Given triangle ABC ~ triangle XYZ, what is the value of cos(Z)

A polyhedron with 4 vertices and 6 edges would have 4 faces, according to Euler's formula.

This question involves the understanding of Euler's formula applied on polygons. Euler's formula, as given in the question is V – E + F = 2, where V is the number of vertices, E is the number of edges, and F is the number of faces. To answer your question, we need to solve the formula for F. Let's replace V and E with the given numbers, which are 4 for vertices and 6 for edges.

So the formula becomes 4 – 6 + F = 2. Simplifying this, we get -2 + F = 2. Solving for F, we find F = 1 + 2, which means F = 4. So, a polyhedron with 4 vertices and 6 edges would have 4 faces.

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Answer:  The required center of the given circle is 2 units.

Step-by-step explanation:  We are given to find the radius of a circle with the following equation:

[tex]x^2+y^2+8x-6y+21=0~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

The standard equation of a CIRCLE with radius 'r' units and center at the point (h, k) is given by

[tex](x-h)^2+(y-k)^2=r^2.[/tex]

From equation (i), we have

[tex]x^2+y^2+8x-6y+21=0\\\\\Rightarrow (x^2+8x+16)+(y^2-6y+9)-16-9+21=0\\\\\Rightarrow (x^2+2\times x\times 4+4^2)+(y^2-2\times x\times 3+3^2)-4=0\\\\\Rightarrow (x+4)^2+(y-3)^2=4\\\\\Rightarrow (x-(-4))^2+(y-3)^2=2^2.[/tex]

Comparing the above equation with the standard equation (i), we get

radius, r = 2 units  and  center, (h, k) = (-4, 3).

Thus, the required center of the given circle is 2 units.

Answer:

[tex]V = (10a^3+91a^2+54a-792)[/tex]

Step-by-step explanation:

We have

[tex]V = lwh[/tex] (I), and

[tex]l=2a+11[/tex] (II)

[tex]w=5a-12[/tex] (III)

[tex]h=a+6[/tex] (IV)

We substitute the expression (II),(III) and (IV) in (I), that is

V= (2a+11)(5a-12)(a+6), solve the first one terms

[tex]V = (10a^2-24a+55a-132)(a+6)[/tex]

[tex]V = (10a^2+31a-132)(a+6)[/tex]

[tex]V = (10a^3+31a^2-132a+60a^2+186a-792)[/tex], simplifying

[tex]V = (10a^3+91a^2+54a-792)[/tex]

Answer: x = 37

Explanation: If two parallel lines are cut by a transversal,

then alternate interior angles are congruent.

So we can say that 3x + 4 = 115.

Subtracting 4 from both sides, we have 3x = 111.

Dividing both sides by 3, we find that x = 37.

So the value of x is 37.

The perimeter of the rectangle is 54 mm longer than the perimeter of the square.

To find the perimeter of the square, we can use the formula P = 4s, where P represents the perimeter and s represents the length of a side.

Given that the perimeter of the square is 216 mm, we can solve for the length of a side: 216 = 4s ⇒ s = 54 mm.

Since the area of the rectangle is the same as the square, we can calculate the length and width of the rectangle using the given information.

Let's assume the short side of the rectangle is x mm, then the long side would be 4x mm according to the given ratio.

Since the area of a rectangle is length × width, we have:

x × 4x = 54 × 54

4x² = 2916

x² = 729

x = 27 mm.

The perimeter of the rectangle can be calculated using the formula P = 2(length + width). Therefore, the perimeter of the rectangle is

P = 2(27 + 4 x 27) mm

P = 2(27 + 108) mm

P = 2(135) mm

P = 270 mm.

The difference in perimeter between the rectangle and the square is calculated by subtracting the perimeter of the square from the perimeter of the rectangle:

270 mm - 216 mm = 54 mm.

Therefore, the perimeter of the rectangle is 54 mm longer than the perimeter of the square.

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Answer:

45 kilogram = 99.18 pounds

Step-by-step explanation:

In this case, it is required to convert weight in kilograms to pounds. Firstly, we will see the relationship between kilogram and pound. It is as follows :

1 kilogram = 2.204 pounds

The weight of an item is 45 kg. We need to convert it into pounds. So,

45 kilogram = 2.204 × 45 pounds

45 kilogram = 99.18 pounds

So, the weight of the item is 99.18 pounds. Hence, this is the required solution.

The answer would be $7.46. If you subtract the delivery fee then divide by how much pizzas there are you would find the amount per each pizza.

The equation of the required line is [tex]y=5x-5[/tex].

Given:

To find:

The equation of the required line in slope-intercept form.

Explanation:

The given equation can be rewritten as:

[tex]y=5x+10[/tex]

On comparing this equation with [tex]y=mx+b[/tex], we get

[tex]m=5[/tex]

Slopes of parallel lines are always equal.

The slope of reqired line is [tex]m=5[/tex] and it passing through the point [tex](3,10)[/tex]. Using the point slope form, the equation of the line is:

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

[tex]y-10=5(x-3)[/tex]

[tex]y=5x-15+10[/tex]

[tex]y=5x-5[/tex]

Therefore, the equation of the required line is [tex]y=5x-5[/tex].

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if the problem is (5x^4y^3)^2 divided by 9

 5^2 = 25

4*2 =8

3*2 =6

 so you get (25x^8y^6)/9

if that isn't how the equation was supposed to be written let me know and I will edit my answer.

The given algebraic expression expressed in the simplest radical form is;

25x⁸y⁶/9

(5x⁴y³)²/9

       [5² × (x⁴)² × (y³)²]/9

      25x⁸y⁶/9

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The maturity value of a 3-month, 14% note for $50,000 is calculated by first determining the interest over the 3-month period and then adding it to the principal. The interest is $1,750, resulting in a maturity value of b) $51,750.

The maturity value of a 3-month, 14% note for $50,000 can be calculated using the formula for simple interest: M = P + (P  × r  × t), where M is the maturity value, P is the principal amount, r is the annual interest rate (as a decimal), and t is the time in years. Let's calculate the interest first and then add it to the principal to find the maturity value.

First, convert the annual interest rate to decimal: 14% = 0.14.

Then, because the note is for 3 months (which is 3/12 or 0.25 of a year), the time period t is 0.25.

Now, calculate the interest: I = P × r × t = $50,000 × 0.14 × 0.25 = $1,750.

Finally, add the interest to the principal to get the maturity value: M = P + I = $50,000 + $1,750 = $51,750.

So, the correct answer is b. $51,750.

Answer:

(x + 3)^2 + (y + 1^)2 = 25

Step-by-step explanation:

The distance formula gives the length of the radius:

r = √(-3-1)^2 + (- 1-2)^2 = √25 = 5

Substituting h = -3, k = -1, and r = 5 into the standard form (x - h)2 + (y - k)2 = r2, you get (x + 3)2 + (y + 1)2 = 52 = 25.

edmentum :)

The volume of the prism is 4320 cubic units

The expression for the volume is given as:

V = 2x^3 + 6x^2

When x = 12, the expression becomes

V = 2 * 12 ^3 + 6 * 12^2

Evaluate the exponent

V = 2 * 1728 + 6 * 144

Evaluate the products

V = 3456 + 864

Evaluate the sum

V = 4320

Hence, the volume of the prism is 4320 cubic units

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Answer:

The length of the base is [tex]b=17cm[/tex]

Step-by-step explanation:

We start by writing the equation of the base :

Given that the base of the triangle is seven less than twice its height we can write that

[tex]b=2h-7[/tex] (I)

Where ''b'' is the base and ''h'' is the height.

Now, the area of a triangle is [tex]\frac{bh}{2}[/tex]

We know that the area is [tex]102(cm^{2})[/tex] ⇒

[tex]\frac{bh}{2}=102(cm^{2})[/tex]

Now we can replace ''b'' by the expression in (I) ⇒

[tex]\frac{bh}{2}=102(cm^{2})[/tex]

[tex]\frac{(2h-7)(h)}{2}=102(cm^{2})[/tex]

Rearraging the expression :

[tex]\frac{(2h-7)(h)}{2}=102(cm^{2})[/tex]

[tex](2h-7)(h)=204(cm^{2})[/tex]

[tex]2(h^{2})-7h=204(cm^{2})[/tex]

[tex]2(h^{2})-7h-204(cm^{2})=0[/tex]

We need the values of ''h'' that satisfy the equation.

We can use the quadratic formula with

[tex]a=2\\b=-7\\c=-204[/tex]

The quadratic formula will be

[tex]h1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex]

and [tex]h2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]

Using [tex]a=2\\b=-7\\c=-204[/tex] in the expression of h1 and h2 we find that

[tex]h1=12\\h2=-8.5[/tex]

Given that ''h'' is a length ⇒ [tex]h\geq 0[/tex]

We conclude that h1 = 12 cm is the correct value of ''h''

With this value of ''h'' we go to the expression of ''b'' ⇒

[tex]b=2h-7\\b=2(12)-7\\b=24-7\\b=17[/tex]

The value of the base ''b'' that satisfies the problem is [tex]b=17cm[/tex]

Answer:

B - The melting point is a lower temperature than the boiling point.

Step-by-step explanation:

Melting point is the temperature at which any given solid will melt. The state of the solid changes from solid to liquid.

Boiling point is the temperature at which a given liquid boils and changes to vapor state. Like water starts to boil at 100 degrees Celsius.

The boiling point of a substance cannot be lower than its melting point.

So, the answer here is - The melting point is a lower temperature than the boiling point.

The set of ordered pairs (-5,-5),(-1,-2),(0,-2),(3,7),(8,9) represent the function.

A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.

As per the information provided:

Let's list the x-coordinates and y-coordinates of the ordered pairs:

x: -5, -1, 0, 3, 8

y: -5, -2, -2, 7, 9

There is no x-coordinate that appears more than once in the list, so there are no two or more ordered pairs with the same x-coordinate.

Therefore, the set of ordered pairs represents a function.

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The solution is, donny drove 70 miles.

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

Speed = Distance/ Time.

here, we have,

we know that,

Speed: The ratio of distance to time.

To find the distance we use the following formula.

Given that

donny drove 60 miles per hour for 45 minutes and 50 miles per hour for 30 minutes.

so, we get,

In 45 minutes, she traveled  = ( 60/60 * 45)

                                               = (1 * 45)

                                               =45 miles.

again, we have,

The she drove 50 miles per hour for 30 minutes.

so, we get,

In 30 minutes, she traveled = ( 50/60 * 30 )

                                             =50/2

                                             = 25 miles

Therefore donny drove (45+25) miles= 70 miles.

Hence, The solution is, donny drove 70 miles.

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The coordinate pair (60, 20) is a solution because it satisfies the inequality. The coordinate pair (60, 20) is a solution because Ezra earns 60 x $15 = $900 mowing lawns and 20 x $10 = $200 walking dogs, for a total of $1100. Ezra can spend 60 hours mowing lawns and 20 hours walking dogs to earn enough money for the laptop.

The number of servings in the box of cereal is:

                                   14

It is given that:

Kevin has a box of cereal that contains 10 1/2 cups of cereal.

i.e. the number of cups of cereal= 21/2 cups

Also,

A serving size of the cereal is 3/4 cup.

This means that:

The number of servings in the box are:

Ratio of number of cups of cereal in box to the number of cups of cereal in one serving

which is calculated as:

[tex]\text{Number of servings}=\dfrac{\dfrac{21}{2}}{\dfrac{3}{4}}\\\\\\\text{Number of servings}=\dfrac{21\times 4}{3\times 2}\\\\\\\text{Number of servings}=14[/tex]

Answer:

A. ∠N ≅ ∠Z

Step-by-step explanation:

I simply aligned both triangles equation. I wish you guys all the luck and love! <3

Answer: Approx 0.39 will be the required probability.

Step-by-step explanation:

Here,Number of,

Male: Sprints=16, Middle distance=11, Long distance= 9

So, total males=36

And, Female: Sprints= 12, Middle distance=14, Long distance=5

So, total females=31

Thus, If one female randomly chosen,

Then, The probability that female runs sprint= Number of females who run sprint / total number of females

⇒ The probability that female runs sprint=12/31= 0.38709677419≈0.39

Answer: 28/p; 7

Step-by-step explanation:

Hope it helps