The Wilsons traveled 860 miles to New York City to attend a wedding. They took a different route on the way home to visit historical landmarks. The trip home was 920 miles. How many more miles did they travel on the way home?

Answer:

Horizontal Translation, Dilation and Reflection along y-axis

Step-by-step explanation:

Answer:

Approximately 391 minutes taken by 20 people to paint 20 walls.                    

Step-by-step explanation:

Given : It takes 48 minutes for 7 people to paint 7 walls.

To find : How many minutes does it take 20 people to paint 20 walls?

Solution :

7 people to paint 7 walls in 48 minutes.

So, 1 people to paint 7 walls in [tex]\frac{48}{7}[/tex] minutes.

and 1 people to paint 1 walls in [tex]\frac{48}{7\times 7}[/tex] minutes.

Now, We have to find minutes does it take 20 people to paint 20 walls.

20 walls will be painted in [tex]\frac{48\times 20}{7\times 7}[/tex] minutes.

20 people to paint 20 walls in [tex]\frac{48\times 20\times 20}{7\times 7}[/tex] minutes.

i.e. [tex]\frac{48\times 20\times 20}{7\times 7}=\frac{19200}{49}=391.83[/tex]

Therefore, Approximately 391 minutes taken by 20 people to paint 20 walls.

The support given to the tent forms a right triangle.

The height of the tent is 5.3 ft

The given parameters are:

[tex]\mathbf{Base = 6}[/tex]

[tex]\mathbf{Hypotenuse= 8}[/tex]

The height is calculated as follows:

[tex]\mathbf{Hypotenuse^2 = Base^2 + Height^2}[/tex]

Substitute known values

[tex]\mathbf{8^2 = 6^2 + Height^2}[/tex]

This gives

[tex]\mathbf{64 = 36 + Height^2}[/tex]

Collect like terms

[tex]\mathbf{Height^2 = 64 - 36 }[/tex]

[tex]\mathbf{Height^2 = 28 }[/tex]

Take square roots

[tex]\mathbf{Height = 5.3 }[/tex]

Hence, the height of the tent is 5.3 ft

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Answer:  The 100th even natural number is 200.

Step-by-step explanation:  Given that the following arithmetic sequence represents the set of natural numbers :

2,  4,  6,  8,  10,  .  .  ..

We are given to find the 100th even natural number, i.e., the 100-th term of the sequence.

We know that

the n-th term of an arithmetic sequence with first term a and common difference d is given by

[tex]a_n=a+(n-1)d.[/tex]

For the given sequence, we have

a = 2  and  d = 4 - 2 = 6 - 4 =  .  .  .  =2.

Therefore, the 100-th term of the sequence will be

[tex]a_{100}=a+(100-1)d=2+99\times2=2+198=200.[/tex]

Thus, the 100th even natural number is 200.

Step-by-step explanation:

Graph is not given.

We have

       n= 2 p+3

and

      n= 5+p

That is

     2 p+3 = 5 + p    

         p = 5 - 3

         p = 2

Substituting in n= 5+p

             n = 5 + 2 = 7

So the solution is n = 7 and p = 2    

Leia can cut a total of 297 triangular patches from 33 pieces of fabric, with each piece yielding 9 patches.

To calculate how many triangular patches can Leia cut from 33 pieces of fabric, we first need to find out how many patches can be cut from a single piece of fabric. The area of each triangular patch is 63 square centimeters. The area of the fabric is length * width, which is 27 cm * 21 cm = 567 square centimeters.

Now, if we divide the area of the fabric by the area of one triangular patch, we get the number of patches per fabric piece: 567 cm2 / 63 cm2 = 9 patches per fabric piece.

Since Leia has 33 pieces of fabric, the total number of patches she can cut is 9 patches * 33 pieces = 297 patches.

Final answer:

To find the weight W such that the support force at A is zero, the principle of static equilibrium is used. By taking moments about point B and setting the sum of moments to zero, W is found to be 342.5 N.

Explanation:

The question requires the application of the principles of static equilibrium to find the unknown weight W that would set the supporting force at point A to zero. In static equilibrium, the sum of all forces and the sum of all torques (moments) about any point must be zero.

We can analyze the forces acting on the beam by taking moments about point B to find the value of W. Because the support at A is required to exert no force, we only consider the gravitational force due to the beam's weight and the weight applied at point B. By setting the sum of moments about B to zero, we can solve for W.

Using the conditions for static equilibrium:

Sum of vertical forces = 0

Sum of moments (torques) = 0

The moment leverage for the 685 N weight is at L/4, and for the unknown weight W, it is at L/2. Assuming the beam is massless the equation for the sum of moments around point B is:

(685 N) * (L/4) - (W) * (L/2) = 0

Solving for W:

W = (685 N) / 2

Thus, W is equal to 342.5 N.

The factored form of  −7ab+10 is (ab−5)(ab−2).

To factor the expression −7ab+10, we look for two binomials whose product gives the original expression. In this case, the factors are

(ab−5)(ab−2).

Expanding

(ab−5)(ab−2) using the distributive property, we get:

(ab−5)(ab−2)=(ab)(ab)−(ab)(2)−(5)(ab)+(5)(2)

Simplifying each term, we get:

−2ab−5ab+10

Combining like terms, we have:

−7ab+10

Therefore, the factored form of  −7ab+10 is (ab−5)(ab−2).

When making enough BLT sandwiches to use 2 full heads of lettuce, Omar will be using 2.5 pounds of bacon and will end up making a total of 40 BLT sandwiches.

The subject of this question is Mathematics, specifically ratios and proportions. Given that Omar uses one full head of lettuce for every 5 tomatoes, for 2 heads of lettuce, he will use 10 tomatoes (2*5). Since he uses 1/2 pound of bacon for every 2 tomatoes, then for 10 tomatoes, he will need 2.5 pounds of bacon (10/2*0.5). Finally, since it takes 1/4 pound of bacon to make 4 sandwiches, with 2.5 pounds of bacon he will make 40 sandwiches (2.5/0.25*4). Therefore, Omar will use 2.5 pounds of bacon and make a total of 40 BLT sandwiches.

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She will cover 35/8 miles.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

total distance in miles = 7/8 miles  per day

So, in 5 days in a week.

She will cover

=5*7/8

=35/8 miles.

Hence, She will cover 35/8 miles.

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The line segment XZ has a length of 16 units. Hence, the 3rd option is the correct choice. Computed using the tangent to the circle and the Pythagoras Theorem.

A tangent to a circle is always perpendicular to it, that is, the radius drawn from the center of the circle to the tangent, is always perpendicular to it.

According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse, that is, the side opposite to the right angle, is equal to the sum of the squares of the legs, that is, the other two sides.

In the question, we are asked to find the length of the line segment XZ.

Firstly, we name the center of the circle O.

The diameter of the circle is given to be 12 units.

Thus, its radius = 12/2 = 6 units,

Joining the radius OW, we get a right triangle OWZ, as the radius from the center of the circle to the tangent is always perpendicular.

In the right triangle OWZ, by Pythagoras Theorem, we can write:

OZ² = OW² + WZ² {Since, OZ is the hypotenuse},

or, (k + 6)² = 6² + (k + 4)² {Since, OZ = OY + YZ = Radius + k = 6 + k, and OW = Radius = 6},

or, k² + 12k + 36 = 36 + k² + 8k + 16 {Using the formula (a + b)² = a² + 2ab + b²},

or, k² + 12k - k² - 8k = 36 + 16 - 36 {Rearranging},

or, 4k = 16 {Simplifying},

or, k = 4 {Simplifying}.

Now, XZ = XY + YZ = Diameter + k = 12 + 4 = 16 units.

Thus, line segment XZ has a length of 16 units. Hence, the 3rd option is the correct choice. Computed using the tangent to the circle and the Pythagoras Theorem.

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Answer: 15

Step-by-step explanation: its 15