x = 1/2, x = -1/2
Simplify:
4|x| + |-4| = |-6|
4|x| + 4 = 6
4|x| = 2
|x| = 1/2
Solutions:
1) x = 1/2
2) x = -1/2
A total of 240 people drove to a meeting. Of those peoplewho attended the meeting, 80% drove there. How manypeople attended the meeting?
The total number of people that drove to the meeting is 240
80% drove to the meeting
Let the total number of people who attended the meeting be x
Using the percentage and whole relationship
Part = percentage x whole
whole = x
part = 240
percentage = 80%
240 = 80/100 * x
240 = 0.8x
Divide both sides by 0.8
240/0.8 = 0.8x/0.8
x = 300
The total number of people that attended the meeting is 300
You want to have $15,000 in 11 years. You will invest how much into an account that has an annual rate of 4.4% compounded daily? Round your answer to two decimal places and assume 365 days per year.
Given:
Future Value = $15,000
time (t) = 11 years
rate (r) = 4.4% or 0.044
number of conversions per year (m) = 365
Find: Initial amount or the Principal
Solution:
Formula for Compound Interest is:
[tex]F=P(1+\frac{r}{m})^{mt}[/tex]From that, we can derive the formula for the Principal or the initial amount.
[tex]P=\frac{F}{(1+\frac{r}{m})^{mt}}[/tex]Let's plug in the given data above to the formula of the principal value.
[tex]P=\frac{15,000}{(1+\frac{0.044}{365})^{365\times11}}[/tex]Then, solve for P.
[tex]P=\frac{15,000}{(1.000120548)^{4015}}=\frac{15,000}{1.622504316}\approx9,244.97[/tex]Answer: You must invest $9, 244.97 to the account in order to get $15,000 after 11 years.
RANGE AND DOMAIN. GRAPSWhat is the Range of this Relation:{(3,0), (-2,6), (-1,4), (-2,0), (1,5)}
Given the relation:
[tex]\mleft\{\mleft(3,0\mright),(-2,6),(-1,4),(-2,0),(1,5)\mright\}[/tex]The range of the relation can be thought of as the set of y-coordinates of a point (x, y). That is, as every second number of the ordered pairs. Additionally, the set should be ordered, and should not contain repeated values. This set is:
[tex]Range=\mleft\lbrace0,4,5,6\mright\rbrace[/tex]express the form in lowest terms 1/3x^3
The expression in the lowest term will be 3^-1x³.
What is a expression?It should be noted that an expression simply has to do with the relationship that can be illustrated having a mathematical operator.
It should be noted that based on the information given, this will be illustrated as:
= 1/3(x³)
This can be illustrated as:
1/3 = 3^-1 multiplied by x³.
= 3^-1x³
This shows the concept of exponents.
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Use the limit definition of the derivative to find the instantaneous rate of change of
SOLUTION:
Step 1:
In this question, we are given the following:
Use the limit definition of the derivative to find the instantaneous rate of change of
Step 2:
The details of the solution are as follows:
An alternative way to find the use the limit definition of the derivative to find the instantaneous rate of change of:
[tex]f(x)\text{ =}\sqrt[]{4x+8\text{ }}\text{ at x = 4}[/tex]Let us take the derivative of the function and we have that:
[tex]\begin{gathered} f(x)\text{ = }\sqrt[]{4x+8}=(4x+8)^{\frac{1}{2}} \\ \end{gathered}[/tex][tex]\begin{gathered} f^I(x)\text{ = }\frac{1}{2}(4x+8)^{-\frac{1}{2}}(4) \\ f^I(x)=2(4x+8)^{-\frac{1}{2}},\text{ when x = 4, we have that:} \\ f^I(4)=2(4(4)+8)^{-\frac{1}{2}} \end{gathered}[/tex][tex]\begin{gathered} f^I(4)=2(16+8)^{-\frac{1}{2}} \\ f^I(4)\text{ = 2 x }\frac{1}{\sqrt[]{24}} \end{gathered}[/tex][tex]f^I(4)\text{ =}\frac{2}{\sqrt[]{24}}[/tex][tex]f^I(4)=\frac{2}{\sqrt[]{24}}=\frac{2}{\sqrt[]{4}X\sqrt[]{6}}=\frac{2}{2X\sqrt[]{6}}=\frac{1}{\sqrt[]{6}}[/tex][tex]f^I(4)\text{ =}\frac{1}{\sqrt[]{6}}[/tex]
Suppose that a certain basketball athlete earned $17,250,000 to play 80 games, each lasting 48 minutes. (Assume no overtime games.)
The amount paid for each is;
1) Amount earned per game = $215625 per game
2) Amount earned per minute played = $4492.1875
3) Amount earned each minute for 2/3 games = $6738.28
4) Amount earned per hour = 4492.1875 * 60 = $269531.25
How to find the rate per game?We are given;
Amount earned by athlete = $17,250,000
Number of games played = 80 Games
Number of minutes per game = 48 minutes
1) Amount earned per game = Amount earned by athlete/Number of games played = 17250000/80 = $215625 per game
2) If he played entire games for the entire minutes;
Amount earned per minute played = 17250000/(80 * 48)
Amount earned per minute played = $4492.1875
3) He played 2/3 of every game. Thus;
Amount earned each minute for 2/3 games = 17250000/((2/3) * 80 * 48)
Amount earned each minute for 2/3 games = $6738.28
4) Since amount earned for every minute is $4492.1875, then we say that;
Amount earned per hour = 4492.1875 * 60 = $269531.25
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2. Refer to the figure shown.a. What is JK?b. What is KM?
Point J is located at 5
Point K is located at 12
Point M is located at 27
a. The length of the segment JK is: 12 - 5 = 7
b. The length of the segment KM is: 27 - 12 = 15
Which of the following is a parent function?O A. f(x) = -3x° +1ОВ.B. f(x) = 2*O c.C. f(x)=23*O D. f(x)=3* - 5
ANSWER:
B.
[tex]f(x)=2^x[/tex]STEP-BY-STEP EXPLANATION:
A parent function is the simplest formula in which no transformations have been made. Therefore, the function that would be the parent one of the answer options is:
[tex]f(x)=2^x[/tex]Im kinda lost on how to solve these could you help me and teach me!
The angles ∠IDA, ∠YDA, and ∠RDI measures 121°, 59°, and 29.5°.
The angle ∠YDF is equal to 121°. The ∠IDA is vertically opposite angle. So, ∠ADI is equal to the ∠YDF. Hence, ∠IDA = 121°.
The angle ∠YDA and the angle ∠ADI form a linear pair. It means ∠YDA and ∠ADI are complimentary angles.
∠YDA + ∠ADI = 180°
∠YDA + 121° = 180°
∠YDA = 180° - 121°
∠YDA = 59°
The ∠FDI is vertically opposite angle to ∠YDA. So, ∠FDI is equal to the ∠YDA. Hence, ∠FDI = 59°. The ray DR bisects the ∠FDI. So, the angle ∠RDI is half of the angle ∠FDI.
∠RDI = (1/2)∠FDI
∠RDI = (1/2)59
∠RDI = 29.5°
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A person tosses a coin 14 times. In how many ways can he get 10 heads?
what value of x is the answer to the equation x - 2 = 16
The value of x is the answer to the equation x - 2 = 16 which is 18.
What is the solution for an equation?An equation is an expression that shows the relationship between two or more numbers and variables. The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of that variable would give a true mathematical statement.
We have been given a linear equation as; x - 2 = 16
We need to find the value of x as the answer to the equation x - 2 = 16.
Therefore, we will eliminate the 2.
x - 2 = 16
Add 2 on both sides of the equation;
x - 2 + 2= 16+ 2
Then ;
x = 18
Hence, the value of x is the answer to the equation x - 2 = 16 which is 18.
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What will be the length of the railing from point A to point B? Show or explain how you got your answer.
To know the length of the railing from point A to point B you can use Pythagoras Theorem.
You draw a right triangle:
You use the given information to know the measure of the legs in the triangle:
You can see that the value of x is the height of 5 steps: 5(7.5 in).
Then:
[tex]x=5(7.5)=37.5in[/tex][tex]x=y=37.5in[/tex][tex]Z=2y=2(37.5in)=75in[/tex]The B is equal to the lenght of 10 steps: 10(9.5in):
Then:
[tex]B=10(9.5in)=95in[/tex]You have the next triangle:
You use the Pythagoras Theorem to find the h:
[tex]h=\sqrt[]{Z^2+B^2}[/tex][tex]h=\sqrt[]{75^2+95^2}[/tex][tex]h=\sqrt[]{14650}[/tex][tex]h=5\sqrt[]{586}\approx121.03in[/tex]The length of the railing from point A to point B is 121.03inWrite 92.5% in a fraction or mixed number in simplest form
FIRST TO ANSWER ALL GETS BRAINEST
Question 1(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
In triangle DEF, m∠D = (3x + 27)°, m∠E = (4x + 22)°, and m∠F = 68°. Determine the degree measure of the exterior angle to ∠D.
54°
58°
122°
126°
Question 2(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
In ΔJKL, m∠J = 78° and m∠L = 90°. Determine the measure of the exterior angle to ∠K.
168°
102°
57°
12°
Question 3(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
Triangle UVW is shown with m∠WUV = 36°. The measure of ∠UVW is (5h − 66)°, and the measure of ∠AWB is (5h − 18)°.
triangle UVW with side VW extended through point A and side UW extended through point B, with angle U labeled as 36 degrees
Determine the value of h.
h = 22.8
h = 23
h = 25.4
h = 48
Question 4(Multiple Choice Worth 2 points)
(Interior and Exterior Angles LC)
One interior angle of a triangle is 95.5°, and the other two interior angles are congruent. What is the degree measure of one of the congruent angles?
42.25°
47.75°
84.5°
90°
Question 5(Multiple Choice Worth 2 points)
(Interior and Exterior Angles LC)
For ΔABC, m∠A = 28.7° and m∠B = 123.8°. Determine m∠C.
27.5°
62.5°
76.25°
152.5°
Question 6(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
For triangle XYZ, m∠X = 38°, m∠Y = (5x − 11)°, and m∠Z = (4x − 45)°. Find m∠Y.
m∠Y = 22°
m∠Y = 43°
m∠Y = 99°
m∠Y = 158°
Question 7(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
Triangle ABC is shown with exterior ∠z.
triangle ABC with angle A labeled 58 degrees, angle B labeled 44 degrees, and side AC extended with angle z labeled as exterior angle to angle C
Determine m∠z.
136°
102°
78°
58°
The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126° so option (D) is correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.
It is known that the sum of all three angles inside a triangle will be 180°.
So, m∠D + m∠E + m∠F = 180°
(3x + 27) + (4x + 22) + 68 = 180
7x + 49 + 68 = 180
7x = 63
x = 9
So, m∠D = (3(9) + 27)° = 54°.
The exterior angle of D = 180- 54 = 126°.
Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126°".
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Which equation is perpendicularl to 2x+3y=12A y=2/3X+5B y=-2/3X+5C y=3/2X+5D y= -3/2X+5
The equation of the line perpendicular to the given equation is;
[tex]y\text{ = }\frac{3}{2}x\text{ + 5}[/tex]Option C is the correct answer
Here, we want to select which of the equations in the option is perpendicular to the given equation
Firstly, we need to understand that for two equations to be perpendicular, then the product of their slopes must be equal to -1
Before we proceed to compare, we need to write the equation in the general form
The equation of the line written in the general form will be;
[tex]y\text{ = mx + b}[/tex]where m represents the slope and the term b represents the y-intercept
Now, let us proceed to write the equation in the standard form;
We have this as;
[tex]\begin{gathered} 3y\text{ = -2x + 12} \\ \\ y\text{ = -}\frac{2}{3}x\text{ + 4} \end{gathered}[/tex]Compared with the general form, we can see that the slope of this line is -2/3
Now let us get the slope of the line that would be perpendicular to it;
[tex]\begin{gathered} \frac{-2}{3}\times\text{ m = -1} \\ \\ m\text{ = }\frac{3}{2} \end{gathered}[/tex]Now, the equation perpendicular to what was given will have a slope of 3/2
Fortunately, all the options in the question have been written in the general form
The one with a slope of 3/2 is option C
[tex]y\text{ = }\frac{3}{2}x\text{ + 5}[/tex]solve the following compound inequality.-6x+7<55 AND 5x-4≤16OA. x<-8 AND x < 4OB. -9< x≤4OC. -8 < x≤4OD. x≤4
The given compound inequality is:
[tex]-6x+7\lt55\text{ and }5x-4\leq16[/tex]Solve the first inequality:
[tex]\begin{gathered} -6x+7<55 \\ -6x<55-7 \\ -6x<48 \\ \text{ Divide both sides by }-6\text{ and reverse the inequality sign:} \\ -\frac{6x}{-6}\gt\frac{48}{-6} \\ x\gt-8 \end{gathered}[/tex]Solve the second inequality:
[tex]\begin{gathered} 5x-4\leq16 \\ \text{ Add }4\text{ to both sides of the inequality:} \\ 5x-4+4\leq16+4 \\ 5x\leq20 \\ \frac{5x}{5}\leq\frac{20}{5} \\ x\leq4 \end{gathered}[/tex]Therefore, the correct answer is choice C:
-8 < x ≤ 4
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
C(x) = 75x + 1908
Step-by-step explanation:
C(x) is the cost function.
The cost of making x bicycles is the sum of the fixed costs and the cost per bicycle.
The fixed cost is $1908.
The cost per bicycle is $75, so the per bicycle cost for x bicycles is 75x.
Add the two costs, and you get:
C(x) = 75x + 1908
Can someone help me
Which graph represents the solution set of the system of inequalities?
{y<−3x−2y≤x−2
Responses
A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1comma 1 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. The region below the dashed line and below the solid line is shaded.
Image with alt text: A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1comma 1 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. The region below the dashed line and below the solid line is shaded.,
A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 1 end ordered pair and begin ordered pair 0 comma negative 3 end ordered pair. A solid line passing through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. The region above the dashed line and above the solid line is shaded.
Image with alt text: A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 1 end ordered pair and begin ordered pair 0 comma negative 3 end ordered pair. A solid line passing through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. The region above the dashed line and above the solid line is shaded.,
The graph that represents the solution to the system of inequalities is given in the attachment below.
How to Determine the Graph to a System of Inequalities?To find the correct graph that represents the solution to the system of inequalities, determine which inequality represents each of the line that is plotted on the graph.
The first inequality, y < -3x - 2, has a slope of -3, a y-intercept of -2, and an inequality sign "<" which means the shaded part will be below the a dotted or dashed boundary line.
The second inequality, y ≤ x − 2, has a slope of 1, a y-intercept of -2, and an inequality sign "≤" which means the shaded region is below a solid boundary line.
The graph that represents the above stated features is the graph of the system of inequalities shown below.
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some one please help me! quick!
m(4) = 110° due to the Transitive Property.
The Transitive Property states a that if a = b and b = c, then a = c.
m(3) + m(4) = 180 due to the definition of Supplementary Angles. All supplementary angles add up to 180°.
m(3) = 70° because 180 - 110 = 70.
If Mary fails her classes then she cannot graduate
Choose the best estimate for the quotient.
27.2/178.6
A) 5
B) 6
C) 50
D) 60
Answer:
B
Step-by-step :
The quotient is 6.5 so the estimate is closest to 6.
For each function graphed below, state whether it is one to one !!
Consideremos la recta y=6x-4.
¿Cuál es la pendiente de una recta paralela a esta recta?
¿Cuál es la pendiente de una recta perpendicular a esta recta?
Pendiente de una recta paralela:
Pendiente de una recta perpendicular:
Slope of a parallel line: 6
Slope of a perpendicular line: -1/6
What is Slope ?
slope, The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytical geometry ("slope equals rise over run").
Given equation,
y=6x-4
The equation of a line with slope m is given as:
y=mx+c
Rearranging the given equation:
y=(6)x+(-4)
By equating the equations we get,
m= 6
Which is slope of a parallel line
Now any parallel line would have the same slope.
And slope of a perpendicular line would be −1/m.
i.e. m(perpendicular)= -1/6
Hence, Slope of a parallel line is 6 and Slope of a perpendicular line is -1/6
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!helpppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
4x + 3
Step-by-step explanation:
Three more means you're adding three to the number. So, you have + 3 right now. Four times the number of shells Talia collects is 4x with x representing Talia's shells. We don't know how many she has so it's represented by x. Now, put everything we have together. 4x + 3.
Hope this helps! :)
Laying down my n buffer is concerned after receiving her weekly paycheck she believes that her deductions for social security,Medicare,and federal income ta withholding (fit) may be incorrect Larsen is paid a salary of 4330 she is married filling jointly and prior to this payroll check has total earnings of 140,460 what are the correct deductions for social security Medicare and fit assume a rate of 6.3% on 142,809 for social security and 1.45% for Medicare
Correct deduction for social security Medicare and fit at 6.3% = 8,996.967
Correct deduction for Medicare at rate of 1.45% = 2,070.731
What is Medicare?Medicare is defined as a type of health insurance that reduces the fees incurred by an individual following the reception of health services.
After deductions the total earning = 140,460
The correct deduction for social security, Medicare and fit at the rate of 6.3% of 142,809;
= 6.3/100 × 142,809
= 899696.7/100
= 8,996.967
The correct deduction for Medicare at the rate of 1.45%;
= 1.45/100 × 142,809
= 207,073.05/100
= 2,070.731.
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A stand at the farmers market sells different types of apples, as shown in the table.
Cost ($)
Weight
Apple A Apple B Apple C
4.90
4 lb
1.00
10 oz
0.45
lb
Which type of apple costs the least per pound? Apple A
The cost of Apple A: $1.225
What is Weight?
The weight of an object is the force exerted on it by gravity. Some standard textbooks define weight as a vector quantity, the force of gravity acting on an object. Some define weight as a scalar quantity that is the magnitude of gravity.
Cost of the different types of the apple have been given as,
Apple A = costing $4.90 for 4 lb
Apple B = costing $1.00 for 10 oz
Apple C = costing $0.45 for 1/2 lb
For Apple A,
Since, cost of 4 lb = $4.90
Therefore, cost of 1 lb = 4.90/4
= $1.225
For Apple B,
Since, 1 oz = 0.0625 lb
Therefore, 10 oz = 0.0625 × 10
= 0.625 lb
Since, cost of 10 oz = $1.00
Therefore, cost of 0.625 lb = $1.00
And cost of 1 lb = 1/0.625
= $1.6
For Apple C,
Since, cost of 1/2 lb = $0.45
Therefore, cost of 1 lb = 0.45 × 2
= $0.90
Hence, Cost of Apple A will be the least with $1.225 per pound.
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hello thank you for viewing my question I seem to be stuck on this problem can you please help thank you
We have 9 boy kittens and 6 girl kittens, a total of 15 kittens.
9 cats will be selected and we have to calculate the probability that 5 boy kitttens and 4 girl kittens are chosen.
We could have modeled as a binomial experiment, but the probability of choosing a boy kitten is not constant after each selection. Then, we have to select an alternative method.
We can think of it of a combinatorial problem.
In this case, it is a combination problem, as the order of selection does not matter and each kitten is equivalent within its category.
Repetition is not allowed: a kitten selected can not be selected again.
We can start finding all the possible combinations for 9 kittens out of the total 15 kittens:
[tex]C(15,9)=\frac{15!}{9!(15-9)!}=\frac{15!}{9!6!}=5005[/tex]The probability of selecting 5 boys and 4 girls will be the relation between the outcomes where there are 5 boys and 4 girls and the total number of outcomes we have just calculated.
Then, we can now calculate how many combinations of 9 kittens have 5 boys and 4 girls as a product of two combinations: the combinations for the boys C(9;5) and the combinations for the girls C(6;4).
We can calculate this as:
[tex]\begin{gathered} C(9,5)=\frac{9!}{5!4!}=126 \\ C(6,4)=\frac{6!}{4!2!}=15 \\ =>C(9,5)*C(6,4)=126*15=1890 \end{gathered}[/tex]We can now calculate the probability as the ratio of combinations 1890/5005:
[tex]p=\frac{1890}{5005}\approx0.378[/tex]Answer: the probability is 0.378.
Al got an estimate for repairs on his bike. Theparts will cost $17.50, and the parts and labortogether will not be more than $40. Whatinequality shows the possible labor costs, L?
Let's list down the pieces of information given the scenario:
Cost of bike parts = $17.50
Bike parts and labor together = not more than $40/ lesser than or equal to $40.
Let's now generate the equation based on the given information,
Let,
L = Labor cost
[tex]\text{ Cost of parts+Labor Cost }\leq\text{ \$40 ;since the total must not be more than \$40}[/tex][tex]\text{ \$17.50 + L }\leq\text{ \$40 ; inequality showing the possible total cost}[/tex]Let's now generate the inequality showing the possible labor cost, L
[tex]\text{ \$17.50 + L }\leq\text{ \$40 }\rightarrow\text{ L }\leq\text{ \$40 - \$17.50}[/tex][tex]\text{ L }\leq\text{ \$22.50}[/tex]Therefore, the cost of labor must not be more than $22.50.
Write the correct equation for the following statement.
You decide to rent a limo for prom. The rate is $250 plus $6 per mile
traveled. Write an equation to calculate your total cost (c) at the end of
the evening for a given number of miles (m).
250+6m
If you travel 45 miles what will be your total bill at the end
of the evening?
Answer:
Easy;
Substitute m (miles) for 45.
250+6(45)
(6 dollars per mile, times 45 miles, plus the 250 flat rate)
250+270
520
So you would be charged 520 dollars total at the end of the evening.
Hope this helped!
Answer:
520
Step-by-step explanation:
so first you would multiply 6 by 45 which is 270 then add 250 which is 520
hope this helped, have a great day
What is the slope of y-9=3(x+12)
Step-by-step explanation: