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3 years ago

Multiply and simplify if possible.

Mathematics

1 answer:

timofeeve [1]3 years ago

7 0

√7x-49<span>√x Tell if you need to see the work

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Solve<br> 7x+2y=16<br> 5x-2y=20<br> x= y= <br><br> (3 marks)

sasho [114]

X=3 and y=-5/2. Here is why, when we do 7x+5x that gives us 12x. -2y+2y=0 and then we have 16 plus 20 which gives us 36. Now we gotta isolate x which right now we have 12x=36. Therefore divide by 12 to get x alone, which 36 divided by 12 is equal to 3. X=3. Plug it back into the equation, 7(3)=21 plus 2y=16. Subtract 21 from both sides 16-21 is equal to -5. Then 2y=-5 divide by 2 on both sides you will have -5/2=y or y=-5/2. Hope this helps!

8 0

2 years ago

Look at this graph:

pickupchik [31]

<h3>Answer:</h3>

The Slope is $2$

<h2>Explanation:</h2>

Notice that both the points, $(60,0)$ and $(70,20)$ , are on the line. So we can use those points to calculate the slope. Recall that that slope of the line $m$ can be calculated by $\frac{y_2 -y_1}{x_2 -x_1}\\$ if we have the points, $(x_1,y_1)$ and $(x_2,y_2)$ .

<h3>Calculating for the slope of the line:</h3>

Given:

$(60,0)$

$(70,20)$

$m = \frac{20 -0}{70 -60} \\ m = \frac{20}{10} \\ m = 2$

3 0

3 years ago

Read 2 more answers

A homeowner has an octagonal gazebo inside a circular area. Each vertex of the gazebo lies on the circumference of the circular

Tcecarenko [31]

If we draw the diagonals of the octagonal gazebo, the 4 diagonals divide the octagon into 8 triangles.

Note that each triangle is an isosceles triangle whose equal sides are x, the radius of the circle.

The top angle of each triangle is obtained by dividing the full angle by 8.

So, each top angle = $\frac{360}{8}$

= 45°

Now, in fig., consider one of the triangles Δ OAB. Draw an altitude OC from O to the opposite side AB.

This altitude OC bisects the top angle 45°.

Therefore, ∠ AOC = 22.5°.

Now, in Δ AOC,

$sin 22.5=\frac{AC}{OA}$

$=\frac{AC}{x}$

So, AC = x sin 22.5°

Note that, AB = 2 AC.

Therefore, AB = 2x sin 22.5°.

Also, $cos 22.5=\frac{OC}{OA}$

$=\frac{OC}{x}$

So, OC = x cos 22.5°.

Area of Δ AOB = $\frac{1}{2}(AB)(OC)$

= $\frac{1}{2}$ × (2x sin 22.5°) × (x cos 22.5°)

= $\frac{1}{2} x^{2}$ (2 sin 22.5° cos 22.5°)

= $\frac{1}{2} x^{2}$ sin 45°

= $x^{2}$ / $2\sqrt{2}$

Area of the octagonal gazebo = 8 × one triangular area

= 8 × ( $x^{2}$ / $2\sqrt{2}$ )

$=2\sqrt{2} x^{2}$

$=2.828x^{2}$

Area required for mulch = circular area - area of the gazebo

$=3.14x^{2} -2.828x^{2}$

$=0.312x^{2}$

Now, cost per unit area = $1.50.

Hence, total cost g(m) = area × cost per unit area

Total cost g(m) = $0.312x^{2}$ × 1.5

$=0.468x^{2}$

Hence, total cost g(m) = $0.468x^{2}$ .

4 0

3 years ago

Graph the solution of the inequality: 3/7 (35x-14) ≤ 21x/2 + 3

hammer [34]

Hello there!

In order to graph the solution, we need to solve it first.

So let's start....

3/7(35x - 14) ≤ 21x/2 + 3

15x -6 ≤ 21x/2 + 3

15x - 21x/2 ≤ 3 + 6

9x/2 ≤ 9

x ≤ 9* 2/9

x ≤ 18/9

x ≤ 2

See the picture for the graph

Please let me know if you have questions about the answer.

Thanks!

5 0

3 years ago

Given d is the midpoint of ab, e is the midpoint of bc, and ac = 24 units. which of the following statements must be true?

yan [13]

Answer:

Step-by-step explanation:

I am pretty sure but get another answer just to be sure.

7 0

2 years ago