Select whether the function is discrete or continuous.Function: The number of footballs manufactured per day.The function is (select)(select)discretecontinuous

Answer:

54

Step-by-step explanation:

ratio is 7:9

7=42

9=?

9×42÷7

Answer:

x = 61

Step-by-step explanation:

Alternate exterior angles must be congruent for the lines to be parallel.

3x - 43 = 2x + 18

x = 61

The total surface area of the doghouse is 1452 ft²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The dog house has many surfaces including the roofs . The total surface area is the sum of all the area of the surfaces.

area of the roof part = 2( 13×11) + 2( 12× 10)×1/2

= 286 + 720

= 1006 ft²

surface area of the building

= 2( lb + lh + bh) -bh

= 2( 10× 11 + 10×8 + 11×8) - 10×11

= 2( 110+80+88)-110

= 2( 278) -110

= 556 -110

= 446ft²

The total surface area = 1006 + 446

= 1452 ft²

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From the graph attached below, the solution to the system of linear inequalities are (1, 4)

A system of linear inequalities is a collection of linear inequalities in the same variables. The solution is any ordered pair that satisfies each of the inequalities.

In the problem given;

y < - x + 5 ...eq(i)

y ≥ 3x + 1 ...eq(ii)

To determine the solution to the system of linear inequalities, it is easier for us to use graphical method. This is simply done by plotting the points and determine the coordinate at which both inequalities intersect.

From the graph of the system of linear inequalities, the solution to this is (1, 4) which is option E

Kindly find attached graph below

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The surface area of given triangular prism = 24 ft².

For the given triangular prism

Base = 2 ft

height = 3 ft

side = 3ft

We know that,

Surface area of triangular prism

= side x base + 3x base x height

=  3 x 2  + 3x2x3

= 6 + 18

= 24 ft²

Thus,

Surface area = 24 ft²

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Answer:

54

Step-by-step explanation:

two ways:

1. find the area of the trapesium

1/2(sum of parallel sides)x height

= 1/2(7+2)×12

1/2(9x12)

1/2(108)

= 54

Or

you can divide the figure into 2 parts, rectangle and triangle,

so you find the area of triangle(1/2basexheight) and then the area of rectangle (length x width)

and then add the two areas. it should also give you same answer.

let me know if it makes sense

Answer:

£131.88 or 13188 pence

Step-by-step explanation:

1 unit = 14p

942 units = 942 x 14

942 units = 13188p

£1 = 100p

13188 ÷ 100 = £131.88

Hope this helps!

The last expression finally simplifies to cot β + tan α using quotient identity in trigonometric identities.

We want to verify the trigonometric  identity;

cos (α - β)/(cos α sin β) = cot β + tan α

Now, according to trigonometric identities in mathematics, we know that;

cos (α - β) = (cos α cos β) + (sin α sin β)

Thus, plugging that back into our left hand side of the main question gives;

[(cos α cos β) + (sin α sin β)]/(cos α sin β)

Rewriting this expression by separating the denominator gives;

[(cos α cos β)/(cos α sin β)] + [(sin α sin β)]/(cos α sin β)

Using quotient identities, this can be simplified to;

cot β + tan α

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A total of 7 Cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

A line plot is drawn with the cyclists' names plotted on the x-axis and their corresponding distances covered plotted on the y-axis.

The dots are then joined to form a line, revealing the relationship between the cyclist's names and their corresponding distance traveled. The cyclist names and their corresponding distances are given in the table below.

Name Distance (in miles) Gina 40 1/2 Rey 50 Faye 35 3/4 Mark 60 John 45 1/2 James 40 1/2 Albert 40 1/4 William 54 1/4 Nathan 40 Kate 40 1/4 Mary 60 Risa 40 Abi 35 3/4 Joan 50 1/2 1. The number of cyclists is 14. 2. The longest distance covered by a cyclist is 60 miles.

Mary and Mark both covered this distance.3. A total of 7 cyclists traveled less than 50 miles. 4. The most common distance traveled by cyclists is 40 1/2 miles. Gina, James, and Albert covered this distance. 5. 2 more cyclists traveled 45 miles than 55 1/4 miles. Only William traveled 55 1/4 miles, while John and James both traveled 45 1/2 miles.6.

A total of 7 cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

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Answer:

y > - x - 4

Step-by-step explanation:

1) Find the equation of the line

2) The equation of the line is y = - x - 4

3) Identify where the graph is shaded

4) It is shaded above and to the right of the line

5) This means that it is more positive/ greater than the unshaded areas

6) Switch the = sign to > to signify the inequality

7) All done!

Step-by-step explanation:

the delimiter line is going through the points (-4, 0) and (0, -4).

the line function

y = mx + b

m is the slope of the line, b is the y-intercept (the y value when x = 0).

the slope is the ratio of "y coordinate change / x coordinate change" when going from one point to another.

so, for the 2 found points :

x changes by +4 (from -4 to 0)

y changes by -4 (from 0 to -4).

the slope m is then

-4/+4 = -1

and the y-intercept is -4 (as explained).

so, the line is

y = -x - 4

and the graphic says that all values greater than our equal to the line values are valid, so

y >= -x - 4

The slope of a given line is m=1.5.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

The coordinate points of a line are (1, -3) and (3, 0).

Substitute, (x₁, y₁) and (x₂, y₂) in m=(y₂-y₁)/(x₂-x₁), we get

m= (0+3)/(3-1)

= 3/2

= 1.5

Therefore, the slope of a given line is m=1.5.

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Answer:

x= - 52

Step-by-step explanation:

we need to multiply  both sides by 4 to leave the x alone

so

\(\frac{-x}{4} *4= 13*4\\-x= 52\\\frac{-x}{-1}=\frac{52}{-1}\\ x=-52\)

Answer:

(5x-4)(x+1)

Step-by-step explanation:

The critical points are within rthe range 3<x<5

These are equations that has a leading degree of 2. Given the expression below.

x²-8x+15<0

Factorize

x²-3x-5x+15<0

Factor out the GCF

x(x-3)-5(x-3) <0

Group

(x-3)(x-5)<0

Find the solution

x < 3 and x <5

Hence the critical points are within rhe range 3<x<5

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Answer:

70

Step-by-step explanation:

saveings +70 the money she added to the money he or she saved

The solution is, the value of the variables are x = 40 and, y = 160.

Notice that "x" and "3x+20" are supplementary angles so their sum is 180°

(x) + (3x + 20) = 180

4x + 20 = 180

4x = 160

x = 40

To solve for "y", you have 2 options: either notice that "x" and "y-20" are supplementary angles so their sum is 180° or notice that "3x + 20" and "y - 20" are vertical angles so are equal to each other. I am going to solve using the first option because it is less work.

(x) + (y - 20) = 180°

40 + y - 20 = 180

y + 20 = 180

y = 160

Answer: x=40, y=160

The solution is, the value of the variables are x = 40 and, y = 160.

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complete question:

Find the value of each variable

distribute the 4:

4x-36=-48x

subtract 4x

-36=-52x

divide by -52

x=1/2

The volume of the cardboard box with given dimensions changes at the fastest average rate over the interval of  option c.  [1,5].

Length of the cardboard box = x + 1

Width of the cardboard box = 5  - x

Height of the cardboard box = x - 1

Volume of the box V (x) =  length × width × height

Substitute the values we have,

V(x) = (x+1)(5-x)(x-1)

Expanding this expression gives,

V(x) = -x³ + 5x² + x - 5

To know where Volume is changing at the fastest average rate,

Find the maximum value of the absolute value of the derivative of V(x) over each of the given intervals.

Taking the derivative of V(x), we get,

V'(x) = -3x²+ 10x + 1

Taking the absolute value of this expression, we get,

|V'(x)| = 3x² - 10x - 1

Now, we can calculate the maximum value of |V'(x)| over each interval,

At [1,2]

|V'(1)| = 8

|V'(2)| = 9

[1,3.5]

|V'(1)| = 8

|V'(3.5)| = 0.75

[1,5]

|V'(1)| = 1

|V'(5)| = 24

[0,3.5]

|V'(0)| = 1

|V'(3.5)| = 0.75

The maximum value of |V'(x)| occurs on interval [1,5].

Therefore, the volume of the box is changing at the fastest average rate over the interval option c . [1,5].

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The above question is incomplete, the complete question is:

A cardboard box manufacturing company is building boxes with length represented by x + 1, width by 5 − x, and height by x − 1. the volume of the box is modeled by the function below. over which interval is the volume of the box changing at the fastest average rate?

a. [1,2]

b. [1,3.5]

c. [1,5]

d. [0,3.5]

Answer:

26 gallons

Step-by-step explanation:

Set up an equation to represent this problem. Parameter (x) represents the gas tank when it is filled. Based on the problem;

\(\frac{1}{5}x + 13 = \frac{7}{10}x\)

Inverse operations;

\(\frac{1}{5}x + 13 = \frac{7}{10}x\\-\frac{1}{5}x\\\\13 = \frac{7}{10}x - \frac{1}{5}x\\\\\)

Convert to combine denominator, and simplify,

\(13 = \frac{7}{10}x - \frac{1}{5}x\\\\13 = \frac{7}{10}x - \frac{2}{10}x\\\\13 = \frac{5}{10}x\\\\13 = \frac{1}{2}x\)

Inverse operations,

\(13 = \frac{1}{2}x\\*2\\\\26 = x\)

26 gallons

Answer: B: 20

Step-by-step explanation: We can take 40% as a fraction to make it 4/10, simplifying gives 2/5. 2/5 of 50 is 20!

Hope this Helps!

Answer:

  x = 1

Step-by-step explanation:

You want to know the value of x in the trapezoid with adjacent angles (43x+2)° and 135°.

The two marked angles can be considered "consecutive interior angles" where a transversal crosses parallel lines. As such, they are supplementary.

  (43x +2)° +135° = 180°

  43x = 43 . . . . . . . . . . . . . . divide by °, subtract 137

  x = 1 . . . . . . . . . . . . . . . divide by 43

The value of x is 1.

__

Additional comment

Given that the figure is a trapezoid, we have to assume that the top and bottom horizontal lines are the parallel bases.

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Step-by-step explanation:

points on the line: (4, -2) & (-5, 3)

gradient of the line = -5/9

general equation for all straight lines: y = mx + c

substitute one coordinate and the gradient into the equation. 3 = (-5/9)(-5) + c

therefore, c = 2/9

so the general equation is y = (-5/9)x + 2/9

If each of X, Y, and N are positive integers, then the value of X+Y+N is 212.1

A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.

WE are given that A red purse contains $7, and a black purse contains $10. Each package contains X red purses and Y black purses.

X = 7

Y = 10

If there are N packages (N ≥ 2) and the total value of them is $2021

X + Y = One packages

N packages = N(X + Y ) = 10 N

if each of X, Y, and N are positive integers, then;

10 N = 2021

N = 2021/10

N = 202.1

Therefore, X+Y+N = 10 + 202.1 = 212.1

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Answer:

The depreciation tax shield for this project in year 4 is $178.24.

Explanation:

To calculate the depreciation tax shield for this project in year 4, we need to first determine the depreciation expense for year 4 using the MACRS three-year class life category and the double-declining balance (DDB) method.

From Table 12.8 on page 415 of the textbook, we can see that the depreciation rate for year 1 is 33.33%, for year 2 it is 44.45%, for year 3 it is 14.81%, and for year 4 it is 7.41%.

Using the DDB method, we can calculate the depreciation expense for each year as follows:

Year 1: Depreciation expense = $14,000 x 33.33% = $4,667

Year 2: Depreciation expense = ($14,000 - $4,667) x 44.45% = $3,554

Year 3: Depreciation expense = ($14,000 - $4,667 - $3,554) x 14.81% = $830

Year 4: Depreciation expense = ($14,000 - $4,667 - $3,554 - $830) x 7.41% = $557

The total depreciation expense over the four years is the sum of the individual year's depreciation expenses, which is:

$4,667 + $3,554 + $830 + $557 = $9,608

Now, we can calculate the depreciation tax shield in year 4. The depreciation tax shield is the amount of the depreciation expense that reduces the firm's taxable income, multiplied by the tax rate. In year 4, the depreciation tax shield is:

Depreciation tax shield = Depreciation expense in year 4 x Tax rate

Depreciation tax shield = $557 x 32% = $178.24

Therefore, the depreciation tax shield for this project in year 4 is $178.24.

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The limit of the difference quotients for f(x) = x^2 + 2x + 1 as x approaches -1 is indeterminate.

To find the limit of the difference quotients for the function f(x) = x^2 + 2x + 1 as x approaches -1, we need to evaluate the following expression:

lim(x→-1) [f(x) - f(-1)] / (x - (-1))

First, let's substitute the values into the expression:

lim(x→-1) \([(x^2 + 2x + 1) - (-1^2 + 2(-1) + 1)] / (x + 1)\)

Simplifying further:

lim(x→-1) \([(x^2 + 2x + 1) - (1 - 2 + 1)] / (x + 1)\)

lim(x→-1)\([x^2 + 2x + 1 - 0] / (x + 1)\)

lim(x→-1) \((x^2 + 2x + 1) / (x + 1)\)

Now, we can directly substitute x = -1 into the expression:

\((-1^2 + 2(-1) + 1) / (-1 + 1)\)

(1 - 2 + 1) / (0)

0 / 0

We have obtained an indeterminate form of 0/0. This indicates that we need to further simplify the expression or use other techniques, such as L'Hôpital's rule, to evaluate the limit. However, without additional information or simplification, we cannot determine the precise value of the limit at x = -1.

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Answer:

$2.25

Step-by-step explanation:

Let "b" be the price of 1 brownie and "c" the price of 1 cookie.

At a bake sale, a student spent $11.00 buying 3 brownies and 5 cookies. Symbolicaly,

3 b + 5 c = 11.00   [1]

His friend spent $3.95 buying 1 brownie and 2 cookies. Symbolicaly,

1 b + 2 c = 3.95

b = 3.95 - 2c   [2]

If we replace [2] in [1], we get

3 (3.95 - 2c) + 5 c = 11.00

11.85 - 6c + 5c = 11.00

c = 0.85

If we replace c = 0.85 in [2], we get

b = 3.95 - 2 (0.85) = 2.25

The equation for the line through the point (-7,-4) and parallel to the line y = 8x - 4 in point-slope form is y = 8x + 52

The first equation is given as

y = 8x - 4

The slope of the above equation is

m = 8

Parallel lines have equal slope

So, the slope of the other line is

m = 8

The equation is then calculated as

y = m(x - x1) + y1

Where

m = 8

(x1, y1) = (-7, -4)

So, we have

y = 8(x + 7) - 4

Expand

y = 8x + 56 - 4

Evaluate the difference

y = 8x + 52

Hence, the equation for the line through the point (-7,-4) and parallel to the line y = 8x - 4 in point-slope form is y = 8x + 52

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Option A is correct that is ASA postulate AC bisects ∠DAB and CA bisects ∠DCB then we proved ΔDAC≅ΔABC.

Given that,

We have to find the missing reasons in the two column.

Given

AC bisects ∠DAB and CA bisects ∠DCB

Prove

ΔDAC≅ΔABC

Statement                                                          Reasons

1. AC bisects ∠DAB                                           Given

2. ∠DAC≅∠BAC                                              definition of angle bisects

3.AC≅AC                                                         reflexive property
4.CA bisects ∠DCB                                           given

5. ∠DCA≅∠BCA                                              definition of angle bisects

6. ΔDAC≅ΔABC                                               ASA postulate

Therefore, Option A is correct that is ASA postulate AC bisects ∠DAB and CA bisects ∠DCB then we proved ΔDAC≅ΔABC.

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