In the triangle below, what is the cosine of 62 degrees?

Answer:

The linear equation for the line which passes through the points given as (-2,8) and $(4,6), is written in the point-slope form as [tex]$y=-\frac{1}{3} x-\frac{26}{3}$[/tex].

Step-by-step explanation:

A condition is given that a line passes through the points whose coordinates are (-2,8) and (4,6).

It is asked to find the linear equation which satisfies the given condition.

Step 1 of 3

Determine the slope of the line.

The points through which the line passes are given as (-2,8) and (4,6). Next, the formula for the slope is given as,

[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

Substitute [tex]$6 \& 8$[/tex] for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and 4&-2 for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows, [tex]$m=\frac{6-8}{4-(-2)}$[/tex]

[tex]$$\begin{aligned}&m=\frac{-2}{6} \\&m=-\frac{1}{3}\end{aligned}$$[/tex]

Step 2 of 3

Write the linear equation in point-slope form.

A linear equation in point slope form is given as,

[tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]

Substitute [tex]$-\frac{1}{3}$[/tex] for m,-2 for [tex]$x_{1}$[/tex], and 8 for [tex]$y_{1}$[/tex] in the above equation and simplify using the distributive property as follows, [tex]y-8=-\frac{1}{3}(x-(-2))$\\ $y-8=-\frac{1}{3}(x+2)$\\ $y-8=-\frac{1}{3} x-\frac{2}{3}$[/tex]

Step 3 of 3

Simplify the equation further.

Add 8 on each side of the equation [tex]$y-8=-\frac{1}{3} x-\frac{2}{3}$[/tex], and simplify as follows, [tex]$y-8+8=-\frac{1}{3} x-\frac{2}{3}+8$[/tex]

[tex]$y=-\frac{1}{3} x-\frac{2+24}{3}$$\\ $$y=-\frac{1}{3} x-\frac{26}{3}$$[/tex]

This is the required linear equation.

Answer:

d) the two triangles are similar by AA

Step-by-step explanation:

The expression 12r - 5 are equivalent to 6(2r+(-1))+1 and -4(2+(-3r))+3 option (A) and (B) are correct.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

= 12r - 5

A) 6(2r+(-1))+1

= 12r + 6(-1) + 1

= 12r -5

B) -4(2+(-3r))+3

= -8 -4(-3r) + 3

= -5 + 12r

or

= 12r - 5

Thus, the expression 12r - 5 are equivalent to 6(2r+(-1))+1 and -4(2+(-3r))+3 option (A) and (B) are correct.

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The values are as follows:

z=50

v= 150

x= 100

y=15

w= 50

Parallel lines are lines in a plane that are always the same distance apart.

z+130= 180   (Linear pair)

z=50

v+ 30 = 180  (Linear pair)

v= 150

x= 180- 30 - 50  (angle sum property)

x= 100

2y=30   (alternate interior angle)

y=15

w+x+2y=180  (Linear pair)

w+ 100 + 30 = 180

w= 50

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Answer:

Y≈4.6

Step-by-step explanation:

Because the hypotenuse is 9rad2 and the angle opposite of it is a 90. You can deduce it is a 90-45-45. From this you can tell the legs are 9. You then do 9 tan 26 to get about 4.4, and after this you subtract it from 9.

Answer:

200 miles

Step-by-step explanation:

Set up a cost equation for each plan using x for miles.

Set the equations equal.

Solve for x, the miles.

For a 1 day rental.

Plan A:

C = 0.18x + 30

Plan B:

C = 66

0.18x + 30 = 66

0.18x = 36

x = 36/0.18

x = 200

Answer: 200 miles

The answers to the various part as well as its reasons are given below

An approximate average rate of change of the graph from x = 3 to x = 5, shows the reduction in profit from  3 to 5.

Based on the above,  the domain is one that is held back or constrained by x = 0 .

We are compelled at x = 6 due to the fact that we have to maneuver a negative profit.

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2104.50 ÷ 122 = 17.25

...

Answer: 20 of banknotes, denomination of Rs. 10 and 15 of banknotes, denomination of Rs. 20.

Step-by-step explanation:

Let the number of banknotes, denomination of Rs. 10 will be equal to x,

and the number of banknotes, denomination of Rs. 20 will be equal to y.

Hence;   [tex]\left \{ {{x+y=35\ \ \ \ } \atop {10*x+20*y=500\ |:10 \ \ }} \right. \ \ \ \ \left \{ {{x+y=35\ \ (1)} \atop {x+2y=50\ \ (2)}} \right. \\[/tex]

From (2) subtract (1):

[tex]y=15\ \ \ \ \ \Rightarrow\\x+15=35\\x=20.[/tex]

Answer: 48

Step-by-step explanation:

By the geometric mean theorem,

[tex]\frac{x}{36}=\frac{64}{x}\\\\x^{2}=36 \cdot 64\\\\x=\sqrt{36 \cdot 64}\\\\x=\sqrt{36} \sqrt{64}=48[/tex]

Answer:

=> 3a

Step-by-step explanation:

=> 4a - 2a + a

=> 2a + a

=> 3a

Answer:

[tex]\boxed{\bf 3a}[/tex]

Step-by-step explanation:

[tex]\bf 4a - 2a + a[/tex]

Combine 4a and -2a = 2a.

Combine 2a and a = 3a

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

Answer:

  B.  y > 3x -7

Step-by-step explanation:

We can choose the correct inequality based on the y-intercept and the shading.

The dashed line crosses the y-axis at approximately y=-7. This is the value of y when x=0. This observation eliminates choices D, E, F.

The shading on the graph is seen to be above and to the left of the line. This means the variables in relation to the inequality symbol must be ...

  y > ( ) . . . . eliminates choice A

and

  x < ( )  or  ( ) > x . . . . eliminates choice C, confirms choice B

The inequality that matches the graph is y > 3x -7.

__

Additional comment

For looking at shading, we are interested in the relation of the inequality symbol to a variable term with a positive coefficient. If the coefficient is negative, you can do either of ...

That is, if you have -3x < ( ), when considering shading, you can consider the relation x > ( ) with the inequality reversed, or you can consider ( ) < x, which has x on the other side of the inequality. Both of these tell you shading is right of the line, where x-values are greater than those on the line.

He ran for 12 km in his journey.

An equation is formed when two algebraic expressions are equated by an equal sign.

It is given that

Speed of Walking =6km/hr  

Speed of Running = 15km/hr

Let he walks and run x hours ( as given)

he covered distance = 21 x km

The total time taken in the journey is 2x

for the same distance

It is also given that

if for the total journey

if he walks walked twice as long on the journey

He walked 6x in the journey so new distance that he walked is  12x  , then the total journey time = 6 minutes longer

Converting speed from km / hr to km/ min

1 km / hr = 60 km/ min

and forming an equation with the given data

12x * 60 /6 + 9x *60/15 = 2x * 60 + 6

120x + 36x = 120x +6

150x = 120

x = 120/150

x = 0.8 hours.

Therefore he spent 0.8 hours walking and 0.8 hours running and He ran 15 * 0.8 = 12 km

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Carl's average speed was 4244 miles/hr during those 2.5 hours

First, the odometer showed palindromic no. 25952 miles

after 2.5 hours odometer showed the next palindromic no. is 36563.

hence the distance covered in 2.5 hours = 36563 - 25952 = 110611 miles.

Now, we have to find the average speed with the distance covered 110611 miles in a particular time of 2.5 hours.

Using formula,

average speed = total distance / total time

                    [tex]\frac{10611}{2.5}[/tex] =4244 miles/hour is the average speed

Hence, Carl's average speed was 4244 miles/hr during those 2.5 hours

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Answer:

87

Step-by-step explanation:

The median of a data set is the value that is exactly in the middle of all other values.

To find the median of a data set, we typically list the values in order of greatest to least, and we look for the number in the middle.

Here, the list-maker has already provided the list in this order!

78, 78, 83, 85, 89, 91, 95, 98

we can see two numbers exactly in the middle here--when this happens, we take the mean/average of the two:

85 + 89 = 174

174 / 2 = 87

So, the median of this data set is 87

hope this helps! have a lovely day :)

You must go 45 miles per hour to reach the longest distance.

The given parameters are:

When the speed increases by 1 mile per hour, the time reduces by 10 minutes.

This means that:

When

Speed = (60 + x) miles per hour

The time is:

Time = 5 hours - 10 minutes * x

Convert minutes to hour

Time = 5 hours - 1/6 * x hour

This gives

Time = 5 - x/6 hour

Hence, the car can run for (5 - x/6) hours

We have:

The distance is calculated using

Distance = Speed * Time

This gives

Distance = (60 + x)(5 - x/6)

Expand

Distance = 300 - 10x + 5x - x^2/6

Evaluate the like terms

Distance = 300 - 5x - x^2/6

Hence, the distance for 1 tank of gas is 300 - 5x - x^2/6 miles

We have:

D = 300 - 5x - x^2/6

Differentiate

D' = -5 - x/3

Set to 0

-x/3 = 5

Solve for x

x = -15

Substitute x = -15 in D = 300 - 5x - x^2/6

D = 300 - 5(-15) - (-15)^2/6

Evaluate

D = 337.5

Hence, the longest distance is 337.5 miles

We have:

x = -15

Substitute x = -15 in Time = (5 - x/6) hours

Time = (5 + 15/6) hours

Evaluate

Time = 7.5 hours

The speed is calculated as:

Speed = Distance/Time

This gives

Speed = 337.5/7.5

Evaluate

Speed = 45

Hence, you must go 45 miles per hour to reach the longest distance.

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Answer:

Step-by-step explanation:

16-2t=t+9+4t  

7=7t  
t=1

Answer:

I don't see any option to choose from.

Step-by-step explanation:

See attached graph.

f(x) = 4( 1 /2)x can be rewritten as y = 2x.  This is a straight line with slope 2 and a y-intercept of 0.

y = 220/ ((10/3) * √22)

It is given that area is 200 square feet. Cost is 3 dollar per foot. Fourth side costs 12 dollars per foot.

This f(x,y) needs to represent the cost of the fence so we can look at each side's price. We can choose the fourth side to be along the x axis and be represented by 13x. The other sides therefore must be represented by 5y, 5y, and 5x.

So, our cost, f(x,y) = 13x + 5x + 5y + 5y = 18x + 10y

Our constraint is xy = 220 as defined by the area of a rectangle.

We can then take our constraint to be put in terms of exclusively x, giving us y = 220/x

Plugging this into our cost, the thing we are minimizing, we get f(x) = 18x + 2200/x

In order to find the minimum we use the first derivative test, taking f'(x) and finding the critical points.

f'(x) = 18 - 2200/x2

Setting this equation to be equal to 0 we find that x = ±√2200/18 . But the negative answer doesn't make sense because distance cannot be negative so we throw it out.

x = (10/3) * √22

We must verify that this is a minimum by confirming the following:

If x < (10/3) * √22, f'(x) < 0. So, f(x) is decreasing when x < (10/3) * √22.

If x > (10/3) * √22, f'(x) > 0. So, f(x) is increasing when x > (10/3) * √22.

Thus, we have guaranteed that (10/3) * √22 is the x dimension. Now we plug in this value in our original equation to find y and that is our y dimension. So, y = 220/ ((10/3) * √22)

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Answer:

Simplify 2x^2-5x-3/x^2-9

The answer is 2x+1 / x+3

Step-by-step explanation:

Simplify the expression.

Answer:

507

Step-by-step explanation:

For the Algebraic Expression,

let the two numbers be X and y

lets assume x = 217

From the question,

217 + y = 724

y = 724-217

y = 507

Therefore, the other number is 507

3.14 x² units

Step-by-step explanation:

Radius = x units. ----(given)

π = 3.14

Area of cirlce = πr²

= 3.14 * x²

= 3.14 x² units.

Answer:

area = πx² square units

Step-by-step explanation:

Formula for the area of a circle:

area = πr²,

where r = radius.

In this problem, the radius is x, so we substitute r in the formula with x.

area = πx² square units

Using proportions, it is found that:

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Point E divides FG in the ratio 3:4, hence:

[tex]E - F = \frac{3}{7}(G - F)[/tex]

This is used to find both the x and y coordinates.

For the x-coordinate, we have that:

[tex]E - F = \frac{3}{7}(G - F)[/tex]

[tex]x - 3.75 = \frac{3}{7}(2 - 3.75)[/tex]

x - 3.75 = -0.75.

x = 3.

For the y-coordinate:

[tex]E - F = \frac{3}{7}(G - F)[/tex]

[tex]y - 9 = \frac{3}{7}(-12 - 9)[/tex]

y - 9 = -9

y = 0.

The coordinates of point E are (3,0).

Point H divides FE in the ratio 2:3, hence:

[tex]H - F = \frac{2}{5}(E - F)[/tex]

This is used to find both the x and y coordinates.

For the x-coordinate, we have that:

[tex]H - F = \frac{2}{5}(E - F)[/tex]

[tex]x - 3.75 = \frac{2}{5}(3 - 3.75)[/tex]

x - 3.75 = -0.3.

x = 3.45.

For the y-coordinate, we have that:

[tex]H - F = \frac{2}{5}(E - F)[/tex]

[tex]y - 9 = \frac{2}{5}(0 - 9)[/tex]

y - 9 = -3.6

y = 5.4.

The coordinates of point H are (3.45,5.4).

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Answer:

The coordinates of point E are (3,0).

The coordinates of point H are (3.45, 5.4).

Step-by-step explanation:

I just got it right on the test

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

Explanation:

Start at $3.50 on the vertical y axis. Draw a horizontal line until you reach the supply curve. Then drop straight down to land somewhere between 650 and 700 units supplied per day. Check out the diagram below.

A good estimate may be to use the midpoint. Add up those values and divide in half.

(650+700)/2 = 1350/2 = 675

Therefore, we estimate that 675 sandwiches per day would be supplied if the price was $3.50 per sandwich.

Answer: 41

Step-by-step explanation:

12+14+15= 41

The margin of error is ±0.1706

The margin of error is a statistical solution for the amount of random sampling error in the survey results.

The 95% confidence interval means from 100 different samples computing a 95% of confidence for each sample. From this, we get the approximate value 95 of the 100 confidence intervals will contain the true mean value.

We have a sample size of n=33

The critical value of the significance level is [tex]\alpha =0.05\\z_{\frac{\alpha }{2} }=1.96[/tex]

Then our sample mean will be 2.5

then the standard deviation is 0.5

from this, we can assume that this is a normal distribution.

then our margin of error will be

[tex]E=[/tex]±[tex]z_{\frac{\alpha }{2} }\frac{deviation}{\sqrt{n} }[/tex]

⇒[tex]E=[/tex]±[tex](1.96)\frac{0.5}{\sqrt{33} }\\[/tex]

≅±0.1706 is the margin of error.

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Answer:

a.) 3(x^2 + 7x + 4) – 14x - 8

Step-by-step explanation:

a.) 3(x^2 + 7x + 4) – 14x - 8

3x^2 + 21x + 12 - 14x - 8

3x^2 + 7x + 4

b.) 3x^2 + 7x + 4 – 14x

3x^2 -7x + 4

c.) 3x^2 + 7x + 4 – 8

3x^2 + 7x - 4

d.) 3x^2 + 7x

Already simplified

Answer:

$95 FOR A DRESS

Step-by-step explanation:

Let's rearrange the given:

  She bought a blouse and skirt for two, a blouse and a dress for two, and a blouse for two.

     A blouse and a skirt cost $107

     A blouse and a dress cost $134

     blouse cost x dollars

The equation:

     2($107) + 2($134) + 2x = $560

SOLUTION:

   $214 + $268 + 2x = $560

   2x = $560 - $214 - $268

   2x = $78

   x = $39 for a single blouse

FIND THE COST OF DRESS:

   A blouse and a dress cost $134 - $39 for a single blouse

      $134 - $39 = $95

$95 IS THE COST OF DRESS

Answer:A rational number can be written as a fraction of two integers. √23 is irrational because we do not know what the square root of 23 is in terms of integers in a fraction. 104.42 is rational because it can be expressed as 10442/100 . We can express it as this because.

Step-by-step explanation:

Answer:

x = 35

Step-by-step explanation:

1. Add all angles

[tex]115+(x+36)+24+(2x+10)+2x[/tex]

= [tex]5x+185[/tex]

2. Match 360 and fix

[tex]5x+185=360[/tex]

[tex]5x=360-185[/tex]

[tex]5x=175[/tex]

[tex]x=175/5[/tex]

[tex]x=35[/tex]

Hope this helps

Answer:

[tex]\boxed{\sf x = 35^o}[/tex]

Step-by-step explanation:

Let's find the value of x :-

[tex]\sf 115 + x + 36 + 24 + 2x + 10 + 2x = 360^o[/tex]

Add the numbers.

Combine like terms.

Subtract 185 from both sides.

Divide both sides by 5.

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