The perimeter of and equilateral triangle is 60mm. What is the size of the other side?

Answer:

Y = -1/4x + 5

Step-by-step explanation:

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]

2 x 5 x 60

600 ÷ 3 = 300

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! :)

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:

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

Step-by-step explanation:

Hey there!

The equation of line which passes through the point (1,2) is (y-2) = m1(x-1)............(i)

The another given equation is y= 2x + 3.........(ii)

Comparing the equation (ii) with y= mx+c we get;

Slope (m2)= 2.

As per the condition of perpendicular lines, m1*m2 = -1.

m1*2 = -1

Therefore, m1 = -1/2.

Keeping the value of m1 in equation (i) we get;

(y-2) = -1/2(x-1)

y - 2 = -1/2x +1/2

y = -1/2 X + 1/2 + 2

Therefore, the required equation is y = -1/2 X + 5/2.

Hope it helps!

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:

5

Step-by-step explanation:

seven has 5 letters

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:

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:

[tex](4+j)-3[/tex]

Step-by-step explanation:

Hope this helps

Answer:

comment if u have questions

Step-by-step explanation:

a)

10x-6=24

10x=30

x=3

b.

10x+5=50

10x=45

x= 45/10 (9/2)

Answer:

this is the correct answer

Answer:

263(usually it would say cm or m)²

Step-by-step explanation:

area = l x w

l= 25

w= 19

25 x 19 = 551

thats the area without subtracting the missing area's.

missing area= 9 x 16

=144

since theres 2 areas missing, times it by two

144 x 2

=288

subtract the missing area from the total because its not there.

551 - 288

= 263

Answer:

Option (1)

Step-by-step explanation:

If a polynomial is given in the form of f(x) = ax³ + bx² + c

By rational root theorem rational roots of the given polynomial will be,

x = [tex]\frac{\pm \text{Factors of c}}{\pm \text{Factors of a}}[/tex]

Given polynomial in the question is,

f(x) = 66x⁴- 2x³ + 11x²+ 35

Possible rational roots will be,

x = [tex]\frac{\pm \text{factor of 35}}{\pm \text{Facors of 66}}[/tex]

Therefore, Option (1) will be the answer.

Answer:

3x + 9

Step-by-step explanation:

1. combine like terms

x and 2x = 3x

4 + 5 = 9

2. put them together

3x + 9 is your answer.

Hope I helped! have a wonderful day!

Answer:

3x + 9

Step-by-step explanation:

Just add the both the x's together:

2x + x = 3x

Then add the regular numbers together:

4 + 5 = 9

then put the answers together:

3x + 9

Answer:

[tex]8\%[/tex]

Step-by-step explanation:

Since question already gives the number of dollars she will tip, I'm assuming it's asking for percent tipped.

Because the total is $75 and Theresa is tipping $6, she is tipping [tex]\frac{6}{75}=0.08[/tex] of the total. To convert this to a percentage, multiply by 100: [tex]0.08\implies 0.08\cdot 100=\boxed{8\%}[/tex]

Answer:

Step-by-step explanation:

4x^2+120x

4x^2+120x=0

4x^2=-120x

4x^2/x=-120

4x=-120

x=-120/4

x=-30

Answer:

1.94

Step-by-step explanation:

Divide 5.95 by 3

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:

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:

2.82

Step-by-step explanation:

Answer:

$11.50

Step-by-step explanation:

0.25 times 6= 1.5, plus 10= 11.50

Step-by-step explanation:

according to the picture☝

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:

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!

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-Chetan K

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:

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:

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