The perimeter of a scalene triangle is 14.5 cm. The longest side is twice that of the shortest side. Which equation can be used to find the side lengths if the longest side measures 6.2 cm?

Answer:

a^2 + b^2 - c^2 + 2ab

Step-by-step explanation:

(a + b - c)(a + b + c)

1. expand

(a^2 + ab + ac + ba + b^2 + bc - ca - cb - c^2)

2. rearrange,

(a^2 + b^2 - c^2 + ab + ba + ac - ca + bc - bc)

3. add and subtract

(a^2 + b^2 - c^2 + 2ab)

Answer:

The correct option is;

SSS congruency theorem

Step-by-step explanation:

Given that opposite sides of a parallelogram are equal, whereby side AB is congruent to side CD and  side BC is congruent to side DA and also that side AC is congruent to side CA, we have;

Triangle ABC with sides AB, BC, and AC is congruent to triangle CDA with corresponding sides CD, DA, and CA, by the Side-Side-Side (SSS) rule of congruency (two or more triangles that have all three sides of one triangle congruent to the three sides of the other triangle are congruent).

The missing reason in the proof is: SSS Congruence Theorem.

Thus, ΔABC and ΔCDA has been shown to have three pairs of congruent sides, therefore, the missing reason in the proof is: SSS Congruence Theorem.

Learn more about SSS Congruence Theorem on:

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Answer:

x = 11

Step-by-step explanation:

Raising both sides to the fifth power, we get:

27(x - 2) = 3⁵

x - 2 = 3⁵ / 27

x - 2 = 3⁵ / 3³

x - 2 = 3⁽⁵⁻³⁾ = 3² = 9

x = 11

Answer:

x-intercept(s):  

( − 4 , 0 ) , ( 6 , 0 )

y-intercept(s):  

( 0 , − 24 )

Step-by-step explanation:

The graph of the function f ( x ) = ( x + 4 ) ( x - 6 ) is plotted

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

y = a ( x - h )² + k

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the parabolic equation be represented as A

Now , the value of A is

f ( x ) = ( x + 4 ) ( x - 6 )   be equation (1)

On simplifying , we get

The graph of the function is plotted and it is increasing only on the interval -4< x < 6

And , the vertex of the function is at P ( 1 , -25 )

Therefore , the function is f ( x ) = ( x + 4 ) ( x - 6 )

Hence , the function is f ( x ) = ( x + 4 ) ( x - 6 )

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Answer:

The volume of the pyramid is 867 inch^3

Step-by-step explanation:

Here in this question, we are interested in calculating the volume of a square based pyramid.

Mathematically, we can use the formula below to calculate the volume V of a square based pyramid.

V = a^2h/3

where a represents the length of the side of the square and h is the height of the pyramid

From the question, the length of the side of the square is 17 in while the height is 9 in

Plugging these values, we have ;

V = (17^2 * 9)/3 = 17^2 * 3 = 867 cubic inch

Answer:

Let's simplify step-by-step.

x(0)+7

=0+7

Combine Like Terms:

=0+7

=(0+7)

=7

Step-by-step explanation:

Answer:

y = 7

Step-by-step explanation:

x · 0 = 0

0 + 7 = 7

y = 7

Answer:

Step-by-step explanation:

h(x)=12/x

h(a)= 12/a  ( a is a variable number just replace x with a)

Answer:

5x+8

Step-by-step explanation:

First find the product of 5 and a number

5x

Then sum it with 8

5x+8

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Hi my lil bunny!

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Let's solve your equation step-by-step.

[tex]-8 + 4m = 2[/tex]

Step 1: Simplify both sides of the equation.

[tex]4m - 8 = 2[/tex]

Step 2: Add 8 to both sides.

[tex]4m - 8 + 8 = 2 + 8 \\4m = 10[/tex]

Step 3: Divide both sides by 4.

[tex]\frac{4m}{4} = \frac{10}{4} \\m = \frac{5}{2}[/tex]

Answer : [tex]\boxed {m = \frac{5}{2} }[/tex]

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Have a great day/night!

❀*May*❀

Answer:

x = 7

Step-by-step explanation:

y = (x – 7)^2 – 3

This equation is in vertex form

y = a(x-h)^2 +k

where (h,k) is the vertex

For a vertical parabola, the line of symmetry is x=h

x = 7

Answer:

y = 3/5×x + 1

Step-by-step explanation:

Slope intercept form y= mx + b

since slope = 3/5 => y= [tex]\frac{3}{5}[/tex]x + b

Plug point (-5,-2) to the equation -2 = [tex]\frac{3}{5}[/tex] x (-5) + b

=> b=1

Area of prism = base area × altitude

1. (2x²-10)(x+4)

= 3x³-2x - 40

2. Base area = 2πr

Volume = (2πr)(r²+ 5r)

=2πr³ + 10πr²

3. Base area=½(6)(x-4)(x+3)=3(x-4)(x+3)

Volume= 3(x-4)(x+3)(⅓)

=(x-4)(x+3)= x² - x -12

4. Base circumference= 10π

Base radius = 10π/(2π) = 5

Base area = πr² = 25π

Volume = 25π(3x²-2x)

=125πx²-50πx

5. Volume = 3π√50

=15π√2

6. Base diameter = 16

Base radius = 16/2 = 8

Base area = 2πr = 16π

Volume = 16π(23a²)

=368πa²

We can solve it through proportionality or ratios

Let lamps required to create 60signals be x

Now

[tex]\\ \sf\longmapsto 2:4=x:60[/tex]

[tex]\\ \sf\longmapsto \dfrac{2}{4}=\dfrac{x}{60}[/tex]

[tex]\\ \sf\longmapsto 4x=60(2)[/tex]

[tex]\\ \sf\longmapsto 4x=120[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{120}{4}[/tex]

[tex]\\ \sf\longmapsto x=30[/tex]

Answer:

D (7a-3)/4

Step-by-step explanation:

7a – 4b = 3

Subtract 7a from each side

7a-7a – 4b = 3-7a

-4b = 3 -7a

Divide by -4

-4b/-4 = (3-7a)/-4

b = (7a-3)/4

Answer:

b = (7a - 3)/4

Step-by-step explanation:

7a - 4b = 3

=> -4b = 3 - 7a

=> b = (3 - 7a)/(-4)

=> b = -(3 - 7a)/4

=> b = (-3 + 7a)/4

=> b = (7a - 3)/4

Answer:

The answer is

Step-by-step explanation:

To solve the fraction reduce the fraction with d

That's we have

Next simplify the expression using the rules of indices to simplify the letters in the fraction

For c

Since they are dividing we subtract the exponents

We have

For e

Substituting them into the expression we have

Reduce the fraction by 3

We have the final answer as

Hope this helps you

Answer:

Volume = 5×8×10.5 = 420 meters3

Step-by-step explanation:

5×8×10.5

Answer:

A

Step-by-step explanation:

The unit price will be the slope of the line which is 8, so the unit price is $8/1 lb

Step-by-step explanation:

Angle:2x+30+3x=180

Angle:2x+b+2b=180( Being in straight line)

Angle:30+3x+a=180

Answer:

1.-4,-1,1,6

2.by substituting the values given, we get

32-|15+8|

32-|23|

32-23=9

3.-15+7=8

4..27-(-12)=27+12=39

5.-6.05+(-2.1)

-6.05-2.1=-8.15

6.-3/4-(-2/5)

-3/4+2/5

=-7/20

7.-9(-12)

=108

8.(3.8)(-4.1)

-15.58

9.(-8x)(-2y)+(-3y)(z)

(16xy)+(-3zy)

(16xy)-(3zy)

10.by substituting the value given,we get

2.5*(-3.2)+5

-8+5

-3

so here are the answers,mark as brainliest if u find it useful

thank you

Answer:

1/25 or 0.04

Step-by-step explanation:

Answer:

0.04

Step-by-step explanation:

5 to the 4th power (5 × 5 × 5 × 5) is 625.

5 to the 6th power (5 × 5 × 5 × 5 × 5 × 5) is 15625.

625/15625 = 0.04.

That's your answer!

Hope that helps and maybe earns a brainliest!

Have a great day! :)

Answer:

PQ = 17

Step-by-step explanation:

Tangents drawn to a circle from an external point are congruent, thus

TS = TU = 6

VU = VO = 20

PO = PQ = 37 - VO = 37 - 20 = 17

That is PQ = 17

Answer:

0'=(0,3)

Step-by-step explanation:

P'=(-5+5,7-5)=(0,3)

Answer:

17 quarters

Step-by-step explanation:

Let q = quarters

n = nickels

.25q + .05n = 5.90

we have 16 more nickels than quarters so add 16 quarters to make them equal

n = q+16

Substitute

.25q + .05( q+16) = 5.90

Distribute

.25q+.5q+.80=5.90

Combine like terms

.30q +.8 = 5.90

Subtract .8 from each side

.30q = 5.10

Divide each side by .3

.3q/.3 = 5.1/.3

q = 17

Answer:

Gisel have:

17

quarters

Step-by-step explanation:

1 nickel = 5 cents

1 quarter = 25 cents

1 dollar = 100 cents

5,90 dollars = 5,9*100 = 590 cents

then:

n = t + 16

5n + 25t = 590

n = quantity of nickels

t = quantity of quarters

5(t+16) + 25t = 590

5*t + 5*16 + 25t = 590

5t + 80 + 25t = 590

30 t = 590 - 80

30 t = 510

t = 510 / 30

t = 17

n = t + 16

n = 17 + 16

n = 33

Check:

5n + 25t = 590

5*33 + 25*17 = 590

165 + 425 = 590

Answer:

Step-by-step explanation:

16, 18, 20

(n) + n+2 + n+4

We only took even numbers

Answer:

20

Step-by-step explanation:

Let the least integer = x. The three consecutive even integers can be denoted as:

x , x + 2 , x + 4

Set the equation:

(x) + (x + 2) + (x + 4) = 54

Simplify. Combine like terms:

(x + x + x) + (2 + 4) = 54

(3x) + (6) = 54

3x + 6 = 54

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, subtract 6 from both sides of the equation:

3x + 6 (-6) = 54 (-6)

3x = 54 - 6

3x = 48

Next, divide 3 from both sides of the equation:

(3x)/3 = (48)/3

x = 48/3

x = 16

~

Next, find the largest of the three integers, which was denoted as x + 4:

x + 4

(16) + 4 = 20

20 is the largest integer.

Check:

x + (x + 2) + (x + 4) = 54

16 + (16 + 2) + (16 + 4) = 54

16 + 18 + 20 = 54

16 + 38 = 54

54 = 54 (True).

~

Answer:

[tex]\large \boxed{\sf \bf \ \ \ D. \ \$ 176 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

After 5 years, we will get

[tex]120*(1+8\%)*(1+8\%)*(1+8\%)*(1+8\%)*(1+8\%)\\\\=120*(1+8\%)^5\\\\=120\cdot 1.08^5\\\\= 176.3193...[/tex]

Thank you

Answer:

[tex]\large \boxed{\mathrm{All \ real \ numbers}}[/tex]

Step-by-step explanation:

The domain of a function is all possible values of x for which the function is real and defined.

[tex]f(x)=-15x^2 +6000[/tex]

The function has no undefined points nor any restrictions on the value of x.

[tex]- \infty < x < \infty[/tex]

The domain of the function is all real numbers.

Answer:

All real numbers

Step-by-step explanation:

The domain is the set of all possible values for x.

f(x) = -15x² + 6000

There are no restrictions on the value of x.

The domain is all real numbers.

Answer:

y = 4/3x - 3

Step-by-step explanation:

slope = (-2 - 4)/(7 - -1) = -6/8 = -3/4

perpendicular slope  = 4/3

midpoint (-1 + 7)/2, (4 + -2)/2

(3, 1)

y = mx + b

1 = 4/3(3) + b

1 = 4 + b

-3 = b

y = 4/3x - 3

Answer:

29.53 ≤ x + 5 ≤ 56.15

Step-by-step explanation:

A $5 in-store coupon for every person who buys a flea control product which ranges between $29.53 to $56.15. This means that if you bought a flea control product you would be given an additional $5 that means that for buying a flea product, $5 is given to you. If you have $x, and you bought a flea product you would have x + 5. The inequality that represents this situation is given as:

29.53 ≤ x + 5 ≤ 56.15

Answer:

300 raisins

Step-by-step explanation:

sum the parts of the ratio, 3 + 27 = 30 parts

Divide the total by 30 for the value of one part of the ratio.

3000 ÷ 30 = 100 ← value of 1 part of the ratio , then

3 parts = 3 × 100 = 300 ← number of raisins in a box