The expression sin 50 cos 40 + cos 50 sin 40 is equivalent to

The normal line to the parabola [tex]y=x-x^2[/tex] at the point [tex](1,0)[/tex] intersect it second time at the point [tex](-1,-2)[/tex].

The given equation is:

at point,

then,

→ [tex]y' = 1-2x[/tex]

So, at (1,0),

→ [tex]y' = 1-2\times 1[/tex]

      [tex]= -1[/tex]

Since,

This is the slope of the tangent, we take its negative reciprocal to get the slope of normal:

= [tex]-\frac{1}{(-1)}[/tex]

= [tex]1[/tex]

The normal line has slope 1 and goes through (1,0):

→ [tex]y-0=1(x-1)[/tex]

→       [tex]y = x-1[/tex]

We want to know where this intersects [tex]y = x-x^2[/tex], we get

→ [tex]x-1=x-x^2[/tex]

→ [tex]x^2=1[/tex]

→ [tex]x = \pm 1[/tex]

hence,

The point corresponding to (1,0) is the one we started with, so we want x=-1:  

→ [tex]x = -1[/tex]

→ [tex]y = x-x^2[/tex]

By substituting the value of "x", we get

→    [tex]= -1-1[/tex]

→    [tex]= -1[/tex]

Thus the answer above is right.

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Answer:

Relative frequency, by row, of students who like both tacos and pizza is:

0.81

Step-by-step explanation:

                                  Like Tacos Do Not Like Tacos      Total

Like Pizza                    57                 13                       70

Do Not Like Pizza            12                  15                       27

Total                            69          28                       97

The relative frequency by row is calculated as the ratio of the frequency of the required field to the total frequency of that row

Hence, relative frequency, by row, of students who like both tacos and pizza is:

57/70

=0.81

The area of 13 feet long by 9 feet wide wildflower garden is 117 square feet.

Use the concept of a rectangle defined as:

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

To find the area of her garden,

Multiply the length and width of the space.

In this case,

the length is 13 feet and the width is 9 feet.

So, the area of Mia's garden would be,

13 feet x 9 feet = 117 square feet.

Hence,

The area of the garden is 117 square feet.

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The car gets 20 miles per gallon.

To find the miles per gallon the car gets, we need to divide the total miles driven by the number of gallons of gas used. In this case, the car goes 332 miles on a single tank, and the gas tank holds 16.6 gallons. So, the miles per gallon can be calculated as:

Miles per gallon = Total miles driven / Number of gallons used

Miles per gallon = 332 miles / 16.6 gallons

Miles per gallon = 20 miles

Therefore, the car gets 20 miles per gallon.

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To find the volume of sand needed for Maija's sandbox, multiply the length, width, and depth. As the sandbox is a square, both the length and width are 3 feet. The depth is 0.85 feet. Thus, Maija needs 7.65 cubic feet of sand.

This question is about calculating volume, specifically the volume of sand that Maija needs for her sandbox. The volume of a box is calculated by the formula: volume = length x width x height. Since the sandbox is square, the length and width are both 3 feet. The height, or in this case, the depth of the sand, is 0.85 feet.

Therefore, the volume of sand needed is calculated as follows: Volume = 3 ft x 3 ft x 0.85 ft = 7.65 cubic feet. So, Maija needs exactly 7.65 cubic feet of sand for her sandbox.

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Recognizing the specific forms of square trinomials and the difference of squares allows you to rewrite them as separate factors, simplifying algebraic expressions and facilitating further mathematical operations.

Knowing when to rewrite square trinomials and the difference of squares as separate factors depends on the algebraic expression you are dealing with. Let's consider each case separately.

1. Square Trinomials:

  - Square trinomials have the form [tex]\(a^2 + 2ab + b^2\) or \(a^2 - 2ab + b^2\)[/tex], where(a) and (b) are algebraic expressions.

  - These trinomials can be factored into the square of a binomial: [tex]\((a + b)^2\) or \((a - b)^2\).[/tex]

  - You should rewrite a square trinomial as separate factors when you encounter an expression that matches the form of a perfect square trinomial. Recognizing this pattern allows you to simplify the expression.

2. Difference of Squares:

  - The difference of squares has the form [tex]\(a^2 - b^2\),[/tex] where (a) and (b) are algebraic expressions.

  - This expression can be factored into the product of conjugates: [tex]\((a + b)(a - b)\).[/tex]

  - You should rewrite a difference of squares as separate factors when you have an expression in the form [tex]\(a^2 - b^2\)[/tex]. Recognizing this pattern helps you simplify and factor the expression efficiently.

Sue divides the initial number (which is 20/3 in this case) by 3, adds 1, and then multiplies by 4. Simplifying this we find her result to be 80/9 or 8 8/9.

Let's denote the initial number as 'x'. If Joe multiplies 'x' by 4, adds 1 and then divides by 3, getting 7, we can say that (4x+1)/3 = 7. Solving this equation, we find that x = 20/3.

Now let's apply this value to Sue's operations. Sue divides the initial number (which is 20/3) by 3, adds 1, and then multiplies by 4. Therefore, Sue's result is 4*((20/3)/3 + 1). Simplifying this expression, we obtain that Sue's result is 80/9 or 8 8/9.

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The length of the diagonal of Kit's bandana tied around her head is approximately 22.63 inches long.

Kit folds a bandana diagonally.

To find the length of the diagonal (hypotenuse of a right triangle), we can use the Pythagorean theorem.

The bandana side length (a) is 16 in.

Let x be the length of the diagonal.

Using a^2 + a^2 = x^2, we get 16^2 + 16^2 = x^2. Solving this gives x ≈ 22.63 in.

The statement x + 6 = 6 + x demonstrates the symmetric property of equality.

The given statement x + 6 = 6 + x represents the symmetric property.

The symmetric property of equality states that if a = b, then b = a. In this case, both sides of the equation are the same, with x and 6 appearing in different orders. Thus, the equation satisfies the symmetric property.

For example, if we let x = 2, the equation becomes 2 + 6 = 6 + 2, which is true.

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Answer:

4

Step-by-step explanation:

replace y with -3

2y + 7 becomes 2(-3) + 7 = -6 +7 =1

-4(-3)-10 = 12-10 = 2

The value of angle ADB in the triangle ADB is determined as m∠ ADB = 95⁰. (Option A).

How to calculate angle ADB?

The value of angle ADB is calculated by applying intersecting chord theorem and principle of sum of angles in a triangle.

The intersecting chord theorem states that the angle at tangent is half of the arc angle of the two intersecting chords.

So the value of angle A is calculated as follows;

m ∠ BAC = ¹/₂ x arc BC

m ∠ BAC = ¹/₂ x 110

m ∠ BAC  = 55

The value of angle ADB is calculated as follows;

m ∠ ABD + m ∠ ADB + m ∠ BAD = 180 (sum of angles in a triangle)

30 + m ∠ ADB + 55 = 180

m ∠ ADB + 85 = 180

m ∠ ADB = 180 - 85

m ∠ ADB = 95⁰

Answer:

2

Step-by-step explanation:

this is right trust

Answer:  The correct option is (A) 25.

Step-by-step explanation:  We are given to find the value of x from the figure shown.

From the figure, we note that there are two parallel lines and a transversal.

Also, the angles with measurements (x + 40)° and (3x - 10)° are corresponding angles.

Since the measures of two corresponding angles are equal, so we must have

[tex](x+40)^\circ=(3x-10)^\circ\\\\\Rightarrow x+40=3x-10\\\\\Rightarrow 3x-x=40+10\\\\\Rightarrow 2x=50\\\\\Rightarrow x=\dfrac{50}{2}\\\\\Rightarrow x=25.[/tex]

Thus, the required value of x is 25.

Option (A) is CORRECT.

Answer:

[tex]x=-2,x=2[/tex]

Step-by-step explanation:

we have

[tex]x^{2}+2=6[/tex]

we know that

The solution of the function is equivalent to solve the following system of equations

[tex]y=x^{2}+2[/tex] ------> equation A

[tex]y=6[/tex] ------> equation B

The x-coordinate of the intersection point both graphs is the solution of the given function

Using a graphing tool

see the attached figure

The intersection points are [tex](-2,6)[/tex] and [tex](2,6)[/tex]

therefore

The solution of the given function are

[tex]x=-2,x=2[/tex]