15 km of walkway still need to be paved after 4 days. There are still 12 miles of trail to be paved after another 6 days. The average rate of the change is 24.
Given that,
The paving of a bike route by a city. Every day, the same amount of the path is paved. 15 km of walkway still need to be paved after 4 days. There are still 12 miles of trail to be paved after another 6 days.
We have to find the average change rate.
1st we find the slope with the points (4,15) and (6,12).
Slope =[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Slope=[tex]\frac{12-15}{6-2}[/tex]
Slope=-3/4
Now,
y=mx+b
15=-3/4(4)+b
b=15+3
b=18
We got the equation of line as y=-3/4x+18
Now take y=0
0=-3/4x+18
-3/4x=-18
x=(18×4)/3
x=72/3
x=24
Therefore, the average rate of the change is 24.
To learn more about average visit: https://brainly.com/question/12322912
#SPJ1
How many solutions will each system of linear equati
solutions.
y = x + 6 and 3x - 3y = -18
y = −4x + 11 and −6x + y = 11
y = -2x + 5 and 2x + y = -7
y = x + 6 and 3x - 3y = -18 will have no solution (parallel lines)
y = −4x + 11 and −6x + y = 11 will have unique solution (intersecting lines)
y = -2x + 5 and 2x + y = -7 will have no solutions (parallel lines)
taking first set of equations,
y = x + 6 and 3x - 3y = -18
rearranging it in the ax+by=c form we get,
x - y = 6
3x - 3y = -18
a1=1, b1= -1, c1= 6
a2=3, b2= -3, c2= -18
now comparing,
1/3 = 1/3 ≠ 6/(-18) 0r -1/3
thus, we get a1/a2=b1/b2≠c1/c2, which satisfies the condition for parallel lines, thus there will be no solution.
taking second set of equations,
y = −4x + 11 and −6x + y = 11
rearranging it in the ax+by=c form we get,
4x+y=11
-6x+y=11
a1=4, b1= 1, c1= 11
a2=-6, b2= 1, c2= 11
4/6 or 2/3≠1/1
thus, we get a1/a2≠b1/b2, which satisfies the condition for intersecting lines, so there will be a unique solution.
taking third set of equations,
y = -2x + 5 and 2x + y = -7
rearranging it in the ax+by=c form we get,
2x+y=5
2x+y=-7
a1=2, b1= 1, c1= 5
a2=2, b2= 1, c2= -7
2/2 or 1/1 =1/1≠ -5/7
thus, we get a1/a2=b1/b2≠c1/c2, which satisfies the condition for parallel lines, thus there will be no solution.
What are intersecting and parallel lines?
Parallel lines never cross, always have distinct ends, and are always spaced at the same distance from one another. Lines that intersect are lines that have a common point and do cross.
to learn more about parallel lines and intersecting lines:
https://brainly.com/question/16742265
#SPJ9
A grocery store sells a bag of 4 oranges for $2.84. How much would it cost for 5 oranges?
Answer: $3.55
Step-by-step explanation:
5 oranges * $2.84/4 oranges =
5 oranges * $0.71/1 orange=
5 oranges/1 orange * $0.71=
5/1 * 0.71=
5*0.71=$3.55
find the coordinates of the point 3/10 of the way from a to b. a= (-3, -5) b = (10, 7)
[tex]\displaystyle\\Answer:\ (0,-\frac{29}{13} )[/tex]
Step-by-step explanation:
[tex]\displaystyle\\A(-3,-5)\ \ \ \ \ B(10,7) \ \ \ \ \ \lambda=3/10=0.3\ \ \ \ \ C(x_C,y_C)=?\\\\\boxed {x_C=\frac{x_A+\lambda x_B}{1+\lambda} }\ \ \ \ \ \ \ \ \ \ \boxed {y_C=\frac{y_A+\lambda y_B}{1+\lambda} }\\\\x_C=\frac{-3+0.3(10)}{1+0.3} \\\\x_C=\frac{-3+3}{1.3} \\\\x_C=\frac{0}{1.3}\\\\x_C=0\\[/tex]
[tex]\displaystyle\\y_C=\frac{-5+0.3(7)}{1+0.3} \\\\y_C=\frac{-5+2.1}{1.3} \\\\y_C=\frac{-2.9}{1.3} \\\\y_C=-\frac{2.9(10)}{1.3(10)} \\\\y_C=-\frac{29}{13}[/tex]
[tex]\displaystyle\\Thus,\ C(0,-\frac{29}{13} )[/tex]
Trevor tutors French for $15 and hour and scoops ice cream for $10 an hour. He iS going to work 15 hours
this week. How many hours does Trevor need to tutor to make at least $180?
hours
Inequality - Trevor needs to tutor more than 6 hours in order to make at least $180.
What is inequality?
inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. Either questions or theorems can be used to express inequality problems, and both can be solved using methods similar to those used to solve equations. The triangle inequality, for instance, states that the length of the remaining side of a triangle is greater than or equal to the sum of the lengths of any two of its sides. Many of these inequalities, including the Cauchy-Schwarz inequality, are used by mathematical analysis to prove some of its most significant theorems.
Total number of hours = 15
Let the hours spent tutoring French is x
Therefor, hours spent in scooping ice cream = (15-x)
Tutoring French is $15 an hour, total for x hours = 15x
Scooping ice cream is $10 an hour, 10×(15-x)= 150-10x
To make more than $180,
= 15x+ (150-10x)> 180
= 15x+150-10x>180
=15x-10x>180-150
=5x>30
=x>6
So, Trevor needs to tutor more than 6 hours.
To learn more about inequality from the given link
https://brainly.com/question/24372553
#SPJ9
30 POINTS FOR AN EXPLANATION TOO (DETAILED PLS)
The value of x based on the equation given as 3(4x + 6) = 9x + 12 is -2.
How to illustrate the equation?It should be noted that an equation shows that relationship between the variables that are given or illustrated in the data.
The value for x based on the equation will be:
3(4x + 6) = 9x + 12
Open bracket
12x + 18 = 9x + 12
Collect like terms
12x - 9x = 12 - 18
3x = -6
Divide
x = -6/3
x = -2
Therefore, x is -2.
Learn more about equations on:
brainly.com/question/13763238
#SPJ1
5. 0.9 -0.2 =
its 5th grade math
Answer:
0.7
Step-by-step explanation:
multiply 2^3x^3.6^3x^3
The expression is multiplied to give 1728x^6
What are index forms?Index forms are simply defined as the power or exponent of a variable, number or element.
It is also seen as an arithmetic method of writing numbers that are too large or too small into simpler forms.
The rules of exponents are;
Add the powers if they are being multiplied the bases are the sameSubtract the exponents if they are divided and have the same base.Multiply the exponents when the bases of the forms are the sameGiven the expression;
2^3x^3.6^3x^3
We have to determine the product of the index forms
First, we have to multiply the numbers, we have;
2^3 = 2 × 2 × 2 = 8
6^3 = 6 × 6 × 6 = 216
Now, substitute the values
8x³ × 216x³
Multiply through
1728x^3 + 3
1728x^6
Thus, the value is 1728x^6
Learn more about index forms here:
#SPJ1
I Will Mark Brainlist please Help !!! Its A Math Question Thank you have a Great Day!
The correct answer is option C that is on step 4 - 5 the right side should have been ± i.
A quadratic polynomial function is the one which can be written in the form ax² + bx + c = y where a, b and c are coefficients and x, and y are independent and dependent variables respectively. The quadratic polynomial function is solved using Completing the square method. In this method the quadratic polynomial is converted into the form (x + a)² in order to find the roots of the quadratic polynomial. Here, the steps 1, 2 and 3 are correct but in step 4 after taking square root on both the sides the value of √-1 is not taken as ± i and further it is solved. This becomes an error as we know that the value of √-1 = ± i and if not taken properly errors occur.
Learn more about quadratic polynomial function at:
brainly.com/question/10061436
#SPJ1
If A = 50 degrees, B = 62 degrees, and a = 4, find b
round to nearest tenth
heeeeelp!!
Using the sine rule we estimate the value of b to be approximately 4.6 units.
The sine law, often referred to as the sine formula, sine rule, or law of sines, is a trigonometrical equation that connects the lengths of any triangle's sides to its sines.
When just two angles and one side of a triangle are known, the rule of sines can be used in the triangulation process to identify the other sides. When two sides and one of the non-enclosed angles are known, it can also be used. These facts do not always prove the triangle, hence the technique in some of these circumstances provides two reasonable estimates for the enclosed angle (this is known as the ambiguous case).The sine rule states that [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex] , where A ,B and C are the three vertices of the triangle and a, b and c are the three side lengths.
Given A = 50° and B = 62 ° and a = 4 .
Now we use the given values to :
[tex]\frac{4}{sin50} =\frac{b}{sin62}[/tex]
or, b = 4.6104...
or , b ≈ 4.6
Hence the length of b is 4.6
To learn more about sine rule visit:
https://brainly.com/question/22288720
#SPJ1
Finn and Elmer are comparing their bank accounts. Finn has $27.10 in his account while Elmer has overdrawn his account and it has -$51.89 in it. How much more money does Finn have in hiss account than Elmer.
A cylindrical container is to be constructed so that the sum of its height and its diameter is 15 feet.
a) Write an equation relating the height of the cylinder, h, to its radius, r. Solve the equation for h in terms of r.
b) The volume of a cylinder is given V=πr^2h. Use your answer in part A to express the volume of the cylindrical container in terms of r alone. Leave your expression in factored form so that it will be easier to analyze.
c) What are the values of r for which this problem makes sense? Explain.
From the characteristics of the given cylinder, we have that:
a) The equation is h = 15 - 2r.
b) The volume of the cylinder is of V = πr²(15 - 2r).
c) The values of r should be in the range of 0 < r < 7.5.
What is the volume of a cylinder?The volume of a cylinder of radius r and height h is given according to the following equation:
V = πr²h.
The sum of the height and the diameter is of 15 feet, hence:
h + d = 15.
The diameter is twice the radius, hence:
h + 2r = 15.
For item a, the solution of h in terms of r is:
h = 15 - 2r.
Hence, in item b, the equation is:
V = πr²h.
V = πr²(15 - 2r).
For item c, there are two constraints, as follows:
r > 0, as the radius of a cylinder cannot be negative nor zero.r < 7.5, as the height must be positive.More can be learned about the volume of a cylinder at https://brainly.com/question/9554871
#SPJ1
f(x)=x^2-2x-10 transforming Q. F. Form general form to vertex form
As a result of this definition, vertices are intersection of two lines that create an angle as well as the corners of polygons and polyhedra.[tex]f(x)=x^2-2x-10[/tex] general form to vertex form is y=[[tex](x-1)^{2}[/tex]-9]
What is a vertex?The intersection of two or more curves, lines, or edges is known as a vertex in geometry (plural: vertices or vertexes), which is frequently represented by the letters S, P, Q, or R. As a result of this definition, vertices are intersection of two lines that create an angle as well as the corners of polygons and polyhedra.
The point where two rays start or meet, where two line segments join or meet, where two lines intersect (cross), or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location is the vertex of an angle.
[tex]f(x)=x^2-2x-10[/tex]
= [[tex](x-1)^{2}[/tex]-9]
Use the form, [tex]ax^{2} + bx+c[/tex]
a=1
b=2
c=-10
Consider a vertex form of parabola,
[tex]a(x+d)^{2} + e[/tex]
find the value of d, using the formula d=[tex]\frac{b}{2a}[/tex]
d=[tex]\frac{2}{2*(-1)}[/tex]
simplify the right side,
d= -1
find the value of e, using e= [tex]c-\frac{b^{2} }{4a}[/tex]
e= [tex]-10\frac{2^{2} }{4*(-1)}[/tex]
simplify the right side,
e= -9
substitute the value of a, d and e into vertex form.
y= [[tex](x-1)^{2}[/tex]-9]
To know more about vertex visit: https://brainly.com/question/12563262
#SPJ9
NEED HELP!! URGENT
Write the polynomial given the following zeros:
4, -3, 3, 0
Please explain process if possible.
Answer:
Step-by-step explanation:
It could be
ax(x - 4)(x - 3)(x + 3) where a is some constant ( a could be 1 of course)
For a = 1 the polynomial is
x(x - 4)(x - 3)(x + 3)
In expanded form this is
x^4 - 4x^3 - 9x^2 + 36x
Write the equation of the line that passes through the given point and is perpendicular to the given line.
(Only need 20 and 22)
Answer:
4x - 5y = 30
4x - 5(0) = 30
x1 = 7.5 y1 = 0
Find y-intercept
The y-intercept is where the graph crosses the y-axis. To find the y-intercept, we set x2=0 and then solve for y.
4x - 5y = 30
4(0) - 5y = 30
y2 = -6 x2 = 0
(x1,y1) and (x2,y2)
(7.5,0) and (0,-6)
Solve for x
To solve for x, we solve the equation so the variable x is by itself on the left side:
4x - 5y = 30
x = 1.25y + 7.5
Solve for y
To solve for y, we solve the equation so the variable y is by itself on the left side:
4x - 5y = 30
y = 0.8x - 6
If you add Alex’s and bobs pie total together, they ate 22 pies, while bobs and chucks pies sum to 24. When you add Alex and chucks pie together, you find that they are 16 total. How many pies did each individual eat?
The number of pie each got-
Alex -7Bob - 15Chuck - 9What is the method of elimination?To create an equation in one variable, use the elimination method and can either add or subtract this same equations. Whenever the coefficients with one variable are opposites, the equations are added to eliminate a variable; when the coefficients with one variable are equal, the equations are subtracted to eliminate a variable.For the given question;
Let the number of pie eaten by Alex be 'a'.
Let the number of pie eaten by Bob be 'b'.
Let the number of pie eaten by Chuck be 'c'.
Then, for the given condition.
If you add Alex’s and bobs pie total together, they ate 22 pies,
a + b = 22 .....eq 1.
Bobs and chucks pies sum to 24.
b + c = 24 .......eq 2
Alex and chucks pie together be 16.
a + c = 16 .......eq 3
Solving equation 1 and 3 by elimination.
Subtract eq 3 from 1.
c = b - 6 .....eq 4
Solving equation 4 and 2.
b = 15
Put in eq 4
c = 9
Put the values of b and c in eq 1.
a = 7
Thus, the number of pie shared by Alex, Bob and Chuck are 7, 15 and 9 respectively.
To know more about the method of elimination, here
https://brainly.com/question/28405823
#SPJ10
Which of the following is equivalent to 6a + 4b + 3c?
10ab + 3c
4b + 6a + 3c
13abc
6a + 7bc
Answer: 4b+6a+3c
Step-by-step explanation:
A box of cereal contains 24 ounces.
It costs $5.52. What is the cost, to the nearest cent,
of the cereal per ounce?
A $0.23
B $2.35
Write and solve an expression.
C $4.26
D $28.89
The cost of one ounce of cereal is $0.23
Given:
Amount of cereals a box contain = 24 ounces
Cost of one box = $5.52
Cost of cereal per ounce = Cost of cereal / Amount of cereals in a box
Cost of cereal per ounce = $5.52 / 24
Cost of cereal per ounce = $0.23
What is Ounce ?An ounce is any of various units of mass, weight or volume derived almost invariably from the ancient Roman unit of measure, the ounce. an avoirdupois ounce is 1⁄16 avoirdupois pound; it is the US and British imperial ounce. 1 ounce is equal to 437.5 grains or 28.349 grams, A US customary fluid ounce is 1⁄16 of a US liquid pint and 1⁄128 of a US liquid gallon or exactly 29.5735295625 mL.
To learn more about Ounce , visit;
https://brainly.com/question/25410143
#SPJ13
step by step 9 divided by 1557
Answer:
0.00578034682
Step-by-step explanation:
9/1557
keep on adding .0 to the end of your number.
You will eventually get the answer.
Answer:
173.
Step-by-step explanation:
What is 149.6 million in standered form
Answer:146,600,000
1.496*10^8
Step-by-step explanation:
3. If f(x) = 2 x x³, which type of function is f?
Answer:
I believe cubic function
Step-by-step explanation:
the x^3 represents a cubic function
What is 1 3/4 x 2 2/3?
A. 2 1/2
B. 3 5/12
C. 4 2 / 3
D. 4 6 /7
Answer:
4 2/3
Step-by-step explanation:
1 3/4 x 2 2/3
We need to change the mixed numbers to improper fractions
1 3/4 = ( 4*1+3) /4 = 7/4
2 2/3 = ( 3*2 +2) /3 = 8/3
7/4 * 8/3
Rewriting
7/3 * 8/4
Simplify
7/3 *2
14/3
Make this a mixed number
4 goes into 14 4 times with 2 left over
4 2/3
Answer:
[tex]4\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]1\frac{3}{4} *2\frac{2}{3}[/tex]
First, make fractions as improper fractions.
[tex]\frac{7}{4} *\frac{8}{3}[/tex]
Now multiply the answers.
[tex]\frac{56}{12}[/tex]
Now make the answer a mixed number.
[tex]4\frac{8}{12}[/tex]
To write the answer in its simplest form, divide the numerator and denominator by 4.
[tex]4\frac{2}{3}[/tex]
Do the ratios 9 6 and 12 8 form a proportion?
The ratios 9:6 and 12:8 does not form a proportion, since the products of the two are not equal.
Given we have two ratios:
9:6 and 12:8
An equation in mathematics that shows that two ratios expressed in fraction form are equivalent is known as a proportion. The rule that says a/b= c/d if and only if ad=bc allows us to assess whether two ratios, a: b and c: d, constitute a proportion.
To determine if 9:6 and 12:8 form a proportion, we use the rule of proportion.
That is, 9/12 = 8/6
If only if 9×6=12×8
Therefore, 9×6=54
and 12×8=96
since these two products are not equal, we have that 9:12 and 8:6 do not form a proportion.
Hence the ratios 9:6 and 12:8 are not in proportion.
Learn more about ratio and proportion here:
brainly.com/question/19994681
#SPJ1
Select three names for the angle.
<B, <ABC, <CBA
based off the image
You earn $100 per month and want to save 10% in a savings account.
Use the savings calculator to find out how much your total savings would be in 1 year
if your account has an annual interest rate of 1%. (Do not include the $ sign in your
response) PLEASE HELP
Answer:
i'm sure you would have a amount of 1,200 dollars because there are 12 months in a year and you just got to x times 100 x 12=1,200 Booyah
Step-by-step explanation:
-3x= 2x^2 -4 solve using quadratic formula
Solution of the given equation -3x =2x² -4,using quadratic formula is (-3 ±√41) /4.
As given in the question,
Given equation is:
-3x =2x² -4
Rearrange the terms in proper order:
2x² + 3x -4 =0
Solve it using quadratic formula
x = (-b ±√b²-4ac)/ 2a
Here compare the given equation with general quadratic equation:
a =2 , b=3 , c=-4
Substitute the values in the quadratic formula we get,
x = [ -3± √(3)² -4(2)(-4)]/2(2)
= (-3 ± √9+32)/4
= (-3 ±√41) /4
Therefore, Solution of the given equation -3x =2x² -4, using quadratic formula is (-3 ±√41) /4.
Learn more about quadratic formula here
brainly.com/question/9300679
#SPJ1
Will give brainly and 20 points
Question 3
Answer:
I think the answer is d..
what is the answer to (b+3f)a=g
Answer:
f= -g/3
Step-by-step explanation:
find the compound interest on $1500 for 2years at 2%per annum compounded anually
Answer:
$1560.60
Step-by-step explanation:
PV (1+V)^n
= 1500 (1+2%)² = 1560.6
Question
What numbers are a distance of 23 unit from 12 on a number line
Answer:
distance: 11
there are 11 points between 12 and 23, they are:
12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 and 23.
Step-by-step explanation:
0.0158 rounded to the nearest tenth
Answer:
Step-by-step explanation: