a rectangle has a diagonal which is 4 times the width if the area is 15root2 what are width andperimeter of the rectangle
Answers
Area: 15√2
Diagonal; 4x
First, you need to find the length using pythagorean theorem.
a=x
c=4x
b=?
Solve this in terms of x and you will find the solution to be; √15x²
Knowing this, plug the number back into the area formula to find the value of x,
(x)(√15x²)=15√2
...
..
x⁴=30
Length= √(15√(30))
Do the calculations just to be sure
Hope I helped :)
Related Questions
The 440 yard dash in track has been replaced by the 400 meter dash. which is the longer distance and by how many meters? hint: 1 yard = 3 feet
Answers
Final answer:
The 400 meter dash is the longer distance by 2.336 meters.
Explanation:
In order to determine which is the longer distance, we need to convert both the 440 yards and the 400 meters into the same unit of measurement. Since 1 yard is equal to 0.9144 meters, we can convert the 440 yards into meters by multiplying it by 0.9144:
440 yards * 0.9144 meters/yard = 402.336 meters
Therefore, the 400 meter dash is the longer distance by 2.336 meters.
Find the coordinates of the other endpoint of the segment with the given endpoint (6,2) and midpoint (2,0)
Answers
TEXASCHIC! :)
1. Sam is observing the velocity of a car at different times. After three hours, the velocity of the car is 51 km/h. After five hours, the velocity of the car is 59 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equation obtained in Part A for the first six hours? (5 points)
My answer:
Part A:
y - 51 = 59 - 51 / 5 - 3 (x-3)
y - 51 = 4 (x-3)
y = 4x -12 + 51
y= 4x + 39
where x is the time and y is the velocity of car at any time x.
Part B:
y =4 * 6 + 39 = 24 + 39 = 63 ~km/h
Answers
slope = (59 - 51) / (5 - 3) = 8/2 = 4
y = mx + b
slope(m) = 4
(3,51)...x = 3 and y = 51
sub and find b, the y int
51 = 4(3) + b
51 = 12 + b
51 - 12 = b
39 = b
so ur equation is : y = 4x + 39...but u need it in standard form
y = 4x + 39
-4x + y = 39
4x - y = -39 <==== this is ur equation...x = number of hrs and y = total velocity
====================
ur x axis is the number of hrs
ur y axis is total velocity in km
y = 4x + 39......slope = 4.....y int = (0,39)....x int is (- 9.75,0) or -9 3/4 for graphing purposes)....so start at (-9.75,0)...and since the slope is 4, go up 4 and to the right 1....plot that...then up 4 and to the right 1...plot that...u will cross the y axis at (0,39)....and just connect ur plotted points and u have ur line......or what u can do since it is asking for the first 6 hrs....sub in 1 for x and solve for y....then sub in 2 for x and solve for y...keep doing this up till 6 and u will have ur line up till 6 hrs
The velocity of the car is represented by the equation y = 4x + 39, where 'x' is time and 'y' is the velocity. You can graph this for the first six hours by substituting x=6 to find: y=63 km/h. Thus, the car's velocity after six hours would be 63 km/h.
Explanation:In order to solve this problem, we first find the equation representing the change in the car's velocity. The point (3, 51) represents the condition that after three hours, the car is moving at 51 km/h. Similarly, the point (5, 59) stands for the velocity being 59 km/h after five hours. We derive the slope of the line connecting these two points by subtracting the y-coordinates and dividing by the difference of the x-coordinates, (59-51)/(5-3) = 4.
This slope represents an increase of 4 km/h for every hour that passes. Our equation then becomes y - 51 = 4(x - 3) which simplifies to y = 4x + 39. In this equation, 'x' represents time in hours and 'y' is the car's velocity at any given time 'x'.
For Part B, we graph the equation over the first six hours by inputting x=6 into the equation, giving us y = 4*6 + 39 = 63 km/h. Therefore, after six hours, the car would be moving at a velocity of 63 km/h.
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Change the column heading for the row sum column which represents the total of each type of session, to total number of sessions
Answers
You can change a column heading by clicking it, then right-clicking to select 'Rename Column' and inputting 'Total Number of Sessions'.
Explanation:To change the column heading for the row sum which represents the total of each type of session to 'Total Number of Sessions', you need to follow these steps:
Firstly, click on the column heading which you want to change. This will usually highlight the entire column.Right-click on the highlighted column heading, and select 'Rename Column' from the drop-down menu.In the text box that appears, type 'Total Number of Sessions' and hit 'Enter'.This will effectively rename your column heading to represent the total number of sessions accurately.
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Factor this expression completely.
mn - 4m - 5n + 20
Answers
Factor by grouping.
[tex]mn-4m-5n+20[/tex]
[tex]m(n-4)-5(n-4)[/tex]
Find the GCF.
[tex](n-4)(m-5)[/tex]
Hope this helps.
-Benjamin
Write the fraction 20/32 in simplest form.
Answers
The fraction given 20/32 can be written as 5/8 in its simplest form.
How to simplify fractions?The principle of simplifying fraction is to make both the numerator and the denominator smaller numbers but as proportional as the original fraction. This is convenient for mathematical operations and even for understanding proportions.
Now, to simplify fractions we need to divide the nominator and the denominator, the process is shown below:
20/32 divide both numbers by 420/ 4 = 532/ 4 = 8This means the new fraction is 5/8.
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how do you find the derivative of 4
Answers
by rule the derivative of a constant is 0
so the answer for this is 0
what is the slope of the line given by the equation y=2.3x
Answers
making the slope of this equation 2.3
I believe this is the correct answer. I hope it helps.
How to do this ?? How
Answers
The two bars | | is used to indicate the function absolute value.
Remember this definition:
| x | = - x if x < 0 and x if x > 0
So, | x | > c =>
x > c or x > - c
Therefore:
|ax - b| > c => ax - b > c or ax - b > - c
That is the third option of the answer list.
How does the volume of a cone compare to the volume of a cylinder with the same radius and height?
Answers
cone volume: π * r^2 * h/3
cylinder volume: π * r^2 * h
Now if you compare both of them with information that the radius and height is same, then the cone:cylinder volume ratio would be:
Cone volume/cylinder volume=
π * r^2 * h/3 / π * r^2 * h= 1/3
Cone volume is 1/3 of cylinder volume
REALLY NEED HELP PLEASE!!
The Smith family rented a recreational vehicle for a seven-day vacation. The cost to rent the recreational vehicle was $560 plus $0.50 per mile. How many miles were driven if the total cost was $1350?
Answers
Its 790
$0.50(x) = $1350 - $560
x = $790/$0.50
x = 1,580 miles
The clean up hitter on a baseball tean batted 1/3 of the runs the team scored. The hitter batted in 3 runs. Select the equation that represents the number of n of runs the team scored. Then solve the equation:
a.1/3n=3B.n/3=1/3C.3n=1/3D.3n=9
Answers
a. 1/3 (n)=3
n=9
Help me please thanks
Answers
Soda is sold in aluminum cans that measure 6 inches in height and 2 inches in diameter. how many cubic inches of soda are contained in a full can?
Answers
v=πr²h (now put in the values to find volume)
v=π(1)²(6)
v=18.85 inches cubed
Therefore, 18.85 inches cubed can be fit into the full can.
Hope I helped :)
A cylinder is a three-dimensional figure that has a radius and a height.
The volume of a cylinder is given as:
Volume = π r²h
The amount of soda in a full can is 18.84 cubic inches.
What is a cylinder?A cylinder is a three-dimensional figure that has a radius and a height.
The volume of a cylinder is given as:
Volume = π r²h
Example:
The volume of a cup with a height of 5 cm and a radius of 2 cm is
Volume = 3.14 x 2 x 2 x 5 = 62.8 cubic cm
We have,
Aluminum cans:
Height = 6 inches
Diameter = 2 inches
Radius = diameter/2 = 2 / 2 = 1 inches
The aluminum can is in the shape of a cylinder.
The volume of the aluminum can:
= πr²h
= 22/7 x 1 x 1 x 6
= 18.84 cubic inches
The amount of soda in a full can is 18.84 cubic inches.
Thus,
The amount of soda in a full can is 18.84 cubic inches.
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what are the zeros of the quadratic function f(x)=8x2-16x-15
Answers
Answer: The zeroes of the given polynomial f(x) are
[tex]x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Step-by-step explanation: We are given to find the zeroes of the quadratic function below:
[tex]f(x)=8x^2-16x-15.[/tex]
To find the zeroes, we must find the roots of the following equation
[tex]f(x)=0\\\\\Rightarrow 8x^2-16x-15=0~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex].
We know that the roots of the quadratic equation of the form [tex]ax^2+bx+c=0,~a\neq 0[/tex] is given by
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]
In the given quadratic equation , a = 8, b = -16 and c = - 15.
Therefore, the roots of the equation are
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\\Rightarrow x=\dfrac{-(-16)\pm\sqrt{(-16)^2-4\times 8\times (-15)}}{2\times 8}\\\\\\\Rightarrow x=\dfrac{16\pm\sqrt{256+480}}{16}\\\\\\\Rightarrow x=\dfrac{16\pm\sqrt{786}}{16}\\\\\\\Rightarrow x=\dfrac{16\pm4\sqrt{46}}{16}\\\\\\\Rightarrow x=\dfrac{4\pm\sqrt{46}}{4}\\\\\\\Rightarrow x=1\pm\sqrt{\dfrac{46}{16}}\\\\\\\Rightarrow x=1\pm\sqrt{\dfrac{23}{8}}\\\\\\\Rightarrow x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Thus, the zeroes of the given polynomial f(x) are
[tex]x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Option (C) is correct.
The zeroes of the given polynomial f(x) = 8x^2-16x-15 are x = 1 + [tex]\sqrt{23}[/tex] / 8 and x = 1 -[tex]\sqrt{23}[/tex] / 8 Thus, Option C is correct.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We are given to find the zeroes of the quadratic function f(x) = 8x^2 - 16x-15
f(x) = [tex]8x^2-16x-15[/tex] = 0
We know that the roots of the quadratic equation ax² + bx + c = 0 is
x = -b ± [tex]\sqrt{b^2 - 4ac}[/tex] / 2a
In the given quadratic equation , a = 8, b = -16 and c = - 15.
So,
x = -b ± [tex]\sqrt{b^2 - 4ac}[/tex] / 2a
x = -(-16) ± [tex]\sqrt{(-16)^2 - 4(8)(-15)}[/tex] / 2(8)
x = 16 ± [tex]\sqrt{256+ 480}[/tex] / 16
x = 16 ± [tex]\sqrt{786}[/tex] / 16
x = 4 ± [tex]\sqrt{46}[/tex] / 4
x = 1 ± [tex]\sqrt{23}[/tex] / 8
Thus, the zeroes of the given polynomial f(x) are
x = 1 + [tex]\sqrt{23}[/tex] / 8 and x = 1 -[tex]\sqrt{23}[/tex] / 8. Option C is correct.
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Evaluate the determinant for the following matrix [144] [522] [155]
Answers
1 4 4
5 2 2
1 5 5
=> Determinant =
1 * (2*5 - 2*5) - 4 * (5*5 - 1*2) + 4 * ( 5*5 - 2*1)
= 1*(10 - 10) - 4*(25 - 2) + 4*(25 -2) = 1*0 + 4* 23 + 4*(25 - 2) = 0 - 4*23 + 4*23 = 0
Answer: 0
Is - √3 a real number, whole number, natural number, rational number, irrational number, an integer, or imaginary number?
Answers
Sarah has a collection of nickels, dimes, and quarters worth $13.80. she has 10 more dimes than nickels and twice as many quarters as dimes. how many coins of each kind does she have?
Answers
22 dimes = $2.20
44 quarters = $11.00
11.00
2.20
+ .60
———
13.80
Which statement best explains whether △PQR is congruent to △XYZ?
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a rotation of 180° about the origin.
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a translation 5 units down followed by a reflection across the y-axis.
△PQR is not congruent to △XYZ because there is no sequence of rigid motions that maps △PQR to △XYZ.
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a reflection across the y-axis followed by a reflection across the x-axis.
Answers
The average rate of change of the function between x = 15 to x = 29 is __________m/s2 and represents the car's acceleration.
Answers
Answer:
sorry guys that other question is absolutely no help at all. The answer is 1.266 m/s squared. I don't know what kind of IDIOT would try and take you to a completely other website.
Step-by-step explanation:
What is the standard form of the following equation?
y=−2/5x+4 Use integers for A, B, and C. Enter your answer in the box.
Answers
so
[tex] \frac{-2}{5} x -y=-4 [/tex]
multiply by -1 to make the x coefficient positive
[tex] \frac{2}{5} x+y=4 [/tex]
so we multiply by 5 to make them integers
[tex]2x+5y=20[/tex]
A=2,B=5,C=20
How do I solve this?
Answers
-c^2-4c+21
From here, we’ll factor out a -1 so that we have:
-(c^2+4c-21)
Let’s focus on the quadratic expression inside the parentheses. To find our factors (c + x)(c + y), we’ll need to find two terms x and y that multiply together to make -21 and add together to make 4. It turns out that the numbers -3 and 7 work out perfectly for that purpose (-3 x 7 = -21 and 7 + (-3) = 4), so substituting them in for x and y, we have:
(c + (-3))(c + 7)
(c - 3)(c + 7)
And adding back on the negative from a few steps earlier:
-(c - 3)(c + 7)
The volume of air inside a rubber ball with radius r can be found using the function v(r)=4/3 πr3 . What does v[5/7] represent?
a. the radius of the rubber ball when the volome equals 5/7 cubic feet
b. the volome of the rubber ball when the radius equals 5/7 feet
c. that the volume of the rubber ball is 5 cubic feet when the radius is 7 feet
d. that the volume of the rubber ball is 7 cubic feet when the radius is 5 feet
Answers
we know that
The volume of a sphere (rubber ball) is equal to
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
where
r is the radius of the sphere (rubber ball)
The volume in function notation is equal to
[tex]V(r)=\frac{4}{3} \pi r^{3}[/tex]
in this problem we have
[tex]V(\frac{5}{7})[/tex]
that means
The radius of the rubber ball is [tex]\frac{5}{7}\ ft[/tex]
and
The volume of the rubber ball is [tex]V(\frac{5}{7})\ ft^{3}[/tex]
therefore
the answer is the option B
the volume of the rubber ball when the radius equals [tex]5/7[/tex] feet
What is the answer for 35=-7z
Answers
Name 3 decimals between 16.4 and 16.5 draw a number line estmating the placement of all five decimals
Answers
annie dome worked from 8:15 am to 11:45 am and from 12:30 pm to 4:15 pm. How many hours did she work? (include steps on how to do this problem)
Answers
Heather works as a waitress at her family`s restaurant. she works 2 hours every morning during the breakfast shift and returns to work work each evening for the dinner shift. In the last 4 days ,she worked 28 hours. If Heather works the same number of hours every evening, how many hours did she work during each dinner shift?
Answers
2 hours x 4 days = 8 hours
Subtract,
28 hours - 8 hours = 20 hours
Divide
20 hours ÷ 4 days = 5 hours each day.
Check you work by Multiplying and adding
5 hours x 4 days = 20
20 hours + 8 hours = 28 hours
Heather worked 5 hours each dinner shift
MATH HELP 20 POINTS!!!
Answers
A) Variable = x ( miles Tim walked )
B) Tim walked X miles, Molly walked 4+x miles ( 4 more than Tim)
Equation: x + x+4 = 10
C) x +x+4 = 10
2x+4 = 10
2x =6
x = 3
D)
Tim walked 3 miles, Molly walked 7 miles
I feel really stupid but how do you solve: v+9/3+8
Answers
The answer is v +11.
The answer would be simply
V 11
Please help with this equation!!! 30 points!
The following equation is shown.
[tex] x^{2} - \sqrt{2.5} -l + ( -\pi + z ) = A[/tex]
Solve for the variable z.
Answers
z= -x²+l+4.72273148+A