By elimination, the solution of the system of equations, 2a + 3b = 12 and 5a - b = 13, is (a , b) = (3 , 2).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in a and b, a variable should be eliminated by adding/subtracting the two equations.
Multiply first equation 2 by 3.
5a - b = 13 (equation 2)
15a - 3b = 39
Adding the two equations will eliminate the variable b.
2a + 3b = 12 (equation 1)
15a - 3b = 39 (equation 2)
17a = 51
a = 3
Substitute the value of a to any of the two equations and solve for b.
2a + 3b = 12 (equation 1)
2(3) + 3b = 12
3b = 12 - 6
3b = 6
b = 2
Hence, the solution of the system of equations is (a , b) = (3 , 2).
Learn more about solving systems of equations by elimination here: https://brainly.com/question/28405823
#SPJ4
Write an equation of a circle with the given center and radius. Check your answers.
center (-6,10) , radius 1
The equation of the circle with radius 1 and center at (-6 , 10) is (x + 6)^2 + (y - 10)^2 = 1.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (-6 , 10)
r = 1
(x - -6)^2 + (y - 10)^2 = 1^2
(x + 6)^2 + (y - 10)^2 = 1
Learn more about equation of a circle here: https://brainly.com/question/14150470
#SPJ4
Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms. y=6 x-x²+1
The function y = 6x - x² + 1 already defined is a quadratic function.
-x² is its quadratic term6x is its linear term1 is its constant valueWhat is a function?A function is the definition of a mathematical expression or equation that helps us to give a visual representation, through graphs to analyze the behavior of the same, a function is not real when it cuts the vertical axis at a same point of x.
The given function is given by means of the expression
y=6x -x²+1
y = -x² + 6x + 1 , it is a quadratic function because of its exponent "2".
Where we can separate each of the terms or parts:
y =f(x) is the image of the function-x² is the quadratic term6x is the linear term1 is the constantLearn more about functions at:
https://brainly.com/question/13473114
#SPJ4
A= h(b+c) solve for b
Answer:
A=h(b+c) solve for c
First, multiply h to b and c
A = hb + hc
Then, transfer hb to the other side and change its sign from positive to negative.
A – hb = hc
To get c, Divide both sides by h
(A – hb)/h = hc/h
(A - hb)/h = c OR c = (A – hb)/h
Example. Let us assume the following. A = 500 ; h= 10;b= 20; c= ?
c = (A – hb)/h
c = (500 – (10*20))/10
c = (500 – 200)/10
c = 300/10
c = 30
To check; use the original equation given.
A = h(b+c)
A = 10(20+30)
A = 200 + 300
A = 500. same as the figure given in the example.
[tex]\displaystyle\\Answer:\ b=\frac{A-hc}{h}[/tex]
Step-by-step explanation:
[tex]\displaystyle\\A=h(b+c)\\A=hb+hc\\A-hc=hb+hc-hc\\A-hc=hb\\Divide\ both\ parts\ of\ the\ equation\ by\ h(h\neq 0):\\\frac{A-hc}{h}=b\\ Hence,\\b=\frac{A-hc}{h}[/tex]
7
2-2
3-3
Question 6(Multiple Choice Worth 1 points)
(02.05 MC)
If the parent function f(x) = |x| is transformed to g(x) = |x - 3|, what transformation occurs from f(x) to g(x)?
The graph of f(x) is shifted upward to create g(x).
The graph of f(x) is shifted downward to create g(x).
The graph of f(x) is shifted to the right to create g(x).
The graph of f(x) is shifted to the left to create g(x).
Question 7(Multiple Choice Worth 1 points)
(02.05 MC)
Set
Answer: The graph of f(x) is shifted to the right to create g(x).
Step-by-step explanation:
g(x) is the graph of f(x) shifted right 3 units.
Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer.
15,36,39
The following set of numbers, 15, 36, and 39, can be the measures of the sides of a right triangle.
A triangle is a polygon with three sides and three vertices.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 15, b = 36, and c = 39
a + b > c 15 + 36 > 39 51 > 39 True
a + c > b 15 + 39 > 36 54 > 36 True
b + c > a 36 + 39 > 15 75 > 15 True
To know what type of triangle based on the length of its side:
1. Take the sum of the squares of the two smaller sides.
15^2 + 36^2 = 1521
2. Compare it to the square of the largest side.
39^2 = 1521
1521 = 1521
If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.
if they are equal, it is a right triangle
if they are smaller, then it is an obtuse triangle.
Hence, 15, 36, and 39 can be the measure of the sides of a right triangle.
To learn more about types of triangle based on side lengths: brainly.com/question/13619935
#SPJ4
Leah is deciding between two truck rental companies. Company A charges an initial fee of $60 for the rental plus $1.50 per mile driven. Company B charges an initial fee of $30 for the rental plus $2.50 per mile driven. Let AA represent the amount Company A would charge if Leah drives xx miles, and let BB represent the amount Company B would charge if Leah drives xx miles. Write an equation for each situation, in terms of x,x, and determine the number miles driven, x,x, that would make the cost of each company the same.
AA=60+1.50x and BB=30+2.50x are the two required situations and the number miles driven, x,x, that would make the cost of each company the same is 30.
What is Equation?Two expressions with equal sign is called as Equation.
Company A charges an initial fee of $60 for the rental plus $1.50 per mile driven= 60+1.50x
Company B charges an initial fee of $30 for the rental plus $2.50 per mile driven=30+2.50x.
60+1.50x=30+2.50x
60-30=2.50x-1.50x
30=x
Therefore, AA=60+1.50x and BB=30+2.50x are the two required situations and the number miles driven, x,x, that would make the cost of each company the same is 30.
To learn more on equation click: https://brainly.com/question/28703027
#SPJ1
the andersons can set up 6 tables in 1 hour how many tables can they set up in 5 hours
They can set up total 30 tables in 5 hours.
How is a multiplication explained?Multiply in mathematics refers to the continual addition of sets of same size.
2 × 3 = 6
It can be interpreted this way:
Three times two equals six.
Three times two equals six.
Six is two threes.
Given,
Andersons can set up 6 tables in 1 hour
Tables they can set up in 5 hours = 5 × 6
= 30
To learn more about multiplication from given link
https://brainly.com/question/4721701
#SPJ9
i thought of a number added 6 divided the results by 4 i got 13 if x is my number what's the equation
Answer:
x+6/4=13
Step-by-step explanation:
the result is 11.5
HELPPP ASAPPPP
which expression is equivalent to 5(2.47y − 2.03)?
A.)12.35y + 10.15
B.)12.35y − 10.15
C.) 12.35y + 2.03
D.) 12.35y − 2.03
Answer:
5(2.47y−2.03)
Use the distributive property to multiply 5 by 2.47y−2.03.
12.35y−10.15
Step-by-step explanation:
Find the value of each variable (3x+31)° (2x-6)°
Answer:
x = 31°Step-by-step explanation:
Angle (3x+31)° and angle (2x-6)° are supplementary angles
(3x + 31)° + (2x - 6)° = 180°
5x + 25° = 180°
5x = 155°
x = 31°
-----------------
check
3 * 31 + 31 + 2 * 31 - 6 = 180
180 = 180 (remember PEMDAS)
the answer is good
Write the equation of the line in slope-intercept form.
(x/6) - (5/12)y = 5/8
The equation of the line in slope-intercept form is y = (2/5)x + (-3/2) .
The equation of a line in slope-intercept form can be written as follows,
y = mx + c equation 1
m in the above equation represents slope of the line and c represents the intercept.
The given equation is (x/6) - (5/12)y = 5/8 .
To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as
(x/6) - (5/12)y = 5/8
On multiplying both sides of above equation by (12/5), we will get
(2/5)x - y = 3/2
⇒ y = (2/5)x + (-3/2) equation 2
On equating equation 1 and equation 2, we will get
Slope of the line = m = 2/5
Intercept = c = -3/2
The equation of the line in slope-intercept form is y = (2/5)x + (-3/2) .
To know more about Slope Intercept form refer to the link:
https://brainly.com/question/19440459
#SPJ4
A 3-gallon bottle of fabric softener costs $40.32. What is the price per pint?
(3-x/2)-(1-x/3)=7-(x-x/2)
(3-[tex]\frac{x}{2}[/tex])-(1-[tex]\frac{x}{3}[/tex])=7-(x-[tex]\frac{x}{2}[/tex])
The value of x is 15.
(3 - x/2) - (1 - x/3) = 7 - (x - x/2)
(6 - x/2) - (3 - x/3) = 7 - (2x - x/2)
(6 - x/2) - (3 - x/3) =14 - 2x +x /2
by solving these equations we get ,
18 - x -6 = 42 - 3x
12 - 42 = - 2x
where, x = 15 .
therefore the value of x is 15.
In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
There are three major forms of linear equations ; point-slope form, standard form, and slope-intercept form.examples of equation and expression.
For example, 3x - 2 is an expression. While on the other hand, an equation means that two different expressions are connected to each other by an equal to sign in between, For example, 3x - 2 = 5 + x is an equation.to know more about mathematical equations;
visit ; brainly.com/question/16392987
#SPJ9
The diagrams below show two cereal boxes of different sizes and prices. (a) big box 500 g $8.00 small box 300 g $5.40 Which of the boxes is better value for money? Show your workings.
Answer: Small box has the lowest amount when divided, that box has the best value.
Step-by-step explanation:
Given data,
Big box = 500 g
It cost is $8.00
Small box = 300 g
It cost is $ 5.40
First switch the box that's in kilograms into grams.
One kilogram=1000 grams.
Then, Big box = 500 g = $ 8.00
Small box = 300 g = $ 5.40
Next divide the amount in each box by the cost of each box.
Big box = 500/8
Big box = 62.5
Small box = 300/540
Small box = 0.5555
Therefore,
So, since small box has the lowest amount when divided, that box has the best value.
Learn more about event correlation here: brainly.com/question/16430111
#SPJ9
3(4x −2)=2(5x +3) yo i need this fast
Answer:
x=2
Step-by-step explanation:
Answer:
x=6
Step-by-step explanation:
3(4x-2)=2(5x+3)
12x-6=10x+6
+6 +6
12x=10x+12
-10x -10x
2x=12
Divide by 2.
x=6
Hope this helps.
Draw a right triangle with side lengths that form a Pythagorean triple. If you double the length of each side, is the resulting triangle acute, right, or obtuse? if you halve the length of each side? Explain.
If you double or halve the length of each of Pythagorean triplet the resulting triangle will always be Right Triangle.
Pythagoras Theorem states that the sum square of two sides of triangle is equal to the square of longest side.
Let us take Pythagorean triplet as (6,8,10).
where base=6
perpendicular = 8
hypotenuse = 10
Part(a)
Let us double the length of each value
base = 12
perpendicular = 16
hypotenuse = 20
By Pythagoras Theorem
[tex]base^{2} +perpendicular^{2} =hypotenuse^{2}[/tex]
[tex]12^{2} +16^{2} =20^{2} \\ \\ 144+256=400\\ \\ 400=400[/tex]
Therefore the Triangle will be a Right Triangle as Pythagoras Theorem is satisfied.
Part (b)
Let us halve the length of each value
base=3
perpendicular = 4
hypotenuse = 5
By Pythagoras Theorem
[tex]base^{2} +perpendicular^{2} =hypotenuse^{2}\\\\3^{2} +4^{2} =5^{2}[/tex]
[tex]9+16=25\\ \\ 25=25[/tex]
Therefore the Triangle will be a Right Triangle as Pythagoras Theorem is satisfied.
Therefore , If you double or halve the length of each of Pythagorean triplet the resulting triangle will always be Right Triangle.
Learn more about Pythagoras Theorem here https://brainly.com/question/11852963
#SPJ4
round 13.891 to the nearest tenth, i need help with math homework
Answer:
13.9
Step-by-step explanation:
13.891
the 9 is greater than 4 so it can round up the 8 to a 9
The measure of an angle is 51.1°. What is the measure of its complementary angle?
Answer:
let the complementary angle be x
51.1°+x=90°
x=90°-51.1°
x=38.9°
i need help asap!!!!!!!
Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition.
Measures less than m∠ 5
The exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).
What is meant by Exterior Angle Inequality Theorem?According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles. The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.
A triangle's exterior angle is always greater than its two remote interior angles.
By the Exterior Angle Inequality Theorem, the exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).
m ∠ 7 < m ∠ 5 and m ∠ 8 < m ∠ 5 .
Therefore, the correct answer is ∠ 7 and ∠ 8.
To learn more about Exterior Angle Inequality Theorem refer to:
brainly.com/question/956912
#SPJ4
Trigonometry question
Answer:
[tex]\frac{8\sin 72^{\circ}\sin 34^{\circ}}{\sin 116^{\circ}}[/tex]
Step-by-step explanation:
In triangle ABD,
[tex]\sin 72^{\circ}=\frac{BD}{8} \implies BD=8 \sin72^{\circ} [/tex]
In triangle BCD,
∠CBD=34° (isosceles triangle)
∠DCB=116° (sum of angles in a triangle)
[tex]\frac{BC}{\sin 34^{\circ}}=\frac{8\sin 72^{\circ}}{\sin 116^{\circ}} \\ \\ BC=\frac{8\sin 72^{\circ}\sin 34^{\circ}}{\sin 116^{\circ}}[/tex]
Answer:
4.59 cm to nearest hundredth.
Step-by-step explanation:
Consider triangle ABD.
sin 72 = DB / 8
DB = 8 sin 72
= 7.608 cm.
Imagine a line from point C perpendicular to DB at point E.
As triangle CDB is isosceles ( DC = BC), this line will cut DB in 2
so, DE = 1/2 * 7.608 = 3.804.
Now consider triangle DCE which is a right-angled triangle at E.
cos 34 = 3.804 / DC
DC = 3.804 / cos 34
= 4.588 cm
BC = DC = 4.588.
A 3-gallon bucket of paint costs $ 81.60. What is the price per pint?
Answer: $3.40 per pint
Step-by-step explanation:
1 gallon=8 pints
3 gallons * 8 pints/1 gallon=
3*8/1=
3*8=24 pints in 3 gallons
$81.6 for 24 pints of paint
81.6/24=$3.40 per pint
Solve the word problem below using the steps given in the lesson.
Skylar needs $56 to buy a new video game. If he doubles the amount of money he has now, he will have enough to buy the game with $8 left over.
How much money does Skylar have right now?
Answer:
32
Step-by-step explanation:
Step-by-step explanation:
If he doubles the amount of money he has now, he will have enough to buy the game with $8 left over. 2x=56+8 ; 2x=64 ; x=64/2 ; x=32. Skylar has $32 right now.Nov 12, 2020©
A rental car company charges $48 per day to rent a car and $0.08 for every mile
driven. Bilquis wants to rent a car, knowing that:
. She plans to drive 175 miles.
. She has at most $110 to spend.
Write and solve an inequality which can be used to determine x, the number of days Bilquis can afford to rent while staying within her budget.
The number of days Bilquis can afford to rent while staying within her budget is 2 days.
How to solve the inequalityThe question has the following data
amount charged = $48
Rent per mile = $0.08
The mile to drive = 175 miles.
Amount to spend = 110 dollars
The inequality would be written as
48x + 0.08(175) ≤ 110
we are to solve for the value of x
this would be
48x + 14 ≤ 110
48x ≤ 110 - 14
48x ≤ 96
We have to divide through by 48
x ≤ 96 / 48
x ≤ 2
Hence we can say that the number of days Bilquis can afford to rent while staying within her budget is 2 days.
Read more on inequalities here:
https://brainly.com/question/24372553
#SPJ1
[tex]\frac{1}{4} + \frac{-3}{4}[/tex]
Answer:
-1/2
[tex] - \frac{1 }{2} [/tex]
First the two fours cancel out so it's becomes
[tex] \frac{1 - 3}{4} [/tex]
then subtract
[tex] \frac{ - 2}{4} [/tex]
simplify
[tex] \frac{ - 1}{2} [/tex]
If x = −4 and y = −5, what is the value of 5x + 3y + 14? A. −49
B. −21 C.41 D. 49
Answer:
the value it's -21
Step-by-step explanation:
5×(-4)+3×(-5)+14=
-20 + (-15) + 14=
-20 -15 + 14=
-35 + 14=
-21.
Below is the relationship for miles per hour for 3 different people and their car speeds. Which "Will" has a greater slope? Identify EACH slope for all THREE graphs to come to a conclusion.
Answer:
Step-by-step explanation:
A sloping line on a speed-time graph represents an acceleration . The sloping line shows that the speed of the object is changing. The object is either speeding up or slowing down. The steeper the slope of the line the greater the acceleration.
Please resolve it and list the steps the simplest way possible, thanks. ASAP if possible
Step-by-step explanation:
Looks like it's a piecewise defined function. Where you see a circle, means it's not inclusive so at f(1) it should be define at y=3
Divide the quantity 3.185 times ten raised to the seventeenth power end quantity divided by the quantity 9.1 times ten raised to the eighth power end quantity.. write the final answer in scientific notation. 3.5 x 108 0.35 x 109 3.5 x 109 0.35 x 1025
On dividing 3.185 × [tex]10^{17}[/tex] by 9.1 × [tex]10^{8}[/tex] the final answer in scientific notation is 3.5 ×[tex]10^{8}[/tex] .
The quantity 3.185 times ten raised to the seventeenth power can written as 3.185 × [tex]10^{17}[/tex] .
The quantity 9.1 times ten raised to the eighth power can written as 9.1 × [tex]10^{8}[/tex] .
On dividing 3.185 × [tex]10^{17}[/tex] by 9.1 × [tex]10^{8}[/tex] ,
( 3.185 × [tex]10^{17}[/tex] )/( 9.1 × [tex]10^{8}[/tex] ) = 0.35 × [tex]10^{17-8}[/tex] = 0.35 ×[tex]10^{9}[/tex] = 3.5 ×[tex]10^{8}[/tex] (in scientific notation)
Scientific notation is a floating-point system in which the numbers are expressed as the products consisting of a number between one to ten multiplied by an appropriate power of ten.
On dividing 3.185 × [tex]10^{17}[/tex] by 9.1 × [tex]10^{8}[/tex] the final answer in scientific notation is 3.5 ×[tex]10^{8}[/tex] .
To know more about Scientific notation refer to the link:
https://brainly.com/question/10401258
#SPJ4
9.233050612 es el número racional o irracional
9.233050612 is a rational number.
What are rational and irrational numbers?Real numbers that can be expressed as a ratio of two integers, such as P/Q, where Q is not equal to zero, are referred to as rational numbers. Finite or repeating numbers are included in the category of rational numbers.
Real numbers are referred to as irrational numbers if they cannot be represented as the ratio of two integers. These are composed entirely of non-terminating, non-repeating numbers.
The given number 9.233050612 can be written in the form P/Q as :
9.233050612 = [tex]\frac{9.233050612}{1000000000}[/tex]
Hence, the given number is a rational number.
To know more about rational and irrational numbers visit:
https://brainly.com/question/17450097
#SPJ9
The correct question is:
"9.233050612 is a rational or irrational number"
