Answers
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
Calculate discriminant :
[tex]\qquad \sf \dashrightarrow \: 3 {x}^{2} + 6x - 1[/tex]
a = 3b = 6c = 1[tex]\qquad \sf \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]
[tex]\qquad \sf \dashrightarrow \: d = (6) {}^{2} - (4 \times 3 \times 1)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 36 - 12[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 24[/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt {d} = 2 \sqrt{6} [/tex]
Now, let's calculate it's roots ( x - intercepts )
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{ - b \pm \sqrt{d} }{2a} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{2 \times 3} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{6} [/tex]
So, the intercepts are :
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{ - 6 - 2 \sqrt{6} }{6} [/tex]
and
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{ - 6 + 2 \sqrt{6} }{6} [/tex]
Answer:
[tex]\left( \dfrac{ -3 + 2\sqrt{3}}{ 3}, \ 0\right), \ \left(\dfrac{ -3 - 2\sqrt{3}}{ 3}, \ 0\right)[/tex]
Explanation:
Given expression:
f(x) = 3x² + 6x - 1
To find x intercepts, set f(x) = 0Use quadratic formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ where \ ax^2 + bx + c = 0[/tex]
Here after finding coefficients:
a = 3, b = 6, c = -1Applying formula:
[tex]x = \dfrac{ -6 \pm \sqrt{6^2 - 4(3)(-1)}}{2(3)}[/tex]
[tex]x = \dfrac{ -6 \pm \sqrt{48}}{6}[/tex]
[tex]x = \dfrac{ -6 \pm 4\sqrt{3}}{6}[/tex]
[tex]x = \dfrac{ -6 \pm 4\sqrt{3}}{2 \cdot 3}[/tex]
[tex]x = \dfrac{ -3 \pm 2\sqrt{3}}{ 3}[/tex]
[tex]x = \dfrac{ -3 + 2\sqrt{3}}{ 3}, \ \dfrac{ -3 - 2\sqrt{3}}{ 3}[/tex]
Related Questions
The youth group is going on a trip to the State Fair trip cost 63 dollars included in that price is 13 dollars for a concert ticket in the cost of 2 passes, one for the rides and one for the game booth. Each of the passes cost the same price, write an equation representing the cost of the trip, and determine the price of one pass, solve your equation by showing your work and steps.
Answers
Answer:
The cost of one pass is 25$
Step-by-step explanation:
Call the cost of one of the passes, P. So we have
63 = 13 + 2P - subtract 13 from both sides
50 = 2P - divide both sides by 2
25 = P
So the cost of one pass = $25
! What are modern numbers? and how are they used?
Answers
Modern numbers are the ten numerical digits used in constructing other numbers.
What are modern numbers?Modern numbers are also called Arabic numerals. They are the ten numerical digits:
0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Uses of modern numbers;
They are used as symbols to write decimal numbers.They are used in writing numbers in other systems like the octal, and for writing identifiers such as computer symbols, trademarks, or license plates.They are used in constructing other numbers.Hence, modern numbers are the ten numerical digits used in constructing other numbers.
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Thirteen-year-old noel was taking her algebra test but was unsure of one of her responses. she decided to go with the answer that felt the ""most right."" this is an example of?
Answers
The concept exhibited by the thirteen year old who was unsure of one of her responses. she decided to go with the answer that felt the ""most right."" is an example of; Intuitive thought.
What is the concept exhibited by the thirteen year old as given in the task content?It follows from the task content that the thirteen year old was unsure of one of her responses. she decided to go with the answer that felt the ""most right."".
Such concept may be attributed to Intuitive thought.
This follows from the fact that the internal impulse which prompts individuals to make decisions is termed; Intuition.
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HELP ME ASAP!!! I WILL GIVE MANY POINTS
Answers
(a) The radius of the small sphere is 2 centimeters.
(b) The measure of the angle XAB is approximately 36.870°.
(c) The area of the shaded region is approximately 3.107 square centimeters.
How to analyze a geometric system
Herein we have a geometric system formed by three big semicircles and a small circle, whose geometric diagram is attached below. (a) The relationship between the semicircles and the circle is represented by two formulae:
8² + h² = (8 + r)² (1)
h + r = 8 (2)
Where r is the radius of the small circle.
Then, we solve the system:
8² + (8 - r)² = (8 + r)²
64 + 64 - 16 · r + r² = 64 + 16 · r + r²
32 · r = 64
r = 2
The radius of the small sphere is 2 centimeters.
(b) The measure of the angle XAB is found by trigonometric relations:
cos m ∠ XAB = OA / AX
cos m ∠ XAB = 8 / 10
m ∠ XAB ≈ 36.870°
The measure of the angle XAB is approximately 36.870°.
(c) The area of the shaded region is the area of the triangle minus the area of the three circular sections:
A = 0.5 · (16 cm) · (10 cm) · sin 36.870° - (36.870° /180) · π · (8 cm)² - 0.5 · (106.260° / 180) · π · (2 cm)²
A ≈ 3.107 cm²
The area of the shaded region is approximately 3.107 square centimeters.
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Find the value of the indicated variable.
Answers
102 degrees
Step-by-step explanation:
Angles in a quadrilateral add to 360 degrees.
y = 360 - (120 + 85 + 53)
y = 360 - 258
y = 102 degrees
A certain type of thread is manufactured with a mean tensile strength of kilograms and a standard deviation of kilograms. How is the variance of the sample mean changed when the sample size is
Answers
In the case above:
(a) If there is an increased from 64 to 196, then the variance decreases.
(b) If there is a decreased from 784 to 49, then the variance increases.
What occurs if the variance increases?Standard Error is known to be the square root of the variance. if a given variance increases, so its standard error also.
Since the standard error takes place in the denominator, hence, if the standard error increases, the variance goes up.
Therefore, In the case above:
(a) If there is an increased from 64 to 196, then the variance decreases.
(b) If there is a decreased from 784 to 49, then the variance increases.
See full question below
A certain type of thread is manufactured with a mean tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilograms. How is the variance of the sample mean changed when the sample size is (a) increased from 64 to 196? (b) decreased from 784 to 49?
What is the variance about?
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Please help with all 3 And explain it please so I understand ty
Answers
A simultaneous equation refers to two or more equations that are solved at the same time.
What is a simultaneous equation?A simultaneous equation refers to two or more equations that are solved at the same time. Now we shall solve each of the equations;
a. 2x + y = 3 ------(1)
x - y = 4 ------ (2)
x = 4 + y ----- (3)
Substituting (3) into (1)
2(4 + y) + y = 3
8 + 2y + y = 3
8 + 3y = 3
3y = 3 - 8
3y = -5
y = -5/3
Hence;
x - y = 4
x - (-5/3) = 4
x = 4 + 5/3
x = 17/3
b. 2x + 6y =9 -----(1)
x + 3y = 2 ------ (2)
x = 2 - 3y ------ (3)
Substitute (3) into (1)
2( 2 - 3y) + 6y =9
4 - 6y + 6y = 9 (From this stage we can see that it is not possible to solve the quadratic)
c. 6x - 3y = 12 -----(1)
4x + 2y = 10 ---- (2)
12x - 6y = 24 ---- (3)
12x + 6y = 30 --- (4)
Add (3) to (4)
24x = 54
x= 54/24 = 9/4
Hence;
4(9/4) + 2y = 10
9 + 2y = 10
2y = 10 - 9
y = 1/2
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Mathematics Literacy Graphs Question 1 Homework
Answers
1. Independent Variable (x) is the number of toys.
Dependent Variable (y) is the amount.
2. Graph A - Income Graph.
Graph B - Expense Graph.
3. Zandi won't make a profit while selling 5 toys.
4. Zandi must sell 10 toys to reach break-even.
5. Zandi's variable cost per toy is $15.
6. The total cost function is, total cost = 100 + 15x.
1. The independent variable will be the number number of toys marked on the x-axis, whereas the dependent variable will be the amount on the y-axis, as the cost and revenue both depend on the units.
2. Graph A will be Zandi's income as when the unit is 0, the income is 0, whereas graph B is the expense graph as when the unit is 0, still some fixed expenses are generated for example rent.
3. Zandi will make a loss while making and selling 5 toys as the amount on graph B corresponding to 5 toys, that is, the expenses, are greater than the amount on graph A corresponding to 5 toys, that is, the income.
4. The break-even is the point where the income = expense, which on the graph is at the point where the number of toys is 10.
Thus, Zandi must sell 10 boys to reach break even.
5. The variable cost per toy can be found as the slope of the expense graph, m = (400 - 100)/(20 - 0) = 300/20 = 15.
Thus, Zandi's variable cost is $15.
6. Total cost = Fixed cost + a number of units*variable costs.
Thus, the total cost = 100 + 15x.
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3. What kind of triangle is represented by the triangle shown below?
Isosceles
Right
O Equilateral
Scalene
Answers
Answer:
c
Step-by-step explanation:
In geometry, an equilateral triangle is a triangle in which all three sides have the same length.
Exponential Decay
Find f(3), where f(x) = 2x(1/2)^x
Answers
f(x) = 2 * (1/2)^x
f(3) = 2 * (1/2)^3
f(3) = 2 * (1/2 * 1/2 * 1/2)
f(3) = 2 * 1/8
f(3) = 2/8
f(3) = 1/4
Hope this helps!
Answer:
[tex]f(x) = 2 \times ( { \frac{1}{2} })^{x} \\ \\ f(3) = 2 \times ({ \frac{1}{2}})^{3} \\ \\ = 2 \times \frac{1}{8} \\ \\ f(3) = \frac{1}{4} = 0.25[/tex]
please help im stuck its math
Answers
Answer:
y = 5x - 6
Step-by-step explanation:
We are given a line, which is parallel to the line y=5x+3.
We also know that this line passes through the point (3,9).
We want to find the equation of this line.
Parallel lines have the same slopes, yet different y intercepts.
So, let's find the slope of the line y=5x+3.
The line is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.
As 5 is in the place of where the slope (m) is, 5 is the slope of the line.
It is also the slope of the line parallel to it (which is the line we are trying to find).
We can write the equation of this new line in slope-intercept form as well, which is also the format your system wants.
Before we write the equation of the line in slope-intercept form, we can write it in point-slope form, then convert it into slope-intercept form.
Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.
As we have already found the slope (5), we can immediately plug it into the formula.
[tex]y-y_1=5(x-x_1)[/tex]
Now, remember that we were also given a point, that passes through the line. This point is (3,9).
We can use its values in the formula.
Substitute 3 as [tex]x_1[/tex] and 9 as [tex]y_1[/tex].
y - 9 = 5(x-3)
Now, we have written the line in point-slope form.
However, we're not done yet; remember that we want it in slope-intercept form.
We can solve the equation for y to get slope-intercept form.
So, on the right, open up the parentheses and distribute 5 to both x and -3.
y - 9 = 5x - 15
Now add 9 to both sides.
y = 5x - 6
An airplane travels 6111 kilometers against the wind in 9 hours and 7911 kilometers with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind
Answers
Answer:
Speed of the plane in still air: [tex]779\; {\rm km \cdot h^{-1}}[/tex].
Windspeed: [tex]100\; {\rm km \cdot h^{-1}}[/tex].
Step-by-step explanation:
Assume that [tex]x\; {\rm km \cdot h^{-1}}[/tex] is the speed of the plane in still air, and that [tex]y\; {\rm km \cdot h^{-1}}[/tex] is the speed of the wind.
When the plane is travelling against wind, the ground speed of this plane (speed of the plane relative to the ground) would be [tex](x - y)\; {\rm km \cdot h^{-1}}[/tex]. When this plane is travelling in the same direction as the wind, the ground speed of this plane would be [tex](x + y)\; {\rm km \cdot h^{-1}}[/tex].The question states that when going against the wind ([tex]v = (x - y)\; {\rm km \cdot h^{-1}}[/tex],) the plane travels [tex]6111\; {\rm km}[/tex] in [tex]9\; {\rm h}[/tex]. Hence, [tex]9\, (x - y) = 6111[/tex].
Similarly, since the plane travels [tex]7911\; {\rm km}[/tex] in [tex]9\; {\rm h}[/tex] when travelling in the same direction as the wind ([tex]v = (x + y)\; {\rm km \cdot h^{-1}}[/tex],) [tex]9\, (x + y) = 7911[/tex].
Add the two equations to eliminate [tex]y[/tex]. Subtract the second equation from the first to eliminate [tex]x[/tex]. Solve this system of equations for [tex]x[/tex] and [tex]y[/tex]: [tex]x = 779[/tex] and [tex]y = 100[/tex].
Hence, the speed of this plane in still air would be [tex]779\; {\rm km \cdot h^{-1}}[/tex], whereas the speed of the wind would be [tex]100\; {\rm km \cdot h^{-1}}[/tex].
Please Help!
A dog is attached to a 35-foot rope fastened to the outside corner of a fenced-in garden that measures 28 feet by 36 feet. Assuming that the dog cannot enter the garden, compute the exact area that the dog can wander.
The dog can wander an area of ___ square feet
(exact answer, using the pi symbol)
Answers
The area that the dog can wander based on the information provided will be 931π.
How to calculate the area?From the information, we are told that the dog dog is attached to a 35-foot rope fastened to the outside corner of a fenced-in garden that measures 28 feet by 36 feet.
In this case, the dog is in an outside corner. The dog can trace 3/4 of a circle when it starts walking in a circle away form the wall.
The area that the dog can wander will be:
= 3/4(π35²) + 1/4(π(35 - 28)²)
= 3/4π(35)² + 1/4π(7)²
= (3/4 × 1225)π + (1/4 × 49)π
= 918.75π + 12.25π
= 931π
Therefore, the area that the dog can wander based on the information provided will be 931π.
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drake has 7 song that he choose to sing in the shower each day of the week, one song per day. If he never sings the same song twice in week, how many different ways can he choose his song throughout the week?
Answers
Answer:
5040 ways
Step-by-step explanation:
7! = 5040
7 choices on day 1
6 choices on day 2
5 choices on day 3
4 choices on day 4
3
2
1 7 x 6 x 5 x 4 x 3 x 2 x1 = 5040
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answers
Answer:
B
Step-by-step explanation:
If x and y vary inversely, then as x increases, y decreases. That eliminates answers A, C, and D.
Answer: B
Evaluate the expression for f = -6 and g = -1.
fg - f =
Answers
Answer:
7
Step-by-step explanation:
Given the information from the question:
[tex]fg - f = f \times g - f[/tex]
Next we can use the order of operations to find the value of the expression.
[tex]fg - f = - 6 \times - 1 - ( - 1) \\ = 6 - ( - 1) \\ = 6 + 1 \\ = 7[/tex]
Solve the problems involving (HCF) highest common factor for each of the the following
B) A restaurant donated 540 pieces of fried chicken and 360 cups of drink for a gathering event. The restaurant has set the condition the every visitor will receive the portion of food equally. Find :
(1) Find the maximum number of visitors that can be invited to the event.
(2) Find the numbers of pieces of chicken to be received by the visitors who attended the event.
Answers
Step-by-step explanation:
the highest or greatest or largest common factor is the product of the prime factors the numbers have in common :
540 ÷ 2 = 270
270 ÷ 2 = 135
135 ÷ 2 no
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 3 no
5 ÷ 5 = 1
540 = 2² × 3³ × 5¹
360 ÷ 2 = 180
180 ÷ 2 = 90
90 ÷ 2 = 45
45 ÷ 2 no
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 3 no
5 ÷ 5 = 1
360 = 2³ × 3² × 5¹
so, the HCF = 2² × 3² × 5¹ = 4×9×5 = 180
(1)
to satisfy the condition max. 180 visitors can be invited.
(2)
540 / 180 = 3
so, every visitor can receive 3 pieces of chicken.
and 360 / 180 = 2 cups of drink.
Please help!! Which figures demonstrate a single translation?
Select each correct answer.
Answers
Answer:
the top 2 and the left bottom corner
Step-by-step explanation:
the first one in the first row is a reflection
the second one in the first row is a rotation
the one on the left bottom corner just moved a unit
Answer:
Option 3
Step-by-step explanation:
The first answer is a reflection across the y-axis, the second is a rotation, and the last one is two translations. So, the third one is correct because it's the only single translation.
One large jar and five small jars can hold 26 ounces of jam. One large jar minus one small jar can hold 2 ounces of jam. Use the given matrix equation to solve for the number of ounces of jam that each jar can hold. Explain the steps that you took to solve this problem.
A matrix with 2 rows and 2 columns, where row 1 is 1 and 5 and row 2 is 1 and negative 1, is multiplied by matrix with 2 rows and 1 column, where row 1 is l and row 2 is s, equals a matrix with 2 rows and 1 column, where row 1 is 26 and row 2 is 2.
Answers
Using a system of equations, it is found that one large jar holds 6 ounces and one small jar holds 4 ounces.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable l: Weight that a large jar holds.Variable s: Weight that a small jar holds.One large jar and five small jars can hold 26 ounces of jam, hence:
l + 5s = 26, which is the first equation in matrix form.
Then:
l = 26 - 5s.
One large jar minus one small jar can hold 2 ounces of jam, hence:
l - s = 2, which is the second equation in matrix form:
Then:
l = 2 + s = 26 - 5s
2 + s = 26 - 5s
6s = 24
s = 4.
l = 26 - 5s = 6.
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A binomial probability experiment is conducted with the given parameters. compute the probability of x successes in the n independent trials of the experiment. n=9, p=0. 3,
Answers
If the probability of obtaining success is 0.3 and the value of n is 9 then the probability at the value of x be 3 is 0.3811.
Given that the value of n is 9 and the value of p is 0.3.
We are required to find the probability when the value of x is equal to 3.
Probability is the calculation of chance of happening an event among all the events possible.It lies between 0 and 1.
Probability=Number of items/total items.
Binomial probability is basically the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes.
[tex](a+b)^{n}[/tex]=[tex]nC_{0}a^{0} b^{n-0} +nC_{1}a^{1} b^{n-1} +................nC_{n}a^{n} b^{0}[/tex]
We have to find the value when n=9, p is 0.3 and r=3.
=[tex]9C_{3} (0.3)^{3} (1-0.3)^{6}[/tex]
=9!/3!6!*0.027*0.16807
=84*0.00453789
=0.381182
Hence if the probability of obtaining success is 0.3 and the value of n is 9 then the probability at the value of x be 3 is 0.3811.
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Students are measuring various objects around the classroom. A pencil measures 8 ⅜ inches while a pair of scissors measures 5 ½ inches. How much longer is the pencil than the pair of scissors?
Answers
The pencil is longer than the pair of scissors by [tex]2\frac{7}{8}[/tex] inches.
A pencil measures [tex]8\frac{3}{8}[/tex] inches.
A pair of scissors measures [tex]5\frac{1}{2}[/tex] inches.
We need to find the difference between the measures of a pencil and the scissors.
We see that the pencil measure is greater than the pair of scissors.
What is a mix fraction?A fraction is a part of a whole number. It has two parts - numerator and denominator.
Example: If you cut a cake into three slices each slice is 1/3.
Where 1 = numerator and 3 = denominator.
Four types of fractions:
Unit fraction - when the numerator is 1.
Proper fraction - When the numerator is less than the denominator.
Improper fraction - When the numerator is greater than the denominator.
Mixed fraction - When the fraction contains a whole number with a proper fraction.
Example: [tex]3\frac{1}{3}[/tex]
The given measure of the pen and the pair of scissors is in mix fraction.
The pencil measure is longer than the pair of scissors measure so,
We will subtract the measure of the pair of scissors from the measure of the pen.
We have,
= [tex]8\frac{3}{8} - 5\frac{1}{2}[/tex]
We can write the mix fraction into an improper fraction.
We multiply the denominator with the whole number and add this product with the numerator to get our numerator of the improper fraction. The denominator will remain the same as the mix fraction in the improper fraction.
So,
[tex]8\frac{3}{8}=\frac{(8\times8)+3}{8}=\frac{64 + 3}{8} = \frac{67}{8}\\ 5\frac{1}{2} =\frac{(5\times2)+1}{2}= \frac{(10+1)}{2} = \frac{11}{2}[/tex]
= 67/8 - 11/2
= (67-44) / 8
= 23 / 8
Writing in mix fraction.
= [tex]2\frac{7}{8}[/tex]
Thus the pencil is longer than the pair of scissors by [tex]2\frac{7}{8}[/tex] inches.
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What is the greatest possible error if irina measured the length of her window as 3.35 feet? 0.5 0.05 0.005 0.0005
Answers
3.35 feet have a maximum inaccuracy of 0.005 feet.
The correct option is C.
What is error analysis?When students consistently commit mistakes, an approach known as error analysis is frequently employed to determine the root of the problem. Reviewing student work is the first step in the process, after which misunderstood patterns are sought out. Mathematics mistakes can be conceptual, procedural, or factual, and they can happen for a variety of reasons.
Given:The window is 3.35 feet long.
Find the biggest error you can
According to the given data:Half of the measuring unit is considered to be the maximum amount of measurement error.
3.35 feet are calculated to the nearest centimeter, or 0.01 feet
Consequently, the largest conceivable error is equal to half of the measurement unit.
= .01/2
= .005
Therefore, the maximum inaccuracy for 3.35 feet is 0.005 feet.
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From the table, calculate the mean score.
Scores 0—4 5—9 10—14
Frequency 2 1 2
Answers
Answer:
7.
Step-by-step explanation:
Calculate the means for each group:
mean of 0-4 is 2
mean of 5-9 is 7
mean of 10-14 is 12
Mean = (Sum of frequencies * mean) / sum of frequencies
= required mean = [ (2(2) + 1(7) + 2(12)] / (2+1+2)
= 35/ 5
= 7.
What is the equation of the line that passes through the point (-5, -3) and has a
slope of -3?
Answers
Answer: y=-3m+13
Step-by-step explanation:
y=mx+c
m is the gradient
y=-3x+c
We know one point
-2=3(-5)+c
Solve for c
-2=-15+c
13=c
y=-3m+13
Use part 1 of the fundamental theorem of calculus to find the derivative of the function. g(x) = x e5t2 − 4t dt 4 g'(x) =
Answers
The derivative of the given equation is [tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex].
According to the statement
we have given that the statement and we have to find the derivative of that term.
So, We know that the
The given equation is
[tex]g(t) = \int\limits^x_4 {e^{5t^{2} - 4t} } \, dt[/tex]
Now find the derivative of that term
We find the derivative of the given term is with the help of the FTC.
And then
[tex]\frac{dg(x) }{dt} = {e^{5x^{2} - 4x} } \, \frac{dx}{dx}[/tex]
Then the equation become is
[tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex]
So, this is the derivative of the given equation.
So, The derivative of the given equation is [tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex].
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Find an equation for the conic that satisfies the given conditions. parabola, focus (−8, 0), directrix x = 2
Answers
The equation of the given parabola is y2=−20(x+3)
A parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.
In general in a parabola, if we have
(y−n)2=4p(x−m),
then the vertex is (m,n)
The axis of symmetry is y=m
The focus is (p+m,n)
The directrix is x=m−p.
Hence, for the given case
p+m=−8
n=0
m−p=2
⇒n=0
m=−3
p=−5
So, the answer will be y2=−20(x+3)
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I need help with this please and thank you.
Answers
Answer: I believe the answer would be as follows:
8.431 grams
5.46 seconds
980 meters
900 miles
Step-by-step explanation:
it would first be which has the largest number after the decimal point, so if there’s three it goes first (0.12*3*). Then you would pick the one that is the smallest form of measurement, which would be meters in this case.
Hope this helped!
After conducting a survey of all his classmates, ryan discovers that the amount of money everyone spends buying clothes each month has a mean of $46. what does the mean say about the amount his classmates spend on clothes?
Answers
The correct option is B.
If the amount spent on snacks per month by all his classmates is , that amount would be $38.
What is Mean?Mean can be defined as the sum of all the observations in a sample, divided by the total number of observations. Mathematically, it is expressed as:
Mean = sum of observations / total number of observations
According to the given information:Amount of money everyone spends buying snacks each month is equal to a mean of $38.
What this means is that the average amount of money spent by everyone is equal to $38.
Therefore,
If the amount spent on snacks per month by all his classmates is leveled, that amount would be $38.
So,
We can conclude by saying, if one classmate paid above $38, and another paid below $38, it will be nullified by leveling the amount paid by all the classmates while calculating the mean.
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I understand that the question you are looking for is:
After conducting a survey of all his classmates, ryan discovers that the amount of money everyone spends buying clothes each month has a mean of $46. what does the mean say about the amount his classmates spend on clothes?
A. Half of his classmates spend exactly $38 per month buying snacks.
B. If the amount spent on snacks per month by all his classmates is leveled, that amount would be $38.
C. The majority of his classmates spend $38 per month buying snacks.
D. Half of his classmates spend more than $38 per month buying snacks
Jason and Britton are driving to St. George. Jason got a 20 mile head start and drove an
average of 65 mph the entire way. Britton drove an average of 75 mph. After how many
hours and miles will Britton catch up to Jason?
Answers
Answer:
2 hours, 150 miles
Step-by-step explanation:
The relation between time, speed, and distance can be used to solve this problem. It can work well to consider just the distance between the drivers, and the speed at which that is changing.
Separation distanceJason got a head start of 20 miles, so that is the initial separation between the two drivers.
Closure speedJason is driving 10 mph faster than Britton, so is closing the initial separation gap at that rate.
Closure timeThe relevant relation is ...
time = distance/speed
Then the time it takes to reduce the separation distance to zero is ...
closure time = separation distance / closure speed = 20 mi / (10 mi/h)
closure time = 2 h
Britton will catch up to Jason after 2 hours. In that time, Britton will have driven (2 h)(75 mi/h) = 150 miles.
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Additional comment
The attached graph shows the distance driven as a function of time from when Britton started. The distances will be equal after 2 hours, meaning the drivers are in the same place, 150 miles from their starting spot.
HELP ASAP PLS
Question 2 of 5
Select all the correct answers.
Which expressions are prime polynomials?
Answers
Answer: the first one and the third one
Step-by-step explanation:
The prime polynomials from the polynomials are:
1. [tex]x^4[/tex] + 3y²x - 1 and 3. x² - 9x + 3.
Options 1 and 3 are the correct answer.
We have,
A prime polynomial is a polynomial that cannot be factored into a product of two polynomials with integer coefficients.
Let's check each expression to see if it is a prime polynomial:
[tex]x^4[/tex] + 3y²x - 1:
This expression cannot be factored further, so it is a prime polynomial.
9y + 4y² + 12y³:
This expression can be factored as y(9 + 4y + 12y²), so it is not a prime polynomial.
x² - 9x + 3:
This expression cannot be factored further, so it is a prime polynomial.
x² - 3x - 10:
This expression can be factored as (x - 5)(x + 2), so it is not a prime polynomial.
x³ - 512y³:
This expression can be factored as (x - 8y)(x² + 8xy + 64y²), so it is not a prime polynomial.
Thus,
The prime polynomials are:
1. [tex]x^4[/tex] + 3y²x - 1 and 3. x² - 9x + 3.
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