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2 years ago

Can anyone help me with both problems please?

Mathematics

1 answer:

Eva8 [605]2 years ago

8 0

Answer:

1.y=2x+7

2.y=1/2x+2

Step-by-step explanation:

Graph 1-

The slope-intercept form is y=mx+b

b= y-intercept which in graph 1 is 7

so y=mx+7

in order to find m you use the y2-y1/x2-x1 equation.

This means find two coordinates on the graph such as (0,7) and (-1,5).

Now find y2:5

y1:7

x2:-1

x1:0

y2-y1= 5-7=-2

x2-x1= -1

That gives you -2/-1 which you then simplify to = 2

So the graph would be y=2x+7

Graph 2:

You will do the same steps: Find where the line passes through y on a graph, which will be y=2.

b=2

y=mx+2

then find two coordinates, (0,2)(2,3)

y2=3

y1=2

x2=2

x1=0

y2-y1=3-2=1

x2-x1=2-0=2

The slope of the graph which is m= 1/2

y=1/2x+2

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The length of a rectangle is five less than its width. The area of the rectangle is 84 square feet. Write a quadratic equation i

salantis [7]

Given:

The length of a rectangle is 5 less than its width.

The area of the rectangle is 84 square feet.

We need to determine the quadratic equation in standard form that represents the area of the rectangle.

Dimensions of the rectangle:

Let l denote the length of the rectangle.

Let w denote the width of the rectangle.

Since, it is given that the length is 5 less than its width, it can be written as,

$l=5-w$ and $w=w$

Area of the rectangle:

The area of the rectangle can be determined using the formula,

$A=length \times width$

Substituting A = 84, $l=5-w$ and $w=w$ , we get

$84=(5-w)\times w$

$84=5w-w^2$

Adding both sides of the equation by w², we have;

$w^2+84=5w$

Subtracting by 5w on both sides, we get;

$w^2-5w+84=0$

Thus, the quadratic equation in standard form for the area of the rectangle is $w^2-5w+84=0$

4 0

3 years ago

Branson and his sister Beatrice combined their allowance of $7 each, so they could buy a movie for $12. They bought $1 container

Andreyy89

Answer:

Step-by-step explanation:

Branson and his sister Beatrice combined their allowance of $7 each. This means that the total amount they had is 7 + 7 = $14

They bought a movie for $12. The amount that they have left is

14 - 12 = $2

They bought $1 containers of fruit salad with the remaining money and split the containers evenly between them. This means that the number of containers that they bought is

2/1 = 2

If they split the containers evenly between themselves, then each person would get

2/2 = 1 container of fruit salad

6 0

3 years ago

3. A fast food restaurant has the following options for toppings on their hamburgers: mustard, ketchup, mayo, onions,

Hunter-Best [27]

Answer:

Step-by-step explanation:

Given that a fast food restaurant has the following options for toppings on their hamburgers: mustard, ketchup, mayo, onions, pickles, lettuce, and tomato.

A customer can choose from these 7 options 4 different options in 7C4 ways

This is because order does not matter here

So we use combinations here

Total no of ways a customer choose four different toppings from these

options=7C4

=35

Answer is 35

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3 years ago

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STatiana [176]

Answer:

Step-by-step explanation:

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3 years ago

∫c x sin y ds, C is the line segment from (0, 1) to (3, 5)

Mnenie [13.5K]

Parameterize the line segment $C$ by

$\mathbf r(t)=\langle x(t),y(t)\rangle=(1-t)\langle0,1\rangle+t\langle3,5\rangle=\langle3t,1+4t\rangle$

where $t\in[0,1]$ . Then

$\mathrm ds=\|\mathbf r'(t)\|\,\mathrm dt$
$\mathrm ds=\|\langle3,4\rangle\|\,\mathrm dt$
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So the integral is

$\displaystyle\int_Cx\sin y\,\mathrm ds=5\int_0^1x(t)\sin y(t)\,\mathrm dt$
$=\displaystyle5\int_0^13t\sin(1+4t)\,\mathrm dt$
$=\dfrac{15}{16}(\sin5-\sin-4\cos5)\approx-2.7516$

3 0

3 years ago