Answer:
l = 10 feet
m = 30 feet
n = 25 feet
Total Perimeter = 65 feet
Step-by-step explanation:
The perimeter of a trianlge is the sum of its three sides, and in this case is equal to 65 feet.
65 feet = l + m + n
l + m + n = 65
We also know that:
l = (1/3)m, and
n = l+m-15
Substitute these definitions of l and n into the original equation:
l + m + n = 65
[(1/3)m] + m + [l+m-15] = 65
[(1/3)m] + m + [[(1/3)m]+m-15] = 65
Simplify:
(1/3)m + m + (1/3)m + m - 15 = 65
2m + (2/3)m = 80
(6/3)m + (2/3)m = 80
(8/3)m = 80
m = 80*(3/8)
m = (10)*(3)
m = 30 feet
Since l = (1/3)m, l = 10 feet
Since n = l+m-15, n = 10 + 30 - 15, or 25 feet
The three sides are
l: 10 feet
m: 30 feet
n: 25 feet
Total = 65 feet
Determine the equation of the hyperbola with and vertices (1, 6) and (1, -12) and
asymptotes y = 3x - 6 and y=-3x.
Option:
The equation of the hyperbola with and vertices (1, 6) and (1, -12) and
asymptotes y = 3x - 6 and y=-3x is [tex]$\frac{(y+3)^2}{9}-\frac{(x-1)^2}{81}=1$[/tex]
The answer provided below has been developed in a clear step by step manner.
Given asymptotes [tex]$\mathrm{y}=3 \mathrm{x}-6$[/tex] and [tex]$\mathrm{y}=-3 \mathrm{x}$[/tex] and
vertices (1,6) and (1,-12)
What is hyperbola ?
Standard hyperbola through origin when values of x for the vertices are equal. [tex]$\frac{y^2}{b^2}-\frac{x^2}{a^2}=1$[/tex]
Now solve the asymptotes [tex]$\mathrm{y}=3 \mathrm{x}-6$[/tex] and [tex]$\mathrm{y}=-3 \mathrm{x}$[/tex]
After solving we get [tex]$\mathrm{x}=1 \quad$[/tex]and [tex]$\quad \mathrm{y}=-3$[/tex]centre =(1,-3)
translation in form of [tex]$\mathrm{x}_1$[/tex] and [tex]$\mathrm{y}_1$[/tex]
[tex]$\mathrm{x}_1=\mathrm{x}-1 \quad$[/tex] and [tex]$\quad \mathrm{y}_1=\mathrm{y}+3$[/tex]
Distance from vertices (1,6) and (1,-12) to centre (1,-3) is [tex]$9=\mathrm{a}$[/tex]vertical symmetry the asymptotes have a slope [tex]$=\pm 3=a / b$[/tex] so [tex]$\mathrm{b}=\frac{9}{3} \Rightarrow \mathrm{b}^2=9$[/tex]
Put all the values of a and b into original equation
[tex]$$\begin{aligned}& x_1=x-1 \quad \text { and } \quad y_1=y+3 \\& \Rightarrow \frac{(y+3)^2}{3^2}-\frac{(x-1)^2}{9^2}=1 \\& \Rightarrow \frac{(y+3)^2}{9}-\frac{(x-1)^2}{81}=1\end{aligned}$$[/tex]
To learn more about vertices visit:https://brainly.com/question/27029296
#SPJ1
Question 2-4
Dad mowed 60% of the yard in 30 minutes. At this rate, how many minutes will it take him to mow the
entire yard?
minutes
The number of minutes will it take him to mow the entire yard will be 50 minutes.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
Dad mowed 60% of the yard in 30 minutes.
Let 'A' be the entire area of the lawn and 'x' be the total time to mow the entire lawn. Then 60% of the lawn is given as,
⇒ 60% of A
⇒ 0.60A
The ratio of the area of the lawn to time remains constant. Then the equation is given as,
0.60A / 30 = A / x
x = 30 / 0.60
x = 50 minutes
The number of minutes will it take him to mow the entire yard will be 50 minutes.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ1
What would you use to graph the inequality y ≥ 4 ?
The coordinate plane
A number line
The origin
This inequality cannot be graphed.
A number line use to graph the inequality y ≥ 4.
How do you graph an inequality?Treat the,, >, or sign as a = sign when putting an inequality on a graph. Graph the equation as a dotted line if the inequality is either or. Graph the equation as a solid line if the inequality is either or. The xy plane is split along this line into two regions: one that fulfils the inequality and the other that does not.Pick a point that is not on the line next. Verify if the inequality is satisfied by this point. The area containing that point should be shaded if it satisfies the inequality. Shade the area that does not contain that point if it does not satisfy the inequality. Every point in the shady area satisfies the inequality.Explanation :
y = − 4 is a horizontal line at -4, since
y ≥ − 4, the area above -4 will be shaded and the line will be solid since it is greater than AND equal to:
graph{y>=-4 [-10, 10, -5, 5]}
To learn more about graph an inequality refer to :
https://brainly.com/question/11234618
#SPJ1
Alice's savings account earns 3.75% interest per year. If she put $9,500 into the savings account, how much interest would be earned in a year?
Hello,
I hope you and your family are doing well!
To calculate the amount of interest earned on a savings account, you can use the following formula:
interest = principal * rate * time
In this case, the principal is $9,500, the rate is 3.75%, and the time is 1 year. Plugging these values into the formula, we get:
interest = $9,500 * 3.75% * 1 year = $356.25
So, in a year, Alice would earn $356.25 in interest on her savings account.
-----
Please consider giving this 5 stars and brainliest if you find it helpful.
Happy Holidays!
CC wants to buy online tickets for a concert. two options are given here. option 1: $85 for each ticket plus a shipping fee of $15 option 2: $95 for each ticket and free shipping. select the equation for option 2.
a. y=85x+15
b. y=-95x
c. y=15x+85
d. y=95x
Answer:
Step-by-step explanation:
i want to know too:((
The equation for the second plan is y = 95x, therefore, option (d) is correct.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, the second plan costs $95 for each ticket and free shipping.
The total cost, y, for x tickets are:
y = 95x.
Hence. the equation for the second plan is y = 95x, therefore, option (d) is correct.
Learn more about equations here:
https://brainly.com/question/10413253
#SPJ1
Find the 96th term of the arithmetic sequence 3, -14, -25,
the 96th term of the arithmetic sequence 3, -14, -25 is -1048.
What is an arithmetic sequence?An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term.
The general form of an arithmetic sequence is
aₙ = a₁ + d(n-1)
where aₙ is the nth term, a₁ is the initial term, and d is the common difference.
Given that n =96, a₁=-3, and d = -11
Substituting these value in the above equation
a₉₆ = -3 - 11(96-1) = -3 - (11*95) = -3-1045 = -1048
Hence, -1048 is the 96th term of the given arithmetic sequence.
To learn more about arithmetic sequence, use the link given below:
https://brainly.com/question/15412619
#SPJ1
A person saves 12.5% of his income how much does he spend in a month if his monthly income is Rs 10,000. Give full explanation 
If person saves 12.5% of his income how much does he spend in a month if his monthly income is Rs 10,000 then he spends 8750 of his monthly income.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that a person saves 12.5% of his income.
The monthly income of the person is 10000.
We need to find how much he spend in a month.
Convert 12.5 % to the decimal value by dividing 12.5 by 100.
12.5/100=0.125
Now multiply 0.125 with 10000
0.125×10000
1250
Subtract 1250 from 10000
10000-1250
8750
Hence, person spends 8750 of his monthly income.
To learn more on Percentage click:
https://brainly.com/question/28269290
#SPJ1
Find BR if D is the circumcenter of △ABC, CD=11.1 and RD=5.2. Round to the nearest tenth
Answer:
BR=9.8
Step-by-step explanation:
a²+b²=c²
5.2²+b²=11.1²
27.04+b²=123.21
b²=96.17
b=[tex]\sqrt{ 96.17}[/tex]
b=9.8
If you spin a 3 circle spinner 120 times, about how many times would you expect it to land on B?
Around 80 times we should expect it to land on B.
What is time?Time is basically a measure of non-stop, consistent change in our own surroundings. Usually we can see through a specific point of view. Concept of time is self-evident and intuitive. Describing the fundamental nature of time is quite difficult.
As per the given condition-
Spin circle=3
Time = 120 sec
the total is 3
the red and orange equals to 2
2/3 times 120
240/3
=80 times
Thus, the correct answer is 80 times.
To know more about time click-
https://brainly.com/question/26046491
#SPJ1
Antonio is saving money to buy a CD player that costs
$120. He also wants to buy some CDs to play in it.
New CDs cost $15 and used CDs cost $5. Antonio
wants to buy the same number of new and used CDs.
Write and solve an equation to find the number of each
type of CD Antonio can buy if he spends all of the $200
he has saved.
Equation : 200 = 15x + 5y + 120
Consider 3x=y. a. Complete the table for the equation. x: 0 1 2
The values of y when x is 0 1 2 is 0,3,6
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
To get the values of y, we substitute for the values of x in the equation 3x=y
When x = 0
3(0)=y; y = 0
When x = 1
3(1)=y; y = 3
When x = 2
3(2)=y; y = 6
x | 3x | y | (x, y)
----------------------------------------
0 | 3(0) | 0 | (0, 0)
----------------------------------------
1 | 3(1) | 3 | (1, 3)
----------------------------------------
2 | 3(2) | 6 | (2, 6)
learn more about the equation at:https://brainly.com/question/14107099
#SPJ1
Hello please solve this with steps Factor
f(x)=x^3-12x^2+36x-32 completely given that (x-2) is a factor.
f(x)=x^3-12x^2+36x-32 completely given that (x-2) is a factor is [tex](x-2)^2(x-8)[/tex].
What is factor?
In mathematics, an integer m that can be multiplied by another integer to produce n is known as a divisor of an integer n, also known as a factor of n. One can also state that n is a multiple of m in this situation.
Knowing that (x−2) is a factor you can divide the polynomial:
2.....|.......1.........-12.........+36.........-32
........|...................2..........-20.........+32
........|.......1.........-10..........+16...........0
and find:
[tex]x^3-12 x^2+36 x-32=(x-2)\left(x^2-10 x+16\right)[/tex]
We could use the quadratic formula to find the factors of [tex]$q(x)=\left(x^2-10 x+16\right)$[/tex]
or go simply by inspection:
1) q(x) has two changes in sign, so it has two positive real roots.
2) The product of the roots is 16
3) the sum of the roots is 10
It's easy to see that x=2 and x=8 are such roots, and thus:
[tex]x^3-12 x^2+36 x-32=(x-2)^2(x-8)[/tex]
To learn more about factor visit:https://brainly.com/question/14067703
#SPJ1
Simplify the following monomials. Express final answers using only positive exponents.
[tex]\frac{8}{8^{3} }[/tex]
[tex]\frac{(-3)^{4} }{(-3)^{3} }[/tex]
The simplified monomial for the first scenario will be 1/8². The simplified monomial for the second situation will be (-3)¹.
What is exponent?Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6*6*6*6. You can write this as 6^4. In this case, the exponent is 4 and the base is 6. This can be understood as 4 increased to the power of 6. A number or letter written above and to the right of a mathematical expression known as the base is termed an exponent. It denotes that the base is to be increased in strength. The base is x, while the exponent or power is n.
Here,
The law of exponents say that,
aⁿ/aˣ=aⁿ⁻ˣ
1. 8/8³
=8¹-³
=8⁻²
=1/8²
2. (-3)⁴/(-3)³
=(-3)⁴⁻³
=-3¹
For first case, the monomial resulted after simplifying will be 1/8². For second case, the monomial resulted after simplifying will be (-3)¹.
To know more about exponent,
https://brainly.com/question/12158740
#SPJ1
0) The sum of the first and second of three
consecutive even integers is 126. Find the
three even integers.
Answer:
The three consecutive even integers are 40, 42 and 44.
Step-by-step explanation:
Let the consecutive even integers be
x, (x + 2) and (x + 4)The sum of the first and second of three consecutive even integers is 126.
So,
x + (x + 2) + (x + 4) = 126
Open the brackets
x + x + 2 + x + 4 = 126
Combine like terms we get,
3x + 6 = 126
Subtract 6 from both sides we get,
3x + 6 - 6 = 126 - 6
3x = 120
Divide 3 from both sides we get,
3x/3 = 120/3
x = 40
The value of x is 40 and the the consecutive even integers are
x = 40
x + 2 = 40 + 2 = 42
x + 4 = 40 + 4 = 44
Thus, The three consecutive even integers are 40, 42 and 44.
PLEASE HELP I BEG I NEED JUST THIS ONE PROBLEM:
In the trapezoid ABCD ( AB ∥ CD ) point M∈ AD , so that AM:MD=3:5. Line l ∥ AB and going trough point M intersects diagonal AC and leg BC at points P and N respectively. Find: BC:BN.
Please give Statement/Reasoning proof as well. THANK YOU PLEASEE
For the given Trapezoid ABCD the value of BC:BN is BC:BN=8:3.
What is Trapezoid?
A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. A trapezium is the term used in British and other varieties of English. In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid's parallel sides are referred to as its bases.
Given:
In the trapezoid ABCD ( AB ∥ CD ) point M∈ AD , so that AM:MD=3:5.
Line l ∥ AB and going trough point M intersects diagonal AC and leg BC at points P and N respectively.
We have to find BC:BN
ABCD is a trapezoid and there is a point m which belongs to AD such that AM:MD=3:5.Line "l" parallel to AB intersects the diagonal AC at p and BD at N.
Now, we know that the parallel lines divide the transversal into the segments with equal ratio, therefore, BN:NC=AM:MD
But, BC= BN+NC
Therefore, BC:BN = (BN + NC): BN
⇒ BC:BN = (3 + 5): 3
⇒ BC:BN = 8:3
Hence, for the given Trapezoid ABCD the value of BC:BN is BC:BN=8:3.
To know more about Trapezoid, click on the link
https://brainly.com/question/1410008
#SPJ1
How many solutions does the equation -2 (4x − 1) = −8x – 1 have?
Answer:
No Solution
Step-by-step explanation:
[tex]\tt -2\left(4x-1\right)=-8x-1[/tex]
Expand:-
[tex]\tt -8x+2=-8x-1[/tex]
Add 8x to both sides:-
[tex]\tt -8x+2+8x=-8x-1+8x[/tex]
Simplify:-
[tex]\tt 2=-1[/tex]
The sides are not equal, therefore there is No Solution.
_____________________
Hope this helps!
Have a nice day!
Identify the vertex, axis of symmetry, and the direction of opening of the graph of g(x) = |x| - 8.
A. (0, -8); y = -8; opens up
B. (0, -8); x = 0; opens up
C. (8, 0); x = 0; opens down
D. (-8, 0); x = -8; opens down
A. (0, -8); y = -8; opens up will be the correct solution for the graph of given modulus function g(x) = |x| - 8.
What is modulus function?
Regardless of whether a number is positive or negative, the modulus function, also known as the absolute value function, determines its magnitude. No matter what the number or variable, it always returns a non-negative value. The expression y = |x| or f(x) = |x|, where f: R (0,) and x R, denotes a modulus function.
When x is a real number, then |x| is its modulus. f(x) will have the same value as x if x is not negative. If x is negative, then f(x) will have the magnitude of x; if x is negative, then f(x) = -x. Here is a summary of the modulus function formula.
As we can see in the graph attached that the f(x) is zero at y=-8 and it is a modulus function so the graph will open upwards
but the graph is little shifted to y=-8 because the equation given to us is |x|-8 =g(x) so it will shift down according to the rule
Learn more about Modulus function from the link below
https://brainly.com/question/10737199
#SPJ1
What is the solution to this system of equations? 3x+y+2z=6 6x−2y=2 3x+y−2z=0
The value of x, y and z are 2/3, 1, and 3/2 if the system of equations 3x+y+2z=6 6x−2y=2 3x+y−2z=0
What is a linear equation?It is defined as the relation between three variables, if we plot the graph of the linear equation we will get a plane.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The linear equations are:
3x+y+2z=6
6x−2y=2
3x+y−2z=0
From equation (I) and (III)
6x + 2y = 6
From the above equation and equation (II)
12x = 8
x = 8/12 = 2/3
y = 1
z = 3/2
Thus, the value of x, y and z are 2/3, 1, and 3/2 if the system of equations 3x+y+2z=6 6x−2y=2 3x+y−2z=0
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ1
Rewrite the following equation in slope-intercept form (y = mx + b), then identify the slope (m =) and y-intercept (b =) of the equation.
-3y – 5 = -2(x + 11) + 2
Answer: y = [tex]-\frac{2}{3} x[/tex] -5
Step-by-step explanation:
Distribute:
-3y-5=-2x(x+11)+2
Rewrite:
-3y-5=-2x-22+2
Combind alike terms:
-2x-20
Rewrite again:
-3y-5=-2x-20
Add 5 to both sides and rewrite:
-3y=-2x-15
Divide by -3:
y=[tex]-\frac{2}{3} x[/tex] - 5
(Sorry if it's incorrect im barely paying attention lol)
What is the equation of a line with a y-intercept of −5 and a slope of 8? A.y=−5x+8 B.y=8x−5 C.y=−5x−8 D.y=8x+5
On solving the provide question, we got that - he equation of a line with a y-intercept of −5 and a slope of 8 is8x - y +5 = 0
What is slope?The change in the y coordinate of a line with respect to the change in x coordinate is called the slope of the line. There was no net change in the x coordinate, but no net change in the y coordinate.
By using the Slope formula
(y - y1) = m (x - x1)
where m is slope
so,
(y - 5) = 8 X (x-0)
8x - y +5 = 0
To know more about slope visit :
https://brainly.com/question/3605446
#SPJ1
Please Help
The product of two consecutive, negative integers is 182.
What equation represents the situation?
Thanks to whoever can solve it
The equation that represent the product of to consecutive numbers being 182 is x^2 + x -182 = 0
What is a quadratic equation?Quadratic equations are second-degree algebraic expressions and are of the form ax^2+ bx + c = 0. The word "Quadratic" is derived from the word "Quad" which means square. In other words, a quadratic equation is an “equation of degree 2.”
let the two consecutive negative numbers be -x and -x-1
their product - x( -x-1) = 182
multiply out you have
x^2 + x = 182
which is finally reduced to
x^2 + x - 182 = 0
In conclusion the equation that represent the above question is x^2 + x - 182 = 0
Learn more about quadratic equation: https://brainly.com/question/28038123
#SPJ1
There are 152 basketball fans who plan to go to a game. How many buses will be needed, given that each bus can hold 31 fans?
Answer:
182
Step-by-step explanation:
152
+31
---------
182
Given the matrices A and B shown below, find A + B.
A = 1 -1 1] B = [-4 -4 0]
HELP ASAP!! graph the system of equations below by graphing both equations below on a piece of paper. what is the solution?
y=x-1
y=3x+1
A. 1, -2
B. -1, -2
C. 2, 1
D. -1, -1
Answer: Our answer set is( -1,-2 )
Step-by-step explanation:
y = x - 1
y = 3x + 1
We can use the combine method here.
==> - 1y + 1x = 1 (y = x - 1)
==> -1y +3x = -1 (y = 3x + 1)
- 1y + 1x = 1
-1y +3x = -1
To single out any of the two variables, we need them to cancel out. Let us choose to cancel out y. We therefore multiply by negative 1 in the first re-arranged equation.
==> -1* (- 1y + 1x )= (1 ) * -1
Now we add the equations
==> 1y -1x = -1
==>-1y +3x = -1
______________
2x = -2
Divide.
==> x = -1
Now we insert x into any of the two original equations;
y = (-1) - 1
==> y = -2
Our answer set is( -1,-2 )
Let y = (5 +b)x-c be perpendicular to 8x + 12y = 40. What is the value of b?
The value of b is -11/2.
What is the slope of the equation?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
To find the value of b, we need to find the slope of the given line and the line that is perpendicular to it.
The slope of the line 8x + 12y = 40 is -8/12 = -2/3.
The slope of a line that is perpendicular to this line is the negative reciprocal of -2/3, which is 3/-2 = -3/2.
The slope of the line y = (5 + b)x - c is 5 + b. Therefore, to find the value of b, we need to set 5 + b equal to -3/2:
5 + b = -3/2
b = -3/2 - 5
b = -11/2
Therefore, the value of b is -11/2.
To learn more about the slope of the equation visit,
brainly.com/question/3493733
#SPJ1
In the continuous Efm=300+20m. series, if mean (x)=15+m and Find the number of terms N.
Answer:
the number of terms N in the series is approximately 8.57, which is approximately equal to 9.
Step-by-step explanation:
The mean of a series is calculated by taking the sum of all the terms in the series and dividing it by the number of terms. In this case, the mean of the continuous series Efm=300+20m is given as x=15+m.
To find the number of terms N in the series, we can use the formula for the mean to solve for N. The formula for the mean is:
mean = sum of terms / number of terms
Substituting the given values, we get:
15+m = (300+20m) / N
We can then multiply both sides of the equation by N to isolate the sum of terms:
(15+m) * N = 300+20m
This simplifies to:
15N + mN = 300 + 20m
We can then combine like terms to get:
(15+20)N = 300
35N = 300
Dividing both sides by 35, we get:
N = 300/35
N = 8.57
Since the number of terms must be a whole number, the number of terms N in the series is approximately 8.57, which is approximately equal to 9.
.
In Alaska, the temperature is currently -14°F, and in Mt. Olive it is currently 67°F.
What is the difference in temperature between Alaska and Mt. Olive?
And please explain
Answer:
81
Step-by-step explanation:
it is asking only for the difference nothing else so do
14+67 because the value is in the - we use addition for this scenario if it's for example
difference between 10f and 50f you minus it
10-50 = 40
The arenas pay for two cars every month they pay $250 for Miss Herrera's car and 375 for Mr. editor struck what kind of expense is a car payment made each month
Which value best estimates the value for the correlation coefficient of the scatter plot below: 1, -0.8, -0.2, 0.2, 0.8, or 1?
how can I solve this
Answer: S=$2 and L=$8
Step-by-step explanation:
This question is a simultaneous equation.
(1) 4L+3S=$34
(2) 2L+S=$16 (*2)
(3) 4L+2S=$32
(1)-(3)
4L+3S=$34
-4L+2S=$32
S=$2
Substitute s=2 into (2)
2L+S(2)=$16
2L+2=$16 (-2)
2L=$16 (/2)
L=$8