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4 years ago

I need help with number 4.... please explain because I don't understand

Mathematics

1 answer:

IrinaK [193]4 years ago

5 0

Y=mx+d

you know m=1/3
->
y=(1/3)x+b

for the complete definition of the line you need to calculate b, for this insert the given point (3,3) into x and y which the line passes:

3=(1/3)*3+b
3=1+b
2=b

so your line is y=(1/3)x+2

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The area of a right triangle is sixty square centimetres. Its base is one centimetre less than twice its height. If the base and

NemiM [27]

Answer:

5. None of the above

Step-by-step explanation:

We have this information:

A = 60 cm2

b = 2*h - 1

Let's find out b and h:

The equation of the are of a triangle is A = (b*h)/2, if we replace it with our information, we have

$60 = ((2*h - 1) * h)/2\\ 120 = 2*h^2 - h\\ 0 = 2*h^2 - h - 120$

Let's find h with the quadratic formula:

$\fbox {Quadratic formula:} \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h = \frac{-(-1)\pm\sqrt{(-1)^2-4*2*(-120)}}{2*2} = \frac{1\pm\sqrt{961}}{4} = \frac{1\pm\ 31}{4}$

h = 8 or h = -7.5

But h represents the height of the triangle, so it has to be a positive number, that's h = 8.

If we replace this in the equation we had for b, we have that b = 2*8 - 1 = 15.

Now we can calculate the hypotenuse with the Pythagorean equation

$\fbox {Pythagorean equation:}$ The square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the two legs (the two sides that meet at a right angle).

The base and the height are our legs. We will use "H" for the hypotenuse

$H^2 = b^2 + h^2 = 15^2 + 8^2 = 289\\ H = \sqrt {289} = 17$

H = 17

If we decrease the base and the height by 2 centimeters, we have

b' = 15 - 2 = 13 and h' = 8 - 2 = 6

With this, let's calculate the new hypotenuse:

$H'^2 = b'^2 + h'^2 = 13^2 + 6^2 = 205\\ H' = \sqrt {205} \approx 14.3$

$H' \approx 14.3$

So, the hypotenuse decreases $H - H' \approx 17 - 14.3 = 2.7$

3 0

3 years ago

Which one is it please help

mestny [16]

Answer:

solid

Step-by-step explanation:

it makes sence

8 0

4 years ago

Read 2 more answers

$74.00 sweatshirt; 5% tax |

guapka [62]

Answer:

the tax amount is $3.7

Step-by-step explanation:

Given that

The price of the sweatshirt is $74

And, there is a 5% tax

So we assume that We need to find out the tax amount

So here the following formula should be used

= Price of the sweatshirt × tax rate

= $74 × 0.05

= $3.7

Hence, the tax amount is $3.7

So the same would be considered and relevant

3 0

3 years ago

Monica is attempting to factor the expression 18x2 + 27x – 5. In her first step, she rewrites the expression as 18x2 + 32x – 5x

lisabon 2012 [21]

Answer:

Step-by-step explanation:

For quadratic expression in this form, the first step is to multiply the number in front of $x^2$ with the last term, the constant (with the sign in front as well). This is the "multiplied number".

Step 2 is to come up with 2 numbers which when multiplied is equal to the "multiplied number" in step 1 above and also add to the number in front of $x$ .

For this problem, we would need 2 numbers that

Add up to 27, and
When multiplied, comes to -90 (18 * -5 = -90)

They already found the 2 numbers as expressed in the form shown $18x^2+32x-5x-5$ . The 2 numbers are +32 and -5.

Do they add up to 27, as required?

Yes, 32-5=27

Do they come to -90 when multiplied?

No, 32 * -5 = -160

Hence, they add up, BUT NOT multiplied.

So the answer choice B is right.

5 0

3 years ago

Suppose a video store charges non-members $4 to rent a video. A membership costs $21 and then videos cost only $2.50 to rent. Ho

densk [106]

Answer:

You need to rent 14 videos, and you'll pay the same amount for both. Renting 15 will make the membership a better method of payment.

Step-by-step explanation:

Let Number of videos to be rented be x;

Given:

For non members;

Cost of renting 1 video = $4

Cost for renting x videos = $4x$

For Members;

Membership cost = $21

Cost of renting 1 video = $2.50

Cost of renting x video = $2.5x$

We can create an equation. Say the number of videos you rent is given by x . We can write that, if we rent x videos without membership, we'll have to pay $4x$ . If we rent the same amount of videos with membership, we'll have to pay $21+2.5x$ .

Hence the equation can written as

$4x=21+2.5x\\4x-2.5x=21\\1.5x=21\\x=\frac{21}{1.5}=14$

Hence You need to rent 14 videos, and you'll pay the same amount for both. Renting 15 will make the membership a better method of payment.

5 0

3 years ago