The dimensions of the garden with the largest area she can enclose are given by 24*14 square yards.
The area (A) of the rectangle with length L and Width W is given by,
A=L*W
The maximum of [tex]y=ax^2+bx[/tex] occurs at x = -b/2a
Let the length and width of the garden be L and W respectively.
Now let my friend use cedar fencing for one width and cheaper metal fencing for rest sides.
Rate of cedar fencing is $17/yard
Then she has to pay for cedar fencing = 17W
rate of cheaper metal fencing is $7/yard
Then she has to pay for metal fencing = 7W+7*2L = 7W+14L
Then according to condition,
17W+7W+14L = 672
24W+14L = 672
12W+7L = 336
7L = 336-12W
L = (336-12W)/7
Then the area of the rectangular garden is given by,
A = L*W
[tex]A=\frac{336-12W}{7}\times W\\A=-\frac{12}{7}W^2+48W[/tex]
So here a = -12/7 and b = 48
Then maximum of W occurs at,
W = -48/(2*(-12/7)) = (48*7)/(2*12) = 336/24 = 14
Then maximum width = 14 yards
then length (L) = (336-12*14)/7 = 168/7 = 24 yards
Hence the dimensions with the leargest area she can enclose is given by = 24 * 14 square yards.
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What is the length of BC¯¯¯¯¯?
Answer:
meight you gotta do better then that
Step-by-step explanation:
a picture is probably necessary
Line l and line m intersect.
Prove: ∡1 ≅ ∡3
Answer:
l & m intersect
2 & 3 are supplementary
1 & 3 are congruent
Step-by-step explanation:
The proof of expression"∡1 ≅ ∡3" is given below.
The complete flow chart is given in the attached image.
As per the provided diagram and the given information "Line l and line m intersect", the proof of the required statement can be done in the following steps.
Step 1:
Given: Line l and line m intersect.
Step 2:
∠1 is supplementary to ∠2
From the property of linear pair theorem.
Step 3:
∠2 is supplementary to ∠3
From the property of linear pair theorem.
Step 4:
As per the property of congruent supplements theorem,
∠1 ≅ ∠3
The complete chart is given below.
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Question 4(Multiple Choice Worth 4 points)
Which of the following is a rational number?
√1. √2. √3, √5
O√1
O √2
O√3
√√5
Answer:
1
Step-by-step explanation:
The square root of 1 is 1 so it is a rational number while others are irrational
David rolls a fair dice 30 times. How many times would David expect to roll a number greater than 3?
Answer:
15
Step-by-step explanation:
so if its a 6 faced dice then there is a 3/6 numbers greater than 3. which simplifies to 1/2. 30(1/2)= 15
Please help! Solve the equation on the interval [0,2pi)
Answer:
[tex]\frac{5pi}{6}[/tex]
Step-by-step explanation:
Answer:
[tex]x = \dfrac{\pi}{6}, \dfrac{5 \pi}{6}[/tex]
Step-by-step explanation:
[tex]\begin{aligned}3 \sin x & = \sin x + 1\\\implies 3 \sin x - \sin x & = 1\\2 \sin x & = 1\\\sin x & = \dfrac{1}{2}\\\implies x & = \sin^{-1}\left(\dfrac{1}{2}\right)\\x & = \dfrac{\pi}{6} \pm 2 \pi n, \dfrac{5 \pi}{6}\pm 2 \pi n\end{aligned}[/tex]
Therefore, the value of x in the interval [0, 2π) is:
[tex]x = \dfrac{\pi}{6}, \dfrac{\boxed{5} \pi}{\boxed{6}}[/tex]
Identify the common ratio and first term and fill in the recursive formula for each of the following geometric sequences.
The first term will be 4 and the common ratio will be 2. And the nth term will be given as [tex]\rm a_n = a_{n -1} \cdot 2[/tex].
The complete question is attached below.
What is the geometric sequences?Let a be the first term and r be the common ratio. Then the geometric sequences will be
[tex]\rm a_n = a_{n -1} \cdot r[/tex]
The geometric sequence is given below.
4, 8, 16, 32, 64,................
Then the first term will be 4 and the common ratio will be 2.
And the nth term will be given as [tex]\rm a_n = a_{n -1} \cdot 2[/tex].
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Find the perimeter of this
Tringle
8 cm
7 cm
5 cm
answer is
A. 35 cm
B. 40 cm
C. 20 cm
D. 12.5 cm
Answer:
C) 20cm
Step-by-step explanation:
Perimeter is the distance around the edge of the shape.
8 + 7 + 5 = 20
Answer:
20 is answer
Step-by-step explanation:
as perimeter= sum of all side
= 8 +7+5=2ocm
A tank weighs 5.6kg when it 1/4 filled with water.If it weighs 10.4kg when it is full ,what will be it's weight when it is empty.
Answer:
4 kg
Step-by-step explanation:
........................
Answer:
4 kg
Explanation:
Let the mass of tank be 't' and water 'w'
First equation : (when it is 1/4 filled with water)
[tex]\sf t + \frac{1}{4} w = 5.6[/tex]Second equation : (when it is filled fully with water)
[tex]\sf t +w = 10.4[/tex][tex]\sf w = 10.4 - t[/tex]Insert second equation into first equation :
[tex]\rightarrow \sf t + \dfrac{1}{4} (10.4 - t) = 5.6[/tex]
[tex]\rightarrow \sf t - \dfrac{1}{4} t + 2.6 = 5.6[/tex]
[tex]\rightarrow \sf \dfrac{3}{4} t = 5.6 - 2.6[/tex]
[tex]\rightarrow \sf \dfrac{3}{4} t = 3[/tex]
[tex]\rightarrow \sf t = 4[/tex]
The tank weights 4 kg when it is empty.
use the point–slope formula to write an equation of the line that passes through(-5, -16 )and has a slope of m = 3 . Write the answer in slope–intercept form (if possible).
Answer:
y + 16 = 3(x + 5)
Step-by-step explanation:
When you write an equation in point-slope form, you only need two things: a point and a slope.
Given:
point: (-5, -16)slope (m): 3The standard point-slope equation is
y - y₁ = m(x - x₁)
Plug in what you know.
y - (-16) = 3(x - (-5))
Simplify.
y + 16 = 3(x + 5)
This is your equation.
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Find the x-intercept of the line whose equation is 8x + 2y = 4.
Answer: Hope this helps you
1/2
Step-by-step explanation:
To find the x-int of any equation, you will need to replace the y with a 0 since when the x-int is when y is 0.
8x+2y = 4 ➨ 8x+2*0 = 4
Now I will do 2*0 which anything times 0 is equal to 0. And we are left with the equation of:
8x = 4
Now I will divide both sides by 8, which isolates our x.
x = 1/2
The x-int is 1/2.
if 50 grams of sweets cost 250 rupees find the cost of 380 grams of sweets.
I need to know the answer
Answer: [tex]f(x)=-(x-5)^{2}(x+2)[/tex]
Step-by-step explanation:
There is a double root at x=5 and a single root at x=-2, so we know f(x) is of the form [tex]f(x)=a(x-5)^{2}(x+2)[/tex] for some constant a.
To find a, we can substitute the coordinates of the y-intercept, (0, -50).
[tex]-50=a(0-5)^{2}(0+2)\\\\-50=50a\\\\a=-1[/tex]
So, [tex]f(x)=-(x-5)^{2}(x+2)[/tex]
Lila wants to represent the following statement: seven times some number plus thirteen. How can she write this as an expression?
Answer: 7x+13
Step-by-step explanation:
7 is being multiplied by some number (x) and then the answer to that is added to 13.
Help me to solve this answer below :((!!!
Answer:
3/2+1/2+17/2=21/2
Answer: 21/2 hours or 10 1/2 hours
Step-by-step explanation:
To find out the total number of hours needed for all activities scheduled for the day, simply add the needed hours for each activity.
You just need to add them because they have the same denominator.
3/2 for homework
1/2 for home chores
17/2 for sleep
[tex]\frac{3}{2} + \frac{1}{2} + \frac{17}{2} = \frac{21}{2}[/tex] hours
How do I find the domain and range in this graph?
Answer:
Domain: [tex]-4 < x \leq 4[/tex]Range: [tex]0 \leq y \leq 4[/tex]Step-by-step explanation:
The domain is the set of x values, and the range is the set of y values.
Mary is going to roll a six-sided die. What is the probability that the die lands on the number 3? Input your answer in fraction form
Answer:
added in the picture
Step-by-step explanation:
added in the picture
Let the Universal set be the letters a through j: U = (a, b, ..., i, jJ. Let A = (b, e, g, i), B = {a, b, e, f), and C = {a, e, i, ji) List the elemefits of the set An (BU C)
Answer:
A ∩ (B U C) = {b , e , i}
Step-by-step explanation:
A = {b , e , g , i}
B = {a , b , e , f}
C = {a , e , i , j}
We note B U C ,The union of the two sets B and C
which is the set that contains all elements
that are in B or in C .
The easiest way to determine B U C :
Step1 : (write all the elements of B and C side by side)
B U C = {a , b , e , f , a , e , i , j}
Step2 : (delete the repeated elements)
B U C = {a , b , e , f , i , j}
FINDING A ∩ (B U C) :
it’s the set of elements that exist in both sets
A and B U C simultaneously:
A = {b , e , g , i}
B U C = {a , b , e , f , i , j}
Then
A ∩ (B U C) = {b , e , i}
Sketch the graph that has an area of under the standard normal curve and to the left of the z-score. Then find the associated z-score.
The normal distribution is also known as the Gaussian distribution. The correct option is B, while the approx z-score is 0.31.
What is Normal Distribution?The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
Since the normal distribution is symmetrical about the mean. Therefore, the correct option is B, while the approx z-score is 0.31.
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The diagram shows a triangle
inside a rectangle. All lengths are in cm.
Work out the area of the rectangle:
15
20
16
Answer:
Area = 180 cm^2
Step-by-step explanation:
See attached image. The width of the rectangle, a , is the hypotenuse of a right triangle with legs 15 and 20.
Use the Pythagorean Theorem: leg^2 +leg^2 = hypotenuse^2
[tex]a^2=15^2+20^2\\\\a^2=225+400\\\\a^2=625\\\\a=\sqrt{625}=15[/tex]
The width, w, is one leg of a right triangle that has hypotenuse 20 and one leg 16.
[tex]w^2+16^2=20^2\\\\w^2+256=400\\\\w^2=144\\\\w=\sqrt{144}=12[/tex]
The rectangle has length 15 cm and width 12 cm so its area is 12 x 15 = 180 cm^2
Answer:
AREA RECTANGLE =300 cm²
Step-by-step explanation:
If 2 of the 3 vertices of a triangle match up with 2 of the 4 vertices of a rectangle,then the area of the triangle will be exactly half of the area of the rectangle
(Or the area of the rectangle will be exactly double of the area of the triangle)
Area right triangle = ½ × base × height.
A = 1/2(15X20)
A=1/2( 300)
Area triangle =150
Area of rectangle is DOUBLE as the area of triangle
AREA RECTANGLE = 300
What is the y - cordanate of the point that divides the directed line segment from j to k into a ratio of 2:3
The coordinate of point P that divides the line segment into 2 parts and 3 parts is (-5,5).
Let's call the point that divides the line segment point P.
Point P divides the line segment into a ratio of 2:3
What is the ratio of 2:3?The ratio of 2:3 means we are dividing the line segment into 2+3=5 equal parts.
The horizontal distance between the two coordinates is 5.
The vertical distance between the two coordinates is 10.
Dividing both vertical and horizontal distance into five equal parts, we have a horizontal distance of 1 and a vertical distance of 2.
Every time we move one unit to the left from point J and two units up, we are dividing the line segment into five equal parts as shown in the picture.
The coordinate of point P that divides the line segment into 2 parts and 3 parts is (-5,5).
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The cost of renting a car is $46/week plus $0.25/mile traveled during that week. An equation to represent the cost would be y=46+0.25x, where x is the number of miles traveled.
a. What is your cost if you travel 57 miles?
The cost is $ ____________.
b. If your cost was $65.00, how many miles were you charged for traveling?
You were charged for traveling ____________ miles.
c. Suppose you have a maximum of $100 to spend for the car rental. What would be the maximum number of miles you could travel?
The maximum number of miles you could travel is ____________ miles.
Answer:
A. $60.25
B. 76 miles
C. 216 miles
Step-by-step explanation:
x is miles
y is total amount spent
For A, 57 miles is the x value. Plug that in to x.
y= 46 + .25(57)
y= 60.25
For B, the total is the y. So plug 65 in for y.
65 = 46 + .25x Subtract 46 from both sides
19 = .25x Divide by .25
76 = x
For C, the maximum you can spend is $100. Plug that in for y.
100 = 46 + .25x Subtract 46 from both sides
54 = .25x Divide by .25
216 = x
The answer for part a is $60.25, for part b the answer is 76 miles, and for part c the answer is 216 miles.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The equation to represent the cost would be y=46+0.25x
x is the number of miles.
a) What is your cost if you travel 57 miles?
Plug x = 57 in the above equation:
y = 46 + 0.25(57)
y = $60.25
b) If your cost was $65.00, how many miles were you charged for traveling?
Plug y = 65 in the equation:
65 = 46 + 0.25x
x = 76 miles
c) Suppose you have a maximum of $100 to spend for the car rental. What would be the maximum number of miles you could travel?
Plug y = 100 in the equation:
100 = 46 + 0.25x
x = 216 miles
Thus, the answer for part a is $60.25, for part b the answer is 76 miles, and for part c the answer is 216 miles.
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A graph titled Janelle's Trip Home. The horizontal axis shows time (minutes) and the vertical axis shows distance from her home (miles). The line shows a decrease as time increases, a constant as time increases, and then another decrease as time continues.
Based on the graph, which statement could describe Janelle’s trip home from school?
Janelle waited for the bus, rode the bus, and then walked home.
Janelle walked the opposite direction from home to the library, rode the bus, and then walked to a friend’s house.
Janelle walked home at a constant speed.
Janelle rode the bus to the bus stop, talked with a friend, and then walked home.
Janelle rode the bus to the bus stop, talked with a friend, and then walked home , Option D is the correct answer.
The missing graph is attached with the answer.
What is a Time -Distance Graph ?A graph which shows change in distance with respect to time is called Time- Distance Graph.
It is used to calculate velocity.
As in the graph we it can be seen that , The distance is decreasing at a constant speed ,
then the distance becomes constant with time
and then again decreases but with a lower rate
This means
Janelle rode the bus to the bus stop (distance to time rate is high)
talked with a friend (distance is constant with time)
and then walked home. (distance to time rate is low)
Therefore Option D is the correct answer.
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Answer:
Janelle rode the bus to the bus stop, talked with a friend, and then walked home.
Step-by-step explanation:
Which statement is true of the function f(x) = Negative RootIndex 3 StartRoot x EndRoot? Select three options.
The function is always increasing.
The function has a domain of all real numbers.
The function has a range of {y|–Infinity < y < Infinity}.
The function is a reflection of y = .
The function passes through the point (3, –27).
the correct options are:
The function has a domain of all real numbers.The function has a range of {y|–Infinity < y < Infinity} (this is the same as saying that the range is the set of all real numbers.Which statements are true about the function?
Here we have the function:
[tex]F(x) = -\sqrt[3]{x}[/tex]
First, this is a cubic root, so its domain is the set of all real numbers (same for the range). And we know that the cubic root is an increasing function, so if we put a negative sign before it, we will have a decreasing function.
Then the correct options are:
The function has a domain of all real numbers.The function has a range of {y|–Infinity < y < Infinity} (this is the same as saying that the range is the set of all real numbers.The fourth option is incomplete, so we can't conclude if it is true or not, it would be true if it said:
"The function is a reflection over the x-axis of y = ∛x"
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Answer:
b, c, d
Step-by-step explanation:
Help help needed for composition of function
Answer:
[tex]\circledast \ \ f\circ f\left( x\right) = x[/tex]
[tex]\circledast \ \ g\circ g\left( x\right) =4x - 21[/tex]
Step-by-step explanation:
[tex]f(x)=\frac{5}{2x}[/tex]
g(x) = 2x - 7
==============
[tex]f\circ f\left( x\right) =\frac{5}{2\left( f\left( x\right) \right) }[/tex]
[tex]=\frac{5}{2\left( \frac{5}{2x} \right) }[/tex]
[tex]=\frac{5}{\left( \frac{5}{x} \right) }[/tex]
[tex]=5\times\frac{x}{5}[/tex]
[tex]=x[/tex]
_____________
[tex]g\circ g\left( x\right) =2(g(x)) - 7[/tex]
= 2(2x - 7) - 7
= 4x - 14 - 7
= 4x - 23
Tina's application for graduate school was ranked 54 out of 300 applications. Her twin sister's application to a
different graduate school was ranked 23 out of 175 applications.
a. Which sister had the higher percentile ranking?
b. If you had the data on the cumulative GPA of each student in each school in June 2019, which measure of
average would be the most meaningful - mean, median, mode? Explain
A percentage is a way to describe a part of a whole. The percentile ranking of Tina's sister is higher than her.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
A.)
The percentile ranking of Tine is,
Tina's Ranking = [1 - (54/300)] × 100% = 82%
Tina's soster Ranking = [1 - (23/175)] × 100% = 86.85%
Hence, the percentile ranking of Tina's sister is higher than her.
B.) It shows that you can succeed in the graduate examination if you exceed this value.
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Please answer all of the questions and if u are correct I will give u brainliest ;) xoxo <3
Answer:
the answer for the 2nd question is 1/4
Step-by-step explanation:
i took the test
In the year 2000, a house was valued at $60 000.
In 2010, the same house was valued at $80 000.
Work out the value of the house in 2010 as a percentage of it value in 2000
The percentage by which the cost is increasing will be 75%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A fraction of 100 can be used to express the ratio.
The percentage of the 8th graders who want to go to the water slides is found from;
In the year 2000, a house was valued at $60 000.
In 2010, the same house was valued at $80 000.
The percentage value is found as;
[tex]\% = \frac{60000}{80000} \times 100 \\\\ \% =75 \%[/tex]
Hence the percentage by which the cost is increasing will be 75%.
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Find an equation for the line that passes through the points (-6, -6) and (4,-2)
Answer:
y = 2/5 x - 18/5
Step-by-step explanation:
y = mx + b
m = (y2 - y1)/(x2 - x1) = [-2 - (-6)]/[4 - (-6)] = 4/10 = 2/5
y = 2/5 x + b
-6 = (2/5)(-6) + b
-30 = -12 + 5b
5b = -18
b = -18/5
y = 2/5 x - 18/5
calculate the median for: 5, 10, 12, 4, 6, 11, 13, 5r
Step-by-step explanation:
please mark me as brainlest
Answer:
8
Step-by-step explanation:
We need to sort your set into Least-to-Greatest order.
4, 5, 5, 6, 10, 11, 12, 13
That is your set in least to greatest order.
Which 2 numbers are in the middle?
They are 6 and 10.
Now, we find the mean of 6 and 10.
(6+10)/2 = 8
8 is your median
what is −4/5+40/75+100%=
-0.8+1.875+100%
1.05+100%
0.1
