Answer:
Step-by-step explanation:
As it is a second order equation, it means that it has two possible answers and they are [tex]x_1[/tex] and [tex]x_2[/tex].
The famous quadratic formula for solving any second order equation is the following:
[tex]x_{1} = \frac{-b + \sqrt{b^2 - 4 ac}}{2a}\\x_{2}=\frac{-b - \sqrt{b^2 - 4 ac}}{2a}[/tex]
Where a is the coefficient of [tex]x^2[/tex], b is the coefficient of x, and c is the free term. In other words,
[tex]a = 3\\b=4\\c=-2[/tex]
as the equation should be in the following form:
[tex]a x^2 + bx+c = 0[/tex]
Therefore the possible answer should be the following,
[tex]\frac{-4 + \sqrt{4^2 - 4*3*(-2)}}{2*3}=\frac{-4 +\sqrt{16 + 24}}{6} =\frac{-4 + \sqrt{40}}{6}=\\ \frac{-4 + \sqrt{4*10}}{6} = \frac{-4 + 2\sqrt{10}}{6}[/tex][tex]\frac{2*(-2 + \sqrt{10})}{2*3} = \frac{-2 + \sqrt{10}}{3}[/tex]
by dividing the numerator and denominator by 2, we can deduce the following,
In a class of 75 students, 50 like visiting and 50 like Picnic. If each student like at least one activity, using Venn diagram, find the number of students who like both.
please help me with this question.
If each student like at least one activity, the number of student that like both is 25
How to solve Venn diagram?The class have 75 students.
50 like visiting and 50 like picnic.
Therefore, if each student like at least one activity, the number of student that like both can be calculated as follows;
let
x = student that like both
75 = 50 + 50 - x
Therefore,
75 = 100 - x
75 - 100 = -x
-25 = -x
x = 25
Therefore, the number of students who like both are 25.
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An adult African elephant weighs approximately 8 tons. Which comparison is true
In circle O, ST is a diameter.
Circle O is shown. Line segment S T is a diameter. Line segments R O and U O are radii. Angles R O U and U O T are congruent. The measure of arc R S is (2 x + 8) degrees, the measure of arc R U is (3 x minus 14) degrees, and the measure of arc U T is (3 x minus 14) degrees.
What must be the value of x?
22.0
25.0
25.4
37.2
A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant. The correct option is B.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
Given the measure of arc, RS is (2 x + 8) degrees, the measure of arc R U is (3 x minus 14) degrees, and the measure of arc U T is (3 x minus 14) degrees.
(3x-14)° + (3x-14)° + (2x+8)° = 180°
8x -20 = 180
8x = 200
x = 25
Hence, the correct option is B.
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Consider a triangle ABC like the one below. Suppose that a = 42, b=44, and c= 52. (The figure is not drawn to scale.) Solve the triangle
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
there is more than one solution, use the button labeled "or".
In the triangle , Angle A is 51.1 degrees, B is 54.5 degrees , C is 74.4 degrees.
What is a Triangle ?A triangle is defined as a polygon with three sides , three angles and three vertices.
Using the Law of Cosine to solve the Triangle and to determine the value of all the angles
c² = a²+ b² -2abCosC
a = 42 , b=44 , c = 52
52² = 42² + 44² -2 * 42 * 44 cos C
2704 = 1764 + 1936 -3696 cos C
cos C = 0.269
C =74.4 ° (degrees)
Similarly calculating for A and B will give
Angle A is 51.1 degrees
Angle B is 54.5 degrees
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The average cost of tuition plus room and board for a small private liberal arts college is reported to be $9,500 per term, but a financial administrator believes that the average cost is higher. a study conducted using 350 small liberal arts colleges showed that the average cost per term is $9,845. the population standard deviation is $1,200. let α = 0.05. what is the p-value for this test?
You paid $16.50 for a prescription plus $1.32 in sales tax. What is the sales tax rate?
Answer:
16.50+1.32 u happy its so easy
A graph titled Fast Freddy has time (minutes) on the x-axis and Distance (miles) on the y-axis. A line goes through points (0, 0) and (4, 1). A 2-column table with 3 rows titled Speed Sam. Column 1 is labeled Time (minutes) x with entries 4, 20, 32. Column 2 is labeled Distance (miles) y with entries one-half, 2 and one-half, 4.
Find the slope from the graph and from the table to compare the speeds of two marathon runners.
What is the constant speed of Fast Freddy?
1/4
What is the constant speed of Speedy Sam?
Who ran faster?
The constant speed of Fast Freddy is 0.25 miles per minute and the constant speed of Speedy Sam is 0.125 miles per minute
The complete questionThe question is incomplete as the graphs and the tables are missing.
However, the points given in the question can be used to represent the graph and the table
The slopes of the graph and the table?By interpreting the points, we have:
Graph
(x, y) = (0, 0) and (4, 1)
Table
x y
4 0.5
20 2.5
32 4
The slope is calculated using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
Graph: [tex]m = \frac{1 -0}{4 -0} = 0.25[/tex]
Table: [tex]m = \frac{4 -2.5}{32 -20} = 0.125[/tex]
Their constant speedsFreddy's speed is represented by the graph, while Sam's speed is represented by the table
Hence, the constant speed of Fast Freddy is 0.25 miles per minute and the constant speed of Speedy Sam is 0.125 miles per minute
Who ran faster?Freddy ran faster because 0.25 is greater than 0.125
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Answer:
1. Freddy ran a speed of 1/4 miles
2. Sam ran a speed of 1/8 miles
3. Freddy ran faster
Step-by-step explanation:
Your welcome :)
flash is the best show to ever exist
Which of the following best describes the graph below A.it is a one to one function B. It is not a function C.it is a many to one function D.It is a function,but it is not one to one
The graph is a one to one function , Option A is the correct answer.
What is a function ?A function is defined as the algebraic expression that identifies relation between a dependent and an independent variable.
All the function have a defined domain and Range.
To test that the given graph is a function ,
A vertical line test will be done , A vertical is passes through different points of the graph and for every unique value of x , we get a single solution of y , therefore it is a function
Then horizontal Line test is done to determine if it is a one to one function, for every y value there is only one x value.
The graph passes the horizontal line test.
Therefore The graph is a one to one function , Option A is the correct answer.
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7x + 2y = −12
3x + 4y = −24
Answer:
x= 0 , y= 6
Step-by-step explanation:
multiplying 1st equation by 2 and subracting equation 2nd from 1st
14x + 4y = -24
- ( 3x + 4y) = - (-24)
11x = 0
so, x=0
keep x=0 in equation 2nd
3*0 + 4y = -24
y = -24 / 4
so , y = 6
Georgia drove 156 miles in 4 hours. If this rate continue, how many miles can he drive in 7 hours
Answer: he drives 273 miles for 7 hours
Step-by-step explanation:
what is the value of 50 US dollar in philippine money?
Answer:
Answer is $2,637.38
Step-by-step explanation:
How to solve for the x??? Pls hep
Answer:
x = 97.5 degrees
Step-by-step explanation:
First, we need to know what the total sum of interior angles. We use the formula (n-2) * 180, n being the number of sides.
Since this is a 6-sided polygon, the sum is (6-2) * 180, or 720 degrees.
We have the total sum of interior angles, so now we have all the information we need.
720 degrees = (2x-50) + (x+40) + 80 + (x+20) + 90(right angle symbol) + 150
720 = 4x + 330 (subtract 330 from both sides)
390 = 4x (divide by 4)
x = 97.5 degrees
what is the solution to the equation 1/5n=3
a n=8
b n=15
c n=25
d n=125
Answer:
[tex]\huge\boxed{\sf n = 15}[/tex]
Step-by-step explanation:
Given Equation:[tex]\displaystyle \frac{1}{5} n = 3\\\\Multiply \ 5 \ to \ both \ sides\\\\n = 3 \times 5\\\\n = 15\\\\\rule[225]{225}{2}[/tex]
In August, Sara and Mel decided to spend a week fishing. On the first day, Sara caught 2 fish, and Mel caught 4 fish. The next day, Sara had 4 fish altogether, and Mel had 8 fish. On the third day Sara had 6 fish altogether while Mel had 12 fish altogether.
1. If the pattern continues, how many fish will each of them have caught by the end of the week? Fill in the rest of the chart.
Fish caught altogether:
Days
1
2
3
4
5
6
7
Sara
2
4
6
Mel
4
8
12
1. If the pattern continues, how many fish will each of them have caught by the end of the week? Fill in the rest of the chart.
Fish caught altogether:
Days
1
2
3
4
5
6
7
Sara
2
4
6
Mel
4
8
12
2. What is the pattern that describes how many fish Sara caught each day? What is the pattern that describes how many fish Sara caught altogether?
3. What is the pattern that describes how many fish Mel caught each day? What is the pattern that describes how many fish Mel caught altogether?
4. What do you notice when you compare Sara’s pattern and Mel’s Pattern?
5. If Sara and Mel continued fishing, how many fish would they have caught by day 10?
this is worth 100 points
Turn into coordinates pair
(2,4)(4,8)(6,12)Slope
m=8-4/4-2=2Equation
y=2x#1
A week is of 7 days
total fishes Sara has=2(7)=14
Total mel will have
y=14(2)=28fishes#2
The each day Sara caught 2fishes
pattern for Sara 's total
2dd is days
#3
Mel also caught 2(2)=4 fishes a day
Mel caught all together is 2(Sara)
#4
They are in proportion to each other
#5
Sara would have 10(2)=20fishes
Mel would have.
20(2)=40fishesAnswer:
Q1)
The number of fish Sara caught increases by 2 each day.
The number of fish Sara caught increases by 4 each day.
[tex]\large \begin{array}{| c | c | c |}\cline{1-3} & \sf SARA& \sf MEL\\\sf Days & \sf fish\:caught & \sf fish\:caught \\& \sf altogether & \sf altogether\\\cline{1-3} 1 & 2 & 4 \\\cline{1-3} 2 & 4 & 8 \\\cline{1-3} 3 & 6 & 12 \\\cline{1-3} 4 & 8 & 16 \\\cline{1-3} 5 & 10 & 20 \\\cline{1-3} 6 & 12 & 24 \\\cline{1-3} 7 & 14 & 28 \\ \cline{1-3}\end{aligned}[/tex]
Q2)
Sara caught 2 fish each day.
The pattern that describes how many fish Sara caught altogether is:
2 times the number of days
Q3)
Mel caught 4 fish each day.
The pattern that describes how many fish Mel caught altogether is:
4 times the number of days
Q4)
The number of fish Mel caught altogether is twice the number of fish Sara caught altogether.
Q5)
The number of fish Sara and Mel would have caught by day 10:
Sara = 10 × 2 = 20 fishMel = 10 × 4 = 40 fishBrian flips a fair coin 3 times
What is the probability of him getting exactly 2 tails?
Answer:
[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
There are a list of possible outcomes:
TTT (1)TTH (2)THT (3) THH (4)HHH (5)HHT (6)HTH (7)HTT (8)This represents 8 outcomes.
The only ones that have two tails are:
TTH (1) THT (2) HTT (3)Because there are 3, this means that the probability in a fraction form of Brian getting exactly 2 tails is 3/8. P ( exactly 2 tails) = 3/8.
Find the measure of
Answer:
r = 76°
Step-by-step explanation:
61° + 43° + r = 180° { <'s on a straight line are supplementary}
104+r=180
r = 180-104
r = 76°
PLEASE HELP I’LL MAKE YOU THE BRAINIEST Find the area of the parallelogram
Answer:
A=5.4×4.4=23.76 in
because the are of the paralelogram is base ×high
Bentley leans a 22-foot ladder against a wall so that it forms an angle of 74 degrees with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary
The Sine or Sin(θ) in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. The Height on the wall till which the ladder reaches is 21.148 ft.
What is Sine (Sinθ)?The Sine or Sin(θ) in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,
Sin(θ) = Perpendicular/Hypotenuse
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The hypotenuse is the longest side of the triangle.
The height of the wall can be found by using the trigonometry ratios, therefore, the height of the wall can be determined as,
Sin(74°) = (Height on the wall)/(Length of the wall)
Sin(74°) = (Height on the wall)/22 ft
(Height on the wall) = 21.148 ft
Hence, the Height on the wall till which the ladder reaches is 21.148 ft.
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Answer:
21.15
Step-by-step explanation:
A store manager wanted to see the relationship between
the number of computers sold, x, and store profit, y, on a
daily basis. The regression line is û = -150 +24x, where
x is the number of computers sold for the day.
What is the predicted store profit if 0 computers are
sold for the day?
O-$150
O-$126
$0
O $176
The predicted store profit if 0 computers are sold for the day is $-150.
What is the predicted store profit?
Profit is the total selling price less the cost price of an item.
Profit = selling price - cost price
Given the regression line, û = -150 +24x, substitute for x
û = -150 +24(0)
û = -150
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Answer:
The answer above is correct -150 is correct
Step-by-step explanation:
EDG2022
Which of the following best describes /JKL?
32°
L
K
The best statement that describes the angle JKL is inscribed angle.
What is an inscribed angle?An inscribed angle in a circle is formed by two chords that have a common end point on the circle. The chord JK and LK intersect in the circle.
The angle ∠JKL is not an obtuse angle because it's less than 90 degrees.
The angle ∠JKL is not a vertical angle because it's not vertically opposite any angle.
The angle ∠JKL is not a central angle because it was not from from the centre of the circle.
The angle is an inscribed angle because it was formed by the intersection of two chords in the circle.
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If [2a -1] [-3-a]= (10), find the value of a.
Step-by-step explanation:
Step-by-step explanation:-6a-2a^2+3+a=10-7a-2a^2=10-32a^2+7a+7=0What is the scale factor for XYZ TO UVW?
Answer:
D. 2
Step-by-step explanation:
If you multiply any side from XYZ by 2 it will equal the same length of one of the sides of UVW.
75 points! what’s the lateral area, total surface area, and volume of this? please help me!
Answer:
yes of course it exists until to you practice a little bit hard. so let's. try
please help with math
Someone pleaseeeee helpp meeeeee!!!!
Answer:
The slope is 0.
Step-by-step explanation:
x is the gradient of the line, so multiplying the slope, zero, by the gradient, x, would make this equal to zero.
help please and only answer if ur sure x
Answer:
9/10
Step-by-step explanation:
First you would have to make the denominators the same, and they have an lcd of 10. So multiply 2/5 by 2 which is 4/10
and then 1/2 by 5 to get 5/10
then add 4/10 and 5/10 together and you get 9/10
What is the distance between the following points?
Answer:
if im not mistaken the andswer is D
may i have help with this
Answer: D. 7^11
Step-by-step explanation:
For exponents with the same base, we just add the exponents and keep the same base. 7 is the same base; therefore 5+6=11 which means the answer is 7^11
Howard sells used helicopters, and he receives a 3% commission on all that he sells. If Howard received $42,000 in commissions last year, how many dollars worth of used helicopters did he Sell?
The worth of helicopter sold is $1,400,000
How to determine the total sales?The given parameters are:
Commission = 3% of salesCommission = $42,000This means that:
3% of sales = $42,000
Divide both sides by 3%
Sales = $1,400,000
Hence, the worth of helicopter sold is $1,400,000
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The table below shows the estimated population of fish living in the local lake as determined by the local
environment council every 10 years between 1960 and 1990.
The equation y = 1500(.9) describes the curve of best fit for the fish population (y). Let z represent the
number of 10-year intervals since 1960.
Year Population
1960
1500
1970
1350
1980 1210
1990 1100
Using this equation, what is the approximate predicted population of fish living in the lake in the year 2020?
A) 980
B) 800
C) 770
D) 720
The approximate predicted population of fish living in the lake in the year 2020 is; B: 800
How to Calculate Estimate population from a Table?
We are told that the equation that describes the curve of best fit for the fish population (y) is;
y = 1500(0.9)^(z)
where z represent the
number of 10-year intervals since 1960.
The table started in the year 1960 and we want to find the population in the year 2020.
Number of years after 2020 is;
2020 - 1960 = 60 years
60 years is 6 decades
Thus;
y = 1500(0.9)⁶ = 797 ≈ 800
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