Area of a rectangle = w*l
w = width
l = length
In our problem,
Area = 105mi^2
l = x
w = x - 8
Let's plug our values into the formula above.
105mi^2 = x(x - 8)
Distribute the x
105mi^2 = x^2 - 8x
Subtract 105mi^2 from both sides.
0 = x^2 - 8x - 105
Let's factor the right side.
0 = (x - 15)(x + 7)
Set both terms equal to 0
x - 15 = 0
Add 15 to both sides.
x = 15
x + 7 = 0
Subtract 7 from both sides.
x = -7
Since the length cant be a negative number, 15 is the correct answer.
Length = x = 15 mi
Width = x - 8 = 15 - 8 = 7 mi
The length of the rectangle is 15 miles while the width is 7 miles.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
The perimeter of rectangle = 2( length + width).
Suppose the length is L while the width is W.
Area of rectangle = length × width.
L x W = 105
W = L - 8
By substitution,
L x (L - 8) = 105
L² - 8L - 105 = 0
L² - 15L + 7L - 105 = 0
L(L - 15) + 7(L - 15) = 0
(L + 7)(L - 15) = 0
L = -7, L = 15
Since length will not be negative thus L = 15 miles.
W = 15 - 8 = 7 miles
Hence "The length of the rectangle is 15 miles while the width is 7 miles."
For more about rectangles,
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Find two consecutive even integers such that four times the first equals three times the second
Answer:
1st: 2x
2nd: 2x+2
--------
Equation:
4(2x) = 3(2x+2)
-------
8x = 6x + 6
2x = 6
x = 3
-----
1st 2x = 6
2nd: 2x+2 = 8
Step-by-step explanation:
The two consecutive even integers such that four times the first equals three times the second is 6 and 8.
What is an integer ?An integer is a number which has no decimal part.
According to the given question we have to find two consecutive even integers such that four times the first equals three times the second.
Let, the first even integer to be x.
∴ The second integer will be (x+2). [ As every consecutive even
integers comes after 2 digits]
Now, Four times the first equals three times the second which is
4x = 3(x+2)
4x = 3x + 6.
4x - 3x = 6
x = 6.
∴ The even integer is 6 and the second integer is 8.
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What is the sum of the solutions of the 2 equations
below?
8x = 12
2y + 10 = 22
A. 23
B. 71
7 1
C.
9
D. 10
E. 17.
8x = 12
Divide both sides by 8
x = 12/8 = 3/2
2y + 10 = 22
Subtract 10 from both sides.
2y = 12
Divide both sides by 2
y = 6
6 + 3/2 = 7 1/2
Answer:
7.5 or 7½
Step-by-step explanation:
8x÷4 = 12÷4
2x = 3
x = 3/2 = 1.5
2y + 10 = 22
2y = 12
y = 6
1.5 + 6 = 7.5 = 7½
Estimate the difference.
689.2 - 263 = ?
To estimate the difference, first round each number to the nearest hundred.
PLZ HELP ME I AM STUCK ON THIS QUESTION :(
Answer:430.2
Step-by-step explanation:
10 x 1/5 in simplest form
Hey there!
ANSWER: [tex]2[/tex]EXPLANATION:[tex]10*1/5[/tex]
Divide 10 by 5.
[tex]10/5=2\\2(ANSWER)[/tex]
Hope this helps!
[tex]-TestedHyperr[/tex]
Answer:
2.
Step-by-step explanation:
[tex]10 *\frac{1}{5} = 2[/tex]
Solve the equation algebraically. x^2-7x-1/7=0
Answer:
[tex]x1=\frac{49+\sqrt{2429}}{14} \\x2=\frac{49-\sqrt{2429}}{14} \\[/tex]
Step-by-step explanation:
[tex]x^2-7x-\frac{1}{7} =0\\7x^2-49x-1=0\\D=b^2-4ac=(-49)^2-4*7*(-1)=2429\\x1=\frac{49+\sqrt{2429} }{14} \\x2=\frac{49-\sqrt{2429} }{14} \\[/tex]
Simplify.
(3x2−2x+2)−(x2+5x−5)
4x2+3x−3
2x2−7x+7
2x2−3x−3
2x2+3x−3
Answer:
2x2+3x-3
Step-by-step explanation:
The first thing you want to do is find all the X2"s and add those together and that looks like this 3x2+(-x2) which would be 2x2. Then you want to find all of the x's and add them together which looks like this -2x+5x which is 3x. Then you find all the whole numbers without a variable and that's 2-5 which equals to be -3.
Point M is the midpoint of AB. The coordinates of point A are (-6, 1) and the coordinates of M are (-3,2).
What are the coordinates of point B?
The coordinates of point B are
Answer:
Let B(a,b) be x1, y1
A(-6,1) be x2,y2
midpoint M(-3,2) be (x,y)
using midpoint formula
(x,y)= [(x1+x2)/2, (y1+y2)/2)
(-3,2) = [(a-6)/2, (b+1)/2}
comparing corresponding value
-3 = (a-6)/2 (b+1)/2 = 2
-6= a-6 b+1=4
a=0 b=3
coordinates of B = (0,3)
pls help math 15 points
3 x's at 1
4 x's at 1 1/4
3 x's at 1 1/2
1 x at 1 3/4
No x's at 2.
Now, let's combine all the recipes with 1 1/4
5/4 * 4 = 20 / 4 = 5 teaspoons
1. Name the indicated geometric figures for the figure shown. Be sure to use correct notation.
A Name a point. _________
B Name a ray through Y. _________
C Name a line through Z. _________
D Name a plane. _________
Answer:
Step-by-step explanation:
A). There are three points given on the plane R.
Point X, point Y and Point Z.
B). A ray from the point Y → [tex]\overrightarrow{XY}[/tex]
A ray starting from point X and passing through Y to infinity.
C). Name of a line → [tex]\overleftrightarrow{YZ}[/tex]
Aline passes through two points with both the ends directing towards infinity.
D). Name of a plane → Plane R or Plane XYZ
A plane is defined by three points lying on the same surface.
9-6=3, 6+3=9, 3+6=9 what is the missing fact family?
Answer:
9-3=6
Step-by-step explanation:
An addition/subtraction fact family has 2 addition equations and 2 subtraction ones.
The question already states both addition ones, but only one subtraction
The subtraction one stated is 9-6=3
The opposite is 9-3=6
Hope this helps :-)
Write an equation for the line that is parallel to y=-4x+2 and goes through (0,7)
Answer: y=-4x+7
Step-by-step explanation:
To find a parallel line, we know that the slope must be the same because parallel lines NEVER touch or cross. All we have to do is use the given point to find the y-intercept.
y=-4x+b
7=-4(0)+b [multiply]
b=7
Now, we know that the final equation is y=-4x+7.
Answer:
The answer is
y = - 4x + 7Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line
The original line is y = - 4x + 2
Comparing with the general equation above
Slope / m = - 4
Since the lines are parallel their slope are also the same
Slope of parallel line = - 4
So the equation of the line using point (0,7) and slope - 4 is
[tex]y - 7 = - 4(x - 0) \\ y - 7 = - 4x[/tex]
We have the final answer as
y = - 4x + 7Hope this helps you
Gabby bought 5.15 kg of apples and 1.6 kg of oranges how much fruit did she buy in all
Answer:
6.75kg of fruit
Step-by-step explanation:
5 + 1 = 6
.15 + .6 = .75
6 + .75 = 6.75
Answer:
6.75
Step-by-step explanation:
Add 5.15 and 1.60
5.15
1.60
6.75
Aretailer is having a promotional sale for 35% off all items. There is a 7% sales tax added to the price. Which
represents the situation, where x is the original cost of the item(s)?
Answer:
.65x(1.07) = 0.6955x
Step-by-step explanation:
An angle measuring 3.6 radians is drawn in standard position?
In what quadrant will the terminal side of this angle lie?
Express your answer as a Roman numeral.
Answer:
III
Step-by-step explanation: I just took the quiz
If f(x) = 2x + 4 and 9 (20) = x - 3, find f (g(x)).
Answer: D
Step-by-step explanation:
To find f(g(x)), you want to take g(x) and plug that into f(x). Since we are given f(x) and g(x), we can go ahead and do that.
f(g(x))=2(x-3)+4 [distribute]
f(g(x))=2x-6+4 [combine like terms]
f(g(x))=2x-2
Now, we know that f(g(x))=2x-2.
Helppppp!!!!!!! Gehjdhdhxjndhzjsvahsj
Answer:
don't worry bbg I got you give me a moment
Lana uses 0.2 pounds of peaches in each mini pie she makes. How many mini pies can she make with 2.50 pound of peaches?
Answer:
12.5 mini pies or 12 depending on what it asks for
Step-by-step explanation:
Divide 2.50 by 0.2 to get 12.5
The answer can also be 12 because some teachers want students to know that you can't really make half a pie. Whatever your teacher prefers.
In an arithmetic progession T7 =20 and T13 =38,. Find the first term and the common difference.
Which of the following inequalities is graphed on the coordinate plane?
Answer: A
Step-by-step explanation:
This picture is very blurry, but the line appears to be a solid line. Since it is a solid line, it tells us that the inequality is ≤ or ≥. We can eliminate C and D. Now, the difference between A and B is the shading. Since the shading is showing that the numbers are increasing, we know that the inequality is ≥. Therefore, A is the correct answer.
3x 40° to Sum of angle measures: 180°
Answer:
yes
Step-by-step explanation:
-2=12/x
pleasee answer
Answer:
Step-by-step explanation:
Find the derivative of the function. y = tan2(8θ)
Answer:
16tan(8θ)sec²(8θ)
Step-by-step explanation:
Given the question :
Find the derivative of the function. y = tan2(8θ)
y = tan²(8θ)
USing chain rule :
dy/dx = (du/dx) × (dv/du) × (dy/dv)
Let u = 8θ ; du/dθ = 8
v = tan u ; dv/du = sec²u
y = v² ; dy/dv = 2v
Hence,
(dy/dθ) × dv/du × dy/dv
8 * sec²u * 2v
Where v = tan u ; u = 8θ
8 * sec²8θ * 2tan8θ
16tan(8θ)sec²(8θ)
Is 8 3/5 greater than 8 6/7
Answer:
no
Step-by-step explanation:
Answer:
8 6/7 is greater than 8 3/5
Step-by-step explanation:
Step 1:
8 3/5 = 8 21/35
Step 2:
8 6/7 = 8 30/35
Answer:
8 6/7 is greater than 8 3/5
Hope This Helps :)
Enter an algebraic expression to model the given context. Give your answer in simplest form.
The price s of a pair of shoes plus 6% sales tax.
The algebraic expression is
(s)+(s×0.06)=t
t is the total
s is the shoes
12x + 9 - 3x - 4. Please go fast!!!!
Answer:
9x +5
Step-by-step explanation:
combine like terms!
Find the weighted average of these values.
Value Weight
5.005.00 75.0%75.0%
6.006.00 15.0%15.0%
7.007.00 10.0%10.0%
Answers:
The Weighted Average = 5.35
Explanation:
The weighted average is given by:
W(avg) = v1*w1 + v2*w2 + v3*w3
v1.v2.v3 are the values
w1,w2,w3 are the weights
W(avg) = 5.00*0.75 + 6.00*0.15 + 7.00*0.10
W(avg) = 3.75+0.9+0.7
W(avg) = 5.35
Hence, the weighted average is equals to 5.35
A store is selling two mixtures of nuts in
-ounce bags. The first mixture has
ounces of peanuts combined with five ounces of cashews, and costs
. The second mixture has five ounces of peanuts and
ounces of cashews, and costs
. How much does one ounce of peanuts and one ounce of cashews cost?
Answer:
gfAnswer:Answer:Answer:Answer:Answer:Answer:Answer:
Step-by-step explanation:
fgAnswer:Answer:Answer:Answer:Answer:Answer:Answer:Answer:Answer:Answer:
If someone is good in theoram please help me I need help with task 3,4,5
Answer:
C²= A²+B²
Step-by-step explanation:
A) 10²=( Base)² + 6²
(Base )²= 10² - 6²:
100-36
= 64
Base = √ 64
8
B) 17² = 8² + (Height)²
(Height) ² = 17²- 8²
= 289-64
= 225
Height = √225
= 15
C) 2.5² = Base ² + 1.5 ²
Base² = 2.5 ²- 1.5²
6.25- 2.25
= 4
Base = √4
= 2
D) 41² = Base²+ 40²
Base²= 41²- 40²
1681-1600
= 81
Base = √81
=9
E)26²=Base² +10²
Base² = 26²- 10²
676-100
= 576
Base= √576
= 24
F)25²= Base²+ 7²
Base² = 25²- 7²
625- 49
=576
Base= √576
= 24
Use the distributive property to fill in the blanks below.
(8 x 5) + (8 x 2) = 8 x (_ + _)
[tex]\boxed{\sf ab+ac=a(b+c)}[/tex]
[tex]\\ \rm\longmapsto (8\times 5)+(8\times 2)[/tex]
[tex]\\ \rm\longmapsto 8(5+2)[/tex]
[tex]\\ \rm\longmapsto 8(7)[/tex]
[tex]\\ \rm\longmapsto 56[/tex]
Compare -9 and square root -9
Answer:
-9 < 3i
Step-by-step explanation:
3i is bigger than -9 because 3i² is equal to -9
i means imaginary number
Hope this helps!