The total distance traveled by the object after 30.0 seconds is 450 meters.
Explain the term quadratic function?f(x) = ax2 + bx + c, for which a, b, and c represent constants and a = 0 represents a quadratic function. The function is known as the quadratic term (abbreviated as ax2), the linear term (abbreviated as bx), and the constant term (abbreviated as c).For the stated function;
Time = 10.0 seconds, distance = 50.0 meters.Time = 20.0 seconds, distance = 200.0 meters.Time = 0.0 seconds, distance = 0.0 meters.As, the total distance is modelled by the quadratic equation-
Let the quadratic equation be-
d = at² + bt + c
For (10, 50)
d = a(10)² + (10)b + c ....eq 1
For (20, 200)
d = a(20)² + (200)b + c ....eq 2
For (0, 0)
d = a(0)² + (0)b + c ....eq 3
Solving eq 1, 2 and 3
a = 1/2 ; b = 0 and c =0
Thus, equation for the distance travelled by the object is-
d = 1/2 t²
For t = 30. sec
d = 1/2 (30)²
d = 450 m
Thus, the total distance traveled by the object after 30.0 seconds is 450 meters.
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If Y is the circumcenter of
Please help I’m
Failing
Answer:
Measures are SV=9 units., SY=14 units, YW= [tex]\sqrt{75units}[/tex], YW=[tex]\sqrt{27units}[/tex]
Step-by-step explanation:
===================================================
Explanation:
The circumcenter is found by intersecting the perpendicular bisectors of the triangle.
Segments VY, WY, and XY are perpendicular bisectors of triangle STU.
A perpendicular bisector has two properties:
It is perpendicular to the given side, i.e. it forms a 90 degree angle.It divides the segment into two equal pieces.Perpendicular bisector WY divides side TU into equal pieces TW and WU
In short:
TW = WU
So
TW = 11
since WU is equal to 11 as well
---------------------------------------
Focus on triangle TWY.
This is a right triangle with the sides of...
TW = 11 = one legYW = unknown = the other legYT = 14 = hypotenuseWe'll use the pythagorean theorem to determine the unknown leg.
Plug in a = 11 and c = 14. Then let's solve for b.
[tex]a^2+b^2 = c^2\\\\11^2+b^2 = 14^2\\\\121+b^2 = 196\\\\b^2 = 196-121\\\\b^2 = 75\\\\b = \sqrt{75}\\\\b \approx 8.66025\\\\b \approx 8.7\\\\[/tex]
Therefore, segment YW is roughly 8.7 units.
Express each set in roster form. You may need to use the internet or some other reference source. C={x|x+6=10}
The roster form of the set C={x|x+6=10} is C={4}
A set is mathematically represented in a straightforward way using roster notation. The components (or members) of a set are listed in a row inside the curly brackets in the roster form. If the set comprises more than one element, a comma is used in a roster notation to indicate the separation of every two elements. Since each person is counted separately, the roster form is also known as an enumeration notation.
In the given set, the value of x is such that when it is added with 6 the result is 10.
∴x+6=10⇒x=10-6=4
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As shown in the diagram below, ABC is parallel to EFG and BF is congruent to EF. SCBF equals 42. 5° then EBF is...
Considering the figure angle EBF is calculated to 68.75 degrees
How to find the < EBFExamining the figure and noting the parallel lines
< CBF = < BFE (alternate angels postulates)
< CBF = 42.5
< BFE = 42.5
Triangle BFE is an isosceles triangle given that the two sides are equal the base angles are also equal
Therefore, applying sum of angels of a triangle = 180 we have
< BFE + < FEB + < EBF = 180 (sum of angles of a triangle)
< FEB = < EBF (base angles of isosceles triangle)
let < FEB = x
42.5 + x + x = 180
42.5 + 2x = 180
2x = 180 - 42.5
2x = 137.5
x = 68.75
angle < EBF is solved to be 68.75
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What is the discriminant of 2x² + 5x - 7 = 0?
[tex]d= \sqrt{ {5}^{2} - 4 \times 2 \times ( - 7) } \\ d= \sqrt{25 + 56} \\ d = \sqrt{81} \\ d = 9[/tex]
Marissa's mom purchased coffee from the local coffee shop. The first cup of coffee was $3.95. Each refill is $1.50. She also decided to get a bagel for $3.00. If Marissa's mom had 2 refills and a $0.50 discount as part of the rewards program, how much did she spend at the coffee shop?
$9.95
$9.45
$8.65
$7.95
Answer:
(b) $9.45
Step-by-step explanation:
You want to know how much Marissa's mom spent at the coffee shop for ...
1st cup of coffee: $3.952 refills: $1.50 each1 bagel: $3.00after her rewards program discount of $0.50 was applied.
TotalAdding up the bill, we find it to be ...
$3.95 + 2×1.50 +3.00 -0.50 = $9.45
Marissa's mom spent (b) $9.45 at the coffee shop.
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100. Inventory You need to arrange 72 boxes on a skid with
the same number of rows and columns in each layer.
One possible arrangement has 6 layers of 3 rows and
4 columns, as shown. Use the factors of 72 to determine
the possible numbers of rows and columns in an
arrangement of 4 layers. Which of these arrangements
do you prefer? Explain your reasoning.
Answer: Given the Total No. of boxes = 72
Step-by-step explanation:
We need to find the number of rows and columns for four layers.
= 74 divided by 4 = 18
For 18 we have some arrangement
= (3 rows, 6 columns) (6 rows, 3 columns) (2 rows, 9 columns) and
(9 rows, 2 columns)
For 4 layers, we have a total of 4 numbers arrangement of rows and columns. Which most preferable is (3 rows and 6 columns) because it gives the balance row and column arrangement. It is always preferred that the number of rows should be lesser than the number of columns.
Find the image of the given point
under the given translation.
P(8,-3) T(x, y) = (x-4, y + 7)
P' = ([?], [ ])
Enter the number that belongs in
the green box.
Enter
Answer:
P'(4,4)
Step-by-step explanation:
⭐ What does it mean to translate a figure?
Translating a figure means to move said figure up/down or left/right on the coordinate plane.You will know how much to move the figure up/down or left/right in the notation you are given.The coordinates of the given figure is the (x,y) in the translation notationIn the notation you are given ([tex]T__ < x-4,y+7 > P = P'[/tex]), point P is going to be moved 4 units to the left and 7 units up.
⭐How do we translate P?
Take the coordinates of point P and compute the rule used on each coordinateP' = (8-4, -3 + 7)
∴ P' = (4,4)
to make cranbeerry jam you need 12 cups of sugar for evey 16 cups of cranberris find the amount of sugar for 4 cups of cranberris
Answer: It takes 3 cups of sugar for 4 cups of cranberry
Step-by-step explanation:
12 cups of sugar, 16 cups of cranberry
Divide both numbers by 4
12/4=3
16/4=4
It takes 3 cups of sugar for 4 cups of cranberry
$......
(c) One month, Gretal spent a total of $360 on presents.
She spent 1/5 of this total on presents for her parents.
She spent 2/3of the remaining money on presents for her friends.
She spent the rest of the money on presents for her sisters.
Calculate the percentage of the $360 that she spent on presents for her sisters.
The percentage that she spent on present for her sister is 26.67%
What does % example mean?
Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.
Given that :
She spent = 360 * 1/5 = $72 on presents for her parents
she spent = 360 - 72 = 288 * 2/3 = $192 on presents for her friends
She spent = 288 - 192 = $96 on presents for her sister
Percentage of the $360 that she spent on presents for her sisters is
96/360 * 100 = 26.67%
Hence the percentage that she spent on present for her sister is 26.67%
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5x^2-x-4=0 find the solutions to the quadratic functions
Answer:
Step-by-step explanation:
Answer:
X = 1
X = -4/5
Hope this helps!
Samir is going to invest $22,000 and leave it in an account for 9 years. Assuming the interest is compounded monthly, what interest rate, to the nearest tenth of a percent, would be required in order for Samir to end up with $38,000?
The interest rate required to get a total amount of $38,000.00 from compound interest on a principal of $22,000.00 compounded 1 times per year over 9 years is 9.0909 % per year.
What is the interest rate?The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR .
r = n[(A/P)1/nt - 1]
r = 1 × [(38,000.00/22,000.00)1/(1)(9) - 1]
r = 0.0909090
Then convert r to R as a percentage
R = r × 100
R = 0.0909090 × 100
R = 9.0909 %/year
The interest rate required to get a total amount of $38,000.00 from compound interest on a principal of $22,000.00 compounded 1 times per year over 9 years is 9.0909 % per year.
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Answer: 6.1
Step-by-step explanation:
what are the steps to -3+7x-9+8x=54
Answer: 67/15
Step-by-step explanation:
-3+7x-9+8x=54
-12 + 15x = 54
15x = 67
x = 67/15
determine which integers will make the inequailty 5x 6 < 2x 15 flase
The value of x (B) 5 makes the inequality 5x + 6 ≤ 2x + 15 FALSE.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
The equal sign (=) indicates that two expressions in an equation are believed to be equivalent.
The symbols >, <, ≤ or ≥ indicate that the two expressions in inequality are not always equal.
So, we have the inequality:
5x + 6 ≤ 2x + 15
Now put the given values and check as follows:
(A) -2
5x + 6 ≤ 2x + 15
-10 + 6 ≤ -4 + 15
-4 ≤ 11
TRUE
(B) 5
5x + 6 ≤ 2x + 15
25 + 6 ≤ 10 + 15
31 ≤ 25
Correct: 31 > 25
FALSE
Therefore, the value of x (B) 5 makes the inequality FALSE.
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Complete question:
Determine which integer will make the inequality 5x + 6 ≤ 2x + 15 false.
a:{−2}
b:{5}
c:{2}
d:{−5}
PLEASE HELP!!! 10 PTS!!!!!
what is the range of the function y = -3/4x + 3/2 when the domain is {-6,-2,6}
Answer:
the range of the function y = -3/4x + 3/2 when the domain is {-6,-2,6} is {15/4, 3, -3/4}. The range is the set of all possible values of y for x in the given domain, which includes the values 15/4, 3, and -3/4.
Step-by-step explanation:
The range of a function is the set of all possible values of the output (y) for a given set of inputs (x). To determine the range of the function y = -3/4x + 3/2 when the domain is {-6,-2,6}, you can plug in each value from the domain into the function and solve for y.
When x = -6, y = (-3/4)(-6) + 3/2 = 9/4 + 3/2 = 15/4.
When x = -2, y = (-3/4)(-2) + 3/2 = 3/2 + 3/2 = 3.
When x = 6, y = (-3/4)(6) + 3/2 = -9/4 + 3/2 = -3/4.
Mike was in charge of collecting
contributions for the Food Bank. He
received contributions of $80, $70, $60, $40,
and $80. Find the mean and the median of
the contributions.
Answer: First, order them in the order of smallest to largest, which is 40, 60, 70, 80, 80. Then, since there are 5 numbers, the 3rd number, which is 70, would be the median.
Then, add all numbers:
40+60+70+80+80=330
and divide that by 5:
330/5=66
So, the median is 70 and the mean is 66.
Step-by-step explanation:
a card is drawn from a pack of 52 playing cards. find the probability that the card will be a jack, given that it is a face card.\
If a card is drawn from a pack of 52 playing cards, then the probability that the card will be jack is 1/13
Total number of playing cards in the pack = 52 cards
Number of jack cards in the pack = 4 cards
The probability is the ratio of the number of favorable outcomes to the total number of outcomes
The probability = Number of favorable outcomes / Total number of outcomes
Substitute the values in the equation
The probability that the card will be a jack = 4/52
Simplify the answer
= 1/ 13
Therefore, the probability that the card will be jack is 1/13
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Answer this question please!
Answer:
i can understand your problem
Answer: 8 hours
Step-by-step explanation:
speed = distance/time
time = distance/speed
[tex]time = \frac{680-80}{75} \\time = \frac{600}{75}\\ time = 8hours[/tex]
the virus that causes bird flu is being spreading through your community quickly. you and your roommate received a flu shot over two months ago. your roommate gets sick and then the doctor confirms it is the bird flu. explain if you have a high, average or low probability of getting the bird flu and why you selected your answer. the virus that causes bird flu is being spreading through your community quickly. you and your roommate received a flu shot over two months ago. your roommate gets sick and then the doctor confirms it is the bird flu. explain if you have a high, average orlow probability of getting the bird flu and why you selected your answer.
It is possible for humans to contract bird flu viruses. There have been outbreaks of two strains, H5N1 and H7N9, that have affected some populations in Asia, Africa, the Pacific, the Middle East, and portions of Europe. Other unusual forms of avian flu that have affected humans in the US have also been reported. The majority of humans who contract bird flu have had direct contact with diseased birds or surfaces that have been contaminated by the saliva, mucus, or droppings of infected birds.
By what means is the avian flu spread?Through their saliva, mucus, and excrement, infected birds spread the bird flu virus. Inhaling the virus or getting it in one's eyes, nose, or mouth can result in human infection with bird flu viruses.
How might we stop the spread of the avian flu?After contacting birds or surfaces that could be contaminated with their saliva, mucus, or feces, whether they are wild or domesticated, avoid touching your mouth, nose, or eyes.
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Solve for the value of x.
Answer:
x=2
Step-by-step explanation:
4(2)= 8
8 + 3 = 11
..........
Only focus on triangle MPQ
Notice that line OQ is a perpendicular bisector and that MO = OP.
MQ must equal QP
11 = 4x + 3
8 = 4x
8/4 = 4x/4
x=2
Hope this helps
1. connie multiplies a number by 2 and gets 60 as her answer. however, she should have divided the number by 2 to get the correct answer. what is the correct answer?
The correct answer is 15.
Given:
connie multiplies a number by 2 and gets 60 as her answer
let x is the number
then, 2x=60
or x=30.
since , she should have divided the number by 2 to get the correct answer
According to the question,
Dividing the number by 2
Therefore , correct answer = 30/2 = 15
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how long in minutes will the energy in an 871 kj (208 kcal) cup of yogurt last in a woman doing work at the rate of 155 w with an efficiency of 20.0% (such as in leisurely climbing stairs)?
The energy in an 871 KJ cup of yogurt will last for 18.71 minutes .
In the question ,
it is given that ,
efficiency is = 20% = 0.20 .
the rate of work is 155W ,
we know that Efficiency = [tex]\frac{E_{obtain} }{E_{consumed} }[/tex]
substituting the values ,
we get ,
[tex]E_{consumed}[/tex] = 155/0.20
= 775 J/sec .
This means that for work of 155W it require to consume energy at the rate of 775 J/sec .
we know that the formula for time , energy and rate is
Time = Energy/Rate
time = 871000/775
= 1123 seconds
= 18.71 minutes
Therefore , The energy in the yogurt will last for 18.71 minutes .
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there are 6 studenjts in the class. one of them is to be selcted as the best studen and another student is to be selceted as a runner-up. how mant different ways can this be done?
As per the combination method, there are 15 different ways are possible for this situation.
Combination method:
Combination method also known as NCR is a formula of combination and arrangement, where the object's order does not matter so much.
Given,
Here we have to find the number of ways to be selected as the best student and another student is to be selected as a runner-up among the 6 students.
Here we know that that the value of
Total number of students = 6
Best student = 1
Runner - up = 1
So, as per the NCR formula, the value of n = 6 and the value of r = 2
Then the possible combinations are calculated as,
=> ⁶C₂ = 6! / 2!(6 - 2)!
=> ⁶C₂ = 6!/2!4!
=>⁶C₂ = 15
Therefore, the resulting number of ways is 15.
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solve for X
A= 75 B= 2+11x C=70
Using the given angles, the value of x in the triangle is x = 3
Calculating angles in a triangleFrom the question, we are to determine the value of x
Given that the measures are the angles of a triangle ABC.
Then, we can write that
A + B + C = 180° (Sum of angles in a triangle)
From the given information,
A = 75
B = 2 + 11x
C = 70
Thus,
75 + 2 + 11x + 70 = 180
147 + 11x = 180
11x = 180 - 147
11x = 33
Divide both sides by 11
11x/11 = 33/11
x = 3
Hence, the value of x is 3
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last year, jarod left a job that pays $60,000 to run his own bike-repair shop. jarod’s shop charges $65 for a repair, and last year the shop performed 3,000 repairs. jarod’s production costs for the year included rent, wages, and equipment. jarod spent $50,000 on rent and $100,000 on wages for his employees. jarod keeps whatever profit the shop earns but does not pay himself an official wage. jarod used $20,000 of his savings to buy a machine for the business. his savings were earning an annual interest rate of 5 percent.
Answer: Accounting profit=$90,000 and Economic profit loss= $28,500
Step-by-step explanation:
Accounting profit = Total revenue - Explicit costs Accounting profit = ($65 × 4,000) - ($50,000 + $120,000) Accounting profit = $260,000 - $170,000 Accounting profit = $90,000
Economic profit = Total revenue - (Explicit costs + Implicit costs) Economic profit = ($65 × 4,000) - ($50,000 + $120,000 + Forgone interest on savings + Forgone wages) Economic profit = ($65 × 4,000) - [$50,000 + $120,000 + (0.06 x $25,000) + $60,000] Economic profit (loss) = $28,500
billie has 2 [tex]\frac{1}{4}[/tex] bars of chocolate she eat 5/8 of a bar how much does she have left. give your answer as a mixed number in its simplest form
Answer:
1 5/8
Step-by-step explanation:
9/4x2/2=18/8
18/8-5/8=13/8,
so the answer will be 1 5/8, yes!
Solvex² - 5x 24 = 0 by factoring.
The solutions are x =
and x =
x = 8 , -3 are the factor of x .
What is factor ?
The definition of a factor is a number that divides another number by itself with no remainder. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them.
Factors are the figures that can divide an amount precisely. There is therefore no residual after division.
x² - 5x - 24 = 0
x² - ( 8 - 3 )x - 24 = 0
x² - 8x + 3x - 24 = 0
x(x - 8 ) + 3 ( x - 8) = 0
( x + 3 ) ( x - 8 ) = 0
x = 8 , -3
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The complete question is -
x² - 5x - 24 = 0 by factoring.
The solutions are x =
If x^2=a. For what values of a are there: 2 solutions or 1 solution or No solutions
Use at least 2 examples in each part to explain your answer. You must include further reasoning to justify your answer but do not write more than 1 page in total.
There are two solutions if a is positive, one solution if a is 0, and no solutions if a is negative.
How to determine for what values of a are there 2 solutions or 1 solution or No solutions?If x² = a, then x can be either positive or negative.
Thus, there are two solutions if a is positive, one solution if a is 0, and no solutions if a is negative.
Example 1: a = 9
If a = 9, then x² = 9,
so x can be either 3 or -3.
Thus, there are two solutions in this case: x = 3 or x = -3.
Example 2: a = 0
If a = 0, then x²= 0,
so x can only be 0.
Thus, there is one solution in this case: x = 0.
Example 3: a = -4
If a = -4, then x² = -4, which is not possible because the square of a real number cannot be negative.
Thus, there are no solutions in this case.
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the issue of capital punishment is a hotly debated topic. do more republicans than democrats support capital punishment? a researcher randomly selects 100 republicans and 100 democrats and asks them if they support or do not support capital punishment. in this problem, we want to make inferences about:
In this problem, we want to make inferences about comparing proportions from dependent samples. So the option F is correct.
In the given question, the issue of capital punishment is a hotly debated topic.
Do more republicans than democrats support capital punishment?
A researcher randomly selects 100 republicans and 100 democrats and asks them if they support or do not support capital punishment.
In this problem, we want to make inferences about:
A. one mean
B. comparing means from dependent samples
C. comparing means from two independent samples
D. one proportion
E. comparing proportions from two independent samples
F. comparing proportions from dependent samples
As we know that,
A hypothesis test can assist in figuring out whether a variation in the estimated proportions actually reflects a variation in the population proportions. An approximation of the normal distribution is shown by the difference between two proportions. The null hypothesis often argues that the two proportions are equal.
So, a researcher randomly selects 100 republicans and 100 democrats and asks them if they support or do not support capital punishment. In this problem, we want to make inferences about comparing proportions from dependent samples. So the option F is correct.
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an integer is randomly selected from the integers 0 through 99, inclusive. what is the probability that the integer is in the range 10 through 20, inclusive? express your answer as a common fraction.
The probability that the integer is in the range 10 through 20, inclusive is 1/10 .
Given :
an integer is randomly selected from the integers 0 through 99, inclusive. what is the probability that the integer is in the range 10 through 20, inclusive.
The number of integers between 0 and 99 is 100.
And the number of integers between 10 and 20 is 10.
Probability = number of favorable outcomes / number of possible outcomes
= 10 / 100
= 1 / 10
Therefore the probability that the integer is in the range 10 through 20, inclusive is is 1/10.
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La masa de un electrón es aproximadamente
9.7x10^-31 kilogramos.
La
masa de un protón es aproximadamente
1.7x10^-27 kilogramos.
Aproximadamente
, ¿cuántas veces mayor es la masa de un protón que la masa de un electrón?
The mass of a proton is 0.18 x 10⁴ times the mass of an electron.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that mass of an electron is approximately 9.7 x 10⁻³¹ kilograms and the mass of a proton is approximately 1.7 x 10⁻²⁷ kilograms.
It is given that -
mass of electron = m{e} = 9.7 x 10⁻³¹ kilograms.
mass of proton = m{p} = 1.7 x 10⁻²⁷ kilograms.
Assume that the mass of a proton is [K] times the mass of an electron. So, we can write -
m{p} = K m{e}
K = m{p}/m{e}
K = (1.7 x 10⁻²⁷/9.7 x 10⁻³¹)
K = (1.7/9.7) x (10⁴)
K = 0.18 x 10⁴
Therefore, the mass of a proton is 0.18 x 10⁴ times the mass of an electron.
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{Question in english language -
The mass of an electron is approximately 9.7 x 10^-31 kilograms. The mass of a proton is approximately 1.7 x 10^-27 kilograms. About ,how many times greater is the mass of a proton than the mass of an electron?}
