1. Solve the equation 2x ^ 3 + 7x ^ 2 - 10x - 24 = 0 in the real number system

The length and the width of the outside edge of the garden will be ( 6x + 12 ) and ( 9x + 6 ) respectively.

In mathematics, a scale factor is the proportion of related dimensions of an object to a description of that object.

Given that:-

The length and width of the outside edge will be:-

The sides are Dilated by factor 3 so the edges of the rectangle will be calculated as;-

Length = 3 ( 2x+4 ) = 6x + 12

Width   = 3 ( 3x+2 ) = 9x + 6

Therefore the length and the width of the outside edge of the garden will be ( 6x + 12 ) and ( 9x + 6 ) respectively.

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Answer:

I believe the answer is 240

Answer:

$16.30

Step-by-step explanation:

Hope this helps! Have a great day!!

The cost of 163 text messages is $16.3

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Steps to Use Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

Given:

price for 28 text messages = 2.80

So, price for 1 text messages = 2.80/ 28

                                                = $ 0.1

Now, the price for 163 messages = 163 * 0.1

                                                       = $16.3

Hence, the price for 163 text messages be $16.30.

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The inference is that the results of the study are statistically significant.

For group 1, we have:

Mean = 1.7

For group 2, we have:

Mean = 3.3

The mean of group 2 is greater than group 1, and the mean difference is:

Difference = 3.3 - 1.7

Evaluate

Difference = 1.6

Based on the sample values, the mean difference of 1.6 is significant.

Hence, the inference is that the results of the study are statistically significant.

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Answer

90*

Step-by-step explanation:

Answer:

s = 30

Step-by-step explanation:

The three angles lie on a line.

The sum of angles on a line are supplementary, meaning they add up to 180 degrees.

Answer:

Step-by-step explanation:

Let the distance between police station and the fire station be x.

According to question we have:

It can be expressed as:

Solve the equation for x:

Correct choice is C

There are 2118760 ways to select 5 patients from 50 patients.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements.

Here, Total patients= 50

         Number of selection is to made = 5

So, total ways of selection = ⁵⁰C₅

                                           = (50X49X48X47X46) / (5X4X3X2X1)

                                          = 2118760 ways

Thus, There are 2118760 ways to select 5 patients from 50 patients.

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Answer:

2118760

Step-by-step explanation:

She can select 5 patients from 50 patients in :

[tex]50c_{5}[/tex]

=  [tex]\frac{50!}{5! (50-5)!}[/tex]

=   [tex]\frac{50!}{5! 45!}[/tex]

= 50 x 49 x48 x47 x46 x45!

= 2118760

The sides of the triangle are (d) 12√2, 12√2, 24

The given parameters are:

In a 45-45-90 degree angle triangle, we have:

Hypotenuse = Opposite√2 and Hypotenuse = Adjacent√2

This means that:

Opposite =Adjacent

So, we have:

24 = Adjacent√2

Divide both sides by √2

Adjacent = 24/√2

Evaluate

Adjacent = 12√2

This means that:

Opposite = 12√2

Hence, the sides of the triangle are (d) 12√2, 12√2, 24

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Answer:

1/2

Step-by-step explanation:

There are 3 numbers greater than 2: 3, 4, 5, and 6. There are 6 numbers, so it is 3/6=1/2.

The equation that models the height of the baseball is determined as H(t) = 5 + 49.64t -16(t)².

The maximum height reached by the baseball is calculated as follows;

H = y₀ + v₀yt + ¹/₂gt²

Assuming negative direction for upward motion

H = y₀ + v₀yt - ¹/₂gt²

0 = y₀ + vt -16(t)²

0 = 5 + 3.2v - 16(3.2)²

0 = 5 + 3.2v - 163.84

3.2v = 158.84

v = 158.84/3.2

v = 49.64

H(t) = 5 + 49.64t -16(t)²

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Answer:C?

Step-by-step explanation:

edge

Answer:

Domain: x < 5

Range: all numbers, -∞, ∞

This is because the problem will be able to be solved with multiple solutions as long as there are no specific values assigned to x. The problem will have a solution from a range of negative infinity to infinity, meaning every number or solution you can think of.

Answer:

Θ ≈11.31°

Step-by-step explanation:

the model is a right triangle with side opposite being the height and side adjacent the horizontal length , in relation to angle Θ , then

using the tangent ration

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{4}{20}[/tex] , then

Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{4}{20}[/tex] ) ≈ 11.31° ( to 2 dec. places )

Answer:

No

Step-by-step explanation:

Since an equilateral triangle has equal sides and angles, each angle measures 60°, which is acute. Therefore, an equilateral angle can never be obtuse-angled. A triangle cannot be right-angled and obtuse angled at the same time. Since a right-angled triangle has one right angle, the other two angles are acute.

Answer:

false

Step-by-step explanation:

Answer:

Increase the slope

Step-by-step explanation:

The slope of this line is '3' ......a steeper line has a higher number than '3' in front of the 'x'    like    y = 4x+3      or      y = 7x + 12

They will be 15 miles apart after one hour if they left the same point at the same time.

The distance between two points in geometry can be calculated by using the Pythagoras theorem.

Mathematically, the Pythagoras theorem can be expressed as:

[tex]\mathbf{d = \sqrt{x^2 +y^2}}[/tex]

where;

[tex]\mathbf{d = \sqrt{(9)^2 +(12)^2}}[/tex]

[tex]\mathbf{d = \sqrt{81+144}}[/tex]

[tex]\mathbf{d = \sqrt{225}}[/tex]

d = 15 miles  

Therefore, we can conclude that they will be 15 miles apart after one hour if they left the same point at the same time.

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Answer: 5

Step-by-step explanation:

Since [tex]\overline{GH} \parallel \overline{DE}[/tex], by the corresponding angles theorem, [tex]\angle FGH \cong \angle FDE, \angle FHG \cong \angle FED[/tex]. This means [tex]\triangle FGH \sim \triangle FDE[/tex] by AA.

As corresponding sides of similar triangles are proportional,

[tex]\frac{10}{x+3}=\frac{10+x}{12}\\(10)(12)=(10+x)(x+3)\\120=x^{2}+13x+30\\x^{2}+13x-90=0\\(x+18)(x-5)=0\\x=-18, 5[/tex]
However, as distance must be positive, we consider the positive solution, x=5.

Therefore, the answer is 5

Answer:

0.55 hope it will help you

The number of ways can the committee be organized will be 2220075. Then the correct option is 3.

A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.

The prom committee is made up of 8 boys and girls.

If there are 12 boys and 15 girls in the group to pick the committee from.

Then the number of ways can the committee be organized will be

Then the number of ways is given by the combination formula. Then we have

Number of ways = ¹²C₀ x ¹⁵C₈ + ¹²C₁ x ¹⁵C₇ + ¹²C₂ x ¹⁵C₆ + ¹²C₃ x ¹⁵C₅ + ¹²C₄ x ¹⁵C₄ + ¹²C₅ x ¹⁵C₃ + ¹²C₆ x ¹⁵C₂ + ¹²C₇ x ¹⁵C₁ +¹²C₈ x ¹⁵C₀

Number of ways = 6435 + 77220 + 330330 + 660660 + 675675 + 360360 + 97020 + 11880 + 495

Number of ways = 2220075

Thus, the correct option is 3.

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y-1=\stackrel{\stackrel{m}{\downarrow }}{2}(x-4)\qquad \impliedby \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}[/tex]

so we're really looking for the equation of a line with a slope of 2 and that it passes through (4 , 1)

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \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}{1}=\stackrel{m}{2}(x-\stackrel{x_1}{4})[/tex]

kinda twins.

Step-by-step explanation:

[tex]4 {x}^{2} -5x-6=0 [/tex]

Solve using quadratic formula

Solution:

We know that

[tex] \rm \: Quadratic \: Formula = \cfrac{ - b± \sqrt{ {b}^{2} - 4(ac) } }{2a} [/tex]

ATQ,here,

Substitute the values into the quadratic formula.

[tex]\rm\implies x = \cfrac{5 ± \sqrt{( - 5) {}^{2} - 4 \times (4 \times - 6) } }{2 \times 4} [/tex]

[tex]\rm\implies{x} = \cfrac{5 ± \sqrt{25 - 4 \times (24) } }{2 \times 4} [/tex]

[tex] \implies \rm \: x = \cfrac{5 ± \sqrt{25 - 96} }{8} [/tex]

[tex] \implies \rm \: x = \cfrac{5± \sqrt{121} }{8} [/tex]

[tex] \implies \rm \: x = \cfrac{5± \sqrt{11 \times 11} }{8} [/tex]

[tex] \implies \rm \: \: x = \cfrac{5±11}{8} [/tex]

[tex]\boxed{x = 2}[/tex]

OR

[tex]x = \boxed{- \cfrac{3}{4}} [/tex]

Answer:

Multiplying 10 by pi will produce an irrational number.

Step-by-step explanation:

10 and 10 are both rational, 10 and 10.5 are both rational, 10 and √4 are both rational (I researched to double check), leaving 10 rational and 3π irrational, meaning that the answer is B 3π.

Answer:

8626

Step-by-step explanation:

use a calculator in instead of here this was a EZ question but thanks for the points and if you have a harder question i'll be waiting

Answer: 8,626

Step-by-step explanation:

PEMDAS

Parenthesis

Exponents

Multiplication

Division

Addition  

Subtraction

Multiplication comes first:

2+ (7x1232)

Next, addition:

2+8624

8626

Hope this helps :)) Brainliest would be appreciated :D

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Work Shown:

Applying the law of cosines

c^2 = a^2 + b^2 - 2*a*b*cos(C)

c^2 = 8^2 + 5^2 - 2*8*5*cos(88)

c^2 = 64 + 25 - 80*cos(88)

c^2 = 86.2080403

c = sqrt(86.2080403)

c = 9.2848285

c = 9

Technically he needs 10 meters of rope because of the extra 0.28 portion, but I'll stick with 9 meters since your teacher said to round to the nearest whole number.

Answer:

Step-by-step explanation:

To determine the number of combinations of 3 playing cards from a standard 52-card deck, we can use the formula for combinations, which is given by:

C(n, k) = n! / (k!(n-k)!)

Where n is the total number of items (in this case, the number of cards in the deck) and k is the number of items chosen (in this case, 3 cards).

Plugging in the values:

n = 52 (total number of cards in the deck)

k = 3 (number of cards chosen)

C(52, 3) = 52! / (3!(52-3)!)

Calculating the factorial terms:

52! = 52 x 51 x 50 x ... x 3 x 2 x 1

3! = 3 x 2 x 1

(52-3)! = 49! = 49 x 48 x ... x 3 x 2 x 1

Simplifying the equation:

C(52, 3) = 52 x 51 x 50 / (3 x 2 x 1)

Cancelling out the common factors:

C(52, 3) = (52 x 17 x 25) / (3 x 2 x 1)

C(52, 3) = 22,100

Therefore, there are 22,100 combinations of 3 playing cards that can be chosen from a 52-card deck.

Answer:

A.

Step-by-step explanation:

For the x value (6) there are two different output values(y) 5 and 6.

If it's a function then there must be one output value for every input.

#1

Yes

#2

No

#3

No

#4

No

Answer:

(-14, 12) and (5, 12)

Step-by-step explanation:

From inspection of the points given, we can see that all pairs of points share the same y-values.

Therefore, each pair of points are on the same horizontal line.

To find the distance between the points, simply find the difference between the x-values.

Given points:  (-14, 12) and (5, 12)

⇒ Difference between x-values = 5 - (-14) = 19 units

Given points:  (-5, 19) and (12, 19)

⇒ Difference between x-values = 12 - (-5) = 17 units

Given points:  (-20, 5) and (1, 5)

⇒ Difference between x-values = -20 - 1 = -21 = 21 units

Given points:  (14, 12) and (5, 12)

⇒ Difference between x-values = 14 - 5 = 9 units

Answer:

table a represents functions table b does not