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3 years ago

Work out the equation of the line which has a gradient of 2 and passes through the point (1, 4)

Mathematics

1 answer:

leva [86]3 years ago

4 0

Answer:

y = 2x + 2

Step-by-step explanation:

The slope is also called the gradient of the line.

The slope that is given is two, and the point is (1, 4).

I made a point slope equation, and then converted it into a slope-intercept equation.

$y-4=2(x-1)\\\\y-4=2x-2\\\\y-4+4=2x-2+4\\\\\boxed{y=2x+2}$

Hope this helps.

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Logan bought 15 balloons four-fifths all of the balloons are purple. How many of the balloons are purple? Draw a model to show h

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Separating the balloons into five equal groups

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<span>each group (fifth) has three balloons ___ four-fifths is twelve</span>

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3 years ago

ASAP PLS

VikaD [51]

Man in gonna tell you something but it might be wrong. about 1 or 2 i think?? i'm not good at this

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3 years ago

98 POINTS! PLEASE HELP! I been stuck on this assignment for over 2 weeks. My teacher gave me a simple explanation when I asked f

Colt1911 [192]

See the attached picture.

Create an equation for the volume of the box, find the zeroes, and sketch the graph of the function.

The resulting box has a volume

$V(x)=x(8-x)(12-x)=x^3-20x^2+96x$

because the volume of a box is the product of its width $(12-x)$ , length $(8-x)$ , and height $(x)$ .

find the zeroes

You know right away from the factored form of $V(x)$ that the zeroes are $x=0,8,12$ . (zero product property)

sketch the graph of the function

Easy to plot by hand. You know the zeroes, and you can check the sign of $V(x)$ for any values of $x$ between these zeros to get an idea of what the graph of $V(x)$ looks like. See the second attached picture.

Here's what I mean by "check the sign" in case you don't follow. We know $V(x)=0$ when $x=0$ and $x=8$ . So we pick some value of $x$ between them, say $x=1$ , and find that

$V(1)=1(8-1)(12-1)=7\cdot11=77$

which is positive, so $V(x)$ will be positive for any other $x$ between 0 and 8. Similarly we would find that $V(x)$ for $x$ between 8 and 12, and so on.

What is the size of the cutout he needs to make so that he can fit the most marbles in the box?

It's impossible to answer this without knowing the volume of each marble...

If Thomas wants a volume of 12 cubic inches, what size does the cutout need to be?

Thomas wants $V(x)=12$ , so you solve

$x^3-20x^2+96x=12$

While this is possible to do by hand, the procedure is tedious (look up "solving the cubic equation"). With a calculator, you'd find three approximate solutions

$x\approx0.1284$

$x\approx7.6398$

$x\approx12.2318$

but you throw out the third solution because, realistically, the cutout length can't be greater than either of the sheet's dimensions.

What would be the dimensions of this box?

The box's dimensions are ( $x$ in) x ( $8-x$ in) x ( $12-x$ in).

If $x\approx0.1284$ , then $8-x\approx7.8716$ and $12-x\approx11.8716$ .

If $x\approx7.6398$ , then $8-x\approx0.3602$ and $12-x\approx4.3602$ .

8 0

2 years ago

Please help me, maths is hard, and at the moment i wish maths wasn't real. brainliest will be given

Evgen [1.6K]

Answer:

£60

Step-by-step explanation:

Let $x$ be the original price.

$x \times (1-10/100) = 54$

$x \times 90/100 = 54$

$0.9x=54$

$x=54/0.9$

$x=60$

7 0

3 years ago

PLEASE HELP! WIL GIVE BRAINLLIEST!

yarga [219]

Answer:

First Graph is Correct

Step-by-step explanation:

We are given the inequality:

$n \leq 46$

This means any number EQUAL TO or LESS than 46

Since, we have "equal to", there should be a "closed" circle on 46 (it means 46 is included).

LESS THAN means all numbers to the "LEFT".

Looking at the 4 number lines, we can eliminate last 2 choices since they don't have closed circles.

As for the first two choices, the first choice is correct because it shows us all the numbers left of 46 and 46 included (signified by the closed circle).

So, the first number line is the solution

4 0

3 years ago