The function -2x^2-8x+42 represents the approximate height of an object (x seconds) after it is thrown off the top of a building. How many seconds does it take for the object to hit the ground?
Answers
The function is given to be:
[tex]-2x^2-8x+42[/tex]The object hits the ground when the function is equal to zero:
[tex]-2x^2-8x+42=0[/tex]Solving the equation by factorization, we have:
[tex]\begin{gathered} 2(-x^2-4x+21)=0 \\ -x^2-4x+21=0 \\ -x^2-7x+3x+21=0 \\ -x(x+7)+3(x+7)=0 \\ \therefore \\ (-x+3)(x+7)=0 \\ Hence \\ x=3,x=-7 \end{gathered}[/tex]Since the time cannot be negative, then the time will be 3 seconds.
Therefore, it will take 3 seconds for the object to hit the ground.
Related Questions
Solve for x.
5(2x - 1) = 6
a. x = 1/10
b. x = 11/10
c. x = 1/2
Answers
Answer:
b
Step-by-step explanation:
5(2x - 1) = 6 ← distribute parenthesis on left side
10x - 5 = 6 ( add 5 to both sides )
10x = 11 ( divide both sides by 10 )
x = [tex]\frac{11}{10}[/tex]
Express the ratio below in its simplest form.
6
:
2
:
6
Answers
Answer:
3 : 1 : 3
Step-by-step explanation:
6 : 2 : 6 ← divide each part ot the ratio by 2
3 : 1 : 3 ← in simplest form
point slope that is parallel and passes through (-1,-1)
Answers
The equation of line parallel to the given line is y = x + 2
Given,
The points that the line passes, (x, y) = (-1, -1)
Slope of the line, m = 1
We have to find the equation of line that is parallel to the given line.
Slope of parallel lines will be same.
So, equation be like:
y = mx + b
y = 1x + b
Here, we can use points and find y intercept:
That is,
-1 = 1 × -1 + b
-1 = -1 + b
b = 1 + 1
b = 2
So, the equation of line be like, y = 1x + 2
That is,
The equation of line parallel to the given line is y = x + 2
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find the larger of 2 consecutive intergers if 4 times the smaller is 53 more than 3 times the larger
Answers
The larger of the two consecutive numbers is 57
What is a consecutive number?
Numbers that follow one another sequentially are known as consecutive numbers. Every time there are two numbers, there is a difference of 1 between them. If n is a number, then examples of consecutive numbers would be n, n+1, and n+2. and 1, 2, 3, 4, 5, and so on.
From the question,
Let's say the smaller integer is x
Then the larger integer will be (x + 1)
According to the question,
4 times the smaller = 4x
3 times the larger = 3(x + 1)
⇒ 4x = 3(x + 1) + 53
⇒ 4x - 3x = 56
⇒ x = 56
(x + 1) = 57
Therefore, the larger of the two consecutive numbers is 57
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Choose ALL answers that describe the quadrilateral PQRS if PQ = RS, QR =SP, and diagonals have equal length: PR = QS.
○ parallelogram
○ rectangle
○rhombus
○square
○ trapezoid
Answers
answer:It's a rectangle
Convert 838% to an improper fraction written in its simplest form
Answers
To convert percent to a number divide it by 100
Then to convert 838% to a number divide it by 100
[tex]838\text{ \%=}\frac{838}{100}[/tex]To simplify divide up and down by 2
[tex]\begin{gathered} \frac{838}{100}=\frac{\frac{838}{2}}{\frac{100}{2}} \\ \frac{838}{100}=\frac{419}{50} \end{gathered}[/tex]The improper fraction is 419/50 in the simplest form
find X. (this is multiple choice the options are 3, 49, or 27
Answers
Ebony is cutting dough for pastries in her bakery. she needs all the pieces to be congruent triangles and has ensured that segment ef ≅ segment on and ∠mon ≅ ∠gef. what would ebony need to compare in order to make sure the triangles are congruent by sas? segment om and segment ef segment eg and segment om segment nm and segment fg segment eg and segment mn
Answers
The parts of the triangles Ebony needs to compare so as to make sure both triangles are congruent by SAS are;
[tex] \overline{EG} [/tex] and [tex] \overline{OM}[/tex]What are congruent triangles?Two triangles are said to be congruent when the three sides and three interior angles of one triangle have the same measure as the three sides and the three interior angles of the other triangle.
The given triangles are ∆MON and ∆GEF
The segments and angles that Ebony has ensured are congruent are;
[tex] \overline{EF} \cong \overline{ON}[/tex]
[tex] \angle{ MON} \cong \angle{ GEF}[/tex]
The method by which Ebony intends to use to make sure that the two triangles are congruent, SAS, Side–Angle–Side congruency postulate.
The Side–Angle–Side congruency postulate states that two triangles are congruent if two sides and an included angle in one triangle are congruent to the corresponding two sides and included angle in the other triangle.
Given that the sides that form included angles with [tex] \angle{ MON} [/tex] are [tex] \overline{ON}[/tex] and [tex] \overline{OM}[/tex] and the sides that form an included angle with [tex] \angle{ GEF}[/tex] are [tex] \overline{EF} [/tex] and [tex] \overline{EG} [/tex], the other segments Ebony needs to compare are therefore the segments;
[tex] \overline{EG} [/tex] and [tex] \overline{OM}[/tex]
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Divide.
(24x³ - 2x² + 3x-9) ÷ (6x - 5)
Your answer should give the quotient and the remainder.
Answers
Answer: 4x^2 + 3x + 3
Step-by-step explanation:
Premises:
If you have a cat, then it will chase mice.
You have a cat.
Conclusion:
Your cat will chase mice.
The Law of ________
Answers
By law of syllogism the statement is true. Your cat will chase mice.
What are premises?
premises is a statement taken to be true and used as a basis for argument or reasoning.
Here it is given that :
If you have a cat, then it will chase mice. is the given statement.
Let p is you have a cat
q is chase mice.
r is cat will chase mice.
by the law of syllogism Your cat will chase mice. because (1) If p , then q . (2) If q , then r . Then we can derive a third true statement: (3) If p , then r .
Hence by law of syllogism the statement is true.
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Write the equation in standard form, x(x+3)=0
Answers
Answer:
x²+3x=0
Step-by-step explanation:
Just distribute and simplify.
Solve for a, b, and c.
a =
b=
C=
C
40⁰
Answers
B = 90 (right angle)
90 - 40 = 50
So C = 50
The amount in Ebony's bank account B(d) is a function of the number of days d since she opened the account.
The graph segments representing her day-by-day bank balance. Although there are no labeled tick marks on the graph, you can answer the questions by using the additional given information as well as your general knowledge of graphs of functions.
Answers
a) Domain of the function 0 ≤ d ≤ 21 (0,21)
Range of the function 0 ≤ B ≤ 400 (0,400)
b) Estimate to the nearest hundreds for B(0) is 200
c) Ebony's bank balance first reached $0 on day 12 can be shown as functional notation as - we can add the number 12 below the first point reaching the horizontal axis.
d) Ebony's bank balance remained $0 from day 12 through day 15. The segment which represents the information is - segment 4.
(a) Domain: the collection of values used as input or arguments for the function.
Range: Either the codomain or the function's image is mentioned.
For three weeks, Ebony's bank account was active (21 days). then the domain is 0 ≤ d ≤ 21 (here 'd' refers to day)
Her highest balance was $400 and her lowest was zero, so the range is 0 ≤ B ≤ 400. (Here, 'B' refers to Balance)
(b) When d = 0, the graph's highest point, which represents her highest balance of $400, is displayed. This means that on the first day, the point will probably only be half as high as the highest point. Therefore, we may calculate the nearest hundred for B(0) is about equal to 0.5 * 400 = 200.
(c) In other words, the line of the function first touches the horizontal axis at d = 12; the balance first reached $0 on day 12. Below the first point that reaches the horizontal axis, we can add the number 12.
(d) From day 12 through day 15, the bank balance stayed at zero dollars; this is shown by the vertical axis of segment 4 of graph 4.
COMPLETE QUESTION:
The amount in Ebony's bank account B(d) is a function of the number of days(d) since she opened the account. The graph shows segments representing her day-by-day bank balance. Although there are no labeled tick marks on the graph, you can answer the questions by using the additional given information as well as your general knowledge of graphs of functions. (Score for Question 1;_ of 4 points) 1. Ebony kept her bank account open for only 3 weeks, and the graph shows the entire 3 weeks. During that time, her greatest balance was $400.
(a) Give the domain and range of the function. 0 ≤ d ≤ 21 domain; 0 ≤ B ≤ 400
(b) Give an estimate to the nearest hundreds for B(0). Explain how you determined your estimate and tell what B(0) means in the context of the situation.
(c) Ebony's bank balance first reached $0 on Day 12. How would you show that information in function notation? B(12) = 0
(d) Ebony's bank balance remained at $0 from Day 12 through Day 15. As you count segments from the left, which segment on the graph1, 2, 3, 4, 5, or 6 represents that information? Explain how you know. 4th segment
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you've done a ton of original research for a statistics project, but you just can't prove your hypothesis that the majority of college students adore katy perry. rather than admit that only .9% of students can tolerate kp, you move the decimal point and declare that 90% of students are katycats. this is an example of:
Answers
This is an example of remix plagiarism.
Remix plagiarism includes collecting information from different sources, combing together into one work by using the method of paraphrasing, and claiming it as your work.
The person basically changes the language of the statements and fit the topic under his or her name. Here the hypothesis that majority of college students adore katy perry, rather use the statement "90% of students are katycats".
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32 = 5v + 7 solve for v simplify your answer as much as possible
Answers
Answer:
v=5
Step-by-step explanation:
32=5v+7 minus 7 on both side
25=5v divide 5 on both side
5=v or v=5
All you need to do is subtract 7 from both sides then divide by 5
what is the volume of the following triangular prism? 288 ft^3480 ft^396 ft^3576 ft^3
Answers
The volume of the triangular prism = base area x height
Since its base is a right triangle, then
[tex]B\mathrm{}A=\frac{1}{2}\times leg_1\times leg_2[/tex]From the figure leg1 = 6 ft and leg2 = 8 ft
[tex]\begin{gathered} BA=\frac{1}{2}\times6\times8 \\ BA=24ft^2 \end{gathered}[/tex]Now multiply it by the height of the prism
Since its height = 12 ft, then
[tex]\begin{gathered} V=24\times12 \\ V=288ft^3 \end{gathered}[/tex]The answer is A
Plot the points of the pre-image and graph the pre-image.
Answers
Given:
The Point is:
[tex]\begin{gathered} W(2,2) \\ \\ X(2,0) \\ \\ Y(0,1) \\ \\ Z(1,2) \end{gathered}[/tex]The scale factor is 3.
Find-:
Create the point W'X'Y'Z'
Explanation:-
The scale factor is 3.
So the point is:
[tex]\begin{gathered} W^{\prime}=3W \\ \\ W^{\prime}=3(2,2) \\ \\ W^{\prime}=(6,6) \end{gathered}[/tex]Point X' is:
[tex]\begin{gathered} X^{\prime}=3X \\ \\ X^{\prime}=3(2,0) \\ \\ X^{\prime}=(6,0) \end{gathered}[/tex]The point Y' is:
[tex]\begin{gathered} Y^{\prime}=3Y \\ \\ Y^{\prime}=3(0,1) \\ \\ Y^{\prime}=(0,3) \end{gathered}[/tex]The point Z' is:
[tex]\begin{gathered} Z^{\prime}=3Z \\ \\ Z^{\prime}=3(1,2) \\ \\ Z^{\prime}=(3,6) \end{gathered}[/tex]The graph of WXYZ.
The graph of W'X'Y'Z'
A student is working on finishing a scale
model of the Eiffel Tower. The actual
tower is 1,083 feet tall and 410 feet wide
at the base. If the model currently has a
base that is 0.75 feet wide, which would
be the scale factor of the model to the
tower?
1:410
3: 1640
1:0.75
Answers
The scale factor of model to the tower is 3:1640.
What is scale factor?The scale factor states the scale by which a figure is bigger or smaller than the original figure.
In other words, scale factor is a ratio between two corresponding sides of similar figures.
Therefore, the actual tower is 1,083 feet tall and 410 feet wide at the base.
The scale model currently has a base that is 0.75 feet wide.
Therefore, the scale factor of the model can be calculated as follows;
The scale factor can be written as a ratio or fraction.
The scale factor of the base to the model is the same with the height of the tower to the model.
0.75 : 410
multiply both side by 100
75 : 41000
divide both sides by 25
Therefore,
3 : 1640
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What percentage of the floor has been covered in tile? A. 14% B. 28% C. 56% D. 70%
Answers
Answer:
Answer down below!
Step-by-step explanation:
We have 25 squares in total, and 14 of them are fill, we can figure out it's percentage with division
25/14 = 0.56
We can do 0.56 *100 to get the percentage!
Which that will give you 56%
There are two cars, green car (gc) and a blue car (bc). gc is $15 plus $0.50 per mile driven, bc is $25 plus $0.15 per mile. how many miles do both cars have to drive to cost the same amount?
Answers
The number of miles that both the green car and the blue car have to drive to cost the same amount is equal to 28.5 miles.
The number of miles both cars have to travel to cost the same amount can be determined using an algebraic expression. An algebraic expression can be defined as a mathematical equation consisting of both letters and numbers.
As the green car (gc) cost $15 plus $0.50 per mile and the blue car (bc) costs $25 plus $0.15 per mile, an algebraic expression for this problem can be given as follows;
15 + 0.50(x) = 25 + 0.15(x)
Solving for x;
0.50x - 0.15x = 25 - 15
0.35x = 10
x = 10 / 0.35
x = 28.5
Hence, both cars have to drive 28.5 miles to cost the same amount.
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The daily changes in the barometric pressure for four days are −0.05, 0.09, −0.04, and −0.08 inches. The mean change after five days is −0.01 inch. What is the change on the fifth day? Write your answer as a decimal.
Answers
The change on the fifth day is 0.03.
What is a mean?A mean simply means the average of.a set of numbers.
Based on the information given, let the change in the fifth day be x. This will be illustrated as:.
= (-0.05 + 0.09 - 0.04 - 0.08 + x)/ 5 = -0.01
Crops multiply
-0.08 + x = -0.05
Collect like terms
x = -0.05 + 0.08
x = 0.03
The change is 0.03.
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Lisa is saving for college. The account is modeled by the function:
f(x) = 250(1.25)x^, when x represents how many years she has saved.
Xavier is also saving for college. His account is modeled by this table:
X 0 1 2 3
g(x) 200 270 364.5 492.08
Answer the following questions:
A. After 5 years, how much does Lisa's account have in it?
B. After 5 years, how much does Xaviers account have in it?
C. What is the positive difference in their accounts after 5 years?
Answers
Using exponential functions, it is found that:
a) Lisa's account has $763 after 5 years.
b) Xavier's account has $897 after 5 years.
c) The difference is of $134.
What is an exponential function?An exponential function is modeled according to the following rule:
[tex]y = ab^x[/tex]
In which the parameters are described as follows:
a is the initial value of the function, that is, the value of the function when x = 0.b is the rate of change of the function.Lisa's function is already given, while for Xavier's, the parameters are given as follows:
a = 200, b = 270/200 = 1.35.
Hence his function is:
[tex]g(x) = 200(1.35)^x[/tex]
In 5 years, the amounts in each account will be given by the numeric values of the functions as follows:
Lisa: [tex]f(5) = 250(1.25)^5 = 763[/tex]Xavier: [tex]g(5) = 200(1.35)^5 = 897[/tex]The positive difference is given by the subtraction of the greater amount by the lesser amount, hence:
897 - 763 = $134.
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Each statement is either a phrase or a clause.
Drag each statement into the correct column of the table.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Phrase Clause
Answers
Answer:
phrase- around the corner- very slowly- Peter and michael
clause- put in the closet- when i go to school
Step-by-step explanation:
A clause is a collection of words with a subject and a verb. The words that make up a phrase do not include a subject or a verb.
Hope this helps! \( ﾟヮﾟ)/
Step-by-step explanation:
phrase- around the corner- very slowly- Peter and michael
clause- put in the closet- when i go to school
Step-by-step explanation:
A clause is a collection of words with a subject and a verb. The words that make up a phrase do not include a subject or a verb.
Question Progress
Homework Progress
12/
Biscuits can be bought in packets of 12 or packets of 18.
All biscuits are identical in size and quality.
Packet of 12 biscuit
for £0.78
Which packet represents better value?
Show how you decide.
Packet of 18 biscuits
for £1.25
Answer:
Answers
Answer:
The pack of 12
Step-by-step explanation:
1.25÷18=0.0694
0.78÷12=0.065
The packet of 12 biscuit have better value.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The cost of Packet of 12 biscuit = £0.78
The cost of Packet of 18 biscuit = £1.25
Now,
Since, The cost of Packet of 12 biscuit = £0.78
Hence, The cost of Packet of 1 biscuit = £0.78/12
= £0.065
And, The cost of Packet of 18 biscuit = £1.25
Hence, The cost of Packet of 1 biscuit = £1.25/18
= £0.0694
Thus, The packet of 12 biscuit have better value.
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Let f(t) be outside temperature t hours after 12 PM. Explain the meaning of f (1)>f(7)
Answers
If f(t) be the outside temperature t hours after 12 PM, then the meaning of f(1)>f(7) is the outside temperature 1 hours after 12 PM is greater than outside temperature 7 hours after 12 PM.
The function f(t) be the outside temperature t hours after 12 PM
Therefore,
f(1) be the outside temperature 1 hours after 12 PM.
f(7) be the outside temperature 7 hours after 12 PM.
Then,
f(1)>f(7) is the outside temperature 1 hours after 12 PM is greater than outside temperature 7 hours after 12 PM.
Hence, if f(t) be the outside temperature t hours after 12 PM, then the meaning of f(1)>f(7) is the outside temperature 1 hours after 12 PM is greater than outside temperature 7 hours after 12 PM.
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Bacteria grow at a rate of 10% per hour in a petri dish. if there is initially one bacterium and a carrying capacity of 1 million cells, how long (in hours) does it take to reach 500,000 cells? (round your answer to two decimal places.)
Answers
Bacteria grow at a rate of 10% per hour in a petri dish. then Bacteria take 50 hour to reach 500000 cells
Bacteria grow at a rate of 10% per hour in a petri dish.
if there is initially one bacterium and a carrying capacity of 1 million cells, how long (in hours) does it take to reach 500,000 cells?
An initial population of bacteria contain 100000 cell.
The population grow 10% every 1 hours.
This gives us an idea that in another 1 hours we will have 100000 cells organisms.
10% 0f 100000=10000 in one hour
then 500000 grow in = 500000/10000
= 50 hour
Hence Bacteria take 50 hour to reach 500000 cells
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what is problem 2/7i
Answers
2/7√-1........ ....................... . .
F (x) =3x+2 and g (x) = x^2 - x, find the value F(8)
Answers
The value of F(8) is 26.
What is function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The collection of values that could result in a function's outputs is known as the co-domain.
Given:
F (x) =3x+2
Now, F(8)= 3x+2
=3(8) +2
=24 +2
=26
Hence, the value of F(8) is 26.
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5k-3(2k-2/3)-9=0 what is equal to k
Answers
[tex]5k - 6k + 2 - 9 = 0 \\ - k - 7 = 0 \\ - k = 7 \\ \frac{ - k}{ - 1} = \frac{7}{ - 1} \\ k = - 7[/tex]
ATTACHED IS THE SOLUTION
At the local dairy farm, Kareem buys a 32-oz container of yogurt for $2.56. Jonah buys a 6-oz container of yogurt for $0.48. Are the cost, y, in dollars and the amount of yogurt, x, proportional?
The quantities Choose... proportional.
Answers
The dollar cost y and the amount of yogurt are proportionate
The formula is y = 0.08x
If y fluctuates as directly as x, you may express it as y = kx.
Where k is the proportionality constant.
Determine the value of the proportionality constant. When y = 2.56 and x = 32, you get:
y = kx
k = y/x
k = 2.56/32
k = 0.08
The equation is then: y = 0.08
Check to see if they are directly proportionate. Substitute the amount of yogurt purchased by Jonah. The outcome must be $0,48:
y = 0.08 (6) (6)
y = 0.48
The cost and amount of yogurt are proportionate in a straightforward manner.
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