A certain recipe asks for 4/9 cup of granola , How much is needed to make 4/9 of a recipe

The width of a rectangle is 12 inches more than the length. The perimeter is 76 inches. Find the width and the length.

stira [4]

Answer:

The length of the rectangle is 13 inches and its width (13 + 12) is 25 inches.

Step-by-step explanation:

You have to consider the formula of the perimeter = 2·length + 2·width.

If we call "x" to the length ⇒ width = x + 12 .

Perimeter = 2x + 2·(x + 12) ⇒ Perimeter = 2x + 2x + 24

⇒Perimeter = 4x + 24. ⇒ 76 = 4x + 24 ⇒ 76 - 24 = 4x ⇒52 = 4x

⇒ 52/4 = x ⇒ x = 13.

So, the length of the rectangle is 13 inches and its width (13 + 12) is 25 inches.

3 0

2 years ago

Y = x² – 4 y = 2r + 4<br><br>Solve algebraicallu for the solutions of equations below.

oksano4ka [1.4K]

Step-by-step explanation:

Okay, the first step is to rewrite this equation in "vertex form." You can search that up but it's basically just (h/k).

y = ( x − 1) 2 + 3

Now, we are going to use the vertex form, "y = a (x - h)2 + k, to get the values of a, h, and k.

By using the form we get 1 for the value a, 1 for the value h, and 3 for the value k.

1 = a

1 = h

3 = k

Becuse the value of a is positive, the parabola opens up! (A parabola is the U shaped line in a graph, so that opens up.)

Now, we find the vertex (h,k)

which is (1,3)

Now we find the p from the vertex to the focus. (vertext the top, focus one of the points.)

Follow this formula to find the distance from the vertex to a focus by using this formula

1/4a.

Now we just gonna substitue 1 for a, since we know that 1 equals a above ^

1/4 * 1

Solving that, we got a nice little 1/4.

Next we find the focus

"Find the focus.

The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down.

(h,k+p)

Substitute the known values of h, p, and k into the formula and simplify.

(1,134)

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

x=1

Find the directrix.

y=114

Use the properties of the parabola to analyze and graph the parabola.

Direction: Opens Up

Vertex: (1,3)

Focus: (1,134)

Axis of Symmetry: x=1

Directrix: y=114

Select a few x values, and plug them into the equation to find the corresponding y values. The x values should be selected around the vertex.

xy−1704132437

Graph the parabola using its properties and the selected points.

Direction: Opens Up

Vertex: (1,3)

Focus: (1,134)

Axis of Symmetry: x=1

Directrix: y=114

xy−17041324"

(Sorry if this is long! But I hope you understand it better now! Thanks for the points!)

3 0

2 years ago

Which of the following is the graph of the rational function? y=x^2+2x-8/x^2-9

rusak2 [61]

Notice that we can simplify both numerator and denominator of our rational function. In the numerator we have a quadratic expression of the form $ax^2+bx+c$ . To to simplify it, we are going to find tow numbers that add to 2 and multiply to -8; those numbers are 4 and -2.
$x^2+2x-8=(x+4)(x-2)$
In the denominator we have a difference of squares:
$x^2-9=x^2-3^2=(x+3)(x-3)$

Now we can rewrite our function:
$y= \frac{x^2+2x-8}{x^2-9} = \frac{(x+4)(x-2)}{(x+3)(x-3)}$

From the simplified form of our rational function we can infer that its graph has two vertical asymptotes at $x=3$ and $x-3$

We can conclude that the graphic of our rational function is:

7 0

2 years ago

An old house has a basement stairway that has steps with 7.25 inch vertical risers and 7 inch horizontal treads. What is the slo

svlad2 [7]

Answer:

1.04 inch

Step-by-step explanation:

Given: Old house has a basement stairways with 7.25 inch vertical riser and 7 inch horizontal treads.

Remember; horizontal treads is known as run in steps.

Now, calculating the slope of the stairways.

Formula: $Slope= \frac{Rise}{Run}$

Rise= 7.25 inch

Run= 7 inch.

Subtituting the value in the formula

Slope= $\frac{7.25}{7}= 1.0357 \approx 1.04$ (∵ Round to two decimal)

∴ Slope of stairways is 1.04.

4 0

2 years ago

A family on a trip budgets $1,000 for meals and gasoline. If the price of a meal for the family is $50 and if gasoline costs $3.

galben [10]

Answer:

They can buy 13meals if they buy 100 gallons of gasoline.

Step-by-step explanation:

3.50 PER gallon so 1 gallon is $3.50

if they buy 100 gallons you have to multiply 3.50 by 100 which gives you 350. you subtract 350 from 1000 so 1000-350 and get 650. now, you divide 650 by 50 because each meal is $50. And you get 13 so there you have it.

3 0

2 years ago