Answer:
The length and width of the rectangular garden are 20 feet and 10 feet.
Step-by-step explanation:
Given that the length of fencing = 60 feet
The area of the garden = 200 sq. feet.
As the length of the fencing is equal to the perimeter of the garden, so the perimeter of the rectangular garden is 60 feet.
Let l and b be the length and width of the rectangular garden.
So, the perimeter of the garden = 2(l+b)=60
[tex]\Rightarrow l+b=60/2=30[/tex]
[tex]\Rightarrow l=30-b\cdots(i)[/tex]
The area of the rectangular garden [tex]= l\times b=200[/tex]
[tex]\Rightarrow (30-b)b=200[/tex] [from equation (i)]
[tex]\Rightarrow 30b-b^2=200[/tex]
[tex]\Rightarrow b^2-30b+200=0[/tex]
[tex]\Rightarrow b^2-10b-20b+200=0[/tex]
[tex]\Rightarrow b(b-10)-20(b-10)=0[/tex]
[tex]\Rightarrow (b-20)(b-10)=0[/tex]
[tex]\Rightarrow b-20=0 \;or\; b-10=0[/tex]
[tex]\Rightarrow b= 20\;or\; 10[/tex]
Now, from equation (i),
If b=20 than l= 30-20=10
or if b=10 than l=30-10=20.
Hence, the length and width of the rectangular garden are 20 feet and 10 feet.
Can someone help me please
Answer:
a. angle 6 and angle 7
b. angle 6 and angle 8
c. angle 3 and angle 1
Step-by-step explanation:
linear pair is two angles that share a base and and add up to 180
vertical angles is the pair of opposite angles formed by two intersecting lines
congruent is the same measure
Answer:
see explanation
Step-by-step explanation:
(a)
A linear pair of angles, are adjacent to each other and sum to 180°
There are 8 linear pairs in the diagram, they are
1 and 2 / 2 and 3 / 3 and 4 / 4 and 1 / 5 and 6 / 6 and 7 / 7 and 8 / 8 and 5
(b)
There are 4 vertical angles in the diagram
1 and 3 / 2 and 4 / 5 and 7 / 6 and 8
Note that vertical angles are congruent
Other congruent angles are
2 and 6 / 3 and 7 / 1 and 5 / 4 and 8 ( All corresponding angles )
4 and 6 / 3 and 5 ( are Alternate angles )
24% of students buy lunch. 190 students bring lunch from home. How many students are in the sixth grade?
Answer:
45.6
Step-by-step explanation:
24% out of 190 = 45.6
Bridgette has $1,000 to invest. She has two different investment options, shown in the table below. Each option would give her a different value over three years.
Number of Years 1 2 3
Option A (amount in dollars) 1100 1200 1300
Option B (amount in dollars) 1100 1210 1331
Part A: What type of function, linear or exponential, would be best to describe the value of the investment over a fixed number of years using Option A? Explain your answer.
Part B: Write a function, a(t), to describe the value of the investment, in dollars, of Option A after t years.
Part C: What type of function, linear or exponential, would be best to describe the value of the investment over a fixed number of years using Option B? Explain your answer.
Part D: Write a function, b(t), to describe the value of the investment, in dollars, of Option B after t years.
Part E: Bridgette wants to invest in whichever option would increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Bridgette's investment after 20 years if she uses Option A over Option B? Explain your answer, and show the investment value after 20 years for each option.
Answer/Step-by-step explanation:
Part A: The function that would best describe Option A is a linear function. This is because an increase in x would have a corresponding additive increase in y. With each increasing year, the value of Option A increases by $100. This is how we know Option A would be a linear function.
Part B: a(t) = y.
a(t) = a + 100t
Part C: The function that would best describe Option B is an exponential function. Unlike linear functions, an increase in x would have a corresponding multiplicative increase in y. Each value of Option B shares a common ratio of 1.1.
Part D: b(t) = y.
b(t) = b(1.1)^t
Part E: a(20) = a + 100(20)
1100 + 2000 = 3100
b(20) = b(1.1)^20
1100(1.1)^20
= 7400
There is definitely a significant difference between the value of Bridgette’s investment in both options. The difference between the values of each option after 20 years is 4300. Bridgette is better off using Option B if she wants more money at the end.
Hope this helps!
Tuition for one year at the University of Houston is about $12,300 Azul plans to attend this university and will save money each month for the next 4 years. His parents have saved 54,860 for his first year of
tuition. Which plan shows the amount of money Azul will need to save in order to pay for his first year at the University of Houston?
(Answer Choices)
Azul will need to save $256 25 per month for the next 4 years
Azul will need to save $1,860 per month for the next 4 years.
Azul will need to save $620 per month for the next 4 years.
Azul will need to save $155 per month for the next 4 years
QUICK ANSWER PLEASE
In triangle NLM, point S is the centroid, QS = (3x – 5) cm, and NS = (4x) cm.
Triangle N L M has centroid S. Lines are drawn from each point to the midpoint of the opposite side to form line segments N Q, L R, and M P. The length of line segment N S is 4 x and the length of line segment S Q is 3 x minus 5.
What is NS?
5 cm
10 cm
20 cm
30 cm
sweet t is making a double batch of Pupcakes. he puts them in the oven at 6:50. they need to bake for 25 minutes
i would love to help but i just need free points
Step-by-step explanation:
Choose the correct pair of expressions to complete the solution of sin r +
37
2
2.
O COS X, 0
O -sin x,-1
O sin x,-1
O-COS X, 0
Answer:
sin x, –1
Step-by-step explanation:
did on edge
Ivian scores 58 out of 80 marks in a maths test what is his score as a percentage
Answer:
72.5%
Step-by-step explanation:
Lets make his score a percentage: 58/80
Now covert it to a percentage: 58/80 = x/100
Cross multiply: 80x = 5800, x = 145/2
Divide 145 by 2: 72 1/2
Answer is 72.5%
I hope this helped, please mark Brainliest, thank you!
Write an equation in point-slope form for the line that passes through the point with the given slope. point: (-1, 5) and m=-4
Answer:
y - 5 = -4(x + 1)
Step-by-step explanation:
The point-slope form is y - k = m(x - h). The point is (h, k): (-1, 5) and the slope is -4.
Here we have y - 5 = -4(x + 1)
The required point-slope form of the equation of the line is y - 5 = -4(x + 1).
Given that, To determine an equation in point-slope form for the line that passes through the point with the given slope. point: (-1, 5) and m=-4.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The point-slope of the equation of the line is given by,
y - y₁ = m(x - x₁)
Put the values in the above equation of the line
y - 5 = -4 (x - (-1))
y - 5 = -4 (x + 1)
Thus, the required point-slope form of the equation of the line is y - 5 = -4(x + 1).
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Which of the following is a rational number?
Answer:
B.)
Step-by-step explanation:
A rational number is a number with no repeating decimals or decimals that go on “forever” like pi. An expample of a rational number is 2 where 2.3333333... is not a rational number. Pi isn’t a rational number either since forth there is no known end to that.
So, when solved:
A.) = 1.58113883... (irrational)
B.) = -8 (rational)
C.) = 8.94427191... (irrational)
D.) = 3.794733192... (irrational)
I hope you see the pattern. Hope this helps!
an office administrator will be purchasing supplies for an upcoming meeting. She will purchase folders, which are $2.15 each, and notebooks, which are $4.60 each. The supply budget for this meeting is $150. Which inequality represents the constraint on the number of folders f and notebooks n the office administrator can purchase?
Given :
Price per folder = $2.15 .
Price per notebook = $4.60 .
The supply budget for this meeting is $150.
To Find :
Inequality represents the constraint on the number of folders f and notebooks n the office administrator can purchase.
Solution :
Let, number of folders and notebooks is f and n.
So, price of buying f and n number of folders and notebooks are :
P = 2.15f + 4.60n
Now, it is given that P ≤ $150 .
So,
2.15f + 4.60n ≤ 150
Hence, this is the required solution.
[tex]2.15f+2.5n\leq 150[/tex] inequality will represent the constraint on the number of folders f and notebooks n the office administrator can purchase.
Given information:
An office administrator will be purchasing supplies for an upcoming meeting.
Staff will purchase folders, which are $2.15 each, and notebooks, which are $4.60 each.
The supply budget for this meeting is $150.
Let f be the number of folders purchased and n be the number of notebooks purchased.
Now, the total amount spent on the whole purchase should not be greater than $150 which is the budget of the shopping.
In the form of inequality, the given condition can be written as,
[tex]2.15f+4.6n\leq 150[/tex]
The total amount spent is less than equal to 150.
Therefore, [tex]2.15f+4.6n\leq 150[/tex] inequality will represent the constraint on the number of folders f and notebooks n the office administrator can purchase.
For a graphical representation of the inequality, see the image attached.
For more details, refer to the link:
https://brainly.com/question/18568636
The length of a rectangular garden is 5 times its width.
Find the length and width if the area is 500 m^2. Has anyone who answer me to this question?
Answer:
10 m and 50 mStep-by-step explanation:
Givenl = 5wA = 500 m²To findLength and widthSolutionArea formula
A = lw A= 5w*w= 5w²5w² = 500w²= 100w = √100w = 10 mThen
l = 5w = 5*10 m = 50 m
satnam is making a cake he uses a batter made out of 400 g of dry ingredients if the liquid has to be 2/7 of the total weight of batter how much liquid should he add
You take [tex]\frac{2}{7}[/tex] of [tex]400[/tex].
Which is: [tex]\frac{800}{7} = 114.8 mL[/tex]
what is the inverse function of c(n) = 4n + 20? show your work
Answer:
c(n) = 4n +20
let m = c(n)
m= 4n +20
make n the subject
m -20 =n
4.
inverse function of c(n)= n-20
4
It is a must that one replaces the m with the n in order to get the final answer
A recipe for 4 cups of trail mix calls for 2··3cup of raisins. Aniyah has 1 1··2cups of raisins. Does Aniyah have enough raisins to make 14 cups of the trail mix? If not, how many more cups of raisins does Aniyah need?
Answer:
Aniyah does not have enough for 14 cups, and needs 1 1/6 more.
Using the required arithmetic concept, we can conclude that Aniya needs 7/6 more cups.
Representing the problem thus:
4 cups of trail = 2/3 cups of raisins
14 cups of trails = x
Cross multiply
4x = (2/3) × 14
4x = 28/3
x = (28/3) ÷ 4
x = (28/3) × (1/4)
x = 7/3
Cups of raisins Aniya has = 1 1/2 = 3/2
Extra cups needed = 7/3 - 3/2 = 7/6 cups
Therefore, Aniya does not have enough, she needs 7/6 more cups.
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Which quadrant does the complex number -4 - 9i lie in?
a. Quadrant I
b. Quadrant III
c. Quadrant II
d. Quadrant IV
Answer:
Quadrant III
Step-by-step explanation:
because in quadrant III there is both negative terms
Choose the correct value for the linear correlation between latitude and August precipitation from: (i) r= -1, (ii) r=-0.700, (iii) r=-0.161 or (iv) r=-0.538
Answer:
hello your question is incomplete attached below is the missing part of the question
answer : r = - 0.161 ( iii )
Step-by-step explanation:
The correct value for the linear correlation between latitude and August precipitation is ; r = - 0.161 and this is because the data points are showing a less negative correlation
The points (2.1, -4.2) and (2.5, -5) form
a proportional relationship. What is the slope of
the line that passes through these two points?
Answer:
m = -2
Step-by-step explanation:
hsavajgsbjxxhisbvzjxb
The slope of the line that passes through the points (2.1, -4.2) and (2.5, -5) that form a proportional relationship is: -2.
Recall:
The slope (m) of a line can be calculated using the formula:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Given the points that a line passes through are:(2.1, -4.2) and (2.5, -5)
To calculate the slope of the line that passes through both points, let,[tex](2.1, -4.2) = (x_1, y_1)\\\\(2.5, -5) = (x_2, y_2)[/tex]
Plug in the values into the formula:Slope (m) = [tex]\frac{-5 -(-4.2)}{2.5 - 2.1} = \frac{-0.8}{0.4} = -2[/tex]
Therefore, the slope of the line that passes through the points (2.1, -4.2) and (2.5, -5) that form a proportional relationship is: -2.
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How do you write the algebraic expression: x=-2.5 like i mean the answer
Answer:
2.5 × t = 2.5 t
Step-by-step explanation:
Will give brainliest if correct
Answer:
y=4
x=2
Step-by-step explanation:
y=4
x=2
I think it's right..
Hope I helped!
Answer:
x - intercept = 2
y - intercept = 4
The table shows the number of coins Kaitlyn has.
penny
4
nickel
9
dime
3
quarter
5
Write the ratio of dimes to all coins that Kaitlyn has as a
fraction in simplest form.
Plz help me again with this math stuff -_-
Answer:
152cm^2
Step-by-step explanation:
What is the rate of change of y with respect to x for 25x-4y=50
Answer:
The rate of change is y with respect to x is [tex]\frac{25}{4}[/tex]
Step-by-step explanation:
Given
[tex]25x - 4y = 50[/tex]
Required
Determine the rate of change of y w.r.t x
[tex]25x - 4y = 50[/tex]
First, make y subject of formula
[tex]4y = 25x- 50[/tex]
Divide through by 4
[tex]y = \frac{25x}{4} - \frac{50}{4}[/tex]
[tex]y = \frac{25x}{4} - 12.5[/tex]
Next, we differentiate the above w.r.t to x
The result of the differentiation is the solution to the question
[tex]y' = 1 * \frac{25x^{1-1}}{4} -0[/tex]
[tex]y' = 1 * \frac{25x^0}{4}[/tex]
[tex]y' = 1 * \frac{25*1}{4}[/tex]
[tex]y' = \frac{25}{4}[/tex]
Hence, the rate of change is y with respect to x is [tex]\frac{25}{4}[/tex]
By calculating derivative of y with respect to x we got rate of change of y with respect to x for 25x-4y=0 is 25/4
What is derivative?Rate of change of a function with respect to a variable is called derivative of that function with respect to that variable .
Here given relation is 25x-4y=0
[tex]\Rightarrow 4y=25x\\\\\Rightarrow y=\frac{25x}{4}[/tex]
We have to calculate rate of change of y with respect to x so we will calculate derivative of y with respect to x.
we can calculate derivative of y with respect to x as
[tex]\frac{dy}{dx}= \frac{d}{dx} (\frac{25x}{4})\\\\[/tex]
As 25/4 is constant we can take it out from derivative function as it is
[tex]\frac{dy}{dx}= (\frac{25}{4})\frac{dx}{dx}\\\\[/tex]
And we know derivative of a variable with respect to itself is 1
so
[tex]\frac{dy}{dx}= (\frac{25}{4})\times 1\\\\ \frac{dy}{dx}= \frac{25}{4}[/tex]
By calculating derivative of y with respect to x we got rate of change of y with respect to x for 25x-4y=0 is 25/4
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PLEASE HELP ASAP!!!!!!!!!!
Answer:
2 31/100
Step-by-step explanation:
From 1990 to 1996, the consumption of poultry per capita is modeled by: y=-.2125t^2 + 2.615t+56.33 where t=0 corresponds to 1990. What was the per capita poultry consumption in 1992?
Answer:
60.71
Step-by-step explanation:
Given that:
Consumption of poultry per capita is modeled by:
y=-.2125t^2 + 2.615t+56.33 ; t = 0 corresponds to 1990
Per capita poultry consumption in 1992;
1992 ; t = 2
y=-.2125t^2 + 2.615t+56.33
Put t = 2 in the equation
y=-.2125(2)^2 + 2.615(2) +56.33
y = -.2125(4) + 2.615(2) + 56.33
y = - 0.85 + 5.23 + 56.33
y = 60.71
three sides of a quadrilateral are the same length. q. the length of the forth side is 7 inches. the perimeter of the quadrilateral is 40 inches
Answer:
3q+7=40 I know im a year late but this is for whoever needs it this year Step-by-step explanation:using algebra the value of q is 11 inches Mark me as brainliestThe length of the equal sides of the given quadrilateral comes to be 11 inches.
What is a quadrilateral?A quadrilateral is a polygon with 4 sides.
Suppose the length of the three equal sides =x inch
Length of the fourth side =7 inches
So, the perimeter of the quadrilateral = x+x+x+7
The perimeter of the quadrilateral = 3x+7
Given that the perimeter of the quadrilateral = 40inches
3x+7=40
3x=33
x=11
So, the length of three equal sides = 11 inches
Therefore, the length of the equal sides of the given quadrilateral comes to be 11 inches.
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Does the set of ordered pairs
represent a function ? Explain.
(7, 8), (9, 10), (0, 1), (-2, -1),
(9,8)
Answer:no
Step-by-step explanation:
Because there’s two number 9’s for the x values
Answer:
no because x = 9 has two y coordintates, and in a function every x value can only have one y value.
Step-by-step explanation:
PLEASE HELP!! (Give reasonable answer)
Answer: B
Step-by-step explanation: You just multiplying 25 with 10 and w which can be simplified as 24(w+10) and adding with the 13.5 x 10 and 13.5 x w, which can be simplified as 13.5(10+w)
The prime factorization of 2020 is 2² × 5¹ × 101¹. How many different whole numbers are factors of 2020?
Answer:
4
Step-by-step explanation:
1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010
A, B, and C are points on the circumference of a circle, centre 0. AOB is a diameter of the circle. Prove that angle ACB is 90° You must not use any circle theorems in your proof.
Answer:
Kindly refer to explanation.
Step-by-step explanation:
Given that:
A,B and C are 3 points on circumference of circle with centre O.
AOB is diameter.
Kindly refer to the attached image.
To prove:
[tex]\angle ACB = 90^\circ[/tex]
Solution:
Let [tex]\angle A = x[/tex] and [tex]\angle B = y[/tex].
Construction: Join point A with centre O.
Considering [tex]\triangle AOC[/tex]:
Side AO = OC because both are the radius.
Angles opposite to equal sides in a triangle are equal.
Therefore, [tex]\angle ACO=\angle A=x[/tex]
Considering [tex]\triangle BOC[/tex]:
Side BO = OC because both are the radius.
Angles opposite to equal sides in a triangle are equal.
Therefore, [tex]\angle BCO=\angle B=y[/tex]
[tex]\angle ACB = \angle ACO + \angle BCO = x+y[/tex] ...... (1)
Now, in [tex]\triangle ABC:[/tex]
Using angle sum property of triangle:
[tex]\angle A + \angle B + \angle ACB =180^\circ\\\Rightarrow x+y+x+y=180^\circ\\\Rightarrow 2(x+y)=180^\circ\\\Rightarrow x+y=90^\circ[/tex]
By equation (1):
[tex]\angle ACB = 90^\circ[/tex]
Hence proved.