The distance from the fence to the edge of the garden using the center as reference point is 4 1/2 feet.
Given data
garden 14 1/2 feet long and 8 3/4 feet wide
Fence 23 1/2 feet long and 17 3/4 feet wide
How to find the distance from the fence to the edge of the garden.We assume:
the fence has no thickness,
the distance considered is in the side of the length
the reference point for the distance is the center
Therefore:
Using the mid points we solve as follows:\
garden length / 2 - fence length / 2
= ( 23 1/2 ) / 2 - ( 14 1/2 ) / 2
= 11.75 - 7.25
= 4.5
= 4 1/2 feet
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the perimeter of a triangle is 13 cm whose two sides are 4 cm and 5cm . find the area
The area of the Triangle is 7.8 cm².
The perimeter of the triangle is given to be 13cm.
As we know,
perimeter of triangle = sum of length of all sides of the triangle.
13cm = 4cm + 5cm + third side
third side = 4cm.
Hence two side of the triangle are equal to 4cm. We can say that this is an isosceles triangle, with the base length as 5cm and the other two equal sides of length 4cm.
Let say the base length is B and the other sides length is A.
So area of the isosceles triangle can be given by,
Area = 1/2 x B x √(A²-B²/4)
Area = 1/2 x 5 x √(4²-5²/4)
Area = 1/2 x 5 x √(16 - 25/4)
Area = 1/2 x 5 x 3.12
Area = 7.8 cm².
The area of the triangle is 7.8cm².
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How long does it take to ride a bicycle 100 miles at each of the following speeds: 5 mph, 10 mph, 15 mph, 20 mph, 25 mph? What is always true about the product speed x time?
Answer:
5mph=20 hours to do 100 miles with a bicycle
10mph=10 hours to do 100 miles with a bicycle
15mph=6hours 40minutes(maybe)to do 100miles with a bicycle
20mph=5 hours to do 100miles with a bicycle
25mph=4 hours to do 100 miles with a bicycle
the faster u go the time will decrease
the slower u go the time will increase
hope that helped I didn't really understand much
5x² - 20x + k = 0 has exactly one real solution, show that k=20
Answer:
x = 2
Step-by-step explanation:
5x^2 - 20x + 20 = 0
5 (x^2 - 4x + 4) = 0
x^2 - 4x + 4 = 0
x -2
x -2
(x - 2)(x - 2) = 0
-------------------------
x - 2 = 0
x = 2
-----------------------------
5x² - 20x + k = 0
k = - 5x² + 20x
k = - 5(2)² + 20(2)
k = -20 + 40
k = 20
Answer + Step-by-step explanation:
Consider the equation :
5x² - 20x + k = 0
∆ = b² − 4bc is the discriminant of the quadratic equation.
In our equation :
a = 5 ; b= -20 ; c = k
Then
∆ = (-20)² − 4×5×k
= 20² − 20k
= 20×(20 − k) (Factoring)
The equation 5x² - 20x + k = 0 has exactly one real solution
if and only if ∆ = 0.
Solving the equation ∆ = 0 :
∆ = 0
⇔ 20×(20 − k) = 0
⇔ (20 − k) = 0 (Zero product property)
⇔ k = 20
Ritzie has 80 metres of fencing wire which she wants to use to fence a rectangular plot for gardening. She wished to get the right length and width such that the area enclosed is the maximum. Let x to represent length and y to represent width.
1) Write two equations one for perimetre and the other for area using X and Y
2)Obtain only one equation in terms of area from the equations in 1
Step-by-step explanation:
1)
the perimeter P
P = 2x + 2y = 80 m
the area A
A = x × y
2)
2x + 2y = 80
2y = 80 - 2x
y = 40 - x
and we use that in the equation for area
A = x × (40 - x) = 40x - x²
we find the maximum (or minimum) of a function by finding the 0s of the first derivative.
A' = 40 - 2x = 0
40 = 2x
x = 20
y = 40 - x = 40 - 20 = 20
and just to be sure :
if the second derivative at that point x is negative, we have a maximum, if it is positive, we have a minimum.
A'' = -2
so, it is negative for all x incl. x = 20.
therefore, we have a maximum.
the rectangle with perimeter of 80 m and the max. area is a square of 20 m side length.
Victor thinks that negative 28 / 6 Is greater than negative 100² root cubed. Sean thinks that 17 / 4 is greater. Who is correct
The numbers arranged in a sequence will be - ∛100² < - 4.67 < - 4.25 Both Victor and Sean are correct.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Victor thinks that negative 28 / 6 Is greater than negative ∛100². Sean thinks that 17 / 4 is greater.
The value of the number negative 28 / 6 will be - 4.67.
The value of the number negative ∛100² will be - 21.54.
And the value of the number negative 17/4 will be - 4.25.
The numbers are arranged in a sequence.
- ∛100² < - 4.67 < - 4.25
Both Victor and Sean are correct.
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help please i’ll give brainlist
Answer:
they all can't be divided
7 + (4 + 8) = (7 + 4) + 8
Answer:
true
Step-by-step explanation:
The slope of the parabola
The equation of the line tangent to the parabola at x = 4 is y = 13 · x - 27. The tangent line has a slope of 13 and a intercept of - 27.
How to determine the equation of a line tangent to a parabola
Parabolae are defined by quadratic equations, that is, equations whose form is y = a · x² + b · x + c. The slope of a line tangent to a point of the curve is defined by a linear equation, that is, an equation of the form y = m · x + b. By derivative rules, the slope of the tangent line can be found by using the following expression:
m = 2 · a · x + b
Then, if we know that y = 2 · x² - 3 · x + 5 and x = 4, then the equation of the tangent line is:
Slope
m = 4 · x - 3
m = 4 · 4 - 3
m = 13
Intercept
b = y - m · x
y = 2 · 4² - 3 · 4 + 5
y = 32 - 12 + 5
y = 25
b = 25 - 13 · 4
b = 25 - 52
b = - 27
The equation of the line tangent to the parabola at x = 4 is y = 13 · x - 27. The tangent line has a slope of 13 and a intercept of - 27.
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HELP PLEASEEEEEEEEEEEEEE
Answer:
Step-by-step explanation:
Solve parts of equation in order:
Brackets
Indices
Division
Multiplication
Addition
Subtraction
8 + 2 x 7 - 9 = 63
8 + (2 x 7) - 9 not = 63 (multiplication is the first thing that applies to this equation)
(8 + 14) - 9 not = 63
22 - 9 = 13
So the error would be it equals 13 not 63
Answer:
9 is supposed to be 7
Step-by-step explanation:
8 + 2 = 10
10 × 7 = 70
70 - 7 = 63
5) Imagine that a family just secured a loan for their new home with the following terms:
Loan amount: $160,000 Interest rate: 7% Length of loan: 30 years
Regular Monthly payments: $1064.48 (that is “R” already calculated for you!)
The wife, a sharp former MATH 170 student, suggests that if they make payments of HALF their regular monthly payments every two weeks (instead of a full payment once per month), they would pay off the loan much more quickly and save A LOT of money overall. Find the total amount they would save if they did this.
Hints (follow these steps): Find the half payment (one half of R that’s given!!). If payments are every two weeks, what is n (how many two weeks periods are there in one year?). Use those terms (new R and n) and solve for time. Now find total payments in this case (Rnt), and compare to original loan’s total payments.
I need a answer for this question and it has to be step by step
Answer:
150 student now school gema plyar
A salesperson earns a commission of $510 for selling $3000 in merchandise find the commission rate
Step 1) : Based on the given conditions, formulate
[tex] \large\bf \longrightarrow \frac{510}{3000} [/tex]
Step 2) : Calculate
[tex] \bf \longrightarrow\frac{51 \cancel{0}}{{300 \cancel{0}} } \: = \frac{51 \div 3}{300 \div 3} = \frac{17}{100} [/tex]
Step 3) : Convert to percentage
[tex] \bf\longrightarrow{\frac{17}{100} = 0.17}[/tex]
Hence, the commission rate is 17%.Round this number to the nearest ten thousand.
84,759
A. 80,000
B. 84,000
C. 85,000
D. 90,000
Answer:
Step-by-step explanation:
Answer:
80,000 A
Step-by-step explanation:
it is under 85000 so it is rounding down to 80,000
The side-by-side stemplot below displays the arm spans, in centimeters, for two classes.
A stemplot titled Arm Span (centimeters). For Class A, the values are 148, 151, 153, 155, 156, 159, 161, 162, 164, 165, 169, 169, 170, 171, 175, 176, 179, 179, 180, 182, 183, 186, 186, 190. For Class B, the values are 153, 155, 16, 160, 162, 162, 162, 163, 163, 165, 166, 167, 170, 173, 180, 181, 182, 189, 192, 202.
Which statement correctly compares the arm spans for Class A to those of Class B?
The mean arm span for Class A is much lower than Class B’s.
The mean arm span for Class B is much lower than Class A’s.
The mean arm span for Class A is much higher than Class B’s.
The mean arm span for Class B is about the same as Class A’s.
Answer:
D
Step-by-step explanation:
I got it right!
Answer:
d
Step-by-step explanation:
took the test
Find the distance between the pair of points: (-14, 9) and (3, 9)
Answer:
[tex] \large{ \boxed{ \star{ \tt \: answer : 14 \: units}}}[/tex]
Please see the attached picture for full solution!
-------- HappY LearninG <3 -----
(0.5r +1.2) - (3.6-4.5r) = (4.8-0.3x) + (10.5r +0.6)
Answer:
Step-by-step explanation:
оп 6 от о
Select the correct answer.
Which expression is equivalent to the given expression?
-5y2 +50y - 105
(5y 35) (-y + 7)
(-5y + 21) (y - 5)
O-5(y - 3)(y-7)
-5(y + 21) (y + 1)
-
The value of the expression become 5(y-3) (y-7) = 0. Thus , The option C is correct.
According to the statement
We have to find that the value of the given expression.
So, For this purpose, we know that the
Algebraic expression definition, a symbol or a combination of symbols used in algebra, containing one or more numbers, variables, and arithmetic operations
From the given information:
-5y^2 +50y - 105
Now to find the value of this
Rearrange the expression by taking the common values from this.
then
-5y^2 +50y - 105 = 0
-5y^2 +50y - 105 = 0
5(-y^2 +10y - 21) = 0
5(-y^2 +10y - 21) = 0
5(y^2 - 10y + 21) = 0
Now make factors of it then
5(y^2 - 7y - 3y + 21) = 0
5(y (y -7) -3(y-7)) = 0
5(y-3) (y-7) = 0
So, The value of the expression become 5(y-3) (y-7) = 0. Thus , The option C is correct.
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Amazon is offering a $17.95 discount on a pair of wireless headphones. You pay $71.80 for the headphones after the discount. Write and solve an equation to find the original price of the headphones.
Use "x" for your variable
Answer:
x - 17.95 = 71.80
Use the commutative property of addition
71.80 + 17.95 = 89.75
$89.75 was the original price.
Step-by-step explanation:
Hope it helps! =D
through: (3,-4), perp. to y=-7x
Answer:
y = x/7 + 31/7
or 7y = x + 31
Step-by-step explanation:
The slopes of two perpendicular lines are negative reciprocals of each other so slope will be 1/7
m = 1/7, y = -4, x = 3
y = mx + b
-4 = 1/7(3) + b
b = 3/7 + 4
b = 3/7 + 28/7
b = 31/7
so
y = x/7 + 31/7
or 7y = x + 31
Find the coordinates of the point 3/10 of the way from A to B. The points given are A(-3,-5) , B(9,6)
[tex]\displaystyle\\Answer:\ (-\frac{3}{13},-2\frac{6}{13} )[/tex]
Step-by-step explanation:
[tex]\displaystyle\\\frac{3}{10} =0.3\\\\(-3,-5)\ \ \ \ \ (9,6)\\\\\boxed {x=\frac{x_1+\lambda x_2}{1+\lambda} }\ \ \ \ \ \ \ \ \ \ \ \boxed {y=\frac{y_1+\lambda y_2}{1+\lambda} }\\\\x_1=-3\ \ \ \ \ x_2=9\ \ \ \ \ y_1=-5\ \ \ \ \ \ \ y_2=6\\\\x=\frac{-3+0.3*9}{1+0.3} \\\\x=\frac{-3+2.7}{1.3} \\\\x=\frac{-0.3}{1.3}\\\\ x=-\frac{0.3*10}{1.3*10}\\\\ x=-\frac{3}{13} \\\\[/tex]
[tex]\displaystyle\\y=\frac{-5+0.3*6}{1+0.3} \\\\y=\frac{-5+1.8}{1.3} \\\\y=\frac{-3.2}{1.3} \\\\y=-\frac{3.2*10}{1.3*10} \\\\y=-\frac{32}{13} \\\\y=-2\frac{6}{13} \\[/tex]
If x² + 6x + 16 = (x + a)² + b for all values of x, find the values of a and b.
Answer:
find the value of 8x³-y³ if 2x-yand xy
=-1
Which is the best estimate of 162% of 79?
112
119
128
136
Answer:
nwm zycze powodzenia kolego drogi
Help me please i need urgently
The equation of the line passing through points (-3,0) and (0,3) is y=x+3.
The equation of the line passing through two points (x₁,y₁) and (x₂,y₂) can be calculated using the formula y-y₁=m(x-x₁) , where m denotes the slope of the line .
from the given graph we can find that the line passes through the two points (-3,0) and (0,3)
we get the values , as x₁=-3 , x₂=0 and y₁=0 , y₂=3 .
Slope of the line can be calculated by using the formula ,
m=(y₂-y₁)/(x₂-x₁)
Substituting the values we get ,
m = (3-0)/(0+3)
m=3/3 = 1
Now substituting the values of x₁, x₂, y₁, y₂ and m in the formula of equation of line we get ,
y-0=1(x-(-3))
y-0=1(x+3)
y-0=x+3
y=x+3
Therefore , the equation of the line passing through points (-3,0) and (0,3) is y=x+3.
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William and his children went into a restaurant where they sell hamburgers for $8 each and drinks for $2.50 each. William has $95 to spend and must buy no less than 18 hamburgers and drinks altogether. If xx represents the number of hamburgers purchased and yy represents the number of drinks purchased, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
95=Xx9 +Yx2.50
Step-by-step explanation:
The inequalities graphically shows the given situation is 95 ≥ +2.50y + 18x. The graph is attached below.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for that equation or inequality might be true. Such values are called solution to that equation or inequality.
Here Set of such values is called solution set to the considered equation or inequality.
We have been given that William and his children went into a restaurant where they sell hamburgers for $8 each and drinks for $2.50 each.
Since William has $95 to spend and must buy no less than 18 hamburgers and drinks altogether.
If x represents the number of hamburgers purchased and y represents the number of drinks purchased then;
95 ≥ +2.50y + 18x
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Which expression is equivalent to (xy-5)2 for all values of x and y where the expression is defined?
Answer:
hi hhhhhhdhwjwheheheuhehegdhue
A planet in another solar system has a solar constant S = 2,000 W/m2, and the distance between the
planet and the star is 100 million km.
What is the total power output of the star? (Give your answer in Watts.)
3.5 * [tex]10^{9}[/tex] WATTS IS THE TOTAL OUTPUT OF THE STAR
WHAT IS POWER ?Electrical power is the rate at which electrical energy transforms into another form, such as motion, heat, or an electromagnetic field. The capital P is frequently employed as a symbol representing authority. The universal unit is the watt, which is represented by the letter W. Utility circuits typically have a kilowatt (kW) indication, which is 1000 W.
CALCULATIONSummarized Version:
1-The values of the solar constants were imparted to us by our planet, the first object in our solar system.
2-We therefore know the value of the solar constant for the given solar system, which consists of a planet and the star it orbits.
3-Therefore, if you assume that the orbit is circular, the radius of the orbit will be determined by multiplying the value of the solar constant by 10 to the power 11 m and the radius.
4-We can therefore state that the star's power output is simply equal to the solar constant times the orbit's area.
5-What. So, this is the star's power output for the particular solar system.
The second part of the inquiry now asks what the solar constant will be if the distance between the planet and the star is reduced to 75,000,000 km.
6-We also need to determine what the new solar constant for the solar system will be.
So, in this case, power is equal to area times the solar constant once more.
The solar constant, multiplied by four, multiplied by 3.14, multiplied by are here is 75 multiplied by 10 to the power nine full square, giving us 25.12 multiplied by 10 to the power 25, which is equivalent to that.
We can calculate the value of the solar constant as follows: 25.12 multiplied by 10 to the power of 25 split by four; 3.14 multiplied by 75 square; and 10 multiplied by10.
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What is the vertical distance (Δ`y`) for this slope triangle
What is the horizontal distance (Δ`x`) for this slope triangle?
The vertical distance (Δ`y`) for the slope triangle as indicated is; (4-2) ; 2.
The horizontal distance (Δ`x`) for the slope triangle as indicated is; (4-0) ; 4.
What is the vertical distance (Δ`y`) and horizontal distance (Δ`x`) for this slope triangle?According to the task content, it follows that the vertical and horizontal distance for the slope triangle in discuss are to be determined.
Hence, by observation, Δ`y` can be obtained on the graph from points 4 and 2; we have; 4-2 = 2.
Also, by observation, Δ`x` can be obtained on the graph from points 4 and 0; we have; 4-0 = 4.
Ultimately, the vertical and horizontal distances of the slope triangle are as indicated.
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What is the difference between the largest prime number less than 50 and the sma
than 10?
O 35
O 36
O 37
O 38
Give the equation of the line through (9,7) with y-intercept = -5
Answer:
y = 4/3x - 5
Step-by-step explanation:
y-intercept will be (0,-5)
so m = (y2-y1)/(x2-x1)
m = (-5 -7)/(0 - 9) = (-12)/(-9) = 4/3
Using m = 4/3, y = 7, x = 9
y = mx + b
7 = 4/3(9) + b
7 = 12 + b
b = -5
so
y = 4/3x - 5
Given f(x) = 4/3 x + 1 determine f^-1 (x)
Answer:
[tex] \sqrt[2]{?5} x25 \geqslant 6 - 9 + 88 = 2[/tex]
Answer:
f^-1(x)=(3/4)x
10. Alice bought 2.3
pounds of apples for $2.99
per pound. How much did
she spend on apples?