The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 29 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.

x = 7.5

y = 1.5

x + y = 9.0  => x = 9 - y

0.50x + 0.20y = 4.05

0.5(9 - y) + 0.2y = 4.05

4.5 - 0.5y + 0.2y = 4.05

4.5 - 4.05 = 0.5y - 0.2y

0.45 = 0.3y

y = 0.45 : 0.3

y = 1.5

x = 9 - 1.5

x = 7.5

Answer:

Leg ED is adjacent to theta

Answer:

.125

Step-by-step explanation:

.125 * 8 = 1

Answer:

Step-by-step explanation:

(1-4)/(2+3)= -3/5 is the slope

y - 4 = -3/5(x + 3)

the solution is F

Answer:

Ellipse when the (tilted) plane intersects only one cone to form a bounded curve.

Step-by-step explanation:

hope it will help :)

Ellipse.

In mathematics, the ellipse is a plane curve, proportional to a closed oval shape. In particular, the ellipse is a curve that encloses two points in such a way that, for each point on the curve, the sum of the two distances from that point to the two points is constant.  

From the perspective of solid shapes, the ellipses can be thought of as a conical section created when a plane intersects the surface of a cone in such a way that it creates a closed curve.

Learn more in https://brainly.com/question/14197032

Answer:

-1/6

Step-by-step explanation:

[tex](-6)^-1\\=\frac{-1}{6}^1\\ =\frac{-1}{6}[/tex]

The rate is 16.1% and the base is the final portion with the rate added on to it.

Chance the percentage into a decimal.

16.1% / 100 = 0.161

Multiply.

454 * 0.161 = 73.094

Add.

454 + 73.094 = 527.094 or 527.09

Therefore, the final base is roughly 527.09

Best of Luck!

Answer: {...-3, -1, 1, 3, 5...}

Step-by-step explanation:

For a point to be discontinuous, the graph doesn't exist at that point. This means, it is represented with an open circle. All we have to do is to list out all the open circles on the graph.

{-3, -1, 1, 3, 5}

Answer:

b. {... –3, –1, 1, 3, ...}

Step-by-step explanation:

so basically it's b. the person above me is right they just added a 5 to the end

Answer:

Step-by-step explanation:

For units conversion, use a conversion factor ratio with the units you do want in the numerator and the units you don't want in the denominator. The numbers in the numerator and denominator give the ratio a value of 1: the numerator is equal to the denominator--just in different units.

__

1. For feet to mm, you need a couple of additional conversion factors besides the ones shown:

  1 foot = 12 in

  1 cm = 10 mm

So, the conversion is ...

  [tex](3\text{ ft})\times\dfrac{12\text{ in}}{1\text{ ft}}\times\dfrac{2.54\text{ cm}}{1\text{ in}}\times\dfrac{10\text{ mm}}{1\text{ cm}}=3\times12\times2.54\times10\text{ mm}\\\\=\boxed{914.4\text{ mm}}[/tex]

__

2. The additional factor you need for this problem is ...

  1 mile = 5280 feet

So, the conversion is ...

  [tex](157\text{ ft})\times\dfrac{1\text{ mi}}{5280\text{ ft}}\times\dfrac{1\text{ km}}{0.62\text{ mi}}=\dfrac{157}{5280\times0.62}\text{ km}\\\\\approx\boxed{0.0479594\text{ km}}[/tex]

_____

Additional comment

You can use Google to do units conversion by typing "3 feet to mm" or "157 feet to km". However, the conversion factor for the latter will be more exact than the one given in this problem. Hence the Google answer to the second question will not be applicable here.

Answer:

320p

Step-by-step explanation:

According to the question,

560p = 7 pencils

Therefore,

1 pencil = 560 / 7

             = 80p

So, for 4 pencils it costs

4 * 80 = 320p

Answer:

easy piizzy lemon squeezyy!!

Step-by-step explanation:

i) 560/7

=80

ii) 80*4

=320

Answer:

In the y=3x-4 section it should be (3,5), (6,14), (5,11)

In the y= (1/2)x + 2 section it should be (4,4) , (2,3)

I hope this works!

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

6/x + 1/2 = 2

x(6/x + 1/2) = 2*x

x*6/x + x*1/2 = 2x

6 + x/2 = 2x

6 = 2x - x/2

6 = 4x/2 - x/2

6 = 3x/2

6*2/3 = x

12/3 = x

x = 4

probe:

6/4 + 1/2 = 2

3/2 + 1/2 = 4/2

Answer:

7a  3  −7a+1

Step-by-step explanation: I hope this help.

STEP

1

:

Equation at the end of step 1

 ((7a3 -  2a) -  2) +  (3 - 5a)

STEP

2

:

Polynomial Roots Calculator :

2.1    Find roots (zeroes) of :       F(a) = 7a3-7a+1

Polynomial Roots Calculator is a set of methods aimed at finding values of  a  for which   F(a)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  a  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  7  and the Trailing Constant is  1.

The factor(s) are:

of the Leading Coefficient :  1,7

of the Trailing Constant :  1

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        1.00      

     -1       7        -0.14        1.98      

     1       1        1.00        1.00      

     1       7        0.14        0.02      

Polynomial Roots Calculator found no rational roots

Final result :

 7a3 - 7a + 1

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{7 {a}^{3} - 7a + 1}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{(7 {a}^{3} - 2a - 2) + ( - 5a + 3) }[/tex]

When there is a ( + ) in front of an expression in parentheses, there is no need to change the sign of each term. That means, the expressions remains the same. Just, remove the parentheses

⇒[tex] \sf{7 {a}^{3} - 2a - 2 - 5a + 3}[/tex]

Collect like terms

⇒[tex] \sf{7 {a}^{3} - 2a - 5a - 2 + 3}[/tex]

⇒[tex] \sf{7 {a}^{3} - 7a - 2 + 3}[/tex]

Calculate

⇒[tex] \sf{7 {a}^{3} - 7a + 1}[/tex]

Hope I helped!

Best regards!!

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

38, 50, 50, 55, 55, 95, 95, 130, 180, 213, 250, 350, 450, 1750, 3000

The range :

(maximum - minimum) = (3000 - 38) = 2962

Variance :

Σ(x - mean)² / (n-1)

Where n = number of observations

Mean = (38+50+50+55+55+95+95+130+180+213+250+350+450+1750+3000) = 6761 / 15 = $450.73

Σ(x - mean)² = 9527804.9333334

N - 1 = 15 - 1 = 14

Hence,

Variance = Σ(x - mean)² / (n-1)

Variance = 9527804.9333334 / 14

Variance = $680557.50

Standard deviation = √variance

Standard deviation = √680557.50

Standard deviation = $824.96

CHECK IF OUTLIERS EXIST:

Using the outlier formula:

Lower outlier = Q1 - (1.5 × IQR)

Upper outlier = Q3 + (1.5 × IQR)

Q1 = 55 ; Q3 = 350 ; IQR = 295

Lower outlier = 55 - (1.5 × 295) = - 387.5

Upper outlier = 350 + (1.5 × 295) = 792.5

Remove values below the lower outlier value and values above the upper outlier value.

Hence outliers in the data are : 1750 and 3000

To save computation time :

We can recalculate our statistical measure by leaving out the outliers using online, excel or calculator functions :

Data without outlier :

38, 50, 50, 55, 55, 95, 95, 130, 180, 213, 250, 350, 450

Range = (450 - 38) = 412

Variance = Σ(x - mean)² / (n-1)

Variance = 201626.77 / 12

Variance = $16,802.23

Standard deviation:

√variance

√16,802.23

= $129.62341

According to the results obtained the presence of outliers has a great effect on the outcome the result.

Answer:1st graph

Step-by-step explanation: did this question already

Answer: First option

Step-by-step explanation:

I did the lesson already

Answer:

The percentage is  [tex]P(0.09 < \mu < 1.2 ) = 34.9\%[/tex]

Step-by-step explanation:

From the question we are told that

  The random number is  [tex]x_1 = 0.09 \ and \ x_2 = 1.2[/tex]

Generally the mean of standard normal distribution is  [tex]\mu = 0[/tex]

                 The  standard deviation of a standard normal distribution is  [tex]\sigma = 1[/tex]

The percentage of the data in a standard normal distribution lies between

  [tex]x_1 = 0.09 \ and \ x_2 = 1.2[/tex] is mathematically represented as

       [tex]P(x_1 < \mu < x_2 ) = P(\frac{x_1 - \mu}{\sigma } <\frac{X - \mu}{\sigma } < \frac{x_2 - \mu}{\sigma } )[/tex]

      [tex]P(0.09 < \mu < 1.2 ) = P(\frac{0.09 - 0}{1 } <\frac{X - \mu}{\sigma } < \frac{1.2 - 0}{1 } )[/tex]

      [tex]P(0.09 < \mu < 1.2 ) = P(0.09 <\frac{X - \mu}{\sigma } < 1.2 )[/tex]

The  [tex]\frac{X - \mu}{\sigma } = Z(The \ standardized \ value \ of \ X )[/tex]

      [tex]P(0.09 < \mu < 1.2 ) = P(0.09 <Z < 1.2 )[/tex]

      [tex]P(0.09 < \mu < 1.2 ) = P (Z < 1.2 )- P( Z<0.09)[/tex]

From the z-table  

      [tex]P (Z < 1.2 )= 0.88493[/tex]

      [tex]P( Z<0.09) = 0.53586[/tex]

So

    [tex]P(0.09 < \mu < 1.2 ) = 0.88493 - 0.53586[/tex]

    [tex]P(0.09 < \mu < 1.2 ) = 0.349[/tex]

Hence the percentage  is  

     [tex]P(0.09 < \mu < 1.2 ) = 34.9\%[/tex]

Responder:

x=6

espero haber ayudado

Answer:

Option b (28 + 63)

Step-by-step explanation:

7(4+9)

7(13)

7×13= 91

28 + 63 = 91

Both give the same answer

Answer:

The sum 28 + 63 can be expressed as 7 ( 4 + 9 )

Step-by-step explanation:

To solve the problem you need to be aware of the distributive property of multiplication.  This property simply says that a multiple of a group of addens, aka the sum in the parenthesis, can be multiplied individually and summed.

The 7 infront of the parenthesis implies the multiplication operation on the grouping of the sum of 4 and 9.

You can rewrite it as such:

7 * ( 4 + 9 )

= 7 * 4 + 7 * 9

= 28 + 63

Note, how we simply used the multiplier 7 distributed to each term within the parenthesis to create our desired sum.

Cheers.

Answer:

  see attached

Step-by-step explanation:

270° CCW is the same as 90° CW. The figure will be moved to the second quadrant. The transformation of coordinates is ...

  (x, y) ⇒ (y, -x) . . . . . rotation 270° CCW or 90° CW

For example, A(-5, -3) ⇒ A'(-3, 5).

Answer:

43

Step-by-step explanation:

The solution to the equation 144 = m - 98 is m = 242 as per the PEMDAS rule.

To solve for m in equation 144 = m - 98, we can follow these steps:

Start with the given equation: 144 = m - 98.

To isolate the variable m, we need to eliminate the -98 on the right side of the equation. We can do this by adding 98 to both sides of the equation:

144 + 98 = m - 98 + 98.

Simplifying the equation, we get: 242 = m.

Now we have m = 242 as the solution to the equation.

Therefore, m = 242 is the value that satisfies the equation 144 = m - 98. By substituting m with 242 in the equation, we can verify that it holds true:

144 = 242 - 98.

144 = 144.

To learn more about the equation;

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The complete question:

144 = m - 98

Solve for m

Answer:

7 cm.

Step-by-step explanation:

Area of the 2 bases = total area - area of curved surface

= 408 - 100 = 308cm^2.

So the area of 1 base = 154 cm^2.

If radius of the base  = r:

pi r^2 = 154

r^2 = 154/pi

r =  sqrt (154/pi)

r = 7.0014 cm

Multiply the hours by how much she makes per hour.

38 * 12 = $456

Therefore, she made $456 last week.

Best of Luck!

Answer:

The table represents a function because each input corresponds to exactly one output.

Step-by-step explanation:

A table can be regarded as representing a function if and only if every input can only be mapped to exactly one output. In other words, it means, only 1 exact output can be assigned to an input. In a table of function, an input cannot have two different outputs. Although, two different inputs can be assigned to the same output.

From the table given, we see that every input has exactly one output. Although, we have different inputs that gives the same output.

Therefore, we can conclude that the table represents a function because each input corresponds to exactly one output.

Answer:

2   =  0

This equation has no solution.

Step-by-step explanation:

A a non-zero constant never equals zero

Answer:

The Domain of the function is the set of ALL Real numbers

Step-by-step explanation:

To find the Domain of a function, one has to examine if there are any mathematical restrictions in the function's expression that could reduce the set of Real numbers to be used in estimating all the possible function's outputs.

Typical examples are:

1) There are x-variables in the denominator of the function (you must consider then which values of x could render a zero in the denominator and therefore make it undefined)

2) the variable x appears inside an even root (like a square root), then you have to consider which values of x are not allowed if they render a negative value inside the root

3) if x appears inside logarithmic expressions (you need to exclude from the domain those x-values that render negative the expression inside the logarithm)

Another important rule to remember,is that all polynomial functions (like the one given in this case) always have for Domain the full number line (all Real numbers) because any Real number used will render another Real number via multiplications, subtractions and additions (which are the operations involved in a polynomial expression)

Answer:

32 mph

Step-by-step explanation:

We want to find the patrolman's rate in miles per hour during the shift. Since we want to find miles per hour, we must divide the miles he drove by the number of hours.

rate = miles / hours

He drove 272 miles.

rate = 272 miles / hours

He drove for 8 hours and 30 minutes. There are 60 minutes in 1 hour. One half of 60 is 30. Therefore, we can also say he drove eight and a half, or 8.5 hours.

rate= 272 miles / 8.5 hours

rate = 32 miles / hour

rate= 32 mph

His average rate during the shift was 32 miles per hour.

Answer:

32 mph

Step-by-step explanation:

To answer this, find the average rate of change

 272 mi

------------- = 32 mph

 8.5 hr

Answer:10th term: -27

5th term: - 12

d= -27+12/5

= -3

a+(n-1)d=-12

a+(5–1)d=-12

a+4d= -12

a=-12–4d

a=-12-(4×-3)

a=-12+12=0

18  term=a + (18–1)d

=0+(17×-3)

51

a+9d=-27......(1)

a+4d=-12.....(2)

make a the subject of equation 2 and put into equation 1

-12+4d+9d=-27

-12+13d=-27

d=-15\13

put d into equation 1

a+9(-15/13)=-27

a=16.6

a+17d=x

17+16.6(-15/13)

x=-2 is the 18th term

25÷2(16.6+15.6(-15/13)

=-208.4

Step-by-step explanation:

By using exactly four 4s it is possible to write a few numbers: at least from 0 - 30.

=> For example, using exactly four 4s, we can write 1 as follows

1 = 44 / 44

The right hand side of the above equation has exactly four 4s and solving it will give 1.

=>Using exactly four 4s, we can write 2 as follows;

2 = (4/4) + (4/4)

Also, there are exactly four 4s in the right hand side of the above equation and solving it gives 2

=> Using exactly four 4s, we can also write 6 as follows;

6 = 4 x .4 + 4.4

The above equation also contains exactly four 4s which will give 6 when solved. i.e

(4 x .4) + 4.4 = (4 x 0.4) + 4.4 = 6

The expressions for numbers 1 through 10 using exactly four 4s have been tabulated and shown in the image attached to this response.

Answer:

$109,9455

Step-by-step explanation:

8x5.25=42

452,97/100=4,5297

4,5297x15=67,9455

42+67,9455=109,9455

Answer:

$109.95

Step-by-step explanation:

rate = $5.25 per hour + tips

tips = 15% of the food sold during 8 hours shift.

Mary Watson will get:

$5.25 x 8 hours = $42

tips = 0.15 x $452.97 = $67.95

a total  of $42 + $67.95 = $109.95

Answer:

The three in the first number, 265,413 has the three in the ones place.

The three in the second number, 4.3 has the three in the tenths place.

So, the value of the three in the first number is ten times greater than the one in the second number.