Answer:
L = [tex]\sqrt{113}[/tex] +4
W = [tex]\sqrt{113}[/tex] -4
or L = 14.63 ft, and W = 6.63 ft
Step-by-step explanation:
Let L be the length and W the width.
We are told that the "length of a rectangle is 8 feet more than its width:"
L = W+8
Area of the rectangle is given by L*W, and is 97 [tex]ft^{2}[/tex]
L*W = 97
Substituting L=W+8, we get:
(W+8)W=97 [tex]ft^{2}[/tex]
[tex]W^{2}[/tex] + 8W = 97
[tex]W^{2}[/tex] + 8W - 97 = 0
The roots to this equation are:
-4-[tex]\sqrt{113}[/tex], and[tex]\sqrt{113}[/tex] -4Only the second gives a positive value, so W = [tex]\sqrt{113}[/tex] -4
Since L=W+8, the length, L, is [tex]\sqrt{113}[/tex] -4 + 8 or [tex]\sqrt{113}[/tex] +4
In decimal:
L = 14.63 ft, and W = 6.63 ft
11] You buy a house for $175,000. The economy goes
down and your house is losing value at 4% semi-annually.
How much is your house worth in 5 years?
Answer:
4% of 175,000 is 7,000
7,000x 5=35,000
175,000-42,000 equals 140,000 the value of the house
To estimate the number of students in your school who play a sport outside of school, you decide to survey the players on the boys' baseball team.
The length of a rectangular garden is 2 m greater than the width. The area is 80 m^2. Find the dimensions of the garden.
The width of the garden is ___m.
The length of the garden is ___m.
Answer:
Length of rectangle = 10 mWidth of the Rectangle = 8 mStep-by-step explanation:
Given :-
Length of a Rectangular garden is 2m greater than the width .Area of garden = 80 m²To Find :-
Dimensions of the gardenSolution :-
Let's assume:
Width of the rectangle = xLength of the rectangle = x + 2We know that,
Area of rectangle = Length × Width↠ (x)(x + 2) = 80
↠ x² + 2x - 80 = 0
↠ x² + 2x - 80 = 0
↠ x² + 10x - 8x - 80 = 0
↠ x(x +10) -8 (x + 10) = 0
↠ (x-8) (x + 10) = 0
↠ x = 8 or -10
↠ x = 8
Hence,
Width of the rectangle = x = 8 mLength of the rectangle = x + 2 = 10 mAnswer:
Given:-
Length of rectangular garden is 2m longer than its widthArea of Rectangular garden is 80m²To Find :-
Dimensions of Rectangular gardenSolution:-
Let the width be x and length be x + 2According to the question ,
Area = 80m²
putting the known values ,
(X)(X+2) = 80m
x² +2x - 80= 0
x² +10x-8x -80m= 0
x(x + 10) - 8(x+10) = 0
(x-8) = 0 ; (x+10) = 0
X = 8 ; X = -10
As dimensions can not be negative so , X = 8Length = X + 2 ; 10 m
Width = X ; 8 m
In a right triangle, sin(β) = 0.292. If the hypotenuse of the triangle has a length of 17.5 cm, what is the length of the side adjacent to angle β. Note: You will also need to use the Pythagorean theorem to answer this question.
16.7 cm
5.1 cm
11.4 cm
4.1 cm
So, the length of the side adjacent to angle β is approximately 17.15 cm. triangle Therefore, the closest option is 16.7 cm.
What is a triangle?A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.
sin(β) = opposite/hypotenuse
[tex]hypotenuse^2 = adjacent^2 + opposite^2\\17.5^2 = adjacent^2 + opposite^2\\306.25 = adjacent^2 + opposite^2\\[/tex]
opposite = sin(β) x hypotenuse = 0.292 x 17.5 = 5.095 cm
[tex]306.25 = adjacent^2 + 5.095^2\\306.25 - 5.095^2 = adjacent^2\\294.81 = adjacent^2\\[/tex]
√294.81 = adjacent
So, the length of the side adjacent to angle β is approximately 17.15 cm. Therefore, the closest option is 16.7 cm.
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
Is there any way for my to view my full highschool transcript online
sorry brain ly won't let me tell you I'm sorry
What is the true solution to the equation below? l n e superscript l n x baseline l n e superscript l n x squared baseline = 2 l n 8
The true solution of the logarithmic equation [tex]\ln e^{\ln x} + \ln e^{\ln x^2} = 2\ln 8[/tex] will be 4.
What is a logarithm?Logarithms are another way of writing exponent. A logarithm with a number base is equal to the other number. It is just the opposite of the exponent function.
The logarithmic equation is given as
[tex]\ln e^{\ln x} + \ln e^{\ln x^2} = 2\ln 8[/tex]
We know that the formula
[tex]\ln e = 1\\\\\ln b^a = a \ln b\\\\\ln a + \ln b= \ln a +b[/tex]
Then we have
[tex]\begin{aligned} \ln x \times \ln e + \ln x^2 \times \ln e = \ln 8^2\\\\\ln x + \ln x^2 = \ln 64\\\\\ln x*x^2 = \ln 64 \end{aligned}[/tex]
Then take antilog, then we get
[tex]\rm x^3 = 64\\\\x^3 = 4^3 \\\\x \ =4[/tex]
More about the logarithm link is given below.
https://brainly.com/question/7302008
Answer:
b, x=4
Step-by-step explanation:
edge 2022
50 points!
Ahmed needs to take a close-up shot of an orange for his art class. He frames a shot of an orange as shown below, so that the lines of sight form tangents to the orange. If the measure of the cameras viewing angle is 34 degrees, what is angle ACB?
Answer:
either 34 or 214
Step-by-step explanation:
Rounded to the nearest tenth of a centimeter, what is the length of arc lmn? 7.9 cm 10.2 cm 12.6 cm 14.2 cm
The length of arc LMN is the number of units on the arc
The length of arc LMN is 14.2 cm
How to calculate the length of the arc?The given parameters are:
Arc LM = 6.3 cmRadius, r = 6 cmAngle MON = 75 degreesStart by calculating the length of arc MN using:
[tex]MN = \frac{\theta}{360} * 2\pi r[/tex]
So, we have:
[tex]MN = \frac{75}{360} * 2 * 3.14 * 6[/tex]
Evaluate the product
MN = 7.85
The length of arc LMN is then calculated using:
LMN = LM + MN
This gives
LMN = 6.3 + 7.85
Evaluate the sum
LMN = 14.15
Approximate
LMN = 14.2
Hence, the length of arc LMN is 14.2 cm
Read more about arc lengths at:
https://brainly.com/question/15589041
Answer:
D ( 14.2 )
Step-by-step explanation:
edg 2022
If m=5, evaluate m^18 divide by m^11
Answer:
78125
Step-by-step explanation:
Using a rule of powers, a^x / a^y = a^(x-y)This gives you m^(18 - 11) = m^7M is 5, so it would be 5^7 or 78125Decide whether y is a function of x.
x2 + y2 = 1
Answer:
Not a function.
Explanation:
x² + y² = 1 is not a function.
Here's the breakdown!
Looking at the type of equation, It is a circle equation.
In a circle equation, y value is not completely determined by the x value.
Shown:
x² + y² = 1y² = 1 -x²y = ±√1 -x²There are multiple values of x for each value of y
Answer:
A function can be described as one-to-one or many-to-one, i.e. each value in the domain ([tex]x[/tex]-values) is mapped to a single value in f(x).
An example of a one-to-one function is a linear function. For every value of x there is one value of y.
An example of a many-to-one function is a quadratic function, where 2 different x-values map to one y-value.
[tex]x^2+y^2=1[/tex] is not a function as some values of [tex]x[/tex] are mapped to two different values of f(x).
For example, let x = 0.5
[tex]\implies (0.5)^2+y^2=1[/tex]
[tex]\implies y^2=0.75[/tex]
[tex]\implies y=\pm\sqrt{0.75}[/tex]
So as x = 0.5 maps to √0.75 and -√0.75, it is one-to-many, and is therefore not a function.
HELPEHEGEDHGDGXCCVCCXVV
Step-by-step explanation:
1) 7x+3y=19
2)2x-7y=12
3) x=5, y=0
4) x=15/2, y=(-63/4)
5) x=9, y=92
6) x=(-2) , y=(-9)
7) x=5, y=(-2)
8) x=2, y=2
The radius of a circle is 3 meters. What is the circle's circumference?
r=3 m
Use 3. 14 for .
Answer: The circle's circumfrence is 18.84
Step-by-step explanation:
When you are finding the circumference of a circle you use the formula
[tex]C=2\pi r[/tex]
[tex]C=2*3.14*3[/tex]
[tex]C=18.84[/tex]
100 POINTS PLEASE ANSWER
What do you think? How do superheroes help teach us about the world we live in? What values should superheroes represent?
Respond in a cohesive paragraph that includes the following:
- provide 3 values and elaborate their importance
- address what your superhero would teach society
- provide a name and superpower
Answer:
Superheroes are meant to inspire. They represent someone we are not, or someone that can do things that we can't. They can provide an escape into a world where someone is there for us even when our protectors or our medical and social institutions have let us down.
Does the table represent a linear or nonlinear function? Explain
Answer:
The table represents a nonlinear function.
Step-by-step explanation:
A linear function has a constant rate of change. However, the y values in the table do not have a constant rate of change. 4pi - pi = 3 pi, 9pi - 4pi = 5pi and so on. The values change each time, so it is a nonlinear function.
This is the answer that I got, hopefully I am correct on this one.
a 2014 mustang originally costs $25000.00 and depreciates at a rate of 8% per year. What is the cost of the car after 7 years?
While cleaning out the garage, Nelson discovers some containers of oil that need to be taken in for recycling. The containers hold 25 fluid ounces, 2 cups, and 7 quarts, respectively. Find the total amount of oil ready to be recycled (in fluid ounces)
Answer:265
Step-by-step explanation: 2 cups is 16fluid Ounce, 7quaryz is 224 fluid ounce
Total will 265 fluid ounce (225+16+224)
Identify the quadrants in following coordinate plane
I NEED ANWSER FAST!!!!!
Answer:
Step-by-step explanation:
starting from the upper right corner and going counterclockwise.
upper right: I
upper left: II
bottom left: III
bottom right: IV
Please help! The possible answers and the question are in the photo below.
Answer:
B
Step-by-step explanation:
The average is in the limits
Julian scored 24 points over the first 12 games of the basketball season. Disappointed with his performance, he started spending extra time after practice working on his shot. He scored 112 points over the last 16 games of the season. How many more points per game did Julian score in the last 16 games of the season
Answer:
5 more points
Step-by-step explanation:
To find the ppg of the first 12 games you do 24/12
for the 16 games: 112/16
24/12=2
112/16=7
7-2=5
What is the difference? startfraction x over x squared minus 2 x minus 15 endfraction minus startfraction 4 over x squared 2 x minus 35 endfraction startfraction x squared 3 x 12 over (x minus 3) (x minus 5) (x 7) endfraction startfraction x (x 3 minus 12) over (x 3) (x minus 5) (x 7) endfraction startfraction x squared 3 x 12 over (x 3) (x minus 5) (x 7) endfraction startfraction x squared 3 x minus 12 over (x 3) (x minus 5) (x 7) endfraction
The difference is StartFraction x squared + 3 x minus 12 Over (x + 3) (x minus 5) (x + 7) EndFraction.
What is a quadratic equation?
A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
The given expression is
[tex]\frac{x}{x^{2} -2x-15} -\frac{4}{x^{2} +2x-35}[/tex]
[tex]\frac{x}{x^{2} -5x+3x-15} -\frac{4}{x^{2} +7x-5x-35}\\\frac{x}{(x-5)(x+3)} -\frac{4}{(x-5)(x+7)}[/tex]
by Taking LCM
[tex]\frac{x(x+7)-4(x+3)}{(x-5)(x+3)(x+7)} \\[/tex]
[tex]\frac{x^{2} +3x -12}{(x-5)(x+3)(x+7)} \\[/tex]
Learn more about a quadratic equation;
https://brainly.com/question/2263981
Answer: The correct answer is D on edge
Step-by-step explanation:
got it right on the pretest
Brandon recorded which donut his nephew picked for breakfast the past few months.
cake donuts 2
chocolate frosted donuts 2
jelly-filled donuts 5
glazed donuts 3
Considering this data, how many of the next 20 donuts Brandon's nephew picks for breakfast would you expect to be glazed donuts?
Answer:
5
Step-by-step explanation:
2+2+3+5=12
12/3=4
4 divided by 20 =5 glazed donuts
Given: AD = BC and AD || BC
Prove: ABCD is a parallelogram.
Answer:BC AND AD is parellogram since it has sides.
Step-by-step explanation:
SOLVE THIS!!!! CAUSE...WELL BRAINLY
please fill in the blanks
Time is an illusion~
that helps things make ____
so we're always living in the present tense
it is unforgiving when a good thing ____
Answer: sense happens
Step-by-step explanation:
Given: PO IPO
Prove:
(-o) (mat) = -1
m
PO
po
P'(-b, a)
P (a, b)
Y-Y
1.me=
PO X2-X
C-a
Q' (d.c)
Q (c,d)
Check
Answer: d-b
Step-by-step explanation:
A cone has a volume of 923.16 cubic meters and a height of 18 meters. What is its radius?
A computer monitor is 20 inches wide. The aspect ratio, which is the ratio of the width of the screen to the height of the screen, is16: 9.
What is the length of the diagonal of the screen, to the nearest whole inch?
Enter your answer in the box
Answer
23
Step-by-step explanation
16/9=width/height
20 is the width of the computer monitor so you would put width as 20
20/x then you would cross multiply to find the height which is x.
20 x 9=180
Then you would divide 180 by 16.
180/16=11.25
So now you have the width and the height 20/11.25=width/height
Then you do the pythagorean theorem a^2+b^2=c^2=20^2+11.25^2=526.5.6^2.Then you would round you answer to get 526.6 Then you would find the square root of 526.6 which is 22.9. Then you would round the answer to get 23.
Solve for the formula for r. C=2πr Question 2 options:
r=C2π
r=2Cπ
r=2πC
r=2πC
Answer:
r = [tex]\frac{C}{2\pi }[/tex]
Step-by-step explanation:
C = 2πr ( isolate r by dividing both sides by 2π )
[tex]\frac{C}{2\pi }[/tex] = r
( Find the Mean Absolute Deviation and the Mean with an explanation )
How many siblings do the students in my math class have?
3,2,2,5,4,1,3,4,1,0,3,2,1,1,6,3
The mean of the data is 1.31, while the mean absolute deviation is 2.56.
What is the Mean Absolute Deviation?The mean is the average of a data set, while the mean absolute deviation is the average distance of the each data point from the mean.
Given the data:
3,2,2,5,4,1,3,4,1,0,3,2,1,1,6,3
Find the Mean:
Mean = (3 + 2 + 2 + 5 + 4 + 1 + 3 + 4 + 1 + 0 + 3 + 2 + 1 + 1 + 6 + 3)/16 = 41/16 Mean = 2.5625
Find the Mean Absolute Deviation:
Mean abosolute deviation = (3 - 2.5625) + (2 - 2.5625) + (2 - 2.5625) + (5 - 2.5625) + (4 - 2.5625) + (1 - 2.5625) + (3 - 2.5625) + (4 - 2.5625) + (1 - 2.5625) + (0 - 2.5625) + (3 - 2.5625) + (2 - 2.5625) + (1 - 2.5625) + (1 - 2.5625) + (6 - 2.5625) + (3 - 2.5625) / 16
Mean abosolute deviation = 21/16 = 1.3125
Therefore, the mean of the data is 1.31, while the mean absolute deviation is 2.56.
Learn more about the mean absolute deviation on:
https://brainly.com/question/447169
State reasons why these two triangles are congruent
What do you think would be a good way to select a random sample of all the students at the 12 schools in the school district?
Step-by-step explanation:
At a birthday party, teams for a game are chosen by putting everyone's name into a jar, and then choosing the names at random for each team