The angle measurements in the diagram are represented by the following expressions

Answer:

Step-by-step explanation:

Answer:

-180

Step-by-step explanation:

its a straight line

Answer:

B

Step-by-step explanation:

(5x - 2)² + 35x - 14 = - 12 ( factor out 7 from each term in 35x - 14 )

(5x - 2)² + 7(5x - 2) = - 12 ( add 12 to both sides )

(5x - 2)² + 7(5x - 2) + 12 = 0

Substitute m = 5x - 2 into the equation then in terms of m, the equation is

m² + 7m + 12 = 0 → B

Answer:

see explanation

Step-by-step explanation:

(i)

[tex]\frac{x}{3}[/tex] + [tex]\frac{y}{2}[/tex] = 1 ( multiply through by 6 to clear the fractions )

2x + 3y = 6 ( subtract 2x from both sides )

3y = - 2x + 6 ( divide through by 3 )

y = - [tex]\frac{2}{3}[/tex] x + 2

(ii)

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope ( gradient ) and c the y- intercept )

y = - [tex]\frac{2}{3}[/tex] x + 2 ← is in slope- intercept form ( that is part (i)

with gradient m = - [tex]\frac{2}{3}[/tex]

Answer:14

Step-by-step explanation:

He takes 2 a week so 2 times 7 is 14

Rule for function

If Domains of relation have unique Range then it's function otherwise not a function.

Now

Answer:

56 total units

Step-by-step explanation:

Here is what the plane would look like if the figure and points were drawn.

Answer:

Step-by-step explanation:

Plot the points and connect.

Note. If you connect the points in the given order you will end up with a weird figure hence we connect as pictured.

Horizontal sides sum to:

Vertical sides sum to:

The perimeter is:

Answer:

2.42

Step-by-step explanation:

I AM VERY SORRY IF ITS WRONG

6×9=57

Step-by-step explanation:

get a multiplication chart and find the answer

Answer:

6.33

Step-by-step explanation:

6.33 x 9 = ~57

the quick brown fox jumped over the lazy dog.

[tex]y =\dfrac 12 \cdot x -4\\\\\implies y = \dfrac{x-8}2\\\\\implies 2y = x-8\\\\\implies x -2y=8[/tex]

Answer:

5

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

Using the quadratic formula :

roots =  [-16 +/-√(16^2 - 4*16*5)] / (2*16)

= -0.5 +/- √(-64) /32

= -0.5 +/- 8i/32

= -0.5 + 0.25i and -0.5 - 0.25i

[tex]\sf\longmapsto 16x^2+16x+5=0[/tex]

[tex]\sf\longmapsto x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\sf\longmapsto x=\dfrac{-16\pm\sqrt{16^2-4(16)(5)}}{2(16)}[/tex]

[tex]\sf\longmapsto x=\dfrac{-16\pm√256-320}{32}[/tex]

[tex]\sf\longmapsto x=\dfrac{-16\pm√-64}{32}[/tex]

[tex]\sf\longmapsto x=\dfrac{-16\pm8i}{32}[/tex]

[tex]\sf\longmapsto x=\dfrac{-2\pm i}{4}[/tex]

[tex]\sf\longmapsto x=\dfrac{-1}{2}\pm\dfrac{1}{4}i [/tex]

Applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12

Properties of Similar Triangles:

Given that ΔABC and ΔDEF are similar triangles, therefore:

Thus:

a/x = b/y = c/z

6/x = 8/y = 12/18

Find x using 6/x = 12/18:

6/x = 12/18

x = [tex]\frac{18 \times 6}{12}[/tex]

x = 9

Find x using 8/y = 12/18:

8/y = 12/18

x = [tex]\frac{18 \times 8}{12}[/tex]

x = 12

Therefore, applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12

Learn more about similar triangles on:

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Answer:

Step-by-step explanation:

c^2 = a^2 + b^2

a = 4

b = ?

c = 8

8^2 = 4^2 + b^2

64 = 16 + b^2

48 = b^2

b = sqrt(48)

b = 4√3

Answer:

x = 4

Step-by-step explanation:

√x + 1 = 3

√x = 3 - 1

√x = 2

(√x)² = (2)²

x = 4

Answer:

Step-by-step explanation:

2 because 8 divided by 4 is 2.

Answer:

2

Step-by-step explanation:

8/4 is 2

Answer:

44 - 47 is -3 if thats what youre asking

Step-by-step explanation:

Answer:

She would have 33 more pages left.

Step-by-step explanation:

You would want to subtract 23 from 56.

|9+40i| = |√9^2 + -40^2| = √1681 = 41

Answer: 41

Answer:

41

Step-by-step explanation:

We know that complex numbers are a combination of real and imaginary numbers

Real part is x and imaginary part y is multiplied by i, square root of -1

Modulus of x+iy =

Here instead of x and y are given 9 and 40

i.e. 9+40i

Hence to find modulus we square the coefficients add them and then find square root

|9+49i| =

By long division method we find that

|9+40i| =41

The value of y from the given coordinates and slope is; y = 11

We are given the coordinates of the 2 points as;

(-4, -3) and (3, y)

Now, formula for slope of a line with two coordinates is;

m = (y2 - y1)/(x2 - x1)

m = (y - (-3))/(3 - (-4))

m = (y + 3)/7

Slope is m = 2. Thus;

2 = (y + 3)/7

y + 3 = 2 × 7

y + 3 = 14

y = 14 - 3

y = 11

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3x - 7 + 2x - 3 = 90

<=> 5x -10=90

<=> 5x = 100

<=> x=20

ok done. Thank to me :>

Answer:

A. 49

Step-by-step explanation:

ratio of houses is 3 new to 7 old

21 new is 7 times more than 3, so 7 will also be 7 times more

so, 21 to 49

I hope that made sense

You're almost there. Write the numbers 0, 1, 2, 3, and 4. Since the mixed number is 3 4/5, we know that the point will be somewhere in between 3 and 4 on the number line. To figure out how many ticks/lines to draw in between each number, look at the fraction attached to the mixed number. Remember, a fraction is a part of a whole. We want to know the total number of parts that are in the whole- so we are looking at the denominator, 5. So there are 5 ticks/lines. The numerator represents the number of parts we need to count: 4. This places the point 4 ticks/lines after the "3." The number line should look like this:

9514 1404 393

Answer:

  x = 38.2

Step-by-step explanation:

Each of the functions of x represents the measure of an angle in the triangle. You write an equation for x by using what you know about the relationships of angles in a triangle: their sum is 180°.

  (2x) +(x -18) +(2x +7) = 180

  5x -11 = 180 . . . . . . . collect terms

  5x = 191 . . . . . . . . . . add 11

  x = 38.2 . . . . . . . . . divide by 5

The given question can be solved by applying the cosine rule. Therefore, Sailboat A is 12.61 miles away from the starting point. Thus it is the farthest from the starting point.

a. To determine the distance of sailboat A from the stating point.

Applying the cosine rule to the path traveled by sailboat A, we have:

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos θ

   = [tex]5^{2}[/tex] + [tex]8^{2}[/tex] - 2(5*8) Cos (180 - 29)

   = 25 + 64 -80 * -0.8746

[tex]c^{2}[/tex] = 89 + 70

[tex]c^{2}[/tex] = 159

c = [tex]\sqrt{159}[/tex]

  = 12.6095

Thus, the distance of sailboat A from starting point is 12.61 miles.

b. To determine the distance of sailboat B from the stating point.

Applying the cosine rule to the path traveled by sailboat B, we have:

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos θ

   = [tex]8^{2}[/tex] + [tex]5^{2}[/tex] - 2(5*8) Cos (180 - 51)

   = 64 + 25 -80 * -0.6293

[tex]c^{2}[/tex] = 89 + 50.344

   = 139.344

c = [tex]\sqrt{139.344}[/tex]

  = 11.8044

c = 11.80 miles

Thus, the distance of sailboat B from starting point is 11.80 miles.

Comparing the distances of the sailboats from the starting point, sailboat A is farther from the starting point.

A sketch is attached to this answer for better reasoning.

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