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2 years ago

Find the equation of a line that passes through the point (-2,1) and has a gradient of -3.

1 answer:

6 0

A straight line passing through the point (-2,1) and having a gradient of -3 yields the equation y = -3x - 5.

We know that a straight line is an infinitely long line with no curves on it. A straight line's equation is

y = mx + c...(1), where m is the gradient of the straight line and c is a constant.

Given that the gradient of the given straight line = m = -3.

Putting this value in (1), we get

y = -3x + c ...(2)

Again, the given straight line passes through the point (-2,1). So, we can put x = -2 and y = 1 to get the value of the constant c.

So, 1 = (-3)(-2) + c

i.e. 6 + c = 1

i.e. c = 1 - 6 = -5

(2) can be written as

y = -3x - 5

Therefore the equation of the given straight line is

y = -3x - 5

Know more about straight lines here -

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In the diagram abc=adb=90, ad=p and dc=q. Use similar triangles to show that x2=pz<br> plzz anyoneee

kramer

Answer:

By comparing the ratios of sides in similar triangles ΔABC and ΔADB,we can say that $x^{2} =pz$

Step-by-step explanation:

Given that ∠ABC=∠ADC, AD=p and DC=q.

Let us take compare Δ ABC and Δ ADB in the attached file , ∠A is common in both triangles

and given ∠ABC=∠ADB=90°

Hence using AA postulate, ΔABC ≈ ΔADB.

Now we will equate respective side ratios in both triangles.

$\frac{AB}{AC}= \frac{AD}{AB}=\frac{BD}{BC}$

Since we don't know BD , BC let us take first equality and plugin the variables given in respective sides.

$\frac{x}{z}= \frac{p}{x}$

Cross multiply

$x^{2}=pz$

Hence proved.

7 0

3 years ago

Find the area of the shaded region. Round to the nearest tenth.

sukhopar [10]

Answer:

Step-by-step explanation:

r = 8.35 ft

area of circle = πr² = 69.7225π ft²

θ = 5π/9 radians

area of unshaded segment = r²(θ-sinθ)/2 ≅ 26.51 ft²

shaded region = 69.7225π - 26.51 ≅ 192.53 ft²

7 0

3 years ago

Simplify the expression.<br> (x 3/2)6

Sliva [168]

For this case we must simplify the following expression:

$(x ^ {\frac {3} {2}}) ^ 6$

We have that by definition of properties of powers that is fulfilled:

$(a ^ n) ^ m = a ^ {n * m}$

Then, rewriting the expression:

$x ^ {\frac {3 * 6} {2}} =\\x ^ {\frac {18} {2}} =\\x ^ 9$

Answer:

$(x^{\frac{3}{2}})^6=x^9$

6 0

3 years ago

Among all pairs of numbers with a sum of 238238, find the pair whose product is maximum. Write your answers as fractions reduced

mylen [45]

Answer:

$x=119119,\;\;\;y=119119$

Step-by-step explanation:

Let the $x$ be the first number, $y$ be the second number and $p$ be the product of the first and second number.

i.e $x+y=238238$ $\Rightarrow x=238238-y$

$p=xy$

$\Rightarrow p=(238238-y)y\\\Rightarrow p=238238y-y^2$

$\Rightarrow \frac{dp}{dy} =238238-2y\\\Rightarrow 0=238238-2y\\\Rightarrow 2y=238238\\\Rightarrow y=119119$

Now,

$x=238238-119119\\\\ \Rightarrow x=119119$

Hence, $x=119119,\;\;\;y=119119$

8 0

2 years ago

24 is 3 more than a number p

rewona [7]

Answer: 24 = 3 + P

Step-by-step explanation: 24 is 3 more than a number P can be represented in the equation form of 24 = 3 + P

To solve it:

3 + P = 24

3 - 3 + p = 24 -3

p = 21

7 0

3 years ago