Find the value of x in each case:

Answer:

[tex]k \approx 5$ units[/tex]

Step-by-step explanation:

In Triangle JKL

[tex]\angle K=120^\circ\\\angle L=40^\circ\\KL=2\\JL=k[/tex]

We want to determine the approximate value of k using the law of sines.

[tex]\angle J+\angle K+\angle L=180^\circ $ (Sum of angles in a \triangle)\\\angle J+120^\circ+40^\circ=180^\circ \\\angle J=180^\circ-(120^\circ+40^\circ)=20^\circ[/tex]

Using Law of Sines

[tex]\dfrac{k}{\sin K} =\dfrac{j}{\sin J} \\\dfrac{k}{\sin 120} =\dfrac{2}{\sin 20} \\k=\sin 120 \times \dfrac{2}{\sin 20}\\k=5.06\\k \approx 5$ units[/tex]

Answer:

5.1

Step-by-step explanation:

Right on EDU

Answer:

33 miles

Step-by-step explanation:

Trip to airport:

distance = d1

speed = s1 = 55 mph

time = t1

Trip home:

distance = d2

speed = s2 = 45 mph

time = t2

We are told the same route was used for both trips, so

d1 = d2

The total time was 1 hr 20 min = 1 hr + 20/60 hr = 4/3 hr.

t1 + t2 = 4/3

t2 = 4/3 - t1

speed = distance/time

distance = speed * time

d1 = s1 * t1

d2 = s2 * t2

d1 = d2, so

s1 * t1 = s2 * t2

t2 = 4/3 - t1; s1 = 55; s2 = 45

55 * t1 = 45(4/3 - t1)

55t1 = 60 - 45t1

100t1 = 60

t1 = 0.6

The time to get the the airport was 0.6 hr. Now we find the distance.

d1 = s1 * t1

d1 = 55 * 0.6

d1 = 33

The distance is 33 miles.

The airport is at a distance of 33 miles from Dara's home.

Speed is directly proportional to distance and inversely proportional to time. Its equation is given as:

Speed = Distance/Time.

The other equations, formed using this equation are:

Distance = Speed*Time

Time = Distance/Speed.

In the question, we are informed that Dara drove from home to the airport to pick up her friend and then came back home on the same route. Her average speed on the way to the airport was 55 miles per hour (mph), and her average speed on the way back home was 45 mph.

We are asked to find the distance between Dara's home and the airport, if the total driving time was 1 hour 20 minutes.

We assume the distance between Dara's home and the airport to be x miles.

As she went to the airport and came back from the airport via the same route, her distance in both the cases will be x miles.

Time taken by Dara to go from home to the airport,

t1 = Distance/Speed = x/55 (Since, her average speed on the way to the airport was 55 mph).

Time taken by Dara on the way back home,

t2= Distance/Speed = x/45 (Since, her average speed on the way back home was 45 mph).

Now, total driving time can be written as,

t1 + t2,

= x/55 + x/45,

= (9x + 11x)/495,

= 20x/495,

= 4x/99.

Now, we know that this time is given as 1 hour and 20 minutes = 1 1/3 hours = 4/3 hours.

Therefore, we an write the equation:

4x/99 = 4/3,

or, x = (4*99)/(4*3) = 33.

Therefore, the airport is at a distance of 33 miles from Dara's home.

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Answer:

4096

Step-by-step explanation:

used a calculator but u always do indicies first due to bidmas

Answer:

4096

Step-by-step explanation:

The little two on top of the 32 means squared or that we need to multiply 32 by itself.

So 32*32 equals 1024

Then we multiply it by 4 to give us 4096.

Answer:

1) decrease in pressure

2) increase in temperature

3) increase in volume

4) accumulation of the product in the reaction system

Step-by-step explanation:

Equilibrium is generally defined as a state in which there is no observable change in the system over a period of time. In chemical systems, equilibrium is dynamic, this implies that the toward and reverse reactions proceed at the same rate.

The Le Chateliers principle states that if an external constraint such as change in temperature, pressure or concentration is imposed on a reaction system in equilibrium, the equilibrium position will shift so as to annul the constraint.

For the system shown in the question, low pressure, increase in volume, increase in temperature and accumulation of the product in the reaction system will make the equilibrium position to shift towards the left (reactants side)

Answer:

Step-by-step explanation:truest

Answer:

Its False

Step-by-step explanation:

to be an identity the equation has to be true for all values in the domain, sqrt3/2 is a specific value

Answer:52

Step-by-step explanation:

104 / 2 = 52 and a inscribed angle is half of a central angle.

Answer:

  (–1.4, 1.5)

Step-by-step explanation:

The blue line and the purple line are the lines corresponding to the equations of interest. Their point of intersection is in the 2nd quadrant, so is nearest to ...

  (–1.4, 1.5)

__

It can be useful to understand that for equations in standard form:

  ax +by = c

the x- and y-intercepts are ...

__

For the equations of interest, the first has intercepts of ...

  x=2/3, y=1/2 . . . . graphed line makes a 1st-quadrant triangle with the axes (blue line)

And the second has intercepts of ...

  x=-1, y=-4 . . . . graphed line makes a 3rd-quadrant triangle with the axes (purple line)

Since the purple line has a steeper slope, the point of intersection of the lines will be in the 2nd quadrant. There is only one 2nd-quadrant answer choice: (-1.4, 1.5).

Answer:

(–1.4, 1.5)

Step-by-step explanation:

Answer:

1.7

Step-by-step explanation:

Answer: 9 Apples

Step-by-step explanation:

Given the following :

Total number of bags = 12

Mean of the distribution(m) = 8

Number of apples (x):

6 - - - - 7 - - - - 8 - - - - 9 - - - - 10

Frequency (f) :

1 - - - - 4 - - - - 2 - - - - 3 - - - - 1

Therefore :

Let number of apples in the 12th bag = y

Frequency of 12th bag : (12 - 11) = 1

Mean of distribution(m) :

Sum of ( f * x) / sum of f

Sum of (f * x) = (6*1)+(7*4)+(8*2)+(9*3)+(10*1)+(y*1)

Sum of (f * x) = (6+28+16+27+10+y) = 87 + y

Sum of f = 12

From :

m = Sum of ( f * x) / sum of f

8 = (87 + y) / 12

87 + y = 12 * 8

87 + y = 96

y = 96 - 87

y = 9

Number of apples in 12th bag is 9 apples

Answer:

28cm^2

Step-by-step explanation:

I find the area of the shape, simply add the square engulfed within it

I was able to find 28! So 28cm^2

Hope this helps

Answer: 28.5 square units

Step-by-step explanation: Count the whole squares in the figure then figure the areas of the triangular areas around the sides. Whole squares 3+5+5+5 = 18

Left side: 5/2 = 2.5

Top (2)( 3/2) = 3

Right: 4/2= 2

Bottom 6/2 = 3

Sum of triangular areas: 10.5

Add squares and triangles:

18+10.5= 28.5

It may be possible to compute the area by using the Pythagorean Theorem to get the lengths of the bases and height, but that's a bit more complicated!

Answer:

A=9675.299

Step-by-step explanation:

A=p(1+r)^t

A compound amount

P is the principle amount invested

r : rate ( semiannually is 0.5 )

t=years ( semiannually 12*2=24)

A=3000(1+0.10/2)^24

A=9675.299

Answer:

the total weight of the hosepipe and the reel is 7.4 kg

Step-by-step explanation:

First, we need to find the weight of the hosepipe, we know that 1/2 metre of the hosepipe has a weight of 150 grams, therefore we can conclude that 1 meter has a weight of (150)(2) = 300 grams.

If one meter weighs 300 grams, then 20 meters have a weight of [tex]20(300) = 6000[/tex] grams. But since 1000 grams are 1 kg, this would be equivalent to 6 kg.

Now, to find the total weight of the hosepipe and the reel we are going to sum up the 2 weights:

Total weight = hose pipe weight + reel weight

Total weight = 6 kg + 1.4 kg

Total weight = 7.4 kg.

Therefore, the total weight of the hosepipe and the reel is 7.4 kg

Step-by-step explanation:

Since the polygon has four vertices (D,E,F and G), it is a quadrilateral (4 vertices).

Answer:quadrilateral

Step-by-step explanation:

It has four points, so it has four sides which makes it a quadrilateral.

Answer:

198

Step-by-step explanation:

Answer:  125 miles

if you do the math you will get the same answer.

Answer:

800 miles

Step-by-step explanation:

Answer:

The first one would be reasonable, because the minutes late is 50, which is a little under 1 hour.

Explanation:

The 2nd one uses a negative value for m, you can't use a negative value when adding time.

The 3rd and fourth have fairly large numbers which are not typical for parents picking up their kids.

Answer:

Step-by-step explanation:

Dilation centered at the origin multiplies every coordinate value by the scale factor.

  K(1, -1) ⇒ K' = 4(1, -1) = (4, -4)

  L(2, -1) ⇒ L' = 4(2, -1) = (8, -4)

  M(2, 2) ⇒ M' = 4(2, 2) = (8, 8)

  N(1, 2) ⇒ N' = 4(1, 2) = (4, 8)

The answer is for this question is c

2(3x+2)+2(2x-1)

=10x+2

This is a polynomial

So the answer is c

Answer:

4.5 < T < 5.5

Step-by-step explanation:

Nearest 5 minutes could be 4.5 to 5.49

The computation of the limits in between is shown below:

Now Multiply these numbers by 30

4.5 × 30 = 135

5.4 × 30 = 162

5.5 × 30 = 165

We can easily round 5.5 would to 6, since we cannot use 5.5.  

Therefore  

135 < T < 162

Therefore If the correct answer is  135 < T < 165

So it must be 4.5 < T < 5.5

Answer:

1) The length of the third side is 5.607 units

2) The sum of the numbers from 1 to 100 is 5050

3) For the x-axis, foci: ((√15/28), 0) and (-(√15/28), 0)

For the y-axis, foci: (0, (√15/28)) and (0, -(√15/28))

Step-by-step explanation:

1) When two sides of the triangle are equal to 4 then the triangle is an isosceles triangle

Given that the included angle (the angle between the two sides) is 89°, we have;

The other two base angles are equal to {180 - 89)/2 = 91/2 = 45.5°

Therefore, we have from cosine rule;

a² = b² + c² - 2·b·c·cos(A)

We note that the angle opposite the third side is the included angle 89°, therefore, when we put a as the third side in the above equation, we have;

a² = 4² + 4² - 2×4×4×cos(89°)

a² = 31.44

a = 5.607

The length of the third side is 5.607 units

2) The numbers 1 to 100 form an arithmetic series with the first term, a = 1 and the common difference, d = 1 with the number of terms n = 100

The sum of an arithmetic progression, Sₙ, is given as follows;

[tex]S_n = \dfrac{n}{2}\cdot (2 \cdot a + (n - 1) d)[/tex]

Therefore, by plugging in the values, we have;

Sₙ = 100/2*(2*1 + (100 - 1)*1) = 100/2*(101) = 5050

The sum of the numbers from 1 to 100 is 5050

3) The foci of an ellipse 7·x² + 8·y² = 30 is found as follows;

Dividing both sides of the equation by 30 gives;

7/30·x² + 8/30·y² = 30/30

7/30·x² + 8/30·y² = 30/30

7/30·x² + 4/15·y² = 1

Which is of the form;

x²/a² + y²/b² = 1

For the x-axis we have

c² = a² - b²

c² = 30/7 - 15/4 = 15/28

h = 0, k = 0

Foci: ((√15/28), 0) and (-(√15/28), 0)

For the y-axis, we have;

x²/b² + y²/a² = 1

The foci are then (0, (√15/28)) and (0, -(√15/28)).

Answer:

If the amount of dough for a small pizza is S, for a large pizza is L and for a medium pizza is M, we have the equations:

M = (3/2)*S

L = (5/2)*S

L = M + S

First, we can convine the second and third equation and get:

(5/2)*S = M + S

and now we can replace M by the first equation:

(5/2)S = (3/2)*S + S = 5/2 S

so we have a trivial equation, S can be any number, this means that the system of equation is not well constructed.

For example, if S = 1Kg then:

M = (3/2)kg

L = (5/2)kg = (3/2)kg + 1 kg = 5/2kg

Answer:

The equation for a small pizza is, 3/2s + s = 5/2s.

Next, to combine like terms the equation is, 5/2s = 5/2s.

After that, for opposite operations you write, 5/2s - 5/2s = 0.

When you combine the like terms for the last equation, you come up with,

0 = 0.

The small sized pizza does not have a specific size and is no longer part of the equation. Its' size can be anything, and the other sized pizzas will equal their equation towards the small pizza, still representing their same value.

Step-by-step explanation:

cheese + sauce + dough + lots of meat + fire = happiness/pizza

(HopE ThIs HeLPs) ‍

Answer:

2m/s south

Step-by-step explanation:

p = mv

Where p is the momentum, m is the mass, while v is the velocity.

Given that

m = 25kg

v = ?

p = 50kgm/s

Substituting the values into the formula.

50kgm/s = 25×v

50kgm/s = 25v

Divide both sides by 25

v = 50/25

v = 2m/s

From the option list, the answer is

2m/s south

Answer:  16 one side 32 second side 48 third side

Step-by-step explanation:

16;32;48

3;4;5

Answer:

24, 32, 40

Step-by-step explanation:

We know that the ratio of the sides is 3:4:5, and that total is 96.

First I tested out some numbers by multiplying them by 3, 4, and 5

Eventually I got to 8;

8×3:8×4:8×5 --> 24:32:40 --> 3:4:5

24+32+40=96

Meaning, the sides were 24, 32, and 40

Hope this helps, and good luck!

Answer:

(5,4)

Step-by-step explanation:

10x + 20y = 130

x + y = 9

you can solve by substitution

x = 9 - y

10 (9 - y) + 20y = 130

90 - 10y + 20y = 130

90 + 10y = 130 (subtract 90 from both sides)

10y = 40

y = 4

Plug the answer back in the original equations to solve for x

x + 4 = 9 (subtract 4 from both sides)

x = 5

The number of activities that cost $10 is 4.

The number of activities that cost $20 is 5.

10a + 20b = 130 equation 1

a + b = 9 equation 2

Where:

Multiply equation 2 by 10

10a + 10b = 90 equation 3

Subtract equation 3 from equation 2

$10b = $40

b = $40 / $10

b = 4

Subtract 4 from 9: 9 - 4 = 5

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Answer:  6

Step-by-step explanation:

Let x represent the number of plates bought for $6

Let y represent the Total number of plates bought = x + 1

Remember that Mrs. Lim bought another plate for $18

Total cost ÷ Total plates = Average Cost

[tex]\dfrac{6x+18}{x+1}=8\\[/tex]

6x + 18 = 8(x + 1)

6x + 18 = 8x + 8

       18 = 2x + 8

       10 = 2x

        5 = x

y = x + 1

  = 5 + 1

  = 6

Answer:

The answer is option D.

Step-by-step explanation:

f(x) = x² + 2x

g(x) = 2x

To find (ƒ ∘ g)(2) first find (ƒ ∘ g)

To find (ƒ ∘ g) wherever you see x in f(x) replace it with g(x)

That's

(ƒ ∘ g) = (2x)² + 2(2x)

= 4x² + 4x

Substitute 2 into the expression

That's

(ƒ ∘ g)(2) = 4(2)² + 4(2)

= 4(4) + 8

= 16 + 8

= 24

Hope this helps you.

Answer:

C & D

Step-by-step explanation:

x² + 3x - 3 = 0

a = co efficient of  x² = 1

b=  co efficient of x = 3

c = constant = -3

roots = (-b ± [tex]\sqrt{b-4ac}[/tex])/2a

    = (-3±[tex]\sqrt{3^{2}-4*1*[-3]}[/tex] )/2*1

    = (-3±[tex]\sqrt{9+12}[/tex])/2

    = (-3±√21)/2

  [tex]x = \frac{-3+\sqrt{21}}{2} ; x =\frac{-3-\sqrt{21}}{2}[/tex]

Answer:

linear: y = x + 1

non-linear: y = x² + 1

Step-by-step explanation:

In a linear relationship, from one pair (x1,y1) to other one (x2,y2) that satisfies the equation, there is a constant k, so that k = (y2 - y1)/(x2 - x1).

Equation: y = x + 1

Computing some points as an example:

x | y

0 | 1

1  | 2

2 | 3

3 | 4

(2-1)/(1-0) = (3-2)/(2-1) = (4-3)/(3-2) = 1. Therefore, the equation is linear.

Equation: y = x² + 1

Computing some points as an example:

x | y

0 | 1

1  | 2

2 | 5

3 | 10

(2-1)/(1-0) ≠ (5-2)/(2-1) ≠ (10-5)/(3-2). Therefore, the equation is not linear.

Answer:

radius = 6.5

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ( where r is the radius )

x² + y² = 42.25 ← is in this form

with r² = 42.25 ( take the square root of both sides )

r = [tex]\sqrt{42.25}[/tex] = 6.5

Answer:

The equation is [tex]y=\frac{-3}{2} x-9[/tex]

Step-by-step explanation:

First, you will have to find the slope of the two points.To do that, you will have to use the formula : [tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

Our points are [tex](1,6)[/tex] and [tex](5,0)[/tex]

We will have to substitute the points into the formula.

[tex]m=\frac{0-6}{5-1}[/tex]

Then, we will simplify

[tex]m= \frac{-6}{4}[/tex]

We could simplify that fraction into [tex]\frac{-3}{2}[/tex]

So, our slope is [tex]\frac{-3}{2}[/tex]

We will have to pick a coordinate point, and choose. I chose [tex](1,6)[/tex]

We will substitute the x-value and the y-value of the coordinate point, including our slope, to calculate the y-intercept.

The formula we will be using is [tex]y=mx+b[/tex]

We will substitute in our values which will make it look like:

[tex]6=\frac{-3}{2} (1)+b[/tex]

We will then multiply [tex]\frac{-3}{2}[/tex] by [tex]1[/tex] which will stay the same.

Then, we will multiply [tex]\frac{-3}{2}[/tex] by [tex]6[/tex] which will equal [tex]-9[/tex]

[tex]-9=b[/tex]

Hence, the equation for our line is [tex]y=\frac{-3}{2} x-9[/tex]

Hope it helped:D

-Jazz