Solve ΔABC with ABC=51°, c=8 and a=11. Draw a diagram.

Answer:

the cat would take 13 steps

Given the area of the rectangular community garden, the length and width of the garden are 30ft and 10ft respectively.

A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

Area of a rectangle is expressed as;

A = length × Width

Given the data in the question;

We substitute the values into the equation

A = length × breadth

300 = 3x × x

300 = 3x²

Divide both sides by 3

x² = 100

Take the square root of both sides

x = ±√100

x = 10, -10

Since, dimension of a rectangle cannot be Negative.

x = 10

Hence;

Width w = x = 10ft

Length = 3Width = 3x = 3( 10 ) = 30ft

Given the area of the rectangular community garden, the length and width of the garden are 30ft and 10ft respectively.

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Answer:

  D.  π/30 + n(π/15)

Step-by-step explanation:

The given equation can be solved by isolating the cosine function and using the inverse function to find the angles.

  30cos(30x) +14 = -16

  30cos(30x) = -30 . . . . . . subtract 14

  cos(30x) = -1

This is an extreme value of the cosine function that first occurs where the argument is π, and repeats every 2π after that:

  30x = π +2nπ

  x = π/30 +n(π/15) . . . . . odd multiples of π/30

__

Additional comment

The answer choices other than D include all multiples of π/30, or only even multiples of π/30. Either way, they are not part of the correct answer.

Answer:

the side length of hypotenuse is 16.28

Step-by-step explanation:

[tex]a^{2}+b^{2}=c^{2}[/tex]

= [tex]11^{2}+12^{2}= C^{2}[/tex]

= [tex]121+144=c^{2}[/tex]

= [tex]265= c^{2}[/tex]

= [tex]\sqrt{265} = c[/tex]

= [tex]c = 16.28\\[/tex]

Answer:

A = 42.5° (nearest tenth)

B = 47.5° (nearest tenth)

C = 90°

a = 11

b = 12

c = √(265) = 16.3 (nearest tenth)

Step-by-step explanation:

Information:

Side a is opposite angle A.

Side b is opposite angle B.

Side c is opposite angle C.

From inspection of the triangle:

To find the missing side length, use Pythagoras Theorem:

Pythagoras Theorem

a² + b² = c²

(where a and b are the legs and c is the hypotenuse of a right triangle).

Substitute the given values of a and b into the formula and solve for c:

⇒ 11² + 12² = c²

⇒ 121 + 144 = c²

⇒ c² = 265

⇒ c = √(265)

To find one of the missing angles, use the Sine Rule.

Sine Rule

[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Substitute the given values into the formula:

[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{\sin B}{12}=\dfrac{\sin 90^{\circ}}{\sqrt{265}}[/tex]

Solve for angle A:

[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{\sin 90^{\circ}}{\sqrt{265}}[/tex]

[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{1}{\sqrt{265}}[/tex]

[tex]\implies \sf \sin A=\dfrac{11}{\sqrt{265}}[/tex]

[tex]\implies \sf A=\sin^{-1} \left(\dfrac{11}{\sqrt{265}}\right)[/tex]

[tex]\implies \sf A=42.51044708...^{\circ}[/tex]

Therefore, A = 42.5° (nearest tenth)

Interior angles of a triangle sum to 180°:

⇒ A + B + C = 180°

⇒ 42.5° + B + 90° = 180°

⇒ B + 132.5° = 180°

⇒ B = 47.5°

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Answer:

[tex]x=-1,\frac{5}{7}[/tex]

Step-by-step explanation:

1) Split the second term in [tex]7{x}^{2}+2x-5[/tex] into two terms.

1 - Multiply the coefficient of the first term by the constant term.

[tex]7\times -5=-35[/tex]

2 - Ask: Which two numbers add up to 2 and multiply to -35?

7 and -5.

3 - Split 2x as the sum of 7x and -5x.

[tex]7x^2+7x-5x-5[/tex]

2)  Factor out common terms in the first two terms, then in the last two terms.

[tex]7x(x+1)-5(x+1)=0[/tex]

3) Factor out the common term x+1.

[tex](x+1)(7x-5)=0[/tex]

4) Solve for x.

1 - Ask: When will (x+1)(7x-5) equal zero?

When x + 1 0 or 7x-5=0

2 - Solve each of the 2 equations above.

[tex]x=-1,\frac{5}{7}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What are the quadratic formulas?}[/tex]

[tex]\bullet\rm{\ \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]

[tex]\bullet\rm{\ ax^2 + bx + c = 0}[/tex]

[tex]\huge\textbf{What are we solving for?}[/tex]

[tex]\rm{7x^2 + 2x - 5 = 0}[/tex]

[tex]\huge\textbf{What do we have to do?}[/tex]

[tex]\rm{7x^2 + 2x - 5 = 0}[/tex]

[tex]\huge\textbf{Factor the LEFT side of the given}\\\\\huge\textbf{equation:}[/tex]

[tex]\rm{(7x - 5)(x + 1) = 0}[/tex]

[tex]\rm{(7x - 5) \times (x + 1) = 0}[/tex]

[tex]\huge\textbf{Set 0 to the factors:}[/tex]

[tex]\rm{7x - 5 = 0\ or\ x + 1 = 0}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{x = \dfrac{5}{7}\ or\ x = -1}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{\mathsf x = \dfrac{5}{7}\ or\ \mathsf{x} = -1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The point that is 5 units from W is (A) (-5, 2)

The point is given as:

W= (-5, -3)

A point 5 unit from W can be any of the following

W' = (-5 ± 5, -3)

W' = (-5, -3 ± 5)

When the above expressions are evaluated, we have:

W' = (0, -3), (-10, -3), (-5, 2) and (-5, -8)

Hence, the point that is 5 units from W is (A) (-5, 2)

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The length of the hypotenuse of the isosceles triangle is 7.1 units.

We can use the distance formula to find the length of ST (base) and TU(perpendicular). Further, using these lengths, we can find the hypotenuse of the isosceles triangle.

The distance formula is given as follows,

d = √(x₂ - x₁)² + (y₂ - y₁)²

Here, d is the distance between the two points (x₁, y₁) and (x₂, y₂)

As shown in the drawn isosceles triangle STU,

The length of the base ST is given as,

ST = √(x₂ - x₁)² + (y₂ - y₁)²

Here,

x₁ = 1 and y₁ = 1

x₂ = 6 and y₂ = 1

∴ ST = √(6-1)² + (1-1)²

ST = √5²

ST = 5 units

Similarly, for TU as the other leg passes through the point(6,2) and is of length 5 units ( STU being isosceles triangle), we have,

x₁ = 6 and y₁ = 1

x₂ = 6 and y₂ = 6

Also, TU = 5 units

Now, using Pythagoras Theorem,

(hypotenuse)² = (base)² + (perpendicular)²

(SU)² = (ST)² + (TU)²

(SU)² = (5)² + (5)²

(SU)² = 50

SU = √50

SU = 7.071 units

SU ≈ 7.1 units (after rounding of to the nearest tenth)

hence, the hypotenuse of the isosceles triangle is of 7.1 units.

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The amount of medicine infused in 8 hours is 1000ml.

According to the statement

we have given that the medicine normal saline (ns) iv to infuse at 125 ml/hr.

and we have to find the total amount of medicine infuse in the 8 hours in the whole number value.

So,

An infusion is the creation of a new substance by steeping another substance in a liquid, usually water

we have given a rate of infusion of medicine per hour which is 125 ml/hr.

And

Amount of medicine infuse in 1 hour is 125 ml

And the Amount of medicine infuse in 8 hours = 125*8

Amount of medicine infuse in 8 hours = 1000 ml.

So, The amount of medicine infused in 8 hours is 1000ml.

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Answer:

57pi

Step-by-step explanation:

First, let's get the area of the entire circle, including the shaded region:

pi*(8+3)^2 = 121pi

Next, let's get the area of the unshaded circle

pi*8^2 = 64pi

If we subtract the inner circle from the full circle, we get the shaded region:

121pi-64pi =

57pi

Answer: 57π

Step-by-step explanation:

You have to calculate the area of the whole circle created by the sum of the inner circle and the ring, so 8+2=11=r, now use the formua for getting area of a circle, π*r², which is "121π"

After that, subtract the area of the inner circle (its area is π*8²)

So 121π-64π = 57π

Hi! ⋇

               - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

The first digit of this number is 3², which is 9.

The Number is : 9xx

________

The second digit is: -2·(-4)=8.

The Number is : 98x.

________

The sum of all the digits is 18. This gives us an equation that we can solve in terms of x!

[tex]\multimap\sf{9+8+x=18}[/tex] (x is the digit we are looking for)

Now it takes a little arithmetic to find x :)

[tex]\multimap\sf{17+x=18}[/tex]. Just subtract 17 from both sides to find x!

[tex]\multimap\sf{x=1}[/tex]. And Now, can you see the number!

It's 981, of course :)

Hope this made sense to you!

             - - - - - - - - - - - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\large\it{\overbrace{Calligrxphy}}[/tex]

Answer:Answer: true

Step-by-step explanation: f(x) is a function because each x value (left oval) has one y value (right oval)!

Answer:

113.04 ft^2

Step-by-step explanation:

area of the circle= 3.14*(6)^2

Answer:

27.183, 27.2

Step-by-step explanation:

First, do the formula for the triangle:

[tex]\frac{1}{2}[/tex] x 4.1 x 2.6 = 5.33

Next, multiply that by the base side:

5.33 x 5.1 = 27.183

Answer:

1/2 x 4.1 x 2.6 = 5.33

5.33 x 5.1 = 27.183

Rounding off to nearest tenth = 27.2 m^3

Answer:

A. f(-x) = f(x)

Step-by-step explanation:

When plugged into a graph, we can see that the y value of -x is equal to x.

This means, that if we compare the y value of x=3 and x=-3, they will be the same on the graph.

The linear functions that match the following graph are given by:

A linear function is modeled by:

y = mx + b

In which:

The system of equations in this problem is composed by two lines.

The decaying line goes though (-2,4) and (2,-4), hence the slope is given by:

m = (-4 - 4)/(2 - (-2)) = -2

Hence:

y = -2x + b

When x = -2, y = 4, hence we find b as follows:

4 = -2(-2) + b

b = 0.

Hence:

y = -2x -> 2x + y = 0.

The increasing line goes though (1,-2) and (2,3), hence the slope is given by:

m = (3 - (-2))/(2 - 1) = 5

Hence:

y = 5x + b

When x = 1, y = -2, hence we find b as follows:

-2 = 5 + b

b = -7.

Hence:

y = 5x - 7.

-5x + y = -7.

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1320 different ways are there to select the officers so that only one person holds each office given that the club has 12 people who would like to choose people for the offices of president, a vice president, and a secretary. This can be obtained by using the formula of permutation.

Total number of people in the club = 12

total number of positions = (president, vice president, secretary) = 3

From 12 people 3 people are taken at a time.

That is, using the formula for permutation we get,

ⁿPₓ = [tex]\frac{n!}{(n-x)!}[/tex]

Here n = 12 and x = 3

P(12,3)= 12!/(12-3)! =12!/9! = 10×11×12 = 1320

Hence 1320 different ways are there to select the officers so that only one person holds each office given that the club has 12 people who would like to choose people for the offices of president, a vice president, and a secretary.

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[tex] \frac{(6x - 4)(3 - 2x)}{(4x - 6)} = \frac{2(3x - 2)(3 - 2x)}{2(2x - 3)} [/tex]

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

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

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

[tex] - (3x - 2) = 2 - 3x[/tex]

Answer:

10 years old

Step-by-step explanation:

Let m = mother's age

Let f = father's age

Let d = Dina's age

m = 4d               d = f-35                f = m+5

Substitute the middle equation in to the first equation

m = 4(f - 35) Use the distributive property

m = 4f - 140 subtract 4f from both sides

*m -4f = -140

In equation 3 above, subtract m from both sides  to get

f = m+5

f - m = 5  rearrange so that the  m term is first

*-m + f = 5  

Now add the equations together that have *

m -4f = -140

-m + f = 5

     -3f = -135  Divide both sides by -3

f = 45  This is the father's age.  To find Dina's age, plug 45 into the second equation above:

d = f -35

d = 45 -35

d = 10.

To find the mom's age, use the third equation:

f = m+5

45 = m + 5

40 = m

You can check this by plugging the answers you found and you can see that all three equations are solved.

m = 4d                        d = f - 35                 f = m + 5

40 = 4(10)                    10 = 45 - 35            45 = 40 + 5

40 = 40                       10 = 10                     45 = 45

Answer:

B. 52= 3.25n

Step-by-step explanation:

Unit price multiplied by quantity equals total. So, each notebook cost $3.25 and she buys 'n' notebooks.

She totally spends $52.

In conclusion, 3.25 (unit price × n [quantity]) = 52.

And that is.. 52 = 3.25n.

<3

Answer:

B

Step-by-step explanation:

Let's think about what does the given info mean.

Because of n notebooks, she spent $52

One notebook is $3.25.

So 3.25n = 52

Take it this way if you don't understand

Let's say I spent 4$ on two (2) pens

What's the value of one pen?

We want to find the value of one pen and then multiply it by 2, to get 4$

So we normally would do 4/2

However, to set up an equation, we would create

v (value of one pen) x 2 (pens) = 4$ (cost)

v = 4$/2 = 2$

Answer:

37

Step-by-step explanation:

6m+5n

plug in your given values

6(2) + 5(5)

12+25

=37

Answer:

37

Step-by-step explanation:

6m + 5n

6*2  +  5*5 = 12 + 25

= 37

Answer:

The chance of the committee being all boys is 28.57% or 29%

The expansion of the series is 16 + 64 + 256 + 1024

The series is given as:

[tex]\sum\limits^4_{n=1} 4^{n+1}[/tex]

When n = 1, we have:

[tex]4^{n+1} = 4^{1+1} = 16[/tex]

[tex]4^{n+1} = 4^{2+1} = 64[/tex]

[tex]4^{n+1} = 4^{3+1} = 256[/tex]

[tex]4^{n+1} = 4^{4+1} = 1024[/tex]

Hence, the expansion of the series is 16 + 64 + 256 + 1024

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Answer:

C). 16 + 64 + 256 + 1,024

Step-by-step explanation:

I took the test and got it right :)

The time it will take before your investment is worth $6000 = 7 years

The amount of money invested per month = $150

Therefore the amount principally invested yearly;

= 12 × 150 = $1,800

Simple interest = $6000

Rate = 4%

Time = ?

Using the formula for Simple interest (SI)= P×T×R/100

Make T the subject of formula,

T = SI × 100/P×R

T = $6000×100/1800×4

T = 600000/7200

T= 83 months/ 12 = 7 years

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Option A is correct. If segment DC bisects segment AB, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. This can be obtained using perpendicular bisector theorem.

Perpendicular bisector theorem : In a plane, if we choose a point, say D, on the perpendicular bisector,say PQ, drawn from segment, say AB, then the point D is equidistant from the endpoints, that is A and B, of the segment.

That is, perpendicular bisector PQ of line segment AB is the line with         Q = 90° and Q is the midpoint of AB ⇒ AQ = BQ. A point on PQ say D is equidistant from A and B ⇒AD and BD.

Thus in the given question we can use perpendicular bisector theorem.

Here DC is the perpendicular bisector of the line segment AB and therefore AD and BD are equal.

Hence it is clear that Option A is correct.

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Answer:

24 % (to the nearest percent)

Step-by-step explanation:

the probability that the student is a graduate is equal to :

[tex]=\frac{\text{the total number of graduates} }{\text{the total number of students} }[/tex]

[tex]=\frac{2610}{10730} \\=0.243243243243[/tex]

Converting to percentage:

0.243243243243×100

= 24.3243243243 %

Taking into account the change of units, the total distance that he biked in his first month of training is 55.8 miles.

In first place, the rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.

That is, what is intended with it is to find the fourth term of a proportion knowing the other three.  

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.

To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:

a ⇒ b

c ⇒ x

So: [tex]x=\frac{cxb}{a}[/tex]

In his first month of training,Landon biked 3.1 miles and ran 0.75 miles each workout. He completed 18 workouts that month.

So you can apply the following rule of three: if for each workout Landon biked 3.1 miles, in 18 workouts he biked how far?

1 workout ⇒ 3.1 miles

18 workouts ⇒ total distance

So: [tex]total distance=\frac{18 workoutsx3.1 miles}{1 workout}[/tex]

Solving:

total distance= 55.8 miles

In summary, the total distance that he biked in his first month of training is 55.8 miles.

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The required order of the number from least to greatest square root is

1/√3 < √1 < √2 < √2.5

Which number is greatest in value:

In the above numbers 1, 1/3 and 2.5 do not have square roots.

So, we will write 1, 1/3 and 2.5 inside the square root as shown below.

√1 = 1

√(1/3) = 1/√3 = 0.577350269

√2.5 = 1.58113883

√2 = 1.414

Arranging these numbers according to their value, we get the order as-

0.577350269 < 1 < 1.414  < 1.581138831

Hence, the required order of the number from least to greatest square root is 1/√3 < √1 < √2 < √2.5.

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The difference between the numbers given is 6.882.

Based on the information given, it should be noted that difference means subtraction.

The difference between the numbers given will be:

= 7 - (7 - 6.882)

= 7 - 0.118

= 6.882

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There is a total of 10 games played.

There are 5 players, If we select a given player, then that player will play one game with each of the other 4 players.

So we have 4 games at the moment.

Now we select one of the other 4 players, (we don't count the one we choose before). The one that we choose now will play one game wich each one of the remaining 3, so we add 3 more games.

Now we do the same with the remaining 3, this time we add 2 more games.

Now we do that with the remaining 2, now we add 1 more game.

Adding all the games we have:

4 + 3 + 2 + 1 = 10

There is a total of 10 games played.

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