We get the dimensions of the park as length = 75 feet and width = 20 feet.
We are given that:
A yard has a perimeter of 190 feet.
Also, four times the length of the yard equals 15 times the width.
Now,
Let the length of the yard be x.
ATQ, we get the width of the yard as:
15 width = 4 x
Width = 4 / 15 x
Perimeter = 2 ( l + b )
190 = 2( x + 4 / 15 x )
95 = 19 x / 15
19 x = 95 × 15
19 x = 1425
x = 1425 / 19
x = 75 feet.
Length = 75 feet
Width = 4 / 15 x = 20 feet.
Therefore, we get the dimensions of the park as length = 75 feet and width = 20 feet.
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hey can anyone help me out withthis question pls? we need to find the total surface area
Answer:
60000 cm squared 600 dm squared or 60 cm squared
Step-by-step explanation:
Solve the following:
1. even integers between 1 and 101
2. first 25 terms of the arithmetic sequence 4, 9, 14, 19, 24 ...
Answer:
1. 2550
2. 1600
Step-by-step explanation:
Question 1Even Integer: A whole number that can be positive, negative, or zero, and that can be divided exactly by 2.
Even integers between 1 and 101:
2, 4, 6, 8, 10, ... , 100This forms an arithmetic sequence with:
first term (a) = 2common difference (r) = 2Sum of the first n terms of an arithmetic series:
[tex]\boxed{S_n=\dfrac12n[2a+(n-1)d]}[/tex]
There are 50 even integers between 1 and 101.
Therefore, to find the sum of the even integers between 1 and 101, substitute n = 50 and the found values of a and r into the formula:
[tex]\begin{aligned}\implies S_{50} & =\dfrac{1}{2}(50)[2(2)+(50-1)2]\\\\& =25[4+(49)2]\\\\& =25[4+98]\\\\& =25[102]\\\\& = 2550\end{aligned}[/tex]
Therefore, the sum of the even integers between 1 and 100 is 2550.
Question 2Given arithmetic sequence:
4, 9, 14, 19, 24, ...From inspection of the given arithmetic sequence:
first term (a) = 4common difference (r) = 9 - 4 = 5Sum of the first n terms of an arithmetic series:
[tex]\boxed{S_n=\dfrac12n[2a+(n-1)d]}[/tex]
To find the sum of the first 25 terms of the given arithmetic sequence, substitute n = 25 and the found values of a and r into the formula:
[tex]\begin{aligned}\implies S_{25} & =\dfrac{1}{2}(25)[2(4)+(25-1)5]\\\\& =\dfrac{25}{2}[8+(24)5]\\\\& =\dfrac{25}{2}[8+120]\\\\& =\dfrac{25}{2}[128]\\\\& = \dfrac{3200}{2}\\\\& = 1600\end{aligned}[/tex]
Therefore, the sum of the first 25 terms of the given arithmetic sequence is 1600.
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ents
PQ bisects ST at R. SR=3x+3 and ST 30. Find z.
S
Ox=8
Ox=6
O x = 2
Ox=4
If line PQ bisects line ST at point R and SR=3x+3 and ST=30 then the value of x = 4.
As given in the question,
Line PQ bisects ST at point R
SR=3x+3
ST=30
R is the midpoint of ST as PQ bisects ST this implies
Line SR=1/2 of line (ST)
⇒SR=ST/2
Substitute the value of SR and ST in the given condition
3x+3=30/2
⇒3x+3=15
Subtract 3 from both the sides
⇒3x=12
Divide both the side by 3
⇒3x/3=12/3
⇒x=4
Therefore, for the line PQ bisects line ST at point R and SR=3x+3 and
ST=30 then the value of x is equal to 4.
The complete question is:
If the line PQ bisects line ST at point R. SR=3x+3 and ST = 30. Find x.
a. x= 8 b. x =6 c. x =2 d. x= 4
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Can someone help me with this question please like I really need this asap.
Using the fact that the two angles are complementary, the we will find that the measures are:
∠1 = = 14°
∠2 = 76°
How to find the measures of the angles?
By looking at the diagram, we can see that the sum of the measures of angles 1 and 2 must be equal to 90° (this means that the two angles are complementary).
We also can see that:
∠1 = x - 5
∠2 = 4x
Then we can solve the linear relation:
(x - 5) + 4x = 90
x - 5 + 4x = 90
5x - 5 = 90
5x = 90 + 5 = 95
x = 95/5 = 19
Then the measures of the two angles are:
∠1 = (x - 5)° = (19 - 5)° = 14°
∠2 = 4x = 4*19° = 76°
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Question 7
Which function below does not have a domain of (-∞0, ∞0)?
○ f(x) = {²+2
²+2,
[4x-1, ifr <1
if x ≥1
O f(x)= 2² +1
Of(x) = √2r-1+4
Of(r) = 3r² - 5x + 2
4.5
Answer:
Step-by-step explanation:
What functions have a domain of (- ∞ ∞?
Which function below does not have a domain of (-∞0, ∞0)?○ f(x) = {²+2²+2,[4x-1, ifr <1if x ≥1O f(x)= 2² +1Of(x) = √2r-1+4Of(r) = 3r² - 5x + 24.5
The domain of any polynomial function (including quadratic functions) is x∈(−∞,∞). Functions of even degree will have a bounded range (from below if the leading coefficient is positive, from above if it's negative), and functions of odd degree will have range y∈(−∞,∞).
If Z is the Circumcenter of TUV, find each missing measure
Answer is
VY = 17
UZ =21
WV = 14.7
TV = 29.4
TU = 38
SOLVING STEPS
WV = [tex]x^{2}[/tex]+[tex]15^{2}[/tex] = [tex]21^{2}[/tex]
⇒[tex]x^{2}[/tex] + 225 = 441
⇒ [tex]x^{2}[/tex] = 441-225
⇒ [tex]x^{2}[/tex] = 216
⇒ x = [tex]\sqrt{216}[/tex]
VY = 17
UZ =21
WV = 14.7
TV = 29.4
TU = 38
The circumcentre of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect. In other words, the point of concurrency of the bisector of the sides of a triangle is called the circumcentre.
Method to Calculate the Circumcentre of a Triangle
Steps to find the circumcentre of a triangle are:
Calculate the midpoint of given coordinates, i.e. midpoints of AB, AC, and BC
how to calculate the slope of the particular line :
By using the midpoint and the slope, find out the equation of the line (y-y1) = m (x-x1)
Find out the equation of the other line in a similar manner
Solve two bisector equations by finding out the intersection point
Calculated intersection point will be the circumcentre of the given triangle
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. Write a variable expression that represents the following word phrase:
Four less than half the difference of 3 and x
Answer: [tex]\frac{3-x}{2}[/tex]-4
Step-by-step explanation:
(3-x)/2 -4=[tex]\frac{3-x}{2}[/tex]-4
Simplify.
[tex](4x^{2})^{3}(3x^{6})^{4}[/tex]
sentence below is True or False.
Any multiplication can be undone by multiplying by the same number.
Answer: False
Step-by-step explanation:
A rectangle with a total of 80 square feet has been broken into two rectangles with areas of 56
square feet and 24 square feet as shown. The common length of the two smaller rectangles is
a whole number that is greater than either width 1 or width 2, which are both whole numbers.
From this information, determine the length, width 1, and width 2. Explain how you found
your answers.
The length of the rectangle is 8 feet, width 1 is 7 feet and width 2 is 3.
A rectangle of area 80 square feet is broken and forms two square rectangles of area 56 square feet and 24 square feet, which has a common length.
Area of the rectangle = length × width
Now suppose the length is x feet, and let width 1 be a and width 2 be b.
Therefore we get that
rectangle first is of area = x a
rectangle second is of area = x b
Therefore original rectangle area = area of first rectangle + area of the second rectangle
80= x a + x b
80 = x( a + b)
As it is given that the length is common and is greater than both the width of the rectangle
56 = 8 × 7
24 = 8 × 3
So we will take x = 8 and a =7, b= 3
Now put these numbers in the equation to see if they fulfill the criteria
80 = 8( 7 + 3)
80 = 80
Therefore we get a length is 8, a width of 1 is 7, and a width of 2 is 3.
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Each day a small business owner sells 200 pizza slices at $2.50 per slice and 85 sandwiches at $2.00 each. Business
expenses come to $60 per day. What is the owner's profit for a ten-day period?
The profit is S
The owner's profit for a ten-day period is equal to $ 6100.
We are given that:
Selling price of 1 pizza slice = $ 2.50
Number of pizza slice sold per day = 200
Selling price for pizza slices in a day = 200 × $ 2.50
SP ( pizza ) = $ 500
Selling price of 1 sandwich = $ 2
Number of sandwich sold per day = 85
Selling price for pizza slices in a day = 85 × $ 2
SP ( sandwich ) = $ 170
Selling price in 1 day = $ 500 + $ 170 = $ 670
Now, Cost price in 1 day = $ 60
Profit in 1 day = $ 670 - $ 60 = $ 610
Profit in 10 days = 10 × $ 610 = $ 6100
Therefore, the owner's profit for a ten-day period is equal to $ 6100.
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Which statement describes the order of rotational symmetry for an isosceles triangle?
An isosceles triangle has an order 0 rotational symmetry because there is no angle at which it can be rotated onto itself.
An isosceles triangle has an order 1 rotational symmetry because it does not have all congruent angles.
An isosceles triangle has an order 2 rotational symmetry because it has 1 pair of congruent angles.
An isosceles triangle has an order 3 rotational symmetry because it has 3 angles.
The statement B is correct which states that the An isosceles triangle has an order 1 rotational symmetry because it does not have all congruent angles.
According to the statement
We have to find that the correct statement about the rotational symmetry for an isosceles triangle.
So, For this purpose, we know that the
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn.
From the given information:
Then from isosceles triangle,
An isosceles is a triangle that has two sides of equal length.
The isosceles theorem says that the angles opposite to the equal sides of a triangle are equal.
Thus, it also has two equal angles and one non equal angle. Thus, it does not have all congruent angles.
The order of rotational symmetry of a figure is the number of times we rotate up to 360° the figure such that it looks exactly the same as the original figure.
When we rotate the isosceles triangle up to 360° , only 1 time it looks exactly same as in the beginning because at each rotation the order of angles changes.
Therefore, The statement B is correct which states that the An isosceles triangle has an order 1 rotational symmetry because it does not have all congruent angles.
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Answer: B. An isosceles triangle has an order 1 rotational symmetry because it does not have all congruent angles.
Step-by-step explanation: right on edge 2023
A standard train ticket in a certain city costs 3 per ride. people who use the train also have the option of purchasing a frequent-rider pass for 18.75 each month. with the pass, a ticket costs only 2.25 per ride. how many train rides in a month make the frequent-rider pass a better deal than standard train tickets?
a. 26 or more rides
b. 24 or more rides
c. 25 or more rides
d. 27 or more rides
Number of train rides to make the frequent-rider pass a better deal than standard train tickets is 26 or more rides.
As given,
Cost of standard train ticket = 3 per ride
Price of frequent rider pass= 18.75 each month
Cost of ticket using rider pass = 2.25 per ride
let x be the number of rides
Equation:
18.75 + 2.25x < 3x
⇒ 0.75x > 18.75
⇒ x > 25
Therefore, number of train rides to frequent-rider pass a better deal than standard train tickets is 26 or more rides.
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Find all the zeros of the quadratic function.
y=x^2+ 8x + 12
If there is more than one zero, separate them with commas.
If there are no zeros, click on "None".
Answer:
x=-2, -6
Step-by-step explanation:
factor the expression
y=x^2+ 8x + 12
y= (x+2)(x+6)
set the equation equal to 0, since you are finding zeros, or solutions
0=(x+2)(x+6)
split the equation into two parts
0=(x+2) and 0=(x+6)
solve the equations
you should get 2 zeros
x=-2, -6
what is (-3, 0) (0, -3) in slope-intercept form
Answer: Y= 1x + 0
Y=mx+b
The sears tower in chicago is 443 m tall. Joe wants to set the world’s stair climbing record and runs all the way to the roof of the tower. If joe’s average upward speed is 0. 60 m/s, how long will it take joe to climb from street level to the roof of the sears tower?.
It will take Joe 738.3 seconds (12.3 minutes) to climb from street level to the roof of the sears tower.
What is speed?The definition of speed is the rate at which an object's position changes in any direction. Speed is defined as the ratio of distance traveled to time spent traveling. Because it has only one direction and no magnitude, speed is a scalar quantity. Speed is a measure of how quickly something moves or is done, or how fast something moves. A car traveling at 45 miles per hour is an example of speed. Someone cleaning a room in 10 minutes is an example of speed. A jaguar's speed is an example of speed.To find how long will it take joe to climb from street level to the roof of the sears tower:
If Joe moves at 0.6 m/s in the vertical direction, the total distance he must cover is 443 meters in the vertical direction. The formula for average speed is now:Average speed = total distance / total timeTotal time = total distance / average speedTotal time = 443/0.6Total time = 738.3 secondsTherefore, it will take Joe 738.3 seconds (12.3 minutes) to climb from street level to the roof of the sears tower.
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The length of a rectangle is four times its width.
If the perimeter of the rectangle is 70 yd whats the length and width
Answer:
length is 20 width is 5
Step-by-step explanation:
35
5 20
The following table shows the number of hours some teachers in two schools expect students to spend on homework each week.
School A
9
14
15
17
17
7
15
6
6
School B
12
8
13
11
19
15
16
5
8
Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (5 points)
Part B: Are there any outliers present for either data set? Justify your answer mathematically. (5 points) (10 points)
Answer:
Part A: School A Interquartile range = 9.5. School B Interquartile range = 7.5
Part B: There are no outliers present for either data set.
Step-by-step explanation:
For Part A, school A interquantile range is 9.5. Five number summary of school A is minimum = 6, quarantine q1= 6.5, median = 14, quarantine q3 = 16, and maximum = 17. Calculate Q3-Q1 = 16 - 6.5 which gives you 9.5
For School B, the interquartile range is 7.5. Five number of summary of school B is minimum = 5, quarantine q1 = 8, median = 12, quarantine q3= 15.5, maximum = 19. IQR Range = Q3-Q1 = 15.5 - 8. Which gives you 7.5
For Part B: All the outcomes of school A in between the values of -7.75 and 30.25. So this means there is no outliers in school A. For school B, all the outcomes of school B in between the values of -3.25 and 26.75. So there are no outlines in school B.
Show that
5x+2
3x
+1⁄/12
can be written in the form
ax+b
CX
where a, b and c are integers.
Answer:
Step-by-step explanation:
When completing the square, an expression like,
ax2 + bx + c is written in the form (Ax + B)2 + C.
We will begin with the simple example where a = 1. In this case we will write expressions in the form
x2 + bx + c as (x + B)2 + C
If we expand (x + B)2 + C we get x2 + 2Bx + B2 + C.
Comparing this with x2 + bx + c shows that
b = 2B and c = B2 + C
which gives B =
b
2
and C = c – B2
square root method 5x+9=134
Answer:
Step-by-step explanation:
What are you trying to find? If you want to find x then:
5x = 134 - 9
5x = 125
x = 25
if you want square root then,
x = √625 or
x = 5^2
How many license plates can be made using either three letters followed by three digits or four letters followed by two digits?
63273600 license plates can be created using either three uppercase English letters preceded by three digits or four uppercase English letters tried to follow by two digits.
What are permutations and combinations?Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement.When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.So,
Uppercase English letters equal 26.and the digits = 10 (0 to 9)Three uppercase English letters, then three digits:
First letter = 26 different waysSecond letter = 26 different waysThird letter = 26 different waysFourth digit = 10 different waysFifth digit = 10 different waysSixth digit = 10 different waysTotal number of possible ways = 26 x 26 x 26 x 10 x 10 x 10 = 17576000
Four uppercase English letters, then two digits:
First letter = 26 waysSecond letter = 26 waysThird letter = 26 waysFourth letter = 26 waysFifth digit = 10 waysSixth digit = 10 waysTotal number of possible ways = 26 x 26 x 26 x 26 x 10 x 10 = 45697600
Three uppercase English letters, three digits, or four uppercase English letters, two digits.
= three uppercase English letters, three digits + four uppercase English letters, two digits= 17576000 + 45697600= 63273600Therefore, 63273600 license plates can be created using either three uppercase English letters preceded by three digits or four uppercase English letters tried to follow by two digits.
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pls helpp que 3d and 3g
Answer:
Step-by-step explanation:
d)
[tex]\displaystyle\\\frac{h}{2h+5} +\frac{5}{6} =\\\\\frac{h*6+5*(2h+5)}{(2h+5)*6} =\\\\\frac{6h+2h(5)+5(5)}{2h(6)+5(6)} \\\\\frac{6h+10y+25}{12h+30} =\\\\\frac{16h+25}{12h+30}[/tex]
g)
[tex]\displaystyle\\\frac{3n}{(2n-1)^2} -\frac{5}{2n-1} =\\\\\frac{3n*1 -5*(2n-1)^}{(2n-1)^2}=\\\\\frac{3n(1)-2n(5)-1(-5)}{(2n-1)^2}=\\\\\frac{3n-10n+5}{(2n-1)^2} =\\\\\frac{-7n+5}{(2n-1)^2}[/tex]
How do I solve
-1 2/3 - -5/6
Answer:
-7/6
Step-by-step explanation:
negative 5 over 6−
5
6
≈negative 0.833−0.833
What is the value of 5k² - 6 when k = 9?
O 84
O 375
O 399
O 2019
Answer:
2019
Step-by-step explanation:
work out the y^3 + 5y when y = 2
Step-by-step explanation:
y³ + 5y
2³ + 5 × 2
8 + 10
18...
Hi!
[tex]\diamondsuit[/tex] Plug in 2 for y:
[tex]\boldsymbol{2^3+5(2)}[/tex]
[tex]\diamondsuit[/tex] Cube 2 first:
[tex]\boldsymbol{8+5(2)}[/tex]
[tex]\diamondsuit[/tex] Multiply 5 times 2 next:
[tex]\boldsymbol{8+10}[/tex]
[tex]\diamondsuit[/tex] Add.
[tex]\boldsymbol{18}[/tex]
Therefore,
[tex]\stackrel{\heartsuit}{\boxed{\boxed{\boldsymbol{Answer:~~18}}}}[/tex]
Cheers!!I hope I helped, have an amazing rest of your day!
If you need any explanation or clarification - comment! :)
6x +3 = 2x - 9
help please
Answer:
the equation is falseStep-by-step explanation:
6x + 3 = 2x - 9
6x - 2 x = -9 - 3
4x = -12
x = -12 : 4
x = -3
----------------
CHECK
6 * (-3) = 2* (-3) - 9
-18 = -15
the equation is false
If you answer you get 15 points.
Answer:D
Step-by-step explanation:
Answer:
I think it's the last one, the one that have month 4,6,8.
Step-by-step explanation:
-2 2/3 divided by 4/3
Answer:
-2
Step-by-step explanation:
[tex]Rule(s): a\frac{b}{c} = \frac{a \cdot c + b}{c}, \frac{-a}{b}=-\frac{a}{b}, \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c} \\2\frac{2}{3}=\frac{2\cdot 3+2}{3}\\=\frac{8}{3}\\=\frac{-\frac{8}{3}}{\frac{4}{3}}\\=-\frac{\frac{8}{3}}{\frac{4}{3}}\\=\frac{-8\cdot \:3}{3\cdot \:4}\\= \frac{-24}{12}\\= -2[/tex]
Analyze the table of values for the continuous function, f(x), to complete the statements.
A local maximum occurs over the interval
.
A local minimum occurs over the interval
.
A local maximum occurs over the interval (-2,0)
A local minimum occurs over the interval (0,2)
How do you find a function's maximum value?
We may calculate the maximum of a continuous and twice differentiable function f(x) by first differentiating it with respect to x and then equating it to 0.
A local maximum occurs over the interval (-2,0)
A local minimum occurs over the interval (0,2)
Step-by-step explanation:
-lukelaws hope i helped if i di please give me brainliest if i was wrong i am very sorry!
Solve for x in this figure.
Enter your answer in the box.
x = °
The value of x in the hexagon given in the image above is: 132°.
What is the Sum of an N-Sided Polygon?The sum of all interior angles of an n-sided polygon = (n - 2)180, where n is the number of angles/sides of the polygon.
The polygon shown is a hexagon with six (6) interior angles. Find its sum.
Sum of the hexagon = (6 - 2)180
Sum of the hexagon = 720°
This means that if we add the measures of all the six interior angles of the given hexagon, we would get 720°.
Therefore:
x + 108 + 113 + 132 + 75 + 160 = 720
x + 588 = 720
x = 720 - 588
x = 132°
Thus, the value of x in the hexagon given in the image above is: 132°.
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