If α and β are the roots of the equation ax2+bx+c=0,αβ=4ax2+bx+c=0,αβ=4 and a,b,,c are in A. P then α+β=
Considering the sum and the product of the roots of the quadratic equation, it is found that the numeric value of the expression is given as follows:
[tex]\alpha + \beta = -2.5[/tex]
What are the sum and the product of the roots of a quadratic equation?A quadratic equation is defined as follows:
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
The roots of the equation are given as follows:
[tex]\alpha, \beta[/tex]
The sum of the roots is given as follows:
[tex]\alpha + \beta = -\frac{b}{a}[/tex]
The product of the roots is given as follows:
[tex]\alpha\beta = \frac{c}{a}[/tex]
In the context of this problem, the product is of 4, as [tex]\alpha\beta = 4[/tex] hence:
c/a = 4
c = 4a.
The coefficients are in an arithmetic progression, hence:
b = a + d. (d is the common difference of the sequence).c = a + 2d.We have that c = 4a, hence:
4a = a + 2d
2d = 3a
d = 1.5a.
Hence coefficient b is calculated as follows:
b = a + d = a + 1.5a = 2.5a.
Then the sum of the roots is given as follows:
[tex]\alpha + \beta = -\frac{b}{a} = -\frac{2.5a}{a} = -2.5[/tex]
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write an equation in slope-intercept form for the line with slope 4/3 and y-intercept -5
Remember the slope-intercept of a line is
[tex]y=mx+b[/tex]where:
• m ,is the slope of the line
,• b, is the y-intercept of the line
Now, let's substitute the data we're given. Thereby, the equation would be
[tex]y=\frac{4}{3}x-5[/tex]The baseball diamond at a playground is a square with sides that measure 80 feet. About how long would a straight line be from home plate to second base? Round your answer to the nearest tenth.
160 feet
113.1 feet
80 feet
12,800 feet
If the baseball diamond at a playground is a square with sides that measure 80 feet. About how long would a straight line be from home plate to second base is: B.113.1 feet.
Determining the distanceGiven data
Sides measure in feet = 80 feet.
Since the diagonal tend to forms the hypotenuse of a right triangle with both sides of 80 feet
Hence,
Using the Pythagoreans theorem to determine the distance
(80)² + (80)² = x²
6400 + 6400 = x²
x² = 12,800
x = √ 12,800
x = 113.1 feet
Therefore the correct option is B.
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Please help this is urgent your effort is appreciated
Answer:
3
Step-by-step explanation:
The area of Eh Kri's rectangular backyard, in square feet, can be found using the expression 2(4x + 5y). Use the distributive property to write an equivalent expression for the area of Eh Kri's backyard.
The area of a rectangular backyard = 2(4x - 5y)
The algebraic expression has a equivalent expression as = 2 x 4x + 2 x 5y
= 8x + 10y
Stanley runs, swims, and bikes every day. During these workouts, he runs at 9 mph, bikes at 16 mph, and swims at 2.5 mph. Yesterday, he ran for half an hour longer than he swam, and his biking time was twice his running time. How long did Stanley run, swim, and bike yesterday if the total distance he covered was 64 miles?
(a
If Stanley swam for t hours yesterday, what was his running time?
Answer:He biked for 3 hours (48 miles)
He ran for 1.5 hours (13.5 miles)
He swam for 1 hour (2.5 miles)
He covered 62 miles in 5.5 hours of activity
Step-by-step explanation:
Answer:
1.5h
Step-by-step explanation:
what is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean? reducing the process standard deviation causes a - select your answer - in the number of defects.
A low standard deviation implies that the data exists grouped around the mean, whereas a large standard deviation indicates that the data exists more dispersed.
What is meant by standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data exists grouped around the mean, whereas a large standard deviation indicates that the data exists more dispersed.
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
Because it aids in comprehending measurements when the data is scattered, standard deviation is significant. The standard deviation of the data will be higher the more evenly dispersed the data is.
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1.Tanisha solved the equation below by graphing a system of equations.log: (5x) = log5 (2x + 8)What are the two equations in the system of equations that could be used to approximate her solution?(Do your best to type out the two equations for the system.)Yi =Y2 =2. What is the approximate solution (x -value) for her system of equations? And where on the graph can tanisha find her solution to the system?
Part 1.
Since we have the equation
[tex]\log _3(5x)=\log _5(2x+8)[/tex]the equations which can be used to approximate the solutions are:
[tex]\begin{gathered} y_1=\log _3(5x) \\ y_2=\log _5(2x+8) \end{gathered}[/tex]Part 2.
Let's make the graph of the 2 equations. The graph is
The approximate solution is given by the intersection point of the 2 graphs, which is the point ( 0.957 , 1.425). Then x-value corresponding to the solution is x= 0.957.
Help me with this please
Answer: say can't help
Step-by-step explanation:
Jaclyn has $120 saved and earns $40 each month in allowance. Pedro has $180 saved and earns $20 a month in allowance.
If they both save their entire allowances, how long will it take before Jaclyn and Pedro have saved the same amount of money?
Enter your answer in the box
Answer:
3 months
Step-by-step explanation:
120 + 40m = 180 + 20m
Collect like terms
40m - 20m = 180 - 120
20m = 60
Divide
m = 60/20
m = 3
It will take them 3 months before Jaclyn and Pedro have saved the same amount of money.
find the missing fraction 1/2+ blank=7/8
To solve this problem we change the structure from
1/2 + ? = 7/8
to
7/8 - 1/2 = ?
Now we need to subtract the fractions and find the difference. To do this, make the denominators (the bottom numbers on the fractions) the same.
1/2 = 4/8
then subtracts the numerator
7/8 - 4/8 = 3/8
there is your answer... 3/8
Please help me out with this!
Answer:
10
Step-by-step explanation:
I am not absolutely sure but i think that is correct
CAN Someone pleasde help me !!!!!
Answer: It will take 3.5-4 months
Step-by-step explanation:
Which graph shows the line y-4-2(x+1)?
The size of a monitor is determined by the length of its diagonal. You want to buy a 19 inch monitor with a height of 11inches. What is the width of this monitor? Express your answer to the nearest tenth.XSubmINTL1217K
In this problem the diagonal of the Tv is 19 and the hight is 11 so we can use the pythagorical theorem to find the width (w) so:
[tex]19^2=11^2+w^2[/tex]and we solve for w so
[tex]\begin{gathered} w^2=19^2-11^2 \\ w=\sqrt[]{361-121} \\ w=\sqrt[]{240} \\ w=15.5 \end{gathered}[/tex]a rope passing through a capstan on a dock is attached to a boat offshore. the rope is pulled in at a constant rate of 6 ft/s and the capstan is 5 ft vertically above the water. how fast is the boat traveling when it is 12 ft from the dock?
Answer:The boat is traveling at a rate of 3 ft/s.
Step-by-step explanation:
Ben walked for 8 1/2 minutes and
covered
3/4 of a mile.
The unit rate of Ben is 8.5 minutes.
What is Unit Rate?An item's unit rate is its price for one of them. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.A ratio that compares two amounts of DIFFERENT types of UNITS is called a rate. When a rate is expressed as a fraction, the denominator is 1 unit. Divide the numerator and denominator of the rate by the denominator to represent a rate as a unit rate.Unit rates may seem difficult to understand, but it explains a specific unit of measurement based on a rate of time (usually).
For this problem, we are looking for how many miles Ben walked per minute — so the goal is miles per minute
We know Ben walked a total of 3/4 of a mile (or .75 miles) and it took him 8 1/2 minutes to do it (or 8.5 minutes)Since we want miles per minute we need to divide the miles by the minutes.So, calculate:
.75 miles. = 0.088 miles per minute8.5 minutesTherefore, the unit rate for Ben is 8.5 minutes.
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Complete question:
Ben walked 3/4 of a mile in 8 1/2 minutes. Find the Unit Rate.
4.74 do you own a tablet? a study20 conducted in june 2015 examines ownership of tablet computers by us adults. a random sample of 959 people were surveyed, and we are told that 197 of the 455 men own a tablet and 235 of the 504 women own a tablet. we want to test whether the survey results provide evidence of a difference in the proportion owning a tablet between men and women. state the null and alternative hypotheses, and define the parameters. give the notation and value of the sample statistic. in the sample, which group has higher tablet ownership: men or women? use statkey or other technology to find the p-value.
Null hypothesis, [tex]H_{0}[/tex] P.1 = P2 (The proportion of tablets owned by men and women are equal.)
Alternative hypothesis,[tex]H_{0}[/tex] P1[tex]\neq[/tex]P2 (The proportion of tablets owned by men and women are not equal.)
Sample proportion for men who own tablets ≈0.433
Sample proportion for women who own tablets ≈0.466
p value of the test is 0.3320.
Test whether the survey results provide evidence of a difference in the proportion owning a tablet between men and women.
Let p, be the proportion of all men who own tablets and p, be the proportion of all women who own tablets.
Null hypothesis, [tex]H_{0}[/tex] P.1 = P2 (The proportion of tablets owned by men and women are equal.)
Alternative hypothesis,[tex]H_{0}[/tex] P1[tex]\neq[/tex]P2 (The proportion of tablets owned by men and women are not equal.)
The notations for the sample statistic are p p1 p2
Pooled proportion p = [tex]\frac{x_{1}+x_{2} }{n_{1}+n_{2} }[/tex]= 197+235/455+504
≈ 0.45
Sample proportion for men who own tablets,
p1 = [tex]\frac{x_{1} }{n_{1} }[/tex]= 197/455
≈0.433
Sample proportion for women who own tablets,
p2 = [tex]\frac{x_{2} }{n_{2} }[/tex] = 235/506
≈0.466
Since p1<p2 women group has higher tablet ownership.
Sample statistic, p1-p2
= 0.433-0.466
p value of the test is 0.3320.
What is Null hypothesis?In mathematics, statistics deals with the study of surveys and reports of numerical data. For questions, we need to define a hypothesis. In general, there are two types of hypotheses. One is the null hypothesis and the other is the alternative hypothesis.
In probability and statistics, the null hypothesis is the general statement or default state that zero or nothing will happen. For example, there is no association between groups or no association between two measured events. Here, a hypothesis is generally assumed to be true until other evidence is presented to disprove the hypothesis.
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What is the average rate of change of the function x increases from -3 to 5
The average rate of change when x increases from -3 to 5 is given as follows:
r = (f(5) - f(-3))/8.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the average rate of change is given by the fraction presented as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
In the context of this problem, the input x increases by -3 to 5, hence the change in the input is given as follows:
b - a = 5 - (-3) = 5 + 3 = 8.
The change in the output is given as follows:
f(b) - f(a).
(the problem is incomplete hence the answer is given in general terms).
Then the average rate of change of the function when x increases from -3 to 5 is given as follows:
r = (f(5) - f(-3))/8.
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4. Write the sentence as an inequality. Graph the inequality. A number d is more than 0
and less than 10.
The required inequality is 0 < d < 10 and the graph given below.
What is inequality?
Inequality, When two integers or algebraic expressions are stated to be greater than, greater than or equal to, less than, or less than or equal to each other in order.
Given two conditions,
The variable d is greater than 0 and the second condition is
The variable d is less than 10.
From the first condition we get 0 < d ..................(1)
From the second condition we get d < 10 ...........(2)
Combining both the inequalities (1) and (2), we get
0 < d < 10
Therefore, the required inequality is 0 < d < 10.
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Cole is investing the relationship between the number of hours he tutors and the amount he is paid in dollars.He made the graph shown to model the relationshipChoose the incorrect statement based on the data shown in Cole’s graph.A) If Cole tutors 5 hours,he will be paid $40B) If Cole tutors 3 hours he will be paid $24C) If Cole tutors 7 hours he will be paid $64D) If Cole tutors 4 hours he will be paid $32
Verify each statement
A) If Cole tutors 5 hours,he will be paid $40------>
B) If Cole tutors 3 hours he will be paid $24
C) If Cole tutors 7 hours he will be paid $64
D) If Cole tutors 4 hours he will be paid $32
Please help, i really need help
Answer: m<1 = 146 degrees, m<3 =146 degrees, m<4 = 34 degrees
Step-by-step explanation:
Since m<2 and m<4 are vertical angles, they will be equal to each other.
By using straight lines, we can easily find out that m<1 = 180-34 = 146
Since m<1 and m<3 are vertical angles, they are equal to each other.
Hope this helped :))
NEEED HELP PLSSSS . Find x in triangles Geometry.
Answer:
10) x = 76,12) x = 8, Perimeter = 77 units=========================
Question 10The triangle is isosceles as marked.
The two opposite angles of equal sides are equal, one of them is x and the angle in between them is 28°.
Use angle sum of the triangle:
2x + 28 = 1802x = 152x = 76Question 12Same as previous question, we have an isosceles triangle. Equal sides are:
3x + 5 = 5x - 115x - 3x = 5 + 112x = 16x = 8Find the perimeter by substituting the value of x:
P = 3*8 + 5 + 5*8 - 11 + 2*8 + 3 = 77 unitsFind the measure of
Answer: ∠BDG = 50°
Step-by-step explanation:
We know that a straight line is equal to 180°, meaning that line CDF is 180°.
Next, we know that angle CDB, angle BDG, and angle GDF should all add up to be 180°, since we know CDF is equal to 180°.
Lastly, with all this information in mind, we will set up an equation and solve.
130° + BDG = 180°
∠BDG = 50°
When Elizabeth left her phone in her house this morning
Solve this system of linear equations. Separate
the x- and y-values with a comma.
8x + 8y = -56
4x + 10y = -46
The value of x is -4 and the value of y is -3.
What is linear equations?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
The linear equation's graph is a straight line.
The given system of linear equations is,
8x + 8y = -56 ...(1)
4x + 10y = -46 ...(2)
Divide equation (1) by 2, we get
4x + 4y = -28 ...(3)
Multiply equation (3) by -1
-4x - 4y = 28 ...(4)
Adding equations (2) and (4),
4x + 10y = -46
+ -4x - 4y = 28
____________________
6y = -18
y = -3
Substitute y = -3 in equation (1) and simplify, we get
x = -4.
Therefore, the value of x is -4 and the value of y is -3.
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Door prizes for entrants in a young inventors competition are $100, $50, $25 and $10. In how many ways can the door prizes be awarded if there are 23 entrants?.
The total number of ways the prizes are awarded is 8855.
The prizes for entrants in a young inventors competition are $100, $50, $25, and $10.
Which are of total 4 types of prizes.
If there are 23 entrants in the competition the prizes can be awarded in the following ways by using Combinations.
Total number of ways = ²³C₄
= [tex]\frac{23!}{4! * (23 - 4)!}[/tex]
= 8855
The total number of ways the prizes are awarded is 8855.
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The midpoint of AB is M(0, -7). If the coordinates of A are (-2,-6), what arethe coordinates of B?Answer:Submit AnswerPASSA
Explanation:
The coordinates are given below are
[tex]\begin{gathered} A(-2,-6) \\ M(0,-7) \\ B=(x,y) \end{gathered}[/tex]The image is given below as
To calculate the coordinate of A,we will use the formula below
[tex]M=\frac{(x_1+x_2}{2},\frac{y_1+y_1}{2})[/tex]By substituting the values, we will have
[tex]\begin{gathered} M=\frac{x_1+x_2}{2},\frac{y_{1}+y_{1}}{2} \\ (0,-7)=\frac{-2+x)}{2},(\frac{-6+y}{2}) \\ \frac{-2+x}{2}=0,\frac{6+y}{2}=-7 \\ -2+x=0,6+y=-14 \\ x=2,y=-14+6 \\ x=2,y=-8 \end{gathered}[/tex]Hence,
The coordinate of B will be
[tex]B=(2,-8)[/tex]
The headlights of an automobile are set such that the beam drops 2.00 in. for each 28.0 ft in front of the car. What is the angle between the beam and the
Road?
The most appropriate choice for trigonometry will be given by -
Angle between beam and road is 0.33°
What is Trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions. They are [tex]sin\theta, cos\theta, tan\theta, cos\theta, sec\theta, cosec\theta[/tex]
[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\\\cos\theta = \frac{base}{hypotenuse}\\\\tan\theta = \frac{perpendicular}{base}\\\\cot\theta = \frac{base}{perpendicular}\\\\sec\theta = \frac{hypotenuse}{base}\\\\cosec\theta = \frac{hypotenuse}{perpendicular}\\[/tex]
Trigonometry is a very important tool in mathematics.
Here,
The headlights of an automobile are set such that the beam drops 2.00 in. for each 28.0 ft in front of the car.
According to the figure attached here, 2.0 inch forms the height of the triangle and 28.0 ft forms the base of the triangle
Let the angle be [tex]\theta[/tex]. Now trigonometry is applied here
[tex]tan\theta = \frac{\frac{2}{12}}{28}\\tan\theta = \frac{1}{6 \times 28}\\tan\theta = \frac{1}{168}\\\theta = tan^{-1}\frac{1}{168}\\\theta = 0.33^{\circ}[/tex]
Angle between beam and road is 0.33°
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Simplify: 15.4 + 3.02
Answer:
18.42
Explanation:
15+3=18
0.4+0.02=0.42
18+0.42=18.42