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3 years ago

BRAINLIEST!!!

Mathematics

1 answer:

Sonbull [250]3 years ago

7 0

Answer:

$\sqrt{37}$

Step-by-step explanation:

The distance d between a point (m , n ) and a line in the form

Ax + By + C = 0 , is calculated as

d = $\frac{|Am+Bn+C|}{\sqrt{A^2+B^2} }$

Here (m, n ) = (6, 2 ) and

6x - y = - 3 ( add 3 to both sides )

6x - y + 3 = 0 → A = 6, B = - 1, C = 3

d = $\frac{|6(6)+-1(2)+3|}{\sqrt{6^2+(-1)^2} }$

= $\frac{|36-2+3|}{\sqrt{36+1} }$

= $\frac{|37|}{\sqrt{37} }$

= $\frac{37}{\sqrt{37} }$ × $\frac{\sqrt{37} }{\sqrt{37} }$

= $\frac{37\sqrt{37} }{37}$ ← cancel 37 on numerator/ denominator

= $\sqrt{37}$

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Make x the subject of y = 4x + 1<br>You may use the flowchart to help you if you wish.<br>X<br>y

Paha777 [63]

Step-by-step explanation:

y = 4x+1

y–1 = 4x

x = (y–1)/4

5 0

3 years ago

Find the value of x

marin [14]

Answer:

$x=14$

Step-by-step explanation:

The given triangle is a right triangle, meaning it is a triangle with a right angle, this is indicated by the box around one of the angles. When given a right triangle, one can use the right triangle trigonometric ratios. These ratios describe the relationship between an angle in a right triangle, and the sides in a right triangle. Such ratios are as follows,

$sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}$

Bear in mind that the way one names the sides, in the sense of (opposite or adjacent) will change based on the angle one uses to describe the triangle. However, the hypotenuse is the same no matter the angle, as the hypotenuse is the side opposite the right angle.

In this case, one is given one of the angles, and the side opposite the angle. One is asked to find the hypotenuse of the triangle. One can use the sine (sin) ratio to achieve this.

$sin(\theta)=\frac{opposite}{hypotenuse}$

Substitute,

$sin(30)=\frac{7}{x}$

Inverse operations,

$x=\frac{7}{sin(30)}$

Simplify,

$x=14$

5 0

3 years ago

Solve 3(4 – x) ≤ 54

algol13

3(4 - x) <= 54

12 - 3x <= 54
-3x <= 42

x >= -14 answer

Its A

7 0

3 years ago

IDK how to do this who else does

Nezavi [6.7K]

Answer:

36 ft²

Step-by-step explanation:

Scale factor means the side length are multiplied by some value. Here, Jack takes 4 feet and multiplies it by a value of 1 1/2.

The side length he wants is one and a half times the length of his neighbor's.

The 'one' means the side length you started with, and the 'one half' means add half to the original length.

one and a half of four is six. (4 plus half of 4, which is 2, so 4 plus 2)

The box is square, so each side is 6 ft, so the area of the box is 6x6 = 36 ft²

3 0

3 years ago

Find the least common multiple of 8y^2 and 7m

Flura [38]

Answer: $56y^2m$

which is the same as writing 56y^2m

====================================================

Explanation:

Let's focus on the coefficients 8 and 7 for now.

To find the LCM of those values, list out the multiples. Circle the smallest number that can be found in both sets at the same time.

multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, ...
multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, ....

We see that 56 is the LCM of 7 and 8.

Or you could use this shortcut

LCM = (x*y)/GCF

where x and y are the two numbers. The mention of "GCF" refers to the GCF of x and y. In this case, the GCF is 1 so,

LCM = (x*y)/GCF = (8*7)/1 = 8*7 = 56.

----------------------

Once we determine that, we look at the variable terms now.

The y^2 and m will be tacked onto the 56 to arrive at the final answer 56y^2m

This is because y and m are the unique variables, and we go for the highest exponent of each. It's similar to the LCM formula used earlier.

4 0

3 years ago