Given: FB ║ CG ∠BFE and ∠C are supplementary. Prove CA ║ FE

Answer:

I am pretty positive it is thirty if you need work shown just let me know if it is wrong for some reason then I apologize.

Step-by-step explanation:

If the model is 15 inches. Then the length of the table will be 10 feet.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

A table blueprint uses the scale 3 inches :2 feet.

The scale factor will be 2 feet: 3 inches.

If the model is 15 inches.

Then the length of the table will be

⇒ (2 feet/ 3 inches) x 15 inches

⇒ 2 x 5

⇒ 10 feet

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Answer:

[tex]\sf x = \dfrac{-1 + i\sqrt{3} }{2} \quad or \quad \dfrac{-1 - i\sqrt{3} }{2}[/tex]

Explanation:

[tex]\sf Given : x^2 + x + 1 = 0[/tex]

Solve it using quadratic formula

[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad \:when\: \: ax^2 + bx + c = 0[/tex]

So, here constants are: a = 1, b = 1, c = 1

When the value's are substituted inside the formula

[tex]\sf \rightarrow x = \dfrac{-1 \pm \sqrt{1^2 - 4(1)(1)} }{2(1)}[/tex]

[tex]\sf \rightarrow x = \dfrac{-1 \pm \sqrt{-3} }{2}[/tex]

[tex]\sf \rightarrow x = \dfrac{-1 \pm i\sqrt{3} }{2}[/tex]

[tex]\sf \rightarrow x = \dfrac{-1 + i\sqrt{3} }{2} \quad or \quad \dfrac{-1 - i\sqrt{3} }{2}[/tex]

The answers are :

This problem can be solved using the quadratic equation.

x = -1 ± √1² - 4(1)(1) / 2a

x = -1 ± √1 - 4 / 2a

x = -1 ± √-3 / 2a

x = -1 ± i√3 / 2a (∴ i = √-1)

The possible values of x are :

Fission of 1 kg of element B releases 2941 times as much energy as burning 1 kg of element A

The given parameters are:

Energy A = 5.1 * 10^7

Energy B = 1.5 * 10^11

The amount of energy B in proportion to energy A is calculated as

Proportion = Energy B/Energy A

So, we have:

Proportion = (1.5 * 10^11)/(5.1 * 10^7)

Divide 1.5 by 5.1

Proportion = 0.2941 * 10^11/10^7

Divide 10^11 by 10^7

Proportion = 0.2941 * 10^4

Evaluate

Proportion = 2941

Hence, fission of 1 kg of element B releases 2941 times as much energy as burning 1 kg of element A

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Answer:

B and D

Step-by-step explanation:

Both B and D cross over the point (4, 8) therefore they share the solution (4, 8)

Answer:

  y = 9x +1000

Step-by-step explanation:

The relation for the total cost of manuals based on the number produced will be the sum of a base cost and a variable cost. The variable cost is the product of the cost per manual and the number of manuals.

The cost per manual can be found by looking at the increase in cost relative to the increase in the number of manuals produced:

  cost per manual = (increase in cost)/(increase in production)

  = ($2350 -1450)/(150 -50) = $900/100 = $9

The base cost will be added to the product of the cost per manual and the number of manuals. For the 2nd year purchase, this is ...

  $1450 = base cost + (50 manuals)×($9/manual)

  $1450 = base cost + $450

  base cost = $1450 -450 = $1000

The equation for the cost in dollars (y) of producing x manuals can now be described by ...

  y = (cost per manual)x +(base cost)

  y = 9x +1000

Answer:

7.534g ring is heavier, by 2.234g

Step-by-step explanation:

Note: mg =

[tex] {10}^{ - 3} grams[/tex]

[tex]5300mg = ( \frac{5300}{ {10}^{3} } )g \\ = ( \frac{5300}{1000} )g \\ = 5.3g[/tex]

From here we can see Ring A (7.534g) is heavier than Ring B(5,300mg)

Difference in Mass = 7.534g - 5.3g

= 2.234g

Answer:

[tex]967.6cm^{2} (1 d.p)[/tex]

Step-by-step explanation:

Total Surface Area of Cylinder = [tex]2\pi rh+2\pi r^{2}[/tex]

Given from the question, r = 7 cm and h = 15cm

Lets Substitute r and h into the formula to find the Total Surface Area of the cylinder.

Total Surface Area of Cylinder = [tex]2\pi (7)(15)+2\pi (7)^{2} \\=210\pi +98\pi \\=308\pi cm^{2} \\=967.6cm^{2} (1 d.p)[/tex]

The type of solution set of the given equation is; "No Solution"

Let's solve for x in the given equation;

8(3x - 2) - 4 = 8x + 4(4x - 3)

Expanding the bracket gives;

8(3x) + 8(-2) - 4 = 8x + 4(4x) + 4(-3)

24x - 16 - 4 = 8x + 16x - 12

24x - 20 = 24x - 12

Subtract 24x from both sides to get;

-20 = -12

This is a false equation as both sides are not the same number and as such the type of solution set is "No Solution"

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Answer:

x=10000

Step-by-step explanation:

Answer:

24ft high

Step-by-step explanation:

Assuming the wall is perpendicular to the ground (so that it forms a right angle, and that when the ladder is placed on the ground and leaned up against the wall that it forms a right triangle), we can use the Pythagorean Theorem to describe the situation mathematically.

For any right triangle (a triangle that has a right angle) the Pythagorean Theorem applies.  The Pythagorean Theorem describes the relationship between side lengths as [tex]a^2+b^2=c^2[/tex], where "c" is the length of the "hypotenuse" (the side across from the right angle), and "a" and "b" are the lengths of the "legs" (the other two sides that are touching the right angle).  Since addition is commutative, it doesn't matter which leg you pick for side "a" or side "b", it only matters that the hypotenuse must be "c".

Given that the ladder is across from the right angle (the angle formed by the wall and the ground... the two "legs"), the ladder represents the hypotenuse in this situation.

Substitute known values, and simplify...

[tex]a^2+(10)^2=(26)^2[/tex]

[tex]a^2+100=676[/tex]

Subtract 100 from both sides...

[tex](a^2+100)-100=(676)-100[/tex]

[tex]a^2=576[/tex]

Apply the square root property...

[tex]\sqrt{a^2}=\pm \sqrt{576}[/tex]

[tex]a=\pm 24[/tex]

[tex]a=24[/tex]  or  [tex]a=- 24[/tex]

Since the distance height the ladder will reach is not a negative number, we reject the negative solution.  Hence, the ladder will reach 24ft high, if placed 10ft from the base of the wall.

After four rounds of the game, it is impossible that Prinyanka's score could be A. 6.

The numbers of the right side are shown to be odd numbers. the lowest numbers that Priyanka can get are:

= 1, 3, 5, 7

Assuming Priyanka picks 1 and 3 which are the lowet number, the total Priyanka would get i:

= 1 + 1 + 3 + 3

= 8

it is therefore not possible to get 6 points after 4 rounds of the game.

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The required mass of the solid is 8.52g. Hence option B is correct.

We have,
mb = mass/89.0, ΔTb = 2.42° C and Kb = 2.53°C•kg/mol.

Mass of the object is defined as the space occupied by an object.

Given equation, ΔTb=Kb x mb
2.42 = 2.53 x mb
mb =0.95
mass / 89.0 x 0.1 = 0.95
mass = 8.52 g

Thus, the required mass of the solid is 8.52g.

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The equation  that can be used to calculate the surface area of the triangular prism net shown below is mathematically given as

SA = (1/2)(5)(12) + (1/2)(5)(12) + (5)(2) + (12)(2) + (13)(2)  

Generally, The region or area that is occupied by the surface of any particular item is referred to as that object's surface area.

In conclusion, the equation surface area of the triangular prism will be one that accommodates all parameters

SA = (1/2)(5)(12) + (1/2)(5)(12) + (5)(2) + (12)(2) + (13)(2)  

SA = (1/2)(5)(12) + (1/2)(5)(12) + (5)(2) + (12)(2) + (13)(2)  

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It's easier to sketch if you simplify [tex]f(x)[/tex]. Factorize the numerator and denominator - simple to do with a difference of cubes or squares.

[tex]\dfrac{x^3 - 1}{x^2 - 1} = \dfrac{(x - 1)(x^2 + x + 1)}{(x - 1) (x + 1)}[/tex]

If [tex]x\neq1[/tex], we can cancel the factors of [tex]x-1[/tex]. Note that [tex]f(1)[/tex] itself is undefined. For all intents and purposes, aside from the singularity at [tex]x=1[/tex], the graph of [tex]f(x)[/tex] will look exactly like the graph of

[tex]\dfrac{x^2 + x + 1}{x + 1}[/tex]

Now, rewrite this as

[tex]\dfrac{x(x + 1) + 1}{x + 1}[/tex]

Then when [tex]x\neq-1[/tex] (note that [tex]f(-1)[/tex] is also undefined), we can cancel [tex]x+1[/tex] to reduce this to

[tex]x + \dfrac1{x+1}[/tex]

On its own, the graph of [tex]x[/tex] is a line through the origin. When [tex]x[/tex] is a large number [tex]\frac1{x+1}[/tex] is small. But as [tex]x[/tex] gets closer to -1, the rational term blows up. Effectively, this means the graph of [tex]f(x)[/tex] looks like [tex]\frac1{x+1}[/tex] around [tex]x=-1[/tex], and far enough away it looks like [tex]x[/tex].

See the attached plot for a sketch of these details.

Answer: Multiplying these factors gives the approximate volume of the original body

Step-by-step explanation:

The given convex body can be approximated by a sequence of nested bodies, eventually reaching one of known volume (a hypersphere), with this approach used to estimate the factor by which the volume changes at each step of this sequence.

Answer:

9

Step-by-step explanation:

I believe the question is stating he can run 3 miles in 1 minute? Though it does make sense, here's the breakdown. :)

3 x 45 = 135 Miles total

135 / 15 = 9 "15" miles ran after 45 minutes.

If this is not what you meant to ask, let me know!

The question was incomplete. Below you will find the missing content.

Use the system of equations and graphs below to complete the sentence.

x - 2y = 5

3x + 15y = -6

The graph that correctly represents the given system of equations is a graph ( ), and the solution to the system is ( , ).

The correct option will be Option B: Graph B and the solution of the given system of equations will be (3,-1).

Given the first equation is x-2y=5

in this equation of line, the x-coordinate is:

x-(2.0)=5

⇒ x=5

The x-coordinate will be (5,0).

in this equation of line, the y-coordinate is:

0- 2y=5

⇒y= -5/2

The y-coordinate will be (0,-5/2).

So the first line equation has x-coordinate (5,0) and y-coordinate (0,-5/2).

Similarly,

Given the second equation is 3x+15y=-6

in this equation of line, the x-coordinate is:

3x+(15.0)=-6

⇒ x=6/3=2

The x-coordinate will be (2,0).

in this equation of line, the y-coordinate is:

(3.0)+15y=-6

⇒y= -6/15= -2/5

The y-coordinate will be (0,-2/5).

So the second line equation has x-coordinate (2,0) and y-coordinate (0,-2/5).

Equation-1: x - 2y = 5

⇒x =2y+5

putting the value of x in equation-2

3x + 15y = -6

⇒ 3(2y+5)+15y=-6

⇒6y+15+15y=-6

⇒21y=-6-15=-21

⇒y=-21/21=-1

putting the value of y in equation of x

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

The solution of system of equations will be (3,-1)

Checking all the options

In option B one line has  x-coordinate (5,0) and y-coordinate (0,-5/2) and another line has x-coordinate (2,0) and y-coordinate (0,-2/5).

And the point of intersection of two lines is (3,-1).

Therefore the correct option will be Option B: Graph B and the solution of the given system of equations will be (3,-1).

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A circle is a curve sketched out by a point moving in a plane. If the distance from A to C is 6 units, then the distance from C to B is 6 units.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

If the distance from A to C is 6 units, then the distance from C to B is 6 units. This is because AC and BC are the radii of the circle, therefore, both are equal to each other.

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Answer: c and 6

Step-by-step explanation:

There is no relationship between the number of hours cycled and the number of hours worked (Option D).

A scatterplot is a graph that is used to show the association between two variables. The relationship between the variables is shown by the use of  line of best fit.

From the scatterplot shown, we can conclude that there is no relationship between the number of hours cycled and the number of hours worked (Option D).

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Answer: 26 × 4

Step-by-step explanation: There are 26 letters in the alphabet lettered A through Z.

Deepak is given the choice of picking a four letter password of his liking, using any four letters. Since the letters he uses can be repeated, it is 26 * 4 possibilities, since there are 26 different possibilities of letters from the alphabet he could choose, for 4 times. Also, since letters can be repeated, 26 stays the same. If letters could not be repeated, it would be 26 * 25 * 24 * 23.

Answer:

B.  26⁴

Step-by-step explanation:

If the password is 4 letters long and he can repeat letters then:

Therefore, to find the total number of passwords he can create, simply multiply the number of permutations for each letter of his password:

⇒ 26 × 26 × 26 × 26 = 26⁴

Answer:

  $959.68

Step-by-step explanation:

The loan amortization formula can be used to find the payment amount.

  A = P(r/n)/(1 -(1 +r/n)^(-nt))

A = payment amount; P = principal borrowed; r = annual interest rate; t = number of years; n = payments per year (and number of times interest is compounded per year).

For a principal amount of $33,000 at an interest rate of 3%, the 36 monthly payments will be ...

  A = $33000(0.03/12)/(1 -(1 +0.03/12)^(-12·3)) ≈ $959.68

The monthly payments will be $959.68.

Answer:

i can't see the picture.

Answer:

See below

Step-by-step explanation:

equal probability    each occurs 1 time out of 16 possibilities

tttt

ttth

ttht

tthh

thtt

thth

thhh

httt

htth

thth

htht

hthh

hhtt

hhth

hhht

hhhh

Answer:

C.y=sin(x-2)

Step-by-step explanation:

Using the topic of transformation of functions(rules shown in picture above)

the the (x-2) moves the graph to places to the right

and as the sine graph goes through 0 and so you add 2 to the right (but there is a problem in the graph should in the picture as it should me labeled 0,90,180,270,360 not these small numbers)

hope it helps!! :)

For calculation of the following entries, the bond interest expense will gotten by multiplying the carrying bond value by the market interest rate.

Date    Account titles                   Debit        Credit

Jan. 1.  Cash                                $407,968

                 Bonds payable                           $380,000

                 Premium on bonds payable      $27,968

                 ($407,968 - $380,000)

Date      Account titles                          Debit      Credit

Dec. 31. Bond interest expense          $24,478

                    Premium bond payable                    $2,122

                    Bond interest payable                      $26,600

Date    Account titles                   Debit        Credit

Jan. 1.  Bond interest payable     $26,600

           ($380000 * 7%)

                   Cash                                            $26,600

Missing words "Prepare journal entries to record (a) The issuance of the bonds, (b) The accrual of interest and the premium amortization on December 31, 2022 and (c) The payment of interest on January 1, 2022"

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33 stone pavers are needed to go around the patio with dimension of 12 ft wide by 14 ft long

An equation is an expression that shows the relationship between two or more variables and numbers.

12 inch = 1 ft

Total perimeter of patio not counting the side against the house = 12 + 12 + 14 = 38 feet

38 feet = 38 feet * 12 inch per feet = 456 in

Number of stone pavers needed = 456 in / 14 in = 32.57 ≅ 33

33 stone pavers are needed to go around the patio with dimension of 12 ft wide by 14 ft long

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The slope of the given line containing the given points is; 7.

The formula for slope of a line between two coordinates is;

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

Now, let us take the last 2 coordinates which are;

(-1, 35) and (2, 56).

Thus, the slope is;

m = (56 - 35)/(2 - (-1))

m = 21/3

m = 7

Thus, the slope of the given line containing the given points is 7.

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The end behavior of the function is the one in option C.

"One end increases and one end decreases"

Here we have the function:

f(x) = -ln(2x) + 4.

Remember that for the natural logarithm, as x tends to zero the function tends to negative infinity.

And as x tends to infinity, the natural logarithm tends to infinity.

So, for our function where we have a negative sign before the logarithm, as x tends to zero the function tends to infinity and as x tends to infinity the function tends to zero.

Then the correct option is C:

"One end increases and one end decreases"

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The graph of the given system of equations is shown below

From the question, we are to graph the given system of equations.

The given system of equations are

y − 2x = −1

x + 3y = 4

The graph of the given system of equations is shown below

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The exponential function that describes the situation is:

[tex]A(t) = 1320(1.2)^t[/tex]

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

The parameters for this problem are:

A(0) = 1320, r = 0.2.

Hence the equation is:

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]A(t) = 1320(1 + 0.2)^t[/tex]

[tex]A(t) = 1320(1.2)^t[/tex]

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