Given the parallelogram TVWY shown above, determine how triangles TUZ and WXV can be shown to be similar. A. Since ZTU VWX and VX = XW, the triangles are similar by angle-side. B. Since TUZ WXV and TU = UZ, the triangles are similar by angle-side. C. Since TUZ VWX and ZTU WXV, the triangles are similar by angle-angle. D. Since TUZ WXV and ZTU VWX, the triangles are similar by angle-angle.

Given that:

- Lucy must have the construction job done within 30 days.

- The bid of the first engineer is $2050 per hour, 8 hours per day.

- The bid of the second engineer is 1¢ per day which will double each day.

Let be "x" the number of days of work and "y" the total cost (in dollars)

• Using the data given, you can set up this equation to represent the bid of the first engineer:

And you can set up this equation to represent the bid of the second engineer:

• In order to graph them, you can give values to the variable "x" and evaluate, in order to get the corresponding y-values.

By substituting this value into the first equation:

You get:

- For the second equation, substitute this value:

And evaluate:

Now you can graph them:

You can identify in the graph that the total cost is greater in the first line than the cost in the second line. Therefore, the cost of the bid given for the first engineer will be greater.

Hence, the answer is:

• Equation 1st:

• Equation 2nd:

• Graph:

• Better deal: The bid of the second engineer (the graph shows that the total cost using this deal will be less than the total cost using the first deal).

The limit exists at all values of x₀ where the function is continuous, i.e. where there is no break in the graph.

So only consider the points where there is a vertical asymptote (x₀=-6), where there are holes and jump discontinuity (x₀=-3,3).

The vertical asymptote is a place where the function is undefined and the limit of the function does not exist.

Hence, the limit does not exist at x₀=-6.

For the point where there is a hole, x₀=-3, notice that the graph approaches the same y-value both from the left and right, hence the limit exists at this point, as this is a removable discontinuity.

For the point, x₀=3 where there is a jump discontinuity, notice that the graph approaches different values from the left and right, respectively. Hence, the left and right limits are not equal and thus the limit does not exist.

So the limit exists over the set of real numbers except {-6,3}.

Answer: 13.01m

Explanation

A right triangle is a triangle with a 90º angle. If the square lot is divided by a diagonal, then two right triangles are formed:

The right triangle satisfies the Pythagorean Theorem:

where c is the diagonal (hypotenuse), and a and b are the sides. In our case, as it is a square, a = b, meaning:

Thus, simplifying and solving for c we can find the diagonal:

ACD has a base (AC) with a length of 3 units.

A'C'D' has a base (A'C') with a length of 9 units.

Therefore, the scale factor is 9/3 = 3.

The value of the given trigonometric function is [tex]\sqrt{3} +1[/tex]

The given trigonometric function is sin(15°)cos(135) + cos(15) sin(135).

Evaluating the expression with the sum and difference identities.

We know, SinACosB + CosASinB = Sin(A +B)

Now, We have :

sin(15°)cos(135) + cos(15) sin(135) = Sin ( 15 +135 ) = Sin150

Now, Sin 150 = Sin(120 +30) =  Sin120Cos30 + Cos120Sin30

Sin 150 =

[tex]=\frac{\sqrt{3} }{2} * \frac{\sqrt{3} }{2} + \frac{1}{2}*\frac{1}{2} = \frac{2\sqrt{3} }{2} +\frac{2}{2} \\\\= \sqrt{3} +1[/tex]

Hence, the value of the given trigonometric function is [tex]\sqrt{3} +1[/tex]

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Answer:

Explanation:

Given:

To find:

The quotient and write it in rectangular form using exact values

Recall the below;

So we can go ahead and rewrite the given expression and simplify as shown below;

So we'll have;

Solution

For this case we can do the following:

Then we can use the Pythagoras theorem and we can solve for d and we got:

Then the answer would be:

69.97 ft

Answer:

Double

Explanation:

If the area of the base remains the same and the altitude is doubled, we have:

Thus, if the area of the base remains the same and the altitude is doubled, the volume will double,

We have to find the equation of the line in standard form, knowing that the slope is m = -5 and it passes through the point (2, 1).

The standard form is:

When we know the slope and one point, we can write the equation in slope-point form. Then, we can rearrange the terms in order to find the standard form.

The slope-point form is:

We then can rearrange it as:

Answer: the standard form of the line is 5x + y = 11.

A 45 minute basketball game, 30 girls want to play. Only 10 can play at once. If each player is to play the same length of time. 15 minutes should each play

10/30=1/3

[tex]\frac{1}{3} \times 45$$[/tex]

Convert element to fraction: [tex]$\quad 45=\frac{45}{1}$[/tex]

[tex]=\frac{1}{3} \times \frac{45}{1}$$[/tex]

Apply the fraction rule:[tex]$\frac{a}{b} \times \frac{c}{d}=\frac{a \times c}{b \times d}$[/tex]

[tex]=\frac{1 \times 45}{3 \times 1}$$[/tex]

[tex]$\frac{1 \times 45}{3 \times 1}=\frac{45}{3}$[/tex]

[tex]=\frac{45}{3}[/tex]

Divide the numbers: [tex]$\frac{45}{3}=15$[/tex]

=15

15 minutes for 3 groups of 10 each to play basketball.

To add or subtract fractions, the denominator must be the same (the bottom value). Subtraction and addition with the same denominators If the denominators are already the same, all that remains is to add or subtract the numerators (the top value).

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We were given two triangles, ABC and XYZ. The problem also states that the angles B and Y are congruent, and the sides AB and XY are also congruent. We need to point out which information is missing so that we can prove the triangles are congruent by SAS.

The term SAS stands for Side-Angle-Side, it means that two triangles are similar when they have two congruent Sides and one congruent Angle. Since the problem already said that one side and one angle are congruent, then we only need one more side. From this, we can conclude that the correct option is B.

The price on sale of the dishwasher is $201.6

From the question, we have the following parameters that can be used in our computation:

Mardown = 20%

Selling price = $252

The price on sale of the dishwasher is calculated using the following equation

Price on sale = Selling price * (1 - Mardown)

Substitute the known values in the above equation, so, we have the following representation

Price on sale = 252 * (1 - 20%)

Evaluate

Price on sale = 201.6

Hence, the price is $201.6

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a parking lot is distracted in the shape of a parallelogram if the base is 200 feet the height is 120 ft and the Dialganal with is 140 feet what is the area of the parking lot?​

we know that

the area of parallelogram is equal to

A=b*h

where

b is the base

h is the height

substitute the given values

A=200*(120)

A=24,000 ft^2

Given:

Required:

To complete the table.

Explanation:

Since

Divide by 8 into both sides.

Final Answer:

Explain in explanation parts.

Let x be the unkown number.

The product of a number and 5: multiplication of x and 5 (5x)

Is always greater than 15: >15

Inequality:

Another form of write the inequality is soving x:

Explanation:

X- intercept is the value of x when y is equal to zero.

On the graph, we have distance(meters) over time (secs).

The time is in the x axis. The value of x when y is equal to zero is a bit above 3.

This means when Olivia's distance is at point 0 meters, the seconds it takes to enter to pool is a bit over 3 secs (around 3,

From the options, the correct answer is It takes Olivia about 3.2 seconds to enter the pool (option B)

We will use the law of sines and law of cosines shown below

Therefore, in our case, finding side c.,

Thus, side c is approximately 21.8km.

Finding the missing angles using the law of sines,

Similarly, in the case of angle B,

Therefore, the answers are

c=21.8km,

So, given

25 < x < 40

So, the numbers will be

26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39

These numbers are the numbers belongs to Z and achieve the inequality

Note: A Cardinal Number is a number that says how many of something there are.

The volume of the pyramid with square base with sides 8 ft long and a height of 16.8 ft is 358.4 ft.

Given,

A pyramid has a square base with sides 8 ft long and a height of 16.8 ft.

we are asked to find out the volume of the pyramid = ?

we have:

side length (s) = 8 ft

height (h) = 16.8 ft

we know the formula of volume as:

v = 1/3 × s² × h

v = 1/3 × (8)² × 16.8

v = 1/3 × 64 × 16.8

v = 64 × 5.6

v = 358.4 ft

Hence we get the volume as  358.4 ft

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The coordinate of P is (-4,4).

A reflection across the line y=-x is given by

In this case we have:

Therefore, the image is (-4,4) and the asnwer is third option.

this is a conversion problem

First you must understand that 1 foot = 12inches

Given a ribbon that is 5 1/2 feet long

To convert to inches, you will simply multiply 5 1/2 by 12 as shown;

= 5 1/2 * 12

convert the mixed fraction to improper fraction

= 11/2 * 12

= 11 * 12/2

= 11 * 6

= 66 inches

Hence the ribbon is 66 inches long

To find the factors of a number we must find all the numbers that divide 24, two numbers are always easy, 1 and the number itself! But how do we find the others? We start at 1 and divide the number (here it's 24) by all the possible numbers until we reach the number we are finding the factor, it the division is an integer number, then it's a factor!

Another thing may help us! if we divide a number, for example, 24 by 2, the result is 12. Then 2 is a factor of 24 but 12 is also a factor of 24! Then when we find one factor, in fact, we have 2 factors. Now let's apply it to our problem:

As we can see, just by 3 divisors we found all the factors of 24! They are 1, 2, 3, 4, 6, 8, 12, 24

Final answers: 1, 2, 3, 4, 6, 8, 12, 24

The area of the square is given by:

Where s is the length of the side. Then s=(2x+1) km.

By replacing this into the formula we have:

Also, the square of a sum is given by:

If a=2x and b=1, then:

Thus, the area of the square in terms of the variable x is:

Given

Solve the following system of linear equations.

x + 3y + z = - 4

2x – 4y – 3z = 7

3x – 3y + 4z = 13

Solution

Substitute x= -4-3y-z

Simplify

Make y the subject

Now substitute

Simplify

Now substitute z=1

Finally, to find x

when z =1 and y =-2

The final answer

∠ BCD has the same measure as ∠ CFG and ∠ FIJ.

If  ∠ GFI measures x degrees, then the measure of HIK is (180 - x) degrees.

The sum of the measures of ∠ CFE and ∠ ACF is 180 degrees.

Given that:-

AD II EG II HJ and BK is the transversal.

As AD II EG

∠ BCD = ∠ CFG

As EG II HJ

∠ CFG = ∠ FIJ

Hence,

∠ BCD has the same measure as ∠ CFG and ∠ FIJ.

As ∠ GFI = x degrees

Hence, ∠ FIJ  = (180 - x) degrees  (Sum of internal angles is 180 degrees)

∠ FIJ = ∠ HIK (Vertically Opposite angles)

Hence,

∠ HIK = (180 - x) degrees.

As ∠ CFE and ∠ ACF are internal angles, hence their sum will be 180 degrees.

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The surface area of a cone is given by the following formula:

Where SA is the surface area, s is the slant and r is the radius. Replace for the given values:

Each ornament has 2 cones, it means that each ornament has a surface area of:

If she needs to paint 70 ornaments, she will have to paint:

According to the question statement, she uses one bottle of paint to paint 202cm^2. To find how many bottles she needs to paint 70 ornaments, divide the total area of the 70 ornaments by 202:

The answers are:

1. The surface area of one ornament is about 191.6 cm^2.

2. She needs 67 bottles.

Solution

For this case we have the following:

then we can find the difference on this way:

Then she has 41/12 miles left

Let's call those numbers a, b and c.

Since their sum is 154, we have:

a + b + c = 154

Also, since the first number is 10 more than the second, we have:

a = b + 10

And, since the third number is 4 times the second number, we have:

c = 4b

Now, we can use the expressions of a and c in terms of b in the first equation:

a + b + c = 154

b + 10 + b + 4b = 154

6b + 10 = 154

6b = 154 - 10

6b = 144

b = 144/6

b = 24

Then, we can use the value of b to find a and c:

a = b + 10

a = 24 + 10

a = 34

c = 4b

c = 4 * 24

c = 96

Therefore,

• First number: ,34

• Second number: ,24

• Third number: ,96

In industrial art class. Elizabeth created a figure from sheet metal. She created a right circular cylinder that has a radius of 6 inches, and a height of 12 inches.

What is the volume in cubic inches of the figure she created

OPTIONS

1,356.48 inches3

648 inches3

339.12 inches3

226.08 inches3​

_________________________

Can you see the updates?

____________________________

Cylinder volume = A(circle) * height

Cylinder volume = π r^2 * h

Cylinder volume = π (6 in)^2 * 12 in

Cylinder volume = π (6 in)^2 * 12 in

Cylinder volume = π 432 in^3

Cylinder volume = 1357. 17

______________

Answer

π= 3.14

1,356.48 inches3