Answer:
c
Step-by-step explanation:
It is measured in the same unit as the original unit, so x will be 1.42x
Add the service charge as it is a constant addition, and we end up with:
y = 1.42x + 13.20
the correct equation representing the monthly water bill is:
[tex]\[ y = 1.42x + 13.20 \][/tex]
The correct option is (c).
Sure, let's break down the calculation step-by-step.
1. Monthly service charge: The monthly service charge is a fixed amount, which is $13.20.
2. Usage charge: The usage charge is $1.42 for every 100 cubic feet of water used. Since x represents the amount of water used in hundreds of cubic feet, the usage charge can be calculated as \(1.42x\).
3. Total monthly cost: To determine the total monthly cost \(y\), we add the monthly service charge to the usage charge. Therefore, the equation representing the total monthly bill is:
[tex]\[ y = \text{Monthly service charge} + \text{Usage charge} \][/tex]
[tex]\[ y = 13.20 + 1.42x \][/tex]
So, the correct equation representing the monthly water bill is:
[tex]\[ y = 1.42x + 13.20 \][/tex]
Therefore, the correct answer is option C.
The high school soccer booster club sells tickets to the varsity matches for $4 for students and $8 for adults. The booster club hopes to earn $200 at each match. Which equation could be used to represent the total amount the booster club would like to earn from ticket sales at each match? a
y = 4x + 8
b
4x + 8y = 200
c
12x = 200
d
y - 4 = 8(x - 200
The correct equation for the booster club aiming to earn $200 per match from student and adult tickets priced at $4 and $8, respectively, is 4x + 8y = 200. This represents the sum of $4 per student ticket (x) and $8 per adult ticket (y) sold to reach the goal.
Explanation:To solve the problem presented by the high school soccer booster club, we need to formulate a linear equation that represents their goal for ticket sales revenue from students and adults. The tickets are priced at $4 for students and $8 for adults. If we let x represent the number of student tickets sold and y the number of adult tickets sold, the total revenue T would be expressed as the sum of $4 per student ticket and $8 per adult ticket.
The booster club aims to earn $200 per match, which gives us the equation for their goal: 4x + 8y = 200. Here, the 4 and 8 are the prices of the tickets for students and adults, respectively, and x and y are the numbers of tickets sold. This clearly aligns with option b from the choices you've provided.
To illustrate with an example similar to your situation, a tutoring school equation of y = 3000x + 500 combines a one-time enrollment fee of $500 with a tuition of $3000 per year. In this case, y represents the total cost of attendance and x the number of years a student is enrolled.
Each week morning sunshine cafe orders coffee packets that costs $2.50 per packet with a 10.00 shipping fee . If morning sunshine Cafe does not want to spend more than $554.00 on coffee packets per week how many packets could they purchase
Answer:
193 packets
Step-by-step explanation:
Each morning they order with a shipping fee of $10 daily.
Considering they order all 7 days of the week, so the total shipping fee for the week would be:
7 * $10 = $70
Their budget for the week is $554, out of which $70 is for shipping for the week, so remaining balance would be:
554 - 70 = $484
This 484 dollars are for coffee packets that cost $2.50 each, so the number of packets would be:
484/2.50 = 193.6
You can't order fractional packets so 193 packets is the max in this budget
ANSWER CORRECTLY!
Which factor inspired the resurgence of the KKK in the 1920s?
A. increased immigration from Eastern Europe and Asia
B. pseudo-scientific racism
C. the film The Birth of a Nation
D. All answers are correct.
Answer:
D. All answers are correct
Step-by-step explanation:
The film The Birth of a Nation promoted the KKK.
There was pseudo-scientific racism also going on.
From these two facts, we know that the answer definitely is D. Also, generally when there is "All of the above" as an answer, "All of the above" is correct.
Tori earns $9 for each hour of dog walking .how many hours in all will it take tori to earn a total of $36
Answer:
4
Step-by-step explanation:
36 / 9 = 4
4 x 9 = 36
How can I factor 48 + 24x??
Answer:
24(x+2)
Step-by-step explanation:
24 can be pulled from both 24 and 48
A chemist is using 357 milliliters of a solution of acid and water. If 13.2 % of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
Final answer:
To find the milliliters of acid in the solution, multiply the total volume of the solution by the acid percentage.
Explanation:
To find the milliliters of acid in the solution, we first need to calculate the volume of acid. We know that 13.2% of the solution is acid, so we can calculate the volume of acid by multiplying the total volume of the solution by the acid percentage:
Volume of acid = 357 mL * 0.132 = 47.124 mL
Rounding to the nearest tenth, we get:
Volume of acid = 47.1 mL
please draw accurately much appreciated
Answer:
draw a square
Step-by-step explanation:
draw a square then write 32mm on all sides
draw a triangle with a wide bottom a small side a medium side
Find the value of the following expression. 9 ( − 4 ) − 3 = a0
Answer: -39
Step-by-step explanation:
9 x -4 -3 = -39
Help me please I need an explanation.!
Answer:
A
Step-by-step explanation:
An ordered pair is a point on a coordinate graph that represents data. The x represents an independent variable and the y a dependent. Your y is your vertical axis. Each square on this graph represents 50 feet. The line on your graph hits the intersection between 2 minutes and 100 feet. Therefore (2,100) Is an ordered pair
gina has 250 in her saving account she puts in 4% of her monthly paycheck of 3,100 each month rodger has 350 in his savings account and put in 3% of his monthly salery of 2,900 each month in how many months to the nearest month will gina have more in her account than rodger does
Answer:
3 months
Explanation:
Amount saved in Gina’s saving account= 250
Amount Gina puts in her account each month= 4% of 3100
=[tex]\frac{4}{100} \times 3100[/tex]
= 4 × 31
= 124
Hence total amount added in each month =124
Therefore money credited x months
= 250 + 124 x
Amount saved in Rodger’s account = 350
Amount Rodger puts in his account each month = 3% of 2900
=[tex]\frac{3}{100} \times 290[/tex]
=87
Hence total amount added in each month = 87
Therefore money credited x months
=350 + 87 x
Now to calculate the nearest month when Gina have more in her account than Rodger does
=Amount of money credited in x months in Gina’s account ≥ Amount of money credited in x months in Rodger’s account
=250+124 x ≥ 350+87 x
=37 x≥100
= x≥2.78
=3
Which of the following is equal to the rational expression when x≠5 or -1?
(x-7)(x + 1)
(x + 1)(x - 5)
Answer: (x-7)/(x-5)
The (x+1) terms divide and cancel out due to the rule that x/x = 1, when x is nonzero. In that rule, we can replace 'x' with any algebraic expression we want.
Please answer this correctly
Answer:
20 cups
Step-by-step explanation:
16 ounces = 1 pound
8 ounces = 1 cup
16 ounces = 2 cups
1 pound = 2 cups
10 pounds = 20 cups
Answer:
20 cups
Step-by-step explanation:
Think
1 pound is 16 oz
So each cup has 8 oz
This you have to convert the 10 pound into ounces
Which then equals 160 ounces
Now divide 160 ounces by 8 and you get..
You get 20
So, 10 pounds of apples fit into 20 cups
2(7k + 1) - 5(3k + 3) = 1 - 2k + 6 + 5k
Answer:
k = -5
Step-by-step explanation:
2(7k + 1) - 5(3k + 3) = 1 - 2k + 6 + 5k
At first, we will break the parenthesis by multiplying by the adjacent number. As we know, (+) x (-) = (-) and (-) x (-) = (+) [Algebraic operation]
or, (2*7k) + (2*1) - (5*3k) - (5*3) = (1 + 6) + 5k - 2k
or, 14k + 2 - 15k - 15 = 7 + 3k
Interchanging the values, we can get,
or, 14k - 15k - 3k = 7 + 15 - 2
or, 14k - 18k = 22 - 2
or, -4k = 20
or, k = 20/(-4)
or, k = -5
Therefore, the answer is -5
Solve equation 9.6=1.2b
Answer:
b = 8 your welcome
Evaluate 6^0 + 6^1 +6^2
18
42
43
Answer:
it's 18 if your talking about multiplication
It's 42 if your talking about the powers
Step-by-step explanation:
Multiplication-(6•0)+(6•1)+(6•2)= 18
The powers-(6^0)+(6^1)+(6^2)=42
Answer:
the answer is 43
Step-by-step explanation:
the perimeterp of rauls picture is 108 centimeters.the length of the picture is 18centimeters.what is the widthof the picture?
Answer:
36 cm
Step-by-step explanation:
We know that the perimeter is 2 l + 2 w.
In this case, the equation is 36 + 2 w = 108
2 w = 72
w = 36
When you are given three side lengths for a triangle, how do you know which length to substitute for a, b, or c in the Pythagorean Theorem?
Answer:
When Sum of square of two Sides is equal to square of third side of triangle.
Step-by-step explanation:
Given:
Three side length of triangle are given we need find the which value to substitute for a, b, c in Pythagoras theorem.
First we will find the squares of all length, then we will check which two square of side are equal to square of third side as per Pythagoras theorem.
Hence the two side would according be a and b and third side will become c.
For example if length of triangle is given as 6 cm, 8 cm and 10 cm.
We will first take square of all
[tex]6^2=36\\8^2=64\\10^2=100[/tex]
Now we can see that
[tex]36+64=100\\6^2+8^2=10^2[/tex]
Now by Pythagoras theorem.
[tex]a^2+b^2=c^2[/tex]
Hence we can say a = 6 cm, b = 8 cm, c= 10 cm
The Pythagorean Theorem is specifically applicable to right-angled triangles and states that:
[tex]\[a^2 + b^2 = c^2\][/tex]
Theorem, follow these steps:
1. Identify the longest side: The hypotenuse c is always the longest side in a right-angled triangle.
2. Assign the longest side to c : Among the three given side lengths, the one with the greatest value should be assigned to c .
Example
Suppose you are given three side lengths: 5, 12, and 13. To determine which lengths correspond to a , b , and c :
1. Identify the longest side: Among 5, 12, and 13, the longest side is 13.
2. Assign the longest side to c : So, c = 13 .
3. Assign the remaining sides to a and b: Thus, a and b can be 5 and 12, respectively (or vice versa).
Verify using the Pythagorean Theorem:
[tex]a^2 + b^2 = c^2[/tex]
[tex]5^2 + 12^2 = 13^2[/tex]
25 + 144 = 169
169 = 169
Since the equation holds true, the side lengths 5, 12, and 13 do indeed form a right-angled triangle, with 13 being the hypotenuse.
General Case
When given any three side lengths x , y , and z :
1. Determine the longest side and assign it to c .
2. The remaining two sides are a and b
3. Check if [tex]\( a^2 + b^2 = c^2 \)[/tex] to verify if the triangle is a right-angled triangle.
By following this process, you can correctly identify the sides to substitute into the Pythagorean Theorem.
15+3x=45 solve the equation
Answer:
x= 10
Step-by-step explanation:
45-15=30
30/3=10
If the scale factor is ⅓, and a side of the original square is 3 units long, what will be the length of a side of the dilated square? A. 9 units B. 6 units C. 1 unit D. ⅓ units
Answer: c) 1 unit
Step-by-step explanation: Because if u take the scale factor and multiply it by 3
Answer:
C: 1 unit
Step-by-step explanation:
(3 units) times scale factor (1/3) comes out to (1/3)(3 units), or 1 unit.
The correct answer is C: 1 unit.
What is the margin of error?
Will measured the diameter of a penny as 1.9 cm using the
ruler.
1.9 cm
1.5 cm to 2.0 cm
1.5 cm to 2.5 cm
1.85 cm to 1.95 cm
1.90 cm to 1.95 cm
@
2
3
4
Note: Ruler is not drawn to scale,
Answer:
The margin of error is 1.85 cm to 1.95 cm.
Step-by-step explanation:
Given:
Will measured the diameter of a penny as 1.9 cm using the ruler.
We need to find the margin error.
Now, as we know that the margin of error is a statistic expressing the amount of random sampling error in a survey's results.
It is an amount (usually small) that is allowed for in case of miscalculation or change of circumstances.
Now, we have the margin of error to be:
1.85 cm to 1.95 cm.
As, the value of change to the left and right of 19 is same and is small it is 0.05.
So, 1.9-0.05 = 1.85 cm
and 1.9+0.05 = 1.95 cm .
Hence, the margin of error is: ± 0.05.
Therefore, the margin of error is 1.85 cm to 1.95 cm.
One lunch table can hold 10 students. There are 60 students in 3rd grade. How many lunch tables are needed so that every student in 3rd grade can eat lunch at the same time?
Answer:
6 lunch tables
Step-by-step explanation:
Since one lunch table can hold 10 students and 60 students are needed to hold,
60 ÷ 10 = 6 lunch tables
Answer:
6
Step-by-step explanation:
1 table is 10
60 divided by 10= 6
9 candies cost less than $10 while 10 cost more than $11 how much does each candy cost
Answer:
this threw me off ,i got the same question:(
Step-by-step explanation:
Barry plays fullback on his high school team. Sometimes he looses yardage and sometimes he gains yardage. Determine Barry's total yardage in the game below:
+6,-3,0,15,-1,8,11,-6
Answer:
30
Step-by-step explanation:
Simplify from left to right
6-3+15-1+8+11-6
=3+15-1+8+11-6
=18-1+8+11-6
=17+8+11-6
=25+11-6
=36-6
=30
prove that 3(x+1)(x+7)-(2x+5)² is never positive
To prove that 3(x+1)(x+7)-(2x+5)² is never positive, we can expand and simplify the expression to -x²+4x-4, which is always negative.
Explanation:To prove that 3(x+1)(x+7)-(2x+5)² is never positive, we can use algebraic manipulation and properties of quadratic equations. Let's expand and simplify the expression:
3(x+1)(x+7)-(2x+5)² = 3(x²+8x+7)-(4x²+20x+25) = 3x²+24x+21-4x²-20x-25 = -x²+4x-4
Since the leading coefficient of the quadratic term is negative (-1), the graph of this equation will be a downward-opening parabola. Therefore, the quadratic expression is never positive.
The expression [tex]\(3(x+1)(x+7)-(2x+5)^2\)[/tex] is never positive for all real values of x.
Step 1
To prove that [tex]\(3(x+1)(x+7)-(2x+5)^2\)[/tex] is never positive for all real values of x, we can simplify the expression and analyze its sign.
Expanding the expression:
[tex]\[3(x+1)(x+7)-(2x+5)^2 = 3(x^2 + 8x + 7) - (4x^2 + 20x + 25)\][/tex]
[tex]\[= 3x^2 + 24x + 21 - 4x^2 - 20x - 25\][/tex]
[tex]\[= -x^2 + 4x - 4\][/tex]
Step 2
Now, we have a quadratic expression [tex]\( -x^2 + 4x - 4\)[/tex]. The coefficient of [tex]\(x^2\)[/tex] is negative, indicating a downward-opening parabola. Therefore, the maximum value of the expression occurs at the vertex, which lies at [tex]\(x = \frac{-b}{2a} = \frac{-4}{2(-1)} = 2\)[/tex].
Substituting x = 2 into the expression, we get:
[tex]\[ -2^2 + 4(2) - 4 = -4 + 8 - 4 = 0 \][/tex]
Since the maximum value is 0, the expression is always non-positive.
The expression [tex]\(3(x+1)(x+7)-(2x+5)^2\)[/tex] is never positive for all real values of x, as proven by its maximum value of 0.
There are between 24 and 40 students in the class
the ratio for boys to girls is 4:7
how many students are in the class
Answer:
33 Students
Step-by-step explanation:
4+7=11 so the number of students in the class must be a multiple of 11. The only multiple of 11 between 24 and 40 is 33.
Answer:
33
Step-by-step explanation:
Let's take the constant of proportionality to be X
4x+7x=between 24 to 40
11x= 24 to 40
X should be a natural number therefore the number of students should be multiple of 11
Only multiple of 11 between 24 and 40 is 33
A rectangle is 10 cm longer than it is wide. If its length and width are both decreased by 2 cm, its area
is decreased by 48 cm'. Find the dimension of the original rectangle.
Answer:
Step-by-step explanation:
Yeah it right thank sweetheart
The original width of the rectangle is 8 cm and the original length is 18 cm. These dimensions are found by setting up an equation based on the change in area when both dimensions are reduced by 2 cm.
Finding Original Dimensions of a Rectangle
Let's denote the width of the rectangle as w, and the length will then be w + 10 cm. The area of the original rectangle is w(w + 10) square centimeters. Now, by decreasing each dimension by 2 cm, the new width becomes w - 2 cm and the new length becomes (w - 2) + 10 cm = w + 8 cm. The area of the new rectangle is (w - 2)(w + 8) square centimeters.
The problem states that the area of the rectangle is decreased by 48 cm2 when the dimensions are reduced. This gives us the equation:
w(w + 10) - (w - 2)(w + 8) = 48
Expanding the terms and solving for w will provide us with the width of the original rectangle. After finding w, we can calculate the original length by adding 10 cm to the width. To solve for w, we proceed with the calculation:
[tex]w_2 + 10w - (w_2[/tex] + 6w - 16) = 48
w2 + 10w - w2 - 6w + 16 = 48
4w + 16 = 48
4w = 32
w = 8 cm.
Therefore, the original width is 8 cm and the original length is 18 cm (that is, 8 cm + 10 cm).
Which set of equations could be parametric equations?
y= x and y= 3x
y= x + 1 and y= 3x2
x= t and y=3t
x= 3y and y= x+1
The set of equations x = t and y = 3t could be parametric equations ⇒ 3rd answer
Step-by-step explanation:
Lets explain the meaning of parametric equations
A parametric equation is where the x and y coordinates are both written in terms of another letter
Examples:
x = 2t and y = 2 - t²x = 0.5 Ф and y = 2Ф, where Ф is measured from the positive x-axisLet us find the set of the parametric equations from the answer
Fist answer:
∵ y = x and y = 3x
∴ It is a set of linear equations
Second answer:
∵ y = x + 1 and y = 3x²
∴ It is a set of linear and quadratic equations
Third answer:
∵ x = t and y = 3t
∵ x and y are represented in terms of t
∴ It is a set of parametric equations
Fourth answer:
∵ x = 3y and y = x + 1
∴ It is a set of linear equations
The set of equations x = t and y = 3t could be parametric equations
learn more:
You can learn more about the parametric equations in brainly.com/question/1600331
#LearnwithBrainly
Please help i’m desperate
Answer:
2x + 2(x - 5) = 78
x + x - 5 = 39
2x = 44
x = 22
Rate of the slower cyclist = 17 mph
Rate of the faster cyclist = 22 mph
| Sample Response: Linear relationships can be
compared using their initial values, or y-intercepts, and
their rates of change, or slopes. Initial values can tell
you which relationship started with a greater value.
Comparing slopes can tell you which relationship is
rising or falling faster.
Which of the following did you include in your
response? Check all that apply.
initial value (y-intercept) of each function
rate of change (slope) of each function
initial value to compare starting points
slope to compare rise or fall
Answer:
Initial value (y-intercept) of each function.
Rate of change (slope) of each function.
Initial value to compare starting points.
Slope to compare rise or fall. (Answer)
Step-by-step explanation:
Sample Response: Linear relationships can be compared using their initial values, or y-intercepts, and their rates of change, or slopes. Initial values can tell you which relationship started with a greater value. Comparing slopes can tell you which relationship is rising or falling faster.
Therefore, I included in the response
Initial value (y-intercept) of each function.
Rate of change (slope) of each function.
Initial value to compare starting points.
Slope to compare rise or fall. (Answer)
Find the slope and the y-intercept of the line.
6x + 3y = -3
Write your answers in simplest form.
Answer:
slope = - 2, y- intercept = - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 6x + 3y = - 3 into this form by subtracting 6x from both sides
3y = - 6x - 3 ( divide all terms by 3 )
y = - 2x - 1 ← in slope- intercept form
with slope m = - 2 and y- intercept c = - 1