Considering the product and the sum of the roots of the quadratic function, the numeric value of the expressions are given as follows:
1. [tex]\beta x^2 + \alpha x^2 - \alpha\beta = \frac{1}{4}(x^2 - 1)[/tex]
2. [tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = -\frac{7}{4}[/tex]
What are the product and the sum of the roots of the quadratic function?A quadratic function is defined according to the following rule:
y = ax² + bx + c.
In which a and b are the coefficients of the equation.
Supposing that the equation has roots [tex]\alpha[/tex] and [tex]\beta[/tex], the product and the sum of the roots of the quadratic function are given as follows:
[tex]\alpha\beta = \frac{c}{a}[/tex][tex]\alpha + \beta = -\frac{b}{a}[/tex]In this problem, the equation is:
4x² - x + 1.
Hence the coefficients are:
a = 4, b = -1, c = 1.
Then the product and the sum of the roots of the quadratic function are given as follows:
[tex]\alpha\beta = \frac{1}{4}[/tex][tex]\alpha + \beta = \frac{1}{4}[/tex]Then the numeric values for the expressions can be found as follows:
[tex]\beta x^2 + \alpha x^2 - \alpha\beta = x^2(\alpha + \beta) - \alpha\beta = \frac{1}{4}x^2 - \frac{1}{4} = \frac{1}{4}(x^2 - 1)[/tex]
For the second expression:
[tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = \frac{\alpha^2 + \beta^2}{\alpha\beta} = 4(\alpha^2 + \beta^2)[/tex]
The sum of the squares of the roots is:
[tex]\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta[/tex]
Hence:
[tex]\alpha^2 + \beta^2 = \frac{1}{16} - \frac{1}{2} = -\frac{7}{16}[/tex]
Then:
[tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = -\frac{28}{16} = -\frac{7}{4}[/tex]
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Omar owns a sandwich shop, and his best selling sandwich is the BLT. When making BLT sandwiches, it takes
3
4
of a pound of bacon to make 4 sandwiches. He uses
1
1
20
pounds of bacon for every 2 tomatoes used and 5 tomatoes for every full head of lettuce used.
If Omar is making enough BLT sandwiches to use 2 full heads of lettuce, then he is going to use pounds of bacon and will make a total of BLT sandwiches.
Reset Next
by using multiplication, we get that 28 BLT sandwiches can be made by Omar.
We are given that:
For every full head of lettuce used,
Number of tomatoes used = 5
Now, we will use multiplication.
2 full heads of lettuce used = 5 × 2 = 10 tomatoes used
Now, we also have:
2 tomatoes used = 1 1/20 pounds of bacon used.
= 21/20 pounds of bacon used.
1 tomato = (21 / 20) × (1 / 2) = 21 / 40 pounds bacon
10 tomatoes = (21 / 40) × 10 = 21 / 4 pounds bacon
Also,
3 / 4 pounds of bacon = 4 sandwiches
1 pound of bacon = 16 / 3 sandwiches.
21 / 4 pounds of bacon = (16 / 3) × (21 / 4) = 28 sandwiches
Therefore, by using multiplication, we get that 28 BLT sandwiches can be made by Omar.
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An egg of a particular bird is very nearly spherical. The radius to the inside of the shell is 4 millimeters and the radius to the outside of the shell is 4.3 millimeters. Use differentials to approximate the volume of the shell. [Remember that V(r) =
#x p3, where r is the radius.]
If the radius to the inside of the shell is 4 millimeters and the radius to the outside of the shell is 4.3 millimeters. the volume of the shell is 19π mm³.
Volume of the shellv = 4 / 3πr³
dv =4 / 3π (3r²) dr
Where:
r= radius = 4 cm
dr = 4.3 -4 = 0.3
Hence,
dv = 4 / 3π (16) 3/10
dv =4 / 3π(16) 0.3
dv = 19.2π mm³
dv = 19π mm³ (Approximately)
Therefore the volume of the shell is 19π mm³.
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y( x+a ) m solve for the variable x.
Answer:
x=y/m-a
Step-by-step explanation:
y=(x+a)m
Divide m on both sides
y/m=x+a
Subtract a on both sides
y/m-a=x
Which classifications of the real number system describe all numbers in the set? (Choose all correct answers.)
{0.4, 10,-√196,1/3)
Answer:
Rational
Step-by-step explanation:
Is the picture below a graph for the following inequality? Why or why not?
y<6x+1
Given picture is not a graph of inequality y < 6x + 1
In this question, we have been given a graph.
We need to determine whether the picture is a graph for the inequality y < 6x + 1 or not.
We know that the graph of equation y = 6x + 1 is a straight line and we represent a straight line graph by a solid line.
This graph represents a shaded region below dotted line. This means, this is the graph of inequality.
From this graph we can see that x-intercept of the equation is (2, 0) and y-intercept is (0, - 4)
If we find the x and y-intercept of y = 6x + 1 then it would be,
x - intercept = (-1/6 , 0)
y - intercept = (0, 1)
This means, given picture is not a graph of inequality y < 6x + 1
Therefore, given picture is not a graph of inequality y < 6x + 1
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Solve for x.
E
G
×
11
C
7
J
D
(3x - 11)°
(2x+16)
H
Answer:
35
Step-by-step explanation:
The consecutive interior angles are supplementary, so:
[tex]3x-11+2x+16=180 \\ \\ 5x+5=180 \\ \\ x+1=36 \\ \\ x=35[/tex]
Mai biked 6\frac{3}{4} miles today, and Noah biked 4\frac{1}{2} miles.
How many times the length of Noah’s bike ride was Mai’s bike ride?
Mai's bike ride was 1.5 times the length of Noah's bike ride
Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
Distance travelled by Mai in miles = 6 3/4 miles
Distance of Mai in improper fraction = 27/4
Distance travelled by Noah in miles = 4 1/2
Distance of Noah in improper fraction = 9/2
Length of Noah's bike ride as compared to Mai's bike ride = (27/4)/(9/2)
= 27/4*2/9
= 3/2 or 1.5 times
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What is the right answer
No solution is the answer of inequality.
What is inequality
The relationship between two values in an imbalanced algebraic statement is represented by an inequality in mathematics. One of the two variables can be larger than, more than or equal to, smaller than, or equal to another value by using a sign of inequality. Make use of the following steps to solve an inequality: Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator. Step 2 Combine like terms on both sides of the inequality to simplify. Step 3 Obtain the unknown on one side and the integers on the other by adding or subtracting quantities.
Given Data
[tex]\frac{4}{3}[/tex]g - 3< g + [tex]\frac{2}{3}[/tex] - [tex]\frac{1}{3}[/tex]g
([tex]\frac{4}{3}[/tex]g - g) + [tex]\frac{1}{3}[/tex]g <( [tex]\frac{2}{3}[/tex] + 3)
Taking LCM,
[tex]\frac{4e+3e+1e}{3}[/tex] < [tex]\frac{2+9}{3}[/tex]
8g < 11
g < [tex]\frac{11}{8}[/tex]
No solution is the answer of inequality.
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Fae is following a recipe to make dough. The amount of water (in ounces) she uses depends on the amount of flour she uses (in cups). The amounts for each ingredient are shown in the graph.
The unit rate of ounces of water per cup of flour for this situation is; 3 ounces per cups
What is the unit rate of the graph?
From the given graph, we are expected to find the unit rate of ounces of water per cup of flour for the situation.
Now, to find the unit rate , all we need to do is to pick two coordinates on the line graph and find the slope. Thus;
Slope = (y2 - y1)/(x2 - x1)
Slope of graph = (12 - 9)/(4 - 3)
Slope = 3/1
Slope = 3
Let us pick another two points to verify;
Slope = (6 - 3)/(2 - 1)
Slope = 3/1
Slope = 3
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What is 21.00$ with a 7%
tax
Answer:
22.47
Step-by-step explanation:
7/100 = 0.07 (the tax rate) 21 * 0.07 = 22.47, the tax adds on 1.47
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
a
Solve.
4x +6 <−6
b
Solve.
−2/5 x −9 < 9/10
bbbbbbbbbbbbbbb bbbbbbbbbbbbbb
Can someone help. fill fill
Answer:
x = 13
calculations in the pic hope it helps
Answer is 13
Step by step
1.4 + x / 6 = 2.4
We want to get rid of the 6 first
It is a divide so we want to do the inverse, which is multiply both sides by 6
1.4 + x * 6/ *6 = 2.4 * 6
Combine (the 6/6 becomes 1)
1.4 + x = 14.4
Now we want to isolate the x
Subtract 1.4 from both sides to solve for x
1.4 - 1.4 + x = 14.4 - 1.4
Combine
x = 13
I need help with this question
he Solution:
iven:
The y-intercept of function 1 is:
[tex]y-\text{intercept}=5\text{ }[/tex]The y-intercept of function 2 is:
[tex]y=1[/tex](a) So, the farthest y-intercept from 0 is function 1.
he slope of function 1 is
[tex]\text{Slope}=\frac{2-5}{1-0}=-\frac{3}{1}=-3[/tex]The slope of function 2 is
[tex]\text{slope=}\frac{3-1}{1-0}=\frac{2}{1}=2[/tex]he solope of function 3 is -1
The slope of function 4 is 5
(b) hus, the steepest graph is the function with the highest slope.
So, the steepest graph is the graph of function 4 since it has the greatest slope.
(c)
Functions with y-intercept greater than -3 are:
unction 1, function 2, amnd function 4.
[tex]\text{ function 3 has y-intercept=-4}<-3[/tex]Sergio has two similar cylindrical pots, Pot A and Pot B. The radius of Pot A is 15 inches, and the radius of Pot B is 3 inches. What is the ratio of the volume of Pot A to the volume of Pot B?
15:3
45:9
125:1
5:1
Answer:
125 : 1
Step-by-step explanation:
given 2 similar objects with ratio of sides a : b , then
ratio of volumes = a³ : b³
here
ratio of pot A : pot B = 15 : 3 = 5 : 1
ratio of volumes = 5³ : 1³ = 125 : 1
The two lines at right represent the growing profits of Companies A and B. Homework Help ✎ Sketch this graph on your paper. If Company A started out with more profit than Company B, determine which line represents A and which represents B. Label the lines appropriately. In how many years will both companies have the same profit? Approximately what will that profit be? Which company’s profits are growing more quickly? How can you tell?
Using concepts of linear functions, it is found that:
They will have the same profit after 3 years.This profit will be of $65,000.Due to the higher slope, Company B profit is growing more quickly.What do the slope and the intercept of a linear function represent?The slope-intercept representation of a linear function is:
y = mx + b.
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).Two linear functions have the same value when they intersect each other, hence, from the graph given at the end of the answer, they intersect around point (3,65), meaning that they will have the same profit after 3 years, and this profit will be of $65,000.
From the Graph, as it assumes higher values as n goes to infinity, company B has the higher slope, hence it's profit is growing more quickly.
What is the missing information?The graph is missing, and is given by the image at the end of the answer.
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I need help with qeustion 36 please
Answer:
8 + 2(x + 3) = 2x + 14
Would be infinitely many solutions.
Step-by-step explanation:
8 + 2x + 6 = 2x + 14
2x + 14 = 2x + 14
0 = 0; True
All real numbers
11) Convert 3 miles to feet
Answer: 15840[tex]covert 3 miles to feet[/tex]
Step-by-step explanation:
3 miles equals 15840 feet
Answer: 15840
Step-by-step explanation:
3 miles have 15840 feet
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Trigonometry please help!
Answer:
the first one
Step-by-step explanation:
a researcher is interested in the sleeping habits of students at the local state college. the average number of hours spent sleeping each night for the entire set of students enrolled at the college is an example of a .
One example of a parameter is the typical number of hours each night that the entire group of college-enrolled students sleeps.
What do we mean by a parameter?In mathematics, a parameter is a variable whose range of possible values identifies a number of unique cases in a problem. A parametric equation is any equation that is expressed in terms of parameters. To describe the entire population under study, a parameter is used. For instance, we are interested in learning the typical length of a butterfly. This information about the entire butterfly population makes it a parameter. The local state college's students' sleeping patterns are of interest to a researcher. One example of a parameter is the typical number of hours each night that the entire group of college-enrolled students sleeps.Therefore, one example of a parameter is the typical number of hours each night that the entire group of college-enrolled students sleeps.
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The correct question is given below:
A researcher is interested in the sleeping habits of students at the local state college. The average number of hours spent sleeping each night for the entire set of students enrolled at the college is an example of a ____.
The longest worm is ? times as long as the shortest worm.
pleaseeee helpp nowwwwwwwww :/
.
.
.
Find the value of m: −3(m − 4) = −6
m = −6
m = −2
m = 2
m = 6
The solution of the equation is m = 6.
How to find the variable of an equation?The variable to find is variable m.
The equation is as follows:
−3(m − 4) = − 6
Hence, let's open the bracket on the left side of the equation
−3(m − 4) = − 6
- 3m + 12 = -6
subtract 12 from both sides of the equation
- 3m + 12 = -6
- 3m + 12 - 12 = -6 - 12
- 3m = - 18
divide both sides of the equation by -3
- 3m / - 3 = - 18 / -3
Therefore,
m = 6
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Answer:
m = 6Step-by-step explanation:
Find the value of m: −3(m − 4) = −6
m = −6
m = −2
m = 2
m = 6
-3(m - 4) = -6
-3m + 12 = -6
-3m = -6 - 12
- 3m = -18
m = -18 : (-3)
m = 6
-----------------------------
check-3(6 - 4) = -6
-18 + 12 = -6
-6 = -6
the answer is gooda new test has been developed to determine whether a given student is overstressed. this test is 95% accurate if the student is not overstressed, but only 85% accurate if the student is in fact overstressed. it is known that 99.5% of all students are overstressed. given that a particular student tests negative for stress, what is the probability that the test results are correct, and that this student is not overstressed?
The probability that the test results are correct, and that this student is not overstressed is mathematically given as
3.08%
This is further explained below.
What is probability?Generally,
Let A: student is overstressed
B: The test is positive. Given
[tex]P(\bar{B} / \bar{A})=0.95, P(B / A)\\P(\bar{B} / \bar{A}) =0.85, P(A)\\P(\bar{B} / \bar{A})=0.995, \\[/tex]
[tex]P\left(\frac{\text { correctresult }}{\text { Test negative }})=P(\bar{A} / \bar{B}) \\\\ =\frac{P(\bar{A} \cap \bar{B})}{P(\bar{B})} \\\\ =\frac{P(\bar{A} \cap \bar{B})}{P(\bar{A} \cap \bar{B})+P(A \cap \bar{B})}\right.[/tex]
[tex]=\frac{P(\bar{B} / \bar{A}) P(\bar{A})}{P(\bar{B} / \bar{A}) P(\bar{A})+P(\bar{B} / \bar{A}) P(A)} \\\\=\frac{0.95 \times 0.005}{0.95 \times 0.005+0.15 \times 0.995} \\[/tex]
=0.0308
=3.08%
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Describe the slope of the line. (0, 3) (5,-1) m= The slope is negative Find the slope.
Answer:
Step-by-step explanation:
Slope formula: m=[tex]\frac{rise}{run}[/tex] so m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]y_1[/tex]=3
[tex]y_2[/tex]=-1
[tex]x_1[/tex]=0
[tex]x_2[/tex]=5
So the formula is, [tex]\frac{(-1)-3}{5-0}[/tex] = [tex]\frac{-4}{5}[/tex]
Slope is negative.
Slope is -4/5
A scuba diver dove from the surface of the ocean to an elevation of −69 9/10
feet at a rate of −21.5 feet per minute. After spending 12.5 minutes at that elevation, the diver ascended to an elevation of −38 9/10
feet. The total time for the dive so far was 19 1/8
minutes. What was the rate of change in the diver's elevation during the ascent? Round your answer to the nearest hundredth.
The rate of change of the divers elevation = 19.274
Given,
The depth to which the Scuba dove = -69 [tex]\frac{9}{10}[/tex] feet
The rate at which he dove = -21.5 feet per min.
The time which he spent at the elevation = 12.5min.
The elevation the diver then ascended to -38 [tex]\frac{9}{10}[/tex] feet
Thee total time for the dove = 19 [tex]\frac{1}{8}[/tex] minutes.
Therefore, the time [tex]t_{d}[/tex] with which the scuba diver descended to -69 [tex]\frac{9}{10}[/tex] feet
is given as follows:
[tex]t_{d} = \frac{Distance}{speed}[/tex] = [tex]= \frac{-69\frac{9}{10} }{-21.5}= \frac{-681}{-21.5}[/tex] = 3.167 minutes
The time [tex]t_{e}[/tex], it took the scuba diver to elevate to -38 [tex]\frac{9}{10}[/tex] feet is given as follows:
[tex]t_{e}[/tex] = 19 [tex]\frac{1}{8}[/tex]minutes - (3.167 + 10.5) minutes = 5.458 minutes
The rate of change of the divers elevation = (Final elevation - Initial elevation)/(Time taken).
∴ The rate of change of the divers elevation
= (-38 [tex]\frac{9}{10}[/tex] - (-69 [tex]\frac{9}{10}[/tex] )) / 5.458 min
=(37.1 - (-68.1))/ 5.458 min
= 19.274 feet/minutes to the nearest hundredth.
Hence, The rate of change of the divers elevation = 19.274
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what property is 3x+2x+1-7=x+22
Solve for X.
x² =50
x³ = 37
Answer:
x^2= 50 ------ (equation 1)
x^3= 37 ------- (equation 2)
dividing (equation 2) by (equation 1)
=> x^3/x^2 = 37/50
=> x = 37/50
Answer: x= 37/50
In a boxplot, if the median is to the left of the center of the box and the right whisker is substantially longer than the left whisker, the distribution is skewed.
The distribution is skewed to the right if the median is to the left of the center of the box and the right whisker is substantially longer the the left whisker
In a boxplot of distribution, the following are the scenarios:
When the median is at the middle of the box, and the whisker are about the same on both ends of the box, the distribution is symmetric.When the median is to the right of the box, the right whisker will be substantially longer than the left whisker and the distribution is skewed to the rightWhen the median is to the left of the box, the left whisker will be substantially longer than the right one, and the distribution will be negatively skewed or skewed to the leftLearn more about Boxplot distribution here:
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Could anybody help me? Math!!!!
The products of the fractions given are:
1. (-3/4)(7/8) → -21/32
2. (2/3)(-4)(9) → -24
3. (5/16)(-2)(-4)(-4/5) → -2
4. (2 3/5)(7/9) → 91/45
How to Multiply Fractions?To multiply two or more fractions, multiply the denominators of both fractions together, and their numerators together.
1. (-3/4)(7/8)
Multiply the denominators of the fractions together, and also multiply their numerators:
= (-3 × 7) / (4 × 8)
= (-21) / (32)
(-3/4)(7/8) → -21/32
2. (2/3)(-4)(9)
Multiply the denominators of the fractions together, and also multiply their numerators:
= (2 × -4 × 9) / (3)
= -72/3 = -24
(2/3)(-4)(9) → -24
3. (5/16)(-2)(-4)(-4/5)
= (5 × -2 × -4 × -4) / (16 × 5)
= -160/80 = -2
(5/16)(-2)(-4)(-4/5) → -2
4. (2 3/5)(7/9)
= (13/5)(7/9)
= (13 × 7)/(5 × 9) = 91/45
(2 3/5)(7/9) → 91/45
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Write an equation that represents the pattern in the table
A mathematical expression known as an algebraic expression includes variables, constants, and algebraic operations (addition, subtraction, etc.). Expressions include terms. Here, y=3x.
What is algebraic expression?The idea behind algebraic expressions is to represent numbers using letters or alphabets rather than giving their exact values. In algebraic basics, we learned how to express an unknown number using letters like x, y, and z. We will refer to these letters as variables from now on. An algebraic expression may have both constants and variables. Any amount that is added to a variable before it is multiplied by another is known as a coefficient.
A mathematical expression known as an algebraic expression includes variables, constants, and algebraic operations (addition, subtraction, etc.). Expressions include terms.
There are 3 main types of the algebraic expressions which include:
Monomial ExpressionBinomial ExpressionPolynomial ExpressionFor the above question:
4x3=12 , 5x3=15 , 6x3=18 ,.....
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The complete question:
"Write an equation that represents the pattern in the table
x 4,5,6,7,8
y 12,15,18,21,24 y = __ x"
Reflect point M across the axis
Answer:
coordinates (-4,6)
Answer:
C the answer is v
Step-by-step explanation:
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