Mathematics High School

Use the substitution method to solve the system of equations. Choose the correct ordered pair. x + 2y = 12 –x = –y – 6

A. (9, 3)
B. (7, 1)
C. (6, 0)
D. (8, 2)

Answers

Answer 1

Answer: D

Step-by-step explanation:

Answer 2

The ordered pair of the system of equations is (8, 2).

Option D is the correct answer.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x  + 4 = 9 is an equation.

We have,

x + 2y = 12 _____(1)

x = 12 - 2y _____(2)

-x = -y - 6 _______(3)

Putting (2) in (3) we get,

-(12 - 2y) = -y - 6

-12 + 2y = -y - 6

-12 + 6 = -y - 2y

-6 = -3y

y = 2

Now,

y = 2 in (2)

x = 12 - 2 x 2

x = 12 - 4

x = 8

Thus,

The ordered pair is (8, 2).

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Related Questions

A nut mixture of walnuts and cashew nuts at a small fair is $1.00 per pound of walnuts and $3.10 per pound of cashew nuts. Over the entire day, 134 pounds of the nut mixture were sold for $241.10. If p is the number walnuts and n is the number of cashew nuts, then the system of equations that models this scenario is: p+n=134p+3.10n=241.10 Determine the correct description and amount of pounds for walnuts and cashew nuts that were sold.

Answers

a) The description given in the problem statement appears to be correct.

b) The solution to the system of equations can be found many ways. Choose your favorite (including posting on Brainly, if you like). It is
.. p = 83
.. n = 51

83 pounds of walnuts and 51 pounds of cashews were sold.

Answer: 83 pounds of walnuts and 51 pounds of cashew nuts.

Step-by-step explanation:

Let p be the amount of pounds for walnuts and n be the amount of pounds for  cashew nuts that were sold.

Given : A nut mixture of walnuts and cashew nuts at a small fair is $1.00 per pound of walnuts and $3.10 per pound of cashew nuts.

Over the entire day, 134 pounds of the nut mixture were sold for $241.10.

Then, system of equation represents the given situation will be :-

[tex]p+n=134----------(1)\\\\p+3.10n=241.10----------(2)[/tex]

Eliminate (1) from (2), we get

[tex]2.10n=107.1[/tex]

Divide 2.10 from both sides , we get

[tex]n=51[/tex]

Put value of n in (1), we get

[tex]p+51=134\\\\\Rightarrow\ p=134-51=83[/tex]

Hence, the correct description will be : 83 pounds of walnuts and 51 pounds of cashew nuts.

There are 190 students taking band, chorus, or both. If there are 180 students taking band and 60 students in both band and chorus, how many students are only in chorus?

70
60
10
120

Answers

The answer would be 10. I know this because I got it right on my assignment. Have a great day!

If there are 180 students taking band and 60 students in both band and chorus, then 180-60=120 students are taking only band.

Now:

120 students are taking band;60 students are taking both band and chorus;190 students in total.

Then 190-(120+60)=190-180=10 students are taking only chorus.

Answer: correct choice is C.

The area of a rectangle is 16, and its diagonal is 68−−√. find its dimensions and perimeter.

Answers

The perimeter of a rectangle is the sum of twice the length and twice the width.  When a diagonal is drawn across the rectangle, two congruent triangles are formed.  The legs of the triangle are the sides of the rectangle.  Right triangles indicates that we can use the Pythagorean theorem. Let length = xLet width = y  Set the equation based on what we know. 2x + 2y = 22 x + y = 11                   eq1  x2 + y2 = [√65]2               eq2   We have two equations to work with. x + y = 11                eq1 x2 + y2 = 65               eq2  Substitute eq1 into eq2.  From eq1, x = 11 - y x2 = (11 - y)2 x2 = (11 - y)(11 - y) x2 = 121 - 22y + y2  (121 - 22y + y2) + y2 = 65 121 - 22y + 2y2 = 65 2y2 - 22y + 56 = 0 2(y2 - 11y + 28) = 0 2(y - 7)(y - 4) = 0 y = 7       and        y = 4  Substitute these y values into eq1 to solve for x. x = 11 - 7                and              x = 11 - 4 x = 4                       and              x = 7  Each pair of solutions has the same dimensions.  Shorter side = 4Longer side = 7
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Which of the following is an advantage of an observational study over a sample survey? A)Observational studies are not dependent on people’s responses, which may not be truthful.
B)Observational studies involve the random selection of subjects.
C)Observational studies do not manipulate variables.
D)Observational studies do not involve treatments.

Answers

I think it is B)Observational studies involve the random selection of subjects.

Observational studies involve the random selection of subjects.

What is an observational study?

An observational study is used in subjects like epidemiology, social sciences, psychology, and statistics to draw inferences from a sample to a population where the independent variable is not under the researcher's control due to ethical concerns or logistical restrictions.

Observational studies are ones in which a researcher makes observations about his thoughts and views. He observes the risk and other effects before the actual test takes place.

This is usually the initial phase of research where observations are made for the suitability of certain things that are to be researched. There is an initial feasibility test conducted to identify whether the further research process is beneficial or not.

Therefore Observational studies involve the random selection of subjects.

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Solve using substitution

Answers

The first step is to isolate one of the variables from one of the equations. We can pick either variable and either equation. The easiest to pick on is the 'x' from the first equation as the coefficient here is 1.

Isolate x in the first equation. Subtract 3y from both sides
x+3y = 8
x+3y-3y = 8-3y
x = 8-3y
So we can see that x is the same as 8-3y

Now move onto the second equation
3x - 5y = -18
3( x ) - 5y = -18 ... rewrite x so it has parenthesis around it
3( 8-3y) - 5y = -18 ... replace x with 8-3y; solve for y
24-9y - 5y = -18
24-14y = -18
24-14y-24 = -18-24
-14y = -42
-14y/(-14) = -42/(-14)
y = 3

If y = 3, then x is...
x = 8-3y
x = 8-3*3
x = 8-9
x = -1

The x and y values are x = -1 and y = 3
Together they pair up to form the ordered pair (x,y) = (-1,3)

The solution is (-1,3)
If you graph the two original lines, then they cross at (-1,3)

Which statement about the figure below is true?


Select one:
a. Points A, B, and E are not collinear.
b. Points C, F, B, and E are coplanar.
c. Points F, B, and C are collinear.
d. Points C, D, B, and F are coplanar.

Answers

the answer to this question is C

The angles of triangle abc are in the ratio of 8:3:4. what is the maesure of the smallest angle

Answers

Each part of the ratio represents the fractional part of the total angle measurement of the triangle (180 degrees). Ex. Angle A is 8/15 of the sum of the angles, angle b is 3/15, etc. therefore, your answer would be 36 degrees.

Which solid figure has a base that is a polygon and a triangular faves that meet at a vertex

Answers

Right Regular Pyramid
where the base is a polygon of 3 or more sides


Which of the following best describes set of numbers? 6, 9, 12, 15, ... infinite alternating sequence finite geometric sequence infinite arithmetic series infinite arithmetic sequence?

Answers

This is an infinite arithmetic series

Answer:

It is an infinite arithmetic sequence

Step-by-step explanation:

we are given a set of numbers:

6,9,12,15,...

As we can see that

9-6=3

12-9=3

15-12=3

So, given set of numbers are a sequence of arithmetic progression with common difference 3 and terms in the sequence are infinite.

Hence, it is an infinite arithmetic sequence

NEED HELP RIGHT NOW. ASAP!!! PLZ PLZ PLZ HELP ME. YOU WILL GET BRAINLIEST. IF YOU ANSWER FIRST OR IF YOU ARE RIGHT!

Answers

Hey there Jessie!

Let's take to heart a important thing to remember, a circle has a sum of [tex]360[/tex]°. So, were going to really brake this down!

[tex]\boxed{x=107/5=21.400}[/tex]

[tex]\boxed{5*x-6-(101)=0} \\ \\ (Solving \ a \ single \ variable \ equation) \\ \\ 5x-107=0 \\ 5x=107 \\ \\ x=107/5=21.400 \\ \\ Hope \ this \ help![/tex]

x= 15


 here is the work:

101 +37 = 138

138/2 = 69

5x-6 = 69

 add 6 to each side

5x = 75

 divide:

x = 75/5

x = 15

△XYZ∼△DEF , YZ is 10 meters, ​ XZ ​ is 15 meters, and EF is 8 meters.

What is ​ DF ​?

____ m


Answers

Answer:

The measure of KL is 12 meters.

Step-by-step explanation:

It is given that  △XYZ∼△DEF.

The corresponding sides of two similar triangles are proportional.

[tex]\frac{YZ}{EF}=\frac{XZ}{DF}[/tex]

[tex]\frac{10}{8}=\frac{15}{DF}[/tex]

[tex]10\times DF=15\times 8[/tex]

Divide both sides by 10.

[tex]DF=\frac{120}{10}[/tex]

[tex]DF=12[/tex]

Therefore we can say that if △XYZ∼△DEF, then the measure of DF is 12 meters.

Find the area of the shaded region of the trapezoid.

Answers

Area of entire trapezoid = ((sum of the bases) ÷ 2) • height
Trapezoid Area = (51 / 2) * 26
Trapezoid Area = 663

UN-shaded triangle area = .5 * base * height
UN-shaded triangle area = .5 * 23 * 26
UN-shaded triangle area = 299

SHADED Trapezoid Area = 663 -299
SHADED Trapezoid Area = 364


Will graphs for these equations show parallel lines? Explain.

y=6x+1
y=6x-5

Answers

Yes these lines are parallel. They will never cross so there are no solutions to this system.

The reason why is because the two slopes for the equations are both 6 each. The equations are in y = mx+b form where m is the slope. The y intercepts are different (1 for the first; -5 for the second). So those two pieces of info lead to non-intersecting parallel lines. 

Which equation can be rewritten as x + 4 = x2? Assume mc006-1.jpg

Answers

the correct question in the attached figure

we have that
x + 4 = x²
step 1
raise to ^(1/2) both members
(x+4)^(1/2)=(x²)^(1/2)
(+-)√(x+4)=x
but remember that x>0
then
√(x+4)=x

the answer is the option C


Answer:

The answer is C

Step-by-step explanation:

Got it right on edge 2020

Which of the following is equal to sqrt 50a^6b^7

Answers

Your question implies there are choices given with possible answers. As I do not have those in front of me, I will show you how to simplify the radical. It is likely that the answer you seek is the simplified radical.

To simplify [tex] \sqrt{50 a^{6} b^{7} } [/tex] we use the following identity: for positive values of a and b, [tex] \sqrt{ab}= \sqrt{a} \sqrt{b} [/tex]

That identity allows us to re-write what we are given as [tex] \sqrt{50} \sqrt{ a^6 } \sqrt{b^{7} [/tex]. Let us now consider each of these separately.

Though 50 is not a perfect square it can be written as 25 x 2 and 25 is a perfect square. Thus, we obtain [tex] \sqrt{50}= \sqrt{25} \sqrt{2}=5 \sqrt{2} [/tex]

Next we consider [tex] a^{6} [/tex] which is a perfect square as it is equal to [tex] (a^{3}) (a^{3}) [/tex]. Thus, [tex] \sqrt{a^{6}} = a^{3} [/tex]

Lastly, we consider [tex] b^{7} [/tex] which can be written as [tex](b^{1})( b^{6}) [/tex] and since [tex] b^{6} [/tex] is a perfect square we obtain the following: [tex] \sqrt{b ^{7} } =\sqrt{b ^{1}} \sqrt{b^6} = b^{3} \sqrt{b} [/tex]

Putting that all together we obtain [tex]\sqrt{50 a^{6} b^{7} }=25a ^{3}b ^{3} \sqrt{2b} [/tex]

The width of a rectangular prism is w centimeters. the height is 2 centimeters less than the width. the length is 4 centimeters more than the width. of the volume of the prism is 8 times the measure of the length, find the dimensions of the prism

Answers

w x (w-2) = 8
w^2 - 2w = 8
w^2 - 2w - 8 = 0
(w-4)(w+2) = 0

w = 4 Or w = -2

However w cannot be less than 0

So w must = 4

Width is 4, height is 2, length is 8
Total Volume =64 which is 8(8).

Classify the polynomial 3x^5 by degree

A: cubic

B:quadratic

C:quintic

D:quartic

Answers

The answer is:  [C]:  "quintic" .
______________________________________________________
Note:  The prefix "quint-"  is ONE of the prefixes (other than "pent-") that means "5" ; and considering:  "3x⁵ "  ;  we consider the "largest exponent value corresponding to a variable"— which, in the question, is "5" — as the "degree of the polynomial" .
______________________________________________________
Consider:  "Choice:  [A]:  "cubic".  This answer is incorrect.
This choice would be correct IF the polynomial was:  " 3x³ " .
___________________________________________________________
Consider:  "Choice:  [B]:  "quadratic" ;  is incorrect.  
  This would refer to an equation, in "quadratic form" ; that is:  
              " ax² + bx + c = 0 ;  { b[tex] \neq [/tex]0 } . " .
___________________________________________________________
Consider:  "Choice:  [D]:  "quartic" ; is incorrect.  This would refer to:  " 3x⁴ " .
___________________________________________________________

The degree of the given polynomial [tex]3x^5[/tex] is quintic that is 5 and this can be determined by comparing the given polynomial with the generalized quintic equation.

Given :

Polynomial  --  [tex]3x^5[/tex]

The following points should be remembered in order to determine the degree of any polynomial:

The generalized quadratic equation is represented by: [tex]ax^2 + bx + c =0[/tex]

The generalized cubic equation is represented by: [tex]ax^3 + bx^2 + cx + d =0[/tex]

The generalized quartic equation is represented by: [tex]ax^4 + bx^3 + cx^2 + dx+e =0[/tex]

The generalized quintic equation is represented by: [tex]ax^5 + bx^4 + cx^3 + dx^2+ex + f =0[/tex]

So, from the above points, it can be concluded that the degree of the given polynomial [tex]3x^5[/tex] is quintic that is 5. Therefore, the correct option is C).

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A vaccine has 90% probability of being effective in preventing a certain disease. the probability of getting the disease if the person is not vaccinated is 50%. in certain geographic region, 25% of the people get vaccinated. if a person is selected at random , find the probability that he or she will contract the disease

Answers

If 25% of the people are vaccinated, then 75% of the people are not vaccinated.  Of those not vaccinated, each has a 50% chance of contracting the disease.  The probability that someone is both not vaccinated and contracts the disease is (0.75)(0.5)=0.375.
The probability that someone is vaccinated and contracts the disease is (0.25)(0.1)=0.025 (it is multiplied by 0.1 because if the vaccine is 90% effective, then there is a 10% chance someone that is vaccinated can contract the disease.
Add these together for the total:  0.375+0.025=0.4
There is a 40% chance that someone chosen at random will contract the disease.

Answer:

The probability that someone is vaccinated and contracts the disease is (0.25)(0.1)=0.025 (it is multiplied by 0.1 because if the vaccine is 90% effective, then there is a 10% chance someone that is vaccinated can contract the disease.  Add these together for the total:  0.375+0.025=0.4

There is a 40% chance that someone chosen at random will contract the disease.

(05.02 MC)Henry wants to laminate the tabletop in his study room. The tabletop is the shape of an isosceles trapezoid shown here. If laminating costs $4 per square foot, what is the total cost to laminate the tabletop?


Can someone please explain step by step.
Offering all of my points and brainliest answer!!!!!
Please, Please, Please help me out

Answers

First we have to find the area of the trapezoid. 
Let's separate the trapezoid into 3 shapes. Two triangles, and 1 rectangle.(I included an image of an isosceles trapezoid for reference)
First let's find the area of the triangles. We'll use this equation.a = areab = baseh = heighta = b · h · 0.5a = b · 3 · 0.5
We need to find the base of the triangle. To do this, we'll subtract 6 from 10, which equals 4. 4/2= 2 which is the base of the left and right triangle. Let me know if you're confused by that!!
a = 2 · 3 · 0.5a = 6 · 0.5a = 3The area of both triangles is 3.
Now we need to find the area of the rectangle. We'll use this equation.a = b · ha = 6 · 3a = 18
So the rectangle's area is 18, and both triangle's area is 3.18 + 3 + 3 = 24
Now we need to find the cost. 24 · 4 = 96
The answer is $96. 
Hope this helps! :)

Answer:

96

Step-by-step explanation:

What is the volume of a cube with length 7 cm? V = lwh

Answers

the answer is 343 due to the fact that it is all the same length it will just multiply to 343 cause 7x7x7=343

Answer:

it is i also took da test

Step-by-step explanation:


Which description compares the vertical asymptote(s) of Function A and Function B correctly?



Function A: f(x)= 1/ x+4

Function B


Both functions have a vertical asymptote at x=−4 .

Function A has a vertical asymptote at x = 1.
Function B has a vertical asymptote at x = 3.

Function A has a vertical asymptote at x = 4.
Function B has a vertical asymptote at x = 2.

Function A has a vertical asymptote at x=−4x=−4 .
Function B has a vertical asymptote at x = 2.

Answers

Function A has a vertical asymptote at x = -4.

The graph B has  vertical asymptote is 2.

We have given function

A : f(x)=1/(x+4)

Since the rational function has the vertical asymptote  at x=-4  then the denominator of function f(x) contains the term (x+4)

Function B :

What is the vertical asymptote?

A vertical asymptote is is a vertical line that guides the graph of function but is not part of it.

So from the graph we can see that the graph does not pass from the point at x=2

Therefore, the vertical asymptote is 2.

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The lower base of the frustum shown in the figure is a square 8 ft on each side. The upper base is a square 4 ft on each side. If the altitude is 6 ft, find the slant height. A. 6 ft B. 5.66 ft C. 6.32 ft D. 4 ft

Answers

the complete question in the attached figure

the answer is the option C 6.32 ft

this answer is based on the fact that the inclined height should be greater than 6 and that is the only option available

Melanie bought 3 adult tickets and 1 children ticket for $38. John bought 3 adult tickets and 2 children tickets for $52. What is the cost of each type of ticket

Answers

If the cost of adult ticket is x and that of children ticket is y
Then 3x +y = $38
         3x+2y =$52, solving simultaneously
we subtract the two equation,
              -y = -14 
thus; y =14 
to get x we substitute y with 14
            3x = 38-14
              3x =24
                x =8
Therefore, the cost of 1 adult ticket is $8 while the cost of children ticket is $14

can anyone help me with this

Answers

It is convenient to let a spreadsheet program fill these in. If you don't know how to use one, learn. Very good ones are available for free on the web.

See the attachment for the table values.

Obviously, the patterns are similar in that each row is multiplied by some constant to get the next row. They are different in that the constants are different. 2 is used for the left column, so the reward grows less fast than in the right column where 3 is used.

The King's Plan 2 will only be cheaper if the number of squares being filled is less than about 5/8 of the number of squares in the original Plan 1.

look at the pictures below // please help // 50 points

Answers

b.-1\4                                                                                                                       i hope that help             
it is 4 you silly gooses

David is filling five 3/4 quart bottles with a sports drink.His measuring cup only holds 1/4 quart.How many times will David need to fill tje measuring cup in order to fill the 5 bottels

Answers

15 times he has to fill up the 5 bottles.

Which number can each term of the equation be multiplied by to eliminate the fractions before solving? -0.75m-0.5=2+0.25m
-2
-3
-4
-5

Answers

What you must do for this case is to rewrite the equation.
 Rewriting we have:
 -0.75m-0.5 = 2 + 0.25m
 - (3/4) m- (1/2) = 2 + (1/4) m
 To eliminate the fractions we must multiply both sides of the equation by -4
 -4 * [- (3/4) m- (1/2)] = - 4 * [2+ (1/4) m]
 3m + 2 = -8-m
 Answer:
 Each term of the equation can be multiplied by -4 to eliminate the fractions before solving.

How can you express (15 + 30) as a multiple of a sum of whole numbers with no common factor? 2 × (7.5 + 15) 3 × (5 + 10) 5 × (3 + 6) 15 × (1 + 2)

Answers

The sum of 15+30 = 45 and can be expressed as a multiple of prime factors:


(3^2)5



So (15+30) could be expressed as 9*5, but it can not be expressed as a non-repeating multiple of prime factors. 

A pair of shoes costs three times as much as a scarf. The total cost of 1 pair of shoes and 1 scarf is $32. If s represents the cost of 1 scarf, which equation could you use to find the cost of 1 scarf?

Answers

3s+s=32

I did it on TTM and it was correct ^^

Answer:

3s+s=32

Step-by-step explanation:

How much interest would an account earn if 3,000 is invested at an interest rate of 4.8% compounded semiannually for 2 years

Answers

(See attached graphic)
Total = 3,000 * (1 + .048/2)^2*2
Total = 3,000 * (1.024)^4
Total = 3,000 * 1.0995116278
Total = 3,298.53
 





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