Answer:
Step-by-step explanation:
x = number of cars
12x = 3.50x + 34
12x - 3.50x = 34
8.5x = 34
x = 34/8.5
x = 4 <=====he would have to sell 4 cars
In this case, Luke must sell [tex]\(\boxed{4}\)[/tex] cars for his revenue to equal his expenses.
To determine how many cars Luke must sell for his revenue to equal his expenses, let's define the variables and set up the equation.
Let x be the number of cars Luke sells.
Revenue:
Luke sells each car for $12, so his revenue for selling x cars is:
[tex]\[ \text{Revenue} = 12x \][/tex]
Expenses:
Luke's expenses include $3.50 per car and a fixed cost of $34 for tools. So his total expenses for x cars are:
[tex]\[ \text{Expenses} = 3.50x + 34 \][/tex]
We need to find the number of cars x such that his revenue equals his expenses:
12x = 3.50x + 34
To solve for x subtract 3.50x from both sides:
12x - 3.50x = 34
8.50x = 34
Now, divide both sides by 8.50:
[tex]\[ \text{Expenses} = 3.50x + 34 \][/tex]
x = 4
Therefore, Luke must sell [tex]\(\boxed{4}\)[/tex] cars for his revenue to equal his expenses.
Determine if each relation is a function. Explain your reasoning.
Answer:
The first picture is a function while the second one is not.
Step-by-step explanation:
Reason - first picture passed the vertical line test, the other didn't.
Explain how to estimate the quotient using compatible numbers. 27 2/3 divided by 3 9/10. Write a Sentence or two.
Answer:
Step-by-step explanation:The first fraction is between 27 and 28, closer to 28. The second fraction is between 3 and 4, closer to 4. Compatible numbers in division are numbers that can be divided mentally. 28 divided by 4 is 7. The quotient will be around 7.
Answer:
Step-by-step explanation:
Sample Response: The first fraction is between 27 and 28, closer to 28. The second fraction is between 3 and 4, closer to 4. Compatible numbers in division are numbers that can be divided mentally. 28 divided by 4 is 7. The quotient will be around 7.
Find the x and y intercepts of the equation: 2x - 3y = 18 (0, 2) and (-3, 0) (0, 9) and (0, -6) (9, 0) and (0, -6) (2, 0) and (0, -3)
The x - intercept is (9, 0) and y - intercept is (0, -6)
Solution:
Given that the equation is: 2x - 3y = 18
We have to find the x and y intercepts of the equation
The x-intercept is the point at which the line crosses the x-axis. At this point, the y-coordinate is zero.
The y-intercept is the point at which the line crosses the y-axis. At this point, the x-coordinate is zero.
Finding x - intercept:
Substitute y = 0 in given equation
2x - 3y = 18
2x - 3(0) = 18
2x = 18
x = 9
Thus the x - intercept is (9, 0)
Finding y - intercept:
Substitute x = 0 in given equation
2(0) - 3y = 18
-3y = 18
y = -6
Thus the y-intercept is (0, -6)
Write the equation of a line that is parallel to
y
=
9
y=9y, equals, 9 and that passes through the point
(
3
,
−
8
)
(3,−8)left parenthesis, 3, comma, minus, 8, right parenthesis.
Answer:
The equation of the line is [tex]y=-8[/tex]
Step-by-step explanation:
we know that
The equation of the line [tex]y=9[/tex] is a horizontal line (parallel to the x-axis)
The equation of a horizontal line is equal to the y-coordinate of the point that passes through it
In this problem, the line passes through the point (3,-8)
The y-coordinate is -8
therefore
The equation of the line is [tex]y=-8[/tex]
Systems of equations with different slopes and different y-intercepts have more than one solution. (5 points) Always Sometimes Never
Answer:
Never
Step-by-step explanation:
we know that
A system of linear equations with the same slope and the same y-intercept has infinite solutions (identical lines)
A system of linear equations with the same slope and different y-intercept has no solutions (parallel lines)
A system of linear equations with different slopes and different y-intercept has only one solution
-15x + 4 < 109 or -6x + 70 > - 2
For this case we must find the solution set of the given inequalities:
[tex]-15x + 4 <109[/tex]
We subtract 4 from both sides of the inequality:
[tex]-15x <109-4\\-15x <105[/tex]
We divide between 15 on both sides of the inequality:
[tex]-x <\frac {105} {15}\\-x <7[/tex]
We multiply by -1 on both sides taking into account that the sense of inequality changes:
[tex]x> -7[/tex]
The solution is given by all values of x greater than -7.
[tex]-6x + 70> -2[/tex]
Subtracting 70 from both sides of the inequality:
[tex]-6x> -2-70\\-6x> -72[/tex]
We divide by 6 on both sides of the inequality:
[tex]-x> - \frac {72} {6}\\-x> -12[/tex]
We multiply by -1 on both sides taking into account that the sense of inequality changes:
[tex]x <12[/tex]
Thus, the solution set is given by:
[tex]x> -7\ U\ x <12[/tex]
Therefore the solution is all real numbers.
Answer:
All real numbers.
Mike bought 20 stamps for 0.40 $5 each and 15 Century 0.32 each how much money did Mike spend on stamp
Answer:
$8
Step-by-step explanation:
Here is the correct question: Mike bought 20 stamps for 0.40 each and 15 Century 0.32 each how much money did Mike spend on stamp.
Given: cost of each stamp is 0.40
Total stamp bought is 20.
Using unitary method
Cost of 1 stamp is 0.40.
∴ cost of 20 stamp is =[tex]20\ stamp \times 0.40= 8[/tex]
Cost of 20 stamp is $8
∴ Total money spent by Mike on buying 20 stamp is $8.
Which of the following is the BEST summary of this
paragraph?
A tsunami is not like normal ocean waves. It's a series
OA) of waves. You need to wait several hours for all of
them to pass.
Because a tsunami is not one wave, but a series of
several waves that can be as far as two hours apart,
OB)
you must wait several hours after the last wave in
order to be sure the tsunami is over.
A tsunami consists of not one but many waves that
come in one after the other. Not knowing whether the
OC)
tsunami is over unless more than two hours have
Answer:
I THINK IT IS OB
HOPE IT HELPS!
Answer:
B
Step-by-step explanation:
A backpacker parked his car and hiked a distance of 1.2 km on the first day. On the second day, he continued hiking away from his car with an average speed of 2.3 km/hr. Write the equation that can be used to find the backpacker's distance in km (d) from his car as a function of time in hours (t) as he hiked on the second day.
d(t) =
Answer:
d = 1.2 + 2.3t
Step-by-step explanation:
A backpacker parked his car and hiked a distance of 1.2 km on the first day. On the second day, he continued hiking away from his car with an average speed of 2.3 km/hr.
Now, on the second day he started from distance 1.2 km from his car and continues to hike with an average speed of 2.3 km/hr.
Therefore, the distance of the backpacker from his car on the second day is given by
d = 1.2 + 2.3t
where d is the distance in km and t is the time in hours he hiked. (Answer)
is y=17 a linear function
Answer:
No.
Explanation:
The term linear function refers to two distinct but related notions. This is just one point.
On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 2), and (1, negative 1). Everything to the right of the line is shaded. The solutions to the inequality y > −3x + 2 are shaded on the graph. Which point is a solution? (0, 2) (2, 0) (1, −2) (−2, 1)
Answer:
(2,0)
Step-by-step explanation:
we know that
If a ordered pair is a solution of the inequality, then the ordered pair must satisfy the inequality
we have
[tex]y > -3x+2[/tex]
Substitute the value of x and the value of y of each point in the inequality and then compare the results
case a) (0, 2)
[tex]2 > -3(0)+2[/tex]
[tex]2 > 2[/tex] ----> is not true
so
the point not satisfy the inequality
therefore
The point is not a solution of the inequality
case b) (2,0)
[tex]0 > -3(2)+2[/tex]
[tex]0 > -4[/tex] ----> is true
so
the point satisfy the inequality
therefore
The point is a solution of the inequality
case c) (1, -2)
[tex]-2 > -3(1)+2[/tex]
[tex]-2 > -1[/tex] ----> is not true
so
the point not satisfy the inequality
therefore
The point is not a solution of the inequality
case d) (-2, 1)
[tex]1 > -3(-2)+2[/tex]
[tex]1 > 8[/tex] ----> is not true
so
the point not satisfy the inequality
therefore
The point is not a solution of the inequality
see the attached figure to better understand the problem
Answer:
(2,0)
Step-by-step explanation:
help me in math tasks please
Answer:
1. 3/5 c
2. 7 c
3. 2/5 b
4. $3.24 c
5. -3.2 b
Step-by-step explanation:
1.
2/5 + 1/5 = 3/5
2.
a negative + a negative = a positive
2+5 = 7
3.
terminating means the decimal ends. When u divide a & c they keep on going but 2/5 ends
4.
divide 16.8 by 5.19 = 3.23 round up so 3.24
5.
multiply the two together to get the answer
In triangle abc, cos A= -0.6. Find A and Tan A
Answer:
Part 1) [tex]A=126.87^o[/tex]
Part 2) [tex]tan(A)=-\frac{4}{3}[/tex]
Step-by-step explanation:
we have
[tex]cos(A)=-0.6[/tex]
The cos(A) is negative, that means that the angle A in the triangle ABC is an obtuse angle and the value of the sin(A) is positive
The angle A lie on the II Quadrant
step 1
Find the measure of angle A
[tex]cos(A)=-0.6[/tex]
using a calculator
[tex]A=cos^{-1}(-0.6)=126.87^o[/tex]
step 2
Find the sin(A)
we know that
[tex]sin^2(A)+cos^2(A)=1[/tex]
substitute the value of cos(A)
[tex]sin^2(A)+(-0.6)^2=1[/tex]
[tex]sin^2(A)=1-0.36[/tex]
[tex]sin^2(A)=0.64[/tex]
[tex]sin(A)=0.8[/tex]
step 3
Find tan(A)
we know that
[tex]tan(A)=\frac{sin(A)}{cos(A)}[/tex]
substitute the values
[tex]tan(A)=\frac{0.8}{-0.6}[/tex]
Simplify
[tex]tan(A)=-\frac{4}{3}[/tex]
y=-2x+5 was shifted down 7 units what equation is it now
Answer:
[tex]y=-2x-2[/tex]
Step-by-step explanation:
we have
[tex]y=-2x+5[/tex]
This is the equation of a line in slope intercept form
where
[tex]m=-2[/tex] ---> the slope
[tex]b=5[/tex] ----> the y-intercept
we know that
If the given line was shifted down 7 units, then the new y-intercept is equal to
[tex]b=5-7=-2[/tex]
The slope of the new line will be the same that the original line, because are parallel lines
so
The new equation is
[tex]y=-2x-2[/tex]
Helllllllllppppppppp
Answer:
[tex]\frac{8}{5} x^{2} - \frac{16}{5} xy + 4x[/tex]
[tex]xy^{2} + \frac{2}{3}y - 8y^{2}z[/tex]
Step-by-step explanation:
We have to simplify the followings:
1) [tex]- \frac{4}{5}x (- 2x + 4y - 5)[/tex]
= [tex]- \frac{4}{5}x \times (- 2x) + - \frac{4}{5}x \times (4y) + - \frac{4}{5}x \times (- 5)[/tex]
{By distributive property of multiplication}
= [tex]\frac{8}{5} x^{2} - \frac{16}{5} xy + 4x[/tex] (Answer)
2) [tex]2y^{2}( \frac{1}{2} x + \frac{2}{6}y - 4z)[/tex]
= [tex]2y^{2} \times (\frac{1}{2} x) + 2y^{2} \times ( \frac{2}{6}y) - 2y^{2} \times (4z)[/tex]
{By distributive property of multiplication}
= [tex]xy^{2} + \frac{2}{3}y - 8y^{2}z[/tex] (Answer)
A rectangular field is 400 meters long and 350 M wide what is the area of the field in square kilometers do not round the answer and be sure to include the correct unit in the answer
Final answer:
The area of a rectangular field that is 400 meters long and 350 meters wide is calculated by multiplying the length and width in meters to get square meters and then converting to square kilometers. The field's area is 0.14 square kilometers.
Explanation:
To calculate the area of a rectangular field, you multiply the length by the width. The area is usually given in square units.
In this case, the field is 400 meters long and 350 meters wide. To find the area in square meters, we do the following calculation:
Area = Length × Width
Area = 400 m × 350 m
Area = 140,000 m2
To convert square meters to square kilometers, you need to remember that 1 square kilometer equals 1,000,000 square meters. Therefore, you divide the area in square meters by 1,000,000 to get the area in square kilometers:
Area in square kilometers = Area in square meters / 1,000,000
Area in square kilometers = 140,000 m2 / 1,000,000
Area in square kilometers = 0.14 km2
The area of the field is 0.14 square kilometers.
To find the area of the rectangular field in square kilometers, the measurements of 400 meters and 350 meters must first be converted to kilometers, resulting in an area of 0.14 square kilometers.
Explanation:To calculate the area of a rectangular field in square kilometers, we can use the formula for the area of a rectangle which is length × width. First, we need to convert the measurements into the same unit, so we will convert meters to kilometers. We know that 1 kilometer is equivalent to 1000 meters. Therefore, a field that is 400 meters long is 0.4 kilometers long (400 ÷ 1000 = 0.4 km), and a field that is 350 meters wide is 0.35 kilometers wide (350 ÷ 1000 = 0.35 km).
Now, with both measurements in kilometers, we can find the area:
To find the area of a rectangular field, you need to multiply its length by its width. In this case, the length is 400 meters and the width is 350 meters. So, the area of the field is 400 * 350 = 140,000 square meters.To convert this to square kilometers, we need to divide the area by 1,000,000 (since there are 1,000,000 square meters in a square kilometer). So, the area of the field in square kilometers is 140,000 / 1,000,000 = 0.14 square kilometers.Therefore, the area of the rectangular field is 0.14 square kilometers.Find a bank account balance if the account starts with $100, has an anual rate if 4%, and the money left in the account for 12 years
Answer:
required bank balance=$148
Step-by-step explanation:
simple interest=[tex]( \right )P\times R\times T\left )\div 100[/tex]
where P=principle=$100
R=rate of interest=4%
T=time=12 year
simple interest=[tex]( \right )100\times 4\times 12\left )\div 100[/tex]
simple interest=[tex]\frac{4800}{100}[/tex]
simple interest=48
required bank balance=principle+simple interest
required bank balance=$100+$48=$148
required bank balance=$148
What is the solution to the following system of equations? x − 4y = 6 2x + 2y = 12 (0, 10) (10, 0) (6, 0) (0, 6)
Answer:
(6,0)
Step-by-step explanation:
The given system has equations:
[tex]x-4y=6[/tex]
[tex]2x+2y=12[/tex]
Multiply the top equation by 2 to get:
[tex]2x-8y=12[/tex]
[tex]2x+2y=12[/tex]
Subtract the top equation form the bottom equation to get:
[tex]2x-2x+2y--8y=12-12[/tex]
[tex]\implies 10y=0[/tex]
[tex]\implies y=0[/tex]
Put y=0 into [tex]x-4y=6[/tex]
[tex]x-4*0=6[/tex]
[tex]\implies x=6[/tex]
Therefore the solution is (6,0)
Your Answer Is:
C: (6,0)
4/7 - -4/7
It’s confusing I calculated it but there’s no answer so I really need help
Answer:
Step-by-step explanation:
4/7 - (-4/7) = 4/7 + 4/7 = 8/7 or 1 1/7......a negative times a negative is a positive...so those two negatives turn into a positive...so ur basically just adding them
Simplify the expression 2 × 36 − 24 ÷ 6
Answer:
68
Step-by-step explanation:
P- parentheses
E- exponential
M- multiplication
D- division
A- addition
S- subtraction
2 x 36 = 72
72 - 24 ÷ 6
24 ÷ 6 = 4
72 - 4 = 68
Answer:
68
Step-by-step explanation:
*Remember the order of operations PEMDAS*(Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)
2 x 36 = 7224 / 6= 4now, 72 - 4= 68hope it helps:)
what is greater 19/34, 19/36
Answer:19/34
Step-by-step explanation:
PLZ ANSWER
SCRENSHOT
Answer:
Marcelino will break even
Step-by-step explanation:
if he spends 45 dollars on profits, and sells each balloon for $1.50 then you multiply 30 balloons by 1.5 and that equals 45 dollars, so he will break even
Answer:
C
Step-by-step explanation:
3. Caleb has $25 to spend on prizes for a game at the school fair. Lip balm costs $1.25 each, and mini-notebooks cost $2.50 each.
a. Write a linear equation in STANDARD FORM that can be used to determine how many of each prize she can buy.
b. Graph the equation using x- and y- intercepts.
Answer:
linear equation in Standard form that can be used to determine how many of each prize Caleb can buy is [tex]1.25x+ 2.50y = 25[/tex]
Step-by-step explanation:
Given:
Total cost spent on prizes for games = $25
Cost of one lip balm = $1.25
Cost of one mini notebook = $2.50
A) linear equation in STANDARD FORM that can be used to determine how many of each prize she can buy.
Let the number of lip balms be x and the number of mini note books be y. Then
[tex]1.25x+ 2.50y = 25[/tex]
B. Graph the equation using x- and y- intercepts.
Now by trial and error method
[tex]1.25(0)+ 2.50(10) = 25[/tex]
[tex]1.25(2)+ 2.50(9) = 25[/tex]
[tex]1.25(4)+ 2.50(8) = 25[/tex]
[tex]1.25(6)+ 2.50(7) = 25[/tex]
[tex]1.25(8)+ 2.50(6) = 25[/tex]
[tex]1.25(10)+ 2.50(5) = 25[/tex]
[tex]1.25(12)+ 2.50(4) = 25[/tex]
[tex]1.25(14)+ 2.50(3) = 25[/tex]
[tex]1.25(16)+ 2.50(2) = 25[/tex]
[tex]1.25(18)+ 2.50(1) = 25[/tex]
[tex]1.25(20)+ 2.50(0) = 25[/tex]
Thus Caleb can buy 0,2,4,6,8,9,10,12,14,1,6,18,20 lip balms and
0,1,2,3,4,5,6,7,8,9,10 mini note books respectively
Now plotting these value in the graph, we get the below graph
Draw to show the numbers write the number to solve. Charlie gathering apples pears and plums the number of apples and plums are 10 partners there are the same number of apples and pears how many pieces of fruit could Charlie gather?
Answer:
Charlie could gather 30 pieces of fruit.
Fetching Information:
As Charlie has gathered apples pears and plums, and the number of apples and plums are 10 partners, and also there are same number of apples and pears.
What to Determine?
How many pieces of fruit could Charlie determine?
Solution:
Let 'a' be the number of apples, 'b' be the number of plums, and 'c' be the number of pears.
As the number of plums and apples is same i.e both are 10 in numbers.
So, a = b = 10
Note that number of pears and apples is also same. So, the the total number of pears will be 10.
So, c = 10
Total number of pieces of fruit = number of apples + number of plums + number of pears
Hence,
Total number of pieces of fruit = a + b + c
= 10 + 10 + 10
= 30
Thus, Charlie could gather 30 pieces of fruit.
Keywords: number, total
Lear more about word problem solving from brainly.com/question/10731035
#learnwithBrainly
Mason has an offer to buy an item with a sticker price of $14,800 by paying
8530 a month for 36 months. What interest rate is Mason being offered?
A 12.8%
B. 25.7%
C6.4%
d8,5%
Answer:
8.83%
Step-by-step explanation:
Using compound interest formula
A = P ( 1+ r) ^t where A = amount = 530 × 36 = $ 19080, P = the amount of the loan = $ 14800, t = 36 / 12 = 3 years
substitute the values into the equation
19080 = 14800 (1 + r) ^3
19080 / 14800 = (1 + r) ^3
1.2892 = (1 + r) ^3
∛(1.2892) = 1 + r
1.0884 = 1 + r
r = 1.0884 - 1 = 0.0884 × 100 = 8.83%
Answer:
d 8,5%, the most probable, provided the error in the question is confirmed!!!
Step-by-step explanation:
Mason has an offer to buy an item with a sticker price of P= $14,800.
He is to pay $8530 a month for 36 months.
Total amount paid by Mason will be
$8530*36= $307,080
This will be very outrageous compared to the sticker price!!!
If we presume he is paying yearly 8530 for 36 months or 3 years.
Then total amount paid will be 8530*3 = $25590
Also very high in my opinion.
Perhaps the dollar sign was wrongly typed as '8' in the question and he pays only $530 monthly,
Then the total amount paid will be $19,080
This is quite reasonable.
If the interest rate is compounded for n (n=3, 36 months = 3 years)
years, thus
19080= ((P*(1+i)^n) , meaning
19080 =((14800(1+i)^3), which when evaluated yields
i=8.8%
PLEASE PLEASE HELP ME SOMEONE I AM BEING TIMED
virgina has 1/2 of a cake leftover. she wants to serve each of her guests 1/10 of a whole cake. how many guests can she serve.
Answer:
5 guests
Step-by-step explanation:
10 slices per cake
half of that is 5 slices
1 slice = 1 guest
Please help! I really need it!
Answer:
1. x > 4
2. m < 2
3. x > 2
4. x < -6
Step-by-step explanation:
These 4 inequalities will be solved the same way we solve equations. We take variables to one side and numbers to another and use algebra to solve. Each of them are solved shown below:
1.
[tex]4+6x<x+6x\\4+6x<7x\\4<7x-6x\\4<x[/tex]
so x is greater than 4, we can write (variable first):
x > 4
2.
[tex]m+16>8m+2\\16-2>8m-m\\14>7m\\\frac{14}{7}>m\\2>m[/tex]
so m is less than 2, we can write:
m < 2
3.
[tex]5x-1>13-2x\\5x+2x>13+1\\7x>14\\x>\frac{14}{7}\\x>2[/tex]
so x is greater than 2, we can write:
x > 2
4.
[tex]-3x-2>-x+10\\-2-10>-x+3x\\-12>2x\\\frac{-12}{2}>x\\-6>x[/tex]
so x is less than -6, we can write:
x < -6
Given the two similar triangles, find y.
A= y = 4
B= y = 5
C= y = 6
D= y = 8
giving brainlist to whoever answers with work.
Answer:
The correct answer is B. y = 5
Step-by-step explanation:
Let's recall that two are triangles are similar when its side lengths are proportional. That is in our case, if Δ ABC is similar to Δ DEF , then the following equation holds:
EF/BC = DF/AC
Replacing with the real values:
6/12 = y/10
Cross multiplication:
12 * y = 10 * 6
12y = 60
y = 60/12
y = 5
The correct answer is B. y = 5
plzzz help rn i need it
Answer:
Therefore the slope of the line shown on the graph is option D)
[tex]-\dfrac{2}{3}[/tex]
Step-by-step explanation:
Given:
Let the Two points on the line be
point A( x₁ , y₁) ≡ ( 0 , 0) one as a Origin
point B( x₂ , y₂) ≡ (-3, 2)
To Find:
Slope AB = ?
Solution:
For a slope we require two points i.e
[tex]Slope=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Substituting the given values we get
[tex]Slope(AB)=\frac{2-0}{-3-0}\\\\Slope(AB)=-\dfrac{2}{3}[/tex]
Therefore the slope of the line shown on the graph is option D)
[tex]-\dfrac{2}{3}[/tex]
Determine whether y2=3x+1 is a function.
The equation y2=3x+1 is a function.
Explanation:Determine whether y2=3x+1 is a function
A function is a relation in which each input has exactly one output. To determine if the equation y2=3x+1 is a function, we need to check if each input value of x corresponds to exactly one output value of y.
In this case, the equation represents a quadratic curve, which passes the vertical line test, meaning that it is indeed a function.
For example, when x=1, we can substitute it into the equation as follows: y2 = 3(1) + 1 = 4.
Therefore, for every value of x, there is a unique value of y, indicating that the equation y2=3x+1 is a function.