MATHEMATICS HIGH SCHOOL

The graphs of f(x) and g(x) are shown below:graph of function f of x open upward and has its vertex at negative 7, 0. Graph of function g of x opens upward and has its vertex at negative 5, 0

If f(x) = (x + 7)^2, which of the following is g(x) based on the translation?

g(x) = (x + 5^)2

g(x) = (x − 5)^2

g(x) = (x − 9)^2

g(x) = (x + 9)^2

Answers

Answer 1

Answer:

Answer:

The equation for g(x) is:

g(x)=(x+5)^2

Step-by-step explanation:

We are given the information about the graph of the function f(x) and g(x) as:

graph of function f of x open upward and has its vertex at (-7,0).

Graph of function g of x opens upward and has its vertex at (-5,0).

If f(x) = (x + 7)^2; which is a parabola with vertex at (-7,0).

Also as g(x) is formed by the translation of the function f(x) so it will also be a quadratic function such that it's vertex is (-5,0).

so, the equation of g(x) will be:

g(x)=(x+5)^2.

Hence, the translation is a shift of the function f(x) 2 units to the right.

Answer 2

Answer: The right answer for the question that is being asked and shown above is that: "g(x) = (x − 5)^2" If f(x) = (x + 7)^2, the expression that is g(x) based on the translation is that g(x) = (x − 5)^2

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OrEvaluate. Write your answer as a whole number or as a simplified fraction.

42 · 42 =

Answers

Answer:

1764

Step-by-step explanation:

A circle is inscribed in an equilateral triangle. A point in the figure is selected at random. Find the probability that the point will be in the part that is NOT shaded. A. About 25%
B. About 40%
C. About 60%
D. About 50%

Answers

If $r$ is the radius of the circle, then the side length of the triangle is $2r\sqrt3$ .

The area of the circle is $\pi r^2$ , while the area of the triangle is $3r^2\sqrt3$ .

So, the probability of selecting a random point in the white space is

$1-(\pi r^2)/(3r^2\sqrt3)=1-(\pi)/(3\sqrt3)\approx0.395\approx40\%$

Answer:

about 60%

Step-by-step explanation:

just took the test

If the diameter of a circle is 6 inches, how long is the arc subtended by an angle measuring 70°?

Answers

Answer:

Length of arc of a circle is given by:

$L = r \cdot \theta$ .....[1]

where

L is the length of an arc

r is the radius of the circle.

As per the statement:

Diameter of the circle(D) = 6 inches.

we know that:

D =2r

6 = 2r

Divide both sides by 2 we get;

3 = r

r = 3 inches

We have to find the long arc arc subtended by an angle measuring 70°.

Substitute the value of r = 3 inches and $\theta = 70^(\circ)$ in [1] we have;

$L =3 \cdot 70$

Simplify:

L = 210 inches

Therefore, 210 inches long is the arc subtended by an angle measuring 70 degree.

C = πD = π6in

Arc = D * 70°/360° = 3.1416*6*7/36=3.67 in

0.34 and 3/4 are equivalent.

True
False

Answers

False because 3/4 is equal to .75 which is not equivalent to .34 . Hope that helps!

Answer: False

3/4 of 1 is 0.75 because..
1 divided by 4 is 0.25
multiply that by 3
which is 0.75

If the shadow of a pole 12m high is 2/3 of its length, what is the angle of elevation of the sun?

Answers

To find the angle of elevation of the sun, you can use the tangent function. Given that the shadow of the pole is 2/3 of its length (12 meters), you can set up the following trigonometric relationship:

tan(angle of elevation) = (height of the pole) / (length of the shadow)

tan(angle of elevation) = 12 / (2/3 * 12)

Now, calculate the length of the shadow:

2/3 * 12 = 8 meters

So, tan(angle of elevation) = 12 / 8

tan(angle of elevation) = 3/2

To find the angle of elevation, take the arctan (inverse tangent) of 3/2:

angle of elevation = arctan(3/2)

Using a calculator or trigonometric tables:

angle of elevation ≈ 56.31 degrees

So, the angle of elevation of the sun is approximately 56.31 degrees.

Which of the following correctly shows the quotient of 75 divided by 5?5/75 = 12
75/5= 15
75÷5= 25
75÷5= 70