Solve each system by eliminantion: -5x+3y=6 x-y=4
Answer: x = -9 , y = -13
Step-by-step explanation:
Multiply the second equation by 5, then add the equations together.
(−5x+3y=6)
5(x−y=4)
Becomes:
−5x+3y=6
5x−5y=20
Add these equations to eliminate x:
−2y=26
Then solve −2y=26 for y:
−2y = 26
Divide both sides by -2
y= -13
Now that we've found y let's plug it back in to solve for x.
Write down an original equation:
−5x+3y=6
Substitute−13 for y in −5x+3y=6:
−5x+(3)(−13)=6
−5x−39=6 (Simplify both sides of the equation)
−5x−39+39=6+39 (Add 39 to both sides)
−5x=45
Divide both sides by -5
x = -9
hope it help
you can proof it in the first equation if you want
Variable costs of producing widgets include the cost of gas required to deliver the widgets to retailers. A widget producer finds the average cost of gas per widget. The expense equation was recently adjusted from E = 4.55q + 69,000 to E = 4.98q + 69,000 in response to the increase in gas prices.
a. Find the increase in the average cost per widget. Round to the nearest cent.
b. If the widgets are sold to retailers for $8.00 each, find the breakeven point prior to the adjustment in the expense function.
(unit)
($) (do not use commas in numbers over 1,000)
c. After the gas increase, the company raised its wholesale cost from $8 to $8.50. Find the breakeven point after the adjustment in the expense function. Round to the nearest integer.
(unit)
($) (do not use commas in numbers over 1,000)
The breakeven point after the adjustment in the expense function.
What is the revenue?
Revenue is the total amount producers receive after selling a good. Profit is the total amount producers earn after subtracting the production costs.
Revenue is the product of the number of units and the price per unit. It is given by:
Revenue = number of units * price per unit
Revenue = x * p(x)
Revenue = 8q Expense = 4.55q + 69,000
To find the breakeven point Revenue = Expense
8q = 4.55q + 69,000 3.3.45q = 69,000 q = 20,000
Equate both and find q
E = 4.55(20,000) + 69,000 = 160,000
E at q = 20,000
(20,000, 160,000)
Hence, the breakeven point after the adjustment in the expense function.
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What is the surface area of the cylinder with height 7 mi and radius 5 mi? Round your answer to the nearest thousandth.
A cone has a radius of 8 m and a height of 30 m. What is the volume of the cone in terms of pi?
Answer:
640[tex]\pi[/tex]
Step-by-step explanation:
The formula for a cone is [tex]\pi r^2*h/3[/tex].r meaning Radius and h meaning Height.Your looking for the answer in terms of [tex]\pi[/tex] so you would take the [tex]\pi[/tex] out of the equation making it [tex]r^2*h/3[/tex].Insert your values in their respective locations, r becoming 8, and h becoming 30.Solve your equation of [tex]8^2*30[/tex]/3 getting 640.Add [tex]\pi[/tex] to the end.Answer:
640π
Step-by-step explanation:
The formula for a cone volume is
[tex]V = \pi r^{2} \frac{h}{3} \\\\V = \pi 8^{2} \frac{30}{3} \\\\V = \pi 64 * 10 \\\\V = 640\pi[/tex]
Complete the quadratic polynomial by filling in the number that makes it a perfect-square.
\mathrm{x}^{2} + 18 \mathrm{x} +x
2
+18x+
To make the quadratic polynomial x² + 18x into a perfect square, we add 81 to it.
What is a quadratic polynomial?A quadratic polynomial is a polynomial in which the highest power of the unknown is 2.
What is a perfect square?A perfect square is a number suvh that it is equal to another number multiplied by itself
How to make the quadratic polynomial a perfect square?Since we have the quadratic polynomial x² + 18x, and we wnat to convert it to a perfect square.
To be a perfect square, we want it in the form (x + a)² = x² + 2ax + a² (1)
Compring the quadratic polynomial with equation (1), we have that
2a = 18
a = 18/2
a = 9
⇒ a² = 9² = 81
So, substituting a = 9 into equation (1), we have
(x + a)² = x² + 2ax + a²
(x + 9)² = x² + 2(9)x + 9²
= x² + 18x + 81
Thus we see that to make x² + 18x into a perfect square, we add 81 to it.
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the base of a parallelogram is 3 times that of the height. the area of the parallelogram is 48. find the height of the parallelogram.
Answer:
height = 4
Step-by-step explanation:
b = 3h
b * h = 48
3h * h = 48
3h² = 48
3/3 h² = 48/3
h² = 16
h = √16
h = 4
b = 4 * 3
b = 12
based on the angle measures list the sides (AB,BC, and AC). In order from shortest to longest:
Order of Sides from smallest to largest is AC, BC , AB.
What is the order of Angles and Sides in a Triangle ?Finding the Triangle's Angles and/or Sides in Order of Largest to Smallest
Step 1: As stated in the issue, sort the supplied angles or sides in the order of smallest to greatest or largest to smallest.
If the sides are supplied in the issue and we are requested to arrange the angles, step 2 is to find the angles that are opposite the given sides.
If the problem specifies the angles and asks us to arrange the sides, find the sides that are perpendicular to the provided angles.
The sides opposing the angles will be listed in the same sequence as step 1's first-identified sides. Therefore, the side across from the biggest angle will be the largest, and the side across from the smallest angle will be the smallest. The angles opposing the sides will also be in the same sequence as those found in step 1 for the angles. As a result, the angle opposite the side with the greatest length will be the largest, while the angle opposite the side with the lowest length will be the smallest.
angle B is smallest , so the smallest side is opposite side of angle B i.e AC.
Again angle C is largest so similarly AB is the largest.
Order of Sides from smallest to largest is AC, BC , AB
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Question is attached
Answer:
Question 62. B) 8Question 63. D) 4/3--------------------
Question 62From the series we can observe:
The first term of the GP is t = 1/2, The common ratio is r = - 1/2,The nth term is - 1/256.Use the nth term equation to find the value of n:
[tex]t_n=t*r^{n-1}[/tex]Apply this to the last term and solve for n:
[tex]-1/256=1/2*(-1/2)^{n-1}[/tex][tex]-1/128= (-1/2)^{n-1}[/tex][tex](-1/2)^7=(-1/2)^{n-1}[/tex][tex]n-1=7[/tex][tex]n=8[/tex]--------------------------------------------------------------------
Question 62Given
Infinite sequence:
2, - 1, 1/2, - 1/4, 1/8, ...It has:
t = 2, r = - 1/2Find the sum of terms:
S = t / ( 1 - r)S = 2 /( 1 + 1/2) = 2 / (3/2) = 4/3Correct choice is D.
Kelli walk no more than 25 dog on Monday. M. Lincoln ha 5 dog that Kelli walk. The inequality hown can be ued to find x, the number of dog Kelli can walk on Monday in addition to M. Lincoln' dog. X 5 25 Which inequality repreent all poible value of x?
All potential values of x are represented by the inequality x≤20.
What is inequality?A mathematical statement that demonstrates the equality of two expressions is known as an equation, whereas a statement that demonstrates the greater or smaller value of one expression is known as an inequality.
An inequality displays the difference between two variables, whereas an equation displays the equivalence of two variables.
So, the inequality that also represents all the possible values of x is:
On Mondays, Kelli walks no more than 25 dogs.
Also, Ms. Lincoln's five dogs are walked by Kelli.
Along with Ms. Lincoln's dogs, the inequality to determine how many additional dogs Kelli walks on Monday is written as:
x+5 ≤ 25
Take 5 away from both sides.
x + 5 - 5 ≤ 25 - 5
x ≤ 20
Therefore, all potential values of x are represented by the inequality x≤20.
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Complete question:
Kelli walks no more than 25 dogs on Mondays. Ms. Lincoln has 5 dogs that Kelli walks. The inequality shown can be used to find x, the number of dogs Kelli can walk on Monday in addition to Ms. Lincoln's dogs. x + 5 25 Which inequality represents all possible values of x?
A parent function is a linear function of the form y=b.
True false question.
True
False
Answer: True
Step-by-step explanation:
If I remember not to mistake y=x is the parent functions. So y=b is the parent function! So this question is true.
A runner runs 2 miles in 9.56 minutes. How many meters per second is this? Explanation please
Thank you!
Answer: 2 miles
Step-by-step explanation:
Select all of the following functions that are quadratic. □ y=2x² 3=2x²-8 y=-2+2x-8 y + 3x = 2x² - 8 Oy+3x²= 2x + 3x²-8
If the degree of the equation is two, then the result leads to the quadratic equation. The following equations are entitled to the quadratic equations.
[tex]- $\mathrm{y}=2 \mathrm{x}^2$- $\mathrm{y}=2 \mathrm{x}^2-8$- $y=2 x^2-3 x-8$[/tex]
What is a quadratic equation?
In the quadratic equation, the maximum power of the variable is 2 . It consists of [tex]$x^2, x$,[/tex] and the constant term.
Given
1 .[tex]$y=2 x^2$[/tex]
2. [tex]$y=2 x^2-8$[/tex]
3. [tex]$\mathrm{y}=-2+2 \mathrm{x}-8$[/tex]
4.[tex]$\mathrm{y}+3 \mathrm{x}=2 \mathrm{x}^2-8$[/tex]
5. [tex]$\mathrm{y}+3 \mathrm{x}^2=2 \mathrm{x}+3 \mathrm{x}^2-8$[/tex]
If the power of x is 2 , then it is said to be a quadratic equation.[tex]y=2 x^2[/tex]
The above expression is a quadratic equation.
2.
[tex]y=2 x^2-8[/tex]
The above expression is a quadratic equation.
3.
[tex]y=2 x-10[/tex]
The above expression is not a quadratic equation.
4.
[tex]\begin{aligned}\mathrm{y}+3 \mathrm{x} & =2 x^2-8 \\\mathrm{y} & =2 x^2-3 x-8\end{aligned}[/tex]
The above expression is a quadratic equation.
5.
[tex]\begin{aligned}\mathrm{y}+3 \mathrm{x}^2 & =2 x+3 x^2-8 \\\mathrm{y} & =2 x-8\end{aligned}[/tex]
The above expression is not a quadratic equation.
Thus, the third and fifth are not quadratic equations and the first, second, and fourth are quadratic equations.
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The Transportation Security Administration (TSA) is responsible for airport security. On some flights, TSA officers randomly select passengers for an extra security check before boarding. One such flight has 76 passengers (12 in first class and 64 in coach). TSA officers selected an SRS of 10 passengers for screening. Let p-hat be the proportion of first class passengers in this sample. So, assuming that you are checking for the probability of choosing a first class passenger out of all passengers on the flight. Is the 10% condition met in this case? Justify your answer. (POS 447#31)
- Yes, 10 passengers out of 76 is less than 10% of the population of the flight.
- yes, 10 passengers out of all passengers on all flights is less than 10% of the population
- No, 10 passengers is the population being studied and is not less than 10% of the 10 total
- No, 10 passengers out of 76 is more than 10% of the population of the flight.
PLS ANSWER ASAP 50 POINTS!!
Determine if you can use the hypotenuse-leg congruency property to prove the triangles are congruent.
A. No, the hypotenuse-leg congruence property cannot be applied, because we don't know if a leg of one triangle is congruent to a leg of the other triangle.
B. No, the hypotenuse-leg congruence property cannot be applied, because we don't know if the hypotenuses are congruent.
C.Yes, the hypotenuse-leg congruence property can be applied.
D. No, the hypotenuse-leg congruence property cannot be applied, because we don't know if the triangles are right triangles.
No, the hypotenuse-leg congruence property cannot be applied, because we don't know if the hypotenuses are congruent.
What is hypotenuse?
The side opposite to the right angle is always the hypotenuse of a right triangle . It is also the longest side in a right triangle.
what is hypotenuse-leg congruence property?
HL (hypotenuse-leg) congruence Property: The hypotenuse-leg congruence property only applies to the right triangles.
According to hypotenuse-leg congruence property, in any two right angle triangles if the length of the hypotenuse of both the triangles are same and the length of one leg of the triangle is the same in both then the triangles are congruent in nature.
In the given case , leg of one triangle is congruent to a leg of the other triangle and also the triangles are right triangles but the hypotenuse-leg congruence property cannot be applied, because we don't know if the hypotenuses are congruent.
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Madelyn is throwing a pizza party. She has 6 pounds of cheese available and she
needs 1/2 pound of cheese to make each pizza. How many pizzas can she make?
Answer:
She can make 12 pizzas
Step-by-step explanation:
There are 2 halves in a pound, so you'll need to do 6 × 2 = 12.
The number of rooms in a house is a function of the number of people who live in the house.
Which of the following statements must be true?
A. The domain of the function is the population of the town.
B. If there are four rooms in the house, then there are four people living in the house.
C. The domain of the function is the number of rooms in a house.
D. The domain of the function is the number of people who live in the house.
The domain of the function described in the problem is given as the number of people living in the house. The correct option is (D).
What is a function?A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.
Suppose the number of rooms in the house be y.
And, the number of people is x.
As per the question, the function can be written as,
y = f(x)
From the definition of the function it is clear that all the possible values of x are domain and all values of y are range.
Thus, the domain of the function is number of people living in the house.
Hence, the domain of the function for the given case is the number of people living in house.
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stella opens her bank account with $500. She deposits $40 each month into the account. What function shows the amount in Stella's bank account after m months?
Answer:
f(x) = 500+40m
Step-by-step explanation:
500 = initial
40m because she deposits 40 each month
The question is in the image
Answer:
The length of side B is 6.25, The length of side A is 8.75, The scale factor is 0.25
Step-by-step explanation:
Divide the left side of the first model by the left side of the scaled version
60 / 15 = 4
divide side A and B by the result
35 / 4 = 8.75
25 / 4 = 6.25
i need help in this asap✋✋✋✋✋
By using the property of congruency of triangles,
[tex]\angle V \cong \angle S[/tex] has been proved
What is congruency of triangles?
Two triangles are said to be congruent if the corrosponding angles are equal and the corrosponding sides are equal.
There are different axioms of congruency. They are
SSS axiom, SAS axiom, AAS axiom, ASA axiom, RHS axiom
UV [tex]\cong[/tex] ST [Given]
QR [tex]\cong[/tex] PQ [Given]
QT [tex]\cong[/tex] QU [Given]
PV [tex]\cong[/tex] RS [Given]
PT = PQ + QT [Additive Property of Length]
RU = QR + QU [Additive Property of Length]
PT = QR + QU [Substitution]
PT = RU [Transitive Property of Equality]
TV = UV + TU [Additive Property of Length]
SU = ST + TU [Additive Property of Length]
TV = ST + TU [Substitution]
SU = TV [Transitive Property of Equality]
[tex]\angle[/tex]SUR [tex]\cong[/tex] [tex]\angle[/tex]VTP [QT = QU]
[tex]\Delta USR \cong \Delta TVP[/tex] [SAS axiom]
[tex]\angle V \cong \angle S[/tex] [Corrosponding parts of congruent triangles are congruent]
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how many miles can you drive, if your car gets 25.00 miles per gallon and you have 12.00 gallons of gas?
3 × 10² miles can you drive, if your car gets 25.00 miles per gallon and you have 12.00 gallons of gas.
What is distance?Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.
Given that,
car gets 25.00 miles per gallon.
In 1 gallon car covers 25 miles distance.
In 12 gallon the car will cover = 25 × 12 miles distance
= 300 miles distance.
Thus, distance covered in 12 gallons = 300 miles.
= 3 × 10² miles.
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If we randomly select a U.S. female, is (pregnant and over 55) = (0.06)(0.27) = 0.0162? Why or why not?
No, because being older than 55 and being pregnant are not independent events.
If we randomly select a U.S. female, is (pregnant and over 55) = (0.06)(0.27) = 0.0162 because being older than 55 and being pregnant are not independent events.
A random number is one that is selected by chance, or randomly, from a set of numbers, as the name suggests. There is an equal chance that any one of the numbers in a given distribution will be chosen at random.
The concepts of randomness are formally defined in the fields of mathematics, probability, and statistics. A random variable in statistics is the process of assigning a numerical value to each potential result of an event space. The identification of the events and the estimation of their probabilities are made easier by this association.
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The sum of two numbers is 20, and
the sum of their squares is 218. Find
the numbers.
The two numbers whose sum is 20 and sum of their squares is 218 are
13 and 7 respectively.
What is a numerical expression?A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.
Let, The two numbers be a and b.
Given, The sum of two numbers is 20 which is, a + b = 20...(1) and the sum of their squares is 218 which is, a² + b² = 218...(2)
We know, (a + b)² = a² + 2ab + b².
Therefore, 20² = 218 + 2ab.
2ab = 400 - 218,
2ab = 182.
ab = 91...(3)
Now, (a - b)² = a² + b² - 2ab.
(a - b)² = 218 - 182.
(a - b)² = 36.
a - b = 6...(4).
Adding (1) and (4) we get,
2a = 26.
a = 13 and hence b = 7.
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Bernard was going on an 3.5 kilometre bushwalk. He needs 1.2 litres of water for every 1.4 kilometres he walks. He only has 500 mL water bottles. How many water bottles will he need to take to make sure he has enough water for his walk?
The number of water bottles Bernard needs to complete a 3.5 kilometer bush walk is 6 bottles of 500 mL
The number of water bottles = 6
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of water bottles required be = A
Now , the equation will be
The total distance of the bush walk = 3.5 km
Bernard's requirement of water for every 1.4 km = 1.2 L of water
So , Bernard's requirement of water for every 3.5 km = ( total distance of the bush walk / 1.4 ) x 1.2 L
Substituting the values in the equation , we get
Bernard's requirement of water for every 3.5 km = ( 3.5 / 1.4 ) x 1.2 L
Bernard's requirement of water for every 3.5 km = 2.5 x 1.2 L
Bernard's requirement of water for every 3.5 km = 3 L
Now , the amount of water one water bottle can hold = 500 mL
The value of 3 L = 3000 mL
So , the number of water bottles required to hold 3 L = 3000 / amount of water one water bottle can hold
Substituting the values in the equation , we get
The number of water bottles required to hold 3 L = 3000 / 500
The number of water bottles required to hold 3 L = 6 water bottles
Therefore , the value of A is 6 water bottles
Hence , The number of water bottles Bernard needs to complete a 3.5 kilometer bush walk is 6 bottles of 500 mL
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At the city museum, child admission is $5.60 and adult admission is $9.50. On Friday, 170 tickets were sold for a total sales of $1228.90. How many child tickets were sold that day?
The number of child tickets sold is 99.
What is a system of equations?A system having more than two equations is known as a system of equations.
Given that, the cost of a child ticket and the cost of an adult ticket are $5.60 and $9.50 respectively.
Let the number of child tickets sold and the number of adult tickets sold be s and a, then
s + a = 170
a = 170 - s
The total cost of s child tickets and a adult tickets is:
5.6s + 9.5a = 1228.90
Substitute a= 170 -s into the above equation:
5.6s + 9.5(170 - s) = 1228.90
5.6s + 1615 - 9.5s = 1228.90
3.9s = 386.1
s = 99
Hence, the number of child tickets sold is 99.
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A relation i plotted a a linear function on the coordinate plane tarting at point A (0, 3)and ending at point B (2, 7). What i the rate of change for the linear function and what i it initial value? Select from the drop-down menu to correctly complete the tatement. The rate of change i Chooe. And the initial value i Chooe.
The rate of change is 2 and initial value is 3.
Given points A (0,3) B(2,7)
What is the slope of line joining between point A and point B
if let's suppose A(x1,y1) B(x2,y2)
then slope(m) = y2-y1/x2-x1
x1=0,y1=3
x2=2 y2= 7
slope(m) = 4/2 = 2
The ratio between the change in the values of the y variables and the change in the values of the x variables is known as the rate of change. The rate of change is the slope of the line if the rate of change is linear and constant.
Rate of change of linear function is also know as slope of that linear function.
So here slope itself is the rate of change.
Initial value is 3 as Coordinate of A is (0,3).
Given Question is incomplete Complete Question here
A relation is plotted as a linear function on the coordinate plane starting at point A (0, 3)and ending at point B (2, 7) .
What is the rate of change for the linear function and what is its initial value?
Select from the drop-down menus to correctly complete the statements.
The rate of change is____ and the initial value is___ .
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suppose that three in ten adults own an answering machine. a researcher selects a random sample of 38 adults, and is interested in the number of people in the sample will own an answering machine. a) find the probability that in a sample of 38, exactly 15 people own an answering machine. b) find the probability that in a sample of 38, at most 15 people own an answering machine.
A sample of 38 adults who has own an answering machine,
a) The probability that in a sample of 38, exactly 15 people own an answering machine is 0.061.
b) The probability that in a sample of 38, at most 15 people own an answering machine is 0.92381.
We have three in ten adults own an answering machine . That is probabilty of success, p = 3/10
Sample size, n = 38
Using Binomial Probability distribution,
X ~ Binom( 38, 0.3)
where X is random variable of adults has own an answering machine.
P(X= x) = ⁿCₓ (p)ˣ1-p)⁽ⁿ⁻ˣ⁾
The probability that in a sample of 38, exactly 15 people own an answering machine. , P(X= 15)
= ³⁸C₁₅(0.3)¹⁵ )(1 - 0.3)²³
= 38!/15!23! (0.3)¹⁵5(0.7)²³
= 0.06075 ~ 0.061
so, P(X= 15) = 0.061
b) The probability that in a sample of 38, at most 15 people own an answering machine, P(X<= 15)
Now, P(X≤ 15) = P( X= 1 ) + P(X= 2) + ... + P(X= 15) or 1 - P(X>15)
= 0.923814121
Hence, required probabilities
are 0.061 and 0.9238.
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It takes Sandra 1 hour to word process 4.5 pages. At this rate, how long will she take to complete 29
pages?
It takes Sandra 6.44 hour to word process 29 pages.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
It takes Sandra 1 hour to word process 4.5 pages.
Now,
Since, It takes Sandra 1 hour to word process 4.5 pages.
Hence, The time to make 29 pages = 29/4.5
= 290/45
= 58/9 hours
Thus, It takes 6.44 hours to complete 29 pages.
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A bookstore took in $167 on sale of 5 copies of a new cookbook and 3 copies of a new novel. The next day it took in $89 on the sales of 3 copies of the cookbook and 1 copy of the new novel. What was the price of each book.
Hint: use elimination or substitution
The price is $14 for each novel and $25 for each Cookbooks when a bookstore made $167 on the sale of 3 new novels and 5 copies of a new cookbook.
Given that,
A bookstore made $167 on the sale of 3 new novels and 5 copies of a new cookbook. Three cookbook copies and one copy of the brand-new book were sold the next day, bringing in $89 for the company.
We have to find what the cost of each book was.
We know that,
A bookstore took in$ 167 on the sale of 5 copies of a new cookbook and 3 copies of a new novel.
The next day it took in $ 89 on the sale of 3 copies of the cookbook and 1 copy of the novel.
What is System of equation?An algebraic expression-based system of equations is a collection of relationships between several unknown variables.
Now,
Let x= cookbook and y= novel.
So,
On first day, 5x + 3y = 167----->equation(1)
On second day, 3x + 1y = 89----->equation(2)
These equations must be solved in order to determine the cost of each book.
From equation(2), we get;
y = 89 - 3x
Now we use this x solution to solve our first equation.
We get;
5x + 3(89-3x) = 167
5x + 267 - 9x = 167
267-167 = 9x - 5x
100 = 4x
x = 25
So, The price is $25 for the each Cookbooks.
Now, By substituting $25 for x in the second equation, we must get the value of y.
y=89-3(25)
y=89-75
y=14
So, The price is $14 dollars for each novel.
So,
Therefore, The price is $14 for each novel and $25 for each Cookbooks when a bookstore made $167 on the sale of 3 new novels and 5 copies of a new cookbook.
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how would this two triangles be called
The triangles ΔUST and ΔVRQ are congruent to each other by the SSS postulates.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
In triangles ΔUST and ΔVRQ, then we have
TU = QV (Given)
ST = QR (Given)
UV = SR
Add RU on both sides, then we have
UV + RU = SR + RU
RV = SU
The triangles ΔUST and ΔVRQ are congruent to each other by the SSS postulates.
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Find the distance between each pair of parallel lines with the given equations Y=7. Y = -1
The distance between the two parallel lines with the equations y = 7 and
y = -1 is 8 units
What is the distance of a line between 2 points?
The distance of a line between 2 points is always positive and given by the formula
Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )
The distance between A and B is D , and the distance D is
[tex]Distance D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]
Given data ,
Let the equation of line be y = 7 and y = -1
Now , the slope of both the lines is 0
Slope m = 0
And the y intercept of the equation 1 or line 1 is = 7
So , the point is ( 0 , 7 )
And the y intercept of the equation 2 or line 2 is = -1
So, the point is ( 0 , -1 )
Now , the distance between the points ( 0 , 7 ) and ( 0 , -1 ) is given by the equation ,
[tex]Distance D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]
Substituting the values in the equation , we get
Distance D = √ ( 7 - ( - 1 ) )²
Distance D = √ ( 8 )²
Distance D = 8 units
Therefore , the value of D is 8 units
Hence , The distance between the two parallel lines with the equations y = 7 and y = -1 is 8 units
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