(Please show your work.)

the common denominator is 10 (between 5 and 2)

for each numerator:

we divide the common denominator with the denominator of each fraction and then multiply with the numerator of the fraction

first fraction's numerator:

10 (c.d.) : 5 (denominator) = 2

2 * 2 (numerator) = 4

second one:

10 (c.d.) : 2 (denominator) = 5

5 * 1 (numerator) = 5

The fractions are 4/10 and 5/10

Answer:

x = -10

Step-by-step explanation:

62 = 12 - 5x

-12 .   -12

62 - 12 = -5x

50 = -5x

__ .  __

-5 .    -5

-10 = x    

Answer:

AB and CD

Step-by-step explanation:

Given

Shape: Parallelogram

Parallel Side: AB and CD

Required

Determine the opposite sides

From the given parameters, we understand that:

AB is parallel to CD

Since they are parallel, then AB is opposite to CD

Hence, the opposite sides are AB and CD

Answer:

.6

...................

Answer: 6 : 10  or 3:5

Step-by-step explanation:

If they are 6 cats and 10 dogs then the ratio of cats to dogs it 6 to 10  or 6/10

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:

3x-12 =7

Step-by-step explanation:

you distribute the 3 to the x and the -4

Answer:

I can only answer the first one for now but the answer is x^2 - 6x + 9.

Step-by-step explanation:

f(x) = x^2 and g(x) = x - 3.

To find f(g(x))  we replace the x in f(x) by g(x).

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

= x^2 - 6x + 9.

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:

O3(-8 + 1) = 3(-8) + 3(1)

Step-by-step explanation:

GOOD LUCK WITH BRAINLY I HOPE I HELPED :)

The expressions demonstrates the distributive property is

3(-8 + 1) = 3(-8)+ 3(1).

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

We know the standard forms for distributive property as

For addition: a x (b+ c) = a x b + a x c

For Subtraction: ax (b- c)= a x b - a x c

1. 3+ 4+ 5 = 4 + 3 + 5 is Associative Property.

2. -2(5 + 7) = -2(7 +5) is Associative Property

3. 3(-8 + 1) = 3(-8)+ 3(1) is Distributive Property

Learn more about Distributive Property here:

https://brainly.com/question/5637942

#SPJ7

Answer:

Step-by-step explanation:

We are presented with three items

two dices and a coin

The sample space for a dice is S=(1,2,3,4,5,6)

and the sample space for a coin is S=(head and tail)

In the options provided all are possible outcomes for the two dices and the coin except for options "C" ,and this is because "8" is not a sample space in a dice

Answer:

2,8 Heads

Step-by-step explanation:

A standard coin has two values, {Heads or Tails}, while a standard die has six values {1, 2, 3, 4, 5, or 6}.  So, obtaining a 2 is possible, however the 8 is not.

Step-by-step explanation:

17 miles = 1 day to work

14 miles =1 day to home

Therefore total miles driven in 5 days =

( 17×5) +(14×5) = 105+60

ANSWER =165 miles per week

Answer:

155 miles each week

Step-by-step explanation:

One day is 17 miles to and 14 miles home = 17+14 = 31

He does this 5 days a week

5 * 31 = 155 miles

Answer:

An algebraic expression (in mathematics) can be defined as an expression which is made up of variables and constants along with algebraic operations( i.e. addition, subtraction etc)

Answer:

It is an expression built up from integer constants and algebric expressions.

Answer:

she can only get 1 servings

Answer:

1 cause 4/8 is a half  of the jug at it's full  brethall

so one 1/2

Answer:

x=−4

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

Given:

Solving for x:

Answer:

the measure of x is 18° and the measure of y is 29°

Step-by-step explanation:

Step 1

Find the measure of angle x

we know that

If ray NP bisects <MNQ

then

m<MNQ=m<PNM+m<PNQ ------> equation A

and

m<PNM=m<PNQ -------> equation B

we have that

m<MNQ=(8x+12)°

m<PNQ=78°

so

substitute in equation A

(8x+12)=78+78-------> 8x+12=156------> 8x=156-12

8x=144------> x=18°

Step 2

Find the measure of angle y

we have

m<PNM=(3y-9)°

m<PNM=78°

so

3y-9=78------> 3y=87------> y=29°

therefore

the answer is

the measure of x is 18° and the measure of y is 29°

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:

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:

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:

k=21

Step-by-step explanation:

Find the slope of MN which is 1/5 (use the slope formula)

Use the slope formula for AB using k as y_2

Substitute and you get k=21

21-2.25/-2.25-1.5=-5

The lines are perpendicular because the slopes are the negative reciprocal of one another.

Answer:

The equation for the parabola that passes through the points (−1,8), (2,−4), and (−6,−12) is [tex]y = -x^{2}-3\cdot x +6[/tex].

Step-by-step explanation:

Let be (−1,8), (2,−4), and (−6,−12) points contained in a parabola, which is represented by a second-order polynomial. To determine the constant of the second-order polynomial, the following system of equations must be solved:

[tex]a - b+c = 8[/tex]

[tex]4\cdot a +2\cdot b +c = -4[/tex]

[tex]36\cdot a -6\cdot b +c = -12[/tex]

There are several methods for solving this: Equalization, Elimination, Substitution, Determinant and Matrix. The solution of this system is: [tex]a = -1[/tex], [tex]b = -3[/tex] and [tex]c = 6[/tex]. Hence, the equation for the parabola that passes through the points (−1,8), (2,−4), and (−6,−12) is [tex]y = -x^{2}-3\cdot x +6[/tex].

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:

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:

The midpoint is ( 1, -1.5)

Step-by-step explanation:

To find the midpoint

Add the x coordinates of the endpoints and divide by 2 to get the x coordinate of the midpoint

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

Add the y coordinates of the endpoints and divide by 2 to get the y coordinate of the midpoint

(3+-6)/2 = -3/2 = -1.5

The midpoint is ( 1, -1.5)

Answer:

mid point = 1,  -1.5

Step-by-step explanation:

mid point between two points C(5, 3) and D(-3, -6)

M = (x1 + x2)/2  , (y1 + y2)/2

mid point = (5 + (-3)) / 2 ,  (3 + -6)/2

mid point = 2/2 , -3/2

mid point = 1,  -1.5

Answer:

14322 * 10¹²

1.4322 * 10¹⁶

Step-by-step explanation:

14322000000000000

14322 * 10¹²

1.4322 * 10¹⁶

Answer:

x + 4  < 12

Step-by-step explanation:

Given

sum of a number x and 4

It can be written mathematically as

x + 4

Then

x + 4 is less than 12

less than is represented as <

Thus,

x + 4  < 12

Thus, inequality is x + 4  < 12

Answer:

5 units

Step-by-step explanation:

Notice that the x-coordinate is the same for both points, but that the y-coordinates differ by five units.  The distance between these two points is therefore 5 units.

Answer:

The distance from the ground to the top of the ladder = 18.7 feet

Step-by-step explanation:

The distance from the ground to the top of the ladder is 9 feet more than the distance from the building to the base of the ladder.

distance from the building to the base of the ladder.= X

The distance from the ground to the top of the ladder = 9+x

Solving the triangle using Pythagorean theorem

X² +(x+9)²= 21²

X² + x² + 18x +81= 441

2x² +18x -360 = 0

X² +9x -180 = 0

X= (-9-28.3)/2 or (-9+28.3)/2

Definitely x is going to be a positive number

So

X= (-9+28.3)/2

X=9.65 feet

The distance from the ground to the top of the ladder = 9+x

The distance from the ground to the top of the ladder = 9+9.65

The distance from the ground to the top of the ladder = 18.65

The distance from the ground to the top of the ladder = 18.7 feet

Building is 9.65 foot far from ladder.

Length of ladder = 21 foot. This diagonal ladder is Hypotenuse to the right angled triangle formed between building & ladder.

Let the distance from building to base of ladder = x. This is the base of right angled triangle.

So, distance from ground to top of ladder = x + 9. This is the height of right angled triangle.

As per Pythagorus Theorem,

[tex]Hypotenuse^2 = Base^2 + Height^2[/tex]

[tex]21^2 = x^2 + (x+9)^2[/tex]

441 = [tex]x^2 + x^2 + 81 + 18x[/tex]  

360 = [tex]2x^2 + 18x[/tex]

[tex]2x^2 + 18x[/tex] - 360 = 0

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

x = 9.65 { Building distance to ladder base }

To learn more, refer https://brainly.com/question/17275943

Answer:

Distance = [tex]\sqrt{113}[/tex]

Step-by-step explanation:

[tex](1, 5) = (x_1,y_1)\\ (-7, -2)=(x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\ \\d = \sqrt{(-7-1)^2+(-2-5)^2}\\ \\d = \sqrt{(-8)^2+(-7)^2}\\ \\d = \sqrt{64+49}\\ \\d = \sqrt{113} \\\\[/tex]

Answer:[tex]\sqrt{113}[/tex]

Step-by-step explanation:

Distance formula: [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

x1=1     x2=-7     y1=5     y2=-2

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

 [tex]\sqrt{(-7-1)^2+(-2-5)^2}[/tex]

=[tex]\sqrt{(-8)^2+(-7)^2}[/tex]

=[tex]\sqrt{64+49}[/tex]

=[tex]\sqrt{113}[/tex]

Hope this helps!! :)

Please let me know if you have any question or need further explanation