how to solve for vertex form
y = -x^2 + 4x – 1

Answer:

Complementary angles

Step-by-step explanation:

When the sum of two angles which adds up to 90° it's called a complementary angle.

You can tell this because <a and <b both form an right angle

Answer:

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, dilation and translation.

Dilation is the increase or decrease in size of a figure by a factor k. If k > 1, then the dilation is an increase whereas if k<1, then the dilation is a decrease.

From the diagram, since triangle LMN is dilated by a factor of 1/4, hence the size of LMN is reduce. Therefore:

L'M' = (1/4)LM, L'N' = (1/4)LN, N'M' = (1/4)NM

Also, the distance from point P to N' is one-fourth of the distance from point P to N.

The correct option is highlighted in the image attached.

Answer:

x³ + 11x² + 36x + 36

Step-by-step explanation:

(x+2)(x+3)

x² + 3x + 2x + 6

x² + 5x + 6

(x² + 5x + 6)(x+6)

x³ + 6x² + 5x² + 30x + 6x + 36

x³ + 5x² + 6x² + 30x + 6x + 36

x³ + 11x² + 36x + 36

Answer:

-1

Step-by-step explanation:

1+4.5x+4.9x=-8.4

4.5x+4.9x=-8.4-1

9.4x=-9.4

x=-9.4/9.4

x=-1

Answer:

x = 0.78723404

Step-by-step explanation:

divide each number by the numbers that don't contain x

Answer:

4th option

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{3}{5}[/tex] x - 6 ← is in slope- intercept form

with slope m = [tex]\frac{3}{5}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{5} }[/tex] = - [tex]\frac{5}{3}[/tex]

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - [tex]\frac{5}{3}[/tex] and (a, b ) = (- 2, 5 ) , then

y - 5 = - [tex]\frac{5}{3}[/tex] (x - (- 2) ) , that is

y - 5 = - [tex]\frac{5}{3}[/tex] (x + 2)

Answer:

Step-by-step explanation:

take angle A as reference amgle

using cos rule

cos A=adjacent/hypotenuse

0.9659=c/25

0.9659*25=c

24.1475=c

Answer:

11.40

Step-by-step explanation:

If we were to divide the shape into a rectangle and triangle, we would have the base of the triangle as 9 because two sides of the rectangle are equal, and 7 for the side because two sides of rectangle are equal and 14/2 is 7. Now we have two sides of a triangle 9 and 7. We know X is the hypotenuse because it is opposite to the right angle. We will plug it into the pythagorean theorem.

a^2+b^2=c^2

9^2+7^2=c^2

81+49=c^2

130=c^2

[tex]\sqrt{130}[/tex]

11.40

Answer:

d. 360°

Hope this help!

Answer:

65

Step-by-step explanation:

130+75+90+x=360

x=65

[tex]\sf \bf {\boxed {\mathbb {C. \: 21n + 7}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]7 \: ( \: 3n + 1 \: )[/tex]

➼[tex] \: 21n + 7[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

x= 31

Step-by-step explanation:

D & F

Step-by-step explanation:

D scale because all sides are different lengths

F obtuse because one angle is greater than 90 degrees

Look up definition of the other properties and you will see they don't apply

The given triangle is a obtuse and scalene triangle

A triangle is a three-sided polygon that consists of three edges and three vertices.

The given triangle is an obtuse triangle and scalene triangle.

A triangle whose any one of the angles is an obtuse angle or more than 90° is known as obtuse triangle.

A triangle in which all the three sides have different lengths then it is called as scalene triangle.

Hence, the given triangle is a obtuse and scalene triangle.

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Answer:

A. 360 degrees

B. 360 degrees all the way around but each individual one is 90 degress

Step-by-step explanation:

Answer:

Step-by-step explanation:

B: the kite's diagonals intersect each other at a 90o degree angle.

A: It should come to 360. Let's if that happens.

Take the top angle (88) first. Notice that if you draw in both diagonals,  the will form Isosceles triangles. Let's deal with the shorter diagonal first.

The two angles at the base of the shorter diagonal are equal. That's because the sides opposite them are equal.

2x +88 = 180       Subtract 88 from both sides.

2x  = 92               Divide by 2

x = 46

Now lets look at the long narrow legs of the bottom isosceles triangle.

2x + 50 = 180      Subtract 50 from both sides

2x = 130               divide by 2

x = 130 /2

x = 65

Now add up all the angles that make up the interior of the kite.

Total = 46 + 46 + 65 + 65 + 50 + 88

Total = 360 just as it should.

Answer:

Let P be thd population of rabbit

P = 2 to the power of n

where n is the period of month

Answer:

3RD

Step-by-step explanation:

Answer:

x⁴-x²+6 = 0

= x²(x²-1)+6=0

Answer:

x = 61.6 degree

Step-by-step explanation:

take x degree as reference angle

using sin rule

sin x = opposite / hypotenuse

sin x = 4.8 / 5.4

sin x = 0.88

x = [tex]sin^{-1} (0.88)[/tex]

x = 61.64

x = 61.6 degree

Answer:

$144

Step-by-step explanation:

Answer:

7 1/3

Step-by-step explanation:

Part A

Use the FOIL rule to expand out the expression below

(2x+7)(5x+9)

2x*5x + 2x*9 + 7*5x + 7*9

10x^2 + 18x + 35x + 63

10x^2 + 53x + 63  is the final answer for part A

==========================================================

Part B

The degree is 2. This is a quadratic trinomial.

The degree is simply the largest exponent after expanding everything out. The degree directly determines the type of polynomial. Since the degree is 2, we have a quadratic. The polynomial is a trinomial because it has 3 terms.

==========================================================

Part C

Imagine we had a machine in which we deposit 2 coins into it. One would happen on either side. After the coins are deposited, a third coin pops out. The 2 coins going in and the third coin coming out are the same currency. This represents an example of closure.

In mathematics, the idea of closure is taking any two objects of the same type, applying an operation on them, and getting the same type of object as the input.

For example, we could take two whole numbers and multiply them together. The result is always a whole number. The set of whole numbers is closed under multiplication because you can't leave the set (hence the gate is closed not letting anything out).

Similarly, taking any two polynomials and multiplying them together will always lead to some other polynomial. Part A shows this in action because (2x+7), (5x+9) and 10x^2 + 53x + 63 are all polynomials.

[tex]\rm 10x^{2} + 53x + 63[/tex] is the expression that represents the area of the rectangle. This is a trinomial expression.

A quadratic equation is the polynomial of second degree in one variable only. The standard form of a quadratic equation is [tex]\rm ax^{2} +bx+c=0[/tex]

Where, x is the variable and a,b, and c are real numbers.

Part A

Let length of a rectangle = (2x+7)

Let width of a rectangle = (5x+9)

The area of the rectangle = length × width

=   (2x+7)(5x+9)

= 2x × 5x + 2x × 9 + 7 × 5x + 7 × 9

= [tex]\rm 10x^{2} + 18x + 35x + 63[/tex]

Therefore, [tex]\rm 10x^{2} + 53x + 63[/tex] is the expression that represents the area of the rectangle.

Part B

The degree is 2 in the expression. This is a trinomial expression.

The degree is simply the largest exponent. The degree directly represents the type of polynomial. Since the degree is 2. The polynomial is a trinomial because it has 3 terms.

Part C

Applying multiplication operations such that taking any two polynomials and multiplying them together will always lead to some other polynomial. Part A shows this multiplication because (2x+7), (5x+9) and [tex]\rm 10x^{2} + 53x + 63[/tex] are all polynomials.

Learn more about quadratic equations;

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Answer:

96.29  mm^3

Step-by-step explanation:

Cylinder

V = pi r^2 h

V = 3.14 ( 2)^2 ( 5)

V = 3.14 *4*5

V =62.8 mm^3

Cone

V = 1/3 pi r^2 h

V = 1/3 (3.14) 2^2 ( 4)

V =1/3 (3.14) 4*4

V =16.746666666 mm^3

There are 2 cones so multiply by 2

Both cones = 33.493333333333 mm ^3

Add the cones and the cylinder together

62.8+33.493333333 =96.293333333

Rounding to the nearest hundredth

96.29  mm^3

Answer:

I did the other guy's answer, and... it was incorrect

the real answer is shown below

9514 1404 393

Answer:

  a) (x +2)(x +3)

  b) x = -2 or -3

Step-by-step explanation:

a) The constants in the binomial factors will be divisors of 6 that have a sum of 5. You know that ...

  6 = 1×6 = 2×3

The sums of these factor pairs are 7 and 5. You want the pair 2, 3. The factors are ...

  x² +5x +6 = (x +2)(x +3)

__

b) The solutions to the equation are the values of x that make the factors zero:

  (x +2) = 0   ⇒   x = -2

  (x +3) = 0   ⇒   x = -3

Answer:

Step-by-step explanation:

The domain indicates all the x values which are {2, 6, 9} in order from least to greatest. As long as none of these numbers is the same, then our relation is also a function. Choice A. is the one you want.

Answers:

========================================================

Explanations:

Answer:

It's 33.33%

Step-by-step explanation:

It's 3/9 = 1/3 = 0.3333 = 33.33%