The gross pay will be $1496.78
What is Unitary Method ?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Brett is paid $18.95 per hour.
For 0 to 40 hours a week,
For any hours over 40, Brett makes
= 1.5 ($18.95)
= $28.425/hour
In Week 1: 40 hours x $18.95/hour = $758
2 hours x $28.425/hour = 56.85
Week 2: 36 hours x $18.95/hour = 682.2
So, total pay= 758 + 56.58+ 682.2 = $1496.78
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Final answer:
Brett's gross pay for working 42 hours one week and 36 hours the next, for a total of 78 hours, is $1495.05, which includes 2 hours of overtime pay.
Explanation:
Brett is paid an hourly wage of $18.95, with overtime paid at 1.5 times his regular rate. To calculate Brett's gross pay for the two-week pay period where he worked 42 hours one week and 36 hours the next week, we have to account for the fact that he worked 2 hours of overtime in the first week (since he worked more than 40 hours).
Step-by-Step Calculation
Regular hours for two weeks: 40 hours + 36 hours = 76 hours.Overtime hours for the first week: 42 hours - 40 hours = 2 hours.Calculate regular pay: 76 hours x $18.95/hour = $1438.20.Calculate overtime pay: 2 hours x ($18.95/hour x 1.5) = $56.85.Add regular and overtime pay: $1438.20 + $56.85 = $1495.05.Brett's gross pay for the 78 hours worked would be $1495.05.
Taxes are used for which of the following?
Depending on the country, most democracies use taxes for:
-public programs (any governmentally run or funded services)
-infrastructure (roads, bridges, etc)
-the military
-schools
-governmental departments (EPA, Department of Homeland Security, etc)
-government employee paychecks
And SOMETIMES:
-universal healthcare
-college/university
-etc.
Taxes are used to fund government services, reduce income inequalities, and support state and local government activities.
Explanation:Taxes are used for a variety of purposes. They are primarily used to fund government services such as military, police, education, infrastructure, and social security. Taxes are also used to reduce income and wealth inequalities by transferring income to lower income groups. Additionally, taxes are used to support state and local government activities and services.
For example, in the United States, the federal government raises revenue through income taxes, corporate earnings taxes, and sales taxes on goods such as gasoline, alcohol, and tobacco. State and local governments also collect taxes, including income, property, and sales taxes, which fund activities like maintaining public parks and providing a police force.
Overall, taxes play a crucial role in financing government operations and essential public services that benefit communities.
At a summer camp, there are 50 girls out of 80 campers.What is this ratio writtin as a fraction in simplest form?
The ratio is 5:8 campers
Answer:
50
--- Ratio: 50:80
80
Step-by-step explanation:
50 would be how many girls were that the summer camp. And the 80 is how many students all together at the summer camp.
Hoped This Helped You
Have A Wonderful day
what are two fractions equivalent to 5/12
Answer:
10/24 and 15/36, more answers possible
Step-by-step explanation:
if you multiply both the numerator and denominator by the same number, it will always be equivalent to 5/12, as you can simplify it back to that fraction.
5/12, multiply both by two, and you have 10/24
5/12, multiply both by three, and you have 15/36
10/24 and 15/36 are fractions equivalent to the given fraction.
10/24: This is equivalent to 5/12 because it can be reduced to 5/12 by dividing both the numerator and the denominator by 2.
15/36: This is another fraction equivalent to 5/12 since it can be reduced to 5/12 by dividing both the numerator and denominator by 3.
The values for three different sets of data are shown below.
Without calculating any statistics, Jadyn knows that data set 1 would have the least mean absolute deviation among the
three sets. Which statement explains how she knows?
Answer:
I'd say C Sets 2 and 3 contain outliers.
Step-by-step explanation:
Set 2 has an outlier of 90, while set 3 has an outlier of 40. 40 isn't as much of an outlier as 90 is, so I'm not absolutely sure. Cmakes the most sense though.
Answer: Third option.
Step-by-step explanation:
The standard deviation increases as we have more values that are far away from the mean.
For example, in data set 2, we can see that most of hour points are between 38 and 49, but we also have a point with a value of 90, so we may expect that this data set has a big standard deviation.
The data set 3 is similar, most of our points are between 24 and 31, and we have a value that is on 40, so again we have an outlier that increases the value of the standard deviation.
Noticing it we can conclude that data set 2 and data set 3 have a greater standard deviation than set 1.
The correct option is the third option.
if tanØ = 3/4, Find sinØ
a. SinØ=1/2
b. sinØ = 3/5
c. sinØ = 2
d sin Ø = 8/5
Answer: This is some information I have gathered to help you since I cannot answer this directly sin θ + (cot θ)(cos θ)
= sin θ + (cos θ / sin θ)(cos θ)
= sin θ + cos² θ / sin θ
Since cos² θ = 1 - sin² θ,
= sin θ + (1 - sin² θ) / sin θ
= sin θ + 1 / sin θ - sin θ
= 1 / sin θ
= csc θ ∎ Sin(x) = tan(x) / [sqrt(1 + tan^2(x)]
Sin(theta) =3/4 / sqrt[1 + .75^2]
Sin(theta) =0.75 / sqrt[ 1.5625 ]
Sin(theta) =0.75 / 1.25
Sin(theta) = 0.60
Which of the following are ordered pairs for the equation y = 11x + 1?
(0,1) (1,12) (-1,-10)
(0,1) (1,-12) (-1,-10)
(0,-1) (1,12) (-1,-10)
(0,1) (1,12) (-1,10)
The equation y = 11x + 1 is a linear equation. All three ordered pairs, (0, 1), (1, 12), and (-1, -10), satisfy this equation.
Explanation:The equation y = 11x + 1 represents a linear equation. To determine which ordered pairs satisfy this equation, we substitute the x and y values into the equation and check if the equation holds true. Let's check each option:
(0,1): Substitute x = 0 and y = 1 into y = 11x + 1:Based on the calculations, we can see that all three ordered pairs are valid solutions for y = 11x + 1.
what are the solutions of this equation 16-2x^2=-64
Answer:
x = ± 2[tex]\sqrt{10}[/tex]
Step-by-step explanation:
Given
16 - 2x² = - 64 ( subtract 16 from both sides )
- 2x² = - 80 ( divide both sides by - 2 )
x² = 40 ( take the square root of both sides )
x = ± [tex]\sqrt{40}[/tex] = ± [tex]\sqrt{4(10)}[/tex] = ± 2[tex]\sqrt{10}[/tex]
What is f(x) + f(x) + f(x)?
3f(x) =
Evaluate 3f(2) =
.
Answer:
the answer on e2020 is 12.
The required answer is,
f(x) + f(x) + f(x) = 3ax² + 3bx + 3c
3f(x) = 3ax² + 3bx + 3c
3f(2) = 12a + 6b + 3c
What is a function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.
Now let the function be,
f(x) = ax² + bx + c
To find,
f(x) + f(x) + f(x)
we have,
f(x) + f(x) + f(x) = (ax² + bx + c) + (ax² + bx + c) + (ax² + bx + c)
⇒ f(x) + f(x) + f(x) = 3(ax² + bx + c)
or, f(x) + f(x) + f(x) = 3ax² + 3bx + 3c
Similarly,
3f(x) = 3(ax² + bx + c)
or, 3f(x) = 3ax² + 3bx + 3c
now to find f(2), put x = 2 in f(x). we get,
f(2) = a2² + b2 + c
or, f(2) = 4a + 2b + c
Therefore,
3f(2) = 3(4a + 2b + c)
or, 3f(2) = 12a + 6b + 3c
hence, the required answer is,
f(x) + f(x) + f(x) = 3ax² + 3bx + 3c
3f(x) = 3ax² + 3bx + 3c
3f(2) = 12a + 6b + 3c
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(b)
5 cm
5 cm
108
cm
1080
1080
5 cm
5 cm
108°
1089
5 cm
Answer:
(b)
5 cm
5 cm
108
cm
1080
1080
5 cm
5 cm
108°
1089
5 cm
Step-by-step explanation:
Ummmmm. :)
well hope it helped you!
Answer:
Given that ΔJKL ≅ ΔUVW and ΔUVW ≅ ΔABC, complete the following statements.
Triangle JKL is congruent to triangle .
Side LK corresponds to sides .
Angle JLK corresponds to angles .
Step-by-step explanation:
If m1 = 110°, an arc with a measure of 250°.
BC
BCA
CTA
Answer:
the correct answer is BCA
Answer:
The correct option is 2.
Step-by-step explanation:
Given information: [tex]m\angle 1=110^{\circ}[/tex].
It is given that [tex]m\angle 1=110^{\circ}[/tex], so arc(BA)=110° and the central angle of arc BCA is
[tex]Arc(BCA)=360^{\circ}-Arc(BA)[/tex]
[tex]Arc(BCA)=360^{\circ}-110^{\circ}[/tex]
[tex]Arc(BCA)=250^{\circ}[/tex]
The measure of arc BC is
[tex]180^{\circ}-110^{\circ}=70^{\circ}[/tex]
The measure of arc CTA is 180° because AC is the diameter.
It means options 1 and 3 are incorrect.
The measure of arc BCA is 250°. Therefore the correct option is 2.
Which of the following are equations for the line shown below? Check all that
apply
(-1,5)
O
A. y-2 = -0.75(x-3)
B. y-5 = -0.75(x-1)
C. y-3 = -0.75(x - 2)
D. y-5-0.75(x+1)
The answer is:
The correct options are:
A) [tex]y-2=-0.75(x-3)[/tex]
and
D) [tex]y-5=-0.75(x+1)[/tex]
Why?To find the correct answers, we need to find a equation that meet the following charactheristics:
From the graph we can se that the function:
- Has a negative slope (is decreasing)
- Pass throught the points: (-1,5) and (3,2)
Now, discarding from the given options, we have:
A.[tex]y-2=-0.75(x-3)[/tex]
We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).
Evaluating the points, we have:
Evaluating (-1,5)
[tex]5-2=-0.75(-1-3)[/tex]
[tex]3=-0.75(-4)[/tex]
[tex]3=3[/tex]
Evaluating (3,2):
[tex]2-2=-0.75(3-3)[/tex]
[tex]0=-0.75(0)[/tex]
[tex]0=0[/tex]
We have that the equation is satisfied, so, the line pass through the given points.
Hence, we have that the equation A is an equation of the line shown.
B.[tex]y-5=-0.75(x-1)[/tex]
We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).
Evaluating the points, we have:
Evaluating (-1,5)
[tex]5-5=-0.75(-1-1)[/tex]
[tex]0=-3.5[/tex]
Hence, we have that since the equation is not satisfied, the line shown is not passing through the point (-1,5) meaning that the equation is not an equation of the line shown.
So, we have that the equation B is not equation of the line shown.
C.[tex]y-3=-0.75(x-2)[/tex]
We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).
Evaluating the points, we have:
Evaluating (-1,5)
[tex]5-3=-0.75(-1-2)[/tex]
[tex]2=-0.75(-3)[/tex]
[tex]2=2.25[/tex]
Hence, we have that since the equation is not satisfied, the line shown is not passing through the point (-1,5) meaning that the equation is not an equation of the line shown.
So, we have that the equation B is not equation of the line shown.
D.(assuming you committed a mistake writing the options and the equality sign is missing)
[tex]y-5=-0.75(x+1)[/tex]
We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).
Evaluating the points, we have:
Evaluating (-1,5)
[tex]5-5=-0.75(-1+1)[/tex]
[tex]0=-0.75(0)[/tex]
[tex]0=0[/tex]
Evaluating (3,2)
[tex]2-5=-0.75(3+1)[/tex]
[tex]-3=-0.75(4)[/tex]
[tex]-3=-3[/tex]
We have that the equation is satisfied, so, the line pass through the given points.
Hence, we have that the equation B is an equation of the line shown.
Finally, we have that the correct options are:
A) [tex]y-2=-0.75(x-3)[/tex]
and
D) [tex]y-5=-0.75(x+1)[/tex]
Have a nice day!
6(3x–5)–5(2x+7)=25 help me
Answer:
18x-30-10x-35=25
8x-65=25
8x-65+65=25+65
8x=90
Divide by 8 for 8x and 90
x=90/8 or 45/4 or 11 1/4 ( Answers)
The mapping diagram shows a function R(x).
Which mapping diagram shows the inverse of R(x)?
Answer:
C
Step-by-step explanation
The mapping diagram which shows the inverse of R(x) is Option (C).
What is a mapping diagram ?A function is a special type of relation in which each element of the domain is paired with exactly one element in the range . A mapping diagram shows how the elements are paired. Its like a flow chart for a function, showing the input and output values. A mapping diagram consists of two parallel columns.
How to find the mapping diagram which contains the inverse of a function ?To identify the mapping diagram for inverse of a function, we simply just change the values of first set of columns into the second set of columns.
This is because if [tex]f(x) = y[/tex] , then [tex]f^{-1}(y) = x[/tex]
For the given function R(x) , values are 6,7,8,9 in first column and 9,10,11,12 in the second column . Thus for the inverse function, 6,7,8,9 will be in the second column and 9,10,11,12 will be in the first column.
From the given Options, Option (C) is the correct mapping of inverse of R(x).
Thus, the mapping diagram which shows the inverse of R(x) is Option (C).
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The histogram shows the weekly attendance of participants in a school's study skills program. Student attendance numbers were the same during which two weeks of the workshop?
A.
weeks 1 and 2
B.
weeks 2 and 4
C.
weeks 5 and 6
D.
weeks 4 and 6
That would be week 2 and 4 (B). They are both at 12 students attending
Hope this helped!
Answer:
The correct option is B. weeks 2 and 4.
Step-by-step explanation:
Consider the provided histogram.
The histogram shows the weekly attendance of participants in a school's study skills program.
Now, consider the Histogram.
In week 1 the Student attendance was 8.
In week 2 the Student attendance was 12.
In week 3 the Student attendance was 15.
In week 4 the Student attendance was 12.
In week 5 the Student attendance was 18.
In week 6 the Student attendance was 16.
Hence the Student attendance numbers were the same during week 2 and week 4 of the workshop.
Therefore, the correct option is B. weeks 2 and 4
In history class, Colin takes a multiple-choice quiz. There are 10 questions. Each question has five possible answers. To the nearest percentage, what is the probability that Colin will get exactly 3 questions correct if he guesses an answer to each question?
Answer:
[tex]P = 0.201[/tex]
Step-by-step explanation:
If the discrete random variable X represents the number of correct Colin responses then X can be represented by a binomial distribution with parameters p, n, x.
In this case p represents the probability that colin gets a correct answer, n represents the number of questions.
So the probability that Colin receives x correct questions is:
[tex]P(x) = \frac{n!}{x!(n-x)!}*p^x*(1-p)^{n-x}[/tex]
Where:
[tex]p=\frac{1}{5}[/tex]
[tex]n=10[/tex]
[tex]x=3[/tex]
[tex]P(x=3) = \frac{10!}{3!(10-3)!}*(\frac{1}{5})^3*(1-\frac{1}{5})^{10-3}[/tex]
[tex]P(x=3) = \frac{10!}{3!*7!}*\frac{1}{125}*(\frac{4}{5})^{7}[/tex]
[tex]P = 0.201[/tex]
The table shows the effect of education on annual income. Based on the data in the table, how much more does a person with an Bachelor’s degree earn than a person with only a high school diploma over 10 years?
A) $20,800
B) $29,690
C) $208,000
D)$290,690
B is the correct answer
what is the location of the point on the number line that is 2/5 of the way from A=-6 to B=9?
Answer:
0
Step-by-step explanation:
Between -6 and 9 are 15 units.
2/5 of 15 units is 6 units. Add this to -6 to obtain 0.
0 is the answer to this question
Step-by-step explanation:
I'm not sure but I think its like the distance between -6 and 9 is 15 or something and 15 divided by 5 is 3 and 2/5 is 6 so 6-6 is 0 and that's that point.
John bought a variety pack of delicious donuts from the famous Donut house of Amy and Anna. Amy ate two-third of the pack and Anna devoured one-fourth of them. Finally David ate the remaining one donut. Find out the total number of donuts in the pack.
Pls show steps...
Answer: 12
Step-by-step explanation:
2/3 = 8/12
1/4 = 3/12
8/12 + 3/12 + 11/12
amy & anna ate 11 and david had 1
Answer:
There were 12 donuts in the box.
Step-by-step explanation:
We are given the following information in the question:
Let x be the number of donuts in the box.
Then, according to the question
Number of donuts eaten by Amy = [tex]\frac{2x}{3}[/tex]
Number of donuts eaten by Anna = [tex]\frac{x}{4}[/tex]
Number of donuts eaten by David = 1
Total number of donuts =
Number of donuts eaten by Amy + Number of donuts eaten by Anna + Number of donuts eaten by David
[tex]\Rightarrow \frac{2x}{3} + \frac{x}{4} + 1 = x[/tex]
Solving the above equation:
[tex]11x + 12 = 12x\\x =12[/tex]
Thus, there were 12 donuts in the box.
fill in the missing exponents in each box (9^4)?=9^1
x=1/4 because, 1/4 will multiply with 4 to cancel out to have an exponent of 1
[tex]\bf (9^4)^{?}=9^1\implies 9^{4\cdot ?}=9^1\implies \stackrel{\textit{same base, the exponents must also be the same}}{4?=1\implies ?=\cfrac{1}{4}}[/tex]
What is the value for x?
ANSWER
y=10
x=5
EXPLANATION
The base angles of an isosceles triangle are equal.
This implies that:
8y-7=73°
Add 7 to both sides:
8y=73+7
8y=80°
y=10°
Interior angles of a triangle sums up to 180°
73+73+6x+4=180
150+6x=180
6x=180-150
6x=30
Divide both sides by 6
x=5
How much is 3 over 15 plus 1 over 3
Answer:
8/15
Step-by-step explanation:
Well to add fractions you have to have the same denominator so you would multiply your 1/3 by 5 to be 5/15 then you can add.
3/15 + 5/15 = 8/15
1 over 3 would change to 5 over 15 to make the denominators equal then you add the numerators and you get 8 over 15
Can someone help me out with this question plz
Answer:
[tex]\left(s\cdot t\right)\left(x\right)=2x^2+12x+16[/tex]
[tex]\left(s-t\right)\left(x\right)=-x[/tex]
[tex]\left(s+t\right)\left(4\right)=20[/tex]
Step-by-step explanation:
Given functions are:
[tex]s\left(x\right)=x+4[/tex]
[tex]t\left(x\right)=2x+4[/tex]
Then [tex]\left(s\cdot t\right)\left(x\right)=s\left(x\right)\cdot t\left(x\right)[/tex]
or [tex]\left(s\cdot t\right)\left(x\right)=\left(x+4\right)\left(2x+4\right)[/tex]
or [tex]\left(s\cdot t\right)\left(x\right)=2x^2+4x+8x+16[/tex]
or [tex]\left(s\cdot t\right)\left(x\right)=2x^2+12x+16[/tex]
---------
Similarly
[tex]\left(s-t\right)\left(x\right)=s\left(x\right)-t\left(x\right)[/tex]
or [tex]\left(s-t\right)\left(x\right)=\left(x+4\right)-\left(2x+4\right)=x+4-2x-4[/tex]
or [tex]\left(s-t\right)\left(x\right)=-x[/tex]
---------
Similarly
[tex]\left(s+t\right)\left(4\right)=s\left(4\right)+t\left(4\right)=\left(4+4\right)+\left(2\left(4\right)+4\right)=\left(8\right)+\left(12\right)=20[/tex]
[tex]\left(s+t\right)\left(4\right)=20[/tex]
What is the surface area of this composite solid?
square feet
let's take a peek
we really have a rectangular prism below a square pyramid.
the prism has a front, back, left and right of a rectangle 2x11 .
its bottom or base is an 11x11 square.
the pyramid 4 triangles, each one has a base of 11 and a height of 7.
[tex]\bf \stackrel{\textit{front, back, left, right}}{4(2\cdot 11)}~~+~~\stackrel{\textit{base}}{(11\cdot 11)}~~+~~\stackrel{\textit{four triangles}}{4\left[ \cfrac{1}{2}(11)(7) \right]} \\\\\\ 88+121+154\implies 363[/tex]
Answer:
The surface area of composite solid = 363 ft²
Step-by-step explanation:
Points to remember
Area of rectangle = Length * Breadth
Area of triangle = bh/2
Where b - Base and h - Height
To find the surface area of composite solid
Surface area = Base area + side area + area of 4 triangles
= (11 * 11) + 4(11 * 2) + 4(11 * 7)/2
= 121 + 88 + 154
= 363 ft²
Therefore the surface area of composite solid = 363 ft²
Given the system of equations, match the following items.
2 x - y = 0
x + y = -3
[0 -1
-3 1]
[2 0
1 -3]
[2 -1
1 1]
The x - determinant of the equation is [tex]\left[\begin{array}{cc}0&-1\\-3&1\\\end{array}\right][/tex]
The y - determinant of the equation is [tex]\left[\begin{array}{cc}2&0\\1&-3\\\end{array}\right][/tex]
The system determinant is [tex]\left[\begin{array}{cc}2&-1\\1&1\\\end{array}\right][/tex]
How to find the determinants of x, y and the entire system?
The given system of equation include the following;
2x - y = 0
x + y = - 3
The x - determinant of the equation will be obtained by replacing coefficient of x with the constant terms.
[tex]\Delta x = \left[\begin{array}{cc}0&-1\\-3&1\\\end{array}\right][/tex]
The y - determinant of the equation will be obtained by replacing coefficient of y with the constant terms.
[tex]\Delta y = \left[\begin{array}{cc}2&0\\1&-3\\\end{array}\right][/tex]
The system determinant is obtained by removing the constant term and writing only the x and y coefficient in the matrix;
[tex]\Delta = \left[\begin{array}{cc}2&-1\\1&1\\\end{array}\right][/tex]
which will result in a difference of squares?
Answer:
C
Step-by-step explanation:
Answer:
The correct option is 3.
Step-by-step explanation:
The difference of squares is defined as
[tex]a^2-b^2=(a-b)(a+b)[/tex]
In option 1,
[tex](-7x+4)(-7x+4)=(-7x+4)^2[/tex]
This expression is a perfect square, therefore this is not the difference of squares. Option 1 is incorrect.
In option 2,
[tex](-7x+4)(4-7x)=(-7x+4)(-7x+4)=(-7x+4)^2[/tex]
This expression is a perfect square, therefore this is not the difference of squares. Option 2 is incorrect.
In option 3,
[tex](-7x+4)(-7x-4)=(-7x)^2-(4)^2[/tex]
This expression is the difference of squares., therefore Option 3 is correct.
In option 4,
[tex](-7x+4)(7x-4)=-(-7x+4)(-7x+4)=-(-7x+4)^2[/tex]
This expression is a perfect square, therefore this is not the difference of squares. Option 4 is incorrect.
What is the solution to the equation?
(A) d = –4 and d = 2
(B) d = –2 and d = 4
(C) d = 1
(D) d = 2
MY LAST QUESTION HELP.
ANSWER
(C) d=1
EXPLANATION
The given equation is
[tex] \frac{ - 3d}{ {d}^{2} - 2d - 8} + \frac{3}{d - 4} = \frac{ - 2}{d + 2} [/tex]
Factor the first fraction to get,
[tex] \frac{ - 3d}{(d + 2)(d - 4)} + \frac{3}{d - 4} = \frac{ - 2}{d + 2} [/tex]
Multiply through by (d+2)(d-4)
[tex] - 3d + 3(d + 2) = - 2(d - 4)[/tex]
Expand:
[tex] - 3d + 3d + 6 = - 2d + 8[/tex]
[tex] 6 = - 2d + 8[/tex]
[tex]6 - 8= - 2d[/tex]
[tex] - 2 = - 2d[/tex]
divide both sides by -2
[tex]d = 1[/tex]
The correct answer is (B) [tex]\( d = -2 \)[/tex] and [tex]\( d = 4 \)[/tex].
To find the solution to the given quadratic equation, we can factor it or use the quadratic formula. The equation is not provided in the conversation, but based on the options given, it seems that the equation could be in the form [tex]\( (d - a)(d - b) = 0 \)[/tex], where [tex]a[/tex] and [tex]b[/tex]are the roots of the equation.
The quadratic equation can be written as [tex]\( d^2 - (a+b)d + ab = 0 \)[/tex]. To have the sum of the roots [tex]\( a + b \)[/tex] equal to 0 and the product of the roots [tex]\( ab \)[/tex] equal to -8, we can set up the following system of equations:
1. [tex]\( a + b = 0 \)[/tex]
2. [tex]\( ab = -8 \)[/tex]
From equation 1, we can express [tex]\( b \)[/tex] in terms of [tex]\( a \): \( b = -a \).[/tex]
Substituting [tex]\( b \)[/tex] into equation 2, we get:
[tex]\( a(-a) = -8 \)[/tex]
[tex]\( -a^2 = -8 \)[/tex]
[tex]\( a^2 = 8 \)[/tex]
Taking the square root of both sides, we find:
[tex]\( a = \pm\sqrt{8} \)[/tex]
[tex]\( a = \pm2\sqrt{2} \)[/tex]
Since [tex]\( b = -a \),[/tex] we have:
[tex]\( a = 2\sqrt{2} \) and \( b = -2\sqrt{2} \)[/tex]
[tex]\( a = -2\sqrt{2} \) and \( b = 2\sqrt{2} \)[/tex]
However, these are not the exact values given in the options. We need to find the exact integer values for [tex]a[/tex] and [tex]b[/tex]. Since the product [tex]\( ab \)[/tex] is -8, we can look for two numbers that multiply to -8 and add up to 0. These numbers are -2 and 4.
Therefore, the solutions to the equation are [tex]\( d = -2 \)[/tex] and [tex]\( d = 4 \)[/tex], which corresponds to option (B).
there are 48 heads and 134 legs how many sheep is there
Answer:
48
Step-by-step explanation:
48 heads =48sheep. .i guess. .......
Something's odd with this question: each sheep has one head, so if you see 48 heads there are 48 sheeps.
But each sheep has also 4 legs, so if you have 48 sheeps you should see
[tex]48\cdot 4 = 192\text{ legs}[/tex]
So, unless you have some sheeps with missing legs, there must be a mistake in the question.
What is the x-intercept of the graph?
Answer:
-3
Step-by-step explanation:
The x-intercept is the plot point where y = 0.
Answer:
-3
Step-by-step explanation:
the x-intercept is the point on the graph where the ploted line crosses the x axes
Question: An arithmetic sequence is a sequence with a common difference. It can be represented by the recursive formula a1 = a (where a is the first term of the sequence); an = an - 1 + d. a) Create your own arithmetic sequence. Write out the first 3 terms. b) What is the common difference of your sequence? c) Write the recursive formula representing your sequence. Use the underscore symbol to indicate a subscript. For example, the recursive formula would be written like a1 = a; a_n = a_(n – 1) + d
Answer:
a) 3,6,9,12,15,..
b) Common Ratio is 3
c) Recursive Formula : aₙ= aₙ₋₁ + d where a₁=3 and d= 3
Step-by-step explanation:
a) Create your own arithmetic sequence. Write out the first 3 terms.
Consider the sequence: 3,6,9,12,15,..
a₁ = 3
a₂ = 6
a₃ = 9
b) What is the common difference of your sequence?
6-3 = 3
9-6 = 3
12 -9 =3
So, common difference is 3
c) Write the recursive formula representing your sequence.
a₁ = 3
a₂ = aₙ₋₁ + d
= a₁ + d
= 3+ 3 = 6
a₃ = aₙ₋₁ + d
= a₂ + d
= 6+3 = 9
so, recursive formula is aₙ = aₙ₋₁ + d where a₁ = 3 and d= 3
An example of an arithmetic sequence can be created with a starting value (a1) of 2 and a common difference (d) of 3. The sequence's terms would be 2, 5, 8, etc. Its recursive formula would be a1 = 2; a_n = a_(n–1) + 3.
Explanation:
Let's create an arithmetic sequence, starting with the first term (a1) of 2 and a common difference (d) of 3. So, the first three terms of the sequence would be 2, 2+3=5, and 5+3=8.
The common difference of this arithmetic sequence is 3 as each term is 3 greater than the previous term.
The recursive formula for this sequence is a1 = 2; a_n = a_(n–1) + 3. What this formula means is that the first term is 2, and each subsequent term (an) is the previous term (an-1) added to the common difference (3).
Learn more about Arithmetic Sequence here:https://brainly.com/question/35880655
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Solve the Equation
2x-3=14
-x+3y=-6
Step-by-step explanation:
If you lost "y" in the first equation.
[tex]\underline{+\left\{\begin{array}{ccc}2x-3y=14\\-x+3y=-6\end{array}\right}\qquad\text{add both sides of the equations}\\\\.\qquad x=8\\\\\text{Put the value of x to the first equation:}\\\\2(8)-3y=14\\16-3y=14\qquad\text{subtract 16 from both sides}\\-3y=-2\qquad\text{divide both sides by (-3)}\\y=\dfrac{2}{3}\\\boxed{x=8,\ y=\dfrac{2}{3}}[/tex]
If first equation is correct.
[tex]2x-3=14\qquad\text{add 3 to both sides}\\2x=17\qquad\text{divide both sides by 2}\\x=8.5\\\\\text{Put the value of x to the second equation:}\\-8.5+3y=-6\qquad\text{add 8.5 to both sides}\\3y=2.5\qquad\text{divide both sides by 3}\\y=\dfrac{2.5}{3}\\y=\dfrac{25}{30}\\y=\dfrac{5}{6}\\\\\boxed{x=8.5,\ y=\dfrac{5}{6}}[/tex]