Answer:
8 ft
Step-by-step explanation:
let width = x
then length= x+2
Area = l(w)
=x(x+2)
168 = x^2 + 2x
x^2 + 2x-168=0
Using quadratic formula we get roots :
x= 12, x=-14
x= 12 (as width cannot be in negative)
then length= x+2 = 14
length of rug= length of floor - 4
= 14- 4
= 10
width of rug= width of floor- 4
= 12-4
= 8
Hence the length (the shorter side) of the rug be 8 feet !
Let f(x)=x^2+x−42 . Enter the x-intercepts of the quadratic function in the boxes. x = and x =
We simply have to solve a quadratic equation [tex]ax^2+bx+c=0[/tex] using the quadratic formula
[tex]x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In your case, [tex]a=b=1,\ c=-42[/tex]. So, the formula becomes
[tex]x_{1,2} = \dfrac{-1\pm\sqrt{1+168}}{2} = \dfrac{-1\pm 13}{2}[/tex]
So, if we choose the two signs, we have
[tex]x_1 = \dfrac{-1-13}{2}=-7,\quad x_2 = \dfrac{-1+13}{2}=6[/tex]
Answer:
x = -7, x = 6
Step-by-step explanation:
f(x) = x² + x − 42
You can use the quadratic formula to find the roots (x-intercepts), or, if it's "factorable", you can use the AC method.
Here, a = 1, b = 1, and c = -42.
The product a times c is -42.
Factors of ac that add up to b are +7 and -6.
So the quadratic factors to:
f(x) = (x + 7) (x − 6)
To find the x-intercepts, we set this equal to 0:
0 = (x + 7) (x − 6)
x + 7 = 0, x − 6 = 0
x = -7, x = 6
(1.8•10^1)(7•10^5) looking for answer please
Answer:
1.26 x [tex]10^{7}[/tex]
Step-by-step explanation:
Find the quotient.
48j 5 k 2 ÷ (-3j 3 k)
A) -16j2k
B) -16j3k2
C) -16j3k
For this case we must find the quotient of the following expression:
[tex]\frac {48 * j ^ 5 * k ^ 2} {- 3 * j ^ 3 * k} =[/tex]
We have to:
[tex]\frac {48} {- 3} = - 16[/tex]
By definition of power properties we have:
[tex]\frac {a ^ m} {a ^ n} = a ^ {m-n}[/tex]
So so:
[tex]\frac {48 * j ^ 5 * k ^ 2} {- 3 * j ^ 3 * k} = - 16 * j ^ {5-3} * k^{2-1}=-16*j^2*k[/tex]
Answer:
Option A
F(x)=9x^3+2x^2-5x+4 and g(x)=5x^3-7x+4. what is f(x)-g(x)?
Show all of your steps and write your finial answer in factored form.
Answer: 4x^3+2x^2-12x+8
I am sorry it takes to long to type in the equation of this problem step by step. I only can just give you an answer.
The results of joes survey show that baseball is the favorite sport for 18 out of 25 people. What percent do not like sports?
well if 18 out of 25 like it, then the remaining 7 doesn't like it, namely 7 out of 25.
if we take 25 to be the 100%, what is 7 off of if in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 25&100\\ 7&x \end{array}\implies \cfrac{25}{7}=\cfrac{100}{x}\implies 25x=700\implies x=\cfrac{700}{25}\implies x=28[/tex]
What is the y intercept of the parabola y = x2 + 8x + 6
6
The formula for a quadratic equation (parabola) is y = ax^2 + bx + c, and c is the y-intercept. Following this, the y-intercept of this parabola is 6.
A company makes plastic beach balls with a radius of 2 inches. How many square inches of plastic does the company need to make 10 beach balls? Use 3.14 for mc017-1.jpg and round to the nearest tenth.
Recall the formula mc017-2.jpg.
mc017-3.jpg
mc017-4.jpg
mc017-5.jpg
mc017-6.jpg
Answer:
125.6 square inches of plastic is needed
Step-by-step explanation:
To make 10 plastic beach balls each with a radius of 2 inches, the company would need approximately 502.4 square inches of plastic.
To determine the amount of plastic needed to make 10 beach balls, we first calculate the surface area of one beach ball. The formula for the surface area of a sphere is 4πr². Given the radius of 2 inches, we plug this into the formula:
A = 4πr² = 4 × 3.14 × (2 inches)² = 4 × 3.14 × 4 square inches = 50.24 square inches.
Since this is for one beach ball, we need to multiply this amount by 10, to account for the total plastic needed for 10 beach balls:
Total surface area for 10 beach balls = 50.24 square inches × 10 = 502.4 square inches.
Therefore, the company would need approximately 502.4 square inches of plastic to make 10 beach balls, rounding to the nearest tenth.
Greatest common factor of 12a and 9a^2
Answer:
3aStep-by-step explanation:
[tex]12a=\bold{(3)}(4)\bold{(a)}\\\\9a^2=\bold{(3)}(3)\bold{(a)}(a)\\\\GCF(12a,\ 9a^2)=\bold{(3)(a)}=3a[/tex]
in this diagram below de is parallel to xy.what is the value of y
Answer:
B. 75°
Step-by-step explanation:
When lines that are parallel are crossed by a transversal , angles in matching corners are equal and called corresponding angles
To get the value of the angle;
180°-105°= 75°.................sum of angles on a straight line
This angle corresponds to angle y because of the parallel lines DE and XY
16.72911 liters rounded to the nearest whole is liters.
Answer:
17 liters
Step-by-step explanation:
0.5 and above will make 1, 0.4 and below makes it the same
In the year 2000 the population of Mexico was about 100 million, and it was growing by 1.53% per year. At this growth rate, the function f(x) = 100(1.0153)^x gives the population, in millions, x years after 2000. Using this model, in what year would the population reach 118 million? Round your answer to the nearest year.
Answer:
11 years
Step-by-step explanation:
Set the function f(x) = 100(1.0153)^x = to 118 and solve for x:
100(1.0153)^x = 118
Taking the natural logarithm of both sides, we get:
ln 100 + x ln 1.0153 = ln 118
Then x ln 1.0153 = ln 118 - ln 100, or
= 4.7707 - 4.6052
... which leads to:
4.7707 - 4.6052
x = --------------------------- = 11 years (rounded up from 10.888 )
0.0152
Answer:
11 years
Step-by-step explanation:
Allison, Brianna, and Celeste went on a hike. Allison brought 9 homemade
cookies and Brianna brought 15 cookies she had made. Celeste forgot to bring
treats, but she had $2.16. Allison and Brianna agreed that if the three were to
share the cookies equally, then the two of them should divide Celeste's money
equitably. Celeste agreed. What was the fair way to divide the money?
I don't get this at all PLEASE HELP!
Answer:
Allison = $0.27
Brianna = $1.89
Step-by-step explanation:
The total cookies that the three girls have are:
Allison's cookies + Brianna's Cookies
= 9+15
=24
There is a total of 24 cookies which has to be divided between the 3.
So
Each girl gets 24/3 = 8 cookies.
Since Celeste had no cookies she will have to pay for the 8 cookies.
Allison had 9, she will give one to Celeste
Brianna had 15 out of which she will use 8 for her self and 7 will be given to Celeste.
Celeste is paying 2.16 for 8 cookies.
Price of one cookie = 2.16/8
=$0.27
So, amount that will be given to Allison = 0.27 * 1 = $0.27
Amount that will be given to Brianna = 0.27 * 7 = $1.89
Each person gets 8 cookies. Allison and Brianna each receive $1.08 of Celeste's $2.16.
To find the fair way to divide Celeste's money, we first need to determine how many cookies each person gets when the total number of cookies is divided equally among them.
Total number of cookies = Allison's cookies + Brianna's cookies
Total number of cookies = 9 cookies + 15 cookies
Total number of cookies = 24 cookies
Now, we'll divide the total number of cookies by the number of people (3) to find out how many cookies each person gets:
Number of cookies per person = Total number of cookies / Number of people
Number of cookies per person = 24 cookies / 3
Number of cookies per person = 8 cookies
So each person will get 8 cookies.
Now, since Celeste forgot to bring treats, Allison and Brianna agreed to divide Celeste's money equally between them. To do this fairly, they'll each receive half of Celeste's money.
Celeste's money = $2.16
Now, we'll find out how much each person gets from Celeste's money:
Amount per person = Celeste's money / Number of people
Amount per person = $2.16 / 2
Amount per person = $1.08
So each person will receive $1.08 from Celeste's money.
In summary:
- Each person will get 8 cookies.
- Each person will receive $1.08 from Celeste's money.
1. Which expression represents the following calculation?"Add 4 and 6, then multiply 5,then add 10.
2.Write an algebraic expression for: 9 times the sum of 9b and 2.
3.What is the coefficient in the expression 40a-61=17?
4. Write the algebraic expression into words.
4/5(9+r)+8w.
5.What is the quotient in the expression c=45/d?
Answer:
1. 5(4 + 6) + 1-0
2. 9(9b + 2)
3. 40
4. Nine plus r multiplied by four over five and then added to eight w.
5. The quotient is [tex]\frac{45}{d}[/tex]
Step-by-step explanation:
What is the equation of a circle with center (3, 8) and radius 2?
Answer:
(x - 3)² + (y - 8)² = 4
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (3, 8) and r = 2
(x - 3)² + (y - 8)² = 4 ← equation of circle
The equation of a circle with center (3, 8) and radius 2 will be given as
[tex]( x -3 )^2 + ( y -8 )^2 = 4[/tex].
Equation of circle is given as,
[tex]( x -a )^2 + ( y -b )^2 = r^2[/tex]
where,
(a,b) are the coordinates of the center of the circle in form (x, y),
r is the radius of the circle.
Now, the equation of a circle with center (3, 8) and radius 2.
Given to us,
a = 3,
b = 8,
r = 2.
substituting the values,
[tex]( x -a )^2 + ( y -b )^2 = r^2[/tex]
[tex]( x -3 )^2 + ( y -8 )^2 = 2^2[/tex]
[tex]( x -3 )^2 + ( y -8 )^2 = 4[/tex]
Hence, the equation of a circle with center (3, 8) and radius 2 will be given as [tex]( x -3 )^2 + ( y -8 )^2 = 4[/tex].
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Arnoldo needs to write this system in slope-intercept form. Which shows how he could do that? 3x-2y=6 0.4(2oy+15)=x
Answer with explanation:
→The equation of line which we have to write in slope intercept form is:
3 x -2 y=6
The equation of line in slope Intercept form is given as:
y = m x +c
Where, m=Slope of line
c=Y- intercept
Slope Intercept form of line can be as follows :
[tex]\Rightarrow 3 x-2 y=6\\\\\Rightarrow \text{Adding 2y on both sides}\\\\\Rightarrow 3 x-2 y+2 y=2 y+6\\\\\Rightarrow 3 x= 2 y+6\\\\\text{Dividing both sides by 3}\\\\\Rightarrow x=\frac{2y}{3}+\frac{6}{3}\\\\\Rightarrow x=\frac{2y}{3}+2[/tex]
Answer:
y = three-halves x minus 3
y = one-eighth x minus three-fourths
Step-by-step explanation:
match each complex number with its equivalent expression
i^223 = -i
i^82 = -1
i^113 = i
i^48 = 1
Match each complex number with its equivalent by using the complex plane, polar coordinates, complex conjugates, and Euler's equation.
Explanation:Matching each complex number with its equivalent expression involves understanding the complex plane, complex conjugates, and Euler's formula. A complex number z is represented by z = a + ib, where a is the real part and b is the imaginary part. Converting this to polar form involves finding the magnitude r and the angle θ, where r = (a² + b²)½ and θ = tan⁻¹(b/a). Euler's formula, z = r exp(iθ), can be used to express the complex number in terms of its magnitude and angle: z = r cos(θ) + ir sin(θ). The complex conjugate of z is z* = a - ib, and it is found by changing the sign of the imaginary part.
25 points!!! In the graph below, line k, y=-x makes a 45° angle with the x- and y-axis.
Complete the following:
R sub k open circle R sub X : (2, 5)
(-5, -2)
(-5, 2)
(5, -2)
Please include the explanation for this thank you!
Step-by-step explanation:
First, reflect over line k:
(2, 5) → (-5, -2)
Then, reflect over the x-axis:
(-5, -2) → (-5, 2)
Consecutive angles in a parallelogram are?
Hello There!
Consecutive Angles In Parallelograms Are "Supplementary"
"Supplementary Angles" Are Angles That Have A Sum of 180 Degrees
Answer:
Step-by-step explanation:
Are "Supplementary
Choose the compound inequality that can be used to solve the original inequality |3x – 5| > 10
Answer: C. would be your option
Step-by-step explanation:
Answer:
3x – 5 < –10 or 3x – 5 > 10
Answer choice C on Edge
PLEASE HELP ME!!!!
The figure shows the location of 3 points around a lake. The length of the lake, BC, is also shown.
Which of the following options is closest to the distance (in miles) between points A and B?
2.24 miles
2.65 miles
3.74 miles
5.29 miles
Answer:
AB² = VAC²-BC²
= V8²-6²
= V64-36 = V28
AB = V7×4 = 2V7 = 5.29
Need help with financial algebra
Answer: [tex]c(x) =\left \{ {{18\qquad 0<x\leq 3} \atop {6.5x+18\quad x>3}} \right.[/tex]
Step-by-step explanation:
The first equation is c(x) = 18 when x is between 0 and 3 (including 3).
The second equation is c(x) = 6.5x + 18 when x is greater than 3
Factor 3k^2+13k-56.
Answer:
(k + 7)(3k - 8)
Step-by-step explanation:
To factor the quadratic
Consider the factors of the product of the k² term and the constant term which sum to give the coefficient of the k- term
product = 3 × - 56 = - 168 and sum = + 13
The factors are + 21 and - 8
Use these factors to split the k- term
3k² + 21k - 8k - 56 ( factor the first/second and third/fourth terms )
= 3k(k + 7) - 8(k + 7) ← factor out (k + 7)
= (k + 7)(3k - 8)
what is the solution to the system of equations represented by these two lines ?!!
The solution is the point where the two lines intersect, so it is (3,1)
A sales representative from a local radio station is trying to convince the owner of a small fitness club to advertise on her station. The representative says that if the owner begins advertising on the station today, the club's total number of members will grow exponentially each month. She uses the given expression to model the number of club members, in hundreds, after advertising for t months. 1.8(1.02)^12t What does the value 1.8 represent?
Answer:
The value 1.8 represent the club's total number of members today or the present number of members
Step-by-step explanation:
Given an exponential function;
[tex]y=ab^{x}[/tex]
b is the base or the growth factor
a is the initial value, that is the value of y when x = 0
We have been given the exponential function;
[tex]y=1.8(1.02)^{12t}[/tex]
The value 1.8 simply represents the initial value of y. Plug in t = 0 in the equation;
[tex]y=1.8(1.02)^{12(0)}=1.8[/tex]
Therefore, the value 1.8 represent the club's total number of members today or the present number of members
What is the surface area of the pyramid
224ft
460ft
112 ft
336ft
The surface area of the pyramid is 160ft^2
Explanation:To find the surface area of a pyramid, we need to calculate the sum of the areas of all its faces. A pyramid has 4 triangular faces and 1 square base. The formula for the surface area of a pyramid is: Surface Area = Base Area + (0.5 × Perimeter of Base × Slant Height). In this case, the base side of the pyramid is 8ft and the slant height is 6ft.
First, we calculate the perimeter of the square base, which is 4 times the length of the base side: Perimeter = 4 × 8ft = 32ft.
The base area of the pyramid is found by squaring the length of one side of the base: Base Area = (8ft)^2 = 64ft^2.
Now we can substitute the values into the formula: Surface Area = 64ft^2 + (0.5 × 32ft × 6ft) = 64ft^2 + 96ft^2 = 160ft^2.
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The surface area of a pyramid with an 8 ft side length and a 10 ft slant height is 224 square ft. Hence, option A is correct.
To find the surface area of a pyramid with a square base, we need to calculate both the base area and the lateral surface area.
The side length of the square base is 8 ft, so the base area is:
Base Area = side × side = 8 ft × 8 ft = 64 square ftThe slant height of the pyramid is 10 ft, and the side length of the base is 8 ft. Each triangular face of the pyramid has a height (slant height) and base equal to the side of the square base. The area of one triangular face is:
Area of one triangle = 1/2 × base × slant height = 1/2 × 8 ft × 10 ft = 40 square ftSince a square-based pyramid has 4 triangular faces, the total lateral surface area is:
Lateral Surface Area = 4 × Area of one triangle = 4 × 40 square ft = 160 square ftAdding the base area and the lateral surface area gives the total surface area:
Total Surface Area = Base Area + Lateral Surface Area = 64 square ft + 160 square ft = 224 square ftTherefore, the total surface area of the pyramid is (Option A) 224 square ft.
Complete Question:
What is the surface area of the pyramid with slant height 10 ft and base 8 ft ?
A. 224ft
B. 460ft
C. 112 ft
D. 336ft
one cook can make enough food for 350 people a night. how many cooks are needed to feed 2,944 a night?
Answer:
9
Step-by-step explanation:
the answer is 8.4 so it might not be rounded up but I figure what about the other people?
9 chefs are needed. you have to divide 2,944 by 350
A fountain is located between two trees. Each tree has a height of 60 feet. The angles of elevation from the
base of the fountain to the top of each tree are 64° and 48° as shown below.
What is the horizontal distance between the two trees (rounded to the nearest foot)
A 40
B 837
C 147
D 190 ft
The answer is:
The correct option is:
B) 83 feet
Why?To solve the problem, we need to use the following trigonometric identity:
[tex]Tan(\alpha)=\frac{Opposite}{Adjacent}[/tex]
Which, translated to our problem, will be:
[tex]Tan(\alpha)=\frac{Height}{Base}[/tex]
We are given two triangles, and we know their height and their angles between their hypothenuse and their bases.
So,
For the first triangle, we have:
[tex]height=60ft\\\alpha=64\°[/tex]
So, using the trigometric identity of the tangent, we have:
[tex]Tan(\alpha)=\frac{Height}{Base}\\\\Tan(64\°)=\frac{60ft}{Base}\\\\Base=\frac{60ft}{Tan(64\°)}=\frac{60ft}{2.05}=29.27ft[/tex]
Therefore, we have that the base of the first triangle is equal to 29.27 feet.
For the second triangle, we have:
[tex]height=60ft\\\alpha=48\°[/tex]
So, using the trigometric identity of the tangent, we have:
[tex]Tan(\alpha)=\frac{Height}{Base}\\\\Tan(48\°)=\frac{60ft}{Base}\\\\Base=\frac{60ft}{Tan(48\°)}=\frac{60ft}{1.11}=54.05ft[/tex]
Therefore, we have that the base of the second triangle is equal to 54.05 feet.
Now, to calculate the horizontal distance between the two trees (x), we need to use the following formula with the obtained values of both triangles:
[tex]HorizontalDistance=FirstTriangleBase+SecondTriangleBase\\\\HorizontalDistance=29.27ft+54.05=83.29ft[/tex]
Hence, we have that the distance between the two trees rounded to the nearest foot is 83 feet.
Have a nice day!
The function f(x) = 50(0.952)x, where x is the time in years, models a declining feral cat population. How many feral cats will there be in 9 years?
a) about 428 feral cats
b) about 42 feral cats
c) about 51 feral cats
d) about 459 feral cats
I need the answer along with an explanation so that I can know how to solve the other problems on my own :) :) :)
Answer:
A)
Step-by-step explanation:
Since we are given the function, we can simply plug in the x as 9. So we get 50(0.952)9. Solving this, we get 450(.952) and this is about 428. SO our answer is a) about 428 feral cats.
There will be 428 feral cats in 9 years.
How to find the value of something when a function is given?We can substitute the given number in the function to find the required value here, years are represented by x. Therefore, we must substitute the value of x = 9 in the function to find the population of feral cats in 9 years.
We can find the population as follows:The function is given as:
f(x) = 50(0.952)x.
We have to find the number of feral cats in 9 years. Therefore, the value of x is 9.
Now, we can substitute the value of x in the function. This can be done as follows:
f(x) = 50(0.952)x
f(9) = 50(0.952)*9
f(9) = 50(8.568)
f(9) = 428.4
f(9) ≈ 428
We have found the number of feral cats in 9 years. The number of feral cats that will be alive after 9 years is found to be 428.
Therefore, we have found that there will be 428 feral cats in 9 years. The correct answer is option A.
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Given f(x) = 3x - 1 and 9(x) = 2x-3, for which value of x does g(x)=f(2)?
Answer:
g(x) = f(2) at x = 4
Step-by-step explanation:
Assuming that you meant g(x) = 2x - 3:
Set f(2) = g(x) and solve the resulting equation for x:
f(2) = 3(2) - 1 = g(x) = 2x - 3.
Thus, 6 - 1 = 2x - 3.
Adding 3 to both sides and simplifying the result, we get:
8 = 2x, or x = 4.
g(x) = f(2) at x = 4.
Stay the amplitude and maximum output for the function!!! Help needed!!
ANSWER
The amplitude is 2 and the maximum value is 2.
EXPLANATION
The given function is
[tex]f(t) = 2 \sin(t) [/tex]
This function is of the form:
[tex]f(t) = a\sin(bt) [/tex]
The amplitude of this function is
[tex] |a| [/tex]
Hence the amplitude is
[tex] |2| = 2[/tex]
Since the amplitude is 2, and there is no vertical shift, it means the function is bounded by
y=-2 and y=2.
The maximum value is :
2