Fill in the missing statements and reasons for the proof. Given ∠2 ≅ ∠3 proof ∠1 ≅ ∠4

The given cubic equation has no roots.

Traditionally, a cubic problem can be solved by converting it into a quadratic equation, which can then be solved by factoring or the quadratic formula. A cubic equation has three roots, just like a quadratic equation has two. Three real roots or one real root and two imaginary roots are both possible for a cubic equation. Cubic equations must also always be arranged in their standard form first.

The following strategies can be used to resolve a cubic equation:

Using Graphical Method to Find Integer Solutions with Factor Lists

Given that the cubic equation is: 8x²-5x³+7-12x

Regrouping the equation in standard form:

- 5x³ + 8x² - 12x + 7

Here, the constant is 7. Take the factors of the constant.

7 = 1, 7

Substitute the value of the factors as follows:

G(1) = - 5(1)³ + 8(1)² - 12(1) + 7 = -5 + 8 - 12 + 7 ≠ 0

G(7) = -5(7)³ + 8(7)² -12(7) + 7 = -1715 + 392 - 84 + 7 ≠ 0

Hence, the given cubic equation has no roots.

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Answer:

2. $240.50

3. See below

Step-by-step explanation:

2.

I = Prt

where I = interest

P = principal amount (amount of investment)

r = annual interest rate

t = time in years

t = 4 months = 4/12 year = 1/3 year

r = 9.25% = 0.0925

I = Prt

I = $7800 × 0.0925 × 1/3

I = $240.50

3. Exact interest takes into account every day of the year. In a regular year, there are 365 days. in a leap year, there are 366 days. Exact interest uses the exact number of days of the specific year for interest calculations of less than a year.

Ordinary interest rounds off a year to 360 days, and calculations are based on a year having 360 days, not 365 of 366 days.

The value of the 'm' and 'b' will be negative 1.44 and 3.61, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + b

Where m is the slope of the line and b is the y-intercept of the line.

The linear equation is given below.

r(t)= √3 - 0.4t√13

r(t)= √3 - (0.4√13) t

Compare the equation with the standard equation. Then we have

m = - (0.4√13)

m = - 1.44

b = √13

b = 3.61

The value of the 'm' and 'b' will be negative 1.44 and 3.61, respectively.

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Answer:its a cool song

Step-by-step explanation:

listening, listened to it, its good

We are given the following inequality.

[tex]5x+38 \leq 4(2-5x)[/tex]

Apply the distributive property on the right side:

[tex]5x+38\leq 8-20x[/tex]

Add both sides by 20x:

[tex]5x+38+20x\leq 8-20x+20x[/tex]

[tex]25x+38\leq 8[/tex]

Subtract both sides by 38:

[tex]25x+38-38\leq 8-38[/tex]

[tex]25x\leq -30[/tex]

Divide both sides by 25:

[tex]25x/25\leq -30/25[/tex]

[tex]x\leq -6/5[/tex]

Out of all the options, only option A accurately depicts this inequality. Thus, the answer is option A.

Let me know if you have any questions, thanks!

The difference in rainfall between the wettest and driest days is 3/8 inches.

The intensity of the rain is typically categorized as light, moderate, or heavy. Light precipitation is defined as less than 0.10 inches per hour. Rainfall that is considered moderate ranges from 0.10 to 0.30 inches per hour. More than 0.30 inches of rain per hour is considered heavy rainfall. under 0.5 mm per hour. Greater than 0.5 mm per hour but less than 4.0 mm per hour is considered moderate rain. Greater than 4 mm per hour but less than 8 mm per hour is considered heavy rain. greater than 8 mm per hour of extremely intense rain.

Rainfall in Rainiest day = 5/8

Rainfall in driest day = 2/8

So, The Difference = 5/8 - 2/8 = 3/8 inches

Hence, rainfall on the rainiest day 3/8 more than driest day

Proper fraction = 3/8

Mixed fraction = 8/2 inches.

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These values do not satisfy the requirement that x, y, and z be positive numbers, so the problem does not have a solution.

What is a three-variable linear equation?

When a, b, and c are constants, a linear equation in two variables has the form ax + by + c = 0. (real numbers). Similar to this, a three-variable linear equation has the form ax by c z plus d = 0, where a, b, c, and d are constants.

Let's call the three numbers x, y, and z, where x is the largest number and z is the smallest number. Then, we have the following information:

x + y + z = 54

x - z = 46

y + z = 13

From the second equation, we can find z:

z = x - 46

Substituting this into the third equation:

y + x - 46 = 13

y = 13 + 46 - x

Substituting both of these into the first equation:

x + (13 + 46 - x) + (x - 46) = 54

Expanding the parentheses:

2x = 154

Dividing both sides by 2:

x = 77

Substituting this value of x into the equation for z:

z = x - 46 = 77 - 46 = 31

And substituting it into the equation for y:

y = 13 + 46 - x = 13 + 46 - 77 = -18

Note that these values do not satisfy the requirement that x, y, and z be positive numbers, so the problem does not have a solution.

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what made the time ater sugauli treaty politically instable and complicated

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The equation that can be used to represent the cost of 4 markers is y = k × 4

5 markers = $6.5

Unit cost of each marker = $6.5 / 5

= $1.3 per marker.

If

y = kx

Where,

y = total cost of markers

k = unit cost of marker

x = number of markers

The equation for the cost of 4 markers:

y = kx

y = 1.3 × 4

y = $5.2

Ultimately, y = k × 4 represents the equation for total cost of 4 markers.

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The equation of a line perpendicular to the line y = 1/4x + 2 and passing through a point (x1, y1) is given by:

y - y1 = -4(x - x1)

This is because the slope of the original line is 1/4, so the slope of the perpendicular line must be -4 (the negative reciprocal).

A perpendicular line is a line that forms a 90-degree angle with another line. In other words, it is a line that is perpendicular to another line at their point of intersection. The slope of two perpendicular lines are negative reciprocals of each other, meaning that if one line has a slope of m, the slope of the perpendicular line is -1/m.

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The solution is, the system represents the situation is, x+y= 20

and, 2x+3y = 48.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Each button has a diameter of either 2 or 3 centimeters.

The combined diameters of all buttons is 48 cm.

If x is the number of 2 cm buttons,

and y is 3 cm buttons.

Kate has a collection of 20 buttons.

So, the system represents the situation is,

x+y= 20

and, 2x+3y = 48.

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The equation which is more appropriate for modeling this DATA is y = 64 × (1.25)^x

The correct answer choice is option A.

y = 64 × (1.25)^x

when,

x = 1

substitute into the equation

y = 64 × (1.25)¹

= 64 × 1.25

= 80

y = 79 × 1.25^x

when x = 1

= 79 × 1.25¹

= 79 × 1.25

y = 98.75

79 + 1.25x

when x = 1

= 79 + 1.25(1)

= 79 + 1.25

= 80.25

64 + 22x

when x = 1

= 64 + 22(1)

= 64 + 22

= 86

Therefore, y = 64 × (1.25)^x is the equation which is more appropriate to represent the data.

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[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ - 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{- 6}(x-\stackrel{x_1}{7})[/tex]

The length of the spring stretched is given by the proportion A = 42 meters

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the length of the spring stretched when 56 kg weight is attached be A

Now , the equation will be

The length of the spring when 8 kg is attached to it = 6 meters

So , the proportion is

A / 56 = 6 / 8

On simplifying the equation , we get

Multiply by 56 on both sides of the equation , we get

A = ( 6 x 56 ) / 8

On further simplification , we get

A = 6 x 7

A = 42 meters

Therefore , the value of A is 42 meters

Hence , the equation is A = 42 meters

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Answer:

B

Step-by-step explanation:

There are two types in this good ol' world, Salary and Hourly.

Hourly gets paid by, well, the hour

Salary has a set amount. Let's say there around is $1000 a week. If they work 70 hours, they get paid $1000, if they work 30 hours, they get paid $1000

The cost of a box of pencils is $4.

The cost of a ream of paper is $7.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 1 = 6 is an equation.

We have,

Pencils = x

Reams of paper = y

Now,

Natalie:

3x + 9y = 75 _____(1)

Ronnie:

8x + 5y = 67 _____(2)

From (1) and (2)

Multiply 8 on (1)

Multiply 3 on (2)

24x + 72y = 600

24x + 15y = 201

(-)     (-)       (-)      

      57y = 399

           y = 7

Now,

3x + 9y = 75

3x + 9 x 7 = 75

3x + 63 = 75

3x = 75 - 63

3x = 12

x = 4

Thus,

The cost of a box of pencils and a ream of paper are $4 and $7.

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The missing coordinates of the cubic equations are filled out as ordered pairs as follows

function                coordinates

y = x³                     (-1, -1),  (0, 0)

f(x) = (x - 4)³ - 6      (-1, -131), (0, -70)

The coordinates of the cubic equation is sought by substituting the values of x in the function and solve for y.

for x = -1

y = x³ = (-1)³ = -1

f(x) = (x - 4)³ - 6 = (-1 - 4)³ - 6 = -131

for x = 0

y = x³ = (0)³ = 0

f(x) = (x - 4)³ - 6 = (0 - 4)³ - 6 = -70

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Answer:

Angle A is 90, angle B is 50, angle C is 90, and angle D is 40.

Answer:

<A = 90

<B = 50

<C = 90

<D = 40

Step-by-step explanation:

C:

vertical angles are congruent so the angle left of C is 40.  The angle right to C is 50 because alternate interior angles are congruent

The three angles together are supplemental

180 - 50 - 40 = 90

A:

A = C vertical angles are congruent

A = 90

D:

A, D and 50 are supplemental

180 -90-50 = 40

B

The sum of the interior angles of a triangle are 180

180 - 40 - 90 = 50

The total amount of Investment A is $6,348.58.

What is the compound interest?

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

To find the total amount of investment A, you can use the formula for compound interest:

A = P * (1 + r/n)⁽ⁿᵗ⁾

Where P is the initial investment ($5,000), r is the annual interest rate (6%), n is the number of times interest is compounded per year (2 times), and t is the number of years invested (4).

A = 5000 * (1 + 0.06/2)⁽²*⁴⁾

= 5000 * (1 + 0.03)⁸

= 5000 * 1.03⁸

= 5000 * 1.269716

= $6,348.58

Hence, The total amount of Investment A is $6,348.58.

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The actual cost per pound of potatoes for the 5-pound bag is $0.76 per pound.

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

A 5-pound bag of potatoes costs  $.3.80.

So the rate of the potato per pound is: 3.80/5 = 0.76

Therefore, the cost of potatoes per pound will be $0.76.

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Complete question:

A 5 pound bag of potatoes costs  $.3.80. How much do the potatoes cost per pound?

The actual cost per pound of potatoes for the 5-pound bag is             per pound.

Answer: The definition of a solution is a value or values which, when substituted for a variable in an equation, make the equation true. For example, the solutions to the equation x2 = 4 are 2 and -2. I hope this helped!

Answer:

398

Step-by-step explanation:

40*2q-p

=40*2*5-2

=400-2

=398

Answer:

2008

Step-by-step explanation:

since p=2

q=5

therefore, 402(q)-p

=402(5)-2

=2,010-2

=2008

The different student number possible if a student I.D number consisting of seven digits (the first digits may be repeated) Followed by three of the letters A,B,C,D and E is 32659200.

A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.

The college ID consists of a total of 10 elements in which the first 7 can be a number and the last three are letters A, B, C, D, E.

Since, the number cannot start with a 0, we have the following combination of numbers:

9 * 9 * 8 * 7 * 6 * 5 * 4 * 5 * 4 * 3 = 32659200

where the first seven places represent digits, and the last three represent letters.

Hence, the different student number possible if a student I.D number consisting of seven digits (the first digits may be repeated) Followed by three of the letters A,B,C,D and E is 32659200.

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1. The company’s degree of operating leverage is 4.

2. The degree of operating leverage is 3.34.

3. The new contribution is $17, 280.

How much a company's operating income alters in reaction to a change in sales is measured by the level of operating leverage.

1. Degree of operating leverage = Contribution /Net Operating Income

and, Contribution = 54,000

Net Operating Income = $13,500

Thus, operating Leverage = 54000/ 13500  = 4

2. If Company's sales increase by 7% then contribution also increases by 7%,

Revised Contribution = $54000 + 7% = $57780

and, Revised net Operating income = $57780- $40500

                                                            = 17280

Degree of operating leverage = 57780 / 17280  = 3.34

3. Contribution format income statement:

Sales = $90000+ 7% = $96,300

Less: Variable Cost 36, 000 + 7% = $38520

So, New Contribution = 57780 - 40500 = $17, 280.

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Answer: If you can explain the question a little bit more i would be happy to help!

Step-by-step explanation:

Answer:

400×30= 12000 in 30yrs

12000

Step-by-step explanation:

12000÷.08= 150000

The length of JM is 24 units.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

<H= <K=  <N= 90

and, GH || JK || MN

then, Using proportion

GL/ GM = HK/ HN

18/ (18+ x) = 15/ (15+20)

18(15+20) = 15(18+x )

18 . 20= 15 x

x= (18)(20)/ 15

x= 24

Hence, the length is 24 units.

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Step-by-step explanation:

The rate of change of the population is proportional to the population, so we can use the exponential growth formula:

P(t) = P0 * e^(kt)

Where P0 is the initial population (300), k is the constant of proportionality, and t is the time in hours. We can use the data from t=24 hours to solve for k:

1000 = 300 * e^(24k)

Dividing both sides by 300 and taking the natural logarithm of both sides:

ln(1000/300) = 24k

ln(3.33) = 24k

k = ln(3.33) / 24

Now that we have k, we can plug it into the formula and solve for t when P(t) = 500:

P(t) = 300 * e^(kt)

500 = 300 * e^(kt)

e^(kt) = 500/300

e^(kt) = 5/3

kt = ln(5/3)

t = ln(5/3) / k

Substituting k = ln(3.33) / 24:

t = ln(5/3) / (ln(3.33) / 24)

t ≈ 11.7 hours.