship,

We will find first difference in every table and then second difference (Second difference is the difference between the first difference).

We have,

Table A;

\(\left \begin{array}{ccccc}x& \ &f(x)&First\ Difference & Second\ Difference \\-2& &4&2-4=-2\\-1& &2&1-2=-1&-1+2=1\\0& \ &1&0.5-1=-0.5&-0.5+1=0.5\\1& &0.5&0.25-0.5=-0.25&-0.25+0.5=0.25\\2& &0.25&0.125-0.25=-0.125\\3& &0.125\end{array}\right\)

So, In the above table we can see that second difference  is not equal that means it is not in quadratic relationship.

Now,

Let Table D;

\(\left \begin{array}{ccccc}x& \ &f(x)&First\ Difference & Second\ Difference \\-2& &-23.4&\\-1& &-23.2&-23.2+23.4=-0.2&0.2-0.2=0\\0& \ &-23&-23+23.2=-0.2&0.2-0.2=0\\1& &-22.8&-22.8+23=-0.2&0.2-0.2=0\\2& &-22.6&-22.6+22.8=-0.2\\3& &-22.4&-22.4+22.6=-0.2\end{array}\right\)

So, here in this table, we can see that second difference  is equal that means it is in quadratic relationship.

Hence, we can say that the table which  represents a quadratic relationship is in option \(D\).

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Answer:

Your equation is \((x - (5))^2 + (y - (6))^2 = (\sqrt{13} )^2\)

Step-by-step explanation:

Well, the center origin of the circle is given (h,k) =  (5,6).

We have to find our radius as they gave us a point. from origin to the edge of the circle.

Using the formula: (x - h)^2 + (y - k)^2 = r^2

Plug in our (h,k) = (5,6) and (x,y) =  (7,9) to solve for radius.

(x - h)^2 + (y - k)^2 = r^2

(7 - (5))^2 + (9 - (6))^2 = r^2

(2)^2 + (3)^2 = r^2

4 + 9 = r^2

r^2 = 13

r = sqrt(13)

The numeric values for this problem are given as follows:

The function in this problem is a piecewise function, meaning that it has different definitions based on the input x of the function.

For x between -2 and 2, the function is defined as follows:

g(x) = -(x - 1)² + 2.

Hence the numeric value at x = -1 is given as follows:

g(-1) = -(-1 - 1)² + 2 = -4 + 2 = -2.

For x at x = 2 and greater, the function is given as follows:

g(x) = 0.5x - 1.

Hence the numeric values at x = 2 and x = 3 are given as follows:

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If tan Ф = 15/8 then we have these trigonometric functions cosec Ф = 17/15, sec Ф = 17/8 and cot Ф = 8/15.

According to the question,

We have the following information:

Tan Ф = 15/8

We know that in this trigonometric function we have perpendicular divided by base.

Now, we can find the hypotenuse using the Pythagoras theorem:

Let's denote hypotenuse with h, perpendicular with p and base with b.

\(h^{2} =p^{2} +b^{2}\)

\(h^{2}\) = \((15)^{2} +(8)^{2}\)

\(h^{2} = 225+64\\h^{2} = 289\\h = \sqrt{289}\)

h = 17 units

Now, we have the following values:

Cosec Ф = 17/15 (Hypotenuse/perpendicular)

Sec Ф = 17/8 (h/b)

Cos Ф = 8/17 (b/h)

Cot Ф = 8/15 (b/p)

Hence, the correct options are A, B and D.

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The polynomial R(x) has degree 9. Two of the roots are 2i and -4-i.

(a) As the non-real roots lies along with its conjugates, the other roots of R(x) will be,

-2i and -4+i.

(b) The maximum number of real zeroes R(x) can have is 5, as there are 4 non-real roots that already exists.

(c).The maximum number of non real zeroes R(x) can have is 4.

Answer:

2

Step-by-step explanation:

\( - 5(4x - 2) = - 2(3 + 6x)\)

\(20x - 10 = 6 + 12x\)

\(8x = 16\)

\(x = 2\)

Answer:

x=2

Step-by-step explanation:

-5(4x-2)=-6-12x

-20x+10=-6x-12x

-8x=-16 | : (-8)

x= 2

The measure of angle DCE in this problem is given as follows:

m < DCE = 22.5º.

The triangles in this problem are right triangles, meaning that the trigonometric ratios are used to find the measures.

The three trigonometric ratios are given as follows:

The segment DB is adjacent to angle of 38º, while the hypotenuse is of 12.2 cm, hence the length of segment DB is calculated as follows:

cos(38º) = DB/12.2

DB = 12.2 x cosine of 38 degrees

DB = 9.6 cm.

BE:ED = 3:1, means that segment DE is one-fourth of segment DB, and thus it's length is given as follows:

DE = 1/4 x 9.6

DE = 2.4 cm.

Then for the angle DCE, we have that the opposite side is of 2.4 cm while the adjacent side is of 5.8 cm, hence the tangent is used to find it's measure, as follows:

tan(x) = 2.4/5.8

x = arctan(2.4/5.8)

x = 22.5º

m < DCE = 22.5º.

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Answer:

x = 22.5°

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

\(\sqrt{(-4-0)^2 + (1-(-2))^2}=5\)

Answer:

1a. Mean pulse rate for A = 60.5

1b. Range for A = 62

2a. Mean pulse rate for B = 73

2b. Range for B = 45

Step-by-step explanation:

1a. Determination of the mean pulse for patient A.

Data => 17, 16, 70, 69, 70, 75, 78, 70, 71, 69

Mean =?

The mean pulse rate for patient A can be obtained as follow:

Summation of data = 17 + 16 + 70 + 69 + 70 + 75 + 78 + 70 + 71 + 69

Summation of data = 605

Number of data = 10

Mean = summation of data / number of data

Mean = 605 / 10

Mean pulse rate for A = 60.5

1b. Determination of the range for patient A

Data => 17, 16, 70, 69, 70, 75, 78, 70, 71, 69

Range =?

Range = Highest – Lowest

Highest = 78

Lowest = 16

Range = Highest – Lowest

Range = 78 – 16

Range for A = 62

2a. Determination of the mean pulse for patient A.

Data => 59, 92, 60, 80, 71, 65, 50, 88, 95, 70

Mean =?

The mean pulse rate for patient B can be obtained as follow:

Summation of data = 59 + 92 + 60 + 80 + 71 + 65 + 50 + 88 + 95 + 70

Summation of data = 730

Number of data = 10

Mean = summation of data / number of data

Mean = 730 / 10

Mean pulse rate for B = 73

2b. Determination of the mean pulse for patient B.

Data => 59, 92, 60, 80, 71, 65, 50, 88, 95, 70

Range =?

Range = Highest – Lowest

Highest = 95

Lowest = 50

Range = Highest – Lowest

Range = 95 – 50

Range for B = 45

Answer:

Total cost, 5 bags of chips and 7 bottles of soda: 12.70

Total cost, x bags of chips and y bottles of soda: 1.35x+0.85y

Step-by-step explanation:

Answer:

624

Step-by-step

480+(480(30%))

=624

Answer:

162

30/100 * 480

3/10 * 480

3/1 * 48

3 * 48

162

The cost of the molding is given as follows:

$119.30.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The parameters for this problem are given as follows:

d = 9 -> r = 4.5.

(as the radius is half the diameter)

Hence the circumference is given as follows:

C = 2 x π x 4.5

C = 28.27 ft.

The cost is of $4.22 per ft, hence the total cost is given as follows:

4.22 x 28.27 = $119.30.

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The angle of the T in the ΔRST is 100° and the value of p is 11.

Define Triangle.

A triangle is a polygon that consists of three sides and three vertices. The fact that the interior angles of a triangle add up to 180 degrees is the most crucial aspect of triangles. This characteristic is known as the angle sum property of a triangle.

i.e., In a give ΔABC, ∠A + ∠B + ∠C = 180°.

Given:

∠R = 37°; ∠S = 43°; ∠T = 10p-10°

Let's take ∠T = x

In ΔRST,

∠R + ∠S + ∠T = 180°

37 + 43 + x =  180°

x = 180 - 80 ⇒ 100

∴ ∠T = 100°

To find the value of p,

 ∠T = 100

10p - 10 = 100

10p = 110 ⇒ 11

∴ p = 11

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If the mean is 8.5 minutes and the variance is 9 minutes then the upper confidence limit is 9.3765  .

In the question ,

it is given that ,

the number of sales person in the random sample (n) = 45 ,

the mean = 8.5 minutes

the variance is = 9 minutes .

So , the standard deviation is = 3.

For the 95% confidence interval the level of significance (α) is 0.05 .

So , α/2 = 0.05/2 = 0.025 .

So , from Z table ;

the value of \(Z_{\frac{\alpha }{2} }\) is = 1.96 .

The formula for the confidence interval is

= [ mean ±  \(Z_{\frac{\alpha }{2} }\)(SD/√n)]

Substituting the values from above ,

we get ,

= [8.5 - 1.96*0.4472 , 8.5 + 1.96*0.4472]

Simplifying further ,

we get ,

= [ 7.6235 , 9.3765 ]

Therefore , the upper limit of the 95% confidence interval is 9.3765  .

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The expression (-9x)^4 can be represented as -6561x^3 without using exponents.

To express the expression (-9x)^4 without using exponents, we can expand it by multiplying the base (-9x) four times using the multiplication property.

(-9x)^4 = (-9x) * (-9x) * (-9x) * (-9x)

To simplify this expression, we can multiply the terms together, taking care to apply the rules of multiplication:

(-9x) * (-9x) = (-9 * -9) * (x * x) = 81 * x^2 = 81x^2

So, by substituting this result back into the original expression, we get:

(-9x)^4 = 81x^2 * (-9x) = -6561 x^3

Therefore, the expression (-9x)^4 can be represented as -6561x^3 without using exponents.

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The correct option that describes the vertical asymptote is; B: There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = infinity

A vertical asymptote of a graph is defined as a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.

A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;

In a graph, these vertical asymptotes are given by dashed vertical lines.

An example is a value of x for which the denominator of the function is 0, and the function approaches infinity for these values of x.

We are given the function;

g(x) = 2(x + 4)²/(x² - 16)

Simplifying the denominator gives;

(x² - 16) = (x + 4)(x - 4)

Thus, our function is;

g(x) = 2(x + 4)²/[(x + 4)(x - 4)]

(x + 4 ) will cancel out to give;

g(x) = 2(x + 4)/(x - 4)

Vertical asymptote:

Point in which the denominator is 0, so:

(x - 4) = 0

x = 4

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Question 1

Question 2

Question 3

Answer:

i think it is D

Step-by-step explanation:

The number of people expected to be living in this county is given as follows:

12,992 people.

The number of people expected to be living on the country is obtained applying the proportions in the context of this problem.

The population density of the county is given as follows:

28 people per square mile.

Hence the expected number of people over a total area of 464 square miles is given as follows:

28 x 464 = 12,992 people.

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The cost of each bag of apple is $6.35

If Miguel buys eggs and apples at the store.

• He pays a total of $56.97.

• He pays a total of $6.17 for the eggs.

• He buys 8 bags of apples that each cost the same amount

The correct equation that represents the statement will be given as:

Make x the subject of the formula

8x = 56.97 - 6.17

8x = 50.8

x = 50.8/8

x = 6.35

Hence the cost of each bag of apple is $6.35

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Answer:

Step-by-step explanation:

hello :

cos²θ +sin²θ = 1 and cosθ =4/5

(4/5)² + sin²θ = 1 so : sin²θ = 1 - 16/25

sin²θ = 9/25 = (3/5)²

sinθ = 3/5 or sinθ = - 3/5 because : (3/5)²= (- 3/5)²= 9/25

is it me or is the photo not showing?

Answer:

no photo lol

Step-by-step explanation:

8a+4b when you combine like terms

Answer:

8a+4b.

Step-by-step explanation:

To simplify the expression you have to combine like terms. 10a and -2a. 10a-2a=8a. 8b-4b=4b. Put them together and you get 8a+4b.

Based on the direct variation relationship between x and y, where y is 33 when x is 11, we find that y is 36 when x is 12.

If x and y vary directly, it means that they have a constant ratio between them. We can express this relationship as:

y = kx,

where k is the constant of variation.

To find the value of k, we can use the given information that when x is 11, y is 33. Substituting these values into the equation, we have:

33 = k * 11.

Dividing both sides by 11, we find:

k = 3.

Now that we have determined the constant of variation, we can find y when x is 12 by substituting this value into the equation:

y = 3 * 12.

Evaluating this expression, we get:

y = 36.

Therefore, when x is 12, y will be 36.

Based on the direct variation relationship between x and y, where y is 33 when x is 11, we find that y is 36 when x is 12.

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The length of the hypotenuse or the value of 'x' is 60.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjacent/hypotenuse and

tan = opposite/adjacent.

From the given diagram respect to the reference angle of 37°,

Hypotenuse is 'x' and adjacent is 48.

And we know,  cos = adjacent/hypotenuse.

Therefore, cos37° = 48/x.

x = 48/0.8.

x = 60.

Q. A right-angle triangle is shown, Find the value of x.

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