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Answer:y=2x-3

Step-by-step explanation:

Answer:

y= 2x-3

Step-by-step explanation:

Answer:

Q1) 104m²

Q2) 121 in.²

Step-by-step explanation:

Q1)

GIVEN :-

TO FIND :-

GENERAL FORMULAES TO BE USED IN THIS QUESTION :-

SOLUTION :-

Area of the triangle = [tex]\frac{1}{2} \times 8 \times 6 = 24m^2[/tex]

Area of the rectangle = [tex]10 \times 8 = 80m^2[/tex]

Area of the figure = (Area of the triangle) + (Area of the rectangle)

                              = 24m²+ 80m²

                              = 104m²

Q2)

GIVEN :-

TO FIND :-

GENERAL FORMULAES TO BE USED IN THIS QUESTION :-

SOLUTION :-

Area of the triangle = [tex]\frac{1}{2} \times 3 \times 7 = \frac{21}{2} = 10.5 \; in.^2[/tex]

Area of the trapezium = [tex]\frac{1}{2} \times (6 +7) \times 17 = \frac{221}{2} = 110.5\; in^2[/tex]

Area of the figure = (Area of the triangle) + (Area of the trapezium)

                              = 10.5 in.² + 110.5 in.²

                              = 121 in.²

Answer:

437.3ft

Step-by-step explanation:

last of sines

a/sin(A) = b/sin(B) = c/sin(C)

sin(90) = 1

the angle between y and 500ft side is 90-29 = 61 degrees.

so,

x/sin(61) = 500/1 = 500

x = 500 × sin(61) = 437.3ft

In a triangle, value of [tex]x = 437.4[/tex] units (round to nearest tenth) using trigonometric ratio.

"Trigonometric ratio is defined as in a right triangle the relation between the ratio of a sides of a triangle and the angle."

Formula used

[tex]sin\theta = \frac{opposite sides}{hypotenuse}[/tex]

[tex]cos\theta = \frac{adjacent sides}{hypotenuse}[/tex]

According to the question,

In a given right triangle ABC,

Hypotenuse [tex]=500 ft[/tex]

Opposite side [tex]= x ft[/tex]

Adjacent side [tex]= y ft[/tex]

As per the diagram drawn,

 [tex]\angle BAC+ 29\° = 90\° \\\\\implies \angle BAC = 90\° -29\° \\\\\implies \angle BAC = 61\°[/tex]

Substitute the value in the above trigonometric ratio formula we get,

[tex]sin61\° = \frac{x}{500}\\\\\implies 0.8747 = \frac{x}{500}\\\\\implies x = 500 \ times 0.8747\\\\\implies x = 437.35 ft[/tex]

[tex]\implies x = 435.4 ft[/tex] (round to nearest tenth)

In trigonometric ratio [tex]cos\theta[/tex] we get,

[tex]cos61\° = \frac{y}{500}\\\\\implies 0.4848 = \frac{y}{500}\\\\\implies y= 500 \ times 0.4848\\\\\implies y = 242.2 ft[/tex]

Hence , In a triangle, value of [tex]x = 437.4[/tex] units (round to nearest tenth) using trigonometric ratio.

Learn more about trigonometric ratio here,

https://brainly.com/question/1201366

#SPJ2

Answer:

Step-by-step explanation:

The intersection point (centroid) divides the medians in ratio 2:1. it does mean that the long segment value is the short segment value multiplied by two. let's call the centroid point G.

BG=DG*2=4*2=8

CG=EG*2=2*2=4

AG=FG*2 =>FG=AG/2=6/2=3

Answer:

The correct answer is 75 dgrees

Step-by-step explanation:

<CDE = arcCBE - arcCE / 2

arcCE = 105°

arcCBE = 360° - 105° =255°

<CDE = 255° - 105°

<CDE = 150 / 2

<CDE = 75°

Therefore the measure of < CDE is 75°

Answer:

125

Step-by-step explanation:

This can be simplified to sqrt(25) ^3

sqrt(25) is 5

          (5*5) = 25

5^3 = 225

          (5*5*5) = 125

Answer:

125

Step-by-step explanation:

[tex]\sqrt[2]{25^3} \\=25\sqrt[2]{25} \\=25*5\\=125[/tex]

Answer:

D

Step-by-step explanation:

∠ABC= ∠DBE (vert. opp. ∠s)

(6x -7)°= (4x +23)°

6x -7= 4x +23

Being x terms to 1 side, constant to the other:

6x -4x= 23 +7

Simplify:

2x= 30

Divide both sides by 2:

x= 15

Substituting the value of x:

m∠ABC

= 6(15) -7

= 83

Answer:

C. 9.9 in.

Step-by-step explanation:

Step-by-step explanation:

Alright, lets get started.

Area is given as 49 square inches.

The formula for area A =  

base is given as x

Height is given as x

Hence area is A

A =  

Multiplying 2 in both sides

Taking square root on both sides

hence the answer is x = 9.9 in   :  Answer

Hope it will help :)

The value of x is 9.9 in.

Solution:

The given image is a triangle.

Base of the triangle = x

Height of the triangle = x

Area of the triangle = 49 sq. in

To find the value of x:

Area of the triangle =  

Substitute the given values in the formula.

Multiply by 2 on both sides, we get

Taking square root on both sides, we get

⇒ x = 9.9 in

Hence the value of x is 9.9 in.

Answer:

1.94

Step-by-step explanation:

Divide 5.95 by 3

7.5cm2

5x3cm=15cm2 because of base x height/2 you would do

15cm2 divided by 2 since it is a triangle (a half of a square) which is 7.5cm2

Answer:

D.

Step-by-step explanation:

Area of a triangle is bh/2

So your base is 5 and your height is 3.

So you do 5*3 which is 15.

And lastly you do 15/2, which is 7.5. 7*2 is 14, and 8*2 is 16

So 7.5 times 2 is 15

Answer:

see below

Step-by-step explanation:

13.  (8-x)/2  = (2x+2)/5

Using cross products

5(8-x) = 2(2x+2)

40 -5x = 4x+4

Add 5x to each side

40-5x+5x = 4x+5x+4

40 = 9x+4

Subtract 4 from each side

40 -4 = 9x

36 =9x

Divide by 9

36/9 =9x/9

4 =x

14.(x+2)/7 = (3x+6)/5

Again using cross products

5(x+2) = 7(3x+6)

5x+10 = 21x+42

Subtract 5x from each side

10 = 21x-5x +42

10 =16x+42

Subtract 42 from each side

-32 = 16x

Divide by 16

-2 =x

15.(1-x)/2 = (3-x)/3

Again using cross products

3(1-x) = 2(3-x)

3 -3x = 6 -2x

Add 3x to each side

3 = 6-2x+3x

3 = 6+x

Subtract 6 from each side

3-6 =x

-3 =x

Answer:

Yes

Step-by-step explanation:

We can make one equation other to the other to solve for x-value first;

=> -4x = x - 5

=> -4x + (-x) = -5

=> -5x = -5

=> x = -5/-5

=> x = 1

Once we have the x-value we can substitute it in for "x" in any equation to find the y-value;

=> y = x - 5

=> y = (1) - 5

=> y = -4

Writing the answer coordinate points would look like (x, y) which would be (1, -4) which is similar to the give, there for yes the solution to the equations is the given coordinate.

Hope this helps!

Answer:

30

Step-by-step explanation:

Given the radical values;

√1000

= √100 * √10

= 10√10

= 10 (3.1623)

= 31.623

Converting to nearest 10,

= 30

Hence the value to the nearest 10 is 30

Answer:

$11.50

Step-by-step explanation:

0.25 times 6= 1.5, plus 10= 11.50

Answer:

60 inches

Step-by-step explanation:

Given data

We have the scale of the drawing as

1cm= 6 inches

Now if 1 cm is equivalent to 6inches

then 10cm will be x inches

Cross multiply we have

x*1= 10*6

x= 60 inches

Hence the length of the actual bed is 60inches

Answer:

7

Step-by-step explanation:

since the whole line is 10 and QR Is a part of the line and is 3. we subtract 3 from 10 to get our answer which is 7.

Answer:

49/8 is the value of k

Step-by-step explanation:

We have the system

x = -2y^2 - 3y + 5

x=k

We want to find k such that the system intersects once.

If we substitute the second into the first giving us k=-2y^2-3y+5 we should see we have a quadratic equation in terms of variable y.

This equation has one solution when it's discriminant is 0.

Let's first rewrite the equation in standard form.

Subtracting k on both sides gives

0=-2y^2-3y+5-k

The discriminant can be found by evaluating

b^2-4ac.

Upon comparing 0=-2y^2-3y+5-k to 0=ax^2+bx+c, we see that

a=-2, b=-3, and c=5-k.

So we want to solve the following equation for k:

(-3)^2-4(-2)(5-k)=0

9+8(5-k)=0

Distribute:

9+40-8k=0

49-8k=0

Add 8k on both sides:

49=8k

Divide both sides by 8"

49/8=k

Answer:=5/2

Step-by-step explanation:

Answer:

x=3 and y=39

Step-by-step explanation:

2y + 3x = 87

y = 6x + 21

2(6x+21) + 3x = 87

12x + 42 + 3x = 87

15x + 42 = 87

15x = 45

x = 3

y = 6(3) + 21

y = 18 + 21

y = 39

Answer:

Volume of the pyramid is 448 cubic meters.

Step-by-step explanation:

Volume of the given pyramid = [tex]\frac{1}{3}(\text{Area of the rectangular base})(\text{Height of the pyramid})[/tex]

Area of the rectangular base = Length × Width

                                                = 12 × 16

                                                = 192 m²

Volume of the pyramid = [tex]\frac{1}{3}(192)(7)[/tex]

                                      = 448 m³

Therefore, the volume is 448 cubic meters.

Answer:

(0, 1)

Step-by-step explanation:

First, we need to make y the subject of the formula from both expressions

For 4x+8y=5

8y = 5- 4x

y = (5-4x)/5

Similarly for x-3y= -3

-3y = -3 - x

3y = x+3

y = (x+3)/3

Since both lines intersects, hence;

(5-4x)/5 = (x+3)/3

Cross multiply

5(x+3) = 3(5-4x)

5x + 15 = 15 - 12x

5x + 12x = 15 - 15

17x = 0

x = 0/17

x = 0

Sustitute x = 0 into any of the equations

Given that y = x+3/3

y = 0+3/3

y = 3/3

y = 1

This shows that the lines intesects at (0, 1)

Answer:

Area = 3.5325 ft² ≈ 3.53 ft²

Perimeter = 7.71 ft

Step-by-step explanation:

This is a semi-circle so we just divide the circumference of the original circle by 2

C = 2πr

C = 2 * 3.14 * 1.5

C = 3.14 * 3

C = 9.42

9.42 / 2 = 4.5 + 0.21 = 4.71 ft

4.71 ft + 3 = 7.71 ft

Area:

A = πr²

A = 3.14 * 2.25

A = 7.065 ft²

7.065 ft² = 3.5 + 0.0325 = 3.5325 ft²

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Step-by-step explanation:

The slope of the line that is perpendicular to the line of AB is: 3.

If two lines are perpendicular to each other, their slopes will be the negative reciprocal of each other. i.e., if the slope of one is 3, the slope of the other would be -1/3.

Slope = change in y / change in x

Slope of AB = (-2 - 2) / (7 -(-5))

Slope of AB = -4/12

Slope of AB = -1/3

Negative reciprocal of -1/3 would be 3.

Therefore, the slope of the line that is perpendicular to the line of AB is: 3.

Learn more about slopes of perpendicular lines on:

https://brainly.com/question/1362601

Answer:

Answers are square root of 2, square root of 7,

Step-by-step explanation:

Irational is a number that is never ending.

Square root of 2 is irrational since there is no pattern to the number after the decimal.

10/ sqrt of 100. Sqrt of 100 is 10. 10/10 = 1 so this is  not a irrational.

Sqrt of 7 does not have a pattern after the decimal point so it is irrational.

5.87 with a dash on top is rational since it means it has a pattern of continues 87's.

Last one it is equal to 2 so it is rattional.

Answer:

The square root of 2 is irrational, also 5.87 repeating,  the square root of 7 and the other two options aren't irrational.

Step-by-step explanation:

Irrational numbers definition: a number that can be expressed as an infinite decimal with no set of consecutive digits repeating itself indefinitely and that cannot be expressed as the quotient of two integers

Hope I helped, have a nice day :)

Answer:

10^-3

Step-by-step explanation:

so if you have 10^2/10^5, you would subtract the exponents since it is division.  2-5=-3

therefore, it would be 10^-2

Hope this helps!

Answer:

1/4

Step-by-step explanation:

Hi there!

[tex]\large\boxed{(0, -1)}[/tex]

-2x + 8y = -8

2x - 3y = 3

We must eliminate a variable to solve. We can add the two equations to eliminate x because -2 + 2 = 0:

-2x + 8y = -8

2x - 3y = 3

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

0x + 5y = -5

5y = -5

y = -1

Substitute this value of y into an equation to solve for x:

-2x + 8(-1) = -8

-2x -8 = -8

x = 0

Thus, the solution of this system is:

(0, -1)

Answer:

(0,-1)

Step-by-step explanation:

Hi there!

We are given the system:

-2x+8y=-8

2x-3y=3

there are 3 ways to solve systems of equations: graphing, substitution, and elimination

let's solve this system by elimination, which we will add the 2 equations together to clear one variable, solve for the other variable, and plug the value of that variable to solve for the variable that was cleared earlier.  

add the two equations together (-2x and 2x clear out to equal 0 and we'll have only y left.)

 -2x+8y=-8

+

 2x - 3y= 3

_________

      5y=-5

divide by 5 on both sides

y=-1

now substitute y as -1 into one of the equations to solve for x

for example, we can do the second equation

2x-3(-1)=3

multiply

2x+3=3

subtract 3 from both sides

2x=0

divide by 2

x=0

therefore the answer is x=0, y=-1. If you need it as a point, it's (0,-1)

Hope this helps! :)