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3 years ago

Substitution method- y=-x+4 and y=3x

Mathematics

1 answer:

kumpel [21]3 years ago

5 0

Substitue y=3x into the other equation to get 3x=-x+4. Solve this to get 4x=4 therefore x=1.
knowing this, y=3

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Solve for t. t/-3.2 < 5

Black_prince [1.1K]

Step-by-step explanation:

t/-3,2 < 5

t > 5 × -3,2

t >-16

4 0

3 years ago

Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.

SashulF [63]

ANSWER

${r}^{2} = 4 \cos2\theta$

EXPLANATION

The Cartesian equation is

${( {x}^{2} + {y}^{2} )}^{2} = 4( {x}^{2} - {y}^{2} )$

We substitute

$x = r \cos( \theta)$

$y = r \sin( \theta)$

and

${x}^{2} + {y}^{2} = {r}^{2}$

This implies that

${( {r}^{2} )}^{2} = 4(( { r \cos\theta) }^{2} - {(r \sin\theta) }^{2} )$

Let us evaluate the exponents to get:

${r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)$

Factor the RHS to get:

${r}^{4} = 4{r}^{2} ({ \cos^{2}\theta } - \sin^{2}\theta)$

Divide through by r²

${r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)$

Apply the double angle identity

$\cos^{2}\theta -\sin^{2}\theta= \cos(2 \theta)$

The polar equation then becomes:

${r}^{2} = 4 \cos2\theta$

7 0

3 years ago

You have 800 ft of fencing to make a pen for hogs. if you have a river on one side of your property, what is the dimension of th

schepotkina [342]

800 ÷ 3 = 266.7

Biggest possible area = 266.6 x 266.7 = 71102.00 ft²

Answer: The dimension is 266.6 ft by 266.7 ft

4 0

4 years ago

Calculate the slope between these two points: (2,-3), (6,-13) please helpp

Andrew [12]

Answer:

m=−5/2

Step-by-step explanation:

you would be using the slope formula

4 0

3 years ago

The tables show linear functions representing the estimated time it takes for the math and language arts portions of standardize

ozzi

Answer: D) The language arts function has the greater slope, which shows that the estimated time per question for language arts is greater than the estimated time per question for math.

Step-by-step explanation:

In the table shown, the estimated time for language arts is greater than the estimated time for math. They can answer 25 math questions in 87 minutes, whereas for language arts, they take 88 minutes to answer 20 questions. Therefore, the slope for LA is greater than the slope for Mathematics. Hope this helps :)

7 0

3 years ago