Answer:
A.) The greatest possible distance between any of the stakes is 53 feet.
B.) A triangle with sides 15, 36, and 39 is a right triangle and has perimeter 90 feet.
Step-by-step explanation:
Given - Fiona wants to rope off a triangular region in her yard for a vegetable garden. She has 90 feet of rope to use, she wants the distance between each stake to be an integer, and the distance between two of the stakes must be 36 feet.
To find - A. What is the greatest possible distance between any of the stakes?
B. If she wants to create a right triangular region and use all of the 90 feet of rope, what would be the lengths of the sides of the region?
Solution -
A.)
Let us assume that,
Length of side 1 = x
Length of side 2 = y
Length of side 3 = z
Now,
Given that,
She has 90 feet of rope to use
⇒x + y + z = 90
And
The distance between two of the stakes must be 36 feet.
So, Let z = 36.
∴ we get
x + y + 36 = 90
⇒x + y = 90 - 36
⇒x + y = 54
Now,
Let x be as large as possible.
i.e. To make x to be large, y has to be as small as possible.
It happens when y = 1.
( We can not take y = 0, or else a triangle won't form)
∴ we get
y = 1
⇒x + 1 = 54
⇒x = 54 - 1
⇒x = 53
∴ we get
The greatest possible distance between any of the stakes is 53 feet.
B.)
We know that,
(5,12,13) is a Pythagorean triple.
Because 5² + 12² = 13²
So,
As, we have a Pythagorean triple,
This means a triangle with sides 5, 12, 13 is a right triangle.
Now,
If a triangle has sides 5, 12, 13,
⇒ The perimeter becomes 5 + 12 + 13 = 30.
By Triple each side we get,
Length of sides 15, 36, 39.
The perimeter i= 15 + 36 + 39 = 90
Also,
We can see that,
15² + 36² = 39².
This means we have a right triangle and (15, 36, 39) is another Pythagorean triple.
Because any scaled version of a Pythagorean triple, is also a Pythagorean triple.
∴ we get
A triangle with sides 15, 36, and 39 is a right triangle and has perimeter 90 feet.
please help with this question
Answer:
211
Step-by-step explanation:
Considering c as center and WZ is a straight line with 180 degrees
the measure of XWZ is equal to 211
Together, teammates Pedro and Ricky got 2861 base hits last season. Pedro had 277 more hits than Ricky. How many hits did each player have
Answer:
Ricky 1292 Pedro 1569
Answer: Ricky had 1292, Pedro had 1569.
Step-by-step explanation: First, you subtract 277 from 2861, then divide that by 2 to find how many hits Ricky had. You then add back the 277, and you get Pedro’s hits.
A diagonal of a polyhedron is a line segment connecting two non-adjacent vertices. How many diagonals does a pentagonal prism have
A pentagonal prism have 35 diagonals.
We know tha in a polygon or polyhedron the formula for finding the number of diagonals is: n(n-3)/2,
where n= the number of sides
We find the number of diagonals of a pentagonal prism.
As we know a pentagonal prism has two pentagonal bases like top and bottom and five rectangular sides.
For a pentagonal prism n = 10
So, using above formula the total number of diagonals would be,
d = [10 × (10 - 3)] / 2
d = (10 × 7) / 2
d = 70/2
d = 35
Therefore, the total number of diagonals would be = 35
Learn more about diagonal here:
https://brainly.com/question/23032581
#SPJ4
Out of 30 students surveyed, 17 have a dog. based on these results, predict how many of the 300 students in the school have a dog?
for each meal, Jeffrey eats either toast, cereal, or pancakes. How many different ways can Jeffrey choose his three meals for the day? PLSS HELP ASAP RN!
Answer:
27
Step-by-step explanation:
Jeffrey has three choices for breakfast: toast, cereal, or pancakes. Then, he has three choices for lunch: toast, cereal, or pancakes. Finally, he has three choices for dinner: toast, cereal, or pancakes.
Putting these together, Jeffrey has 3 * 3 * 3 = 27 possible ways to select the three meals.
The approximate circumference of a circle that has a center at (8,6) and passes
through the point (8, 12) is:
units.
:: 12
:: 36
38
:: 113
Answer:
????
Step-by-step explanation:
Find an expression which represents the difference when (-3x - 9y) is subtracted from (-4x + 6y) in simplest terms.
Answer:
15y - x
Step-by-step explanation:
(-4x + 6y) - (-3x - 9y) = -4x + 6y + 3x + 9y
combine like terms:
15y - x
The price p (in dollars) and the quantity x sold of a certain product obey the demand equation p= -1/7x+200. A) Find a model that expresses the revenue R as a function of x. (Remember, R= xp). R(x)=____ B) What is the domain of R? C) What is the revenue if 200 units are sold? D) What quantity maximizes revenue? What is maximum revenue? E) What price should the company charge to maximize revenue?
A) The model that expresses the revenue R as a function of x is R(X) = -1/7x + 200
B) The domain of R is (-∞, +∞)
C) If 200 units are sold, then the revenue is $228.57
D) The quantity that maximizes revenue is 200 and the maximum revenue is $228.57
E) The price should the company charge to maximize revenue $228.57
Here we have given the function that can be model that expresses the revenue R as a function of x is written as,
=> R(X) = -1/7x + 200
Here the domain value of R has take the value from negative infinity to positive infinity.
When we take the value of x as 200, then the revenues of the sold goods is calculated as,
=> R(200) = -1/7 (200) + 200
When we simplify this one then we get the value of R as
=> R = 28.57 + 200
=> R = 228.57
As per the given function the maximum number of units sold is written as 200, and the maximum revenue is written as 228.57
To know more about function here.
https://brainly.com/question/28193995
#SPJ4
could anyone help me with this?
Answer:
[tex]A(t) = a(1+r)^t\\\\A(10) = 2000( 1+ .04)^{10}\\\\[/tex]
= $2960.49
option 1
Find the surface area of a cylinder that has a radius of 5.5 m and a height of 15 m.
Answer:
the Total surface area is your answer. it is 708.4 meters squared.
Step-by-step explanation:
see answer above.
For triangle ABC use the Triangle Proportionality Theorem to solve for x
1. what is the value of x?
2. What is the perimeter of triangle ABC?
show ALL work-- PLEASE HELP!
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here's the solution ~
The two triangles in the shown figure are similar, therefore conclusion can be made that :
Ratio of its it's corresponding sides is equal.
[tex]\qquad \sf \dashrightarrow \: \dfrac{2x - 4 + 6}{6} = \dfrac{24}{4} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{2x + 2}{6} = 6[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x + 2 = 6 \times 6[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x + 2 = 36[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x = 36 - 2[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x = 34[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 17[/tex]
Therefore, The value of x is " 17 "
Now, the measure of side BC is :
[tex]\qquad \sf \dashrightarrow \: 2x - 4[/tex]
[tex]\qquad \sf \dashrightarrow \:2 (17) - 4[/tex]
[tex]\qquad \sf \dashrightarrow \: 34 - 4[/tex]
[tex]\qquad \sf \dashrightarrow \: 30 \: \: units[/tex]
So, its perimeter will be :
[tex]\qquad \sf \dashrightarrow \: p = AB + AB + BC [/tex]
[tex]\qquad \sf \dashrightarrow \: p = 24 + 26 + 30[/tex]
[tex]\qquad \sf \dashrightarrow \: p = 80 \: \: units[/tex]
Answer:
1) x = 17,2) P = 86 units.------------------------------------
Part 1According to Triangle Proportionality Theorem we have the following equal proportions:
(24 - 4)/4 = (2x - 4)/620/4 = (x - 2)/35 = (x - 2)/3x - 2 = 5*3x - 2 = 15x = 17Part 2The missing side is:
BC = 6 + 5*6 = 6 + 30 = 36 unitsThe perimeter is:
P = 24 + 36 + 26 = 86 unitsx + y = 3
Which of the following equations is equivalent to the given equation?
3x + 2y = 18
2x + 3y = 18
3x + 2y = 3
The equation equivalent to the equation x + y = 3 is 6x + 6y = 18.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
x + y = 3
Multiply 6 on both sides.
6x + 6y = 18
Thus,
The equation that is equivalent is 6x + 6y = 18.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ1
Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
24/25
Step-by-step explanation:
Please see the attached image.
The cosine of an angle is the adjacent side relative to that angle over the hypotenuse.
Answer: 24/25
Work out the equation of the straight line
shown below.
Give your answer in the form y = mx + C,
where m and c are integers or fractions in
their simplest forms.
Y
6
5
4
3
2-
1
-6 -5 -4 -3 -2 -1 0
-14
-2-
-3+
-4-
-5-
-6-
1 2 3 4 5 6
X
Where m and c are integers or fractions, the equation of a straight line in the form of y = mx + c becomes y = x/2 + 8.
What is a straight line?A straight line is made up of many points connected at each end. Any straight line's slope, m, is determined by the formula. The slope-intercept formulation of a linear equation is y = mx + b. The equation's variables are X and Y. The slope of the line (m) and the value of y when x is 0 are represented by the values m and b, respectively.
[tex]m = \frac{y2-y1}{x2 - x1}[/tex]
given
the graph is,(0,8) and (9,2)
The slope of the line is,
m = 1/2
Because it crosses the y-axis at the point where the intercept C is equal to 8,
The equation of the line will be :
⇒ y = mx + c
⇒ y = (1/2)x + (8)
⇒ y = x/2 + 8
Where m and c are integers or fractions, the equation of a straight line in the form of y = mx + c becomes y = x/2 + 8.
To know more about straight line visit :-
https://brainly.com/question/3493733
#SPJ1
Six cars pull up to a red light, one at a time. At the light, there are three lanes, one left-turn lane, one straight-going lane, and one right-turn lane. How many ways can the cars stack up so that all three lanes are occupied
According to the probability, there are 540 arrangements that can the cars stack up so that all three lanes are occupied.
How is card probability determined?Mathematicians use addition and division as well as counting to calculate probability.
There are three partitions of six using digits 1-3.
(4,1,1), (3,2,1), (2,2,2) (2,2,2)
These could be dispersed between the lanes in order that
(3) Possible solutions to (4,1,1)
There are six possible ways to solve the equation (3,2,1).
There is only one possible solution to the equation (2,2,2).
Cars must now move in the lanes in proper order.
The arrangements for (4,1,1) will be 6C4 * 2C1 = 30. Six cars are chosen, sorted, and placed in the appropriate lanes. then decide on 1 of the 2 surviving vehicles.
then place it in a lane.
The arrangements for (3,2,1) will be 6C3 * 3C2 = 60.
There will be 6C2 * 4C2 = 90 arrangements for (2,2,2).
Consequently, there will be 540 arrangements (3*30 + 6*60 + 1*90 = 90+360 + 90).
To know more about probability visit:-
brainly.com/question/11234923
#SPJ4
Please help
Find the value of x
Find the measure of the two marked angles
PLEASE ALSO FIND X
(Mathematics)
On solving the provided question, by properties of parallel lines we got to know that - 1 - A 2 - C 3 - B 4 - D
what is alternate exterior angles?When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.
Matches are -When two parallel lines cross one other, the horizontal line is divided into two angles. Interior angles develop between the parallel lines, whereas alternative outside angles develop outside the parallel lines.
1 - A
2 - C
3 - B
4 - D
To know more about alternate exterior angles visit:
brainly.com/question/2279752
#SPJ1
Find the a if c = 5
;;;;;;
Answer:
Step-by-step explanation:
Solve this by writing an equation of ratios:
1 a
----- = -----
√3 5
5
Then 5 = √3*a, or a = -----------
√3
5√3
Rationalize the denominator: a = ----------
3
Is the first side “LM and HG” or the other way around?
Step-by-step explanation:
Since there is one tick, use LM and HG. but in some cases it doesnt matter
The following system of equations is _____.
y = - x +
2x + 6y = 4
independent
inconsistent
equivalent
Answer:
"equivalent"
Step-by-step explanation:
Right!!
rewrite in Y = MX +b form show your work -6x+2y=10
Answer:
answer y= 3x +5
Step-by-step explanation:
-6x+2y=10
we need to get y by itself so move the -6x to the other side
you get
2y=6x+10
divide everything by 2
2y/2=6x/2+10/2
y= 3x+5
Jim wrote the following derivation of a term with a rational exponent based on a term consisting of a radicand that is less than 0
The equivalent form [tex][latex] {{8}^{\frac{1}{3}}}[/latex][/tex]can be determined where the origin of the numerator of 1.
When rewriting a radical with a fractional exponent, the numerator is the power to which the radicand is increased, and the denominator is the root or index.
The link between [tex][latex] \sqrt[n]{{{a}^{m}}}[/latex]and [latex] {{a}^{\frac{m}{n}}}[/latex][/tex]also applies to rational exponents with a numerator of 1. For instance, the radical [tex][latex] \sqrt[3]{8}[/latex][/tex]
can also be expressed as [tex][latex] \sqrt[3]{{{8}^{1}}}[/latex][/tex].
Since any number retains its value when raised to the first power, [/latex]. Now that you have the equivalent form of [tex][latex] {{8}^{\frac{1}{3}}}[/latex][/tex], you can determine where the origin of the numerator 1.
Know more about rational exponent
https://brainly.com/question/20726608
#SPJ4
aleris is sending a fancy organic fruit basket to her grandma for her birthday. apples cost $3 and oranges cost $2. Aleris can spend no more than $24 on the gift. write an inequality that describes the situation
The inequality when apples cost $3 and oranges cost $2 and Aleris can spend no more than $24 on the gift is 3a + 2o ≤ 24.
How to illustrate the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
In this case, Aleris is sending a fancy organic fruit basket to her grandma for her birthday. apples cost $3 and oranges cost $2 and Aleris can spend no more than $24 on the gift.
Let apple = a
Let orange = o
Therefore, the inequality will be:
3a + 2o ≤ 24.
Learn more about inequalities on:
brainly.com/question/24372553
#SPJ1
If 2E measures 45, ZF measures 98°, and e is 5 feet, then find f using the Law of Sines. Round y
nswer to the nearest foot.
e
4 feet
5 feet
6 feet
7 feet
Answer:
7 feet
Step-by-step explanation:
15. At what rate per cent of interest will a sum of money become 6 times itself in
15 years?
Answer:
The rate of interest will be 40%
Step-by-step explanation:
So first consider the principal to be x
Then the SI (Simple interest) will become six times of itself that is 6x
The time is 15 years
Rate = SI × 100 / P × T
Now put the values
Rate = 6 × x × 100 / x × 15
Then after simplifying the rate will come 40 %
help me please !!!!!
Answer:
The answer is $28,620.
Step-by-step explanation:
$53,000 * 2.7% = 1431
$1,431 * 20 = $28,620
Hope this helped you!!!
What is the inverse of +5?
The inverse of +5 as calculated is found to be +1 / 5.
To find the inverse of +5 we can simply reciprocate it and the result will be the required answer.
reciprocal of +5 = 1 / 5.
Therefore, the answer is 1 / 5.
The opposite or reciprocal of a number or term in math is known as it's inverse. There are two types of inverse in math, the additive inverse and the multiplicative inverse.
The multiplicative inverse of a number for any n is given as 1/n. It is also called as the reciprocal of a number and 1 is called the multiplicative identity. On the other hand subtraction is the inverse of addition.
To learn more about inverse
brainly.com/question/26257987
#SPJ4
h(a) = a^2 + 4 when a = -3
Answer:
[tex] \sf \: h(-3) = 13[/tex]
Step-by-step explanation:
Given information,
→ h(a) = a² + 4
The value of h(a) when a is -3,
→ h(a) = a² + 4
→ h(-3) = (-3)² + 4
→ h(-3) = 9 + 4
→ [ h(-3) = 13 ]
Hence, required answer is 13.
the equation t=s/5 gives the number of cups pf tomatoes,t,required per cup of salad,is. what is the constant of proportionality
The given equation t = s/5 represents a proportional relationship and the value of the constant of proportionality is 1/5.
What is the constant of proportionality?The constant of proportionality is the constant value of the ratio of two proportional values. A proportionality relation exists between two changing quantities when either their ratio or product gives a constant.
Proportional relationships are written in the form y = kx
where k is the constant of proportionality.
The given equation below which is given in the question:
t = s/5
The above equation represents a proportional relationship.
According to the given question, k = 1/5 so the answer is 1/5.
Thus, the value of the constant of proportionality is 1/5.
To learn more about the constant of proportionality here:
https://brainly.com/question/17302514
#SPJ1
Xxxxxxxxxxxxxxxxxxxx
Answer:
XXXXXXXXXXXXXXXXXXXX Ion know
I need help with these questions can someone help please
Answer:you just have to find the slope
Step-by-step explanation:
so all you have to do is start by doing y=Mx+b. You start by placing down you b point on the y axis and then Do your Mx it should look something like this