Can the mixed number 7 and 13/100 be simplified?

Answer:

y + 8 = -4(x - 2)

Step-by-step explanation:

Point-slope form of an equation is a fill-in-the-blank, shortcut way to write an equation of a line. This is the format:

y - Y = m(x - X)

You just fill in the slope for m and fill in the point for the X,Y.

Just leave the first y; it stays a y and the first x in the parenthesis stays as an x. You just have to be careful with your minus and negative signs.

Slope is given as -4 so fill that in for m.

and put (2,-8) in place of the X and Y.

y - Y = m(x - X)

y - -8 = -4(x - 2)

y + 8 = -4(x - 2)

Done! Hope this helps!

The number of different batting orders are possible using the starting lineup is 3628800

The given parameter is

Players, n = 10

The different batting orders are possible using the starting lineup is calculated using the following permutation expression

Ways = nCn

Substitute the known values in the above equation

Ways = 10P10

Apply the permutation formula

Ways = 10!/(10 - 10)!

Evaluate the difference

Ways = 10!/0!

0! = 1

So, we have:

Ways = 10!/1

Evaluate

Ways = 10!

Expand

Ways = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

Evaluate the product

Ways = 3628800

Hence, the number of different batting orders are possible using the starting lineup is 3628800

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Events A and B are dependent (option B).

Dependent events are events that can occur together. If event A occurs then event B would occur. In a standard deck of cards, cards that are hearts are red in colour. If a heart card is picked, then it would be red in colour.

Independents events are events whose occurrence do not depend on each other. They are random events.

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Two lines are said to be parallel if and only if the value of the angle between them is [tex]180^{o}[/tex].

Thus the required proofs for each question are stated below:

6. A bisector is a line that divides a given line or angle into two equal parts.

Thus to prove that: AD ║BC

Given that: AC ⊥ BD, then:

BX ≅ DX (midpoint property of a line)

<ADX ≅ <DBX (alternate angle property)

<DAX ≅ <BCX (alternate angle property)

<AXD ≅ <BXC (vertical opposite angle property)

Also,

ΔAXD ≅ ΔBXC (congruent property of similar triangles)

Therefore, it can be deduced that;

AD ║BC

7. Given: CD ≅ CE

<B ≅ <D

proof: AB ║DE

<ABC  ≅EDC

Thus,

CB  ≅ CA (congruent property of similar triangle)

<BAC  ≅ <EDC (alternate angle property)

ABC  ≅ <DEC (alternate angle property)

Also,

CA ≅ CB (congruent side of similar triangles)

ΔABc ≅ ΔCDE (congruent property of similar triangles)

Thus,

AB ║DE (congruent property)

8. Prove: AB ║ DE

Given: <1 ≅ < 3

Then,

<1 ≅ <2 ≅ <3 ≅ [tex]90^{o}[/tex]

So that,

BC ≅ EF

also,

<1 + <2 = [tex]180^{o}[/tex] (supplementary angles)

Therefore it can be inferred that;

AB ║ DE (congruent property of parallel lines intersected by transversals)

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The value of the sine of the angle J is equal to 5 / 13 (approx. 0.38).

The image attached aside shows us a right triangle with two known side lengths (JL, KJ) and a angle measure (m ∠ K). The measure of the missing angle can be found by using the trigonometric function of cosine:

cos m ∠ J = KJ / JL

cos m ∠ J = 12 / 13

m ∠ J = 22.620°

The measure of the angle J within the triangle JKL is approximately 22.620°.

And the sine of the angle J, which helds the same positive sign than cosine as the angle is in the first quadrant on Cartesian plane, is:

sin m ∠J = √(1 - cos² m ∠J)

sin m ∠J = √[1 - (12 / 13)²]

sin m ∠J = 5 / 13

The value of the sine of the angle J is equal to 5 / 13 (approx. 0.38).

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The correct expressions are sinC = 12/25.5 = 24/51, <A = 62 degrees and tan A = 1.875

The given figure is a right triangle with legs 12.0 and 22.5cm and the hypotenuse 25.5cm

For sinA, <A is the reference angle, hence the opposite side will be 22.5cm

sin A = opp/hyp

sinA = 22.5/25.5

For cos C, the adjacent side will be 22.5cm, hence the measure of cos C is 22.5/25.5

cosC = 22.5/25.5

Similarly, sinC = 12/25.5 = 24/51

<A = 180-(90 +38)

<A =180 - 128
<A = 62 degrees

tan A = opp/adj

tan A = 22.5/12 = 1.875

tan C = 12/22.5

tan C = 0.533

Hence the correct expressions are sinC = 12/25.5 = 24/51, <A = 62 degrees and tan A = 1.875

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Answer:

The distance is 36 miles.

Step-by-step explanation:

distance in either direction = d

total time = 5

time going = t

time returning = 5 - t

speed = distance/time

going:

speed = distance/time

18 = d/t

d = 18t       Eq. 1

returning:

speed = distance/time

12 = d/(5 - t)

60 - 12t = d

d =  60 - 12t     Eq. 2

Eq. 1 and Eq. 2 form a system of equations.

d = 18t

d = 60 - 12t

Since d = d, then 18t must equal 60 - 12t

18t = 60 - 12t

30t = 60

t = 2

d = 18t = 18(2) = 36

The distance is 36 miles.

The correct option is option(A) (5x-1)(x+6).

The factors of the given equation are (5x-1)(x+6).

An algebraic expression or number that divides another expression or number equally, leaving no remainder is known as factor.

The quadratic equation [tex]ax^{2} +bx+c=0[/tex]  can be expressed as the product of its linear factors as (x - k)(x - h), where h, k are the roots of the equation. This is known as factoring quadratics.

Dividing the middle term into two factors is used in quadratic factorization in this method. In splitting of the middle term, where x is the product of two factors and last term is the sum of the two factors.

Use the splitting middle term formula

[tex]5x^{2} +29x-6[/tex]

=[tex]5x^{2} +30x-x-6[/tex]

=5x(x+6)-1(x+6)

=(5x-1)(x+6)

The factors of the given equation are (5x-1)(x+6).

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[tex]2 \sqrt{5} \: + \: 7 \sqrt{5} \\ \sqrt{5} \: ( \: 2 + \: 7 \: ) \\ \sqrt{5} \: ( \: 9 \: ) \\ 9 \sqrt{5} [/tex]

The simplification of the expression 2√5 + 7√5 is: 9√5.

So, Option A. is correct.

To simplify the expression 2√5 + 7√5, we can combine the like terms.

Both terms have the same radical expression, which is √5, so we can add their coefficients together.

2√5 + 7√5 = (2 + 7)√5

Now, simplify the coefficients:

2 + 7 = 9

Therefore, the simplified expression is:

2√5 + 7√5 = 9√5

So, the final answer is 9√5.

So, Option A. is correct.

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Step-by-step explanation:

Use the Factor Theorem,

" if x-a is a factor of f(x), then f(a) =0,

So here, since x-3 is a factor then f(3)=0,

So first step, plug in 3 for x for the serperate equations.

[tex] {3}^{2} + ( p + q)3 - q = 0[/tex]

[tex]2(3) {}^{2} + (p - 1)3 + (p + 2q) = 0[/tex]

Simplify both equations,

[tex]9 + 3p + 2q = 0[/tex]

[tex]15 + 4 p + 2q = 0[/tex]

Isolate the constants,

[tex]3p + 2q = - 9[/tex]

[tex]4p + 2q = - 15[/tex]

We have a system of equations so let eliminate a variable, by subtracting the two equations.

[tex] - p = 6[/tex]

[tex]p = - 6[/tex]

Plug p back in for any one of the equations to find q.

[tex]3( - 6) + 2q = - 9[/tex]

[tex] - 18 + 2q = - 9[/tex]

[tex]2q = 4.5[/tex]

So p is -6

q is 4.5

The complete questions is:

The ice cream shop needs 5 pounds of strawberries for every gallon of strawberry ice cream. the shop chooses to produce 4 gallons of chocolate ice cream. how many pounds of strawberries should the shop purchase?

Pounds of strawberry ice cream needed to be bought by the shop exists 20 pounds.

The ice cream shop requires 5 pounds of strawberries for every gallon of strawberry ice cream and the shop chooses to make 4 gallons of ice cream,

Quantity of chocolate ice cream created in the shop = 4 gallons

Quantity of strawberries needed for each gallon of ice cream = 5 pounds

Pounds of strawberries needed to be bought by the shop = Quantity of chocolate ice cream created by the shop [tex]*[/tex] Quantity of strawberries needed for each gallon of ice cream

[tex]$= 4 * 5[/tex]

= 20 pounds.

Pounds of strawberries needed to be bought by the shop exists 20 pounds.

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Answer:

12

Step-by-step explanation:

Get your associates, neighbors, friends, family, or even your local government concerned. It's much more comfortable and more useful to apply environmental attention and create a local project if you cooperate with others in our community.

Get your associates, neighbors, friends, family, or even your local government concerned. It's much more comfortable and more useful to apply environmental attention and create a local project if you cooperate with others in our community. Encouraging environmental awareness exists a vital aspect of being an environmental guardian.

Facilitate knowledge transfer from workers approaching retirement to workers of all ages. Work with families to support children in school and control illiteracy. Provide young people from deprived backgrounds the norms to study. Improve access to education for Aboriginal people.

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Answer:

140 in^2

Step-by-step explanation:

Take the outside dimensions of the LARGE rectangle

11 x 17 = 187 in^2

 subtract the two corner cutout rectangles

    187 - 8x4   -  3 x 5   = 140 in^2

Diagram

Answer: negative slope

constant slope

decreasing function

B-C-E

Step-by-step explanation:negative slope

constant slope

decreasing function

Answer:

£218

Step-by-step explanation:

price of the car = £27000

reduce 30% = 30/100 x 27000 = £8100

£27000 - £8100 = £18900

£18900 - £8000 = £10900

installment per month = £10900/50 = £218

Answer:  48 cm

Step-by-step explanation:

A perimeter(P) of a rectangle is equal to 2(L + W), or 2L + 2W, so we write the equation as:  

1st way:

W = 50%(16) = 0.5 x 16 = 8

   P = 2(L + W)

   P = 2(16 + 8)

   P = 2(24)

   P = 48 cm

2nd way:

   P = 2L + 2W

   P = 2(16) + 2[50%(16)]

   P = 2(16) + 2[0.5 X 16]

   P = 32 + 2(8)

   P = 32 + 16

   P = 48 cm

Answer:

Step-by-step explanation:

B is the best answer

The Confidence interval for 95% who believes that the local businesses overcharge = (0.7026, 0.7574)

The range of values we see in our sample and hope to identify the value that most closely represents the population are referred to as a confidence interval.

Sample size n = 1000

73% of town residents believed that local businesses overcharged for their products over 1000 resident.

= (1000/100) x 73

= 730

Sample proportion p = 730/1000

                                    = .73

q = 1-p = 0.23

Std error of proportion = √(pq/n)

                                      = √((.73*0.27)/1000)

                                      = 0.0140

95% Z critical value = 1.96

Margin of error = 1.96*0.0140

                          = 0.0274

Confidence interval = sample proportion ±margin of error

(0.7026, 0.7574)

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Answer:

0.2857

Step-by-step explanation:

We want to determine,

The probability that the battery life is at least 11 hours is 0.2857.

Answer: equation y= 3/2x+ 4/3

Answer:

4x+2y = 14  The original equation

2y = 14-4x  Subtract 4x from both sides

2y = -4x+14  Rearrange so x is first

y = -2x+7  Divide everything by 2

Explanation:

The steps above practically explain everything needed, so there's not much to add. The standard form is Ax+By = C while slope intercept form is y = mx+b

In the case of y = -2x+7, we have a slope of m = -2 and y intercept of b = 7. This means (0,7) is one point on the line. Use the slope to move down two and to the right one unit to arrive at (1, 5) as another point on this line.

The x-intercept of the function g(x) = -5(x - 3)^2 is (3, 0) and the vertex of the function g(x) = -5(x - 3)^2 is (3, 0)

The function is given as:

g(x) = -5(x - 3)^2

Set g(x) to 0, to determine the x-intercept.

-5(x - 3)^2 = 0

Divide through by -5

(x - 3)^2 = 0

Take the square root of both sides

x - 3 = 0

Add 3 to both sides

x = 3

Hence, the x-intercept of the function g(x) = -5(x - 3)^2 is (3, 0)

The function is given as:

g(x) = -5(x - 3)^2

A quadratic function is represented as:

g(x) = a(x - h)^2 + k

Where, the vertex is

Vertex = (h, k)

By comparing g(x) = a(x - h)^2 + k and g(x) = -5(x - 3)^2, we have

(h, k) = (3, 0)

Hence, the vertex of the function g(x) = -5(x - 3)^2 is (3, 0)

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Answer:

===========================

Minimum:

Maximum:

Median:

Lower quartile:

Upper quartile:

a. The rocket splashes down after 63.94 seconds.

b. The rocket peaks at 7386.68 m

Since the height of the rocket is h(t) = -4.9t² + 370t + 402, the rocket splashes down when h(t) = 0.

So, h(t) = 0

-4.9t² + 370t + 402 = 0

Using the quadratic formula, we find t.

[tex]t = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]

where a = -4.9, b = 370 and c = 402

So, [tex]t = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}\\= \frac{-307 +/- \sqrt{(307)^{2} - 4(-4.9)(402)} }{2(-4.9)}\\= \frac{-307 +/- \sqrt{94249 + 7879.2} }{-9.8)}\\= \frac{-307 +/- \sqrt{102128.2} }{-9.8)}\\= \frac{-307 +/- 319.58}{-9.8)}\\= \frac{-307 + 319.58}{-9.8)} or \frac{-307 - 319.58}{-9.8)}\\= \frac{12.58}{-9.8)} or \frac{-626.58}{-9.8}\\= -1.28 or 63.94[/tex]

Since t cannot be negative t = 63.94 s

So, the rocket splashes down after 63.94 seconds.

Since h(t) = -4.9t² + 370t + 402, to find the time the rocket reaches it peak, we differentiate h(t) with respect to t and equate to zero.

Soi, dh(t)/dt = d(-4.9t² + 370t + 402)/dt

= -9.8t + 370

dh(t)/dt = 0

-9.8t + 370 = 0

-9.8t = -370

t = -370/-9.8

t = 37.76 s

Substitung t = 37.76 into h(t), we have

h(t) = -4.9t² + 370t + 402

h(37.76) = -4.9(37.76)² + 370(37.76) + 402

h(37.76) = -4.9(1425.82) + 370(37.76) + 402

h(37.76) = -6986.518 + 13971.2 + 402

h(37.76) = 7386.682 m

h(37.76) ≅ 7386.68 m

So, the rocket peaks at 7386.68 m

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The prove that BOC = 90° + A/2. is given below:

Note that, bisectors of angles B and C and that of a triangle ABC is one that pass across each other at the point O.

Hence: one need to to prove that ∠BOC = 90° + A/2

Since:

BO is said to be the bisector of angle B e.g. ∠OBC = (∠1)

CO is said to be the bisector of angle C e.g.  ∠OCB = (∠2)

Looking at the triangle BOC, to interpret  by the use of angle sum property, then:

∠OBC + ∠BOC + ∠OCB = 180°

∠1 + ∠BOC + ∠2 = 180° ---- ( equation 1)

Looking at triangle ABC and by the use of angle sum property, So;

∠A + ∠B + ∠C = 180°

∠A + 2(∠1) + 2(∠2) = 180°

Then we divide by 2 on the two sides, and it will be:

∠A/2 + ∠1 + ∠2 = 180°/2

∠A/2 + ∠1 + ∠2 = 90°

∠1 + ∠2 = 90° - ∠A/2 ---(equation 2)

Then one need to Substitute (2) in (1), So:

∠BOC + 90° - ∠A/2 = 180°

∠BOC - ∠A/2 = 180° - 90°

∠BOC - ∠A/2 = 90°

Hence , ∠BOC = 90° + ∠A/2

Therefore, from the above, we care able to prove that BOC = 90° + A/2.

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The number of combinations of balloons that can be chosen is 1716.

Selections and combinations are synonyms. Combinations represent the choosing of items from a predetermined group of items. We're not trying to arrange anything here. We're going to pick them.

Utilizing the combinations formula, it is simple to determine how many distinct groups of r objects each may be created from the provided n unique objects.

Number of red balloons = 12

Number of blue balloons = 8

First, we figure out how to choose from 13 red and 9 blue balloons.

There are 7 balloons left out of the 29 total (i.e. 29 - 13 - 9)

So, n = 7+7-1

n = 13

r = 7

Number of combinations of balloons = [tex]_{13} C_{7}[/tex]

                                                               = 13!/(13-7)!7!

                                                               = 13!/6!7!

                                                               = 1716

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28. 1.45l ÷ 0.32l = 4.53125

so approximately 5 glasses to leave the bottle empty

29. 5.6kg + 2.5kg = 8.1kg

8.1kg ÷ 0.48 = 16.875

he can make 16 complete doughs

there will be 0.875kg of flour left

Answer:

calculate the number of atom in 3 mol helium

The answers to the questions are as follows:

We have E = {1, 3,5, 7, 9, 11, 13, 15, 17, 19}

A= { 3, 7, 9, 11, 15}

B = {5, 7, 11, 13}

We have A n B = numbers that are contained in both of the sets

= 7, 11

a.) We have to count the total number in the dataset. That is the total number of odd numbers that are less than 20.

Hence total numbers in the set = 10

b. The probability that the number is in set AnB

= 7, 11

= 2/10

= 1/5

We can conclude that the probability that the number is in A intersect B = 1/5

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