The two quadratic equations are; y = x² + 2·x - 3 and y = -x² - 2·x + 3
Given,
x - intercepts = (−3,0) and (1,0).
The x-intercepts are given by the point at which the y-value of the equation are zero.
Therefore;
The quadratic equation are;
(x + 3)·(x - 1) = 0
x² + 2·x - 3 = 0
Quadratic equations;-
The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).
Here,
The equation can also be written in the form;
(-x - 3)·(x - 1) = 0
-x² - 2·x + 3 = 0
The quadratic equations are;
y = x² + 2·x - 3 and y = -x² - 2·x + 3
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In your lab, a substance's temperature has been observed to follow the function T(x) = (x − 5)3 + 9. The turning point of the graph is where the substance changes from a liquid to a gas. Using complete sentences in your written answer, explain to your fellow scientists how to find the turning point of this function. Hint: The turning point of the graph is similar to the vertex of a quadratic function.
The turning point is at x = 5, and this means that the substance changes from liquid to gas when x = 5.
How to find the turning point?
Here we have the temperature function:
T(x) = (x - 5)^3 + 9
The turning point is the point where the curvature of the function changes, by differentiating the function two times and finding the zero, we can get the turning points.
T'(x) = 3*(x - 5)^2
T''(x) = 3*2*(x - 5) = 6*(x - 5)
This is zero when x = 5, then:
T''(5) = 6*(5 - 5) = 0
So the turning point is there.
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Hunter bought 3 chicken wings for $6.60. How much does each wing cost?
Answer:
$2.20
Step-by-step explanation:
6.6/3=2.2
K
Choose the measurement closest to 30 km: 10 mi, 20 mi or 30 mi.
Choose the correct answer below.
20 mi
30 mi
10 Ini
O
O
O 10
Answer:
20 miles
Step-by-step explanation:
1.6km is equivalent to 1 mile
so 30km / 1.6 = 18.75 miles
therefore 20 miles is the closest to 30km
The adult daily dosage for a certain medicine is 260 mg (milligrams) of medicine for every 40 pounds of body weight. a. At this rate, find the daily dose for a man who weighs 195 pounds. b. If the man is to receive 600 mg of this medicine every 8 hours, is he receiving the proper dosage? a. The daily dose for a man who weighs 195 pounds is (Round to the nearest tenth as needed.) mg.
a) Daily dose for a man who weighs 195 pounds is 30 mg.
b)Here 422.5 mg is less than 600mg. Then, He doesn't receive proper dosage.
What is proportional ?
Any relationship that always has the same ratio is referred to be proportionality. For instance, the average number of apples per tree determines the proportionality between the quantity of apples in a crop and the number of trees in the orchard.
Here , The adult daily dosage for a certain medicine is 260 mg
=> [tex]\frac{40}{260} = \frac{195}{x}[/tex]
=> x = [tex]\frac{260*195}{40}[/tex]
=> x =1267.5 mg.
a) Daily dose for a man who weighs 195 pounds is 30 mg.
b) Here for 24 hours = 1267.5 then,
=> 8 hours = x
=> x = [tex]\frac{1267.5*8}{24}[/tex]
=> x = 422.5 mg.
Here 422.5 mg is less than 600mg. Then, He does'nt receive proper dosage.
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Find the value of x. Then find the measure of each labeled angle.
(x - 58)° =
(x-58)
Answer:
x° = 119°(x-58)° = 61°Step-by-step explanation:
You want the measures of supplementary angles x° and (x-58)°.
Supplementary anglesConsecutive interior angles where a transversal crosses parallel lines are supplementary.
x° +(x -58)° = 180°
2x = 238
x = 119
x -58 = 61
The two angles are ...
x° = 119°(x-58)° = 61°<95141404393>
Select the correct answer. What is this equation rewritten in logarithmic form? 9x = 3
A. log9 3 = x
B. logx 3 = 9
C. log3 9 = x
D. log3 x = 9
Answer:
A. [tex]\log_9{3}=x[/tex]
Step-by-step explanation:
[tex]y=e^x\rightarrow\log_e{y}=x[/tex]
Therefore,
[tex]3=9^x\rightarrow\log_9{3}=x[/tex]
Anna makes a round pizza. She wants to put a cheese layer on the pizza. If the
pizza is 11 in in diameter, how many square cm of cheese layer does she need
to put on the pizza?
The number of square cm of cheese layers that Anna needs to put on the pizza is 30.25π square cm.
What is the area of a circle?
In geometry, the area of a circle is the space occupied by the circle.
To find the area of a circle having radius "r", we can use the formula.
Area of a circle = π×r².
In the given question, the diameter of the pizza is 11 cm.
so the radius will be = 11/2 = 5.5 cm.
Area of the pizza = π×r²
= π×(5.5)²
= 30.25π square cm.
Hence, the number of square cm of cheese layers that need to be put on the pizza is 30.25π square cm.
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Ten men working 6 hours a day takes 12 days to complete a job.How long will it take 8 men working 12 hours a day to complete the same job
Answer:
It will take 7.5 days to complete the job.
Step-by-step explanation:
First, find how many total hours the ten men worked to complete the job
10 x 6 = 60 hours a day
12 x 60 = 720 hours total
Now compare that with the 8 men's hours
8 x 12 = 96 hours a day
720 / 96 = 7.5 days
Devontae claimed that the line y=-3/4x forms an angle of about 53.13° with the positive x-axis. Which statement proves his claim correct or incorrect?
a) Correct because arctan(4/-3) = -53.13
b) Correct because arccos(-3/4) = 53.13
c) Incorrect because arctan(-3/4) = -36.87
d) Incorrect because arccos(-3/4) = -138.59
The statement that proves the claim about the angle is incorrect is that;
c) Incorrect because arctan(-3/4) = -36.87
How to solve Trigonometric Ratios?The 6 main trigonometric ratios of a right angle triangle are;
Sine θ = length of the opposite leg / length of the hypotenuse
Cosine θ = length of the adjacent leg / length of the hypotenuse
Tangent θ = sine θ/cosine θ = opposite leg / adjacent leg.
cosecant θ = 1 / sine θ = hypotenuse / opposite leg
secant θ = 1 / cosine θ = hypotenuse / adjacent leg
cotangent θ= 1 tangent θ = adjacent leg / opposite leg.
Now, we are told that the angle formed is 53.13°. Since the options are either arctan or arccos, we will use them to verify the angles;
cos 53.13° = 0.6
tan 53.13° = 1.33
They are both positive and it means both x and y values are positive since we are told that it involves the positive x-axis.
Thus, y/x cannot be negative or -3/4 as given.
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PLEASE HELP! ALGEBRA 1 HW I WILL GIVE BRAINLYEST FOR ANSWER!!
please answer all questions (a, b, and c)
proof that (x-1/x)(x^4/3+x^2/3) = x⅓(x²-1/x²)
The given polynomial solved as same as RHS is x^3/3(x^2- 1/x^2)
What is polynomial?Polynomial is defined as the sum of variable terms in the form of k×x^n, where k is constant and x variable and n is an integer.
According to give data:we have given a polynomial,
(x-1/x)(x^4/3+x^2/3) = (x^3/3)(x²-1/x²)
Take LHS
⇒ (x-1/x)(x^4/3+x^2/3)
⇒ (x^2-1/x)×(x^4 + x^2/3)
⇒ (x^2-1/x) x^2(x^2+1/3)
⇒ x^2/3x (x^2-1)(x^2+1)
⇒x^2/3x(x^4-1) ∴(a^2-b^2 = (a+b)(a-b))
multiply numerator and denominator by x
⇒x^3/3 (x^4-1/x^2)
⇒x^3/3(x^2- 1/x^2) = RHS
Hence, given problem has solved.
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5 Math on the Spot Robin says, "I can find 6 × 9 by
multiplying 4 X 9 and doubling it." Does her statement
make sense? Justify your answer.
If Robin says, "I can find 6 × 9 by multiplying 4 X 9 and doubling it, her statement didn't make any sense because it is not possible.
What is distributive property?
The same outcome will be obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend separately by the number and then adding the resulting products.
A × (B + C) = AB + AC
A (B - C) = AB - AC
Here,
we can write 6 × 9 as,
= 6 × 9 = 6 × (6 + 3) = (6 × 6) + (6 × 3), by applying distributive property
Hence, If Robin says, "I can find 6 × 9 by multiplying 4 X 9 and doubling it, her statement didn't make any sense because it is not possible.
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If f(x) = 3x and g(x)=1/x, what is the domain of (gof)(x)?
For the given functions f(x) = 3x and g(x) = 1/x then domain of
(gof)(x) =1/3x is all the real numbers excluding zero.
As given in the question,
Given functions are as follow:
f(x) = 3x
g(x) = 1/x
Now ,
(gof)(x)
= g(f(x))
Substitute f(x) = 3x in the above function we have,
=g(3x)
Replace the value of x by 3x in the given function g(x) we get,
= 1/ 3x
For x = 0 (gof)(x) =1/3x is undefined.
Domain include all the real numbers except zero.
Therefore, for the given functions f(x) = 3x and g(x) = 1/x then domain of (gof)(x) =1/3x is all the real numbers excluding zero.
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2 step equation:12. Amy wants to start taking gymnastics. There is a one-time fee of $35 to sign up, then it costs $85 per month. If Amy saves up $225, how many months of gymnastics can she take?
The number of months Amy can take the Gymnastic = 2 months.
Amy wants to start taking gymnastics.
The fee structure of the gymnastics is divided into two parts.
There is a one time fee payment of 35$ and there is a monthly payment that costs 85$ per month.
So the first month fee of the gymnastics = 35 + 85 = 120$
Savings of Amy = 225$
If Amy pays the 1st month fee ,
then the she will be left with the savings = 225$ - 120$ = 105 $
It means Amy can join the gymnastics for one more month .
Hence the number of months Amy can take the Gymnastic = 2 months .
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In the fall of 2017, there were 48 thousand more female undergraduate students enrolled at a college than male
undergraduate students. If the total undergraduate enrollment was 414 thousand that fall, find the numbers of female
undergraduate students and male undergraduate students who were enrolled.
The number of female undergraduate students was
thousand.
Answer: 231 thousand
Step-by-step explanation:
given,
total number of undergraduate students enrolled = 414000
let us take number of total number of male students as, X
then, total number of female students will be X + 48000
now we get,
total number of male students + total number of female students = total number of students enrolled.
X + (X + 48000) = 414000
X + X + 48000 = 414000
2X = 414000 - 48000
X = 366000/2
X = 183000
total number of male students is 183000
total number of female students is
X + 48000
183000 + 48000 = 231000
a packet of crisps weighs 32 grams to the nearest gram. a multipack of crisps contains 10 packets. work out the least and the greatest weights of the multipack. you can ignore the weight of the multipack wrapper
If a multipack of crisps contains 10 packets. the least and the greatest weights of the multipack is 315, 325.
How to determine the least and greatest weight?Range = 31.5≤ x < 32.5
Range = 31.5≤ 10 < 32.5
Hence,
Lowest and greatest possible for 32 grams
Lowest possible = 31.5 grams
Greatest possible =32.4 grams
Since multipack of crisps contain is 10 packets hence.
Least weight = 31.5 grams × 10
Least weight =315
Greatest weight = 32.5 grams × 10
Greatest weight = 325
Therefore 315 and 325 are the weight.
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Add and simplify.
7/12 + 2/15
A researcher believes that 8% of pet dogs in Europe are Labradors. If the researcher is right, what is the probability that the proportion of Labradors in a sample of 694 pet dogs would differ from the population proportion by less than 3%? Round your answer to four decimal places.
The probability that the proportion of Labradors in a sample of 694 pet dogs would differ from the population proportion by less than 3% is 0.9964
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = p = 8% = 0.08
sample size, n = 694
standard deviation, σ
= √{(p(1 - p)) / n}
= √{(0.08(1 - 0.08)) / 694}
= √{(0.08 * 0.98) / 694}
= 0.0103
The probability
differ from the population proportion by less than 3%
|X - 0.08| < 0.03
X < 0.11 OR X > 0.05
0.05 < X < 0.11
P(z < 0.11) - P(z < 0.05 )
z score for z < 0.05
z = (0.05 - 0.08) / 0.0103
= -2.9126
p value for z < -2.9126 = 0.001792
z score for z < 0.12
z = (0.12 - 0.09) / 0.0102
= 2.9412
p value for z < 2.9412 = 0.9982
The probability required = 0.9982 - 0.0016 = 0.9964 or 99.64%
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A2 Lesson 3.2 Practice
1. Does the graph shown represent a function for 0 < x < 6? Explain.
Yes, the graph shown represents a function for 0 < x < 6 because its domain is true about the given interval.
What are the domain and range of the function?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
The function is given in the represented graph
According to the given graph, we can see the value of the domain of the given function f(x) when the function includes all possible variables of x values of a function.
Here the domain of the given function is 0 < x < 6
Therefore, the graph shown represents a function for 0 < x < 6 because its domain is true about the given interval.
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HELPP!!! Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
A business owner wants to have the front window of her store painted and is considering two artists for the job. Grace has quoted a flat rate of $99 for the job. Eva's quote is $10 per hour, plus $89 to cover the cost of materials. Depending on how long it takes Eva to paint the window, these two could end up charging the same amount. How much would it cost? How long would Eva have to take? You hav Vide
Answer:
The cost would be $99 with each artist if the job took Eva 1 hour
Step-by-step explanation:
99=10x+89
subtract 89 from both sides
10=10x
1=x
Convert the height of a person who is 5.2 feet tall to centimeters. Include the inches-centimeter conversion
factor. Use the table given to create conversion factors. Show all conversion factors needed.
Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional
analysis that you learned.
The height of a person is 5.2ft in centimeter: 158.49cm
What are the Factors?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.So, the conversion of measurement from the unit feet to centimeters is provided by the feet-to-centimeter calculator.
The letters "ft" and "cm" stand for feet and centimeters, respectively. The centimeter is used in the International System of Units and is regarded as a component of the metric system. The US customary measurement system uses the unit foot.Approximately 30.48 cm makes up one foot.
1 ft = 30.48 cm
Now, the formula for 5.2 feet to centimeters is as follows:We are aware that 1 foot equals 30.48 centimeters.Therefore, 5.2 feet equals 5.2 x 30.48 centimeters.
5.2 ft = 158.49 cm.5.2 feet is therefore equal to 158.49 cm in centimeters.
Hence, the height of a person who is 5.2 feet tall to centimeters is 158.49cm.
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The length of the segment is _____centimeters
The scale is __cm : __mm.
Answer:
I'm assuming it's just a conversion of mm into cm?? in that case it will be 2.4 cm
what is the present value of $2525 per year, at a discount rate of 10 percent, if the first payment is received 9 years from now and the last payment is received 24 years from now?
The present value of $2525 per year, at a discount rate of 10 percent, if the first payment is received 9 years from now and the last payment is received 24 years from now is; $9215.77
What is the Present Value of Annuity?
An annuity is defined as a fixed amount of cash that is received or paid periodically over a certain period of time. This would mean that the amount in each cash flow of the annuity would be equal and occur for a specific period of time.
The formula for present value is;
PV = P[1 - (1 + r)⁻ⁿ)/r]
where;
PV is present value
P is periodic cash flow
r is interest rate
n is time
We are given the following;
Periodic cash flow (P) = $2525 /Year
Interest rate (r) = 10% /Year = 0.1
Time (n) = 16 Year (from 9 years to 24 years)
Thus;
PV = 2525[1 - (1 + 0.1)⁻¹⁶)/0.1]
PV = $19754.86
This is the present value in 9 years
Thus, the present value in 24 years which is now will be expressed by the formula;
PV = FV/(1 + i)^(t)
where;
PV is present value
FV is future value
i is interest rate
t is time
Thus;
PV = 19754.86/(1 + 0.1)^(8)
PV = $9215.77
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what is the expected value of x? where x/p equals 0/.15, 4/.05, 8/.25, 12/.05, 16/.5
The expected value of x is 10.8
How calculate the expected value of x?Expected value is defined as the predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.
Given :
x| 0 4 8 12 16
p| 0.15 0.05 0.25 0.05 0.5
The expected value of x, E(x) =Σ xp
E(x) = (0×0.15) + (4×0.05) + (8×0.25) + (12×0.05) + (16×0.5)
E(x) = 0 + 0.2 + 2 + 0.6 + 8
E(x) = 10.8
Therefore, the expected value of x is 10.8
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On a website that sells funny T-shirts, the number of customers has been falling 10% per month. If the site had 14,000 customers this month, then how many should it expect to have 10 months from now?
If necessary, round your answer to the nearest whole number.
customers
It should expect 4881 customers to have 10 months from now.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
Given that T-shirts, the number of customers has been Falling 10% per month
There are 14,000 customers this month
Now Creating the function :
Let y be the remaining customers and x be the number of months from now
y = (14,000)(1 - 0.1)ˣ
y = (14,000)(0.9)ˣ
Solving :
y = (14,000)(0.9)¹⁰
y = (14,000)(0.34867844)
y = 4881 customers
(nearest whole person)
Hence, it should expect 4881 customers to have 10 months from now.
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Answer:
It should expect 4881 customers to have 10 months from now.
let o be the point of intersection for the diagnols of quadrilateral abcd prove that abcd could be a trapezoid (that is if it has one sides parallel) is Aaod = Aboc
From the given proof below, we have been able to show that quadrilateral ABCD is a Trapezoid.
How to identify a Trapezoid?A trapezoid is also called a trapezium and it is characterized by four straight sides and one set of parallel sides. The parallel sides are referred to as the base, while the non-parallel sides are referred to as the legs.
We are told that;
O is the point of intersection for the diagonals of quadrilateral ABCD;
where;
AO/BO = CO/DO
This can also be expressed as;
AO/CO = BO/DO
Thus, if we create line OE to be parallel to DC which is OE || DC. Then it means that point E lies on BC.
Using the Basic Proportionality Theory, in ΔBDC, we can say that;
BO/OD = BE/EC ............................1
We are also given that:
AO/CO = BO/DO ..........................2
Thus, from Equations 1 and 2, we have;
AO/CO = BE/EC
Using the converse form of the Basic Proportionality Theorem, we have;
OE || AB
Therefore, AB || OE || DC.
Therefore we can conclude that ABCD is a Trapezoid.
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Determine if the line segment YX is tangent to circle Z.
The segment XY is a tangent to circle Z.
What is tangent to a circle?
Tangent to a circle is the line that touches the circle at only one point. There can be only one tangent at a point to circle. Point of tangency is the point at which tangent meets the circle.
To check the segment YX is tangent to circle z, first we have to check that the triangle formed XYZ is right angle triangle or not.
If the triangle XYZ is a right triangle, then we have
XY² +XZ² = YZ²
3.6² +2.7² = (1.8 +2.7)²
12.96 +7.29 = 20.25 it's true.
Therefore, the segment XY is a tangent to circle Z.
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Jan works from 30 to 40 hours per week during the summer. She earns $12.00 per hour. Her friend Rachel also has a job. Rachel's pay for t hours is given by the function r(t) = 11t, where 20 ≤ t ≤ 30. Find the domain and range of each function. Compare their hourly wages and the amount they earn per week.
j(t) domain:
≤ t ≤
j(t) range:
≤ j(t) ≤
r(t) domain:
≤ t ≤
r(t) range:
≤ r(t) ≤
select: Jan or Rachel
earns more per hour than
select: Jan or Rachel
. Jan earns from $ (blank)
to (blank) $
per week and Rachel earns from (Blank) $
to (Blank) $
per week.
Jan earns more than Rachel. The range of what Jan earns is 360 dollars to 480 dollars per week. The range of what Rachel earns is 220 dollars to 330 dollars per week.
How to solve for the Range and the domain of the functionsJan's pay function is given as /(t) = 12 dollars this is the same as 12 dollars in one hour
the time that she has to work is given a 30 hours to 40 hours.
Hence the domain would be written as
domain : 30 ≤ t ≤ 40
we have to make use of the values of t
f(t) = 12 * 30 = 360
f(t) = 12 * 40 = 480
The range of Jan is going to be
range : 360 ≤ t ≤ 480
b. For Rachel, t is going to vary between 20 ≤ t ≤ 30
domain : 20 ≤ t ≤ 30
r*t = 11t
= 11 x 20 = 220
= 11 x 30 = 330
The range is given as
range: 220 ≤ t ≤ 330
Jan earns more per hour than Rachel
The amount earned is, Jan earns from 360 dollars to 480 dollars per week.
Rachel earns from 220 dollars to 330 dollars per week.
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A student raises the flag up at a steady speed of 3m/s. The flag is 2kg in mass. What is the average power exerted.
The average power exerted on the flag of mass 2 kg by the student is 58.8 Watt.
What is power?Power can defined as the rate at which work is done.
To calculate the average power exerted on the flag, we use the formula below.
Formula:
P = mgv............ Equation 1Where:
P = Power exertedm = Mass of the flagg = Acceleration due to gravityv = Velocity at which the flag was raisedFrom the question,
Given:
m = 2 kgv = 3 m/sg = 9.8 m/s²Substitute these values into equation 1
P = 2×3×9.8P = 58.8 WattHence, the average power exerted is 58.8 Watt.
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In a class of 152 students, 100 are taking math (M), 77 are taking science (S), and 55 are taking both math and science. One student is picked at random. Find the probability.
P(taking math or science or both)
The probability of taking math or science or both is 123/152
The total number of students = 152 students
Number of students who take math = 100 students
Number of student who take science = 77 students
Number of students who take both math and science = 55 students
The probability = Number of favorable outcomes / Total number of outcomes
We have to find each term
The number of favorable outcomes =55+45+23
= 123
Total number of outcomes = 152
Substitute the values in the equation
Probability of taking math or science or both = 123/152
Hence, the probability of taking math or science or both is 123/152
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