Translate the phrase to mathematical language. Then simplify the expression.
Subtract 81 from −55.
What is a numerical expression for the phrase?__
(Do not simplify.)
Simplify the expression.__
Without graphing, tell which statements are true for the graph of the function y = x2 + 2.
I. All points on the graph are above the origin.
II. All points on the graph have positive x-values.
III. All points on the graph have positive y-values.
Statements (... and ...) are true. Statement (...) is true because x^2 is non-negative for all values of x, so the minimum value of x^2 is 0. Thus, the minimum y−value for the function is (...) and the lowest point on the graph is (0, ...), which is above the origin. Statement (...) is true because the lowest point on the graph is (0, ...) so all other points have a y−value that is greater than (...) and must be positive.
Statements I and III are true as per the defined function y=x^2+2. The graph of this function would have all points above the origin and all points would have positive y-values. Statement II is incorrect as x can take both negative and positive values.
Explanation:Considering the three statements given, only the statements I and III are true. This is because for the function y = x^2 + 2, all points on the graph are above the origin and all points on the graph have positive y-values.
Statement I is true because the function x^2 is non-negative for all values of x, which means that the minimum value of x^2 is 0. As a result, the minimum y−value for the function is 2 when x=0 and the lowest point on the graph is (0, 2), which is indeed above the origin.
Statement III is true because the lowest point on the graph is (0, 2) and since 2 is positive all other points have a y−value that is greater than 2 and therefore must be positive. Statement II is not true as x can take both negative and positive values in the function y=x^2+2.
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Order these numbers from least to greatest. 14325 , 5.753 , 534 , 5.34
The volume of this rectangular prism is 6x3. What does the coefficient 6 mean in terms of the problem?
A. The total volume of the prism is 6 cubic units.
B. The length is 6 times the width.
C. The width is 6 times the height and the length.
D. The length of the prism is 6 units.
Answer:
B. The length is 6 times the width
Step-by-step explanation:
The proper solution is choice B. The length is 6 times the width.
How do you resolve rectangular prisms?
To find the quantity of a rectangular prism, multiply its 3 dimensions: duration x width x height. The volume is expressed in cubic gadgets.
What are examples of square prisms?Right rectangular prisms or cuboids are all around us. a few examples are books, packing containers, homes, bricks, forums, doorways, containers, cabinets, mobiles, and laptops.
What does the coefficient mean?Any of the elements of a product taken into consideration with regards to a specific element particularly: a constant thing of a term as outstanding from a variable.
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Which of the following is a sample of the population of bookstores on the West Coast of the United States? I. All book stores in California II. Randomly selected children's book stores III. Internet book stores A. I only B. II only C. I and III D. III only E. I and II
Answer:
It would be I - All bookstores in California
Step-by-step explanation:
Internet book stores and random children's bookstores do not specify that they're on the West Coast and could be taken from anywhere
Differentiate f and find the domain of f. (enter the domain in interval notation.)f(x) = ln(x2 − 12x)derivative f '(x) = 2x−12x2−12x correct: your answer is correct.domain
The median for the given set of 6 ordered data values is 32.5.
9, 12, 25, _, 41, 48
What is the missing value?
How to find the derivative of functions: y=(5x+7)(x+5)^3
Is it possible to construct a triangle with side lengths of 11 cm, 15 cm, and 21 cm? Why or why not?
how to solve an equation for x with natural log of x
A logarithmic equation involving natural logarithms can be solve by taking the exponent of both sides
How to solve a natural logarithmic equation for x
To solve an equation involving the natural logarithm of x, you generally follow these steps:
Isolate the natural logarithm termExponentiate both sidesSolve for x: After removing the natural logarithm, solve the resulting equation for x.Take for instance, the equation is of the form
2 + ln(x) = 7
Isolate the natural logarithm
ln(x) = 5
Take the exponent of both sides
So, we have
[tex]x = e^5[/tex]
Evaluate the exponent
x = 148.41
Hence, the logarithmic equation solved for x is x = 148.41
select the graph that represents the given set a={(1,2),(2,3),(3,4),(4,5)
Determine whether the fractions -4/5, -4/6, -4/7, and -4/8 are arranged in order from least to greatest. explain
Shelly used exactly 1/ 3 of a cup of oil and 3/ 8 of a cup of water in a recipe. How many cups of liquid did Shelly use in all?
Answer: =[tex]\dfrac{17}{24}[/tex]
Step-by-step explanation:
Given : The amount of oil is used in a recipe. = [tex]\dfrac{1}{3}[/tex]
The amount of water used in a recipe = [tex]\dfrac{3}{8}[/tex]
The total number of cups of liquid used by Shelly:-
[tex]\dfrac{1}{3}+\dfrac{3}{8}=\dfrac{8+3\times3}{24}\\\\\=\dfrac{8+9}{24}=\dfrac{17}{24}[/tex]
Hence, the total number of cups of liquid used in all =[tex]\dfrac{17}{24}[/tex]
Th local park has 4 bike racks. Each bike rack can hold 15 bikes. There are 16 bikes in the bike racks. What expression shows the total number of empty spaces in the bike racks?
ABCD is a trapezoid. = 2.5 cm, and = 4 cm, and the area = 6.5 cm2. What is the altitude of the trapezoid?
Answer:
Altitude of the trapezoid is 2 cm.
Step-by-step explanation:
ABCD is a trapezoid. Since two bases of the trapezoid are
B1 = 2.5 cm and B2 = 4 cm.
Area given is 6.5 cm²
Then we have to calculated he altitude of the trapezoid.
Now we know the formula of area of the trapezoid = [tex]\frac{1}{2}[/tex] ( Base1 + Base2)
By putting the values in the formula
6.5 = [tex]\frac{1}{2}[/tex] ( 2.5 + 4 ) × h
6.5 = [tex]\frac{6.5}{2}[/tex] × h
h = \frac{2\times 6.5}{6.5} = 2 cm.
Answer is altitude of the trapezoid is 2 cm.
When hired at a new job selling jewelry, you are given two pay options:
Option A: Base salary of $16,000 a year, with a commission of 7% of your sales
Option B: Base salary of $25,000 a year, with a commission of 2% of your sales
In order for option A to produce a larger income, you would need sell at least $_______ of jewelry each year
You are required to sell a minimum of 180,001 of jewelry each year.
Given that,
The base salary is $16,000 per year and there is a 7% commission on sales for option A. The base salary is $25,000 per year and there is a 2% commission on sales for option B.Also, let us assume the sales be xBased on the above information, the following expression should be made:
16,000 + 0.07x > 25,000 + 0.02x
0.07x - 0.02x > 25,000 - 16,000
0.05x > 9000
x > 9000 ÷ 0.05
x > 180,000
Therefore we can conclude that you are required to sell a minimum of 180,001 of jewelry each year.
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mr. renato had $150 in his bank account. he deposited $50. acuple of days later he withdrew $20. a week later he deposited $75 .the next week he withdrew $100. what is mr. Renato balance after all the transactions
PLZ HELP!!!!! D: D: IM FAILING PLZ HELP ;cccc
FREE POINTS!!!!!!!!!! 10 POINTS Len's recipe for blueberry muffins calls for 110.25 grams of brown sugar for the muffin batter and an additional 55.45 grams of brown sugar for the topping. Len wants to make 4.5 batches of muffins. Enter the total amount of brown sugar that Len will need
the answer is 745.65
hope i helped:)
what is the decimal of 77/200?
Deanna has 80 books in her collection. If 60% of the books are fiction, how many of the books are nonfiction?
if 60% is fiction, then 40% are non fiction
80 x 40% =
80 x 0.40 = 32
32 books are nonfiction
What is the interquartile range of 4 5 7 9 10 14 16 24
Answer:
The answer is 9
Step-by-step explanation: ? i did the the tetst or whatever and 9 is the correct answer.
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what is -8 3/4 + -11 1/3
A rectangular floor is 24 feet long and 9 feet wide. What is the area of the floor in square yards?
katie and carol bought toys for charity toy drive.katie bought 125 dolls for 13$ each. carol bought 65 toy boats for 32$ each.who spent more money altogher
Which BEST describes the construction of a triangle if given one side length of 10 cm and one right angle?
A)
Unique triangle
B)
More than one triangle
C)
Triangle not possible
D)
Cannot be determined
Answer:
b
Step-by-step explanation:
scuba diver is swimming 30 feet below sea level . A hand glider passes over the position of the scuba diver. The hand glider is 215 ft above sea level.
draw a number line to represent the distance between the scuba diver and the hand glider (include sea level at zero feet)
x+29=−11
what does X equal
Jerry lost his credit card and instead of reporting it right away, he decides to continue looking for it believing he could find it. Some time passes and after two weeks, he logs into the account activity page of his credit card and sees a recent $500 internet purchase that was made by someone else. At that moment, he calls to report his card stolen. How much of this $500 charge is Jerry at risk for having to pay?
Jerry did not report his lost credit card right away believing that he could find it. Fraudulent transactions were made on his account and he is responsible to pay the maximum amount of $50 under the Fair Credit Billing Act (FCBA).
Jason bought 5 movie tickets and a bag of popcorn Jeremy bought 2 movie tickets they spent 54$ total. If the popcorn cost 5$, how much did each movie ticket cost?