a triangular piece of stained glass has an area of 6 square inches and a height of 3 inches. what is the length of the base

Answer:

[tex]x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}[/tex] shows correct substitution of the values a, b, and c  from the given quadratic equation  [tex]-3x^2-2x+6=0[/tex]  into quadratic formula.

Step-by-step explanation:

Given: The quadratic equation [tex]-3x^2-2x+6=0[/tex]

We have to show the correct substitution of the values a, b, and c from the given quadratic equation  [tex]-3x^2-2x+6=0[/tex]  into quadratic formula.

The standard form of quadratic equation is [tex]ax^2+bx+c=0[/tex] then the solution of quadratic equation using quadratic formula is given as [tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Consider the given  quadratic equation [tex]-3x^2-2x+6=0[/tex]

Comparing with general  quadratic equation, we have

a = -3 , b = -2 , c = 6

Substitute in quadratic formula, we get,

[tex]x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}[/tex]

Simplify, we have,

[tex]x_{1,2}=\frac{2\pm\sqrt{76} }{-6}[/tex]

Thus, [tex]x_{1}=\frac{2+\sqrt{76} }{-6}[/tex] and x_{2}=\frac{2-\sqrt{76} }{-6}

Simplify, we get,

[tex]x_1=-\frac{1+\sqrt{19}}{3},\:x_2=\frac{\sqrt{19}-1}{3}[/tex]

Thus, [tex]x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}[/tex] shows correct substitution of the values a, b, and c  from the given quadratic equation  [tex]-3x^2-2x+6=0[/tex]  into quadratic formula.

You can use the standard form of quadratic equation to find the correct substitution of the values a, b and c.

The correct substitution of the value a,b and c from the given quadratic equations into the solution form is [tex]x = \dfrac{-(-2) \pm \sqrt{(-2)^2 - 4 \times -3 \times 6}}{2 \times (-3)}[/tex]

The standard form of quadratic equations is [tex]ax^2 + bx + c = 0[/tex]

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

From given equation [tex]0 = -3x^2 -2x + 6[/tex], we deduce that a = -3, b = -2 and c = 6.

Thus, substituting these values in the solutions' equation:

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\ \\ x = \dfrac{2 \pm \sqrt{4 + 72}}{-6} = \dfrac{2\pm 2\sqrt{19}}{-6} = \dfrac{-1 \mp 2\sqrt{19}}{3}[/tex]

Thus, the correct substitution of the value a,b and c from the given quadratic equations into the solution form is [tex]x = \dfrac{-(-2) \pm \sqrt{(-2)^2 - 4 \times -3 \times 6}}{2 \times (-3)}[/tex]

Learn more about solutions of quadratic equations here:

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a square needs to rotate 90 to coincide with  itself

 but the hexagon would need to rotate 180

the answer is 180 degrees

Answer:

Option B 180° is the right answer.

Step-by-step explanation:

Given is : GHIJ is a square and ABCDEF is a regular hexagon having common centre O.

We know that a square is symmetric at a rotational angle of 90°.

A regular hexagon is symmetric at a rotational angle of 60°.

We will find the LCM of 90 and 60, to know how much to rotate, to get a preimage.

Moreover, a hexagon needs to rotate 180 degrees to coincide with itself.

LCM(60°,90°)=180°.

So, the correct option is B. 180°.

Answer:

everything except for a quadrilateral

Step-by-step explanation:

Answer: Conditional statement

Step-by-step explanation:

In discrete mathematics, a conditional statement denoted by "if R then S " is an if-then statement where R represents a hypothesis and S represents a conclusion.

For example : If a number is divisible by 6 ,then it must be divisible by 2 ."

Here, Hypothesis R: " number is divisible by 6"

Conclusion S: "it must be divisible by 2"

Hence, an conditional statement  has the form " if A, then B" .

The dashed line segments form 30-degree angles in the given diagram of a regular hexagon and triangle.

In the given diagram, hexagon GIKMPR and triangle FJN are regular. The dashed line segments form 30-degree angles.

Since hexagon GIKMPR is regular, all its interior angles are equal. Each angle of a regular hexagon is 120 degrees, so angle GIK is 120 degrees.

The angle at GIK can be split into two equal angles by the dashed line segment, so each of these angles measures 60 degrees.

Similarly, since triangle FJN is regular, each of its angles measures 60 degrees.

Therefore, the dashed line segments form two 30-degree angles each side of the regular hexagon and triangle.

The correct answer is option d. The image of [tex]\overline{OQ}[/tex] after a rotation of 300 degrees about point O is [tex]\overline{OF}[/tex].

To find the image of line segment [tex]\( \overline{OQ} \)[/tex] after a rotation of [tex]\( 300^\circ \)[/tex] about point O, we need to understand that a rotation of [tex]\( 300^\circ \)[/tex] is equivalent to rotating [tex]\( 60^\circ \)[/tex] clockwise. This is because rotating [tex]\( 360^\circ \)[/tex] would bring us back to the original position, so a rotation of [tex]\( 300^\circ \)[/tex] is the same as rotating [tex]\( 360^\circ - 60^\circ = 300^\circ \)[/tex].

Given that line segment [tex]\( \overline{OQ} \)[/tex] forms a [tex]\( 30^\circ \)[/tex] angle with the dashed lines, after a rotation of [tex]\( 300^\circ \)[/tex], it will form a [tex]\( 30^\circ \)[/tex] angle with the new position of the dashed lines.

Therefore, the image of line segment [tex]\( \overline{OQ} \)[/tex] after the rotation is [tex]\( \overline{OF} \)[/tex].

The complete question

The hexagon GIKMPR and FJN are regular. The dashed line segments form 30 degree angles.

Find the image of [tex]\overline{OQ}[/tex] after a rotation of 300 degree about point O.

a. [tex]\overline{OJ}[/tex]

b. [tex]\overline{OH}[/tex]

c. [tex]\overline{OQ}[/tex]

d. [tex]\overline{OF}[/tex]

To find the angle of elevation of the sun, set up a right triangle with the height of the tree and the length of the shadow.

To find the angle of elevation of the sun, we need to set up a right triangle with the height of the tree (50 feet), the length of the shadow (60 feet), and the line from the top of the tree to the end of the shadow.

Using the information given, we can apply the tan(angle) = opposite/adjacent formula to find the angle of elevation.

By calculating the inverse tangent of the ratio of the height of the tree to the length of the shadow, we can determine the angle of elevation to be approximately 45 degrees.

The angle of elevation to the nearest degree of the sun is approximately 40 degrees.

To find the angle of elevation to the sun, we can use the tangent function in trigonometry.

Let's denote:

- Height of the tree = h = 50 feet

- Length of the shadow = b = 60 feet

The tangent of the angle of elevation (θ) is given by:

tan(θ) = opposite / adjacent

tan(θ) = h / b

Substitute the given values:

tan(θ) = 50 / 60

tan(θ) = 5 / 6

Now, to find the angle θ, we need to take the arctangent (inverse tangent) of the ratio:

θ = arctan(5/6)

θ ≈ 39.8 degrees

Therefore, the angle of elevation to the nearest degree of the sun is approximately 40 degrees.

divide total weight by weight of each box

10250 / 20.5 = 500 boxes total

We are given a graph of a quadratic function y = f(x) .

We need to find the solution set of the given graph of a quadratic function .

Note: Solution of a function the values of x-coordinates, where graph cut the x-axis.

For the shown graph, we can see that parabola in the graph doesn't cut the x-axis at any point.

It cuts only y-axis.

Because solution of a graph is only the values of x-coordinates, where graph cut the x-axis. Therefore, there would not by any solution of the quadratic function y = f(x).

Answer:

Option B. ∅

Step-by-step explanation:

If a quadratic function f(x) is in the form of f(x) = ax²+bx+c then the solution of the function is the value of x.

If we analyze the graph for f(x) ≤ 0 solution of the function is null because parabola doesn't intercept at x axis.

Therefore there is no solution for the graphed function f(x).

Option B is the answer.

The whole container can hold [tex]5\frac{5}{6}[/tex] liters, calculated by setting up a proportion based on the part of the container currently filled with water ([tex]2\frac{1}{3}[/tex]  liters representing 2/5 of the container).

To determine the full capacity of the container, we set up a proportion. Since [tex]2\frac{1}{3}[/tex]  liters represent 2/5 of the container's capacity, we want to find out how much 5/5 (the whole) of the container can hold. To set up the proportion, we have:

(2/5) of the container = [tex]2\frac{1}{3}[/tex]  liters
(5/5) of the container = x liters
Then, we multiply [tex]2\frac{1}{3}[/tex]  liters by 5/2 to solve for x:

x = ([tex]2\frac{1}{3}[/tex] liters) * (5/2)

x = (7/3 liters) * (5/2)

x = 35/6 liters

x =  [tex]5\frac{5}{6}[/tex] liters

So the whole container would hold  [tex]5\frac{5}{6}[/tex] liters.

Answer:

between 67 and 103 beats per minute inclusive

Answer:

has two rays that share a common endpoint

Step-by-step explanation:

An angle is formed by a two rays that share a common endpoint.  The distance between the two rays is what makes the measure of the angle wider or smaller.  Each ray extends in one direction forever; however since they share an endpoint, the rays do not extend in both directions forever.  There is only one endpoint, not two, and there is only one center point (vertex), not two.

The number of yards that she will need to make 8 uniforms and 15 uniforms will be 96 yards and 180 yards, respectively.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A pattern for 1 uniform uses 12 yards of material. Boleslaw wants to know how many yards are needed for 8 uniforms will be given as,

⇒ 8 x 12

⇒ 96 yards

Chantal wants to know how many yards she will need to make 15 uniforms will be given as,

⇒ 15 x 12

⇒ 180 yards

The number of yards that she will need to make 8 uniforms and 15 uniforms will be 96 yards and 180 yards, respectively.

More about the Algebra link is given below.

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Answer:

one of these is wrong cause i got a three out of four but thats better than nothing i guess.

Step-by-step explanation:

x≤0, y=1, x≥1, this one is the one i think is wrong but y=-1

Answer:

40 x 50 = 2,000

Step-by-step explanation:

When we round a number, first identify the digit to round. Then proceed with the following two rules:

(a) If the number to the right of the digit to round is 0, 1, 2, 3, or 4 (that is, less than 5), then keep the digit to round and change the rest of the digits to the right of the digit to round to zero.

(b) If the number to the right of the digit to be rounded is 5, 6, 7, 8, or 9 (that is, greater than or equal to 5), then add one to the digit to round and change the rest of the digits to the right of the digit to round to zero.

In our case, we apply the two rules, rounding to the nearest ten, as follows:

For 38 = 40

Apply rule (b) since 8 is greater than or equal to 5, then add 1 to 3 to get 4, then change 8 to zero. The result is 40.

For 47 = 50

Apply rule (b) since 7 is greater than or equal to 5, then add 1 to 4 to get 5, then change 7 to zero. The result is 50.

Now, multiply to estimate the amount of grapes that Jerry customers buy every day.

40 x 50 = 2,000

Hope this helps!

Answer: The answer is C.

A Linear parent function is a function of the form f(x) = x

or y = x. This is the simplest of the linear functions, where the slope is 1 and the function pases for the point (0,0) (which is the same of saying that the intercept is 0).

a) isnt a linear function.

b) is a quadratic function.

d) is also a linear function, but it has a slope = 2, so it isn't the linear parent function.