When two parallel lines are cut by a transversal, argles A and B are alternate Interior angles that each measure 105°. What is the measure of
each of the other alternate interior angles

Answer:

17

Step-by-step explanation:

Here in this question for finding the numbers that will divide 398, 436 and 542 leaving remainder 7, 11 and 15 respectively we have to first subtract the remainder of the following. By this step we find the highest common factor of the numbers.

And then the required number is the HCF of the following numbers that are formed when the remainder are subtracted from them.

Clearly, the required number is the HCF of the numbers 398−7=391,436−11=425, and, 542−15=527

We will find the HCF of 391, 425 and 527 by prime factorization method.

391=17×23425=52×17527=17×31

Hence, HCF of 391, 4250 and 527 is 17 because the greatest common factor from all the numbers is 17 only.

So we can say that the largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively is 17.

Note: - whenever we face such a type of question the key concept for solving this question is whenever in the question it is asking about the largest number it divides. You should always think about the highest common factor i.e. HCF. we have to subtract remainder because you have to find a factor that means it should be perfectly divisible so to make divisible we subtract remainder. because remainder is the extra number so on subtracting remainder it becomes divisible.

Answer:

[tex]x^\frac{3}{5} = (x^3 )^\frac{1}{5}[/tex]

[tex]x^\frac{3}{5} = \sqrt[5]{x^3}[/tex]

[tex]x^\frac{3}{5} = (\sqrt[5]{x})^3[/tex]

Step-by-step explanation:

Given

[tex]x^\frac{3}{5}[/tex]

Required

The equivalent expressions

We have:

[tex]x^\frac{3}{5}[/tex]

Expand the exponent

[tex]x^\frac{3}{5} = x^{ 3 * \frac{1}{5}}[/tex]

So, we have:

[tex]x^\frac{3}{5} = (x^3 )^\frac{1}{5}[/tex] ----- this is equivalent

Express 1/5 as roots (law of indices)

[tex]x^\frac{3}{5} = \sqrt[5]{x^3}[/tex] ------ this is equivalent

The above can be rewritten as:

[tex]x^\frac{3}{5} = (\sqrt[5]{x})^3[/tex] ------ this is equivalent

Answer:

L1=78

W1=46

L2=78+4=82

W2=46+4=50

Area=L2×W2-L1×W1

82×50-78×46

Ans- 512ft^2

Answer:

Does the answer help you?

Answer:

6 * 12 / (6+12) = 72 / 18

If they work together they can finish in 4 days.

Source: http://www.1728.org/work.htm

Step-by-step explanation:

The measures of the angles between the peaks are;

m∠BSC = 22.5°

m∠ASB = 67.5°

The reason for arriving at the above angles is as follows:

The known values are;

The location of the surveyor = Point S

The angle between peaks A and B = m∠ASB = 3 times as large as the angle between peaks B and C = 3 × m∠BSC

The measure of angle m∠ASC = A right angle = 90°

Required:

To find m∠ASB and m∠BSC

From the given diagram, we have;

m∠ASC = 90°

m∠ASC = m∠ASB + m∠BSC (angle addition postulate)

m∠ASB = 3 × m∠BSC

∴ m∠ASC = 3 × m∠BSC + m∠BSC = 4 × m∠BSC

m∠ASC = 4 × m∠BSC = 90°

m∠BSC = 90°/4 = 22.5°

m∠BSC = 22.5°

m∠ASB = 3 × m∠BSC

∴ m∠ASB = 3 × 22.5° = 67.5°

m∠ASB = 67.5°

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Answer:

Graph C.

*See attachment below

Step-by-step explanation:

A graph that shows a set of ordered pairs representing a function would have each x-value being plotted against only one y-value. That is, every x-value must have exactly one y-value. Every x-value must not have more than 1 y-value being plotted against it.

The graph that shows this is the graph in option as shown in the attachment below.

Answer:

Total magic cakes =300

chocolate cakes =90

so if you want the percentage of chocolate you will divide the number of chocolate cakes over the total number of chocolates

% of chocolate cakes = 90/300×100%

=30%

Opportunity Cost of attending college, in terms of room and board is $4000 . Explicit Cost, Implicit Cost of attending college is $14000, $20000. Total Opportunity Cost of attending college is $34000

1. Opportunity Cost is the cost of next best alternate foregone, as in value of sacrifice made, while choosing an alternative.

2. Explicit Cost is the actual out of pocket cash expenses outflow, done for choosing an option. Eg : Cash expenditures

3. Implicit Cost is the implied estimated cost of self supplied factors of production, like value of self labour & self owned land etc.

4. Total opportunity cost of attending college = Explicit Cost + Implicit Cost = 14000 + 20000 = 34000

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Answer:

(-1,4)

Step-by-step explanation:

The interval in which the function is decreasing is (-1, 4)

Answer:

The domain of a function is the set of all possible inputs for the function.

Using the table provided, the set of all possible inputs is the interval [-6 ; 4].

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. In plain English, the definition means: The range is the resulting y-values we get after substituting all the possible x-values.

Using the table provided, the range is estimated on the interval [-10;20]

The y-intercept is the value on the Y-axis where the function crosses the Y-axis.

Using the table provided, the function crosses the Y-axis for f(0)=18 so for the value y = 18 in the table.

The x-intercept is the value on the X-axis where the function crosses the X-axis.

It happens twice, for f(-6)=0 and f(3)=0.

We estimate the Maximum to be 20, and the Minimum -10.

The function is positive over the interval [-6, 3], and negative over (3;4]

The function is decreasing approximately at f(-1)=20 so at the estimated interval (-1;4]

Answer:

Part A)

0.1 liters per minute.

Part B)

There was initially 3.8 liters of water.

[tex]\displaystyle V(t) = 0.1(t - 10) + 4.8[/tex]

Part C)

562 minutes.

Step-by-step explanation:

A tank is filled at a constant rate. After 10 minutes, the tank contains 4.8 L of water and after 35 minutes, the tank contains 7.3 L of water.

Part A)

We can represent the current data with two points: (10, 4.8) and (35, 7.3). The x-coordinate is measured in minutes since the tank began to be filled and the y-coordinate is measured in how full the tank is in liters.

To find the rate at which the tank is being filled, find the slope between the two points:

[tex]\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{(7.3)-(4.8)}{(35)-(10)} = \frac{2.5}{25} = 0.1[/tex]

In other words, the rate at which the tank is being filled is 0.1 liters per minute.

Part B)

To find the function of the volume of the tank, we can use the point-slope form to first find its equation:

[tex]\displaystyle y - y_1 = m( x - x_1)[/tex]

Where m is the slope/rate of change and (x₁, y₁) is a point.

We will substitute 0.1 for m and let (10, 4.8) be the point. Hence:

[tex]\displaystyle y - (4.8) = 0.1(x - 10)[/tex]

Simplify:

[tex]\displaystyle y = 0.1(x-10) + 4.8[/tex]

Since y represent how full the tank is and x represent the time in minutes since the tank began to be filled, we can substitute y for V(t) and x for t. Thus, our function is:

[tex]\displaystyle V(t) = 0.1(t - 10) + 4.8[/tex]

The initial volume is when t = 0. Evaluate:

[tex]\displaystyle V(0) = 0.1 ((0) - 10) + 4.8 = 3.8[/tex]

There was initially 3.8 liters of water.

Part C)

To find how long it will take for the tank to be completely filled given its maximum capacity of 60 liters, we can let V(t) = 60 and solve for t. Hence:

[tex]60 = 0.1(t - 10) + 4.8[/tex]

Subtract:

[tex]55.2 = 0.1(t - 10)[/tex]

Divide:

[tex]552 = t - 10[/tex]

Add. Therefore:

[tex]t = 562\text{ minutes}[/tex]

It will take 562 minutes for the tank to be completely filled.

Answer:

Domain { -6,3,4,6,10}

The range is the output values, listed from smallest to largest with no repeats

Range { -13,-9,2,14,19}

Step-by-step explanation:

The domain is the input values, listed from smallest to largest with no repeats

Domain { -6,3,4,6,10}

The range is the output values, listed from smallest to largest with no repeats

Range { -13,-9,2,14,19}

Answer:

Range: 14, 19, -9, 2, -13

Domain: -6, 10, 4, 3, 6

Step-by-step explanation:

I don't know but this is it I think .

Answer:

ur box cannot be opend  repain the window

Step-by-step explanation:

please mark this answer as brainlist

Answer:

D. -4

Step-by-step explanation:

the slope formula is

m=(y2-y1)/(x2-x1)

(x2,y2) = (4,7)

(x1, y1) = (5,3)

So (7-3)/(4-5) = 4/-1 = -4

Answer:

-4

Step-by-step explanation:

I say so

Answer:

y = z /n

Step-by-step explanation:

Answer:

y=z/n

Step-by-step explanation:

To isolate the y, divide both sides by n

Answer:

20 yards

Step-by-step explanation:

First, we have to know how to get from inches to yards. 12 inches = 1 foot, and 3 feet = 1 yard.

Next, we have

[tex]\frac{720 in}{1}[/tex]

as a given. We want to multiply this by our conversions to get the end amount in yards.

We can first multiply our expression by 12 inches = 1 foot. To do this, we can set one number as the divisor and one as the dividend, e.g. 12 inches /  1 foot. However, to figure out which number should be the numerator/denominator, we first must examine our original expression. We want to multiply it by a value that cancels something out in conversion. To do this, we can have the same unit of something in the numerator in one and the denominator in the other in terms of what we're multiplying. Here, we can see that [tex]\frac{720 in}{1}[/tex] has inches on the top, so we want inches on the bottom in 12 inches = 1 foot. Therefore, we have

[tex]\frac{720 in}{1} * \frac{1 foot}{12 inches}[/tex]

= [tex]\frac{720feet}{12}[/tex]

= 60 feet

= [tex]\frac{60 feet }{1}[/tex]

We have feet as the numerator, so we want feet in the denominator in what we're multiplying this by. In 3 feet = 1 yard, we can multiply this to get

[tex]\frac{60 feet }{1} * \frac{1 yard}{3 feet} \\= \frac{60 yards}{3}[/tex]

= 20 yards

Answer:

I am pretty sure that your answer would be 3.

Step-by-step explanation:

The reason why is because if B if half of line segment AD and AD is equal to 12, then B must be equal to 6 since half of 12 is 6. Next, since C is the mid-point for line segment BD then C must be 3 since half of 6 is 3. And finally, that means line segment BC is three since it is 1/2 of BD.

Hope this helps! :)

Answer:

BC = 3

Step-by-step explanation:

If B is the midpoint of AD, that means AB = BD

AD = 12 so BD = 1/2 of AD  and BD = 6

If C is the midpoint of BD, that means BC = CD

BD = 6 so BC = 1/2 of BD  and BC = 3

9514 1404 393

Answer:

  -0.84

Step-by-step explanation:

In decimal, the expression is ...

  -1.34 +1.50 -1.00 = -0.84

__

As fractions, the expression is ...

  -67/50 +75/50 -50/50 = (-67+75-50)/50 = -42/50 = -21/25

Answer:

B

Step-by-step explanation:

the data value of x is 0 the the value would be .75 times that by 2 get 1.25

Answer:

I think you mean this :

[tex] \sqrt{x - 5} = 6 \\ = > {( \sqrt{x - 5} })^{2} = {6}^{2} \\ = > x - 5 = 36 \\ = > x = 36 + 5 \\ = > x = 41[/tex]

Or,

Square root of x-5=6 is :

[tex] \sqrt{x - 5} \:=\:\sqrt{6} [/tex]

Answer:

C

Step-by-step explanation:

the fibrin definition tells us that the first term of the sequence a1 = 6

so, B is out.

and for every following term we always add 7 to every previous term to create the next one.

so, when I add 7 to 6, what is my second term in the sequence ? 7+6 = 13

not 42, not -7

therefore, only C is correct.

and 13+7 = 20

and 20+7 = 27

it all fits

Answer:

this will give you the answer: for cylinder

V = 3×2^2×7 = 84cm

this will give you the answer for cone:

V = 3× 2^2 × 6/3 = 24cm

then we just add

84 + 24 = 108cm^3

Step-by-step explanation:

hope it helps!

Answer:

2 Inches

Step-by-step explanation:

Area of a triangle = (1/2)* Base * Hight

lets consider the base of the triangle is X inches,

then, Hight of the triangle is 2X

Then the Area of the Angle is = (1/2)*X*2X

                                               4 = x^{2}

                                               X = 2

Answer:5

Step-by-step explanation:

Where the above parameters are given,  you need to walk a distance of approximately √41 miles back to your car.

To calculate the total distance you need to walk, you can use the Pythagorean theorem since you have a right triangle formed by the north and east displacements.

Distance = √((Distance north)² + (Distance east)²)

= √((5 miles)² + (4 miles)²)

= √(25 miles + 16 miles)

= √41 miles

Hence, you need to walk a distance of  approximately √41 miles back to your car.

As for the direction, based on the net displacements, you are 5 miles north and 4 miles east of your car, so the direction would be a combination of north and east, often referred to as northeast.

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Answer:

6x+36=180

6x=144

x=24

Step-by-step explanation:

this is the correct answer

Answer:

what are you telling Id understand

Step-by-step explanation:

became

the answer will be 0.092 as a decimal

Answer:

601 in²

Step-by-step explanation:

To obtain the amount of wrapping needed to cover the cube shaped gift box, including the bow

Area of bow = 115 in²

Surface area of cube shaped box = 6a²

a = side length of cube = 9

Hence,

Surface area of gift box = 6 * 9²

Surface area = 6 * 81 = 486 in²

Total wrapping required = area of gift box + area of bow = (486 in² + 115 in²) = 601 in²

Answer:0.8

Step-by-step explanation:

Answer:

a) The rocket travels 200 meters horizontally.

b) The height of the rocket mid-flight is of 1000 meters.

Step-by-step explanation:

Height of the rocket:

The height of the rocket, in meters, after an horizontal distance of x, is given by:

[tex]y = 0.1x(200 - x)[/tex]

a) How far does the rocket travel horizontally?

This is x when [tex]y = 0[/tex]. So

[tex]0.1x(200 - x) = 0[/tex]

Then

[tex]0.1x = 0[/tex]

[tex]x = 0[/tex]

And

[tex]200 - x = 0[/tex]

[tex]x = 200[/tex]

So

The rocket travels 200 meters horizontally.

b How high does the rocket reach mid-flight?

This it the height y when x = 0, so:

[tex]y = 20*100 - 0.1*100^2 = 1000[/tex]

The height of the rocket mid-flight is of 1000 meters.