4x + y = 4
2x + 6y = 24

Which action creates an equivalent system that will eliminate one variable when they are combined?

Answer:

x=17.771mm

Step-by-step explanation:

given a right triangle

to find vslue of x

solution (perpendicular) ² + (base) ² =(hypotenus) ²

using pythagorus theorem

(16.5)²+(6.6)²=(x)²

272.25+43.56=(x)²

315.81=(x)²

√315.81=x

x=17.771mm

Answer:

By Pythagoras theorem

H^2=P^2+B^2

x^2=(6.6)^2+(16.5)^2

x^2=43.56+272.25

x^2=315.81

x=√315.81

x=17.771mm

Answer: 15

Step-by-step explanation:

Answer:

(2a-b)(2a+b-1)

Step-by-step explanation:

Using a system of equations, it is found that the equation that could be used to find the value of b is given by:

3×4−8=b

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

Fatima has 3 packs of batteries. Each pack contains 4 batteries, hence:

b = 3 x 4

She gives her brother 8 batteries to put in his toy robot, hence:

b = 3 x 4 - 8

Which means that the first expression is correct.

More can be learned about a system of equations at https://brainly.com/question/24342899

Answer:

Step-by-step explanation:

Scale:- 1box=1units

So

Take one side of each

Scale factor(A to B)

[tex]\\ \rm\rightarrowtail \dfrac{6}{10}=\dfrac{3}{5}[/tex]

#6

Scale factor (A to B)

[tex]\\ \rm\rightarrowtail \dfrac{12}{6}=2[/tex]

Scale factor (B to A)

[tex]\\ \rm\rightarrowtail \dfrac{6}{12}=0.5[/tex]

Check the picture below.

so the surface area of the pyramid will be the sum of the areas of the base and the four triangular faces.

[tex]\stackrel{\textit{\Large Areas}}{\stackrel{\textit{4 triangular faces}}{4\left[ \cfrac{1}{2}(7.5)(16) \right]}~~ + ~~\stackrel{\textit{rectangular base}}{(7.5)(7.5)}}\implies 240~~ + ~~56.25\implies 296.25~ft^2[/tex]

For one year, plan B would be recommended, because it would be cheaper.

An equation is an expression that shows the relationship between two or more numbers and variables.

The cost of plan A is given by f(x) = 50x + 199 and the cost of plan B is given by g(x) = 90x + 50

For one year, plan B would be recommended, because it would be cheaper.

Find out more on equation at: https://brainly.com/question/2972832

Answer: Plan A

Step-by-step explanation:

f(x) = 50x + 199 = A

g(x) = 90x + 50 = B

Plan A = (1,249) (2, 299) (3,349) (4,399) (5,449) (6,499)

Plan B = (1, 140) (2, 230) (3, 320) (4,410) (5, 500) (6, 590)

Plan A would be recommended because plan A you pay the least amount = 499 dollars over 6 months versus 590 dollars over 6 months with plan B.  

Answer:

Step-by-step explanation:

B) 9 and 36

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

9 is a common factor of

9 and 36.

Here's why:

6 is not evenly divisible by 9

16 is not divisible evenly by 9 (it is divisible by 8)

All the other numbers are divisible by 9.

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

Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I will comment and/or edit my answer. :)

Answer:

A. 3.    B. 20

Step-by-step explanation:

2 divided by 2/3 is 2/ 2/3 or  6/2   which is 3.

3 divided by 1/10 is  3/ 1/10 or 30.

Answer:

h=9

g=61

Step-by-step explanation:

16-h=7

g+4=65

&

Opposite angles and sides are equal in a paralleogram

Amd

Answer:

[tex] \orange{ \boxed{ \sf{ ( \: {x}^{2} + 11x + 18 \: ) \: sq. \: units}}}[/tex]

Solution :

Lenght = x + 9

Width = x + 2

[tex] \sf \green{area \: = \: (x + 9)(x + 2)} \\ \sf \green{ = \: { {x}^{2} + 11x + 18}} [/tex]

Answer:

[tex]x^2+11x+18\: \sf(square\:units)[/tex]

Step-by-step explanation:

To use the area model of solving multiplication and division problems, calculate the area of each of the colored rectangles and add them together.

Area of a rectangle = Length × Width

Area of blue rectangle:  [tex]x \times x = x^2[/tex]

Area of pink rectangle:  [tex]x \times 9 = 9x[/tex]

Area of green rectangle:  [tex]2 \times x=2x[/tex]

Area of orange rectangle:  [tex]2 \times 9=18[/tex]

Area of entire rectangle = blue + pink + green + orange

                                        = [tex]x^2+9x+2x+18[/tex]

                                        = [tex]x^2+11x+18\: \sf(square\:units)[/tex]

so we know that 40% for the rent payment is for food, and we also know that those 40% are really 200 bucks, so what would it be for the 100%?

[tex]\begin{array}{ccll} \%&amount\\ \cline{1-2} 40 & 200\\ 100& x \end{array} \implies \cfrac{40}{100}=\cfrac{200}{x}\implies \cfrac{2}{5}=\cfrac{200}{x} \\\\\\ 2x=1000\implies x=\cfrac{1000}{2}\implies x=500[/tex]

Answer:

D should be the answer because the rate of Mason and Evan is 3 pages per a minute because three goes into both like so 30÷10=3 and 12÷4=3. Which is why D is your answer.

Answer:

50°

Step-by-step explanation:

In a parallelogram opposite angles have the same measure. Angle ABC has then the same measure of angle ADC, which is 38°+12°=50°

Answer:

an = a1 + d (n - 1)

aⁿ = a₁ˣ⁻1

Answer:

$149 - skateboard price

$52 - carly's money

$20 × 5 cars = $100

$100 + $52 = $152

$152 - $149 = $3 left

the lcm would be 79380

Step-by-step explanation:

5×7×7

2×2

×3×3×3×3

muliply all the 3 numbers and then you get 79380

Answer:

Step-by-step explanation:

Let the width of the rectangle = x

As length is 5 inches longer than width, we have to add 5 to width

Length = x + 5

Perimeter of ractangle = 56 in

2* (length + width) = 56

2*( x + 5 + x) = 56

2* (2x + 5)    = 56

Use distributive property: a*(b +c) =(a*b) + (a * c)

2*2x + 2*5   = 56

4x  + 10 = 56

Subtract 10 from both sides

4x = 56- 10

4x = 46

Divide both sides by 4

x = 46/4

x = 11.5

Width = 11.5 in

length = 11.5 + 5

            = 16.5 in

Answer:

x = 9,-21

Step-by-step explanation:

Given:

[tex]\displaystyle \large{|x+6|-7=8}[/tex]

Transport -7 to add 8:

[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]

Cancel absolute sign and add plus-minus to 15:

[tex]\displaystyle \large{x+6=\pm 15}[/tex]

Transport 6 to subtract ±15:

[tex]\displaystyle \large{x=\pm 15-6}[/tex]

Consider:

[tex]\displaystyle \large{x= 15-6}[/tex] or [tex]\displaystyle \large{x = -15-6}[/tex]

[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]

Solution:

[tex]\displaystyle \large{x = 9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]

__________________________________________________________

Second Method

Given:

[tex]\displaystyle \large{|x+6|-7=8}[/tex]

Transport -7 to add 8:

[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]

Absolute Function Property:

[tex]\displaystyle \large{|x-a| = \begin{cases} x-a \ \ (x \geq a) \\ -x+a \ \ (x < a) \end{cases}}[/tex]

Consider both intervals:

When x ≥ a then:

[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{x+6=15}[/tex]

Transport 6 to subtract 15:

[tex]\displaystyle \large{x=15-6}\\\displaystyle \large{x=9}[/tex]

When x < a then:

[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{-(x+6)=15}\\\displaystyle \large{-x-6=15}[/tex]

Transport -6 to add 15:

[tex]\displaystyle \large{-x=15+6}\\\displaystyle \large{-x=21}[/tex]

Transport negative sign to 21:

[tex]\displaystyle \large{x=-21}[/tex]

Solution:

[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]

__________________________________________________________

Let me know if you have any questions regarding this question, my answer or explanation. Hope this answer and explanation helps you and good luck with your assignment!

Answer:

half a circle

Answer:

54

Step-by-step explanation:

9x6=54

The measure of the angle that would maximize the area of this isosceles trapezoid is equal to 0.4395 rad.

Given the following data:

Mathematically, the area of a trapezium is given by this formula:

A = ½ × (a + b) × h

A = ½ × (12 + 2l) × h

A = h(6 + l)

Next, we would derive a mathematical expression for A in terms of h as follows;

A = (6 + 4sin(θ)) × 4cosθ

In order to determine the value of θ for which the area of this isosceles trapezoid is maximized, we would differentiate the area (A) with respect to angle (θ):

Note: sin²θ + cos²θ = 1   ⇒ cos²θ = 1 - sin²θ.

[tex]\frac{dA}{d\theta} =16 cos^{2} \theta - 4sin \theta(6+4sin \theta)\\\\\frac{dA}{d\theta} = 16 cos^{2} \theta - 16 sin^{2} \theta - 24sin\theta\\\\\frac{dA}{d\theta} =16(1-sin^{2} \theta)- 16 sin^{2} \theta - 24sin\theta\\\\\frac{dA}{d\theta} = - 32 sin^{2} \theta - 24sin\theta+16\\\\32 sin^{2} \theta + 24sin\theta-16=0[/tex]

Next, we would use the quadratic formula to solve for the value of sinθ.

Mathematically, the quadratic formula is given by this equation:

[tex]sin\theta = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

Where:

Substituting the parameters into the formula, we have;

[tex]sin\theta = \frac{-24\; \pm\; \sqrt{24^2 - 4(32)(-16)}}{2(32)}\\\\sin\theta = \frac{-24\; \pm\; \sqrt{2624}}{64}\\\\sin\theta = \frac{-24\; \pm\; 51.23}{64}\\\\sin\theta = \frac{-24\;+\; 51.23}{64}\\\\sin\theta = \frac{27.23}{64}\\\\sin\theta = 0.4255\\\\\theta = sin^{-1}(0.4255)[/tex]

θ = 0.4395 rad.

Note: We would only consider the positive value of the quadratic root.

For the obtuse interior angles of the trapezoid, we have [tex](\frac{\pi}{2} +0.4395)[/tex]

Similarly, the measure of the acute interior angles of the trapezoid is [tex](\frac{\pi}{2} -0.4395)[/tex]

Read more on isosceles trapezoid here: https://brainly.com/question/4758162

Answer:

[tex]\displaystyle \textcolor{black}{4.}\:[-3, -5][/tex]

[tex]\displaystyle \textcolor{black}{3.}\:[8, -1][/tex]

[tex]\displaystyle \textcolor{black}{2.}\:[4, -7][/tex]

[tex]\displaystyle \textcolor{black}{1.}\:[3, -2][/tex]

Step-by-step explanation:

When using the Elimination method, you eradicate one pair of variables so they are set to zero. It does not matter which pair is selected:

[tex]\displaystyle \left \{ {{2x - 3y = 9} \atop {-5x - 3y = 30}} \right.[/tex]

{2x - 3y = 9

{⅖[−5x - 3y = 30]

[tex]\displaystyle \left \{ {{2x - 3y = 9} \atop {-2x - 1\frac{1}{5}y = 12}} \right. \\ \\ \frac{-4\frac{1}{5}y}{-4\frac{1}{5}} = \frac{21}{-4\frac{1}{5}} \\ \\ \boxed{y = -5, x = -3}[/tex]

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

[tex]\displaystyle \left \{ {{x - 2y = 10} \atop {x + 3y = 5}} \right.[/tex]

{x - 2y = 10

{⅔[x + 3y = 5]

[tex]\displaystyle \left \{ {{x - 2y = 10} \atop {\frac{2}{3}x + 2y = 3\frac{1}{3}}} \right. \\ \\ \frac{1\frac{2}{3}x}{1\frac{2}{3}} = \frac{13\frac{1}{3}}{1\frac{2}{3}} \\ \\ \boxed{x = 8, y = -1}[/tex]

_______________________________________________

[tex]\displaystyle \left \{ {{y = -3x + 5} \atop {y = -8x + 25}} \right.[/tex]

{y = −3x + 5

{−⅜[y = −8x + 25]

[tex]\displaystyle \left \{ {{y = -3x + 5} \atop {-\frac{3}{8}y = 3x - 9\frac{3}{8}}} \right. \\ \\ \frac{\frac{5}{8}y}{\frac{5}{8}} = \frac{-4\frac{3}{8}}{\frac{5}{8}} \\ \\ \boxed{y = -7, x = 4}[/tex]

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

[tex]\displaystyle \left \{ {{y = -x + 1} \atop {y = 4x - 14}} \right.[/tex]

{y = −x + 1

{¼[y = 4x - 14]

[tex]\displaystyle \left \{ {{y = -x + 1} \atop {\frac{1}{4}y = x - 3\frac{1}{2}}} \right. \\ \\ \frac{1\frac{1}{4}y}{1\frac{1}{4}} = \frac{-2\frac{1}{2}}{1\frac{1}{4}} \\ \\ \boxed{y = -2, x = 3}[/tex]

_______________________________________________

I am joyous to assist you at any time.

In order to balance the equation, John should multiply the second side of the equation by s.

Why?

Remember the Golden Rule of Algebra:-

[tex]\bigstar{\boxed{\sf{Whatever~you~do~to~one~side,~you~do~to~the~other.}}[/tex]

So if you multiply 1 side of the equation by s, you multiply the second side by s.

Please tell John about the Golden Rule of Algebra ;)

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

Answer:

Line 2

Step-by-step explanation:

When factoring the second bracket, 1 x -8 is -8.

Answer:

4

Step-by-step explanation:

Answer:

She was finished with dinner at 6:50

Step-by-step explanation:

3:45 + 2 = 5:45

5:45 + 30 = 6:05

6:05 + 45 = 6:50