Complete the following proof.

Given: 2x + 11 = 15
Prove: x = 2

Statements Reason
1. 2x + 11 = 15 1. Given
2. 2x = 4 2.
3. x = 2 3. Division Property of Equality

The weight of cargo of the truck is represented by;

w ≤ 2,000

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The cargo of the truck weighs at most 2,000 pounds.

Since, The weight of a cargo is at most 2,000 pounds.

Hence, The weight of cargo is less than or equal to 2,000.

Thus, The weight of cargo of the truck is represented by;

w ≤ 2,000

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The weight of the cargo truck is given as w ≤ 2,000

Now it is given that cargo of the truck weighs at most 2,000 pounds.

Let 'w' be the symbol used to represent the weight of the cargo

Thus according to given information, the weight of the cargo can be less than or equal to 2000 pounds

Now a relation by which we can compare two or more mathematical expression is called an inequality.

Thus, the weight of cargo of the truck is represented using inequality as :

[tex]w\leq 2000[/tex]

This is the required answer.

Answer:

Jadzia finished 80% of her homework.

Divide the first number by the second number for each ratio:

A. 1 to 4 = 1/4 = 0.25 = 25%

B. 4 to 1 = 4/1 = 4 = 400%

C. 2 to 5 = 2/5 = 0.4 = 40%

The answer is C.

An equivalent ratio to 40% is 2 to 5, which is option C. The percentage is simplified by dividing it by the greatest common divisor to find its simplest ratio form.

To find a ratio equivalent to 40%, we first understand that percentages are a way of expressing a ratio where the second term is 100. Therefore, 40% is the same as saying 40 out of 100 or 40/100.

Next, we simplify this fraction to its lowest terms. Dividing both numerator and denominator by their greatest common divisor, which is 20 in this case, gives us 2/5. Thus, the ratio equivalent to 40% in its simplest form is 2 to 5, which corresponds to option C.

If we were to check the other options given, A (1 to 4) and B (4 to 1) are equivalent to 25% and 400% respectively, while D (5 to 2) is equivalent to 250%. Hence, these are not correct.

To illustrate the concept, let's consider an example. If the scale dimension is 4 cm, then to find the actual dimension using the proportion 1:2=4:x, we would cross-multiply to find x, which would be 8 cm, showing how ratios can be used to find corresponding values.

I think the answer is C because the question says in one row there are 100 seats so with a total of 100 seats there is a row.

Answer:

D

Step-by-step explanation:

The answer is D because 100 divided by 10 = 10. Hope this helps! ☺

Answer:  a) x = {-3, 3, -3i, 3i}

               b) x = {-√5, √5}

               c) x = {-√3, √3, -i√2, i√2}

Step-by-step explanation:

[tex]a)\ x^4-81=0\\\\(x^2-9)(x^2+9)=0\\\\x^2=9\quad and\quad x^2=-9\\\\x=\pm 3\quad and\quad x=\pm3i[/tex]

[tex]b)\ x^4+10x^2+25=0\\\\(x^2+5)^2=0\\\\x^2=-5\\\\x=\pm i\sqrt5[/tex]

[tex]c)\ x^4-x^2-6=0\\\\(x^2-3)(x^2+2)=0\\\\x^2-3=0\quad and\quad x^2+2=0\\\\x^2=3\qquad and\quad x^2=-2\\\\x=\pm\sqrt3\quad and\quad x=\pm i\sqrt2[/tex]

Answer: OPTION B

Step-by-step explanation:

 Use the following formula:

[tex]SA=\frac{pl}{2}+B[/tex]

Where p is the perimeter of the base, l is the slant height and B is the area of the base.

The perimeter is:

[tex]p=6*s=6*3m=18m[/tex]

Where s is the lenght of a side.

The slant height is given:

[tex]l=6,2m[/tex]

The area of the base is:

[tex]B=\frac{3\sqrt{3}s^2}{2}=\frac{3\sqrt{3}(3m)^2}{2}=23.382m^2[/tex]

Where s is the length of a side.

Substitute values. Then, the result is:

[tex]SA=\frac{(18m)(6.2m)}{2}+23.382m^2=79.18m^2[/tex]

Answer:

The correct answer option is B. 79.18 m^2.

Step-by-step explanation:

We are given a diagram of a regular hexagonal pyramid with height 5.6 m, slant height 6.2 m and base edge length 3m.

We know that the surface area of a regular hexagonal pyramid is given by:

[tex]\frac{PI}{2} +B[/tex]

where P = perimeter of the base, I = slant height and B = base area.

Perimeter of base = [tex]3 \times 6[/tex] = 18 m^2

Base area (area of hexagon) = [tex]\frac{3\sqrt{3} }{2} a^2[/tex] =  [tex]\frac{3\sqrt{3} }{2} 3^2[/tex] = 23.38 m^2

Surface area of hexagonal pyramid = [tex]\frac{18 \times 6.2}{2} +23.38[/tex] = 79.18 m^2

Answer with explanation:

We will use [tex]\frac{28}{36}[/tex] rule here, to prove that, the statement given is Incorrect,which is you can afford to pay a maximum of 1/2 of your monthly income for rent.

[tex]\frac{28}{36}[/tex] rule, states that,you can use , 28% of gross monthly Income for Housing expenses, and 36 % of your gross monthly income is used for Debt purposes.

→→[tex]\frac{1}{2}[/tex] of monthly income =50 % of Monthly Income

we can use ,only 28% of Monthly income for rent Purpose.

False Statement

Answer:

The sides length x of each square windowpane is [tex]10\ in[/tex]

Step-by-step explanation:

we know that

[tex]924\ in^{2}=(6+3x+6)(6+x+6)\\ \\924=(12+3x)(12+x)\\ \\924=144+12x+36x+3x^{2}\\ \\ 3x^{2}+48x- 780=0[/tex]

Solve the quadratic equation

using a graphing tool

The solution is [tex]x=10\ in[/tex]

see the attached figure

Answer:

10 inches is the side length of each square windowpane.

Step-by-step explanation:

Length of the single window plane = x

Width of the single window plane = x

On combining all the windows pane ,length becomes , l= 3x

On combining all the windows pane ,width becomes , b= x

Length of the frame = L = 6 + 3x+ 6 = 12 + 3x

Width of the frame = B = 6 + x+ 6 = 12 + x

Area of the frame, A = L × B = [tex](12+3x)\times (12+x)[/tex]

Given sum of combined area of the 3 windowpanes and frame = [tex]924 inch^2[/tex]

[tex]a + A=924[/tex]

[tex](12+3x)\times (12+x)=924[/tex]

[tex]144+48x+3x^2=924[/tex]

[tex]3x^2+48x-780=[/tex]

[tex]x^2+16x-260=0[/tex]

[tex]x^2+26x-10x-260=0[/tex]

[tex]x(x+26)-10(x+26)=0[/tex]

[tex](x+260)(x-10)=0[/tex]

x = 10 (accept)

x  = -26 (reject)

10 inches is the side length of each square windowpane.

Answer:

Step-by-step explanation:

Supplementary angles mean the angles add up 90 degrees.

So, 4x + 18 + 2x + 12 = 90.

Combine like terms...

6x + 30 = 90

Subtract 30 from both sides.

6x = 60

Divide by 6

x = 10

Then to find the measure of angles RST, we plug in 10 for x.

4(10) + 18 = RST

RST = 40 + 18

RST = 58

Answer:

[tex]\large\boxed{q=4P+4r}[/tex]

Step-by-step explanation:

[tex]\dfrac{q}{4}-r=P\qquad\text{muliply both sides by 4}\\\\4\!\!\!\!\diagup^1\cdot\dfrac{q}{4\!\!\!\!\diagup_1}-4r=4P\\\\q-4r=4P\qquad\text{add}\ 4r\ \text{to both sides}\\\\q=4P+4r[/tex]

➷ It would be y + 23

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The algebraic expression for 23 more than y is y + 23

An algebraic expression usually shows the relationship between a variable and a whole number with its arithmetic operations.

In the given question,

Now when y is more than 23, we have the algebraic expression for 23 more than y as:

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Answer:

t = 1

Step-by-step explanation:

Formula

i = prt

Givens

P = 500

i = 25

r = 5% = 5/100

t = ?

Solution

25 = 500 * 5/100 * t       Cancel out 100 on the right

25 = 5*5*t                        Combine the right

25 = 25 * t                       Divide by 25

25/25 = 25*t/25              

t = 1

Answer:   " 1 year . "

_________________________________________________

Step-by-step explanation:

_________________________________________________

Use the formula/equation:

        I = Prt ;   that is;  " I = P × r × t "  ;

in which:  

" Interest (in dollars) =

     Principal amount ("P" ; in dollars) * r ["rate"]   *  time ("t", in years) ]  ;

Note: the rate, "r" ; refers to the interest rate.

We wish to solve for the "time, "t" .

_________________________________________________

 I = Prt ;

_________________________________________________

Let us isolate "t" one one side of the equation;

    by rearranging the formula;

We know:  I = Prt   ;

Divide each side of the equation by "Pr" :

I/ (Pr) = [ (Prt) / (Pr) ]  ;

to get:

I / (Pr) = t ;

↔  t = I (P * r ) ;

Now, plug in our given values, and solve for "t" ; time, in years.

Given:  P = 500 (dollars) ;

            I  = 25 (dollars) ;  

           r = 5% ;  Note, for the purposes of this formula; we write this as a "decimal" ;

           r = 5% = 5/100 = 0.05 ;

_________________________________________________

 t  =  I / (P * r)  ;

t = 25  / (500 * 0.05) ;

t =  25 / (25) ;

t = 1  yrs.

_________________________________________________

Hope this helps!

 Best wishes in your academic pursuits

        — and within the "Brainly" community, as well!

_________________________________________________

Answer:

4.422, 4.769, 4.904

Step-by-step explanation:

Answer:

LEAST: 4.422

AVERAGE: 4.769

GREATEST: 4.904

I HOPE THIS HELPED !!

Answer:

so A = 45degrees because tan^-1(1) = 45 and c = 30 because the half triangle is a 30-60-90 triangle so d = 105

Since its a 30-60-90 triangle and you know that one of the sides is 6, you can now infer that the rest of the sides are 8, and 10.

Also using the 6 side you can use a 3-4-5 triangle by dividing 6 by 4 wich equals 1.5 then multiply that by 3 to get the other sides by using Pythagorean therom. so the sides are 10, 7.5 and 12.5 witch gives you the bas and since area = 1/2bh area= 1/2(12.5 times 6)= 37.5

A = 37.5

Answer:

The attached picture is the requested graph

Step-by-step explanation:

The system

[tex]y=\frac{3}{2}x-1\\ y= \frac{1}{2}x+3[/tex]

Has the following solution

x = 4 and y = 5 , which serves us to plot the desire graph, both function are lines and they intercept in (4,5)

Answer: A

Step-by-step explanation:

Answer:

Step-by-step explanation:

So you want to start by multiplying so 5×8 = 40 , 5×1=5 , 2×3=6, 7×3=21 , now you take all that and add it together 40+5+6+21

Which your answer is 72

Answer: the answer is D

Step-by-step explanation: there is 8 different strands of outcomes

Answer: D, or 8.

Step-by-step explanation: The first part is a pretty simple win or lose diagram.

That's two possibilities.

The next choice has both Win, both Lose, Lose-Win, or Win-Lose.

That's four possibilities.

The next and last choice is the following: All Win, All Lose, Win-Win-Lose, Lose-Lose-Win, Lose-Win-Win, Win-Lose-Lose, Win-Lose-Win, and Lose-Win-Lose. That leaves a total of 8 combinations.

Answer:

=x=1

 y=1

2nd choice is the correct answer, (1, 1).

The answer is 3 units up

Answer:

25/12 - pounds more vegetables

Step-by-step explanation:

first we need to put these variables into like terms

36/12 - 3

8/12 - 2/3

3/12 - 1/4

add the last two up and subtract from the first and you get how much you need left over

Tim already has 11/12 pounds of vegetables. He requires Problem Solving for an additional 2 1/12 pounds of vegetables to reach the desired 3 pounds for his soup recipe. Therefore, option B is the correct answer.

The problem is asking about the amount of vegetables Tim needs to add to reach a total of 3 pounds for his soup. Given, he already has 2/3 pound of carrots and 1/4 pound of celery, he already has a combined total of 2/3 + 1/4 = 11/12 pounds of vegetables.

Now, we need to find out how many more pounds of vegetables he needs to reach 3 pounds. To do this, subtract the weight of the vegetables he has from the total weight required: 3 pounds - 11/12 pounds = 25/12 or 2 1/12 pounds.

So, Tim needs to add an additional 2 1/12 pounds of vegetables for his soup. Looking at the options given, Tim should choose option B) 1 1/12 pounds of zucchini.

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The probable question may be:

Tim is preparing a vegetable soup recipe that requires a total of 3 pounds of vegetables. Currently, he has 2/3 pound of carrots and 1/4 pound of celery. To make exactly 3 pounds of vegetables, what additional amount of vegetables should Tim add to his existing ingredients?

Additional Information:

  Tim needs 3 pounds of vegetables in total.

  He already has 2/3 pound of carrots.

  He also has 1/4 pound of celery.

Options for Tim to add to his existing ingredients to make a total of 3 pounds:

A) 5/12 pound of broccoli

B) 1 1/12 pounds of zucchini

C) 2/3 pound of spinach

D) 3/4 pound of tomatoes

Answer:

[tex]\large\boxed{4n^5+3.5n^5+(-2.1n^5)=5.4n^5}[/tex]

Step-by-step explanation:

[tex]4n^5+3.5n^5+(-2.1n^5)=4n^5+3.5n^5-2.1n^5\qquad\text{combine like terms}\\\\=(4+3.5-2.1)n^5=5.4n^5[/tex]

Answer:

Because when you square 8 or -8, you will still end up at 64

8 x 8 = 64

(-8) x (-8) = 64

Step-by-step explanation:

Ok so the square root of 64 is both positive and negative 8 because :

8^2= 64 but at the same time:

(-8)^2=64 because - to the power of two becomes positive so it has two answers because both 8 and -8 to the power of 2 is 64

Answer:

Option A

Step-by-step explanation:

We are given that a height is labeled on the triangle in given figure.

We have to find the  that segment which shows the base that correspond to the given height of the triangle

We know that base is that side of triangle on which height is perpendicular.

In the given figure, Height is perpendicular to side A.

Therefore, side A represent the base of triangle.

Hence, line segments A shows base that corresponds to the given height of the triangle.

Option A is true.

No picture

Step-by-step explanation:

Answer:

Step-by-step explanation:

"y/3"  is the symbolic representation of "an unknown number, y, divided by 3."

Note that all terms in 8xy − 9x2 y − 5x + 6, except for the 6, involve a variable, either x or y.  6 is the constant term.

Answer:

2.87

Step-by-step explanation:

2x^2-7=9

2x^2=9+7

2x^2/2=16/2

(square root)x^2=(square root)8

x=2.87

I used this method because I don't know any other method.

Answer:

Sample Response:  I would use the square root property of equality. Because there is no x term, I would just add and divide to get x^2 by itself.  Then I would take the square root.

2x^2 - 7 = 9

2x^2 - 7 + 7 = 9 + 7

2x^2 = 16

2x^2/2 = 16/2

x^2 = 8  (square root of 8 would be square root of 4*2 = 2*square root of 2

x = +/- 2*square root of 2

Answer:

x = -14

Step-by-step explanation:

x/2 = -7

Multiply each side by 2 to get the x by itself

x = -7 * 2

x = -14

The answer would be x= -14

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ 2x-3y=3

First:

Add -2y to both sides

-3y=-2x+3

Next:

Divide both sides by -3

y= 2/3x - 1

The answer

y= 2/3x - 1

✽

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TROLLER

First one is #2

Second one is #1

I'm positive about this

Answer:

Hi there, you can use Pitagoras relationship to solve this up (Without using any other "tool".

Point A is located wheter in (-6,8) or could be located in (-6,8)

Step-by-step explanation:

Point A is 10 units away from the origin, and its x coordinate is -6, using this information, you can draw a triangle  from 0 to -6 (the basis) and using 10 as the hypotenuse, so, you have this equation:

[tex]H^{2} = x^{2} +y^{2}[/tex]

solving for Y variable, you have this

y=±[tex]\sqrt{10^{2}-(-6)^{2}  }[/tex]

Note the combined sing ±, meaning that y=8 is a valid answer and that y= -8 is also a valid answer.

Hope It helps