Write a rule that represents the function.
(1,1/2),(2,1/4),(3.1/8),(4,1/16),(5,1/32)

Answer:

width: 33 ft

length: 74 ft

Step-by-step explanation:

The perimeter of a rectangle is calculated by adding all of the sides together which includes two lengths and two widths. Since the formula for the length is given (l = 41ft + w) and the perimeter is given, then we can simply use the perimeter formula and substitute the value of length with its formula which would only leave us with one variable in the equation w. Now we must solve for w.

l + l + w + w = 214

(41 + w) + (41 +w) + w + w = 214  ... combine like terms

82 + 4w = 214  ... subtract 82 from both sides

4w = 132 ... divide both sides by 4

w = 33 ft

Finally, we can see that the value of the width is 33 ft . Now we plug this value into the formula for length to calculate its value.

l = 41 + w

l = 41 + 33

l = 74 ft

Answer:

 In seven minutes she can do 91 push ups

Step-by-step explanation:

26*3=78

78+13=91

Answer:

he would have to read 3.307692308 hour

Step-by-step explanation:

Step-by-step explanation:

[tex]{ ({6}^{ - 4} ) }^{ - 9} \div 6^{6} = {6}^{( - 4) \times (- 9)} \div {6}^{6} = {6}^{( 36)} \div {6}^{6} = {6}^{ (36)- 6} = {6}^{ 30} [/tex]

Answer:

Step-by-step explanation:

the objective is to maximize profit

let x be corn and y be oat

let us begging by formulating the linear program for the problem

The objective function is

  111x+47y=P

The constraints are

1. capital

 36x+18y=2100------------1

2. labor

6x(8)+2y(8)=2400

48x+16y=2400-------------2

solving 1 and 2 we apply substitution method

36x+18y=2100------1

36x=2100-18y

x=(2100-18y)/36

put x=(2100-18y)/36 in 2 we have

48(2100-18y)/36+16y=2400

(100800-864y)/36+16y=2400

2800-24y+16y=2400

-8y=2400-2800

-8y=-400

8y=400

y=400/8

y=50

to find x put y=50 in 36x+18y=2100------------1

36x+18(50)=2100------------1

36x+900=2100

36x=2100-900

36x=1200

x=1200/36

x=33.33

profit is

111x+47y=P

111(33.33)+47(50)=P

3699.63+2350=P

P=6049.63

$6049.63

the planning comnination is to work on

33.33 acre of corn and 50 acre of oat

Answer:

There are two sets of solutions:

Step-by-step explanation:

The question states that [tex]a[/tex] and [tex]r[/tex] should represent the first term and the common ratio of this geometric sequence, respectively. Therefore:

Let [tex]n[/tex] denote a positive whole number. In general, the [tex]n\![/tex]-th term of this geometric sequence would be [tex]r^{n-1}\, a[/tex].

The sixth term of this sequence would thus be [tex]r^{6-1}\, a = r^5\, a[/tex].

The fact that the second term is [tex]2[/tex] and the sixth term is [tex]32[/tex] gives two equations about [tex]a[/tex] and [tex]r[/tex]:

[tex]\displaystyle \left\lbrace\begin{aligned}& r\, a = 2 \\ & r^5\, a= 32\end{aligned}\right.[/tex].

Take the quotient of these two equations to eliminate [tex]a[/tex]:

[tex]\displaystyle \frac{r^5\, a}{r\, a} = \frac{32}{2}[/tex].

[tex]r^4 = 16[/tex].

There are two possible roots: either [tex]r = 2[/tex] or [tex]r = -2[/tex].

When [tex]r = 2[/tex], substitute back to the first equation and solve for [tex]a[/tex]: [tex]a = 1[/tex].

On the other hand, when [tex]r = -2[/tex], substituting back and solving for [tex]a[/tex] would give [tex]a = -1[/tex].

Substitute these values into the second equation. Either set of values will work.

Answer:

A)---(2,2)

B)---(-6,4)

C)---(-4,7)

D)---(2,4)

Answer:

A= (2,2) B= (-6,4) C= (-4,7) D= (2,4)

Step-by-step explanation:

Answer:

6 * (8 - x)

Step-by-step explanation:

When you said "a number" I just wrote x

hope this helps I may have written it wrong

Answer:

The answer is D

Step-by-step explanation:

I took the test and got it right <3

Answer: The first question in the selection is correct!

Step-by-step explanation:

Answer:

10%

Step-by-step explanation:

(a) What percentage of meals had less than 10 grams of fat?

(b) Round your answer to the nearest tenth of a percent.

To find the percentage of meals with less than 10 grams of fat, count the number of meals with less than 10 grams of fat and divide by the total number of meals; multiply this figure by a hundred.

(A) Total number of meals = 550

Number of meals having less than 10 grams of fat = 77

Percentage of meals having less than 10 grams of fat = 77/550 × 100

= 0.14 × 100 = 14%

(B) Rounding the answer to the nearest tenth of a percent means approximating it to the nearest multiple of 10 that is not more than 100 (where 100 here represents a full cent or 'percent').

The multiples of 10 that are close to 14 are 10 and 20. The closest being 10, your answer becomes 10%

Bachelor's degree salary = $53000

Master's degree salary = $66000

Step-by-step explanation:

Given that :

Let Salary of bachelor's degree holder = x

Salary of Master's degree holder = 2x - 40000

Master's salary + bachelor's salary = $119,000

Hence,

Master's salary + bachelor's salary = 119,000

2x - 40000 + x = 119,000

3x = 119000 + 40000

3x = 159000

x = 159000 / 3

x = $53,000

Bachelor's degree salary = $53,000

Master's degree salary ; 2x - 40000 ; 2(53000) - 40000 = $106,000 - $40,000 = $66000

Answer:

1 the line hits the y line at 1

Answer:

80 degrees

Step-by-step explanation:

The total sum of all angles is 180 in every triangle, 70 + 30 = 100, 180 - 100 = 80

The Answer is 80 degrees

Answer:

addition

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

10-2=8

8/2=4

Hope this helps!

A stem of 2 would have 3 leaves.

The correct answer is option (B) 3.

"It is a special table where each data value is split into a 'stem' (the first digit) and a 'leaf'( the last digit)."

For given data,

17, 22, 53, 74, 42, 26, 93, 15, 67, 29, 50

A stem-and-leaf representation would be:

Stem              Leaf/leaves

1                       7, 5

2                      2, 6, 9

4                      2

5                      3, 0

6                      7

7                      4

9                      3

From above plot, we can observe that a stem of 2 would have three leaves.

Therefore, option (B) is the correct answer.

Learn more about stem-and-leaf plot here:

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Answer:

13

..................

Answer:

[tex]y = \frac{2}{3}x + \frac{7}{3}[/tex]

Step-by-step explanation:

Given

Line A:

[tex]y = -\frac{2}{3}x - 4[/tex]

Line B:

[tex](-2,1)[/tex]

Required

Determine the equation of Line B

First, we need to determine the slope of A using

[tex]y =mx + b[/tex]

Where:

[tex]m = slope[/tex]

By comparison:

[tex]y = -\frac{2}{3}x - 4[/tex]

[tex]m = -\frac{2}{3}[/tex]

Since A and B are perpendicular:

The slope of B (m2) is:

[tex]m_2 = \frac{-1}{m}[/tex]

[tex]m_2 = -1/\frac{-2}{3}[/tex]

[tex]m_2 = -1 * \frac{-3}{2}[/tex]

[tex]m_2 = \frac{3}{2}[/tex]

The equation of B is calculated as thus:

[tex]y - y_1 = m(x - x_1)[/tex]

Where

[tex](x_1,y_1) = (-2,1)[/tex]

[tex]m = \frac{2}{3}[/tex]

So, the equation becomes

[tex]y - 1 = \frac{2}{3}(x - (-2))[/tex]

[tex]y - 1 = \frac{2}{3}(x + 2)[/tex]

Open bracket

[tex]y - 1 = \frac{2}{3}x + \frac{4}{3}[/tex]

Make y the subject

[tex]y = \frac{2}{3}x + \frac{4}{3} + 1[/tex]

[tex]y = \frac{2}{3}x + \frac{4 + 3}{3}[/tex]

[tex]y = \frac{2}{3}x + \frac{7}{3}[/tex]

Answer:

-0.4

hope this helps :)

Answer:

9 and 5 is thesum of 15

5×3=15and in sum 15×3=45 and 5×9 =45 and 9 and 45 cut and remaining 5

thus the different between is solve

Answer:

942.50

Step-by-step explanation:

725×30% or 0.3 = 217.5

217.5+725=942.5

Answer:

m= -2

Step-by-step explanation:

For future reference, you should try using Symbolab, it works really well and I use it ALL the time!

Answer:

1. 332

2. 177

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

Answer:is D

Step-by-step explanation:

Answer: B

Coordinates: A’ (-3,2). B’ (-3,-3). C’(0,-2)

Answer:

2, 8

Step-by-step explanation:

Answer:

Angle JKN and Angle JKI are supplementary angles.

Step-by-step explanation:

When these two angles are added together, they will equal to 180 degrees.

Answer:

left bottom option

Step-by-step explanation:

when the value of their angles are added they sum up to be 180

Answer: 240

Step-by-step explanation:

The price of the tablet before the sale is, $240.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

Sol brought a tablet on sale for 45% off the original price.

And, He paid $132 for tablet.

Now, Let the original price of tablet = x

So, We can formulate;

⇒ x - 45% of x = $132

⇒ x - 45x/100 = $132

⇒ (100x - 45x) / 100 = $132

⇒ 55x = $13200

⇒ x = $13200 / 55

⇒ x = $240

Learn more about the percent visit:

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Answer:

There are four possible combinations of root types for a 7th degree polynomial:

(i) 7 rational roots. ([tex]a_{\mathbb{Q}} = 7[/tex], [tex]a_{\mathbb{I}} = 0[/tex], [tex]a_{\mathbb{C}} = 0[/tex])

(ii) 6 rational roots, 1 irrational root. ([tex]a_{\mathbb{Q}} = 6[/tex], [tex]a_{\mathbb{I}} = 1[/tex], [tex]a_{\mathbb{C}} = 0[/tex])

(iii) 2 rational roots, 1 irrational root, 4 complex roots. ([tex]a_{\mathbb{Q}} = 2[/tex], [tex]a_{\mathbb{I}} = 1[/tex], [tex]a_{\mathbb{C}} = 2[/tex])

(iv) 3 irrational roots, 4 complex roots. ([tex]a_{\mathbb{Q}} = 0[/tex], [tex]a_{\mathbb{I}} = 3[/tex], [tex]a_{\mathbb{C}} = 2[/tex])

Step-by-step explanation:

According to the Fundamental Theorem of Algebra, every polynomial with degree higher than zero has at least a solution and at best [tex]n[/tex] complex roots, where [tex]n[/tex] is the degree of the polynomial. In this case, we have 7 roots.

We can rewrite the 7th degree polynomial as a product of a 3rd degree polynomial and 4th degree polynomial. That is:

[tex]p_{7}(x) = p_{3}(x)\cdot p_{4}(x)[/tex] (Eq. 1)

From Algebra we know that both 3rd degree and 4th degree polynomials are solvable by analytical means:

1) All 4th degree polynomials are solvable by Ferrari's method, whose posible solutions are, respectively:

(i) 4 rational roots.

(ii) 4 irrational roots.

(iii) 2 rational roots, 2 irrational roots.

(iv) 3 rational roots, 1 irrational root.

(v) 1 rational roots, 3 irrational roots.

(vi) 2 rational roots, 2 complex roots.

(vii) 2 irrational roots, 2 complex roots.

(viii) 1 rational root, 1 irrational root, 2 complex roots.

(ix) 4 complex roots.

2) All 3rd degree polynomials are solvable by Cardano's method, whose possible solutions are, respectively:

(i) 3 rational roots.

(ii) 3 irrational roots.

(iii) 1 rational root, 2 complex roots.

(iv) 1 irrational root, 2 complex roots.

(v) 3 complex roots.

Please note that complex roots are always presented in conjugated pairs by Quadratic Formula.

The number of solutions of a polynomials are represented by the following expression:

[tex]n = a_{\mathbb{Q}}+a_{\mathbb{I}}+2\cdot a_{\mathbb{C}}[/tex] (Eq. 2)

Where:

[tex]a_{\mathbb{Q}}[/tex] - Number of rational roots, dimensionless.

[tex]a_{\mathbb{I}}[/tex] - Number of irrational roots, dimensionless.

[tex]a_{\mathbb{C}}[/tex] - Number of pairs of complex roots, dimensionless.

Based on this expression, we find the possible root types for a 7th degree polynomial:

(i) 7 rational roots. ([tex]a_{\mathbb{Q}} = 7[/tex], [tex]a_{\mathbb{I}} = 0[/tex], [tex]a_{\mathbb{C}} = 0[/tex])

(ii) 6 rational roots, 1 irrational root. ([tex]a_{\mathbb{Q}} = 6[/tex], [tex]a_{\mathbb{I}} = 1[/tex], [tex]a_{\mathbb{C}} = 0[/tex])

(iii) 2 rational roots, 1 irrational root, 4 complex roots. ([tex]a_{\mathbb{Q}} = 2[/tex], [tex]a_{\mathbb{I}} = 1[/tex], [tex]a_{\mathbb{C}} = 2[/tex])

(iv) 3 irrational roots, 4 complex roots. ([tex]a_{\mathbb{Q}} = 0[/tex], [tex]a_{\mathbb{I}} = 3[/tex], [tex]a_{\mathbb{C}} = 2[/tex])

Answer:

2812 people

Step-by-step explanation: There are 38 buses and each holds 74 people so 38 x 74= 2812

Hope this helps :)