solve the simultaneous equation 2x+5y=6 and 5x-2y=9​

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {21}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]3 \: ( \: x + 2 \: )[/tex]

Plugging in the value [tex]x = 5[/tex] in the above expression, we have

[tex] = 3\:( \: 5 + 2 \: )[/tex]

[tex] = 3 \: ( \: 7 \: )[/tex]

[tex] = 3 \times 7[/tex]

[tex] = 21[/tex]

[tex]\sf\pink{PEMDAS\: rule.}[/tex]

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35☂}}}}}[/tex]

Answer:

1. option c

2. option b

3. option b

Step-by-step explanation:

1 . option C

Square of longer side = sum of squares of other side

a)

5, 6 , 11

[tex]121 = 25 + 36\\does\ not \ satisfy[/tex]

b)

9, 12, 16

[tex]256 = 144 + 81\\Does\ not \ satisfy[/tex]

c)

7, 24, 25

[tex]625 = 576 + 49\\Does\ satisfy[/tex]

d)

12, 20, 25

[tex]625 = 400 + 144\\does \ not \ satisfy[/tex]

2. Option B

Square of longer side = sum of squares of other side

15 ² = 8 ² + r²

225 = 64 + r²

161 = r²

r = 12.688

r = 13ft

3 . Option b

To find length  of AB,  Use distance formula

[tex]AB = \sqrt{(x_2- x_1)^2 + (y_2 - y_1)^2}[/tex]

    [tex]= \sqrt{(14-3)^2 + (6-1)^2}\\\\=\sqrt{11^2 + 5^2}\\\\=\sqrt{121 + 25}\\\\= \sqrt{146} \\= 12 \ ft[/tex]

Answer: 5 Units

Step-by-step explanation:

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Answer:

C.

Step-by-step explanation:

Answer:

its the 2nd one

hope that helps<3

Answer:

jhkkkhj

Step-by-step explanation:

jkjkjkjkj

The area of the shaded region is (area of the circle) - (area of the square) - (area of the triangle)

Option A is the correct answer

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

The shaded region consists of the area inside the circle but outside the square, as well as the area inside the equilateral triangle but outside the square.

Now,

The area of the circle is πr²

Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square.

Let's say the side length of the square is s.

By the Pythagorean theorem,

s² + s² = (diameter)²

2s² = (2r)²

s² = r²

The area of the square is s² = r².

The area of an equilateral triangle with side length s is √(3)/4 x s².

Since the side length of the square is equal to the height of the equilateral triangle, the side length of the equilateral triangle is also equal to s.

The area of the shaded region.

= (area of the circle) - (area of the square) - (area of the triangle)

Thus,

The area of the shaded region is (area of the circle) - (area of the square) - (area of the triangle)

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ7

Answer:

1 centimeter

Step-by-step explanation:

nope

Answer:

16 boxes large

Step-by-step explanation:

if the weigth is 1280 wilhich means its 1280÷80 =16

Answer:

EQUATION: X - 12 = 7X. SOLUTION: X = - 2.

Step-by-step explanation:

First, we do not know the number. When the number is unknown, it is a variable. I chose the variable, "X."

12 less than signals that we subtract 12. So that would be X - 12.

A product of 7 AND that number means we multiply 7 by X. That can be notated as 7X.

12 less than X is EQUAL to the product of 7 and X. So X - 12 = 7X.

To find the solution, we want to know the value of X. Move X to one side of the equation.

X - 12 = 7X

-X           -X

_________

-12     =   6X

Divide both sides by 6 to get X by itself.

X = - 2.

Answer:

2300 mm^2

Step-by-step explanation:

Answer:

X=2, y=-1

Step-by-step explanation:

-4x +8y=-16 equation 1

4x +3y=5 equation 2

     11y=-11 add two equations to eliminate x

y=-1

solve for x by inputting y value into either equation

4x+3y=5

4x+3(-1)=5

4x-3=5

4x=8

x=2

Answers:

He has  27   quarters and  31   dimes

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

Work Shown:

d = number of dimes

q = number of quarters

d+q = 58 since there are 58 coins of only these two types

d = 58-q

10d+25q = 985 .... note that 985 cents is $9.85

10(58-q)+25q = 985 .... replace d with 58-q

580-10q+25q = 985

15q+580 = 985

15q = 985-580

15q = 405

q = 405/15

q = 27 ..... Mike has 27 quarters

d = 58-q

d = 58-27

d = 31 .... Mike also has 31 dimes

-----------

As a way to check:

d+q = 31+27 = 58 so that works out

and

10d+25q = 10*31+25*27 = 310+675 = 985

so that works out as well. The answer is confirmed.

Answer:

[tex]C = 2[/tex] (A)

Step-by-step explanation:

We assume the constant A is different than 0

We notice that the graph of the function intercepts the x-axis when x = -0.5

we know that cos(x) = 0 when x = π/2 or x = -π/2

thus, [tex]-0.5 + C = \pi /2[/tex]    or  [tex]-0.5 + C = -\pi /2[/tex]

then [tex]C = \pi /2 + 0.5 = 2[/tex]  or [tex]C = -\pi /2 = 0.5 = -1[/tex]

so [tex]C = 2[/tex]

Answer:

Step-by-step explanation:

Area of rectangle:

Given:

The area is:

A = (2x - 7)(3x² + 4x) =

   2x(3x² + 4x) - 7(3x² + 4x) =

   6x³ + 8x² - 21x² - 28x =

   6x³ - 13x² - 28x

Answer:

Area of rectangle = 6 x ³ - 13 x ² + 28

step by step explanation

Given That :-

To Find :-

Area of rectangle = Length × Width

Using Formula

Area of rectangle = Length × Width

substitute the values.

Area of rectangle = ( 2 x - 7 ) × ( 3 x ² + 4 )

= 2 x ( 3 x ² + 4 ) - 7 ( 3 x ² + 4 )

= 6 x ³ + 8 x - 21 x ² + 28

= 6 x ³ - 13 x ² + 28

Answer:

[tex]sin 2 \theta = \frac{4 \sqrt5}{9}[/tex]

Step-by-step explanation:

Identities used :

[tex]1. sin^2 \theta = 1 - cos^2\theta\\\\2. tan^2 \theta + 1 = sec^2 \theta\\\\3.cos \theta = \frac{1}{sec \theta} \\\\4. sin 2 \theta = 2 sin\theta cos\theta[/tex]

[tex]Given \ tan \theta = -\frac{2 \sqrt5}{5}\\[/tex]

[tex]we \ know \ tan ^2 \theta + 1 = sec^2\theta[/tex]

            [tex](-\frac{2 \sqrt 5}{5})^2 + 1 = sec^2 \theta\\\\\frac{4 \times 5}{25 } + 1 = sec^2 \theta \\\\\frac{20 + 25}{ 25} = sec^2 \theta \\\\\frac{45}{25} = sec^2 \theta \\\\sec \theta = \sqrt{ \frac{45}{25}}\\\\sec \theta = \sqrt{ \frac{9 \times 5}{5 \times 5}} \\\\sec \theta = \frac{3 \sqrt {5}}{5}\\\\[/tex]

[tex]We \ know \ cos \theta = \frac{1}{ sec \theta}[/tex]

[tex]So , \cos \theta = \frac{5}{3 \sqrt5}[/tex]

[tex]Next \ sin^2 \theta = 1 - cos^2 \theta[/tex]

                 [tex]= 1 - (\frac{5}{3 \sqrt5})^2\\\\=1 - \frac{25}{9 \times 5}\\\\=1 - \frac{25}{45}\\\\=\frac{45 - 25}{45}\\\\=\frac{20}{45}\\\\=\frac{4}{9}[/tex]

    [tex]sin \theta = \sqrt{ \frac{4}{9}} = \frac{2}{3}[/tex]

[tex]Find \ sin 2 \theta[/tex]

[tex]sin 2 \theta = 2 (sin \theta \times cos \theta)[/tex]

        [tex]= 2 \times \frac{2}{3} \times \frac{5}{3\sqrt5}\\\\= \frac{4 \times \sqrt5 \times \sqrt5}{9 \times \sqrt 5}\\\\=\frac{4 \sqrt5}{9}[/tex]

Answer:

Rate = 10.4%

Step-by-step explanation:

Given :

P = $30000

A = $42520

Interest earned = 42520 - 30000 = $12520

Time = 4years

Find R

     [tex]Interest = \frac{PRT}{100}[/tex]

        [tex]12520 = \frac{30000 \times R \times 4}{100}\\\\12520 = 300 \times 4 \times R\\\\12520 = 1200 \times R\\\\R = \frac{12520}{1200}\\\\R = 10.43 \%[/tex]

Round to 1 decimal place, Rate = 10.4%

Answer:

OA . -6

Step-by-step explanation:

correct me if I'm wrong

Answer:

What is your question for probabilities?

Answer: 15

Step-by-step explanation: 5+9+11+12+13+14+17=81

Make an equation based on this and solve for the variable (x)

81+x/8=12

12*8=96

81+x=96

96-81=15

x=15

Answer:

x = 25

Step-by-step explanation:

Correct question

In a right triangle Sin (40-x)=cos(3x) what is the value of x

Since Sin theta = Cos(90-theta)

Sin (40-x) = Sin(90-3x)

40 - x = 90 - 3x

-x+3x = 90 - 40

2x = 50

x = 25

Hence the value of x is 25

Answer:

35 is correct

Step-by-step explanation:

hope this helps.

Answer:

35°

Step-by-step explanation:

Angle ACD is 70°. The little tick marks on the angle mean both sides of the split are the same amount. This means if you divide the angle in half, you will find out what both of them are equal to.

Answer:

Sorry for the late response, I had to have lunch.

1. >

2. =

3. <

4. >

Step-by-step explanation:

Have a great summer :)

Answer:

11b^3+14b^2+b+9

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

         b2

Step-by-step explanation:

Answer:

105mm

Step-by-step explanation:

To find the rainfall during the month of April simply multiply the number of days in April times the average daily rainfall

Number of days in April: 30

Average daily rainfall: 3.5mm

Rainfall during the month = 30 * 3.5 = 105mm

Answer:

[tex]\sqrt{x+6}[/tex]

Step-by-step explanation:

So, there are a few things we need to go over to graph a function,

When a number is outside of a root, it changes the y value. For example:

y=[tex]\sqrt{x}+6[/tex]

With the +6, y will always be 6 higher than normal.

If it was -6, then y will always be 6 lower than normal.

What if the number is inside the root? Well, it works a little differently.

Instead of changing the y value, it changes the x value. For example:

y=[tex]\sqrt{x+6}[/tex]

So if you put a number in for x, lets say -6, wht would you get?

You would get -6+6=0

The square root of 0 is 0, so when x=-6, y=0

Normally, x would have to equal 0 for the y value to be 0.

So basically, when we see the number isnide of the root, we can think the our x coordinate being subtracted by that number.

This makes since, because if we subtract the +6 from x:

x-(+6)= x-6, and -6 is our x coordinate.

If it was -6 at the start, this would also work:

x-(-6)= x+6. So our x coordinate would start at 6.

Now, lets look at our graph.

As we can see, the x values start at -6, and the y values starts at 0.

This eliminates A and D, since the +6 would change the y value, not the x.

Remember that x-6 would make x a postive 6.

x+6 however, would make x a negative 6.

So we need x+6 in a square root.

This eliminates B, since it has a x-6, making the x coordinate postive 6, not negative 6.

So c is our answer.

Hope this helps!

Answer:

13

Step-by-step explanation:

The IQR = Interquartile Range is the difference between the first and third quartile

Rearranged data set:

3, 7, 16, 17, 20, 45

Step 1

We find the first quartile = Q1

= 1/4(n + 1)th number

n = 6

= 1/4(6 + 1)th

= 1/4(7)th

= 1 3/4th number

This = 7

Step 2

We find the third quartile = Q3

= 3/4(n + 1)th number

n = 6

= 3/4(6 + 1)th

= 3/4(7)th

= 21/4th number

= 5 1/4 th number

This = 20

Step 3

IQR = Q3 - Q1

= 20 - 7

= 13