The cost of one book is $6.
Step-by-step explanation:
Given,
Lizzie paid for 8 books = $50 bill
Alex paid for 3 books = $20 bill
As the both received same change.
Let,
x represent cost of one book.
y represent the change received.
According to given statement;
50-8x=y Eqn 1
20-3x=y Eqn 2
Putting value of y from Eqn 1 in Eqn 2
[tex]20-3x=50-8x\\-3x+8x=50-20\\5x=30[/tex]
Dividing both sides by 5
[tex]\frac{5x}{5}=\frac{30}{5}\\x=6[/tex]
The cost of one book is $6.
Keywords: linear equation, substitution method
Learn more about substitution method at:
brainly.com/question/10699220brainly.com/question/10703930#LearnwithBrainly
What is an equivalent expression for 1.5(3x + 4) + 0.25(6x + 8)?
Answer:
6x+8
Step-by-step explanation:
To answer this question we just simply use the distributive property to get rid of the parenthesis.
1.5*3x=4.5x
1.5*4=6
So the first parenthesis cancelled out would be : 4.5x+6
Now, onto the second:
0.25*6x=1.5x
0.25*8=2
So the second one is : 1.5x+2
Not that we have distributed both things, we add these.
4.5x+6+1.5x+2 we combine like terms
4.5x+1.5x=6x
6+2=8
So, the answer is 6x+8
Answer:
6x+8
Step-by-step explanation:
Took the question
May someone please help me???
Answer
14x+8y=6
Step-by-step explanation:
9x+5x=14, 7y+y=8y , 15-9=6
Answer:
?
Step-by-step explanation:
?
Robert has seven more than five times the number of video games Sam has. All together they have 25 video games. How many video games does Robert have?
Answer:
Step-by-step explanation:
r = 5s + 7
r + s = 25
5s + 7 + s = 25
6s + 7 = 25
6s = 25 - 7
6s = 18
s = 18/6
s = 3 <=== sam has 3 video games
r = 5s + 7
r = 5(3) + 7
r = 15 + 7
r = 22 <=== robert has 22 video games
(10 points) Using this graph, how can I graph y=x
Answer:
You would graph a point at the origin with a slope of 1
Step-by-step explanation:
Y=x means whatever the y value is, the x is the same.
Answer:
1
Step-by-step explanation:
The equation for graphing is y=mx+b and if it’s y=x then it means y=1x because when x is left alone it equals to 1
An engineer is planning a new water pipe installation. The circular pipe has a diameter of d=20\text{ cm}d=20 cmd, equals, 20, start text, space, c, m, end text.
What is the area AAA of the circular cross section of this pipe?
Give your answer in terms of pi.
Area of circular pipe in terms of pi is found as [tex]100 \pi[/tex] square centimeter
Solution:
Given that an engineer is going to install a new water pipe. The diameter of this circular pipe is, d = 20 cm
We have to find the area 'A' of the circular cross-section of the pipe.
Given, diameter of the circular section is:
diameter = 20 cm
Let us find the radius
[tex]radius = \frac{diameter}{2}\\\\r = \frac{20}{2} = 10[/tex]
Thus radius = r = 10 cm
The area 'A' of the circular cross-section of the pipe measn we can use the area of circle formula
The area of circle is given as:
[tex]area = \pi r^2[/tex]
Where "r' is the radius of circle
We have to find area in terms of pi
[tex]area = \pi (10)^2\\\\area = \pi \times 10 \times 10\\\\area = 100 \pi[/tex]
Thus area of circular pipe in terms of pi is found as [tex]100 \pi[/tex] square centimeter
What is the measure of angle A?
g is the centroid of triangle abc what is the length of gf
Answer:
26
Step-by-step explanation:
The length of GF if, G is the centroid of the triangle ABC is 26.
What is triangle?
Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol and consists of three connected vertices.
Given:
G is the centroid of the triangle ABC,
The line segment BD can be written as,
40 is 2x as long as 9x+2
The equation can be written as for the above statement.
40 = 2(9x + 2)
40 = 18x + 4
36 = 8x
x = 2
Put the value of x = 2 in 19X + 14, and divide that answer by 2, because GF is 2x smaller than AG
19x + 14
19 (2) + 14
52
Thus, the length of GF = 52 / 2 = 26.
To know more about Triangles:
https://brainly.com/question/16886469
#SPJ3
Find the slope of the line passing through the points (2,3) and (2,-4)
Answer:
Undefined
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-4-3)/(2-2)
m=-7/0
undefined
Answer:
UndefinedStep-by-step explanation:
[tex]\bold{METHOD\ 1:}\\\\\text{The first coordinates of the points (abscissa) are the same.}\\\text{Conclusion: This is a vertical line.}\\\text{The vertical line has the equation x = a (here x = 2). It has no slope.}\\\\\boxed{\text{Answer: unde}\text{fined}}[/tex]
[tex]\bold{METHOD\ 2:}\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{Substitute the coordinates of the given points}\ (2,\ 3)\ \text{and}\ (2,\ -4).\\\\m=\dfrac{-4-3}{2-2}=\dfrac{-7}{0}\\\\\text{The denominator must be different from 0.}\\\text{The expression}\ \dfrac{-7}{0}\ \text{ has no numerical sense.}\\\\\boxed{\text{Conclusion and naswer: unde}\text{fined}}[/tex]
how do you solve for x on this problem?
3x=7.5
Answer:X=2.5
Step-by-step explanation:
Divide both sides by 3
3 over 3 cancels out and 7.5 over 3 equals 2.5
Answer:
x= 2.5
Step-by-step explanation:
divide both sides by 3
Solve both equations.
Equation 1:
Answer:
x = 1.22
Step-by-step explanation:
[tex]\frac{5x-1}{8} -\frac{5-7x}{2} = \frac{3(6-x)}{6}[/tex]
[tex]\frac{2(5x-1) - 8(5-7x)}{16} = \frac{3(6-x)}{6}[/tex]
[tex]\frac{(10x-2) - (40-56x)}{16} = \frac{3(6-x)}{6}[/tex]
[tex]\frac{(10x-2-40+56x)}{16} = \frac{3(6-x)}{6}[/tex]
[tex]\frac{(66x-42)}{16} = \frac{3(6-x)}{6}[/tex]
[tex]\frac{(66x-42)}{16} = \frac{(18-3x)}{6}[/tex]
[tex](66x-42) \times 6 = (18-3x) \times 16[/tex]
[tex](396x-252) = (288-48x)[/tex]
[tex](396x +48x) = (288+252)[/tex]
[tex]444x = (540)[/tex]
[tex]x = \frac{540}{444}[/tex]
x = 1.22
Equation 2:
Answer:
x = -13.97
Step-by-step explanation:
[tex]\frac{x}{3} - \frac{7(x-2)}{9} = 4- \frac{2x-5}{6}[/tex]
[tex]\frac{9x-3(7(x-2))}{27} = 4- \frac{2x-5}{6}[/tex]
[tex]\frac{9x-3(7x-14))}{27} = 4- \frac{2x-5}{6}[/tex]
[tex]\frac{9x-(21x-42))}{27} = 4- \frac{2x-5}{6}[/tex]
[tex]\frac{9x-(21x-42)}{27} = \frac{24 - (2x-5)}{6}[/tex]
[tex]\frac{-12x+42}{27} = \frac{-2x+29}{6}[/tex]
[tex](-12x+42) \times 6 = (-2x+29) \times 27[/tex]
[tex](-72x+252) = (-34x+783) [/tex]
[tex](252-783) = (-34x +72x) [/tex]
[tex](-531) = (38x) [/tex]
[tex]x =\frac {-531}{38}[/tex]
x = -13.97
(8,-3) and (8,4)
Linear functions
Answer:
[tex]\displaystyle x = 8[/tex]
Step-by-step explanation:
Anything set to equal x is considered an undefined rate of change [slope], which is a vertical line. This is not a function, since it flunks the vertical line test.
I am joyous to assist you anytime.
10. What is the distance between (8,7) and (3,-5)?
Answer:
distance between points=13 units
Step-by-step explanation:
distance between points=[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
put [tex](x_1,x_2)[/tex]=(8,7) and [tex](y_1,y_2)[/tex]=(3,-5)
distance between points=[tex]\sqrt{(3-8)^2+(-5-7)^2}[/tex]
distance between points=[tex]\sqrt{(-5)^2+(-12)^2}[/tex]
distance between points=[tex]\sqrt{25+144}[/tex]
distance between points=[tex]\sqrt{169}[/tex]
distance between points=13 units answer
If you awnser please iclude work
Answer:
B and D
Step-by-step explanation:
The graph of a proportional relationship is a straight line graph which must pass through the origin.
The only straight line graphs which pass through the origin are B and D
if 42 butterflies were seen in 3 hours at that rate how many butterflies were seen per hour
Answer: 14 butterflies per hour
Step-by-step explanation: "Per hour" means in 1 hour so we can rewrite the given statement using fractions.
42 butterflies over 3 hours = ___ butterflies per hour.
I have attached my work in the image provided.
To find out what goes in the blank, notice that we have a 1 in the denominator of our second fraction. So we want to find a fraction that is equivalent to 42/3 that has a 1 in the denominator.
If we divide the numerator and denominator of 42/3 by 3, we get the equivalent fraction 14/1 or 14 butterflies over 1 hour. So now we have 14 butterflies over 1 hour = ___ butterflies per hour.
Now we can easily see that a 14 must go in the blank which means that the unit rate for 42 butterflies in 3 hours is 14 butterflies per hour.
find the x- intercept and y- intercept from the following linear equation
-9x+4y+=36
please help ????
Answer:
x intercept- (-4,0) y intercept- (0, 9)
Step-by-step explanation:
Subsitute 0 for x to get y = 9. That is your y intercept. Subsitute 0 for y and get -4 for your x intercept
How long did the sound take(in seconds) from the rocket motors at Time=0 to reach the people 500 meters away.
The speed of sound in early mornomg temperatures is 339.5 meters per second.
Sound will generally obey the basic equation of distance=rate×time
Answer:
It takes approximately 1.5 seconds to reach the people 500 metres away
Step-by-step explanation:
Since ; distance=rate×time
time= distance/ rate
Distance= 500 metres ,rate= 339.5 m/s
Time= 500/339.5
Time= 1.5 seconds
hey guys
im new here
please solve this for me with steps!
ill mark as the best answer
Answer:
The factors of [tex]2(x+y)^2-9(x+y)-5[/tex] is ((x+y)-5)(2x+2y+1)
Step-by-step explanation:
Given polynomial
=>[tex]2(x+y)^2-9(x+y)-5[/tex]
To Find:
The factors of the polynomial =?
Solution:
Lets assume k = (x+y)
Then [tex]2(x+y)^2-9(x+y)-5[/tex] can be written as [tex]2k^2-9k-5[/tex]
Now by using quadratic formula
k =[tex]\frac{-b\pm\sqrt{(b^2-4ac}}{2a}[/tex]
where
a= 2
b= -9
c= -5
Substituting the values, we get
k =[tex]\frac{-b\pm\sqrt{(b^2-4ac)}}{2a}[/tex]
k =[tex]\frac{-(-9) \pm \sqrt{((-9)^2-4(2)(-5)}}{2(2))}[/tex]
k =[tex]\frac{-(-9) \pm \sqrt{(81+40)}}{4}[/tex]
k =[tex]\frac{-(-9) \pm \sqrt{(121)}}{4}[/tex]
k =[tex]\frac{-(-9) \pm 11}}{4}[/tex]
k= [tex]\frac{ 9 \pm 11}{4}[/tex]
k = [tex]\frac{20}{4}[/tex] k = [tex]\frac{-2}{4}[/tex]
[tex]k_1 =5[/tex] [tex]k_2 = -\frac{1}{2}[/tex]
[tex]2k^2-9k-5= 2(k-5)(k+\frac{1}{2})[/tex]
Solving the RHS we get
[tex]\frac{2}{2}(k-5)(2k+1)[/tex]
[tex](k-5)(2k+1)[/tex]
Substituting k = x+y
[tex]((x+y)-5)(2(x+y+1)[/tex]
[tex]((x+y)-5)(2x+2y+1)[/tex]
Select the correct answer.
Does the equation below represent a relation, a function, both a relation and a function, or neither a relation nor a function?
y = 3:2 – 93 + 20
A.
neither a relation nor a function
B. both a relation and a function
C.
function only
D.
relation only
Answer:
A
Step-by-step explanation:
neither a relation nor a function
Answer:
NOTE: This is the answer for the equation (y=3x^2-9x+20) Both a Relation and a Function
Step-by-step explanation:
Because a Relation can be represented as a verbal descriptions, graphs, mapping diagrams, equations, list ordered pairs, and tables. Which in this case is an equation so its a RELATION.
A function is a type of relation in which every x-value in the domain is paired with exactly one y-value. Which in this case every x-value is paired with one Y-value.
Let me know if this helps. :)
Which of the following is equivalent to i^33?
Answer:
i
Step-by-step explanation:
The expression (x−3)(x+3)(3x) represents the volume of a rectangular prism, where x−3 is the width, x+3 is the length, and 3x is the height.
The value of x is tripled. Which statement must be true about the new prism?
A
The volume is tripled.
B
The width is tripled.
C
The length is tripled.
D
The height is tripled
Answer:
width = (x-1)
Step-by-step explanation:
The volume of the prisms is defined in the problem as
Volume = x^3 + 9x^2 + 6x − 16
Volume = width*height* length
And we know that,
length = (x+2)
height = (x+8)
We can find the roots of the equation, which happen to be
x = -8
x = -2
x = 1
(See image below)
This means that the volume can be represented as
Volume = x^3 + 9x^2 + 6x − 16 = (x+8)(x+2)*(x-1)
Therefore,
The width = (x-1)
Step-by-step explanation:
The function f(x) = 37x + 20 models the total cost for Rachel to be a member at a gym for x months. What can be interpreted from the y-intercept of the function?
A Rachel must pay $37 per month to use the gym.
B. Rachel must pay $20 per month to use the gym
C. Rachel must pay a $37 membership fee to join the gym.
D. Rachel must pay a $20 membership fee to join the gym.
" Rachel must pay a $20 membership fee to join the gym " can be interpreted from the y-intercept of the function ⇒ D
Step-by-step explanation:
The form of the linear function is f(x) = mx + b, where
m is the slope (rate of change) of the functionb is the y-intercept (initial amount) of the function∵ f(x) = 37 x + 20 models the total cost for Rachel to be a member
at a gym for x months
∵ f(x) = m x + b
∴ m = 37 and b = 20
∵ m represents the rate of change
- That means she must to pay 37 per month for x months
∴ Rachel must pay $37 per month to use the gym
∵ b represents the initial amount
- That means she pays a fixed amount one time
∴ Rachel must pay a $20 membership fee to join the gym
" Rachel must pay a $20 membership fee to join the gym " can be interpreted from the y-intercept of the function
Learn more:
You can learn more about the linear function in brainly.com/question/1284310
#LearnwithBrainly
PLEASE PLEASE HELP ME PLEASE I AM SO DUM I DONT KNOW THE ANSWER PLEASE JUST HELP ME
Scientists studied two animal populations. Function f(x) = 830(0.8)x models a bear population in a given region x years after the study began. The table models the cougar population in the same region.Use the table of data to interpret a linear function.
In the year the study began, how many more bears than cougars were in the given region?
Answer:
Cougar population was 790 at the beginning
830-790=40
Each member of the school chess team receives a chess set and clock. The total cost of these items for 5 members is $125. Jenna knows that a chess set costs $10, but she does not know how much a clock costs. She sets up the equation below to solve for the cost of a clock, represented in her equation by x.
The question deals with setting up and solving an equation to find the cost of a clock, when the total cost for a chess set and clock is given. The cost of a clock is found to be $15.
Explanation:The subject of this question is Mathematics, specifically dealing with setting up and solving an equation. The total cost of the chess set and clock for each member is $125/5 = $25. Jenna knows that the chess set costs $10. So, the cost of a clock would be $25 - $10 = $15. Therefore, the cost of a clock is $15.
Learn more about Equation Solving here:
https://brainly.com/question/18262581
#SPJ2
if an object has an acceleration of 7 m/s, and a mass of 3 kg, what is its force?
Answer:
force = 21 kg m/s^2 = 21 N
Step-by-step explanation:
If an object has mass (m) 3 kg, and its acceleration (a) is 7 m/s^2, its force is given by Newton's second law of motion: Force = M * a
Force = 3 kg * 7 m/s^2= 21 kg * m/s^2
This combinations of units (kg * m/s^2) is defined as Newtons in physics and abbreviated "N".
So we can say that the force on this object is of magnitude 21 N
Identify the given item as probability distribution, continuous random variable, or discrete random variable. The number of oranges purchased in a grocery store.
Answer:
Discrete random variable
Step-by-step explanation:
We are given the following in the question:
x is the number of number of oranges purchased in a grocery store.
Thus, it have the following properties.
The number of oranges can always be counted and not measured.They will always have a finite value.They will have discrete values.They cannot take any value within an interval.Thus, it is a discrete random variable
a 168 cm tall barrel has a circumference of 69.08 cm. what is the volume of the barrel using the formula for the volume of a cylinder as an estimate. round to the nearest hundredth of a cubic centimeter
Answer:
[tex]V=63,829.92\ cm^3[/tex]
Step-by-step explanation:
step 1
Find the radius of the circle
we know that
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]C=69.08\ cm[/tex]
assume
[tex]\pi =3.14[/tex]
substitute
[tex]69.08=2(3.14)r[/tex]
solve for r
[tex]69.08=6.28r[/tex]
[tex]r=69.08/6.28[/tex]
[tex]r=11\ cm[/tex]
step 2
Find the volume of the cylinder
we know that
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]h=168\ cm[/tex]
[tex]r=11\ cm[/tex]
assume
[tex]\pi =3.14[/tex]
[tex]V=(3.14)(11)^{2}(168)[/tex]
[tex]V=63,829.92\ cm^3[/tex]
Help me to prove the given below. Thank you in advance
Answer:
Construct MO, where O is the midpoint of CG. (As shown in the attached figure)
(1) LM = MG //given, CM is the median to the hypotenuse
(2) CO = OG // construction
(3) MO is a mid-segment //(1), (2) , Definition of a mid-segment
(4) MO // LC //triangle mid-segment theorem
(5) ∠MOG ≅ ∠LCO // corresponding angles in two parallel lines intersected by a transversal line (CG)
(6) m∠LCO=90° //given, ΔLCG is a right triangle
(7) m∠MOG=90° //(5), (6), definition of congruent angles
(8) m∠MOC=180° – 90° = 90° // linear pair
(9) ∠MOG ≅ ∠MOC //(7),(8), definition of congruent angles
(10) MO=MO //common side, reflexive property of equality
(11) ΔMCO ≅ ΔMGO //(2), (9), (10) Side-Angle-Side postulate
(12) MC = MG // Corresponding sides in congruent triangles (CPCTC)
(13) MG= ½LG // Given, CM is the median to the hypotenuse
(15) MC = ½LG //(12) , (13), substitution
Find the constant of proportionality if y is directly related to x when y = 12 and x = 6
Answer:
2
Step-by-step explanation:
Please see attached picture for full solution.
Viu
uc.COM
Question 35/40
Correctly complete this sequence: 131,517,?,
123
Xe-b+ b² - 4ac.
VO
Mathematics
y=2.x²
Question:
Correctly complete this sequence: 131, 517, ?, 123
Answer:
The completed sequence: 131, 517, 192, 123
Step-by-step explanation:
Given sequence is 131, 517, ?, 123
Step 1: Now, write the given numbers without any commas as below,
131517?123
Step 2: Then, split it into two digit numbers as 13, 15, 17, _ _, 23
Step 3: Fill the sequence with the missing two digit odd numbers. So, we can write as below
13, 15, 17, 19, 21, 23
Step 4: Again, rewrite and form the sequence without any commas.
131517192123
Step 5: Place the class after every three digits.
131, 517, 192, 123
Step 6: At last, found that the missing number is 192.
This is a simple addition sequence. The next number in the sequence would be 903, resulting from the addition of 386 to the previous term 517. So, the completed sequence is 131, 517, 903, 123.
Explanation:The sequence in question appears to be a simple addition sequence between consecutive terms. If you subtract the first number from the second number, you get 386 (517-131 = 386). Assuming this addition pattern continues, you can find the next number in the sequence by adding 386 to 517. So, the next number in the sequence would be 903 (517 + 386).
This means the completed sequence should read: 131, 517, 903, 123. Always remember to check the difference between your terms when working with sequences like this one.
Learn more about Addition Sequence here:https://brainly.com/question/34274431
#SPJ12
A local college offers scholarships to students who graduate in the top 1% of their high school classes according to GPA. If a high school has 400 students graduating one year , how many students from that high school would be eligible for these scholarships.
Answer:
4 students would be eligible for the scholarships
Step-by-step explanation:
Final answer:
In a high school with 400 graduating students, only 4 students would be eligible for scholarships that are offered to students in the top 1% of their class by GPA.
Explanation:
To determine how many students from a high school with 400 graduating students would be eligible for scholarships offered to those in the top 1% of their class, we simply need to calculate 1% of 400. Mathematically, this is represented as:
400 students * 1% = 400 students * 0.01 = 4 students
Therefore, in a high school graduating class of 400 students, only 4 students would be eligible for these scholarships based on being in the top 1% of their class according to GPA.