By substitution, the solution of the system of equations, r + s = -12 and 4r - 6s = 12, is (-6 , -6).
A system of linear 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 both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in r and s,
r + s = -12 (equation 1)
4r - 6s = 12 (equation 2)
Using the first equation, find the value of one variable, lets say r, in terms of the other.
r + s = -12 (equation 1)
r = -12 - s
Substitute the value of r to the second equation.
4r - 6s = 12 (equation 2)
4(-12 - s) - 6s = 12
-48 - 4s - 6s = 12
Combining all terms containing the variable s on one side and the constants on the other side of the equality, and solving for s.
-48 - 4s - 6s = 12
-4s - 6s = 12 + 48
-10s = 60
s = -6
Substitute the value of s in the equation of r and solve for r.
r = -12 - s
r = -12 - (-6)
r = -12 + 6
r = -6
Hence, the solution of the given system of equations is (-6 , -6).
To learn more about solving systems of equations: brainly.com/question/25869125
#SPJ4
In Exercises 21-23, write and graph an inequality for the given solution set.
21. {x|x > 3}
22. {p p ≤ 0}
23. {ww≥-6}
if you already have the answer and just need the graph, you can look for it on Desmos. Just write the answer and it will show you. Hope this helps.
Look at the pattern shown.
144,72,36,. . .
b. What is the first non-integer number in this pattern?
Non-Integer numbers are those that are not whole numbers, whole numbers that are negative numbers, or zero.
The first non-integer number in this pattern is 4.5
What is a non- integer?Non-Integer numbers are those that are not whole numbers, whole numbers that are negative numbers, or zero.Any number that isn't a member of the integer set is referred to as a non-integer, and its expressions are -4, -3, -2, -1, 0, 1, 2, 3, 4.Imaginary numbers, fractions, and decimals are a few non-integer examples.Example = 3.14, 1.414, and 1.763The pattern is as follows,
144/2 = 72
72/2 = 36
36/2 = 18
18/2 = 9
9/2 = 4.5.
4.5 is the first non-integer number in this pattern.
Therefore, the first non-integer number in this pattern is 4.5.
To learn more about non-integers, refer to:
https://brainly.com/question/24337155
#SPJ4
Solve each equation. 4 y-6=2 y+8
The solution of the linear equation in one variable 4y - 6 = 2y + 8 is at y = 7.
According to the given question.
We have a linear equation in one variable.
4y - 6 = 2y + 8
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, the solution of the linear equation in one variable 4y - 6 = 2y + 8 is given by
4y - 6 = 2y + 8
⇒ 4y - 2y - 6 = 8 ( subtracting 2y from both the sides)
⇒ 2y -6 -8 = 0 (subtracting 8 from both the sides)
⇒ 2y - 14 = 0
⇒ 2y = 14
⇒ y = 14/2
⇒ y = 7
Hence, the solution of the linear equation in one variable 4y - 6 = 2y + 8 is at y = 7.
Find out more information about equation here:
https://brainly.com/question/28583552
#SPJ4
Solve each formula for the indicated variable. A = 1/2h(b₁ + b₂) , for b₂
The solution of the formula A = 1/2h(b₁ + b₂) for the indicated variable b₂ is (2A/h) - b₁.
According to the given question.
We have a formula A = 1/2h(b₁ + b₂).
Since, we have to solve the given formula A = 1/2h(b₁ + b₂) for the indicated variable b₂.
Therefore, the solution of the formula A = 1/2h(b₁ + b₂) for the indicated variable b₂ is given by
A = 1/2h(b₁ + b₂)
⇒ 2A = h(b₁ + b₂) (multiplying both the sides by 2)
⇒ 2A/h = b₁ + b₂ (dividing both the sides by h)
⇒ 2A/h - b₁ = b₂ ( subtracting b₁ from both the sides)
⇒ b₂ = (2A/h) - b₁
Hence, the solution of the formula A = 1/2h(b₁ + b₂) for the indicated variable b₂ is (2A/h) - b₁.
Find out more information about formula here:
https://brainly.com/question/14870407
#SPJ4
Find each measure. Assume that segments that appear to be tangent are tangent.
m XYZ-
The angle made by ∠MLPQR = 49°.
What is an Angle:
In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The word “angle” is derived from the Latin word “angulus”, which means “corner”. The two rays are called the sides of an angle, and the common endpoint is called the vertex. The angle that lies in the plane does not have to be in the Euclidean space. In case if the angles are formed by the intersection of two planes in the Euclidean or the other space, the angles are considered dihedral angles. The angle is represented using the symbol “∠”. The angle measurement between the two rays can be denoted using the Greek letter θ, α, β etc. If the angles are measured from a line, we can find two different types of angles, such as a positive angle and a negative angle.
Now,
We know that One unit circle. = 360°
intercepted arc PSR = 360° - 131°= 229°
Now,
MLPQR = 1 / 2 (Difference of intercepted arcs)
1/2 (MPSR - MRP)
=1 /2 (229-131)
= 98 / 2 = 49°
To know more about "Angle"
Refer this link:
https://brainly.com/question/25716982
#SPJ4
What is -1 1/2 x -5 2/3 ?
Answer:
17/2 (or) 8.5
Step-by-step explanation:
Let's solve the problem,
→ -1 1/2 × -5 2/3
→ (-3/2) × (-17/3)
→ 17/2 (or) 8.5
So, the answer is 17/2.
A (vector, reflection) is a congruence transformation.
Congruent transformations can be divided into three categories: rotation, translation, and reflection. We can accurately characterize translations by using vectors.
What is the name of a congruence transformation?
A congruent transformation, also known as a congruence transformation, is: Isometry's other name; see congruence (geometry).
Is reflection a transition that congruence?
Congruence transformations can be divided into three categories: reflections (flips), rotations (turns), and translations (slides). These transformations for congruence can be applied to obtain congruent shapes or to confirm the congruence of two shapes.Learn more about congruence
brainly.com/question/7888063
#SPJ4
Mr Ankomah bought some story books at Ghc5.00 each from a bookshop. Twelve of the books got missing. He then sold the rest at Ghc 7.00 each and made a profit of Ghc150.00. How many books did Mr. Ankomah buy?
From the calculation below, the number of books bought by Mr. Ankomah was 87 books.
How do we calculate the number of units bought?Let x represent present the number of books bought.
Therefore, we have:
Number of books sold = x - 12
Total revenue from units sold = Number of books sold * Unit selling price = (x - 12) * 7 = 7x - 84
Total cost of units sold = Number of books sold * Cost price per unit = (x - 12) * 5 = 5x - 60
Profit = Total revenue from units sold - Total cost of units sold ........... (1)
Since he made a profit of Ghc150.00, we substitute all the relevant values into equation (1) and solve for x as follows:
150 = (7x - 84) - (5x - 60)
150 = 7x - 84 - 5x + 60
150 + 84 - 60 = 7x - 5x
174 = 2x
x = 174 / 2
x = 87
Learn more about profit here: https://brainly.com/question/15293328.
#SPJ1
A zoo has an agreement with the local farmers. they sell the daily waste from their elephants to the farmers for $5.00 per pound. if the amount of waste produced by the elephant on a given day is at the 10th percentile of the distribution of waste, how much money would the zoo make selling the waste that day?
Answer:0.86
Step-by-step explanation:
The Perez family saves 3% of their monthly income for their summer vacation. This past year, they saved $774 for their vacation. What is their monthly income?
Answer:2,166
Step-by-step explanation:
Find the center and the radius of each circle. (x+3)²+(y-5)²=38
The equation of the circle (x + 3)^2 + (y - 5)^2 = 38 has a radius of √38 and a center located at (-3 , 5).
The standard 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.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, (x + 3)^2 + (y - 5)^2 = 38, is in standard form, then
h = -3
k = 5
r = √38
Hence, the equation of the circle (x + 3)^2 + (y - 5)^2 = 38 has a radius of √38 and a center located at (-3 , 5).
Learn more about equation of a circle here: https://brainly.com/question/1559324
#SPJ4
Subtract
5/2 - 6/8
help!
Answer:
11/12
Step-by-step explanation:
Point K is located at (-6, -3) on the coordinate plane. Point K is reflected over
the y-axis to create point K'. What ordered pair describes the location of K'?
Point K is located at (-6, -3) on the coordinate plane. Point K' is produced by reflecting point K over the y-axis. The ordered pair of the described location is K'(6,-3).
Given that,
Point K is located at (-6,-3) on the coordinate plane.
The sign of the x-coordinate is altered by reflection across the y-axis:
When a point is reflected across the x-axis, the x-coordinate stays constant, but the y-coordinate is thought to be the additive inverse. The x-axis shows a reflection of the point (x, y) as (x, -y).
When a point is reflected across the y-axis, the y-coordinate remains constant, but the x-coordinate is believed to be the additive inverse. The y-axis shows a reflection of the point (x, y) as (-x, y).
That is,
(x,y)⇒(-x,y)
K(-6,-3)⇒[tex]K^{'}[/tex](6,-3)
Therefore, the Point K is reflected over the y-axis to create point K'(6,-3).
To learn more about reflecting visit: https://brainly.com/question/15487308
#SPJ1
Gavin bikes 7.6 miles each day. How far does Gavin bike in 10 days?
Use the given information to determine whether LM is a perpendicular bisector, median, and/or an altitude of ΔJ K L .
LM ⊥ JK and JL ≅ KL
If LM ⊥ JK and JL ≅ KL, we can prove ΔJLM ≅ KLM by HL. Therefore, we know that JM ≅ MK by CPCTC, making M the midpoint of JK. Therefore, is the perpendicular bisector, median, and altitude of ΔJKL.
What is meant by CPCTC?CPCTC is an abbreviation for "corresponding parts of congruent triangles are congruent," and it states that if two or more triangles are congruent, their corresponding angles and sides are also congruent.
CPCTC is frequently used at or near the end of a proof in which the student is asked to demonstrate that two angles or two sides are congruent. It means that if two triangles are proven to be congruent, the three pairs of sides that correspond must also be congruent, as must the three pairs of angles that correspond.
Since LM ⊥ JK and JL ≅ KL, we can prove ΔJLM ≅ KLM by HL. Therefore, we know that JM ≅ MK by CPCTC, making M the midpoint of JK. Therefore, is the perpendicular bisector, median, and altitude of ΔJKL.
To learn more about CPCTC refer to:
https://brainly.com/question/6076251
#SPJ4
If kirndeep borrows $3000 at 14%/a compounding daily for 38 months. What is the time of this loan in years, rounded to one decimal?
Answer:
Time of loan in years = 3.167 = 3.2 years rounded to 1 decimal
Step-by-step explanation:
The question is only asking for the number of years, not the accrued principal. This should be straightforward:
38 months = 38/12 years = 3.166.... = 3.2 years rounded to 1 decimal point
Here are the accrued amount and interest computations in case you need them:
14% interest annually = 0.14 decimal
Since it is compounded daily we have to divide by 365, the number of days in a year
Also the time period will now be 365 x number of years = 365 x 3.2 = 1168 since it is being compounded daily
At 14% compounded daily, the accrued amount will be
[tex]A = \left( 1 + \dfrac{0.14}{365}\right)^{(365)( 3.2)} = \$4,695.13\\\\\mathrm{Interest } = \$4,695.13 - \$3000 = \$1,695.13[/tex]
HELP NOW PLEASE
Write the domain and range of each relation in interval notation, and then determine if each relation is a function or not.
Answer:
Perhaps this could help :) xx
Answer:
Step-by-step explanation:
A: D:(-6,6)
B: D:(-7,5]
C: Not a function D: -5
D: Not a function D:(-4,4)
E: Not a function D:(0,∞)
F: D:[0,∞)
G: D:[-3,5)
H: D:(-4,2)
I: D:[-3,4]
J: Not a function D:(-3.-4)
K: D:(-∞,∞)
L: D:(-∞,∞)
Circle J has a radius of 10 units, ®K has a radius of 8 units, and BC = 5.4 units. Find the measure.
AD
A circle is a curve sketched out by a point moving in a plane. The length of the side AD is 30.6 units.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
The Diagram for the given details is shown below.
The length of the different sides of the triangle can be written as,
AJ = JC = Radius of circle J = 10 units
BK = KD = Radius of circle K = 8 units
BC = 5.4 units
JB = JC - BC
= Radius of circle J - BC
= 10 units - 5.4 units
= 4.6 units
KC = KB - BC
= Radius of circle K - BC
= 8 units - 5.4 units
= 2.6 units
Now, the length of AD can be written as,
AD = AJ + JB + BC + CK + KD
= 10 units + 4.6 units + 5.4 units + 2.6 units + 8 units
= 30.6 units
Hence, the length of the side AD is 30.6 units.
Learn more about Circle here:
https://brainly.com/question/11833983
#SPJ4
give the prime factors
1.75
2.102
3.98
4.250
5.54
6.36
sagutin nyu bukas pasahan neto bilissssss hyup bagal broo
Answer:
to solve for a¹,replacen=1
Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample. [Lesson 2.3]
If x²=25 , then x=5 ,
According to the given statement the given data is true.
we can see that the number 5 is a perfect square of 25.
In math, what constitutes a perfect square?Informally: When someone multiplies an integer (a "whole" number, positive, negative, or zero) by itself, mathematics resulting product is known as a square number, a perfect square, or simply "a square." So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on are all square numbers.
How do you find a perfect square?To check the accuracy of your square, simply calculate the exact square root of something like a given value. If the square root seems to be an integer, your number is the perfect square. Let's compute the squares of something like the following numbers: 49 and 53. 49 = 7 - 7 is an integer number 49 is a perfect square.
Briefing:As can be seen, the calculated value is:
x²=25 , then x=5
While find the square root of the given number of:
x²=25
x = √25
x=5
So,
we can see that the number 5 is a perfect square of 25.
To know more about perfect square visit:
https://brainly.com/question/385286
#SPJ4
Position and label each triangle on the coordinate plane.
equilateral ΔD E F with sides 4 b units long
Equilateral ΔD E F with sides 4 b units long has been plotted below.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.
An equilateral triangle is a triangle whose all sides are the same.
The all interior angle of an equilateral triangle is 60 degrees.
The length of each side of the given equilateral ΔDEF is 4b.
Hence "Equilateral ΔD E F with sides 4 b units long has been plotted below".
For more about triangles,
https://brainly.com/question/2773823
#SPJ4
A salesperson earns 11% commission on sales. The equation for the amount she earns in commission is c = 0.11s, where s is the amount sold. How much commission will she earn if the amount sold is $5000?
Answer:
550$
Step-by-step explanation:
Plug in 5000 as [tex]s[/tex] is our equation: [tex]c=0.11s[/tex] → [tex]c=0.11(5000)[/tex].
Answer:
550
Step-by-step explanation:
Write an explicit formula for each sequence. Then generate the first five terms. a₁ =7, r=1
The formula of the geometric sequence is a(n) = 7, which is a constant sequence. The first five terms are 7, 7, 7, 7, 7.
Parameters given in the problem:
a₁ =7, r=1
Since there is r (ration), this is a geometric sequence. To find its explicit formula, substitute the given parameters into the formula of the n-th term of a geometric sequence:
a(n) = a₁ . r^(n-1)
Where:
a₁ : the first term
r : ratio which is equal to a(n)/a(n-1)
Substitute a₁ =7, r=1
a(n) = 7 . 1ⁿ⁻¹
Note that 1ⁿ⁻¹ is always equal to 1, no matter the value of n. Therefore,
a(n) = 7
We can see here, the nth term is constant, it is not a function of n.
Therefore, the first five terms are: 7, 7, 7, 7, 7
Learn more about geometric sequence here:
https://brainly.com/question/28093501
#SPJ4
David requires at least $250 to hold his birthday party.If David can save $43 by the end of each month, how many months will he need to save to be able to affords his party?
a.Write an inequality that describes this situation.
b.Solve ye inequality. SHOW ALL YOUR WORK
c.write you answer in a complete sentence
Part a
x = number of months
43x = amount saved at $43 per month
43x ≥ 250 is the inequality
===============================================
Part b
43x ≥ 250
43x/43 ≥ 250/43
x ≥ 5.81395 approximately
Since x is a positive integer, the value 5.81395 rounds to 6
So it would be x ≥ 6
================================================
Part c
He needs 6 months to be able to save at least $250.
Five months gets him 43x = 43*5 = 215 which is 35 dollars short of the goal of 250.
But 6 months gets him 43x = 43*6 = 258 which is 8 dollars over the goal of 250.
Identify the constant of variation. 4 y-5 x=0
The constant of variation in 4 y-5 x=0 is (5/4)
y = kx (Where k is the constant)
Here,
⇒ 4y - 5x = 0
⇒ 4y = 5x
⇒ y = 5x/4
⇒ y = (5/4) x
So, k = (5/4)
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
Learn more about linear equations
brainly.com/question/14323743
#SPJ4
please help with the question above
a) 1.515 is the distance in Angstrom between the two hydrogen atom.
b) 0.01515 mm is the value in millimetres of 1.515
What Armstrong unit?The angstrom is a metric length unit equal to 1010 m; that is, one ten-billionth (US) of a metre, one hundred-millionth of a centimetre, 0.1 nanometre, or 100 picometres. Its symbol is is a letter from the Swedish alphabet. The unit is named after Swedish physicist Anders Jonas Ångström.
As Both H atom is equidistance from O atom The triangles shown here is isosceles triangle, where two sides are equal
So, H0 = 0H = 0.958 Angstrom
And therefor Both angle of H = 37.75°
Now using the Law of Cosines for SAS triangles
c² = a² + b² - 2ab cos(c)
Here c is the distance of H and H atoms
c² = 0.958² + 0.958² - 2(0.958)(0.958) cos(104.5°)
c² = 1.835528 + 0.45958
c² =2.295108
c = √2.295108
c = 1.514961
Thus, 1.514961 is the distance in Angstrom between the two hydrogen atom.
Learn more about Angstrom
https://brainly.com/question/13190185
#SPJ9
I need help asap right now
Answer:
52 cm
Step-by-step explanation:
since all sides of a square is equal u do 4*13 and get 52 cm!
Answer: 52
Step-by-step explanation:
Square has 4 equal sides
13 x 4
Mark decided to make Christmas presents for his classmates. He bought 10 lb of two types of candies: caramel candies for $2.80 per pound and chocolate candies for $3.50 per pound.
**Write a function f(x) that represents the total cost of the candy, where x is the weight of the less expensive candy.**
The total cost f(x) of the candy is given by the expression -0.7x + 35, where x is the weight of the less expensive candy
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the weight of the less expensive candy and y represent that of the other candy, hence:
x + y = 10
y = 10 - x
Total cost = f(x)
Hence:
f(x) = 2.8x + 3.5(10 - x) = -0.7x + 35
The total cost f(x) of the candy is given by the expression -0.7x + 35, where x is the weight of the less expensive candy
Find out more on equation at: https://brainly.com/question/13763238
#SPJ1
How do I solve this question?
The real interest rate is 1 percent.
The inflation rate is 3 percent.
What are the nominal and real interest rate and inflation rate?
Inflation rate is a rate that estimate the rise on prices of goods and services. The interest rate is a gain rate per unit time associated to invested capital. There are two kinds of interest rates: (i) Nominal interest rate - Inflation is neglected, (ii) Real interest rate - Inflation is not neglected.
Please notice that the difference between nominal interest rate (i) and the real interest rate (i') is the inflation rate (i''). That is:
i'' = i - i'
Now we proceed to find each missing variable:
(i = 4, i'' = 3)
i' = i - i''
i' = 4 - 3
i' = 1
The real interest rate is 1 percent.
(i' = 3, i = 6)
i'' = i - i'
i'' = 6 - 3
i'' = 3
The inflation rate is 3 percent.
To learn more on interest rates: https://brainly.com/question/13324776
#SPJ1
Suppose you select a number at random from the sample space 5,6,7,8,9,10,11,12,13,14 . Find each probability. P (integer)
Answer:
1/10
Step-by-step explanation:
If each number has an equal outcome(and there are 10 numbers), 100%/10 would equal 10%(or 1/10, or 0.1%) It is completely random though, if you got a 6 you could pull a 6 again. (I think this is correct I'm so sorry if it isn't) If you pulled two of the same numbers in a row you would do 1/10*1/10. That would equal 1/20, which is a 0.05%
