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3 years ago

15

< 5 and <7 are vertical angles.

1 answer:

marishachu [46]3 years ago

7 0

Answer:

value of x = 19°

Step-by-step explanation:

we know that vertical opposite angles are equal hence Angle 5 = Angle 7

so,

5x+10 = 105°
5x = 95°
x = 19°

hence value of x = 19°

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Find the value of the expression when b= 9 c= 5 and d=10 ............ ½d + c² - b

Minchanka [31]

Answer:

1/2d+c^2-b = 21

Step-by-st ep explanation:

= 1/2(10) + 5^2 -9

= 5 + 25 - 9

= 30 - 9

= 21

4 0

2 years ago

You have 600 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river

inn [45]

Answer:

The length and width of plot is $L=300\:ft$ , $W=150\:ft$

Largest area of the plot is $A=45000 ft^{2}$

Step-by-step explanation:

Assume width as x and length as y. Given that length of fencing is 600 feet and fencing is enclosed on 3 sides. So perimeter is given as,

Perimeter = width + length + width

Substituting the value,

$600=x+y+x$

$600= 2x+y$ ….1

Now area of fence of rectangular box is given as follows,

$A=xy$ ….2

Solving equation 1 for y, subtracting 2x from both sides,

$600-2x= y$

Substituting the value in equation 2,

$A=x\left (600-2x \right )$

Simplifying

$A=600x-2x^{2}$

Rewriting,

$A=-2x^{2}+600x$

Above equation looks like quadratic equation $f\left ( x \right )=ax^{2}+bx+c$ whose graph looks like parabola.

Comparing equation f(x) and A values of a, b and c are, $a=-2,b=600$ and $c=0$ .

Now maximum of $f\left ( x \right )$ occurs at vertex.

The x coordinate of the vertex is given as $-\dfrac{b}{2a}$

Substituting the values,

$x=-\dfrac{600}{2\left (-2 \right )}$

Simplifying,

$x=\dfrac{600}{4}$

$x=150$

So width of plot is 150 feet.

Now to calculate value of length by using equation 1,

$600= 2x+y$

Substituting the values,

$600= 2\left (150 \right )+y$

$600= 300+y$

Subtracting 300 from both sides,

$300= y$

So length of plot is 300 ft.

The y coordinate of the vertex is given as $y=f\left ( -\dfrac{b}{2a} \right )$ which also means, $y=f\left ( 150 \right )$

$\therefore A=-2\left (150 \right )^{2}+600\left (150 \right )$

Simplifying,

$\therefore A=-2\left (22500 \right )^{2}+600\left (150 \right )$

$\therefore A=-45000+90000$

$\therefore A=45000$

So, area of the plot will be $A=45000 ft^{2}$

7 0

3 years ago

a multiplication that corresponds to each division 10 divided by 5=?, b. 4.5 divided by 3, 1/2 dvided by 4=?

katen-ka-za [31]

Answer:

10 divided by 5=2

2*5=10

4.5 divided by 3=1.5

3*1.5=4.5

1/2 divided by 4=1/8

4*1/8=4/8=1/2

6 0

2 years ago

Which statement about the area of a right triangle is true?

timurjin [86]

Answer:

H

Step-by-step explanation:

This is because a rectangle can be divided into two triangles.

5 0

3 years ago

The table shows the temperatures in degrees Celsius, y, inside a shed at x hours past noon. The maximum and minimum temperatures

kolbaska11 [484]

Answer:

B

y = 3 cos (pi/12x - pi/4) + 17

Step-by-step explanation:

First find the average temperature which is 20 + 14/2 = 17

Find the amplitude

20 - 17 = 3

This means that that at noon, the shift is 3hrs past

the best equation that represents this scenario is $y = 3 cos (\frac{\pi}{12}x - \frac{\pi}{4}) + 17$

5 0

2 years ago