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3 years ago

A bicycle, a motorcycle, a sports car, and a garbage truck are stuck on the side of the

Mathematics

2 answers:

natta225 [31]3 years ago

8 0

Answer: Garbage truck

Step-by-step explanation:

Because its already all dirty and messed up, what would change about it?

mamaluj [8]3 years ago

7 0

Answer:

D. sports car. i hope this helps

Step-by-step explanation:

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Find the missing lengths.

Rama09 [41]

Answer:

x = 5√2

Step-by-step explanation:

The triangle on the right is a special right triangle, so we know that the adjacent side to 60° is 5. Since the left triangle is a 45-45-90, the hypotenuse is the leg times √2, so the value of x is 5√2

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3 years ago

7.5 divided by 0.5 = x <br> Find x

dangina [55]

Answer:

Step-by-step explanation:

7.5 divided by 0.5 = 15

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3 years ago

Read 2 more answers

Nina graphs the function y=⌊x⌋ to learn the properties of the parent floor function. what is the value of y when x=5.7? 5 5.50 5

morpeh [17]

The values of y when x=5.7 will be 5. In the graphs, the function is represented as y=⌊x⌋

<h3>What is a graph?</h3>

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

In the graphs the function y=⌊x⌋

The value of the y obtaining will be the whole number of the left axis of the integers.5 is the nearest whole number to the 5.7.

The given value of the function is ;

y = [ 5.7 ] = 5

Hence the value of the y is 5.

To learn more about the graph refer to the link;

brainly.com/question/14375099

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2 years ago

Help please! h(x) = -(x+2)^2 +8

Mariulka [41]

Answer:

The maximum value occurs at point (-2, 8) where x = -2 represents the axis of symmetry.

Step-by-step explanation:

<h3>General Concepts: </h3>

Quadratic functions.

Vertex form.

Standard form.

Axis of symmetry.

Maximum value.

Minimum value.

BPEMDAS Order of Operations:

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

<h2>Vertex Form:</h2>

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where <em>a</em> ≠ 0 and (<em>h, k </em>) represents the coordinates of the vertex.

a: Vertical stretch or compression factor.

a > 0 ⇒ The graph opens <u>upward</u>, and the y-coordinate of the vertex represents the minimum value.
a < 0 ⇒ The graph opens <u>downward</u>, and the y-coordinate of the vertex represents the maximum value.

h: Horizontal translation.

h > 0 ⇒ The graph shifts <em>"h"</em> units to the right.
|h| < 0 ⇒ The graph shifts <em>"h" </em>units to the left.

k: Vertical translation.

k > 0 ⇒ The graph shifts <em>"k"</em> units upward.
|k| < 0 ⇒ The graph shifts <em>"k"</em> units downward.

<h3>Axis of symmetry:</h3>

The axis of symmetry is an imaginary vertical line that goes through the vertex of a parabola and divides the graph into two symmetrical halves. The axis of symmetry is also the <u>x-coordinate</u> of the vertex, (h, k). Hence, the axis of symmetry is: <em>x </em>= <em>h</em>.

$\boxed{\\\begin{minipage}{5.4cm}\\\indent\quad\sf{\large \underline{Axis\:of\:Symmetry:}}\quad\displaystyle\mathsf{x\:=\:\frac{-b}{2a} \:\:\:}\\\end{minipage}}$

<h3>Find the axis of symmetry:</h3>

Step 1: Transform the given quadratic function into its general form, h(x) = ax² + bx + c.

Given: h(x) = - (x + 2)² + 8

$\displaystyle\mathsf{\Rightarrow\:h(x) = - (\:x^2 + 2x + 2x + 4\: ) + 8\: \rightarrow \textsf{[\:Expand the binomial using the \textbf{FOIL method\:}\:].}}$

$\displaystyle\mathsf{\Rightarrow\: h(x) = - (\:x^2 + 2x + 2x + 4\: ) + 8\:\rightarrow \textsf{[\:Combine like terms\:].}}$

$\displaystyle\mathsf{\Rightarrow\: h(x) = - (\:x^2 + 4x+ 4\: ) + 8\:\rightarrow \textsf{[\:Distribute the negative sign into the parenthesis\:].}}$

$\displaystyle\mathsf{\Rightarrow\: h(x) = - \:x^2 - 4x - 4 + 8\:\rightarrow \textsf{[\:Simplify\:].}}$

$\displaystyle\mathsf{\Rightarrow\: h(x) = - \:x^2 - 4x + 4\:\rightarrow \textsf{[\:\textbf{General form}, where: a = -1, b = -4, and c = 4\:].}}$

Step 2: Solve for the axis of symmetry.

Substitute the derived values for <em>a</em> = -1 and <em>b</em> = -4 into the following formula:

$\boxed{\\\begin{minipage}{6cm}\\\indent\qquad\quad\quad\sf{\large \underline{Axis\:of\:Symmetry:}}\\\\\indent\quad\displaystyle\mathsf{x\:=\:\frac{-b}{2a}\:=\:\frac{-(-4)}{2(-1)}\:=\:\frac{4}{-2}\:=\:-2. }\\\end{minipage}}$

Step 3: Find the <u>maximum value</u>.

Substitute the derived value for the axis of symmetry, x = -2, into h(x) = -x² - 4x + 4.

h(x) = -x² - 4x + 4 ⇒ General form.

$\displaystyle\mathsf{\Rightarrow\:h(-2) = - \:(-2)^2 - 4(-2) + 4\: \rightarrow \textsf{[\:BPEMDAS: Exponent\:].}}$

$\displaystyle\mathsf{\Rightarrow h(-2) = - \:4 - 4(-2) + 4\:\rightarrow \textsf{[\:BPEMDAS: Multiplication\:].}}$

$\displaystyle\mathsf{\Rightarrow\:h(-2) = - 4 + 8 + 4\:\rightarrow \textsf{[\:BPEMDAS: Addition\:].}}$

$\displaystyle\mathsf{\Rightarrow h(-2) = 8\:\rightarrow \: \textsf{[\:\textbf{Maximum value}\:].}}$

Hence, the maximum value (vertex) occurs at point (-2, 8).

<h2>Graph the parabola: </h2><h3>Find other points to plot:</h3>

In order to find other points to plot on the graph, we can substitute different x-values into the vertex form. A good starting point is to solve for the y-intercept, which is the point on the graph where it intersects the y-axis.

<h3>Solve for the y-intercept:</h3>

Solve for the y-intercept by setting x = 0:

Vertex form: h(x) = - (x + 2)² + 8

⇒ h(0) = -(0 + 2)² + 8 → [Let <em>x</em> = 0 in h(x) = - (x + 2)² + 8].

⇒ h(0) = -(2)² + 8 → [PEMDAS: Parenthesis].

⇒ h(0) = -4 + 8 → [PEMDAS rule: Exponent].

⇒ h(0) = 4 → [PEMDAS: Addition].

Hence, the y-intercept is (0, 4).

<h3>Graph the axis of symmetry:</h3>

We can graph the <em>axis of symmetry</em> by drawing a <u>vertical line</u> from x = -2, and use it as a reference point in finding other points to plot on the graph.

Since the y-intercept, (0, 4) is 2 units to the right of the <em>axis of symmetry</em>, then it means that going 2 units to the left will give us (-4, 4).

We have the following points to plot on the graph: