Which statements justify that the dilation of triangle STU is an enlargement increasing its size by the magnitude of the scale factor? Check all that apply.

A. The triangle pre-image is closer to the point of dilation than the image.
B. The triangle image is closer to the point of dilation than the pre-image.
C. The value of the scale factor, , is between 0 and 1.
D. The value of the scale factor, 6, is greater than 1.
E. The vertices of the pre-image are collinear with the vertices of the image.

In the given hour, Dale ran 5 miles and Chan ran 2.5 miles.

Let Dale's running miles be represented by the variable D and let Chan's running miles be represented by the variable C.

In-order to compare Dale's running miles to Chan's by using division we get:

[tex] \frac{D}{C}=\frac{5}{2.5} = \frac{2}{1} [/tex]

[tex] D=2C [/tex]

Thus, Dale ran twice the distance Chan ran in the same amount of time of 1 hour.

Equivalently we can say that Chan ran half the distance Dale ran in the same amount of time of 1 hour.

Answer:

The value of a is 14 unit and the value of b is [tex]6\sqrt{2}[/tex] unit

EXPLANATION:

Draw a perpendicular line from vertex B to DC at E.

Labeling the diagram as shown in the attachment:

Now, as you can see from the Figure as shown in the attachment that [tex]ABDE[/tex] represents the rectangle because a rectangle is a quadrilateral with four right angles and  their opposite sides would be parallel.

Therefore, we have the sides [tex]AB=DE=8[/tex] unit , and [tex]AD=BE=6[/tex] unit.

Consider the right triangle BEC

BY 45 45 90 triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.

therefore, the length of side, [tex]BE=EC=6[/tex] unit

Using trigonometric ratio; to find the value of b:

[tex]\sin \theta =\frac{perpendicular}{Hypotenuse}[/tex]

∴ using trigonometric sine ratio in triangle BEC, we have

[tex]\sin 45^{\circ} =\frac{6}{b}[/tex] or

[tex]\frac{1}{\sqrt{2} }= \frac{6}{b}[/tex]

On Simplify:

[tex]b=6\sqrt{2}[/tex] unit

and the value of a = DC = DE+EC=8+6=14 unit

Therefore, the value of a is 14 unit and b is [tex]6\sqrt{2}[/tex] unit

Answer:

43.82 units.

Step-by-step explanation:

We have been given a triangle. We are asked to find the value of b using Law of Sines.

[tex]\frac{a}{\text{sin}(A)}=\frac{b}{\text{sin}(B)}=\frac{c}{\text{sin}(C)}[/tex], where, a, b and c are opposite sides of angles A, B and C respectively.

Upon substituting our given values in above formula, we will get:

[tex]\frac{50}{\text{sin}(58^{\circ})}=\frac{b}{\text{sin}(48^{\circ})}[/tex]

Switch sides:

[tex]\frac{b}{\text{sin}(48^{\circ})}=\frac{50}{\text{sin}(58^{\circ})}[/tex]

[tex]\frac{b}{0.743144825477}=\frac{50}{0.848048096156}[/tex]

[tex]\frac{b}{0.743144825477}*0.743144825477=\frac{50}{0.848048096156}*0.743144825477[/tex]

[tex]b=43.81501643866[/tex]

[tex]b\approx 43.82[/tex]

Therefore, the value of b is approximately 43.82 units.

Option: B is the correct answer.

B) Traditionalism.

Beat generation was a literary movement that was started by a group of authors and  belongs to the post World War || period.

They started this movement to reject literary formalism and the American culture built on capitalism and materialism.

It has a major impact on both poetry as well as culture in America.

Hence, the Beat generation writers try to defeat in America is:

Traditionalism.

Answer:

$1.3425

Step-by-step explanation:

The regular price of the dinner buffet is 8.95. If this has a discount of 15%, we would have to multiply the total price by 0.15 and this would give us how much of the total amount is 15% and therefore it would give us how much of a discount the senior receives off of the 8.95 price

8.95 x 0.15 = 1.3425

Therefore, a senior citizen gets $1.3425 discount.

The largest interior angle of the heptagon, given the angle measures as x, x, x-2, x-2, x+2, x+2, x+4, is 132 degrees after solving for x.

The problem is to determine the degree measure of the largest interior angle in a heptagon. The degree measures of the interior angles are given as x, x, x-2, x-2, x+2, x+2, and x+4 degrees. To solve this, we first use the fact that the sum of the interior angles of a heptagon (7-sided polygon) is given by the formula (n-2) 180 degrees, where n is the number of sides. So, for a heptagon, the sum is

We then set up the equation based on the given interior angles: 3x + (2x - 4) + (2x + 4) + (x + 4) = 900. Simplifying, we get 7x + 4 = 900. Solving for x, we find x = 896/7 = 128 degrees. The largest interior angle is x + 4, which equals

Answer:

We have then:

f(x) = 2/5x^2-2 The function g (x) is a vertical stretch of f(x) by a factor of 2:

g(x) = 2f (x)

g(x) = 2 (2/5x^2-2)

g(x) = 4/5 x^2-4 is a required equation.

Answer:

The triangle is A = 48°, a = 32, B = 38.83°, b = 27, C = 93.17° and c = 42.99

Step-by-step explanation:

We have sine rule,

             [tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

Here given A = 48°, a = 32, b = 27

Substituting

          [tex]\frac{32}{sin48}=\frac{27}{sinB}=\frac{c}{sinC}\\\\sinB=0.627\\\\B=38.83^0[/tex]

We have

          A + B + C = 180°

          48 + 38.83 + C = 180

          C = 93.17°

Using sine rule again

          [tex]\frac{32}{sin48}=\frac{c}{sin93.17}\\\\c=42.99[/tex]

So the triangle is A = 48°, a = 32, B = 38.83°, b = 27, C = 93.17° and c = 42.99

The graph of a quadratic function, or a parabola, is U or n-shaped and its direction depends on the sign of the coefficient of the x-squared term. The vertex and line of symmetry can be found using formulas based on this coefficient.

The graph of a quadratic function, also known as a parabola, generally takes on a 'U' or 'n' shape. The direction that the 'U' faces depends on the sign of the coefficient, which is the number associated with the x-squared term in the equation. If this coefficient is positive, the graph opens upwards; if it's negative, the graph opens downwards. The vertex (the highest or lowest point on a parabola) can be calculated using the formula -b/2a. The line of symmetry can be found using the equation x = -b/2a.

For example, consider the quadratic function f(x)=x^2. This equation represents a parabola that opens upwards. Its vertex is at the point (0,0) and its line of symmetry is x=0.

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Answer: $720.

Step-by-step explanation:

The formula to find the simple interest is given by :-

[tex]I=Prt[/tex], where P is the principal amount , r is the rate of interest in decimal and t is the time in years.

Given : Rate of interest : r= 0.025

Simple interest : I= $180

Time : t=10

Let P be the Natalie’s initial deposit when she opened the account, then we have:-

[tex]180=P(0.025)(10)\\\\\Rightarrow\ P(0.25)=180\\\\\Rightarrow\ P=\dfrac{180}{0.25}=\dfrac{18000}{25}=720[/tex]

Hence, the Natalie’s initial deposit when she opened the account was $720.

Final answer:

The set of ordered pairs represents a function Yes, because every x-value corresponds to exactly one y-value(C).

Explanation:

The set of ordered pairs {(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)} represents a function because every x-value corresponds to exactly one y-value. In a function, each input (x-value) has only one output (y-value). The set does not have two different y-values for the same x-value, so option D is incorrect. Therefore, option C is the correct answer.

(C). Yes, because every x-value corresponds to exactly one y-value.

You can see that each unique x-value corresponds to exactly one y-value, and there are no repeated x-values. Therefore, this set of ordered pairs represents a function.

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