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4 years ago

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I really need help on this question

1 answer:

Talja [164]4 years ago

7 0

To find the slope, we need two points that are located on this line.

The following two points are on this line: (0,-4) and (3,1).

Let m = slope

m = (1 -(-4))/(3-0)

m = (1 + 4)/3

m = 5/3

The slope is 5/3.

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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre

Margarita [4]

Add one to 24
5x=25
divide by 5
x=5

7 0

3 years ago

Read 2 more answers

Complete the arithmetic sequence and then find the nth term.<br>__,__,6,__,15,__, 24, ...

Rudik [331]

Given:

The arithmetic sequence is

__, __, 6, __, 15, __, 24, ...

To find:

The missing values and the nth term of the sequence.

Solution:

The nth term of an arithmetic sequence is

$a_n=a+(n-1)d$ ...(1)

Where, a is the first term and d is the common difference.

3rd term of the sequence is 6.

$a_3=a+(3-1)d$

$6=a+2d$ ...(i)

5th term of the sequence is 15

$a_5=a+(5-1)d$

$15=a+4d$ ...(ii)

Subtracting (i) from (ii), we get

$15-6=a+4d-a-2d$

$9=2d$

$\dfrac{9}{2}=d$

$4.5=d$

Putting d=4.5 in (i), we get

$6=a+2(4.5)$

$6=a+9$

$6-9=a$

$-3=a$

Putting a=-3 and d=4.5 in equation (1).

$a_n=-3+(n-1)4.5$

$a_n=-3+4.5n-4.5$

$a_n=4.5n-7.5$

The nth term of the given arithmetic sequence is $a_n=4.5n-7.5$ .

For n=1,

$a_1=4.5(1)-7.5$

$a_1=4.5-7.5$

$a_1=-3$

For n=2,

$a_2=4.5(2)-7.5$

$a_2=9-7.5$

$a_2=1.5$

For n=4,

$a_4=4.5(4)-7.5$

$a_4=18-7.5$

$a_4=10.5$

For n=6,

$a_6=4.5(6)-7.5$

$a_6=27-7.5$

$a_6=19.5$

The missing values are -3, 1.5, 10.5, 19.5 respectively. So, the complete arithmetic sequence is -3, 1.5, 6, 10.5, 15, 19.5, 24, ... .

5 0

3 years ago

A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating the parabola x^2=4y around

Nadya [2.5K]

Answer:

1.00 inches

Step-by-step explanation:

The distance from vertex to focus is "p" in the quadratic equation ...

x^2 = 4py

In the given equation, p=1. Since units are inches, ...

the bulb should be placed 1.00 inches from the vertex.

7 0

3 years ago

Yakvenalex [24]

Answer:

x = -4

y = 7

graph like this

Step-by-step explanation:

hope it helps ☺️

5 0

3 years ago

The floor of a shed given on the right has an area of 85 square feet. The floor is in the shape of a rectangle whose length is 7

lesya692 [45]

Answer: Length = 10 feet and width = 8.5 feet.

Step-by-step explanation:

Let x be the width of the floor.

Then length of the floor = $2x-7$

Given : The area of the floor = 85 square feet

We know that the area of a rectangle is given by :-

$A=l\times w$

$\Rightarrow\ 85=(2x-7)\times x\\\\\Rightarrow\ 2x^2-7x-85=0\\\\\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\Rightarrow\ x=\dfrac{7\pm\sqrt{49-4(2)(-85)}}{4}\\\\\Rightarrow\ x=\dfrac{7\pm27}{4}\\\\\Rightarrow\ x=\dfrac{17}{2}, -5$

But dimension cannot be negative

So, the width of the floor = $x=\dfrac{17}{2}=8.5\text{ feet}$

And the length of the floor = $2(8.5)-7=10\text{ feet}$

6 0

4 years ago

Read 2 more answers