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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What is the length of AC?
Answer:
126 units!
Step-by-step explanation:
I hope this helped!! c:
The sum of an integer and 2 times the next consecutive even integer is -2. Find the value of the lesser integer.
The value of the lesser integer is -2.
According to the question,
We have the following information:
The sum of an integer and 2 times the next consecutive even integer is -2.
Let's take the lesser integer to be x.
Now, the next consecutive integer will be (x+2).
So, we have the following expression:
x + 2(x+2) = -2
x+2x+4 = -2
3x+4 = -2
Moving 4 from the left hand side to the right hand side will result in the change of the sign from plus to minus:
3x = -2-4
3x = -6
x = -6/3
x = -2
Hence, the value of the lesser integer is -2.
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What is the exponential form of sq.rt (5^x)?
Answer:
Step-by-step explanation:
Comment and Answer
√5^x
The square root is really 0.5 as a decimal or 1/2 as a fraction. Both are powers.
So the square root of 23 can be written as 23^.5
For your question, you divide the power (x) by 2 so it looks like this.
5^(x/2)
What is the domain of f(x)?
(-6 , 6)
[-4 , 5]
[-6 , 6]
(-4 , 5)
Answer:
{−6,−4}
Step-by-step explanation:
the domain is all the x- values of the points.
so -6 and -4 are repeated so they are the domain of the points.
Five less than a number is at least eight
What.
is it 13?
.......................
what does x =?
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Divide write the answer as a fraction in simplest form 7/8 divided by 6 =
Answer:
[tex]\frac{7}{48}[/tex]Explanation: We have been given a fraction 7/8 and we need to divide it by 6 and write it in simplest terms.
Dividing and simplifying gives us following:
[tex]\frac{7}{8}\text{ Divied 6}\rightarrow\frac{7}{8}\times\frac{1}{6}=\frac{7}{48}=\frac{7}{48}[/tex]Describe in words where cube root of 35 would be plotted on a number line. between 3 and 4, but closer to 3 between 3 and 4, but closer to 4 between 2 and 3, but closer to 2 between 2 and 3, but closer to 3
The ∛35 will be plotted between 3 and 4, but closer to 3 on the number line.
In basic mathematics, real numbers are shown as a fine graphic of a graduated straight line which is called a number line.
Every point on a number line is considered to correspond to a real number, and every real number is assumed to correspond to a point.The integers are typically shown as lines of specially chosen, evenly spaced dots. Even though the image only shows the integers from -3 to 3, as well as values that are in between the integers, the product contains all real numbers, going forever in both directions. When teaching the very foundations , addition and subtraction with negative numbers, it is widely used as a teaching technique.We know that 35 lies between 27 and 64 , and 27 = 3³ and 64 = 4³.
Hence the ∛35 will be plotted between 3 and 4 and since 35 is closer to 27 than 64 , therefore it will be closer to 3.
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a newsletter publisher believes that 333% of their readers own a rolls royce. a testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. after performing a test at the 0.100.10 level of significance, the testing firm fails to reject the null hypothesis. what is the conclusion regarding the publisher's claim?
There is sufficient evidence at the 0.10 level of significance that the percentage is not 33%.
According to the newsletter publisher that 33% of their readers own a Rolls Royce.
The testing firm says that this is an inaccurate issue and performs a test to dispute the publisher's claim, after performing the test at the 0.10 level of significance the results are as follows,
Null hypothesis:
H₀ : p = 0.33
Alternative hypothesis:
H₁ : p ≠ 0.33
We reject H₀ at the 0.10 level of significance.
Therefore, There is sufficient evidence at the 0.10 level of significance that the percentage is not 33%.
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what is the slope for 5/3 x-4
Answer:
The slope is 5/3
Step-by-step explanation:
y = 5/3x - 4
The equation is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 5/3 and the y intercept is -4
Nancy spent 2 1/2 hours working on her homework on the weekend. she spent 4/5 of her time working her ela homework. how much time did nancy spend working on her ela homework?
The time Nancy spent working on her ela homework is equal to 2 hours.
The time Nancy spent working on her ela homework can be calculated by multiplication.
We can calculate it by multiplying the fraction of time spent by her on ela homework by the total time she spent on her homework.
As the total time spent by her on homework is 2 1/2 hours we can covert it into decimals as;
2 1/2 = 5/2 = 2.5 hours
Now multiplying it by the fraction of her time spent on ela homework,
Time spent on ela homework = 4/5 × 2.5
Time spent on ela homework = 10/5
Time spent on ela homework = 2 hours.
Hence Nancy spent 2 hours working on her ela homework.
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Select the correct answer from each drop-down menu.
AABC is translated 6 units up and 3 units left to create AABC
If vertex A is at (-1, 2) and vertex B is at (1, 5), then vertex A' is at
Reset
V
and vertex B is at
Next
From the translation described, If vertex A is at (-1, 2) and vertex B is at (1, 5), then vertex A' is at (-4, 8). See the justification for the same below.
What is a vertex?A vertex is a specific point of a mathematical object that is often where two or more lines or edges intersect. Angles, polygons, polyhedra, and graphs are the most typical places to find vertices. Nodes are another name for graph vertices.
The explanation of the translation is given as follows:
According to the translation rule for translating a point h units left is given as:- (x, y) → (x-h, k)
The translation rule for translating point k units up is given as:
(x,y) → (x, y+k).
Since ∆ABC is translated 6 units up and 3 units left to create ∆A'B'C'. If vertex A is at (-1, 2) and vertex B is at (1, 5).
Then,
The vertex A' =
A (-1, 2) → (-1 -3, 2+6)
= (-4, 8)
Therefore, the vertex A' is at (-4,8).
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From the translation described, the vertex A' is at the point (-4,8).
What is a vertex?A vertex is a specific point of a mathematical object that is often where two or more lines or edges intersect.
Angles, polygons, and graphs are the most typical places to locate the vertices.
The explanation of the translation will be:
Based on the translation rule for translating a point h units left is follows as
(x, y) → (x-h, k)
The translation rule for point k units up is follows as:
(x,y) → (x, y+k).
Since ∆ABC is translated to the 6 units up and 3 units left to create ∆A'B'C'. If vertex A is at (-1, 2) and vertex B is at; (1, 5).
The vertex A' ;
A (-1, 2)
(-1 -3, 2+6)
= (-4, 8)
Therefore, the vertex A' is at the point (-4,8).
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A cardboard box, which weighs 0.6 pound when empty, is filled with 15 bags of beans and a 4-pound bag of rice. The total weight of the box and the contents inside it is 25.6 pounds. One way to represent this situation is with the equation 0.6 + 15b + 4 = 25.6.
What does the solution represent in this situation?
The solution b = 1.4 represents the weight of one bag of bean.
In the question;
it is given that
weight of cardboard box when empty = 0.6 pounds
number of bean bags = 15 bags
weight of rice bag = 4 pounds
let the number of bean bags = b
total weight of carboard box with contents= 25.6 pounds
So , according to the question
0.6 + 15b + 4 = 25.6
solving further , we get
15b+4.6 = 25.6
15b = 25.6-4.6
15b = 21
b = 21/15
b = 1.4
Therefore , the solution b = 1.4 represents the weight of one bag of bean.
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Please Help i will give brainliest Its a emergency please help with this equation i am not sure what to do its a math problem
Answer:
the last choice is the 6th term of expression
Step-by-step explanation:
all the work and steps is in the pic go check it out sorry if wrong and have a wonderful day:)
determine the equation of line from the graph
Answer:
y = -x
Step-by-step explanation:
Answer: Y=-X
Step-by-step explanation:
When the summer started, Janie needed to fill her empty pool. At first, she used a garden hose to fill the pool, but this was taking too long. She got tired of watching the pool fill so slowly, so she turned off the water and went for a walk. She spotted a truck in the neighborhood that was filling pools and flagged them down to come fill her pool too. They were able to fill the pool at a faster rate. Which graph best represents this situation?
The statement mentions that the pool started empty, which implies that the graph must start at the point (0,0).
Then, the pool slowly filled, so the amount of water in the pool remained constant when Janie turned off the water and went for a walk.
Finally, thanks to a truck in the neighborhood the pool filled up quickly, and when it was filled the amount of water remained constant.
Therefore, the graph that best represents this situation is the one shown in option B.
Hi thank you so for all your time and help
Hello there. To solve this question, we'll have to remember some properties about trigonometric functions and the right triangle.
We want to find x such that:
[tex]\tan (x)=\sqrt[]{3}[/tex]We'll use the second right triangle to show what we want.
First, given a triangle:
We know that the hypotenuse will be:
[tex]\sqrt[]{x^2+y^2}[/tex]But most importantly, the tangent of the angles α and β can be calculated by only using the legs of the triangle: it is the ratio between the opposite side and the adjacent side to an angle.
[tex]\tan (\alpha)=\frac{y}{x}[/tex]and
[tex]\tan (\beta)=\frac{x}{y}[/tex]Now look at the triangle we have:
We can easily check that:
[tex]\sqrt[]{3}=\frac{\sqrt[]{3}}{1}[/tex]So it would be good to find something that relates the ratio between those two numbers: the tangent of 60º!!
Therefore, we have:
[tex]\tan (60^{\circ})=\frac{\sqrt[]{3}}{1}=\sqrt[]{3}[/tex]And the solution to x is:
[tex]x=60^{\circ}[/tex]Choose the correct answer for each row.
Match each equation to the value of x that is the solution. Values of x may be used more than once and some will not be used.
Answer:
Step-by-step explanation:
5 (u - 5) + 6u = 8 solve for u and simplifly your answer as much as possible
Answer:
u = 3
Step-by-step explanation:
Step 1: Distribute 5 in u - 5
[tex]\displaystyle{5\cdot u - 5\cdot 5 +6u=8}\\\\\displaystyle{5u-25+6u=8}[/tex]
Step 2: Add like terms together (u-term)
[tex]\displaystyle{11u-25=8}[/tex]
Step 3: Add both sides by 25
[tex]\displaystyle{11u-25+25=8+25}\\\\\displaystyle{11u=33}[/tex]
Step 4: Divide both sides by 11
[tex]\displaystyle{\dfrac{11u}{11}=\dfrac{33}{11}}\\\\\displaystyle{u=3}[/tex]
Answer Check
Step 1: Substitute u = 3 in the equation
[tex]\displaystyle{5(3-5)+6(3)=8}[/tex]
Step 2: Evaluate & Simplify
[tex]\displaystyle{5(-2)+18=8}\\\\\displaystyle{-10+18=8}\\\\\displaystyle{8=8}[/tex]
Since the equation is true after substituting u = 3. Therefore, the answer is u = 3.
Please let me know if you have any questions!
Marsha is filing her federal income tax return with the Single filing status. She had an adjusted gross income of $56,800 last year and is trying to decide whether to take the standard deduction of $5700 or to itemize deductions. Last year she had $4900 in medical expenses, $3100 in state and local income taxes paid, $1940 in mortgage interest paid, $530 in charitable contributions, and $1200 in non-reimbursed work expenses
Marsha must claim for itemized deductions.
Given,
Last year's gross income is $56,800.
Medical expenses = $4900
State and local income taxes paid = $3100
The mortgage interest paid = $1940
Charitable contributions = $530
Non-reimbursed work expenses = $1200
Standard deduction = $5700
The sum of all the expenses of last year = $4900 + $3100 + $1940 + $530 + $1200 = $11,670
And the Standard deduction is $5700.
Which is, $11,670 - $5700 = $5970 lesser.
Therefore, Marsha must claim for itemize deductions rather than the standard deductions.
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Assume the given function is one to one.Find the indicated values
To solve this question, you have to look for the answers in the table.
Let's analise each part of the question to solve it:
(a) f(1) =
f(1) means the output of the function [f(x)] when x = 1.
Looking for x =1 in the table, you can see that f(x) = 0.
f(1) = 0.
(b) f(x) = 3, x =
Now, you have to find the input (x) when the outpout [f(x)] is 3.
Looking for f(x) = 3, you can see that x = 7.
f(x) = 3, x = 7.
(c) f⁻¹(0) =
Now, you have to evaluate the inverse function.
To look for the values of the inverse function, x will be the output and f⁻¹ will be the input.
To look for f⁻¹(0), look for f(x) = 0 (input) and the output will be 1
f⁻¹(0) = 1.
(d) f⁻¹(x) = 7; x =
Again, you have an inverse function. So, 7 will be the input in the table (x). x is 7 (output).
f⁻¹(x) = 7; x = 3.
Last month, Sally and Roger sold candy to raise money for their debate team. Roger sold 1/3 as much candy as Sally did. If Sally sold 2 9/10 boxes of candy, how many boxes of candy did Roger sell?
The boxes of candy sold by Roger are 29/30.
According to the question,
We have the following information:
Roger sold 1/3 as much candy as Sally sold.
Sally sold [tex]2\frac{9}{10}[/tex] boxes of candy.
Now, first we will convert the boxes of candy sold by Sally from the mixed fraction.
(More to know: there are three kinds of fraction: mixed fraction, proper fraction and improper fraction. We need to change mixed fraction in most of the cases to solve the questions further.)
We have:
29/10
Now, we know that the boxes of candy sold by Roger is 1/3 of 29/10.
So, we have the following expression:
[tex]\frac{1}{3}* \frac{29}{10}[/tex]
29/30
Hence, the boxes of candy sold by Roger is 29/30.
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It took Brian 3 hours to drive to a rock concert. On the way home, he was able to increase his average speed by 23 mph and make the return drive in only 2 hours. Find his average speed on the return drive.The equation from part 2 is 3x=2(x+23)Step 3 of 3: Solve the equation found in part 2 for x. Use this information to answer the given word problem.
Answer:
69 mph
Explanation:
The equation that represents this situation is:
[tex]3x=2(x+23)[/tex]We are required to determine Brian's average speed on the return drive.
To do this, we first find the value of x.
[tex]\begin{gathered} \text{Open the bracket} \\ 3x=2x+46 \\ \text{Subtract 2x from both sides} \\ 3x-2x=46 \\ x=46\; \text{mph} \end{gathered}[/tex]Using the value of x, we find the average speed on the return drive.
[tex]x+23=46+23=69\text{mph}[/tex]Therefore, the average speed on the return drive will be 69 mph.
by what factor does the intensity increase for each whole number increase in the richter scale?
Answer:
By adding the gravity of the earth ang subtracting the number of the enumeration and multiply the square root of need to be the first divorcee you know that I love ckicen nuggets
Step-by-step explanation:
Me to mama o sige na kain na kau
enter 2 Expressions that represent the retail price of the clothes you see for your variable and exclusive clothing boutiques quadruples the price of the items it purchases for resale.
Explanation
Step 1
Let
c represent the original price
if the boutiques quadruples the price of the items it purchases for resale.then
[tex]\begin{gathered} \text{new price=4}\cdot c \\ percentage \\ 4=4\cdot\frac{100}{100} \\ 4=\frac{400}{100} \\ 4=400\text{ per cent} \end{gathered}[/tex]400 percent
Step 2
expressions
[tex]\begin{gathered} \text{new price=4}\cdot c \\ \text{new price= 400 percent of C} \end{gathered}[/tex]4c and 400%c
I hope this helps you
2) m angle2=x+88 50° 2 A) -8 C) 8 B) -7 D) 7
A
1) Since the sum of the interior angles of any triangle is 180º, and this is an isosceles triangle
2) Then the other angle, has the same measure 50º since this is an isosceles triangle, at least two congruent sides, and two congruent angles.
We can finally write
x+88 +50 +50 = 180
x +188 =180 subtract 188 from both sides
x= 180-188
x= -8
3) So x=-8 is the answer.
given that tank=8 and sinx is negative determine sin(2x) cos(2x) and tan(2x)
Answer:
sin2x = 16/65
cos2x = -63/65
tan2x = -16/63
Explanation:
the tangent of an angle is equal to the opposite side over the adjacent side. So, if the tan(x) = 8, we can represent this as the following diagram:
Therefore, we can calculate the value of the hypotenuse as:
[tex]\text{Hypotenuse = }\sqrt[]{8^2+1^2}=\sqrt[]{64+1}=\sqrt[]{65}[/tex]With the hypotenuse, we can calculate sin(x) and cos(x) as follows:
[tex]\begin{gathered} \sin x=\frac{Opposite}{hypotenuse}=-\frac{8}{\sqrt[]{65}} \\ \cos x=\frac{\text{Adjacent}}{\text{hypotenuse}}=-\frac{1}{\sqrt[]{65}} \end{gathered}[/tex]We type the negative sign because the question says that sin(x) is negative.
Now, we will use the following trigonometric identities to find sin(2x), cos(2x) and tan(2x)
[tex]\begin{gathered} \sin 2x=2\sin x\cos x \\ \cos 2x=1-2\sin ^2x \\ \tan 2x=\frac{2\tan x}{1-\tan ^2x} \end{gathered}[/tex]Therefore, replacing the values, we get:
[tex]\sin 2x=2(\frac{-8}{\sqrt[]{65}})(\frac{-1}{\sqrt[]{65}})=\frac{16}{65}[/tex][tex]\cos 2x=1-2(\frac{-8}{\sqrt[]{65}})^2=1-2(\frac{64}{65})=-\frac{63}{65}[/tex][tex]\tan 2x=\frac{2(8)}{1-8^2}=-\frac{16}{63}[/tex]So, the answers are:
sin2x = 16/65
cos2x = -63/65
tan2x = -16/63
This is to hard for me help me out please
stephan is reviewing the data on product returns for an online retailer. thus far, 3.5% of all sold units were returned. if stephan takes 200 sold unit records, what is the probability that at most 6 units were returned?
3.5% of all sold units have been returned so far. The probability that at most 6 units were returned out of 200 sold unit records is 0.7323.
Given that,
For an online store, Stephan is evaluating the data on product returns. 3.5% of all sold units have been returned so far.
We have to find what is the probability that at most 6 units were returned out of 200 sold unit records.
From binomial,
Binomial to normal approximations without continuity factor Sample size ,
n = 200
Probability of an event of interest,
p = 0.035
P(0<=n<=2)
=0.7323
Therefore, the probability that at most 6 units were returned out of 200 sold unit records is 0.7323.
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all you need is in the photo please answer fastplease
Answer:
The cost of cupcakes and cookies are;
[tex]\begin{gathered} \text{cupcakes = \$2.75} \\ \text{cookies = \$3.00} \end{gathered}[/tex]Explanation:
Let x and y represent the cost of a cupcake and cookie respectively.
Given that;
Five cupcakes and two cookies cost $19.75.
[tex]5x+2y=19.75-------1[/tex]Two cupcakes and four cookies cost $17.50.
[tex]2x+4y=17.50-------2[/tex]Let's solve the simultaneous equation by elimination;
multiply equation 1 by 2;
[tex]10x+4y=39.50-------3[/tex]subtract equation 2 from equation 3;
[tex]\begin{gathered} 10x-2x+4y-4y=39.50-17.50 \\ 8x=22 \\ \text{divide both sides by 8;} \\ \frac{8x}{8}=\frac{22}{8} \\ x=2.75 \end{gathered}[/tex]since we have the value of x, let substitute into equation 1 to get y;
[tex]\begin{gathered} 5x+2y=19.75 \\ 5(2.75)+2y=19.75 \\ 13.75+2y=19.75 \\ 2y=19.75-13.75 \\ 2y=6 \\ y=\frac{6}{2} \\ y=3.00 \end{gathered}[/tex]Therefore, the cost of cupcakes and cookies are;
[tex]\begin{gathered} \text{cupcakes = \$2.75} \\ \text{cookies = \$3.00} \end{gathered}[/tex]
