The right triangle drawn on the road sign is 10 inches high. If the base of the right triangle is 5 inches, what is the
area of the right triangle formed in the sign?
O 48 sq.in.
O 64 sq.in.
O 25 sq.in.
O 36 sq.in.

Adding yes or no to the information that is enough to proof lines l and m are parallel

m<2 + m<4 = 180 degrees  no

m<1 = m<7  no

m<2 = m<6  yes

m<6 + m<3 = 180 degrees no

m<1 = m<8 yes

This is a term used in geometry to refer to lines that will never intersect. The concept of parallel lines is used to find angles that are related or equal to each other by the following theorems:

Using the mentioned theorems we apply to the statements as follows: The first statement is correct but not used to prove parallel lines. The second statement is not correct.

The third statement is correct, it represents transitive property of equality angles, where m<2 equals m<3 by Vertical angles theorem and m<3 is equal to m<6 as by Alternate interior angles theorem.

m<6 + m<3 = 180 degree: the two angles are equal as earlier explained but their sum is not 180 degrees

m<1 = m<8: The equality of these two angles is shown by transitive property of equality angles, and it is enough to prove that line l and m are parallel lines

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Answer:

since x=-14

9(-14)-7

-126-7=-133.

Use the polynomial remainder theorem. The remainder upon dividing a polynomial [tex]p(x)[/tex] by a linear factor [tex]x-c[/tex] is exactly [tex]p(c)[/tex].

In this case,

[tex]p(x) = 2x^{10} - 3ix^8 + (1+i)x^2 - (3+2i)x + 1[/tex]

and [tex]c=i[/tex]. Then the remainder is

[tex]p(i) = 2i^{10} - 3i^9 + (1+i)i^2 - (3+2i)i + 1[/tex]

Since [tex]i^2=-1[/tex] and [tex]i^4=1[/tex],

[tex]p(i) = -2 - 3i - 1 - i - 3i + 2 + 1 = \boxed{-7i}[/tex]

Earth's diameter is 0.0092 times less than the sun's diameter.

The Diameter of Earth = 1.3 * 10⁴ km

The Diameter of Moon = 3.5 * 10³ km

Let the diameter of sun be x km

According to the question

The diameter of the sun is 400 times that of the moon.

x = 400 * 3.5 * 10³ km

= 14 * 10⁵ km

The Diameter of earth / diameter of sun

=  1.3 * 10⁴ / 14 * 10⁵

= 0.0092

Hence, The diameter of the Earth is 0.0092 times that of the Sun.

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The nearest decimal which is the approximate value of x is 18°..

The two slanting lines given in the diagram are parallel.

Furthermore, the horizontal line crosses both parallel lines given above.

Then the measure of the angles marked in the question is equal.

Therefore, we have 5x + 7° = 9x - 63°.

⇒ 63° + 7° = 9x - 5x

⇒ 70° = 4x

⇒ x = 70°÷ 4 = 17.5° ≈ 18°(approximate to the nearest decimal)

Therefore, x = 18°

Let us now compute the magnitude of each angle.

5x + 7 = 5 × 18 + 7 = 90 + 7 = 97

9x - 63 = 9 × 18 - 63 = 162 - 63 = 99

The measurement of these two angles differs by two degrees.. Because the value of x is not exact. We used the approximated value.

Let us recalculate the angle measurements using the exact value 17.5.

5x + 7 = 5 × 17.5 + 7 = 87.5 + 7 = 94.5

9x - 63 = 9 × 17.5 - 63 = 157.5 - 63 = 94.5

So, the exact value of x is 17.5°.

Hence, The nearly value of x to the nearest decimal is 18°.

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the fraction form of the number will be 5 / 18.

We are given the decimal number as:

0.83(bar on 3) = F ...(1)

Now, we need to convert this into fraction.

For this, we will first multiply both the sides by 10

Do, we get that:

8.33 ( bar on 3) = 10 F ...(2)

Now, we will Subract (1) from (2), we get that:

9 F = 8.33 (bar on 3) - 0.83 (bar on 3)

9 F = 7.5

F = 7.5 / 9

F = 2.5 / 9

F = 25 / 90

Reducing the fraction into simplest form:

F = 5 / 18.

Therefore, we get that the fraction form of the number will be 5 / 18.

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Answer:

$132.74

Step-by-step explanation:

First: divide the sales price by 100

6.75 ÷ 100 = 0.0675

Second: multiply the answer from the first step by the original price

0.0675 x 124.35 = 8.393625

round to the hundredths place

8.393625

8.39

Third: add the original price with the answer from the second step

124.35 + 8.39 = 132.74

Answer:

  x = -1

Step-by-step explanation:

You want to find the value(s) of x that satisfy the equation |x-2| = |4+x|.

The behavior of each absolute value function changes at the point where its argument is zero. For this equation, that will be two points:

  x -2 = 0   ⇒   x = 2

  x +4 = 0   ⇒   x = -4

These two points on the number line divide the domain of the equation into three parts:

The behavior of the equation will be different in those three domains.

In this domain, both absolute value functions negate their arguments. That means the equation is equivalent to ...

  -(x -2) = -(4 +x)

  2 = -4 . . . . . . . . . . add x to both sides

This has no solutions: there are no values of x that will make this true.

In this domain, the absolute value function on the left negates its argument, so the equation is equivalent to ...

  -(x -2) = (4 +x)

  -2 = 2x . . . . . . . . . add x-4 to both sides

  -1 = x . . . . . . . . . divide by 2

This value of x is in the domain, so represents a solution to the equation.

  x = -1

In this domain, neither absolute value function negates its argument, so the equation is equivalent to ...

  x -2 = 4 +x

  -2 = 4 . . . . . . . subtract x

This has no solutions: there are no values of x that will make this true.

The given equation has one solution: x = -1.

__

Additional comment

When solving an equation like this graphically, it is often useful to put it in the form f(x) = 0. We can obtain that form by defining ...

  f(x) = |x -2| -|4 +x|

The graph of this is attached. The only solution is where f(x) = 0, at x = -1.

Note that the function is parallel to the x-axis outside of the middle domain, so will not have any x-intercepts in those regions.

Answer:

40 students

Step-by-step explanation:

I think it is 40 students because 60 + 40= 100  then 100 x 40 = 4,000

then the SCHOOL has to pay a $30 cleaning fee so that will add up to $4,030! I hope this helps everybody!

40 students will be going on the trip

Each student will pay $60 for food and lodging

Each student will also pay $40 for the bus

Total amount of fee that will be paid by each student is

= 60 +40

= 100

The school will pay $30 cleaning fee for the bus, it's only the school that will be paying this fee, the students are not included. This will will be subtracted from the total cost which is $4,030 leaving us with $4,000

Therefore the number of students going on the trip can be calculated as follows

= 4,000/100

= 40

Hence 40 students will be going on the trip

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If no extra men were engaged then the work would have been completed in 45.5 days.

So,

The time required by 24 men to complete their work is:

Therefore, if no extra men were engaged then the work would have been completed in 45.5 days.

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Answer:

  1.5×10³

Step-by-step explanation:

You want to know the value of the expression given with numbers in scientific notation.

The usual rules of arithmetic and exponents apply. Your calculator or spreadsheet can use and display the numbers in scientific notation for you.

  [tex]\dfrac{6.48\times10^5}{(2.4\times10^4)(1.8\times10^{-2})}=\dfrac{6.48}{2.4\times1.8}\times10^{5-4-(-2)}=\boxed{1.5\times10^3}[/tex]

Answer:

x=5$

$y=-4

Step-by-step explanation:

the solution is easy no more you have to put the first numbers and put it in order

Answer: (a) The equation is so called "time equation"

D/12 + 16*60 + D/8 = 19*60 seconds

(b)  To determine the distance D, solve the equation

D/12 + D/8 = 19*60 - 16*60 = 3*60

multiply both sides by 24

2D + 3D = 3*60*24

5D          =4320

D             =4320/5 = 864 ft

Step-by-step explanation:

The original equation will be x + x + 1 = 67 and the left page will have 33 page number and the right one will have 34 page number.

Let x be the first consecutive integer.

So,  x + 1  is the first consecutive integer.

Sum of the two integers = 67

⇒ x + x + 1 = 67    (This is the original equation)

Combining the like terms:

⇒ 2x + 1 = 67

Subtract 1 from both the sides:

⇒ 2x = 67 - 1

⇒ 2x = 66

Divide both sides by 2:

⇒ x = 66/2 = 33

Therefore, the original equation will be x + x + 1 = 67 and the left page will have 33 page number and the right one will have 34 page number.

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Answer: Its quadrant 3

Step-by-step explanation:

Hope this helps!

Answer:

Quadrant 3

Step-by-step explanation:

Lets have an example

Lets say we are plotting the point (-4,-4)

so, we would go left on the x-axis, to -4. So we will be in either Quadrant 2 or Quadrant 3

Now we go down 4, so we end up in Quadrant 3

Hence, The answer is Quadrant 3

Hope this helps!^^

The evaluation of the given angles are as follows;

Complementary angles sum up to 90°

Supplementary angles sum up to 180°

1. Let A and B represent the two angles, we have;

A + B = 180°

A - B = 35°

Which gives;

A + B + (A - B) = 180° + 35° =215°

A + B + (A - B) = A + A = 2•A

Which gives;

2•A = 125°

A = 215°/2 = 107.5°

A + B = 180°

B = 180° - A

Therefore;

B = 180° - 107.5° = 72.5°

The two angles are; A = 107.5° and B = 72.5°

2. ‹E + ‹F = 90° Definition of complementary angles.

‹E = ‹F + 54°

Which gives;

2•‹F + 54° = 90°

Therefore;

‹F = 18°

‹E = 72°

3. Let A represent the angle, we have;

A + A - 76° = 180°

A = 256°/2 = 128°

The measure of the angle is 128°

The measure of its supplement is 52°

4. ‹Q + ‹Q + 26 = 90

‹Q = (90-26)/2 = 32

‹Q = 32°

‹R = 32° + 26°= 58°

5. Let A represent the angle, we have;

A + 3•A = 180°

4•A = 180°

A = 180°/4

A = 45°

The measure of the supplement = 3 × 45° = 135°

6. Angle left = 90° - 35° = 55°

Speed= 35°/(21 s) = 5/3°/s

Time remaining for the bridge= 55°/(5/3°/s) = 33 s

7. 3•r + 5 + 5•r - 27 = 90

8•r - 22 = 90

r = 112/8 = 14

‹ABD = 3•r + 5 = 47°

‹DBC = 5•r - 27 = 43°

8. 4•a + 58 = 2•b - 18 = 90

a = 8

b = 54

9. a + 15 + a + 35 = 90

a = 40/2 = 20

10. 3•a + 10 + 13•a = 90

16•a = 80

a = 80/16 = 5

m‹ADB = 3•a + 10 = 25°

m‹BDC = 13•a = 65°

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The statistical measures for the 10-day vacation are given as follows:

a) Mean: $2470.

b) Standard deviation: $189.74.

c) Variance: $²36,001.

To find the mean for n days, we take the mean amount in a single day and multiply by n.

Hence:

247 x 10 = $2470.

To find the standard deviation for n days, we take the standard deviation for a single day and multiply by the square root n.

Hence:

60 x sqrt(10) = $189.74.

The variance is the square of the standard deviation, hence:

($189.74) = $²36,001.

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Answer:

32° degree Fahrenheit is converted to celcius

Answer:

use 273k that is if is changing from celcius to Kelvin

The two expressions for the volume of a cube with a side length of S are:

V = S^3

V = S*S*S

A cube is a rectangular prism where the 3 dimensions have the same measure, which we will call the side-length of the cube.

So, if S is the sidelength of the cube, the volume will be given by the product between the product between the dimensions of the cube, and the 3 dimensions measure the same thing, which is S, then:

V = S*S*S

That is the expression without exponents, and the expression with an exponent is really trivial, we have S multiplied by itself 3 times, so we get:

V = S^3

These are the two expressions for the volume.

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Answer: 8x^10

Step-by-step explanation:i guessed but when you multiply exponents you just add them so the exponent is 10 and then 2 cubed is 8

Randy's percentage change from Week 1 to Week 2 was 2.37% greater than Week 2 to Week 3.

The percentage change will be calculated by the relation -

Percentage change = change in timing ÷ original time × 100

Calculating percentage change between Week 1 and Week 2

Change = 28.8 - 27.6

Change = 1.2 seconds

Percentage = (1.2 ÷ 28.8) × 100

Percentage = 4.17%

Calculating percentage change between Week 2 and Week 3

Change = 27.6 - 27.1

Change = 0.5 seconds

Percentage = (0.5 ÷ 27.6) × 100

Percentage = 1.8%

So, percent of change from Week 1 to Week 2 than from Week 2 to Week 3 was = 4.17 - 1.8

Percentage change = 2.37%

Therefore, the percentage change from Week 1 to Week 2 was 2.37% greater than Week 2 to Week 3.

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Answer:C=8

Step-by-step explanation:

32 divided by 4 = 8

The inequality expression 4/z >= 3 is false, when z = 2 because 2 is not greater than or equal to 3

The inequality expression is given as

4/z >= 3

The value of z is given as

z = 2

Substitute 2 for z in the inequality expression given as

4/z >= 3

So, we  have:

4/2 >= 3

Evaluate the quotient

2 >= 3

The above inequality expression is false.

This is so because 2 is not greater than or equal to 3

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The total cost for a first draft that took 14 hours to complete is $2430.

It should be noted that when the work takes longer than 8 hours, the architect charges $105 for each additional hour. For 14 hours, the additional hours will be:

= 14 - 8

= 6 hours

Therefore, the total cost will be:

= 1800 + (105 × 6)

= 1800 + 630

= 2430

Therefore, the total cost for a first draft that took 14 hours to complete is $2430.

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The solution to the equation where the equation is given as -2(5z + 8) = 14 + 6z is z = -15/8

The equation is given as

-2(5z + 8) = 14 + 6z

Open the bracket

So, we have

-10z - 16 = 14 + 6z

Collect the like terms

So, we have

-10z - 6z = 14 + 16

Evaluate the like terms

So, we have

-16z = 30

Divide both sides of the equation by 16

So, we have

z = -15/8

Hence, the solution to the equation where the equation is given as -2(5z + 8) = 14 + 6z is z = -15/8

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Answer: R'=(-4, -3)

S'=(-4, -10)

T'=(-8, -10)

U'=(-8, -3)

Step-by-step explanation:

When rotated around the origin by 180 degrees, the rectangle will have all its coordinates' x and y values negated.

R=(4,3) ==> R'=(-4, -3)

S=(4,10) ==> S'=(-4, -10)

T=(8,10) ==> T'=(-8, -10)

U=(8,3) ==> U'=(-8, -3)