61.45 times 8.5% = 5.22
61.45 + 5.22 = 66.67 total bill with tax
66.67 * 15% = 10.00
66.67 + 10 = 76.67 Total bill with tip
Justify each step in solving the equation 6x = 3(x+4) by writing a reason for each statement.
given h(x) = -x + 1, find h(0)
Algebraic Expressions Question
A company charges $59.99 for cable TV installation and $49.99 per month for basic cable service.
Part A
Write an algebraic expression to represent the total cost of m months of basic cable service, including installation.
Algebraic Expression: ________________
Part B
How much will it cost for installation and one year of basic cable service?
Explain:
Total Cost: ______________
This problem is continued on the next page.
Part C
After the first 12 months, the charge will be increased to $69.95 per month. What is the total cost of installation and basic cable service for the first two years?
Explain:
Part A.
We can create a linear equation from this problem. Let us say that C is total cost and m is number of months, therefore:
C = 59.99 + 49.99 m
Part B. For m = 12 months, the total cost is:
C = 59.99 + 49.99 * 12
C = $659.87
Part C. We have already calculated in part B the total cost for the 1st year:
C1 = $659.87
For the 2nd year, the equation becomes:
C = 59.99 + 69.95 m
C = 59.99 + 69.95 * 12
C2 = $899.39
Therefore the total cost C1 + C2 is:
$1,559.26
The total cost of m months of basic cable service, including installation, can be represented by the algebraic expression 59.99 + 49.99m. For installation and one year of basic cable service, the cost is 659.87. For the first two years, including installation and basic cable service, the cost is 1549.23.
Explanation:Part A:
To represent the total cost of m months of basic cable service, including installation, we can use the algebraic expression:
59.99 + 49.99m
Part B:
To calculate the total cost for installation and one year of basic cable service, we substitute 12 for m in the expression:
59.99 + 49.99(12) = 59.99 + 599.88 = 659.87
Part C:
For the first two years, the cost includes the installation and basic cable service for the first 12 months at $49.99 per month, and the following 12 months at $69.95 per month. So we write the expression as:
59.99 + 49.99(12) + 69.95(12) = 709.83 + 839.4 = 1549.23
What is the expanded form of 53.327 using fractions
I need an answer what is 1.03 ÷ (-10.3)=?
The answer to 1.03 ÷ (-10.3) is -0.1.
Explanation:To divide 1.03 by -10.3, you can use the division algorithm. Divide the absolute values of the two numbers and obtain the quotient. Since the signs of the two numbers are different, the quotient will be negative. Therefore, 1.03 ÷ -10.3 = -0.1.
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There are 7.2 milligrams of iron in a dozen eggs.Because there are 12eggs in a dozen,how many milligrams of iron are in 1egg?
Which shows three equivalent rational numbers?
A. 13/-14= -13/14=-13/14
B. -3/5 = 3/5=-3/5
C. -1/17=1/-17=1/17
D. -5/37 = 5/37=-5/37
Don’t answer if you aren’t sure.
Lucie drank 3/4 of a pint of bottled water. One serving of the water is 7/8 of a pint. How much of a serving did she drink.
On the field trip, Toni collected 4 times as many bugs as Kaylie. Kaylie collected 14 bugs. How many bugs did Toni collect? Draw a bar diagram. Write and solve an equation to represent the problem
a contractor purchases motors listed at $6800 and receives successive discounts of 20% and 10%. what is the net cost
Create an original rational function that has at least one asymptote (vertical, horizontal, and/or slant) and possibly a removable discontinuity. List these features of your function: asymptote(s) (vertical, horizontal, slant), removable discontinuity(ies), x-intercept(s), y-intercept, and end behavior.
The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation f(x) = –0.3x2 + 2x, where f(x) is the height of the path of the water above the ground, in feet, and x is the horizontal distance of the path of the water from the end of the hose, in feet. When the water was 4 feet from the end of the hose, what was its height above the ground?
Answer:
its a and c
Step-by-step explanation:
Which unit rates would be appropriate for describing the amount of rainfall over time? Choose two answers.
centimeters per day
meters per second
milliliters per minute
inches per hour
Which expressions are perfect square trinomials? Check all that apply.
x2 + 16x + 8
x2 + 14x + 49
x2 – 5x + 25
x2 – 24x + 144
x2 + 9x – 81
The expressions that give perfect square trinomials are:
[tex]x^2+14x + 49[/tex] and [tex]x^2-24x+144[/tex]
A quadratic trinomial of the form [tex]ax^2+bx+c[/tex] is a perfect trinomial if it can be expressed as [tex](mx + n)^2[/tex]
Let us consider [tex]x^2+14x + 49[/tex]
[tex]x^2+14x+49\\x^2+7x+7x+49\\x(x+7)+7(x+7)\\(x+7)(x+7)\\(x+7)^2[/tex]
Let us consider:
[tex]x^2-24x+144\\x^2-12x-12x+144\\x(x-12)-12(x-12)\\(x-12)(x-12)\\(x-12)^2[/tex]
All other options do not give a perfect square when tested
Therefore, the expressions that give perfect square trinomials are:
[tex]x^2+14x + 49[/tex] and [tex]x^2-24x+144[/tex]
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Which statement is true about the result of a rigid transformation? (4 points)
The image will be larger than the pre-image.
The pre-image will be larger than the image.
Each one is unique; no general statement can be made about size.
The pre-image will be congruent to the image
Answer:
The pre-image will be congruent to the image : True
Step-by-step explanation:
The transformation falls broadly into two types.
Rigid Transformation and Non Rigid Transformation .
Rigid Transformation: The new image has the same size and the shape as that of pre image. Thus both the images are congruent to each other.
Non Rigid Transformation : The new image is has the same shape. however the size of the new image changes. hence they are similar to each other but not congruent.
Hence our third option is correct.
What is 75 1/2 Times 100 3/4
A hiker leaves camp and hikes 9 miles north and than hikes 7 miles east. What is the resulting displacement of the hiker?
PLEASE HURRY
Which set of angles can form a triangle?
A. 1 acute and 2 right
B. 2 acute and 1 right
C. 1 acute and 2 obtuse
D. 1 acute, 1 right, and 1 obtuse
A box of 8 snack bars costs $24.72. A single snack bar costs $3.47. What is the savings on each snack bar if you buy a box of 8 snack bar?
Nicole has $9 to spend on cards.She finds friends with the same amount of money to split the cost of a set. One set cost $27. Each friend gets the same number of cards. How many cards does each friend get?
Answer: Number of cards each friend gets is given by
[tex]\frac{x}{3}[/tex]
Step-by-step explanation:
Let the number of cards be x.
Since we have given that
Amount Nicole used to spend on cards = $9
Total cost of one set =$27
Since she finds friends with the same amount of money to split the cost of a set.
So, Number of friends she finds is given by
[tex]\frac{27}{9}=3\\\\\text{ Nicole finds 2 friends who has same amount to split the cost}[/tex]
Now, Number of cards each friend gets is given by
[tex]\frac{x}{3}[/tex]
Most cars get their best gas mileage when traveling at a relatively slow speed. The gas mileage M for a certain new car is modeled by the function
M(s)= -1/28s^2+3s-31
where s is the speed in mi/h and M is measured in mi/gal.
Final answer:
The quadratic function represents the gas mileage of a car in relation to its speed. By calculating the vertex of the parabola, it is determined that the best gas mileage for the given new car model occurs at a speed of 42 mi/h, which can lead to more efficient driving.
Explanation:
Understanding Gas Mileage and Speed
The question revolves around the mathematics found in the relation between speed and gas mileage for cars. Specifically, a quadratic function M(s) = -1/28s²+3s-31 represents the gas mileage M, in miles per gallon (mi/gal), at a given speed s in miles per hour (mi/h) for a new car model. To analyze this model, one may want to find the speed that provides the best gas mileage, which typically requires finding the vertex of the parabolic graph that this equation represents.
To find the speed that gives the maximum gas mileage, we would complete the square or use the vertex formula for a parabola given by s = -b/(2a), where a and b are the coefficients of the quadratic term and the linear term, respectively. For our function, a = -1/28 and b = 3. Plugging these into our formula gives a speed of s = -3 / (2 * -1/28) = 42 mi/h. This suggests that the best gas mileage for this car model occurs at a speed of 42 miles per hour.
It is essential to understand the relationship between speed and gas efficiency because it can help reduce fuel consumption and costs, as well as lessen environmental impact. By finding the optimal speed for gas mileage, drivers can make informed decisions about their driving habits for financial and ecological benefits.
A box of nutmeg weighs 99.66 grams. If there are 22 teaspoons of nutmeg in the box, how much does one teaspoon of nutmeg weigh? (Round your answer to the nearest thousandth.)
There was 2/3 of a pizza for 6 friends to share equally. What fraction of the pizza did each person get
Each person get 1/9 of a pizza.
What is Fraction?
A fraction is defined as a part of a whole.
Given that;
There was 2/3 of a pizza for 6 friends to share equally.
Now,
Total amount of pizza = 2/3
Number of friends = 6
So, For finding the amount of pizza get by each person we formulate.
= 2/3 × 1/6
= 2/18
= 1/9
Thus, Each person get 1/9 of a pizza.
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Line R T and line S U slightly inclined with horizontal intersects at V. The upward and downward angles of the intersecting lines are obtuse. The left and right angles of the intersecting lines are acute. The measure of angle R V U is labeled as left parenthesis 8 y minus 33 right parenthesis degrees. The measure of angle S V T is labeled as left parenthesis 5 y plus 9 right parenthesis degrees.
Answer:
14=y
or y=14
Step-by-step explanation:
Which graph represents the function f(x) = −|x − 2| − 1?
The correct answer is C.
Thanks and have a good day :)
A rectangular park, with dimensions of 1500ft x 2000ft has a diagonal walking path that goes from corner to corner. How long is the walking path?
250 ft
2500 ft
3500 ft
5000 ft
Help me I don’t get this problem...
I am multiple of 70. I am between 300 and 500. I am 20 more than a multiple of 100. who am i?
choose the graph below that correctly represents the equation 2x + 4y = 24.
A.
B.
C.
D.
Answer:
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Step-by-step explanation:
The perimeter of a rectangle is 524cm. The length is is 42cm more than the width. What is the length of the rectangle?