Answer:
width of the garden is 50 ft and the length is 70 ft
Step-by-step explanation:
Solution:-
- We will denote the width and and the length of the rectangular garden as:
Width: x
Length: x + 20
- We are given the area ( A ) of the garden is 3500 ft^2. We are to determine for what dimensions is the area A = 3500 ft^2.
- Recall that the area ( A ) of a rectangle is the product of length and width as follows:
A = Length * width
A = x*( x + 20 )
3500 = x^2 + 20x
x^2 + 20x - 3500 = 0
- Use the quadratic formula to determine the value of ( x ):
[tex]x = \frac{-b +/- \sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{-20 +/- \sqrt{20^2 - 4*-3500} }{2}\\\\x = \frac{-20 +/- 120 }{2} = -10 +/- 60\\\\x = -70 , 50[/tex]
- Ignore the negative value of ( - 70 ft ). Physical impractical to have a negative value. Hence, the width of the garden is 50 ft and the length is 70 ft
Y + 1 1/6 = 7 5/6 what is Y
Answer:
6[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
y + 1[tex]\frac{1}{6}[/tex] = 7[tex]\frac{5}{6}[/tex]
y + [tex]\frac{7}{6}[/tex] = [tex]\frac{47}{6}[/tex]
y = 40/6 = 20/3 = 6[tex]\frac{2}{3}[/tex]
Given that r = ( 7, 3, 9) and v = ( 3, 7, -9), evaluate r + v
a. (-21,-21,81)
b. (10,10,0)
c. (21,21,-81)
d. (-10,-10,0)
Answer:
b. (10,10,0)
Step-by-step explanation:
r+v can be evaluated if the vectors/matrices have the same dimensions.
These do. They are both 1 by 3 vectors.
Just add first to first in each.
Just add second to second in each.
Just add third to third in each.
Example:
(5,-5,6)+(1,2,3)
=(5+1,-5+2,6+3)
=(6,-3,9)
Done!
In general, (a,b,c)+(r,s,t)=(a+r,b+s,c+t).
r+v
=(7,3,9)+(3,7,-9)
=(7+3,3+7,9+-9)
=(10,10,0)
Done!
You pick two students at random, one at a time. What is the probability that the second student is a sophomore, given that the first is a freshman
Answer:
0.40
Step-by-step explanation:
The computation of the probability for the second student be sophomore and the first is a freshman is shown below:
Let us assume
Sophomore = S
Freshman = F
Based on this assumption, the probability is as follows
So,
[tex]= \frac{P(S\cap F)}{P(F)} \\\\ = \frac{P(S) \times P(F)}{P(F)} \\\\ = \frac{16}{40}[/tex]
= 0.40
Hence, the probability for the second student be sophomore and the first student be freshman is 0.40
letry. 14 Chapter 9: Chapter 9 rest Chapter Test
A roof has a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section. Find the height of the roof.
Round your answer to the nearest tenth.
15 ft
h
8 ft
17 ft
Answer:
h = 7.1 cm
Step-by-step explanation:
To find the height of the triangle, we can first find the area of the triangle using the Heron's formula:
[tex]S = \sqrt{p(p-a)(p-b)(p-c)}[/tex]
Where a, b and c are the sides of the triangle and p is the semi perimeter of the triangle:
[tex]p = \frac{a+b+c}{2} = \frac{15 + 8 + 17 }{2} = 20\ cm[/tex]
So the area of the triangle is:
[tex]S = \sqrt{20(20-15)(20-8)(20-17)}[/tex]
[tex]S = 60\ cm^2[/tex]
Now, to find the height, we can use the following equation for the area of the triangle:
[tex]S = base * height/2[/tex]
The height draw in the figure is relative to the side of 17 cm, so this side is the value of base used in the formula. So we have that:
[tex]60 = 17 * h/2[/tex]
[tex]h = 120/17[/tex]
[tex]h = 7.06\ cm[/tex]
Rounding to the nearest tenth, we have h = 7.1 cm
Answer:
7.1 cm
Step-by-step explanation:
:D
Please Help!!! Find X for the triangle shown.
Answer:
[tex] x = 2 [/tex]
Step-by-step explanation:
Given a right-angled triangle as shown above,
Included angle = 60°
Opposite side length = 3
Adjacent side length = x
To find x, we would use the following trigonometric ratio as shown below:
[tex] tan(60) = \frac{3}{x} [/tex]
multiply both sides by x
[tex] x*tan(60) = \frac{3}{x}*x [/tex]
[tex] x*tan(60) = 3 [/tex]
Divide both sides by tan(60)
[tex] \frac{x*tan(60)}{tan(60} = \frac{3}{tan(60} [/tex]
[tex] x = \frac{3}{tan(60} [/tex]
[tex] x = 1.73 [/tex]
[tex] x = 2 [/tex] (approximated to whole number)
Let x and y be real numbers satisfying 2/x=y/3=x/y Determine the value of x^3
Answer:
64/27Step-by-step explanation:
If x and y be real numbers satisfying 2/x=y/3=x/y, then any two of the equation are equated as shown;
2/x = y/3 ... 1 and;
y/3 = x/y... 2
From equation 1, 2y = 3x ... 3
and from equation 2; y² = 3x ... 4
Equating the left hand side of equation 3 and 4 since their right hand sides are equal, we will have;
2y = y²
2 = y
y = 2
Substituting y = 2 into equation 3 to get the value of x;
2y = 3x
2(2) = 3x
4 = 3x
x = 4/3
The value of x³ will be expressed as (4/3)³ = 4*4*4/3*3*3 = 64/27
If f(x) = 2x2 + 2 and g(x) = x2 – 1, find (f – 9)(X).
Answer:
x^2 +3
Step-by-step explanation:
f(x) = 2x^2 + 2
g(x) = x2 – 1,
find (f – g)(X).
f(x) - g(x) = 2x^2 + 2 -( x^2 – 1)
Distribute the minus sign
= 2x^2 +2 -x^2 +1
= x^2 +3
PLZ HELP IM STUPID. A teacher surveyed her class to find out how many texts the students send in a week. She created this box plot to show the data. Find the interquartile range. 50 points!
Answer:
236
Step-by-step explanation:
The interquartile range is the right edge of the box minus the left edge of the box
The right edge of the box is 301
The left edge of the box is 65
301 -65 =236
The interquartile range is 236
Answer:
65
Step-by-step explanation:
To find interquartile range, you substract upper quartile( 130 in this problem) and the lower quartile(65 in this problem)
Finally, you get the answer 65.
Hope this helps!
Find the coordinate vector [Bold x ]Subscript Upper B of x relative to the given basis BequalsStartSet Bold b 1 comma Bold b 2 comma Bold b 3 EndSet.
Answer:
3
Step-by-step explanation:
3
Find the circumference of a circular field with a diameter of 16 yards.
(Let it = 3.14)
Answer:
Hey there!
The circumference of a circle is [tex]\pi(d)[/tex], where d is the diameter, and [tex]\\\pi[/tex] is a constant roughly equal to 3.14.
The diameter is 16, so plugging this into the equation, we get 3.14(16)=50.24.
The circumference of the circle is 50.24 yards.
Hope this helps :)
Consider the line – 5x – 8y= 3.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Answer:
Perpendicular Slope: 8/5
Parallel Slope: -5/8
Step-by-step explanation:
First, let's rewrite the line into slope intercept form.
-5x - 8y = 3
-8y = 5x + 3
y = -5x/8 + -3/8
Okay, so now we know the slope, -5/8, and the y-intercept, -3/8.
For a line to be perpendicular, the slope needs to be opposite of the given line's slope. This will cause the two lines to cross at a 90-degree angle, and therefore be perpendicular.
So a perpendicular line could be as follows:
y = 8x/5 + -3/8
So the perpendicular slope would be 8/5.
For a line to be parallel, the slope needs to be the same so that the two lines will never cross.
So a parallel line could be as follows:
y = -5x/8 + 1
So the parallel slope would be -5/8.
Cheers.
Answer:
Perpendicular Slope: [tex]\boxed{\frac{8}{5}}[/tex]
Parallel Slope: [tex]\boxed{-\frac{5}{8}}[/tex]
Step-by-step explanation:
Part 1: Rewrite into slope-intercept form
Firstly, the equations are written in standard form and not slope-intercept form, so to change that, follow the steps below.
Note: Remember the slope-intercept form equation - [tex]\boxed{y=mx+b}[/tex]
[tex]-5x-8y=3\\\\5x + (-5x-8y)=3+5x\\\\-8y=5x+3\\\\\frac{-8y}{-8} =\frac{5x+3}{-8} \\[/tex]
[tex]y=-\frac{5}{8}x-\frac{3}{8}[/tex]
Add [tex]5x[/tex] to both sides of the equation to isolate the y-variable. Then, divide by the coefficient of y to isolate it entirely. The equation is now in slope-intercept form.
Part 2: Determine the perpendicular slope
Perpendicular slopes are reciprocals of the given slopes. To turn the original slope into its reciprocal counterpart, follow these steps:
If the current slope is positive, add a negative sign. If the current slope is negative, remove the negative sign.The denominator becomes the numerator and the numerator becomes the denominator.To follow this for the slope of the given equation:
[tex]\boxed{-\frac{5}{8} \dashrightarrow \frac{8}{5} }[/tex]Part 3: Determine the parallel slope
Parallel slopes are equal - otherwise, the lines would eventually intersect. Therefore, the given slope is also the parallel slope.
The parallel slope is [tex]\boxed{-\frac{5}{8}}[/tex].
1. Which of the following ordered pairs are solutions to the system of equations below?
4x + 4y = -9
Y = 2x - 13
A : (-3, -7)
B : (3-7)
C : (3,7)
D : (-3,7)
Answer:
43\ 12 , 35/ 6
Step-by-step explanation:
43\ 12 , 35/ 6
Answer: B: (3, -7)
Step-by-step explanation:
4x + 4y = -9
y = 2x - 13
Use Substitution:
4x + 4(2x - 13) = -9
4x + 8x - 52 = -9
12x - 52 = -9
12x = 43
[tex]x=\dfrac{43}{12}[/tex]
None of the options provided are valid so either there is a typo on your worksheet or you typed in one of the equations wrong.
Plan B: Input the choices into the equation to see which one makes a true statement.
4x + 4y = -9
A) (x, y) = (-3, -7)
4(-3) + 4(-7) = -9
-12 + -28 = -9
-40 ≠ -9
B) (x, y) = (3, -7)
4(3) + 4(-7) = -9
12 + -28 = -9
-16 ≠ -9
C) (x, y) = (3, 7)
4(3) + 4(7) = -9
12 + 28 = -9
40 ≠ -9
D) (x, y) = (-3, 7)
4(-3) + 4(7) = -9
-12 + 28 = -9
16 ≠ -9
Obviously there is something wrong with the first equation because none of the options provide a true statement.
y = 2x - 13
A) (x, y) = (-3, -7)
-7 = 2(-3) - 13
-7 = -6 -13
-7 ≠ -19
B) (x, y) = (3, -7)
-7 = 2(3) - 13
-7 = 6 -13
-7 = -7 this works!!!
C) (x, y) = (3, 7)
7 = 2(3) - 13
7 = 6 -13
7 ≠ -7
D) (x, y) = (-3, 7)
7 = 2(-3) - 13
7 = -6 -13
7 ≠ -19
Option B is the only one that provides a true statement so this must be the answer.
I don’t know this one
Answer:
[tex]\sqrt{x-4} +5[/tex]
Step-by-step explanation:
the conjugate of [tex]\sqrt{x-4} -5[/tex] is the term that completes a²-b² when multiplied by each other
a = [tex]\sqrt{x-4}[/tex] b = 5a²-b² = (a+b)(a-b)
(a-b)(a+b) =([tex]\sqrt{x-4}[/tex] -5)([tex]\sqrt{x-4}[/tex] +5)The area of a triangle is 14 square inches. The base is 28 inches. What is the height in inches? Do not include units in your answer.
Answer:
Hey there!
A=1/2bh
14=1/2(28)h
14=14h
h=1
Hope this helps :)
Answer:
the height is 1 inchStep-by-step explanation:
Area of a triangle is
[tex] \frac{1}{2} \times b \times h[/tex]
where b is the base
h is the height
From the question
Area = 14in²
b = 14 inches
So we have
[tex]14 = \frac{1}{2} \times 28 \times h[/tex]
which is
[tex]14 = 14h[/tex]
Divide both sides by 14
That's
[tex] \frac{14}{14} = \frac{14h}{14} [/tex]
We have the final answer as
h = 1
Therefore the height is 1 inch
Hope this helps you
Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to approximate the sum of the series with an error of less than 0.0001.
Answer:
yeyyyaya
Step-by-step explanation:
What is the size of the matrix resulting from...
Answer:
1 x 3
Step-by-step explanation:
The order of the first matrix is 1 × 3
The order of the second matrix is 3 × 3
that is (1 × 3 ) × (3 × 3 )
The bold values at the ends of the orders give the order of the product, that is
1 × 3
Find the slope of the line that passes through (1, 14) and (4,9)
Which two numbers in the points represent x values? Select both in the
list.
In any coordinate pair, the first number is the x-value and the second number is the y-value.
To find the slope, simply take the difference of the y values and divide by the difference in the x values: (14-9)/(1-4) is equal to -5/3.
The slope of the line that passes through (1, 14) and (4,9) is -5/3.
It is find the slope of the line.
what is slope?The slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).
The slope is always calculated from the rise divided by the run. Typically, the equation is presented as:
m = Rise/Run
If you have two points, the points should be [tex]P_{1} (x_{1} ,y_{1} )[/tex] and [tex]P_{2} (x_{2} ,y_{2} )[/tex] So, the equation would be:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
In any coordinate pair, the first number is the x-value and the second number is the y-value.
The difference of the y values and divide by the difference in the x values:
m=(14-9)/(1-4) is equal to -5/3.
The slope of the line that passes through (1, 14) and (4,9) is -5/3.
Learn more about slope here:
https://brainly.com/question/17114095
#SPJ5
for f(x)=1/x-5 and g(x)=x^2+2 find the expression for g(x) and substitute the value of g(x) into the function in place of x to find the value of f(g(x))
Answer:
f(x) = (1/x) - 5
g(x) = x^2 + 2
=> f[g(x)] = [1/(x^2 +2)] - 5
Linda earned $13,500 in 3 months. What is her annual salary?
Answer:
$54,000
Step-by-step explanation:
Assuming that her salary does not change. Note that annual means "a year", which would mean 12 months.
First, find how much Linda makes per month. Divide the total earned in 3 months with 3 months:
13,500/3 = 4,500
Next, multiply 4,500 (the amount made per month) with 12 to get your annual salary:
4,500 x 12 = 54,000
Linda makes $54,000 annually.
What is the input value other than -7, for which h (x) = 3?
Answer:
x=5
Step-by-step explanation:
h (x) = 3
We want the x values where y =3
The values are x = -7 and x=5
A man is standing 20 feet away from the base of a tree and looking at the top of a tree wondering it’s height. If the man’s eyes are located 6 feet off the ground and the angle of elevation is 67°, how tall is the tree? Round to the nearest tenth of a foot.
Answer: 53.1ft
Step-by-step explanation:
We can draw a triangle rectangle.
Where the distance between the man and the tree is one cathetus, (the vertex is on the man's eyes)
The tree itself is the other cathetus, and the line that connects the man's eyes and the tip of the tree is the hypotenuse.
We know that:
The angle at the vertex of the man's eyes is 67°
And the adjacent cathetus, the distance between the man and the tree, is 20ft.
Then using the relation:
Tan(A) = (opposite cathetus)/(adjacent cathetus)
We can find the height of the treee:
Tan(67°) = X/20ft
Tan(67°)*20ft = X = 47.1ft
But remember that this is measured from the mans eye's, and the man's eyes are 6ft away from the ground.
Then the height of the tree is 47.1ft + 6ft = 53.1ft
the sum of place value of 5 in 15954
Answer:
5050
Step-by-step explanation:
Place value of a digit is the value of digit based on its position the given number.
to determine the place value of a digit
we multiply the digit by number of 10's which is equal to number of digits in its right.
example
for a number 1234687
the place value of 3 is
we take 3 and
multiply it by number of 10' in its right
number of 10's in the right is 4
thus place value of 3 = 3*10*10*10*10 = 30000
________________________________________________
15954
place value of 5 at thousandth position = 5*10*10*10 = 5000
place value of 5 at tens position = 5*10 = 50
Thus, sum of place value of 5 in 15954 = 5000+50 = 5050
Find the number. PLEASE HELP!!!
Answer:
X=18
Step-by-step explanation:
Answer:
x = 18or x = - 20
Step-by-step explanation:
Given
x² + 2x = 360 ( subtract 360 from both sides )
x² + 2x - 360 = 0 ← quadratic in standard form
Consider the factors of the constant term (- 360) which sum to give the coefficient of the x- term (+ 2)
The factors are + 20 and - 18, since
20 × - 18 = - 360 and 20 - 18 = 2 , thus
(x + 20)(x - 18) = 0
Equate each factor to zero and solve for x
x + 20 = 0 ⇒ x = - 20
x - 18 = 0 ⇒ x = 18
Thus the number could be 18 or - 20
a circle has a radius of 6/7 units and is centered at (-2.3,0) What is the equation of the circle
Answer:
(x+2.3)^2 + (y) ^2 = (6/7)^2
Step-by-step explanation:
The equation of a circle can be written as
(x-h)^2 + (y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
(x- -2.3)^2 + (y-0) ^2 = (6/7)^2
(x+2.3)^2 + (y) ^2 = (6/7)^2
4. A bank vault has 3 locks with a key for each lock. Key A is owned by the bank manager. Key B is owned by the senior bank teller. Key C is owned by the trainee bank teller. In order to open the vault door at least two people must insert their keys into the assigned locks at the same time. The trainee bank teller) can only open the vault when the bank manager is present in the opening. X= Bank Manager Y= Senior Bank teller Z= Trainee bank teller. (25 marks) LO 01 a) Construct a truth table for this system
1 means that he is present, 0 means that he is not.
True means that they can open.
[tex]\begin{array}{cccccccccccc} \text{X} &&& \text{Y} &&& \text{Z} &&& \text{True} \\1 &&& 1 &&& 1&&& 1 \\ 1 &&& 1 &&& 0&&&1 \\ 0 &&& 1 &&& 1&&&0 \\ 1 &&& 0 &&& 1&&&1 \\ 0&&& 1 &&& 0&&&0 \\ 0 &&& 0 &&& 1&&&0 \\ 1 &&& 0 &&& 0&&&0 \\ 0 &&& 0 &&& 0&&&0 \\ \end{array}[/tex]
Answer:
police
Step-by-step explanation:
Square root of 5 + square root of 3 the whole divided by sqaure root of 5 - square root of 3
Answer:
The answer is 4 + √15 .
Step-by-step explanation:
You have to get rid of surds in the denorminator by multiplying it with the opposite sign :
[tex] \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } [/tex]
[tex] = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } [/tex]
[tex] = \frac{ {( \sqrt{5} + \sqrt{3} ) }^{2} }{( \sqrt{5} - \sqrt{3} )( \sqrt{5} + \sqrt{3}) } [/tex]
[tex] = \frac{ {( \sqrt{5} )}^{2} + 2( \sqrt{5} )( \sqrt{3}) + {( \sqrt{3}) }^{2} }{ {( \sqrt{5}) }^{2} - { (\sqrt{3} )}^{2} } [/tex]
[tex] = \frac{5 + 2 \sqrt{15} + 3 }{5 - 3} [/tex]
[tex] = \frac{8 + 2 \sqrt{15} }{2} [/tex]
[tex] = 4 + \sqrt{15} [/tex]
Dion recorded his heart rate as 204 beats in 3 minutes. How many beats does his heart make in 1 minute?
Answer:
68
Step-by-step explanation:
Answer:
The answer is
68 beatsStep-by-step explanation:
To solve this problem we use ratio and proportion
For 3 minutes his heart rate was 204 beats
So 1 minute will be
[tex] \frac{204 \: beats}{3} \times 1[/tex]
= 68 beatsHope this helps you
in the number 23.45 the digit 5 is in ?
Answer: hundredths place
Step-by-step explanation:
What is the slope of the line graphed below?
(3, 3) (0,-6)
Answer:
3
Step-by-step explanation:
Use this equation
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] substitute
-6-3/0-3 subtract
-9/-3 simplify
-3/-1 two negitives cansle out
3/1=3
Hope this helpes, if it did, please consider giving me brainliest, it will help me a lot. If you have any questions, feel free to ask.
Have a good day! :)
Answer:
3
Step-by-step explanation:
To find the slope, we use the slope formula
m= ( y2-y1)/(x2-x1)
= ( -6 -3)/(0 -3)
= -9/-3
= 3
What is the solution to the equation -0.2(x - 20) = 44 - x? x = -90 x = 50 x = -50 x = 90
Answer:
x= 50
Step-by-step explanation:
First, simplify the equation
Expand the terms on the left hand side to make it easier to rearrange
-0.2(x-20) =44-x
-0.2x+4 =44-x
Rearrange the equation by moving the numbers to one side and the variables to the other
-0.2x +x= 44-4
0.8x = 40
Isolate for x
x= 40/0.8
x= 50