John rented the limousine for 6 hours.
The minimum fee charged by the transportation company to rent a limousine is $125.The hourly fee charged by the transportation company to rent a limousine is $50.The amount of money paid by John to rent a limousine is $425.Let the number of hours for which John paid for the rent of the limousine be "x".A formula that represents the equality of two expressions by linking them with the equals sign is known as an equation.The above-given data helps us to form the linear equation given below :425 = 125 + 50x300 = 50xx = 6Thus, John rented the limousine for 6 hours.To learn more about equations, visit :
https://brainly.com/question/10413253
#SPJ1
Answer the following questions
WILL GIVE BRAINLIEST
You decide you need a new computer. The cost of the computer is $864. However, the store also offers a rent to own option which will cost $41 per week for 24 weeksHow much more will the rent to own option cost after you have made all of the payments?
Answer:
120
Step-by-step explanation:
the difference = 24×41-864=120
Sub: x=4 into
Y= x^2 +4x -3
Y= 5x + 3
PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!!
The probability that if 3 donations are made, all 3 of them can be safely used on blood transfusion with someone that has type A will be D. (0.27 + 0.49)³ = 0.4390
How to calculate the probability?It should be noted that probability simply means the chance that a particular event will occur.
In this case, the probability that if 3 donations are made, all 3 of them can be safely used on blood transfusion with someone that has type A will be:
= (27% + 49%)³
= (0.27 + 0.49)³
= 0.4390
The probability is 0.4390.
Learn more about probability on:
brainly.com/question/24756209
#SPJ1
Find the slope-intercept form of the line through (−1,3) and (7,−8)
Answer:
[tex]\sf y =\dfrac{-11}{8}x +\dfrac{13}{8}[/tex]
Step-by-step explanation:
Slope-intercept form: y = mx + bHere, m is the slope and b is the y-intercept.
( -1, 3) ; x₁ = -1 & y₁ = 3
(7, -8) ; x₂ = 7 & y₂ = -8
Slope can be obtained by the formula:
[tex]\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{-8-3}{7-[-1]}\\\\\\=\dfrac{-8-3}{7+1}\\\\\\=\dfrac{-11}{8}[/tex]
Now, we can find the y-intercept,
[tex]\sf y = \dfrac{-11}{8}x + b\\\\Substitute \ any \ one \ of \ the \ point \ in \ the \ above \ equation.\\\\\text{Here, we are substituting (-1 ,3)}\\\\3 = \dfrac{-11}{8}*(-1) + b\\\\3 = \dfrac{11}{8}+b\\\\b = 3 - \dfrac{11}{8}\\\\b = \dfrac{3*8}{1*8}-\dfrac{11}{8}\\\\b= \dfrac{24-11}{8}\\\\b= \dfrac{13}{8}[/tex]
Slope-intercept form:
[tex]\sf y =\dfrac{-11}{8}x +\dfrac{13}{8}[/tex]
Two ships A and B take off at the same time from the same spot at a harbour. Ship A travels west with a speed of 40 km/h, while ship B travels north at a speed of 50 km/h. Determine, to the nearest integer, how fast the distance between the ships is increasing when they are 0.5 hours away from the harbour. Use the units as given in the question but write down only the numerical value of your answer without the unit.
Using the Pythagorean Theorem and implicit differentiation, it is found that the distance between them is increasing at a rate of 2050 km/h when they are 0.5 hours away from the harbor.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
For this problem, we have that since the ships are moving west and north, the distance between them as a function of the time will be given by the hypotenuse of a right triangle, as follows:
d² = x² + y².
In which;
x is the position of Ship A(moving horizontally).y is the position of Ship B(moving vertically).Applying implicit differentiation, the rate of change of the position is given as follows:
[tex]2\frac{dd}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]
[tex]\frac{dd}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]
From the velocities, we have that:
[tex]\frac{dx}{dt} = 40, \frac{dy}{dt} = 50[/tex]
From the velocities, and the time of half an hour, the positions are given as follows:
x = 0.5 x 40 = 20, y = 0.5 x 50 = 25.
Hence:
[tex]\frac{dd}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]
[tex]\frac{dd}{dt} = 20(40) + 25(50)[/tex]
dd/dt = 2050.
The distance between them is increasing at a rate of 2050 km/h when they are 0.5 hours away from the harbor.
More can be learned about the Pythagorean Theorem at https://brainly.com/question/343682
#SPJ1
To get to 1, divide 60 by
From 1, multiply by
OR, in a single step, multiply 60 by
to get to 25.
to get to 25. Submit Answer
To get to 1 we have to divide 60 by 60, and to get 25 we have to multiply 60 with 5/12 or 0.41.
Given that we have to get 1 by dividing 60 by something and multiply 60 by something to get 25.
We are required to find those numbers.
Take first result:
Suppose the number which divides 60 be x.
So,
60/x=1
x=60
Number will be 60.
Take second result:
Suppose the number which multiplied with 60 to get 25 be y.
So,
60*y=25
y=25/60
y=0.41
Number will be 0.41.
Hence to get to 1 we have to divide 60 by 60, and to get 25 we have to multiply 60 with 5/12 or 0.41.
Learn more about division at https://brainly.com/question/941863
#SPJ9
Abby knows that 1 mile is about 1.61 kilometers. She wants to write an equation she can use to convert
any given distance in miles (m) to kilometers (k).
How should Abby write her equation?
Abby should write her equation as k = 1.61m.
The correct option is B.
What is an equation?A pair of algebraic equations with the equal symbol (=) in the center and the same value are referred to as an equation.
Given:
Abby knows that 1 mile is about 1.61 kilometers.
To write an equation, which she can use to convert any given distance in miles (m) to kilometers (k):
Let m be the total number of miles and k be the kilometers.
So, the equation is,
k = 1.61m
Where 1.61 is multiplied by m.
Therefore, the equation is k = 1.61m.
To learn more about the equation;
https://brainly.com/question/12788590
#SPJ5
Please help, been stuck on this for far too long and due in tmrw!
From rectangle F to G translation is -4 units to the x- direction and -3 units to the y- direction.
From rectangle G to H translation is 6 units to the x- direction and -1 units to the y- direction.
From rectangle F to H translation is 2 units to the x- direction and -4 units to the y- direction.
Given that,
In the picture we have a graph with 3 rectangles that is F, G, and H.
We have to find the translation of the rectangles.
We know that,
What is translation?The transformation, i.e., f: X X, is a function, f, that maps to itself. Following the transformation, the pre-image X changes into the image X. Any operation, including translation, rotation, reflection, and dilation, may be used to create this transformation. A function can be moved in one direction or another by translation, rotated around a point by rotation, reflected in its mirror image by reflection, and scaled by dilation.
So,
From rectangle F to G translation is -4 units to the x- direction and -3 units to the y- direction.
From rectangle G to H translation is 6 units to the x- direction and -1 units to the y- direction.
From rectangle F to H translation is 2 units to the x- direction and -4 units to the y- direction.
To learn more about translation visit: https://brainly.com/question/11805053
#SPJ1
Please help me with 1-4. I will give an Brainly and a bunch of extra points.
Answer: 1. {a, b, c, d, e}
2. {a, b, d}
3. {c, f, g, h}
4. {a, c}
Step-by-step explanation:
1. AUC ==> Means take all parameters from A and C.
A+C=
{a, b, c, d}+{a, e}={a, b, c, d, e}
2. B∩A ==> Means take the common parameters from B and A
B: {b, e, a, d}
A: {a, b, c, d}
Both B and A have a, b, and d.
So answer is {a, b, d}.
3. B' is every parameter that isn't in B
Reminder: B={b, e, a, d}.
All parameters: {a, b, c, d, e, f, g, h}
Remaining Parameters(B'): {c, f, g, h}
4. A-B∩C'
First, let's find C'.
C' is every parameter that isn't in C.
Reminder: C={a, e}
All parameters: {a, b, c, d, e, f, g, h}
Remaining Parameters(C'): {b, c, d, f, g, h}
Then lets find B∩C'
B: {b, e, a, d}
C': {b, c, d, f, g, h}
Both B and C' have b and d, so B∩C' is {b, d}
A-{b, d}=
{a, b, c, d}-{b, d}={a, c} ==> Answer for 4
Answer:
[tex]\sf 1) \quad \sf A \cup C = \{a, b, c, d, e\}[/tex]
[tex]\sf 2) \quad B \cap A = \{a, b, d\}[/tex]
[tex]\sf 3) \quad B' = \{c, f, g, h \}[/tex]
[tex]\sf 4) \quad A -(B \cap C') = \{a, c \}[/tex]
Step-by-step explanation:
Set Notation
[tex]\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}[/tex]
Given sets:
U = {a, b, c, d, e, f, g, h}A = {a, b, c, d}B = {b, e, a, d}C = {a, e}Therefore:
Universal set = {a, b, c, d, e, f, g, h}B' = not in B = {c, f, g, h}C' = not in C = {b, c, d, f, g, h}Question 1
[tex]\begin{aligned}\sf A \cup C & = \sf \{a, b, c, d\} \cup \{a,e\}\\& = \sf \{a, b, c, d, e\}\end{aligned}[/tex]
Question 2
[tex]\begin{aligned}\sf B \cap A & = \sf \{b, e, a, d\} \cap \{a, b, c, d\}\\& = \sf \{a, b, d\}\end{aligned}[/tex]
Question 3
[tex]\begin{aligned}\sf B' & = \rm U - \sf B\\& = \sf \{a, b, c, d, e, f, g, h \}-\{b, e, a, d\}\\& = \sf \{c, f, g, h \}\end{aligned}[/tex]
Question 4
[tex]\begin{aligned}\sf A -(B \cap C') & = \sf \{a, b, c, d \}- \left( \{b, e, a, d \} \cap \{b, c, d, f, g, h \} \right)\\& = \sf \{a, b, c, d \}- \{b, d \} \\& = \sf \{a, c \}\end{aligned}[/tex]
Learn more about set notation here:
https://brainly.com/question/28353607
The function is not differentiable at x
The correct value of m = 6 and b = -9.
The function f(x) is differentiable at x = 3 and we know that if a function is differentiable at some point means that it is continuous at that point also.
Here function is continuous at x = 3 piecewise
m(3) + b = (3)²
3m + b = 9 .....(1)
and function is differentiable at ( x = 3 ) piecewise
d/dx ( m * x + b ) = d/dx (x)² at ( x= 3 )
( m + 0 ) = 2x at ( x = 3 )
m = 2 * 3
m = 6
By placing the value of m in equation (1)
3m + b = 9
3 * 6 + b = 9
18 + b = 9
b = 9 - 18
b = -9
Therefore, the value of m = 6 and b = -9.
Learn more about differentiable here:
https://brainly.com/question/24898810
#SPJ9
state whether each function is a linear function. write yes or no. explain.
xy = - 1
Answer: It's not linear.
Step-by-step explanation: A linear function must have a degree of 0 or 1. This function equals to y= -1/x. -1/x has a degree of negative 1 since x^-1 =1/x. So this is not linear.
given the function f(x)=-13+7x find the indicated function values
a. f(5)
b. f(-9)
c. f(0)
The answers of the following part are:
a) 22
b) -76
c) -13
For solving this particular sum we need to know the about functions Function is generaaly defined as a set of inputs having one output each. every function as a domain and a co-domain or range. A function is generally denoted by f(x) where x is the variable and it is also the input.The general representation of function is y = f(x).
In the given sum we will just put the values in place of x and will find the answer
The given equation is f(x)=-13+7x
a) Here it is given f(5) so we will put 5 in all places of x
Substituting the value x as 5 we will get :
f(5) = -13+7*5
= -13+35
=22
the value f(5) will be 22
b) In this part of the vaule of x is given as -9
Substituting the value of x as -9 we get
f(-9)=-13+7*(-9)
= -13-63
= -76
the valur of f(-9) is -76
c) here the value of x is given as 0
Substituting the value of x as 0
f(0)= -13+7*0
= -13+0
=-13
the value of f(0) is -13
Learn more about function here :
https://brainly.com/question/20337778
#SPJ9
By rounding to 1 significant figure, estimate the answers to these questions: 476 × 2354
answer:
1,120,504
Step-by-step explanation:
I don't really have one but I'm sure
You have 8 times as many dimes as nickles. You have 18 dimes and nickles altogether. How much money do you have in all?
Answer:
$1
Step-by-step explanation:
If you have x dimes, you have 8x nickels.
So, this means x + 8x = 18.
9x = 18 (combine like terms)x = 2 (divide both sides by 2)This means you have 2 dimes and 16 nickels, which have a combined value of 2(0.10)+16(0.05)=$1.
The sum of two numbers is 4. Three times the larger number plus two times the smaller number is 26. Find the numbers.
The larger number is and the smaller number is
The larger integer number is 18 and the smaller integer number is -14.
Integers are the subset of Rational numbers which contains all numbers except fraction and decimals
Numbers are the building blocks of mathematics. Numbers are used to count ,measure or label quantities.
The different types of numbers are:
Real numbers: 89.26 , -847 , 4/5irrational numbers √2 ,√3 imaginary numbers (5 + 9i) Integers -89 , 65 , 45Let the smaller number be x. The sum of the numbers is 4 .
So the larger number is 4 - x
Again given that sum of three times the larger number and 2 times the smaller number is 26.
∴3 ( 4-x )+ 2x = 26
or, 12 -3x +2 x = 26
or, -x = 26-12
or, x = -14
Therefore the larger number is 4-(-14)= 18
Hence the larger integer number is 18 and the smaller number is -14 .
To learn more about integer visit:
https://brainly.com/question/15276410
#SPJ9
here are four lengths of wood
Square root 3 x square root 2 x square root 5
Answer:
=sqrt of 30
Step-by-step explanation:
=sqrt of 3×2×5
=sqrt 30
PLS HELP ASAP
(50 POINTS)
3. Do the functions below show a direct linear variation or not? Explain why or why not.
You may want to use a graphing calculator, like Desmos, to look at the shapes these equations make.
Using proportional relationships, we have that:
A. The function does not show a direct linear relationship.
B. The function shows a direct linear relationship.
C. The function does not show a direct linear relationship.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, in the case of a direct relationship, as follows:
y = kx
In the case of an inverse relationship, we have that:
y = k/x.
From the format of these equations, we have that:
Item a shows an inverse relation, as x is in the denominator.Item b shows a direct relation, as x is in the numerator.A function is classified as linear if the exponent of x is of 1, hence item c does not show a linear function.
What is the missing information?The functions A, B, C are missing, and are given as follows.
A. 9/x.
B. x/11.
C. x²/8.
More can be learned about proportional relationships at https://brainly.com/question/10424180
#SPJ1
Hector earns $12 an hour plus a daily per diem of $15. This week he worked 4 days and earned a total of $444. Write an equation to find how many hours Hector worked this week.
The number of hours Hector worked this week is 32 hours.
Equation to find how many hours Hector worked this week.Amount Hector earned per hour = $12Additional amount earned daily = $15Number of days Hector worked this week = 4 Total amount Hector earned = $444Number of hours worked = x444 = 15(4) + 12(x)
open parenthesis444 = 60 + 12x
substract 60 from both sides444 - 60 = 12x
384 = 12x
divide both sides by 12x = 384/12
x = 32 hours
check:
444 = 60 + 12x
444 = 60 + 12(32)
444 = 60 + 384
444 = 444
Therefore, the number of hours Hector worked this week is 32 hours.
Learn more about equation:
https://brainly.com/question/2972832
#SPJ1
XZ is the perpendicular bisector of segment WY. WY = 64. Solve for k. Enter a NUMBER only.
2(6k+2)=64
12k+4=64
12k=60
k=5
Write the slope-intercept equation of the function f whose graph satisfies the given conditions.
The graph of f passes through (-8,6) and is perpendicular to the line that has an x-intercept of 4 and a y-intercept of -8.
The equation of the function is
(Use integers or fractions for any numbers in the equation.)
Answer:
i don't know the answerStep-by-step explanation:
33575357853222467
ufee
Elise and her mom are volunteering at an emergency relief center. To help prepare in case of a flood, they pack emergency kits with food and water. Elise puts 4 water bottles into each kit they pack. In all, she packs 120 water bottles. Which equation can you use to find the number of emergency kits K Elise packs?
4K = 120 can be used to find the number of emergency kits K Elise packs. The total number of emergency kits packed by Elsie and her mom are 30.
Here, we are given that Elise puts 4 water bottles into each emergency kit.
Let the number of kits packed = K
Then the total number of bottles packed = 4 × K
= 4K
Also, we are given that Elsie packs a total of 120 bottles.
Thus, we get the following linear equation-
4K = 120
We can use this equation to find the number of emergency kits K Elise packs.
dividing by 4 on both sides, we get
4K/4 = 120/4
K = 30
Hence, the total number of emergency kits packed by Elsie and her mom are 30.
Learn more about linear equations here-
https://brainly.com/question/13738061
#SPJ9
Can you please tell me how to solve this????
Answer:
-2
Step-by-step explanation:
You have to simplify numerator and denominator through factoring. The you should get an expression involving only a + b which is given as -2
Take numerator
[tex]a^2-b^2-12b-36[/tex]
Factor
[tex]-b^2-12b-36[/tex]
[tex]= - (b^2 + 12b + 36)\\\\= -(b+6)^2[/tex]
So numerator becomes
[tex]a^2-\left(b+6\right)^2[/tex]
Apply difference of squares formula: [tex]\displaystyle x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
[tex]\mathrm{with\;} x^2 == > a^2, and y^2 == > (b + 6)^2[/tex]
[tex]\implies a^2-\left(b+6\right)^2 \\== \left(a+\left(b+6\right)\right)\left(a-b-6\right)[/tex]
Denominator
[tex]a^2-6a-b^2-6b[/tex]
can be factored as follows
[tex]a^2-b^2 = (a + b) (a -b)[/tex]
[tex]-6a-6b = -6\left(a+b\right)[/tex]
So denominator becomes
[tex]\left(a+b\right)\left(a-b\right)+-6\left(a+b\right)[/tex]
Factor out common term (a+b) to get
[tex]\left(a+b\right)\left(a-b-6\right)[/tex]
So the original expression with Numerator and denominator
[tex]\displaystyle =\frac{\left(a+b+6\right)\left(a-b-6\right)}{\left(a+b\right)\left(a-b-6\right)}[/tex]
Cancel the common factor (a-b-6) to get
[tex]\displaystyle \frac{a+b+6}{a+b}[/tex]
Since a + b = -2, plug in this value of (a+b) in both numerator and denominator to get
[tex]\displaystyle \dfrac{-2 + 6}{-2}[/tex]
[tex]\displaystyle = - 2[/tex]
Answer: -2
If DE = 4x + 10, EF = 2x-1, and DF = 9x-15, find DF
The measure of segment DF from the given question is 21
Addition postulateIn line geometry, a line is the distance between two points while an angle is the point where two lines intersect.
Given the following parameters
DE = 4x + 10, EF = 2x-1, and DF = 9x-15,
Required
DF
Using the addition postulate
DE + EF = DF
Substitute
4x+10 + 2x -1= 9x - 15
6x + 11 = 9x - 1
6x - 9x = -1 - 1
-3x = -12
x = 12/3
x = 4
For DF
DF = 9(4) - 15
DF = 21
Hence the measure of segment DF from the given question is 21
Learn more on addition postulate here: https://brainly.com/question/2134445
#SPJ1
After an accident, police can use the formula v=2/5L to estimate the speed, v, in miles per hour, that a car was traveling by measuring the length of the skid marks, L in feet. Estimate the speed of a car that left skid marks 69 ft long. If the posted speed limit is 35 mi/h, was the car speeding?
Answer: The car was not speeding. It went 27.6 mi/h.
Step-by-step explanation: The equation v=2/5L is given where v is measured in mi/h. L is measured in ft. Since we have the value 69 for L, we sub it into the equation. We end up getting 27.6 mi/h after evaluating.
(3x-3)
(4y+4)°/60°
Solve for x and y. Explain.
The value of x and y is y=29, X=21.
180-60=120
4y+4=120 get y by itself and remember that what ever you do to one side you do to the other.
Alternate interior angles are congruent so 3x-3=60
What is an angle ?
Angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles.
Learn more about angles here:https://brainly.com/question/28451077
#SPJ9
What inequality represents all the values of x for y <
-5(x - 8) - 2 when y = 7?
Answer:
(−∞, 31/5) or x <31/5 (the graph will start a little bit past 6 and will be a open circle and head to the left)
Answer:
x< 6[tex]\frac{1}{5}[/tex]
Step-by-step explanation:
7<-5(x -8) - 2 Distribute the 5
7<-5x + 40 - 2
7<-5x +38 Subtract 38 from both sides
-31<-5x Divide both sides by -5
[tex]\frac{31}{5}[/tex] >x When you divide both sides by a negative number, you must flip the sign.
or
x < 6 [tex]\frac{1}{5}[/tex]
4. The average mass of a grain of one type of sand is 7 x 10-4 gram. There are 1,000 grains of the sand in 1 cubic centimeter. What is the mass, in grams, of 1 cubic centimeter of the sand in scientific notation?
The mass, in grams, of 1 cubic centimeter of the sand in scientific notation is 7 x 10^(-1).
What is scientific notation?Scientific notation is a way of writing very large or very small numbers.
Now it is given that,
Average mass of grain = 7 x 10-4 gram
Number of grains in 1 cubic centimeter = 1,000 grains = 10^3 grains
Thus,
Mass of 1 cubic centimeter of the sand = Average mass of grain * Number of grains in 1 cubic centimeter
⇒ Mass of 1 cubic centimeter of the sand = 7 x 10-4 * 10^3 grams
⇒ Mass of 1 cubic centimeter of the sand = 7 x 10^(-4+ 3) grams
⇒ Mass of 1 cubic centimeter of the sand = 7 x 10^(-1) grams
Thus, the mass, in grams, of 1 cubic centimeter of the sand in scientific notation is 7 x 10^(-1).
To learn more about scientific notation :
brainly.com/question/22331466
#SPJ1
Express the formula V = r². H in terms of the height, H. Use that formula to find the height when the volume is
45 and the radius is 3.
H =
-²; H = 30
H =
₁H=5
C H =
₁; H = 7.5
2.zr
C H = 1; H = 15
The formula in terms of H is H = V ÷ πr². Value of height is 5.
We are given the formula -
V = πr²H, where V represents volume and H represents height. To rewrite the formula in terms of H, we will shift it to Left Hand Side -
H = V ÷ πr²
Keep the value of Volume and radius in formula to find the height.
H = 45π ÷ π(3)²
Taking square of 3 and cancelling π
H = 45 ÷ 9
Performing division to find the value of height
H = 5
Therefore, the formula is V ÷ πr² and value of height is 5.
Learn more about volume -
https://brainly.com/question/463363
#SPJ9
The complete question is attached in figure.