McKenzie would take 6 hours to complete the landscaping job alone if Lindy calls in sick.
If McKenzie and Lindy can complete the landscaping job in 4 hours working together, it means their combined work rate is 1/4 of the job per hour. Let x be the number of hours it takes Lindy to complete the job alone, then McKenzie can complete the job in x-6 hours.
Using the formula for their individual work rates, we have:
[tex]1/x + 1/(x-6) = 1/4[/tex]
Multiplying both sides by [tex]4x(x-6)[/tex], we get:
[tex]4(x-6) + 4x = x(x-6)[/tex]
Expanding and simplifying, we get:
[tex]2x^2 - 12x - 48 = 0[/tex]
Dividing both sides by 2 and using the quadratic formula, we get:
[tex]x = (12 ± \sqrt{12^2 + 4248}) / (2*2)[/tex]
x = (12 ± 18) / 4
x = 7.5 or -1.5
Since we cannot have a negative time, the answer is that it would take Lindy 7.5 hours to complete the job alone, and McKenzie would take 1.5 hours less, or 6 hours, to complete the job alone if Lindy calls in sick.
Therefore, McKenzie would take 6 hours to complete the landscaping job alone if Lindy calls in sick.
For more questions like Functions visit the link below:
https://brainly.com/question/26535687
#SPJ11
Multiply.
2 1/4 x 5
Answer with a mixed number in simplest form.
Answer: 11 1/4
Step-by-step explanation:
To multiply fractions, you must use the improper form so...
2 1/4 x 5 =
9/4 x 5 =
45/4 =
11 1/4
Hope this helps!
According to the Funda equation of the given polynomial equatior f(x)=-3x^(2)+4x-1
The solutions to the given polynomial equation are x = 1/3 and x = 1.
According to the given polynomial equation f(x)=-3x^(2)+4x-1, we can find the values of x by using the quadratic formula, which is x = (-b ± √(b^(2)-4ac))/(2a).
In this equation, a = -3, b = 4, and c = -1.
Plugging these values into the quadratic formula, we get:
x = (-(4) ± √((4)^(2)-4(-3)(-1)))/(2(-3))
Simplifying this equation, we get:
x = (-4 ± √(16-12))/(-6)
x = (-4 ± √4)/(-6)
x = (-4 ± 2)/(-6)
Therefore, the two possible values of x are:
x = (-4 + 2)/(-6) = -2/(-6) = 1/3
x = (-4 - 2)/(-6) = -6/(-6) = 1
To know more about polynomial equation click on below link:
https://brainly.com/question/30127172#
#SPJ11
vIf you go out to eat with 3 friends and your meal was $54.55, and you should tip the waiter 20%. If the bill is shared equally, how much should each person pay?
Each person should pay $16.37.
Calculate the costIf the meal was $54.55 and you should tip the waiter 20%, the total cost of the meal would be $54.55 + ($54.55 * 0.20) = $65.46.
If the bill is shared equally among 4 people, each person should pay $65.46 / 4 = $16.37.
Therefore, each person should pay $16.37 for the meal. Step-by-step explanation:
1. Calculate the tip by multiplying the cost of the meal by 20% (0.20): $54.55 * 0.20 = $10.91
2. Add the tip to the cost of the meal to get the total cost: $54.55 + $10.91 = $65.46
3. Divide the total cost by the number of people to get the cost per person: $65.46 / 4 = $16.37
4. The final answer is $16.37 per person.
Learn more about total cost at
https://brainly.com/question/28652728
#SPJ11
What is the solution of this inequality?
The whole number that is a solution for the inequality x ≥ 4 but is not a solution for the inequality x > 4 is 4.
Option B is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
here,
We have,
x ≥ 4 and x > 4
Now,
x ≥ 4 means that x can be 4 and greater than 4.
x > 4 mean x is greater than 4.
So,
4 is a solution to x ≥ 4 but not a solution to x > 4.
Thus,
4 is the whole number.
Learn more about inequalities here:
brainly.com/question/20383699
#SPJ1
A quadrilateral has two angles that measure 216° and 102°. The other two angles are in a ratio of 10:11. What are the measures of those two angles?
(I would do this, but I'm in a rush right now sorry!)
Answer:
20° and 22°
Step-by-step explanation:
Quadrilaterals are shapes with 360°. Since we are given two known angles, we can subtract them from 360. 360 - 216 - 102 = 144 - 102 = 42
Because the others are in a ratio of 10:11, the only possible degree combination will be 20° and 22°
When 3x^(2)-22x+26 is divided by a polynomial, the quotient is 3x-4 and the remainder is 2 . Find the polynomial.
The polynomial that 3x^(2)-22x+26 is divided by is x - 6.
To find the polynomial that 3x^(2)-22x+26 is divided by, we can use the formula:
Dividend = Quotient * Divisor + Remainder
In this case, the dividend is 3x^(2)-22x+26, the quotient is 3x-4, and the remainder is 2. We can plug these values into the formula and solve for the divisor:
3x^(2)-22x+26 = (3x-4) * Divisor + 2
Next, we can rearrange the equation to isolate the divisor:
Divisor = (3x^(2)-22x+26 - 2) / (3x-4)
Divisor = (3x^(2)-22x+24) / (3x-4)
Now, we can use polynomial long division to find the divisor:
```
3x - 4 | 3x^2 - 22x + 24
- (3x^2 - 4x)
-------------
-18x + 24
- (-18x + 24)
-------------
0
```
Therefore, the divisor is x - 6.
To know more about polynomial click on below link:
https://brainly.com/question/11536910#
#SPJ11
Simplify $\frac{\sqrt{40\cdot9}}{\sqrt{49}}$.
The simplified expression of the given expression is [tex]\frac{6\sqrt{10}}{7}$.[/tex]
What is expression ?
An expression is a mathematical phrase that can contain numbers, variables, operators, and symbols. It can be a combination of terms, factors, and/or coefficients, and may involve addition, subtraction, multiplication, division, exponents, roots, and/or other mathematical operations. Expressions can be simplified, evaluated, or manipulated using algebraic rules and properties.
We can simplify the expression as follows:
[tex]\frac{\sqrt{40\cdot9}}{\sqrt{49}}=\frac{\sqrt{4\cdot10\cdot3\cdot3}}{\sqrt{7\cdot7}}\\ \\ \\=\frac{\sqrt{4}\cdot\sqrt{10}\cdot\sqrt{3}\cdot\sqrt{3}}{\sqrt{7}\cdot\sqrt{7}}\\ \\ \\=\frac{2\cdot3\sqrt{10}}{7}\\ \\ \\={\frac{6\sqrt{10}}{7}}.[/tex]
Therefore, the simplified expression of the given expression is [tex]\frac{6\sqrt{10}}{7}$.[/tex]
To know more about expressions visit :
https://brainly.com/question/1859113
#SPJ1
Write the standard equation of an ellipse with vertices at (2,-2) and (12,-2) and covertices at (7,1) and (7,-5).
(a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1
(b) (x+7)^2 / 25 + (y-2)^2 / 9 = 1
(c) (x-7)^2 / 9 + (y+2)^2 / 25 = 1
(d) (x+7)^2 / 100 + (y-2)^2 / 36 = 1
(e) (x-7)^2 / 100 + (y+2)^2 / 36 = 1
The correct answer is (a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1.
The standard equation of an ellipse is (x-h)^2 / a^2 + (y-k)^2 / b^2 = 1, where (h,k) is the center of the ellipse, a is the distance from the center to the vertices, and b is the distance from the center to the covertices.
In this case, the center of the ellipse is the midpoint of the vertices and covertices, which is (7, -2). The distance from the center to the vertices is 5 (12-7) and the distance from the center to the covertices is 3 (1-(-2)).
Therefore, the standard equation of the ellipse is (x-7)^2 / 25 + (y+2)^2 / 9 = 1, which corresponds to answer choice (a).
So the correct answer is (a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1.
Learn more about standard equation
brainly.com/question/12452575
#SPJ11
Ps show work :D
Will mark BRAINLIST!!!
Given trigonometric equation is equal to 2 so the it has been proved.
what is trigonometric identity?
A trigonometric identity is a mathematical equation that expresses a relationship between trigonometric functions of an angle. These identities are true for all values of the angle, and they allow us to simplify expressions involving trigonometric functions, manipulate them algebraically, or evaluate them more easily.
Trigonometric identities include basic relationships such as [tex]sin^2(x) + cos^2(x) = 1,[/tex] as well as more complex identities involving multiple functions such as the Pythagorean identity.
According to the question:
Let us begin by applying the trigonometric identity[tex]cos^2(x) + sin^2(x) = 1,[/tex]which is true for any angle x. Solving for[tex]cos^2(x)[/tex], we get [tex]cos^2(x) = 1 - sin^2(x).[/tex]
Using this identity, we can rewrite the given equation as
[tex]1 - sin^2((1/8)^2) + 1 - sin^2(3n/8) + 1 - sin^2(5n/8) + 1 - sin^2(7n/8) = 2[/tex]
Simplifying, we get:
[tex]4 - (sin^2((1/8)^2) + sin^2(3n/8) + sin^2(5n/8) + sin^2(7n/8)) = 2[/tex]
Rearranging, we get:
[tex]sin^2((1/8)^2) + sin^2(3n/8) + sin^2(5n/8) + sin^2(7n/8) = 2[/tex]
Now, let us apply the trigonometric identity [tex]sin^2(x) + cos^2(x) = 1[/tex], which is true for any angle x. Solving for [tex]sin^2(x),[/tex] we get [tex]sin^2(x) = 1 - cos^2(x)[/tex].
2=2
Therefore, the equation is true
To know more about trigonometric identities visit:
https://brainly.com/question/30396301
#SPJ1
Please help me i have a screenshot
2 1/8 pints
2.125 pints
work. 32. Write an equation for a function that has the shape of y=x^(2), but shifted right 2 units and down 1 unit.
The answer of equation for the function is y=(x-2)^(2)-1.
The equation for a function that has the shape of y=x^(2), but shifted right 2 units and down 1 unit is y=(x-2)^(2)-1.
To shift a function to the right, we subtract the amount of the shift from the x variable.
In this case, we want to shift the function 2 units to the right, so we subtract 2 from x: (x-2).
To shift a function down, we subtract the amount of the shift from the entire function.
In this case, we want to shift the function down 1 unit, so we subtract 1 from the entire function: (x-2)^(2)-1.
Therefore, the equation for the function is y=(x-2)^(2)-1.
To know more about equation for a function refer here:
https://brainly.com/question/22964920#
#SPJ11
find the sale price of a $36 item after a 50% discount
Answer:$18
Step-by-step explanation: Since 50% is half of a hundred and the item is half off, you multiply 36 by 0.5 and get $18. This is the price of the item with the sale and the the discount
Answer:
18$
Step-by-step explanation:
go to Safari and look it up is how I got the answer
Kayleigh walks 5/8 to school every day how far does she walk to school in 5 days
Answer:
Step-by-step explanation: First you do 5*5 and get 25. Then you do 25/8 and get 3 1/8.
Solve the equation. 4(x - 2) = 2(2x + 6) 4x – [?] = [__] + [__] First we must use the distributive property to expand our equations. Hint: Calculate and enter the value of 4•2. ______________
The equation 4(x - 2) = 2(2x + 6) has no solution.
To solve the equation 4(x - 2) = 2(2x + 6), we must first use the distributive property to expand the equations. The distributive property states that a(b + c) = ab + ac.
Using the distributive property, we can expand the equation as follows:
4(x - 2) = 2(2x + 6)
4x - 8 = 4x + 12
Next, we must isolate the variable on one side of the equation. We can do this by subtracting 4x from both sides of the equation:
-8 = 12
This equation is not true, so there is no solution to the equation 4(x - 2) = 2(2x + 6).
In conclusion, the equation 4(x - 2) = 2(2x + 6) has no solution.
Learn more about Distributive property
brainly.com/question/5637942
#SPJ11
College Algebra -3.1Modeling with Quadratics Angry Birss: * Cire cact aniwns. Hhe enty the fusctien to obraln yoar answerc. - Show all nocensary cakiadsina. - Wine your ancurers is complrte aeatrnces 1. Whor is the s-inerreept and nhat does a repreiert? 2. What is the ponatire eimerreps and whas doest throsetinaly tepereset? socirt?
The x-intercept is (-3,0) and the y-intercept is (0,9).
The x-intercept of a quadratic function is the point where the function intersects with the x-axis. This point represents the value of x for which the function is equal to 0. The x-intercept can be found by setting the function equal to 0 and solving for x.
The y-intercept of a quadratic function is the point where the function intersects with the y-axis. This point represents the value of y for which the function is equal to 0. The y-intercept can be found by setting x equal to 0 and solving for y.
1. The x-intercept of the function is (-3,0) and it represents the point where the function intersects with the x-axis.
2. The y-intercept of the function is (0,9) and it represents the point where the function intersects with the y-axis.
To find the x-intercept, set the function equal to 0 and solve for x:
0 = x^2 + 6x + 9
0 = (x+3)(x+3)
x = -3
To find the y-intercept, set x equal to 0 and solve for y:
y = 0^2 + 6(0) + 9
y = 9
Therefore, the x-intercept is (-3,0) and the y-intercept is (0,9).
To know more about y-intercept click on below link:
https://brainly.com/question/14180189#
#SPJ11
What is the order on a number line left to right of 1.25, -1.25, 2 2/5, -2.1, 1/3
What is the solution of this inequality?
Answer: C
Step-by-step explanation:
Isha is a pet sitter.
She earns $5 for each cat.
She earns $12 for each dog.
Last week, Isha pet sat for 11 cats and 7 dogs.
How much money did Isha earn pet sitting last week?
Answer: $139.00
Step-by-step explanation: 5x11 = 55
12x7 = 84
55+84=139
For the piecewise function, find the values h(- 8), h(-3), h(2), and h(5). -2x 10, for x< -7 2. x+3, forx22 h(x) = for 7sx<2 h(-8) = h(-3) = h(2) = h(5)
The numeric values of the piece-wise function are given as follows:
h(-8) = 26.h(-3) = 16.h(2) = 4.h(5) = 7.How to calculate the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we replace each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression.
A piece-wise function is a function that has different definitions, based on the input interval of the function.
For x < 2, the function is defined as follows:
h(x) = -2x + 10.
Hence the numeric values on the interval are obtained as follows:
h(-8) = -2(-8) + 10 = 26.h(-3) = -2(-3) + 10 = 16.For x >= 2, the function is defined as follows:
h(x) = x + 2.
Hence the numeric values on the interval are obtained as follows:
h(2) = 2 + 2 = 4.h(5) = 5 + 2 = 7.Learn more about the numeric values of a function at brainly.com/question/28367050
#SPJ1
Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive.)
The expression [tex]log(x^4)[/tex] can be expanded as a constant multiple of log(x).
What is the logarithms?
A logarithm is a mathematical function that measures the number of times a given value (called the base) must be multiplied by itself to produce a specified value.
We can use the following properties of logarithms to expand the expression:
log(a * b) = log(a) + log(b)log(a / b) = log(a) - log(b)[tex]log(a^n) = n * log(a)[/tex]The expression [tex]log(x^4[/tex]) can be expanded using the following property of logarithms:
[tex]log(a^n) = n * log(a)[/tex]
Using this property, we can write:
[tex]log(x^4) = 4 * log(x)[/tex]
Hence, the expression [tex]log(x^4)[/tex] can be expanded as a constant multiple of log(x).
To learn more about logarithms, Visit
https://brainly.com/question/25710806
#SPJ1
What is the value of m
Answer:
Step-by-step explanation:
Ok so we're just going to be doing a lot of supplementary work:
The angle adjacent to 85 degrees is equal to 180 - 85 = 95
We want to find the angle measures in the triangle where 95 degrees is. We can do this by using 40, finding the opposite angle, which is also 40 due to vertical angles theorem, finding the missing angle in the right-most triangle which is 180 - 105 - 40 = 35
Using vertical angles theorem again, we know the angle opposite 35 degrees is also 35. We found another angle for the middle triangle.
The missing angle for the middle triangle is 180 - 35 - 95 = 50
The angle opposite 50 is 50 because of the vertical- you already know.
Now the left triangle has angles Z, 60 and 50.
m<Z = 180 - 60 - 50
m<Z = 70
Hope this helps!
Does someone mind helping me with this problem? Thank you!
The amount we would have after 40 years will be $8183.27
What is an exponential growth?Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.
Given that, an amount increasing exponentially every two years and with a rate of 15% and the amount is $500, we need to find the amount we would have after 40 years.
Since, the amount is increasing exponentially every two years, therefore,
T = 40 / 2 = 20 years
A = P(1+0.15)²⁰
A = 500(1+0.15)²⁰
A = 500(1.15)²⁰
A = 8183.27
Hence, the amount we would have after 40 years will be $8183.27
Learn more about exponential growth click;
https://brainly.com/question/12490064
#SPJ1
What are the quotient and remainder when 3x^(4)-x^(2) is divided by x^(3)-x^(2)+2?
When [tex]3x^{4}-x^{2}[/tex] is divided by [tex]x^{3}-x^{2}+2[/tex], the quotient is 3x and the remainder is [tex]5x^2-2x[/tex].
To see why, we perform long division as follows:
[tex]3x[/tex]
[tex]x^3 - x^2 + 2 | 3x^4 + 0x^3 - x^2 + 0x + 0[/tex]
[tex]- 3x^4 + 3x^3 - 6x^2[/tex]
-----------------------
[tex]3x^3 - 7x^2[/tex]
[tex]- 3x^3 + 3x^2 - 6x[/tex]
-------------------
[tex]5x^2 - 2x[/tex]
The divisor is [tex]x^3 - x^2 + 2[/tex] and the dividend is [tex]3x^4 - x^2[/tex]. We start by dividing the highest degree term of the dividend by the highest degree term of the divisor, which gives 3x. We then multiply the divisor by this quotient and subtract the result from the dividend. We repeat this process with the resulting polynomial until the degree of the remainder is less than the degree of the divisor.
In this case, the remainder is [tex]5x^2-2x[/tex], which has a degree of 2 (less than the degree of the divisor). Therefore, we have found the quotient and remainder of the division.
For more questions like Division visit the link below:
https://brainly.com/question/12011210
#SPJ11
Distributive Property of 7/8(4+8b)
Answer: 7/2 + 7b
Step-by-step explanation:
When applying the distributive property, you want to start by identifying which value you are distributing. That value in this case will be 7/8.
7/8 is going to be multiplied with 4, then multiplied with 8b, and you will then find the sum of those to products:
( (7/8) * 4 ) + ( (7/8) * (8b) )
The first product simplified will be 7/2.
The second product simplified will be 7b.
The sum of those two products is: 7/2 + 7b.
Hope this helps.
Find the unit rate.
Drove 275 miles in 5 hours
.02 miles per hour
275 miles per hour
50 miles per hour
55 miles per hour
Answer: 55 miles per hour.
To find the unit rate, divide the miles traveled by the time taken:
275 miles ÷ 5 hours = 55 miles per hour
Step-by-step explanation:
write an expression and then solve. three less than one-fourth of the the product of eight thirds and nine
Step-by-step explanation:
3 - (1/4)×(8/3 × 9)
3 - (1/4)×(8×9/3)
3 - (1/4)×(8×3)
3 - (1/4)×24
3 - 24/4
3 - 6 = -3
Find all values of 1 for which det(A) = 0, using the method of this section. A=|λ-6 0 0| . |0 λ 4| . |0 5 λ-1| λ 1=_____ λ 2=_____ λ 3=_____ Fill the upper blank with the greater value of lif it exists. Fill the blank with the symbol "x" if there is no corresponding 1.
A = |λ-6 0 0| . |0 λ 4| . |0 5 λ-1| λ 1= 4.79 λ 2= 4.79 λ3 = 4.79, as the highest value of lif it exists is 4.79. therefore X=4.79
To find the values of λ for which det(A) = 0, we need to solve the equation det(A) = 0. The matrix determinant of a 3x3 matrix A is given by:
[tex]det(A) = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)[/tex]
In this case, the matrix A is:
A = |λ-6 0 0|
|0 λ 4|
|0 5 λ-1|
So, the determinant of A is:
[tex]det(A) = (λ-6)(λ(λ-1) - 4*5) - 0(0(λ-1) - 4*0) + 0(0*5 - λ*0)[/tex]
Simplifying the equation, we get:
[tex]det(A) = (λ-6)(λ^2 - λ - 20)[/tex]
Setting det(A) = 0, we can find the values of λ:
[tex](λ-6)(λ^2 - λ - 20) = 0[/tex]
This equation has three solutions:
[tex]λ 1 = 6λ 2 = (-1 + √81)/2 ≈ 4.79λ 3 = (-1 - √81)/2 ≈ -5.79[/tex]
So, the answer is:
λ 1 = 6
λ 2 = 4.79
λ 3 = -5.79
The greater value of λ is λ 2 = 4.79.
To know more about determinant here:
https://brainly.com/question/4470545
#SPJ11
36.7 divided by 0.7
Answer:
52.4285714286
Step-by-step explanation:
use a calculator
Answer: 52.4
Step-by-step explanation:
Which of the following lists the sides of the triangle in order of length, from longest to shortest?
Answer: EF, DF, DE
Step-by-step explanation:
The smaller the opposite angle, the smaller the side, and vice versa.
∠EDF = 85°
∠DEF = 60° (Because the total degrees in a triangle must be 180°)
∠DFE = 35°
EF, DF, DE
Hope this helps!
How are the side lengths of the preimage and dilated image related?
Answer:
The dilated image has half the dimensions of the pre-image
So the pre-image is dilated by a scale factor of 1/2 (0.5)
Step-by-step explanation:
The side lengths of the dilated image is related to the preimage by a division of 2
How to determine the how the side lengths are relatedFrom the question, we have the following parameters that can be used in our computation:
The figure
Where we have
Pre-Image = PQRS
Image = P''Q'R'S'
From the figure, we can see that
The side lengths of P''Q'R'S' is half of the side lengths of PQRS
This means that
(x, y) = 1/2(x, y)
Hence, the transformation is (x, y) = 1/2(x, y)
Read more about transformation at
brainly.com/question/27224272
#SPJ1